Left Termination proof of /tmp/tmpWj9hLa/prime.pl

Left Termination of the query pattern
prime(g)
w.r.t. the given Prolog program could successfully be proven:

0 Prolog

↳1 PrologToPiTRSViaGraphTransformerProof (⇒, 15.5 s)

↳2 PiTRS

↳3 DependencyPairsProof (⇔, 5400 ms)

↳4 PiDP

↳5 DependencyGraphProof (⇔, 1037 ms)

↳6 AND

    ↳7 PiDP

        ↳8 UsableRulesProof (⇔, 0 ms)

        ↳9 PiDP

        ↳10 PiDPToQDPProof (⇒, 0 ms)

        ↳11 QDP

        ↳12 QDPSizeChangeProof (⇔, 0 ms)

        ↳13 YES

    ↳14 PiDP

        ↳15 UsableRulesProof (⇔, 0 ms)

        ↳16 PiDP

        ↳17 PiDPToQDPProof (⇒, 0 ms)

        ↳18 QDP

        ↳19 QDPSizeChangeProof (⇔, 0 ms)

        ↳20 YES

    ↳21 PiDP

        ↳22 UsableRulesProof (⇔, 0 ms)

        ↳23 PiDP

        ↳24 PiDPToQDPProof (⇒, 0 ms)

        ↳25 QDP

        ↳26 QDPSizeChangeProof (⇔, 0 ms)

        ↳27 YES

    ↳28 PiDP

        ↳29 UsableRulesProof (⇔, 0 ms)

        ↳30 PiDP

        ↳31 PiDPToQDPProof (⇒, 0 ms)

        ↳32 QDP

        ↳33 QDPSizeChangeProof (⇔, 0 ms)

        ↳34 YES

    ↳35 PiDP

        ↳36 UsableRulesProof (⇔, 0 ms)

        ↳37 PiDP

        ↳38 PiDPToQDPProof (⇒, 0 ms)

        ↳39 QDP

        ↳40 QDPSizeChangeProof (⇔, 0 ms)

        ↳41 YES

    ↳42 PiDP

        ↳43 UsableRulesProof (⇔, 0 ms)

        ↳44 PiDP

        ↳45 PiDPToQDPProof (⇒, 0 ms)

        ↳46 QDP

        ↳47 QDPSizeChangeProof (⇔, 0 ms)

        ↳48 YES

    ↳49 PiDP

        ↳50 UsableRulesProof (⇔, 0 ms)

        ↳51 PiDP

        ↳52 PiDPToQDPProof (⇒, 0 ms)

        ↳53 QDP

        ↳54 QDPSizeChangeProof (⇔, 0 ms)

        ↳55 YES

    ↳56 PiDP

        ↳57 UsableRulesProof (⇔, 0 ms)

        ↳58 PiDP

        ↳59 PiDPToQDPProof (⇒, 0 ms)

        ↳60 QDP

        ↳61 QDPSizeChangeProof (⇔, 0 ms)

        ↳62 YES

    ↳63 PiDP

        ↳64 UsableRulesProof (⇔, 0 ms)

        ↳65 PiDP

        ↳66 PiDPToQDPProof (⇒, 0 ms)

        ↳67 QDP

        ↳68 QDPSizeChangeProof (⇔, 0 ms)

        ↳69 YES

    ↳70 PiDP

        ↳71 UsableRulesProof (⇔, 0 ms)

        ↳72 PiDP

        ↳73 PiDPToQDPProof (⇒, 0 ms)

        ↳74 QDP

        ↳75 QDPSizeChangeProof (⇔, 0 ms)

        ↳76 YES

    ↳77 PiDP

        ↳78 UsableRulesProof (⇔, 0 ms)

        ↳79 PiDP

        ↳80 PiDPToQDPProof (⇒, 0 ms)

        ↳81 QDP

        ↳82 QDPSizeChangeProof (⇔, 0 ms)

        ↳83 YES

    ↳84 PiDP

        ↳85 UsableRulesProof (⇔, 0 ms)

        ↳86 PiDP

        ↳87 PiDPToQDPProof (⇒, 0 ms)

        ↳88 QDP

        ↳89 QDPSizeChangeProof (⇔, 0 ms)

        ↳90 YES

    ↳91 PiDP

        ↳92 UsableRulesProof (⇔, 0 ms)

        ↳93 PiDP

        ↳94 PiDPToQDPProof (⇔, 0 ms)

        ↳95 QDP

        ↳96 QDPSizeChangeProof (⇔, 0 ms)

        ↳97 YES

    ↳98 PiDP

        ↳99 UsableRulesProof (⇔, 0 ms)

        ↳100 PiDP

        ↳101 PiDPToQDPProof (⇒, 0 ms)

        ↳102 QDP

        ↳103 QDPSizeChangeProof (⇔, 0 ms)

        ↳104 YES

    ↳105 PiDP

        ↳106 UsableRulesProof (⇔, 0 ms)

        ↳107 PiDP

        ↳108 PiDPToQDPProof (⇒, 0 ms)

        ↳109 QDP

        ↳110 QDPSizeChangeProof (⇔, 0 ms)

        ↳111 YES

    ↳112 PiDP

        ↳113 UsableRulesProof (⇔, 0 ms)

        ↳114 PiDP

        ↳115 PiDPToQDPProof (⇒, 31 ms)

        ↳116 QDP

        ↳117 QDPSizeChangeProof (⇔, 0 ms)

        ↳118 YES

    ↳119 PiDP

        ↳120 UsableRulesProof (⇔, 0 ms)

        ↳121 PiDP

        ↳122 PiDPToQDPProof (⇒, 0 ms)

        ↳123 QDP

        ↳124 QDPSizeChangeProof (⇔, 0 ms)

        ↳125 YES

(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).

Query: prime(g)

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

Transformed Prolog program to (Pi-)TRS.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
2 [label="A: prime(T1)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
6 [label="6: prime(T1), SCOPE: 1, CLAUSE: 4\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: pr(s(s(T3)), s(T3))\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: 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];
16 [label="16: pr(s(s(T3)), s(T3)), SCOPE: 2, CLAUSE: 5\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: pr(s(s(T3)), s(T3)), SCOPE: 2, CLAUSE: 6\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="B: ','(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];
31 [label="31: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="N11: not_divides(s(s(T14)), s(s(s(T14))))\n\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="N13: pr(s(s(s(T14))), s(T14))\n\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: not_divides(s(s(T14)), s(s(s(T14)))), SCOPE: 3, CLAUSE: 7\n\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="N12: ','(div(s(s(s(T20))), s(s(T20)), X34), ','(times(X34, s(s(T20)), X35), neq(s(s(s(T20))), X35)))\n\nT20 is ground\nX34 is free\nX35 is free", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="N15: div(s(s(s(T20))), s(s(T20)), X34)\n\nT20 is ground\nX34 is free", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="N40: ','(times(T22, s(s(T20)), X35), neq(s(s(s(T20))), X35))\n\nT20 is ground\nT22 is ground\nX35 is free", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: div(s(s(s(T20))), s(s(T20)), X34), SCOPE: 4, CLAUSE: 0\n\nT20 is ground\nX34 is free", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: quot(s(s(s(T26))), s(s(T26)), s(s(T26)), X59)\n\nT26 is ground\nX59 is free", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: quot(s(s(s(T26))), s(s(T26)), s(s(T26)), X59), SCOPE: 5, CLAUSE: 1 | quot(s(s(s(T26))), s(s(T26)), s(s(T26)), X59), SCOPE: 5, CLAUSE: 2 | quot(s(s(s(T26))), s(s(T26)), s(s(T26)), X59), SCOPE: 5, CLAUSE: 3\n\nT26 is ground\nX59 is free", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: quot(s(s(s(T26))), s(s(T26)), s(s(T26)), X59), SCOPE: 5, CLAUSE: 2 | quot(s(s(s(T26))), s(s(T26)), s(s(T26)), X59), SCOPE: 5, CLAUSE: 3\n\nT26 is ground\nX59 is free", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: quot(s(s(s(T26))), s(s(T26)), s(s(T26)), X59), SCOPE: 5, CLAUSE: 2\n\nT26 is ground\nX59 is free", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: quot(s(s(s(T26))), s(s(T26)), s(s(T26)), X59), SCOPE: 5, CLAUSE: 3\n\nT26 is ground\nX59 is free", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: quot(s(s(T31)), s(T31), s(s(T31)), X98)\n\nT31 is ground\nX98 is free", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: quot(s(s(T31)), s(T31), s(s(T31)), X98), SCOPE: 6, CLAUSE: 1 | quot(s(s(T31)), s(T31), s(s(T31)), X98), SCOPE: 6, CLAUSE: 2 | quot(s(s(T31)), s(T31), s(s(T31)), X98), SCOPE: 6, CLAUSE: 3\n\nT31 is ground\nX98 is free", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: quot(s(s(T31)), s(T31), s(s(T31)), X98), SCOPE: 6, CLAUSE: 2 | quot(s(s(T31)), s(T31), s(s(T31)), X98), SCOPE: 6, CLAUSE: 3\n\nT31 is ground\nX98 is free", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: quot(s(s(T31)), s(T31), s(s(T31)), X98), SCOPE: 6, CLAUSE: 2\n\nT31 is ground\nX98 is free", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: quot(s(s(T31)), s(T31), s(s(T31)), X98), SCOPE: 6, CLAUSE: 3\n\nT31 is ground\nX98 is free", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: quot(s(T36), T36, s(s(T36)), X137)\n\nT36 is ground\nX137 is free", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: quot(s(T36), T36, s(s(T36)), X137), SCOPE: 7, CLAUSE: 1 | quot(s(T36), T36, s(s(T36)), X137), SCOPE: 7, CLAUSE: 2 | quot(s(T36), T36, s(s(T36)), X137), SCOPE: 7, CLAUSE: 3\n\nT36 is ground\nX137 is free", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: quot(s(T36), T36, s(s(T36)), X137), SCOPE: 7, CLAUSE: 2 | quot(s(T36), T36, s(s(T36)), X137), SCOPE: 7, CLAUSE: 3\n\nT36 is ground\nX137 is free", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: quot(s(T36), T36, s(s(T36)), X137), SCOPE: 7, CLAUSE: 2\n\nT36 is ground\nX137 is free", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: quot(s(T36), T36, s(s(T36)), X137), SCOPE: 7, CLAUSE: 3\n\nT36 is ground\nX137 is free", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: quot(s(T46), T46, s(s(s(T46))), X168)\n\nT46 is ground\nX168 is free", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: quot(s(T46), T46, s(s(s(T46))), X168), SCOPE: 8, CLAUSE: 1 | quot(s(T46), T46, s(s(s(T46))), X168), SCOPE: 8, CLAUSE: 2 | quot(s(T46), T46, s(s(s(T46))), X168), SCOPE: 8, CLAUSE: 3\n\nT46 is ground\nX168 is free", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: quot(s(T46), T46, s(s(s(T46))), X168), SCOPE: 8, CLAUSE: 2 | quot(s(T46), T46, s(s(s(T46))), X168), SCOPE: 8, CLAUSE: 3\n\nT46 is ground\nX168 is free", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: quot(s(T46), T46, s(s(s(T46))), X168), SCOPE: 8, CLAUSE: 2\n\nT46 is ground\nX168 is free", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: quot(s(T46), T46, s(s(s(T46))), X168), SCOPE: 8, CLAUSE: 3\n\nT46 is ground\nX168 is free", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: quot(s(T56), T56, s(s(s(s(T56)))), X199)\n\nT56 is ground\nX199 is free", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: quot(s(T56), T56, s(s(s(s(T56)))), X199), SCOPE: 9, CLAUSE: 1 | quot(s(T56), T56, s(s(s(s(T56)))), X199), SCOPE: 9, CLAUSE: 2 | quot(s(T56), T56, s(s(s(s(T56)))), X199), SCOPE: 9, CLAUSE: 3\n\nT56 is ground\nX199 is free", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: quot(s(T56), T56, s(s(s(s(T56)))), X199), SCOPE: 9, CLAUSE: 2 | quot(s(T56), T56, s(s(s(s(T56)))), X199), SCOPE: 9, CLAUSE: 3\n\nT56 is ground\nX199 is free", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: quot(s(T56), T56, s(s(s(s(T56)))), X199), SCOPE: 9, CLAUSE: 2\n\nT56 is ground\nX199 is free", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: quot(s(T56), T56, s(s(s(s(T56)))), X199), SCOPE: 9, CLAUSE: 3\n\nT56 is ground\nX199 is free", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: quot(s(T66), T66, s(s(s(s(s(T66))))), X230)\n\nT66 is ground\nX230 is free", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: quot(s(T66), T66, s(s(s(s(s(T66))))), X230), SCOPE: 10, CLAUSE: 1 | quot(s(T66), T66, s(s(s(s(s(T66))))), X230), SCOPE: 10, CLAUSE: 2 | quot(s(T66), T66, s(s(s(s(s(T66))))), X230), SCOPE: 10, CLAUSE: 3\n\nT66 is ground\nX230 is free", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: quot(s(T66), T66, s(s(s(s(s(T66))))), X230), SCOPE: 10, CLAUSE: 2 | quot(s(T66), T66, s(s(s(s(s(T66))))), X230), SCOPE: 10, CLAUSE: 3\n\nT66 is ground\nX230 is free", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: quot(s(T66), T66, s(s(s(s(s(T66))))), X230), SCOPE: 10, CLAUSE: 2\n\nT66 is ground\nX230 is free", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: quot(s(T66), T66, s(s(s(s(s(T66))))), X230), SCOPE: 10, CLAUSE: 3\n\nT66 is ground\nX230 is free", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: quot(s(T76), T76, s(s(s(s(s(s(T76)))))), X261)\n\nT76 is ground\nX261 is free", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: quot(s(T76), T76, s(s(s(s(s(s(T76)))))), X261), SCOPE: 11, CLAUSE: 1 | quot(s(T76), T76, s(s(s(s(s(s(T76)))))), X261), SCOPE: 11, CLAUSE: 2 | quot(s(T76), T76, s(s(s(s(s(s(T76)))))), X261), SCOPE: 11, CLAUSE: 3\n\nT76 is ground\nX261 is free", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: quot(s(T76), T76, s(s(s(s(s(s(T76)))))), X261), SCOPE: 11, CLAUSE: 2 | quot(s(T76), T76, s(s(s(s(s(s(T76)))))), X261), SCOPE: 11, CLAUSE: 3\n\nT76 is ground\nX261 is free", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: quot(s(T76), T76, s(s(s(s(s(s(T76)))))), X261), SCOPE: 11, CLAUSE: 2\n\nT76 is ground\nX261 is free", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: quot(s(T76), T76, s(s(s(s(s(s(T76)))))), X261), SCOPE: 11, CLAUSE: 3\n\nT76 is ground\nX261 is free", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: quot(s(T86), T86, s(s(s(s(s(s(s(T86))))))), X292)\n\nT86 is ground\nX292 is free", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: quot(s(T86), T86, s(s(s(s(s(s(s(T86))))))), X292), SCOPE: 12, CLAUSE: 1 | quot(s(T86), T86, s(s(s(s(s(s(s(T86))))))), X292), SCOPE: 12, CLAUSE: 2 | quot(s(T86), T86, s(s(s(s(s(s(s(T86))))))), X292), SCOPE: 12, CLAUSE: 3\n\nT86 is ground\nX292 is free", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: quot(s(T86), T86, s(s(s(s(s(s(s(T86))))))), X292), SCOPE: 12, CLAUSE: 2 | quot(s(T86), T86, s(s(s(s(s(s(s(T86))))))), X292), SCOPE: 12, CLAUSE: 3\n\nT86 is ground\nX292 is free", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: quot(s(T86), T86, s(s(s(s(s(s(s(T86))))))), X292), SCOPE: 12, CLAUSE: 2\n\nT86 is ground\nX292 is free", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: quot(s(T86), T86, s(s(s(s(s(s(s(T86))))))), X292), SCOPE: 12, CLAUSE: 3\n\nT86 is ground\nX292 is free", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: quot(s(T96), T96, s(s(s(s(s(s(s(s(T96)))))))), X323)\n\nT96 is ground\nX323 is free", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="C: quot(s(T96), T96, s(T97), X323)\n\nT96 is ground\nT97 is ground\nX323 is free", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: quot(s(T96), T96, s(T97), X323), SCOPE: 13, CLAUSE: 1 | quot(s(T96), T96, s(T97), X323), SCOPE: 13, CLAUSE: 2 | quot(s(T96), T96, s(T97), X323), SCOPE: 13, CLAUSE: 3\n\nT96 is ground\nT97 is ground\nX323 is free", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: quot(s(T96), T96, s(T97), X323), SCOPE: 13, CLAUSE: 2 | quot(s(T96), T96, s(T97), X323), SCOPE: 13, CLAUSE: 3\n\nT96 is ground\nT97 is ground\nX323 is free", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: quot(s(T96), T96, s(T97), X323), SCOPE: 13, CLAUSE: 2\n\nT96 is ground\nT97 is ground\nX323 is free", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: quot(s(T96), T96, s(T97), X323), SCOPE: 13, CLAUSE: 3\n\nT96 is ground\nT97 is ground\nX323 is free", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: quot(s(T111), T111, s(T112), X358)\n\nT111 is ground\nT112 is ground\nX358 is free", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: quot(s(0), s(T118), s(T118), X374)\n\nT118 is ground\nX374 is free", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: quot(s(0), s(T118), s(T118), X374), SCOPE: 14, CLAUSE: 1 | quot(s(0), s(T118), s(T118), X374), SCOPE: 14, CLAUSE: 2 | quot(s(0), s(T118), s(T118), X374), SCOPE: 14, CLAUSE: 3\n\nT118 is ground\nX374 is free", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: quot(s(0), s(T118), s(T118), X374), SCOPE: 14, CLAUSE: 2 | quot(s(0), s(T118), s(T118), X374), SCOPE: 14, CLAUSE: 3\n\nT118 is ground\nX374 is free", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: quot(s(0), s(T118), s(T118), X374), SCOPE: 14, CLAUSE: 2\n\nT118 is ground\nX374 is free", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: quot(s(0), s(T118), s(T118), X374), SCOPE: 14, CLAUSE: 3\n\nT118 is ground\nX374 is free", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: quot(0, T127, s(T127), X413)\n\nT127 is ground\nX413 is free", fontsize=16, style=filled, fillcolor=lightyellow];
243 [label="243: quot(0, T127, s(T127), X413), SCOPE: 15, CLAUSE: 1 | quot(0, T127, s(T127), X413), SCOPE: 15, CLAUSE: 2 | quot(0, T127, s(T127), X413), SCOPE: 15, CLAUSE: 3\n\nT127 is ground\nX413 is free", fontsize=16, style=filled, fillcolor=lightyellow];
246 [label="246: quot(0, T127, s(T127), X413), SCOPE: 15, CLAUSE: 1\n\nT127 is ground\nX413 is free", fontsize=16, style=filled, fillcolor=lightyellow];
247 [label="247: quot(0, T127, s(T127), X413), SCOPE: 15, CLAUSE: 2 | quot(0, T127, s(T127), X413), SCOPE: 15, CLAUSE: 3\n\nT127 is ground\nX413 is free", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="250: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
251 [label="251: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
252 [label="252: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="253: quot(0, T127, s(T127), X413), SCOPE: 15, CLAUSE: 3\n\nT127 is ground\nX413 is free", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="D: quot(0, s(0), s(0), X443)\n\nX443 is free", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="259: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
262 [label="262: quot(0, s(0), s(0), X443), SCOPE: 16, CLAUSE: 1 | quot(0, s(0), s(0), X443), SCOPE: 16, CLAUSE: 2 | quot(0, s(0), s(0), X443), SCOPE: 16, CLAUSE: 3\n\nX443 is free", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: quot(0, s(0), s(0), X443), SCOPE: 16, CLAUSE: 1\n\nX443 is free", fontsize=16, style=filled, fillcolor=lightyellow];
266 [label="266: quot(0, s(0), s(0), X443), SCOPE: 16, CLAUSE: 2 | quot(0, s(0), s(0), X443), SCOPE: 16, CLAUSE: 3\n\nX443 is free", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="267: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
268 [label="268: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
269 [label="269: quot(0, s(0), s(0), X443), SCOPE: 16, CLAUSE: 3\n\nX443 is free", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="270: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
271 [label="271: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
274 [label="274: quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X477)\n\nX477 is free", fontsize=16, style=filled, fillcolor=lightyellow];
275 [label="275: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
277 [label="277: quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X477), SCOPE: 17, CLAUSE: 1 | quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X477), SCOPE: 17, CLAUSE: 2 | quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X477), SCOPE: 17, CLAUSE: 3\n\nX477 is free", fontsize=16, style=filled, fillcolor=lightyellow];
278 [label="278: quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X477), SCOPE: 17, CLAUSE: 2 | quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X477), SCOPE: 17, CLAUSE: 3\n\nX477 is free", fontsize=16, style=filled, fillcolor=lightyellow];
282 [label="282: quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X477), SCOPE: 17, CLAUSE: 2\n\nX477 is free", fontsize=16, style=filled, fillcolor=lightyellow];
283 [label="283: quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X477), SCOPE: 17, CLAUSE: 3\n\nX477 is free", fontsize=16, style=filled, fillcolor=lightyellow];
292 [label="292: quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X512)\n\nX512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
296 [label="296: quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X512), SCOPE: 18, CLAUSE: 1 | quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X512), SCOPE: 18, CLAUSE: 2 | quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X512), SCOPE: 18, CLAUSE: 3\n\nX512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
297 [label="297: quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X512), SCOPE: 18, CLAUSE: 1\n\nX512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
298 [label="298: quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X512), SCOPE: 18, CLAUSE: 2 | quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X512), SCOPE: 18, CLAUSE: 3\n\nX512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
299 [label="299: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
300 [label="300: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
301 [label="301: quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X512), SCOPE: 18, CLAUSE: 3\n\nX512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
304 [label="304: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
305 [label="305: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
308 [label="308: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X546)\n\nX546 is free", fontsize=16, style=filled, fillcolor=lightyellow];
309 [label="309: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
310 [label="310: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X546), SCOPE: 19, CLAUSE: 1 | quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X546), SCOPE: 19, CLAUSE: 2 | quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X546), SCOPE: 19, CLAUSE: 3\n\nX546 is free", fontsize=16, style=filled, fillcolor=lightyellow];
313 [label="313: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X546), SCOPE: 19, CLAUSE: 2 | quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X546), SCOPE: 19, CLAUSE: 3\n\nX546 is free", fontsize=16, style=filled, fillcolor=lightyellow];
315 [label="315: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X546), SCOPE: 19, CLAUSE: 2\n\nX546 is free", fontsize=16, style=filled, fillcolor=lightyellow];
316 [label="316: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X546), SCOPE: 19, CLAUSE: 3\n\nX546 is free", fontsize=16, style=filled, fillcolor=lightyellow];
322 [label="322: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X581)\n\nX581 is free", fontsize=16, style=filled, fillcolor=lightyellow];
329 [label="329: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X581), SCOPE: 20, CLAUSE: 1 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X581), SCOPE: 20, CLAUSE: 2 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X581), SCOPE: 20, CLAUSE: 3\n\nX581 is free", fontsize=16, style=filled, fillcolor=lightyellow];
332 [label="332: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X581), SCOPE: 20, CLAUSE: 1\n\nX581 is free", fontsize=16, style=filled, fillcolor=lightyellow];
333 [label="333: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X581), SCOPE: 20, CLAUSE: 2 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X581), SCOPE: 20, CLAUSE: 3\n\nX581 is free", fontsize=16, style=filled, fillcolor=lightyellow];
339 [label="339: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
340 [label="340: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
342 [label="342: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X581), SCOPE: 20, CLAUSE: 3\n\nX581 is free", fontsize=16, style=filled, fillcolor=lightyellow];
343 [label="343: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
346 [label="346: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
354 [label="354: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X615)\n\nX615 is free", fontsize=16, style=filled, fillcolor=lightyellow];
355 [label="355: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
360 [label="360: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X615), SCOPE: 21, CLAUSE: 1 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X615), SCOPE: 21, CLAUSE: 2 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X615), SCOPE: 21, CLAUSE: 3\n\nX615 is free", fontsize=16, style=filled, fillcolor=lightyellow];
361 [label="361: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X615), SCOPE: 21, CLAUSE: 2 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X615), SCOPE: 21, CLAUSE: 3\n\nX615 is free", fontsize=16, style=filled, fillcolor=lightyellow];
366 [label="366: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X615), SCOPE: 21, CLAUSE: 2\n\nX615 is free", fontsize=16, style=filled, fillcolor=lightyellow];
367 [label="367: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X615), SCOPE: 21, CLAUSE: 3\n\nX615 is free", fontsize=16, style=filled, fillcolor=lightyellow];
371 [label="371: quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X650)\n\nX650 is free", fontsize=16, style=filled, fillcolor=lightyellow];
376 [label="376: quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X650), SCOPE: 22, CLAUSE: 1 | quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X650), SCOPE: 22, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X650), SCOPE: 22, CLAUSE: 3\n\nX650 is free", fontsize=16, style=filled, fillcolor=lightyellow];
380 [label="380: quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X650), SCOPE: 22, CLAUSE: 1\n\nX650 is free", fontsize=16, style=filled, fillcolor=lightyellow];
382 [label="382: quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X650), SCOPE: 22, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X650), SCOPE: 22, CLAUSE: 3\n\nX650 is free", fontsize=16, style=filled, fillcolor=lightyellow];
387 [label="387: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
388 [label="388: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
391 [label="391: quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X650), SCOPE: 22, CLAUSE: 3\n\nX650 is free", fontsize=16, style=filled, fillcolor=lightyellow];
393 [label="393: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
396 [label="396: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
401 [label="Y: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X684)\n\nX684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
402 [label="402: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
407 [label="407: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X684), SCOPE: 23, CLAUSE: 1 | quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X684), SCOPE: 23, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X684), SCOPE: 23, CLAUSE: 3\n\nX684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
410 [label="410: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X684), SCOPE: 23, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X684), SCOPE: 23, CLAUSE: 3\n\nX684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
413 [label="413: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X684), SCOPE: 23, CLAUSE: 2\n\nX684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
414 [label="414: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X684), SCOPE: 23, CLAUSE: 3\n\nX684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
418 [label="418: quot(0, s(s(s(0))), s(s(s(s(0)))), X719)\n\nX719 is free", fontsize=16, style=filled, fillcolor=lightyellow];
424 [label="424: quot(0, s(s(s(0))), s(s(s(s(0)))), X719), SCOPE: 24, CLAUSE: 1 | quot(0, s(s(s(0))), s(s(s(s(0)))), X719), SCOPE: 24, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(0)))), X719), SCOPE: 24, CLAUSE: 3\n\nX719 is free", fontsize=16, style=filled, fillcolor=lightyellow];
427 [label="427: quot(0, s(s(s(0))), s(s(s(s(0)))), X719), SCOPE: 24, CLAUSE: 1\n\nX719 is free", fontsize=16, style=filled, fillcolor=lightyellow];
428 [label="428: quot(0, s(s(s(0))), s(s(s(s(0)))), X719), SCOPE: 24, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(0)))), X719), SCOPE: 24, CLAUSE: 3\n\nX719 is free", fontsize=16, style=filled, fillcolor=lightyellow];
436 [label="436: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
437 [label="437: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
439 [label="439: quot(0, s(s(s(0))), s(s(s(s(0)))), X719), SCOPE: 24, CLAUSE: 3\n\nX719 is free", fontsize=16, style=filled, fillcolor=lightyellow];
440 [label="440: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
441 [label="441: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
446 [label="T: quot(s(0), s(s(s(0))), s(s(s(0))), X753)\n\nX753 is free", fontsize=16, style=filled, fillcolor=lightyellow];
447 [label="447: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
452 [label="452: quot(s(0), s(s(s(0))), s(s(s(0))), X753), SCOPE: 25, CLAUSE: 1 | quot(s(0), s(s(s(0))), s(s(s(0))), X753), SCOPE: 25, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(0))), X753), SCOPE: 25, CLAUSE: 3\n\nX753 is free", fontsize=16, style=filled, fillcolor=lightyellow];
453 [label="453: quot(s(0), s(s(s(0))), s(s(s(0))), X753), SCOPE: 25, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(0))), X753), SCOPE: 25, CLAUSE: 3\n\nX753 is free", fontsize=16, style=filled, fillcolor=lightyellow];
458 [label="458: quot(s(0), s(s(s(0))), s(s(s(0))), X753), SCOPE: 25, CLAUSE: 2\n\nX753 is free", fontsize=16, style=filled, fillcolor=lightyellow];
459 [label="459: quot(s(0), s(s(s(0))), s(s(s(0))), X753), SCOPE: 25, CLAUSE: 3\n\nX753 is free", fontsize=16, style=filled, fillcolor=lightyellow];
462 [label="462: quot(0, s(s(0)), s(s(s(0))), X788)\n\nX788 is free", fontsize=16, style=filled, fillcolor=lightyellow];
470 [label="470: quot(0, s(s(0)), s(s(s(0))), X788), SCOPE: 26, CLAUSE: 1 | quot(0, s(s(0)), s(s(s(0))), X788), SCOPE: 26, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(0))), X788), SCOPE: 26, CLAUSE: 3\n\nX788 is free", fontsize=16, style=filled, fillcolor=lightyellow];
475 [label="475: quot(0, s(s(0)), s(s(s(0))), X788), SCOPE: 26, CLAUSE: 1\n\nX788 is free", fontsize=16, style=filled, fillcolor=lightyellow];
476 [label="476: quot(0, s(s(0)), s(s(s(0))), X788), SCOPE: 26, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(0))), X788), SCOPE: 26, CLAUSE: 3\n\nX788 is free", fontsize=16, style=filled, fillcolor=lightyellow];
480 [label="480: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
481 [label="481: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
483 [label="483: quot(0, s(s(0)), s(s(s(0))), X788), SCOPE: 26, CLAUSE: 3\n\nX788 is free", fontsize=16, style=filled, fillcolor=lightyellow];
487 [label="487: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
488 [label="488: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
493 [label="P: quot(s(0), s(s(0)), s(s(0)), X822)\n\nX822 is free", fontsize=16, style=filled, fillcolor=lightyellow];
494 [label="494: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
499 [label="499: quot(s(0), s(s(0)), s(s(0)), X822), SCOPE: 27, CLAUSE: 1 | quot(s(0), s(s(0)), s(s(0)), X822), SCOPE: 27, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(0)), X822), SCOPE: 27, CLAUSE: 3\n\nX822 is free", fontsize=16, style=filled, fillcolor=lightyellow];
500 [label="500: quot(s(0), s(s(0)), s(s(0)), X822), SCOPE: 27, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(0)), X822), SCOPE: 27, CLAUSE: 3\n\nX822 is free", fontsize=16, style=filled, fillcolor=lightyellow];
504 [label="504: quot(s(0), s(s(0)), s(s(0)), X822), SCOPE: 27, CLAUSE: 2\n\nX822 is free", fontsize=16, style=filled, fillcolor=lightyellow];
505 [label="505: quot(s(0), s(s(0)), s(s(0)), X822), SCOPE: 27, CLAUSE: 3\n\nX822 is free", fontsize=16, style=filled, fillcolor=lightyellow];
510 [label="510: quot(0, s(0), s(s(0)), X857)\n\nX857 is free", fontsize=16, style=filled, fillcolor=lightyellow];
517 [label="517: quot(0, s(0), s(s(0)), X857), SCOPE: 28, CLAUSE: 1 | quot(0, s(0), s(s(0)), X857), SCOPE: 28, CLAUSE: 2 | quot(0, s(0), s(s(0)), X857), SCOPE: 28, CLAUSE: 3\n\nX857 is free", fontsize=16, style=filled, fillcolor=lightyellow];
522 [label="522: quot(0, s(0), s(s(0)), X857), SCOPE: 28, CLAUSE: 1\n\nX857 is free", fontsize=16, style=filled, fillcolor=lightyellow];
523 [label="523: quot(0, s(0), s(s(0)), X857), SCOPE: 28, CLAUSE: 2 | quot(0, s(0), s(s(0)), X857), SCOPE: 28, CLAUSE: 3\n\nX857 is free", fontsize=16, style=filled, fillcolor=lightyellow];
526 [label="526: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
527 [label="527: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
530 [label="530: quot(0, s(0), s(s(0)), X857), SCOPE: 28, CLAUSE: 3\n\nX857 is free", fontsize=16, style=filled, fillcolor=lightyellow];
533 [label="533: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
535 [label="535: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
537 [label="537: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
539 [label="539: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
543 [label="E: times(T22, s(s(T20)), X35)\n\nT20 is ground\nT22 is ground\nX35 is free", fontsize=16, style=filled, fillcolor=lightyellow];
545 [label="L: neq(s(s(s(T20))), T157)\n\nT20 is ground\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
550 [label="550: times(T22, s(s(T20)), X35), SCOPE: 29, CLAUSE: 11 | times(T22, s(s(T20)), X35), SCOPE: 29, CLAUSE: 12\n\nT20 is ground\nT22 is ground\nX35 is free", fontsize=16, style=filled, fillcolor=lightyellow];
552 [label="552: times(T22, s(s(T20)), X35), SCOPE: 29, CLAUSE: 11\n\nT20 is ground\nT22 is ground\nX35 is free", fontsize=16, style=filled, fillcolor=lightyellow];
553 [label="553: times(T22, s(s(T20)), X35), SCOPE: 29, CLAUSE: 12\n\nT20 is ground\nT22 is ground\nX35 is free", fontsize=16, style=filled, fillcolor=lightyellow];
558 [label="558: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
559 [label="559: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
561 [label="561: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
567 [label="F: ','(times(T169, s(s(T170)), X907), add(X907, s(s(T170)), X908))\n\nT169 is ground\nT170 is ground\nX908 is free\nX907 is free", fontsize=16, style=filled, fillcolor=lightyellow];
568 [label="568: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
573 [label="573: times(T169, s(s(T170)), X907)\n\nT169 is ground\nT170 is ground\nX907 is free", fontsize=16, style=filled, fillcolor=lightyellow];
574 [label="G: add(T173, s(s(T170)), X908)\n\nT170 is ground\nT173 is ground\nX908 is free", fontsize=16, style=filled, fillcolor=lightyellow];
577 [label="577: add(T173, s(s(T170)), X908), SCOPE: 30, CLAUSE: 13 | add(T173, s(s(T170)), X908), SCOPE: 30, CLAUSE: 14 | add(T173, s(s(T170)), X908), SCOPE: 30, CLAUSE: 15\n\nT170 is ground\nT173 is ground\nX908 is free", fontsize=16, style=filled, fillcolor=lightyellow];
578 [label="578: add(T173, s(s(T170)), X908), SCOPE: 30, CLAUSE: 14 | add(T173, s(s(T170)), X908), SCOPE: 30, CLAUSE: 15\n\nT170 is ground\nT173 is ground\nX908 is free", fontsize=16, style=filled, fillcolor=lightyellow];
580 [label="580: add(T173, s(s(T170)), X908), SCOPE: 30, CLAUSE: 14\n\nT170 is ground\nT173 is ground\nX908 is free", fontsize=16, style=filled, fillcolor=lightyellow];
581 [label="581: add(T173, s(s(T170)), X908), SCOPE: 30, CLAUSE: 15\n\nT170 is ground\nT173 is ground\nX908 is free", fontsize=16, style=filled, fillcolor=lightyellow];
585 [label="585: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
586 [label="586: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
587 [label="587: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
593 [label="593: add(T188, s(s(T189)), X932)\n\nT188 is ground\nT189 is ground\nX932 is free", fontsize=16, style=filled, fillcolor=lightyellow];
594 [label="594: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
599 [label="599: neq(s(s(s(T20))), T157), SCOPE: 31, CLAUSE: 8 | neq(s(s(s(T20))), T157), SCOPE: 31, CLAUSE: 9 | neq(s(s(s(T20))), T157), SCOPE: 31, CLAUSE: 10\n\nT20 is ground\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
600 [label="600: neq(s(s(s(T20))), T157), SCOPE: 31, CLAUSE: 8\n\nT20 is ground\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
601 [label="601: neq(s(s(s(T20))), T157), SCOPE: 31, CLAUSE: 9 | neq(s(s(s(T20))), T157), SCOPE: 31, CLAUSE: 10\n\nT20 is ground\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
603 [label="603: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
604 [label="604: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
607 [label="607: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
608 [label="608: neq(s(s(s(T20))), T157), SCOPE: 31, CLAUSE: 10\n\nT20 is ground\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
613 [label="613: neq(s(s(T203)), T204)\n\nT203 is ground\nT204 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
614 [label="614: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
617 [label="617: neq(s(s(T203)), T204), SCOPE: 32, CLAUSE: 8 | neq(s(s(T203)), T204), SCOPE: 32, CLAUSE: 9 | neq(s(s(T203)), T204), SCOPE: 32, CLAUSE: 10\n\nT203 is ground\nT204 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
619 [label="619: neq(s(s(T203)), T204), SCOPE: 32, CLAUSE: 8\n\nT203 is ground\nT204 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
620 [label="620: neq(s(s(T203)), T204), SCOPE: 32, CLAUSE: 9 | neq(s(s(T203)), T204), SCOPE: 32, CLAUSE: 10\n\nT203 is ground\nT204 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
623 [label="623: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
624 [label="624: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
626 [label="626: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
629 [label="629: neq(s(s(T203)), T204), SCOPE: 32, CLAUSE: 10\n\nT203 is ground\nT204 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
633 [label="M: neq(s(T216), T217)\n\nT216 is ground\nT217 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
634 [label="634: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
639 [label="639: neq(s(T216), T217), SCOPE: 33, CLAUSE: 8 | neq(s(T216), T217), SCOPE: 33, CLAUSE: 9 | neq(s(T216), T217), SCOPE: 33, CLAUSE: 10\n\nT216 is ground\nT217 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
641 [label="641: neq(s(T216), T217), SCOPE: 33, CLAUSE: 8\n\nT216 is ground\nT217 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
642 [label="642: neq(s(T216), T217), SCOPE: 33, CLAUSE: 9 | neq(s(T216), T217), SCOPE: 33, CLAUSE: 10\n\nT216 is ground\nT217 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
645 [label="645: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
646 [label="646: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
647 [label="647: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
648 [label="648: neq(s(T216), T217), SCOPE: 33, CLAUSE: 10\n\nT216 is ground\nT217 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
655 [label="H: neq(T229, T230)\n\nT229 is ground\nT230 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
656 [label="656: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
660 [label="660: neq(T229, T230), SCOPE: 34, CLAUSE: 8 | neq(T229, T230), SCOPE: 34, CLAUSE: 9 | neq(T229, T230), SCOPE: 34, CLAUSE: 10\n\nT229 is ground\nT230 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
663 [label="663: neq(T229, T230), SCOPE: 34, CLAUSE: 8\n\nT229 is ground\nT230 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
664 [label="664: neq(T229, T230), SCOPE: 34, CLAUSE: 9 | neq(T229, T230), SCOPE: 34, CLAUSE: 10\n\nT229 is ground\nT230 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
667 [label="667: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
668 [label="668: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
669 [label="669: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
673 [label="673: neq(T229, T230), SCOPE: 34, CLAUSE: 9\n\nT229 is ground\nT230 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
674 [label="674: neq(T229, T230), SCOPE: 34, CLAUSE: 10\n\nT229 is ground\nT230 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
677 [label="677: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
678 [label="678: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
679 [label="679: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
683 [label="683: neq(T247, T248)\n\nT247 is ground\nT248 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
685 [label="685: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
690 [label="690: 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];
694 [label="694: pr(s(s(s(T14))), s(T14)), SCOPE: 35, CLAUSE: 5\n\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
695 [label="695: pr(s(s(s(T14))), s(T14)), SCOPE: 35, CLAUSE: 6\n\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
699 [label="699: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
700 [label="700: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
701 [label="701: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
707 [label="N14: ','(not_divides(s(s(T263)), s(s(s(s(T263))))), pr(s(s(s(s(T263)))), s(T263)))\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
708 [label="708: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
711 [label="N16: not_divides(s(s(T263)), s(s(s(s(T263)))))\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
712 [label="N18: pr(s(s(s(s(T263)))), s(T263))\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
715 [label="715: not_divides(s(s(T263)), s(s(s(s(T263))))), SCOPE: 36, CLAUSE: 7\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
720 [label="N17: ','(div(s(s(s(s(T269)))), s(s(T269)), X1030), ','(times(X1030, s(s(T269)), X1031), neq(s(s(s(s(T269)))), X1031)))\n\nT269 is ground\nX1030 is free\nX1031 is free", fontsize=16, style=filled, fillcolor=lightyellow];
723 [label="N20: div(s(s(s(s(T269)))), s(s(T269)), X1030)\n\nT269 is ground\nX1030 is free", fontsize=16, style=filled, fillcolor=lightyellow];
724 [label="N41: ','(times(T271, s(s(T269)), X1031), neq(s(s(s(s(T269)))), X1031))\n\nT269 is ground\nT271 is ground\nX1031 is free", fontsize=16, style=filled, fillcolor=lightyellow];
728 [label="728: div(s(s(s(s(T269)))), s(s(T269)), X1030), SCOPE: 37, CLAUSE: 0\n\nT269 is ground\nX1030 is free", fontsize=16, style=filled, fillcolor=lightyellow];
732 [label="732: quot(s(s(s(s(T275)))), s(s(T275)), s(s(T275)), X1055)\n\nT275 is ground\nX1055 is free", fontsize=16, style=filled, fillcolor=lightyellow];
734 [label="734: quot(s(s(s(s(T275)))), s(s(T275)), s(s(T275)), X1055), SCOPE: 38, CLAUSE: 1 | quot(s(s(s(s(T275)))), s(s(T275)), s(s(T275)), X1055), SCOPE: 38, CLAUSE: 2 | quot(s(s(s(s(T275)))), s(s(T275)), s(s(T275)), X1055), SCOPE: 38, CLAUSE: 3\n\nT275 is ground\nX1055 is free", fontsize=16, style=filled, fillcolor=lightyellow];
735 [label="735: quot(s(s(s(s(T275)))), s(s(T275)), s(s(T275)), X1055), SCOPE: 38, CLAUSE: 2 | quot(s(s(s(s(T275)))), s(s(T275)), s(s(T275)), X1055), SCOPE: 38, CLAUSE: 3\n\nT275 is ground\nX1055 is free", fontsize=16, style=filled, fillcolor=lightyellow];
745 [label="745: quot(s(s(s(s(T275)))), s(s(T275)), s(s(T275)), X1055), SCOPE: 38, CLAUSE: 2\n\nT275 is ground\nX1055 is free", fontsize=16, style=filled, fillcolor=lightyellow];
746 [label="746: quot(s(s(s(s(T275)))), s(s(T275)), s(s(T275)), X1055), SCOPE: 38, CLAUSE: 3\n\nT275 is ground\nX1055 is free", fontsize=16, style=filled, fillcolor=lightyellow];
749 [label="749: quot(s(s(s(T280))), s(T280), s(s(T280)), X1094)\n\nT280 is ground\nX1094 is free", fontsize=16, style=filled, fillcolor=lightyellow];
751 [label="751: quot(s(s(s(T280))), s(T280), s(s(T280)), X1094), SCOPE: 39, CLAUSE: 1 | quot(s(s(s(T280))), s(T280), s(s(T280)), X1094), SCOPE: 39, CLAUSE: 2 | quot(s(s(s(T280))), s(T280), s(s(T280)), X1094), SCOPE: 39, CLAUSE: 3\n\nT280 is ground\nX1094 is free", fontsize=16, style=filled, fillcolor=lightyellow];
754 [label="754: quot(s(s(s(T280))), s(T280), s(s(T280)), X1094), SCOPE: 39, CLAUSE: 2 | quot(s(s(s(T280))), s(T280), s(s(T280)), X1094), SCOPE: 39, CLAUSE: 3\n\nT280 is ground\nX1094 is free", fontsize=16, style=filled, fillcolor=lightyellow];
760 [label="760: quot(s(s(s(T280))), s(T280), s(s(T280)), X1094), SCOPE: 39, CLAUSE: 2\n\nT280 is ground\nX1094 is free", fontsize=16, style=filled, fillcolor=lightyellow];
761 [label="761: quot(s(s(s(T280))), s(T280), s(s(T280)), X1094), SCOPE: 39, CLAUSE: 3\n\nT280 is ground\nX1094 is free", fontsize=16, style=filled, fillcolor=lightyellow];
768 [label="768: quot(s(s(T285)), T285, s(s(T285)), X1133)\n\nT285 is ground\nX1133 is free", fontsize=16, style=filled, fillcolor=lightyellow];
772 [label="772: quot(s(s(T285)), T285, s(s(T285)), X1133), SCOPE: 40, CLAUSE: 1 | quot(s(s(T285)), T285, s(s(T285)), X1133), SCOPE: 40, CLAUSE: 2 | quot(s(s(T285)), T285, s(s(T285)), X1133), SCOPE: 40, CLAUSE: 3\n\nT285 is ground\nX1133 is free", fontsize=16, style=filled, fillcolor=lightyellow];
774 [label="774: quot(s(s(T285)), T285, s(s(T285)), X1133), SCOPE: 40, CLAUSE: 2 | quot(s(s(T285)), T285, s(s(T285)), X1133), SCOPE: 40, CLAUSE: 3\n\nT285 is ground\nX1133 is free", fontsize=16, style=filled, fillcolor=lightyellow];
779 [label="779: quot(s(s(T285)), T285, s(s(T285)), X1133), SCOPE: 40, CLAUSE: 2\n\nT285 is ground\nX1133 is free", fontsize=16, style=filled, fillcolor=lightyellow];
780 [label="780: quot(s(s(T285)), T285, s(s(T285)), X1133), SCOPE: 40, CLAUSE: 3\n\nT285 is ground\nX1133 is free", fontsize=16, style=filled, fillcolor=lightyellow];
783 [label="783: quot(s(s(T295)), T295, s(s(s(T295))), X1164)\n\nT295 is ground\nX1164 is free", fontsize=16, style=filled, fillcolor=lightyellow];
784 [label="784: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
791 [label="791: quot(s(s(T295)), T295, s(s(s(T295))), X1164), SCOPE: 41, CLAUSE: 1 | quot(s(s(T295)), T295, s(s(s(T295))), X1164), SCOPE: 41, CLAUSE: 2 | quot(s(s(T295)), T295, s(s(s(T295))), X1164), SCOPE: 41, CLAUSE: 3\n\nT295 is ground\nX1164 is free", fontsize=16, style=filled, fillcolor=lightyellow];
794 [label="794: quot(s(s(T295)), T295, s(s(s(T295))), X1164), SCOPE: 41, CLAUSE: 2 | quot(s(s(T295)), T295, s(s(s(T295))), X1164), SCOPE: 41, CLAUSE: 3\n\nT295 is ground\nX1164 is free", fontsize=16, style=filled, fillcolor=lightyellow];
803 [label="803: quot(s(s(T295)), T295, s(s(s(T295))), X1164), SCOPE: 41, CLAUSE: 2\n\nT295 is ground\nX1164 is free", fontsize=16, style=filled, fillcolor=lightyellow];
804 [label="804: quot(s(s(T295)), T295, s(s(s(T295))), X1164), SCOPE: 41, CLAUSE: 3\n\nT295 is ground\nX1164 is free", fontsize=16, style=filled, fillcolor=lightyellow];
808 [label="808: quot(s(s(T305)), T305, s(s(s(s(T305)))), X1195)\n\nT305 is ground\nX1195 is free", fontsize=16, style=filled, fillcolor=lightyellow];
809 [label="809: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
812 [label="812: quot(s(s(T305)), T305, s(s(s(s(T305)))), X1195), SCOPE: 42, CLAUSE: 1 | quot(s(s(T305)), T305, s(s(s(s(T305)))), X1195), SCOPE: 42, CLAUSE: 2 | quot(s(s(T305)), T305, s(s(s(s(T305)))), X1195), SCOPE: 42, CLAUSE: 3\n\nT305 is ground\nX1195 is free", fontsize=16, style=filled, fillcolor=lightyellow];
816 [label="816: quot(s(s(T305)), T305, s(s(s(s(T305)))), X1195), SCOPE: 42, CLAUSE: 2 | quot(s(s(T305)), T305, s(s(s(s(T305)))), X1195), SCOPE: 42, CLAUSE: 3\n\nT305 is ground\nX1195 is free", fontsize=16, style=filled, fillcolor=lightyellow];
819 [label="819: quot(s(s(T305)), T305, s(s(s(s(T305)))), X1195), SCOPE: 42, CLAUSE: 2\n\nT305 is ground\nX1195 is free", fontsize=16, style=filled, fillcolor=lightyellow];
820 [label="820: quot(s(s(T305)), T305, s(s(s(s(T305)))), X1195), SCOPE: 42, CLAUSE: 3\n\nT305 is ground\nX1195 is free", fontsize=16, style=filled, fillcolor=lightyellow];
830 [label="830: quot(s(s(T315)), T315, s(s(s(s(s(T315))))), X1226)\n\nT315 is ground\nX1226 is free", fontsize=16, style=filled, fillcolor=lightyellow];
831 [label="831: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
835 [label="835: quot(s(s(T315)), T315, s(s(s(s(s(T315))))), X1226), SCOPE: 43, CLAUSE: 1 | quot(s(s(T315)), T315, s(s(s(s(s(T315))))), X1226), SCOPE: 43, CLAUSE: 2 | quot(s(s(T315)), T315, s(s(s(s(s(T315))))), X1226), SCOPE: 43, CLAUSE: 3\n\nT315 is ground\nX1226 is free", fontsize=16, style=filled, fillcolor=lightyellow];
838 [label="838: quot(s(s(T315)), T315, s(s(s(s(s(T315))))), X1226), SCOPE: 43, CLAUSE: 2 | quot(s(s(T315)), T315, s(s(s(s(s(T315))))), X1226), SCOPE: 43, CLAUSE: 3\n\nT315 is ground\nX1226 is free", fontsize=16, style=filled, fillcolor=lightyellow];
841 [label="841: quot(s(s(T315)), T315, s(s(s(s(s(T315))))), X1226), SCOPE: 43, CLAUSE: 2\n\nT315 is ground\nX1226 is free", fontsize=16, style=filled, fillcolor=lightyellow];
842 [label="842: quot(s(s(T315)), T315, s(s(s(s(s(T315))))), X1226), SCOPE: 43, CLAUSE: 3\n\nT315 is ground\nX1226 is free", fontsize=16, style=filled, fillcolor=lightyellow];
848 [label="848: quot(s(s(T325)), T325, s(s(s(s(s(s(T325)))))), X1257)\n\nT325 is ground\nX1257 is free", fontsize=16, style=filled, fillcolor=lightyellow];
849 [label="849: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
855 [label="855: quot(s(s(T325)), T325, s(s(s(s(s(s(T325)))))), X1257), SCOPE: 44, CLAUSE: 1 | quot(s(s(T325)), T325, s(s(s(s(s(s(T325)))))), X1257), SCOPE: 44, CLAUSE: 2 | quot(s(s(T325)), T325, s(s(s(s(s(s(T325)))))), X1257), SCOPE: 44, CLAUSE: 3\n\nT325 is ground\nX1257 is free", fontsize=16, style=filled, fillcolor=lightyellow];
858 [label="858: quot(s(s(T325)), T325, s(s(s(s(s(s(T325)))))), X1257), SCOPE: 44, CLAUSE: 2 | quot(s(s(T325)), T325, s(s(s(s(s(s(T325)))))), X1257), SCOPE: 44, CLAUSE: 3\n\nT325 is ground\nX1257 is free", fontsize=16, style=filled, fillcolor=lightyellow];
863 [label="863: quot(s(s(T325)), T325, s(s(s(s(s(s(T325)))))), X1257), SCOPE: 44, CLAUSE: 2\n\nT325 is ground\nX1257 is free", fontsize=16, style=filled, fillcolor=lightyellow];
864 [label="864: quot(s(s(T325)), T325, s(s(s(s(s(s(T325)))))), X1257), SCOPE: 44, CLAUSE: 3\n\nT325 is ground\nX1257 is free", fontsize=16, style=filled, fillcolor=lightyellow];
865 [label="865: quot(s(s(T335)), T335, s(s(s(s(s(s(s(T335))))))), X1288)\n\nT335 is ground\nX1288 is free", fontsize=16, style=filled, fillcolor=lightyellow];
866 [label="866: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
869 [label="869: quot(s(s(T335)), T335, s(s(s(s(s(s(s(T335))))))), X1288), SCOPE: 45, CLAUSE: 1 | quot(s(s(T335)), T335, s(s(s(s(s(s(s(T335))))))), X1288), SCOPE: 45, CLAUSE: 2 | quot(s(s(T335)), T335, s(s(s(s(s(s(s(T335))))))), X1288), SCOPE: 45, CLAUSE: 3\n\nT335 is ground\nX1288 is free", fontsize=16, style=filled, fillcolor=lightyellow];
874 [label="874: quot(s(s(T335)), T335, s(s(s(s(s(s(s(T335))))))), X1288), SCOPE: 45, CLAUSE: 2 | quot(s(s(T335)), T335, s(s(s(s(s(s(s(T335))))))), X1288), SCOPE: 45, CLAUSE: 3\n\nT335 is ground\nX1288 is free", fontsize=16, style=filled, fillcolor=lightyellow];
879 [label="879: quot(s(s(T335)), T335, s(s(s(s(s(s(s(T335))))))), X1288), SCOPE: 45, CLAUSE: 2\n\nT335 is ground\nX1288 is free", fontsize=16, style=filled, fillcolor=lightyellow];
880 [label="880: quot(s(s(T335)), T335, s(s(s(s(s(s(s(T335))))))), X1288), SCOPE: 45, CLAUSE: 3\n\nT335 is ground\nX1288 is free", fontsize=16, style=filled, fillcolor=lightyellow];
884 [label="884: quot(s(s(T345)), T345, s(s(s(s(s(s(s(s(T345)))))))), X1319)\n\nT345 is ground\nX1319 is free", fontsize=16, style=filled, fillcolor=lightyellow];
885 [label="885: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
888 [label="I: quot(s(s(T345)), T345, s(T346), X1319)\n\nT345 is ground\nT346 is ground\nX1319 is free", fontsize=16, style=filled, fillcolor=lightyellow];
890 [label="890: quot(s(s(T345)), T345, s(T346), X1319), SCOPE: 46, CLAUSE: 1 | quot(s(s(T345)), T345, s(T346), X1319), SCOPE: 46, CLAUSE: 2 | quot(s(s(T345)), T345, s(T346), X1319), SCOPE: 46, CLAUSE: 3\n\nT345 is ground\nT346 is ground\nX1319 is free", fontsize=16, style=filled, fillcolor=lightyellow];
892 [label="892: quot(s(s(T345)), T345, s(T346), X1319), SCOPE: 46, CLAUSE: 2 | quot(s(s(T345)), T345, s(T346), X1319), SCOPE: 46, CLAUSE: 3\n\nT345 is ground\nT346 is ground\nX1319 is free", fontsize=16, style=filled, fillcolor=lightyellow];
896 [label="896: quot(s(s(T345)), T345, s(T346), X1319), SCOPE: 46, CLAUSE: 2\n\nT345 is ground\nT346 is ground\nX1319 is free", fontsize=16, style=filled, fillcolor=lightyellow];
897 [label="897: quot(s(s(T345)), T345, s(T346), X1319), SCOPE: 46, CLAUSE: 3\n\nT345 is ground\nT346 is ground\nX1319 is free", fontsize=16, style=filled, fillcolor=lightyellow];
900 [label="900: quot(s(s(T360)), T360, s(T361), X1354)\n\nT360 is ground\nT361 is ground\nX1354 is free", fontsize=16, style=filled, fillcolor=lightyellow];
901 [label="901: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
905 [label="905: quot(s(s(0)), s(T367), s(T367), X1370)\n\nT367 is ground\nX1370 is free", fontsize=16, style=filled, fillcolor=lightyellow];
906 [label="906: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
907 [label="907: quot(s(s(0)), s(T367), s(T367), X1370), SCOPE: 47, CLAUSE: 1 | quot(s(s(0)), s(T367), s(T367), X1370), SCOPE: 47, CLAUSE: 2 | quot(s(s(0)), s(T367), s(T367), X1370), SCOPE: 47, CLAUSE: 3\n\nT367 is ground\nX1370 is free", fontsize=16, style=filled, fillcolor=lightyellow];
909 [label="909: quot(s(s(0)), s(T367), s(T367), X1370), SCOPE: 47, CLAUSE: 2 | quot(s(s(0)), s(T367), s(T367), X1370), SCOPE: 47, CLAUSE: 3\n\nT367 is ground\nX1370 is free", fontsize=16, style=filled, fillcolor=lightyellow];
912 [label="912: quot(s(s(0)), s(T367), s(T367), X1370), SCOPE: 47, CLAUSE: 2\n\nT367 is ground\nX1370 is free", fontsize=16, style=filled, fillcolor=lightyellow];
913 [label="913: quot(s(s(0)), s(T367), s(T367), X1370), SCOPE: 47, CLAUSE: 3\n\nT367 is ground\nX1370 is free", fontsize=16, style=filled, fillcolor=lightyellow];
918 [label="918: quot(s(0), T372, s(T372), X1409)\n\nT372 is ground\nX1409 is free", fontsize=16, style=filled, fillcolor=lightyellow];
921 [label="921: quot(s(0), T372, s(T372), X1409), SCOPE: 48, CLAUSE: 1 | quot(s(0), T372, s(T372), X1409), SCOPE: 48, CLAUSE: 2 | quot(s(0), T372, s(T372), X1409), SCOPE: 48, CLAUSE: 3\n\nT372 is ground\nX1409 is free", fontsize=16, style=filled, fillcolor=lightyellow];
922 [label="922: quot(s(0), T372, s(T372), X1409), SCOPE: 48, CLAUSE: 2 | quot(s(0), T372, s(T372), X1409), SCOPE: 48, CLAUSE: 3\n\nT372 is ground\nX1409 is free", fontsize=16, style=filled, fillcolor=lightyellow];
924 [label="924: quot(s(0), T372, s(T372), X1409), SCOPE: 48, CLAUSE: 2\n\nT372 is ground\nX1409 is free", fontsize=16, style=filled, fillcolor=lightyellow];
925 [label="925: quot(s(0), T372, s(T372), X1409), SCOPE: 48, CLAUSE: 3\n\nT372 is ground\nX1409 is free", fontsize=16, style=filled, fillcolor=lightyellow];
928 [label="928: quot(0, T377, s(s(T377)), X1440)\n\nT377 is ground\nX1440 is free", fontsize=16, style=filled, fillcolor=lightyellow];
929 [label="929: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
932 [label="932: quot(0, T377, s(s(T377)), X1440), SCOPE: 49, CLAUSE: 1 | quot(0, T377, s(s(T377)), X1440), SCOPE: 49, CLAUSE: 2 | quot(0, T377, s(s(T377)), X1440), SCOPE: 49, CLAUSE: 3\n\nT377 is ground\nX1440 is free", fontsize=16, style=filled, fillcolor=lightyellow];
933 [label="933: quot(0, T377, s(s(T377)), X1440), SCOPE: 49, CLAUSE: 1\n\nT377 is ground\nX1440 is free", fontsize=16, style=filled, fillcolor=lightyellow];
934 [label="934: quot(0, T377, s(s(T377)), X1440), SCOPE: 49, CLAUSE: 2 | quot(0, T377, s(s(T377)), X1440), SCOPE: 49, CLAUSE: 3\n\nT377 is ground\nX1440 is free", fontsize=16, style=filled, fillcolor=lightyellow];
937 [label="937: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
938 [label="938: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
939 [label="939: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
940 [label="940: quot(0, T377, s(s(T377)), X1440), SCOPE: 49, CLAUSE: 3\n\nT377 is ground\nX1440 is free", fontsize=16, style=filled, fillcolor=lightyellow];
943 [label="J: quot(0, s(s(0)), s(s(0)), X1470)\n\nX1470 is free", fontsize=16, style=filled, fillcolor=lightyellow];
944 [label="944: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
945 [label="945: quot(0, s(s(0)), s(s(0)), X1470), SCOPE: 50, CLAUSE: 1 | quot(0, s(s(0)), s(s(0)), X1470), SCOPE: 50, CLAUSE: 2 | quot(0, s(s(0)), s(s(0)), X1470), SCOPE: 50, CLAUSE: 3\n\nX1470 is free", fontsize=16, style=filled, fillcolor=lightyellow];
948 [label="948: quot(0, s(s(0)), s(s(0)), X1470), SCOPE: 50, CLAUSE: 1\n\nX1470 is free", fontsize=16, style=filled, fillcolor=lightyellow];
949 [label="949: quot(0, s(s(0)), s(s(0)), X1470), SCOPE: 50, CLAUSE: 2 | quot(0, s(s(0)), s(s(0)), X1470), SCOPE: 50, CLAUSE: 3\n\nX1470 is free", fontsize=16, style=filled, fillcolor=lightyellow];
952 [label="952: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
953 [label="953: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
954 [label="954: quot(0, s(s(0)), s(s(0)), X1470), SCOPE: 50, CLAUSE: 3\n\nX1470 is free", fontsize=16, style=filled, fillcolor=lightyellow];
955 [label="955: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
960 [label="K: quot(s(0), s(0), s(0), X1501)\n\nX1501 is free", fontsize=16, style=filled, fillcolor=lightyellow];
961 [label="961: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
962 [label="962: quot(s(0), s(0), s(0), X1501), SCOPE: 51, CLAUSE: 1 | quot(s(0), s(0), s(0), X1501), SCOPE: 51, CLAUSE: 2 | quot(s(0), s(0), s(0), X1501), SCOPE: 51, CLAUSE: 3\n\nX1501 is free", fontsize=16, style=filled, fillcolor=lightyellow];
964 [label="964: quot(s(0), s(0), s(0), X1501), SCOPE: 51, CLAUSE: 2 | quot(s(0), s(0), s(0), X1501), SCOPE: 51, CLAUSE: 3\n\nX1501 is free", fontsize=16, style=filled, fillcolor=lightyellow];
971 [label="971: quot(s(0), s(0), s(0), X1501), SCOPE: 51, CLAUSE: 2\n\nX1501 is free", fontsize=16, style=filled, fillcolor=lightyellow];
972 [label="972: quot(s(0), s(0), s(0), X1501), SCOPE: 51, CLAUSE: 3\n\nX1501 is free", fontsize=16, style=filled, fillcolor=lightyellow];
979 [label="979: quot(0, 0, s(0), X1540)\n\nX1540 is free", fontsize=16, style=filled, fillcolor=lightyellow];
983 [label="983: quot(0, 0, s(0), X1540), SCOPE: 52, CLAUSE: 1 | quot(0, 0, s(0), X1540), SCOPE: 52, CLAUSE: 2 | quot(0, 0, s(0), X1540), SCOPE: 52, CLAUSE: 3\n\nX1540 is free", fontsize=16, style=filled, fillcolor=lightyellow];
985 [label="985: quot(0, 0, s(0), X1540), SCOPE: 52, CLAUSE: 2 | quot(0, 0, s(0), X1540), SCOPE: 52, CLAUSE: 3\n\nX1540 is free", fontsize=16, style=filled, fillcolor=lightyellow];
987 [label="987: quot(0, 0, s(0), X1540), SCOPE: 52, CLAUSE: 3\n\nX1540 is free", fontsize=16, style=filled, fillcolor=lightyellow];
996 [label="996: quot(0, s(0), s(0), X1564)\n\nX1564 is free", fontsize=16, style=filled, fillcolor=lightyellow];
999 [label="999: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1003 [label="1003: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1010 [label="1010: quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1584)\n\nX1584 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1011 [label="1011: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1015 [label="1015: quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1584), SCOPE: 53, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1584), SCOPE: 53, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1584), SCOPE: 53, CLAUSE: 3\n\nX1584 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1019 [label="1019: quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1584), SCOPE: 53, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1584), SCOPE: 53, CLAUSE: 3\n\nX1584 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1024 [label="1024: quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1584), SCOPE: 53, CLAUSE: 2\n\nX1584 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1025 [label="1025: quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1584), SCOPE: 53, CLAUSE: 3\n\nX1584 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1034 [label="1034: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X1623)\n\nX1623 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1036 [label="1036: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X1623), SCOPE: 54, CLAUSE: 1 | quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X1623), SCOPE: 54, CLAUSE: 2 | quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X1623), SCOPE: 54, CLAUSE: 3\n\nX1623 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1037 [label="1037: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X1623), SCOPE: 54, CLAUSE: 2 | quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X1623), SCOPE: 54, CLAUSE: 3\n\nX1623 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1041 [label="1041: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X1623), SCOPE: 54, CLAUSE: 2\n\nX1623 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1042 [label="1042: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X1623), SCOPE: 54, CLAUSE: 3\n\nX1623 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1050 [label="1050: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1658)\n\nX1658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1052 [label="1052: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1658), SCOPE: 55, CLAUSE: 1 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1658), SCOPE: 55, CLAUSE: 2 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1658), SCOPE: 55, CLAUSE: 3\n\nX1658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1053 [label="1053: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1658), SCOPE: 55, CLAUSE: 1\n\nX1658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1054 [label="1054: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1658), SCOPE: 55, CLAUSE: 2 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1658), SCOPE: 55, CLAUSE: 3\n\nX1658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1059 [label="1059: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1060 [label="1060: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1061 [label="1061: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1658), SCOPE: 55, CLAUSE: 3\n\nX1658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1064 [label="1064: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1067 [label="1067: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1068 [label="1068: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1073 [label="1073: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X1695)\n\nX1695 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1074 [label="1074: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1078 [label="1078: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X1695), SCOPE: 56, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X1695), SCOPE: 56, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X1695), SCOPE: 56, CLAUSE: 3\n\nX1695 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1079 [label="1079: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X1695), SCOPE: 56, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X1695), SCOPE: 56, CLAUSE: 3\n\nX1695 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1083 [label="1083: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X1695), SCOPE: 56, CLAUSE: 2\n\nX1695 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1084 [label="1084: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X1695), SCOPE: 56, CLAUSE: 3\n\nX1695 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1089 [label="1089: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X1734)\n\nX1734 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1095 [label="1095: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X1734), SCOPE: 57, CLAUSE: 1 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X1734), SCOPE: 57, CLAUSE: 2 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X1734), SCOPE: 57, CLAUSE: 3\n\nX1734 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1096 [label="1096: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X1734), SCOPE: 57, CLAUSE: 2 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X1734), SCOPE: 57, CLAUSE: 3\n\nX1734 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1103 [label="1103: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X1734), SCOPE: 57, CLAUSE: 2\n\nX1734 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1104 [label="1104: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X1734), SCOPE: 57, CLAUSE: 3\n\nX1734 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1110 [label="1110: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X1769)\n\nX1769 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1114 [label="1114: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X1769), SCOPE: 58, CLAUSE: 1 | quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X1769), SCOPE: 58, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X1769), SCOPE: 58, CLAUSE: 3\n\nX1769 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1117 [label="1117: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X1769), SCOPE: 58, CLAUSE: 1\n\nX1769 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1118 [label="1118: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X1769), SCOPE: 58, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X1769), SCOPE: 58, CLAUSE: 3\n\nX1769 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1120 [label="1120: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1122 [label="1122: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1124 [label="1124: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X1769), SCOPE: 58, CLAUSE: 3\n\nX1769 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1128 [label="1128: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1130 [label="1130: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1131 [label="1131: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1140 [label="1140: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X1806)\n\nX1806 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1141 [label="1141: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1142 [label="1142: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X1806), SCOPE: 59, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X1806), SCOPE: 59, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X1806), SCOPE: 59, CLAUSE: 3\n\nX1806 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1143 [label="1143: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X1806), SCOPE: 59, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X1806), SCOPE: 59, CLAUSE: 3\n\nX1806 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1150 [label="1150: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X1806), SCOPE: 59, CLAUSE: 2\n\nX1806 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1151 [label="1151: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X1806), SCOPE: 59, CLAUSE: 3\n\nX1806 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1157 [label="1157: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X1845)\n\nX1845 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1160 [label="1160: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X1845), SCOPE: 60, CLAUSE: 1 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X1845), SCOPE: 60, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X1845), SCOPE: 60, CLAUSE: 3\n\nX1845 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1161 [label="1161: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X1845), SCOPE: 60, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X1845), SCOPE: 60, CLAUSE: 3\n\nX1845 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1165 [label="1165: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X1845), SCOPE: 60, CLAUSE: 2\n\nX1845 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1166 [label="1166: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X1845), SCOPE: 60, CLAUSE: 3\n\nX1845 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1171 [label="1171: quot(0, s(s(s(0))), s(s(s(s(s(0))))), X1880)\n\nX1880 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1176 [label="1176: quot(0, s(s(s(0))), s(s(s(s(s(0))))), X1880), SCOPE: 61, CLAUSE: 1 | quot(0, s(s(s(0))), s(s(s(s(s(0))))), X1880), SCOPE: 61, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(s(0))))), X1880), SCOPE: 61, CLAUSE: 3\n\nX1880 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1177 [label="1177: quot(0, s(s(s(0))), s(s(s(s(s(0))))), X1880), SCOPE: 61, CLAUSE: 1\n\nX1880 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1178 [label="1178: quot(0, s(s(s(0))), s(s(s(s(s(0))))), X1880), SCOPE: 61, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(s(0))))), X1880), SCOPE: 61, CLAUSE: 3\n\nX1880 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1179 [label="1179: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1180 [label="1180: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1182 [label="1182: quot(0, s(s(s(0))), s(s(s(s(s(0))))), X1880), SCOPE: 61, CLAUSE: 3\n\nX1880 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1183 [label="1183: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1185 [label="1185: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1187 [label="1187: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1194 [label="1194: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X1917)\n\nX1917 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1195 [label="1195: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1198 [label="1198: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X1917), SCOPE: 62, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X1917), SCOPE: 62, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X1917), SCOPE: 62, CLAUSE: 3\n\nX1917 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1200 [label="1200: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X1917), SCOPE: 62, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X1917), SCOPE: 62, CLAUSE: 3\n\nX1917 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1208 [label="1208: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X1917), SCOPE: 62, CLAUSE: 2\n\nX1917 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1209 [label="1209: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X1917), SCOPE: 62, CLAUSE: 3\n\nX1917 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1220 [label="1220: quot(s(0), s(s(s(0))), s(s(s(s(0)))), X1956)\n\nX1956 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1223 [label="1223: quot(s(0), s(s(s(0))), s(s(s(s(0)))), X1956), SCOPE: 63, CLAUSE: 1 | quot(s(0), s(s(s(0))), s(s(s(s(0)))), X1956), SCOPE: 63, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(0)))), X1956), SCOPE: 63, CLAUSE: 3\n\nX1956 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1225 [label="1225: quot(s(0), s(s(s(0))), s(s(s(s(0)))), X1956), SCOPE: 63, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(0)))), X1956), SCOPE: 63, CLAUSE: 3\n\nX1956 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1229 [label="1229: quot(s(0), s(s(s(0))), s(s(s(s(0)))), X1956), SCOPE: 63, CLAUSE: 2\n\nX1956 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1230 [label="1230: quot(s(0), s(s(s(0))), s(s(s(s(0)))), X1956), SCOPE: 63, CLAUSE: 3\n\nX1956 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1236 [label="1236: quot(0, s(s(0)), s(s(s(s(0)))), X1991)\n\nX1991 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1239 [label="1239: quot(0, s(s(0)), s(s(s(s(0)))), X1991), SCOPE: 64, CLAUSE: 1 | quot(0, s(s(0)), s(s(s(s(0)))), X1991), SCOPE: 64, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(0)))), X1991), SCOPE: 64, CLAUSE: 3\n\nX1991 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1241 [label="1241: quot(0, s(s(0)), s(s(s(s(0)))), X1991), SCOPE: 64, CLAUSE: 1\n\nX1991 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1242 [label="1242: quot(0, s(s(0)), s(s(s(s(0)))), X1991), SCOPE: 64, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(0)))), X1991), SCOPE: 64, CLAUSE: 3\n\nX1991 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1247 [label="1247: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1248 [label="1248: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1249 [label="1249: quot(0, s(s(0)), s(s(s(s(0)))), X1991), SCOPE: 64, CLAUSE: 3\n\nX1991 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1250 [label="1250: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1251 [label="1251: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1254 [label="1254: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1261 [label="Z: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2028)\n\nX2028 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1262 [label="1262: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1269 [label="1269: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2028), SCOPE: 65, CLAUSE: 1 | quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2028), SCOPE: 65, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2028), SCOPE: 65, CLAUSE: 3\n\nX2028 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1271 [label="1271: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2028), SCOPE: 65, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2028), SCOPE: 65, CLAUSE: 3\n\nX2028 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1279 [label="1279: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2028), SCOPE: 65, CLAUSE: 2\n\nX2028 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1280 [label="1280: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2028), SCOPE: 65, CLAUSE: 3\n\nX2028 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1287 [label="1287: quot(s(0), s(s(0)), s(s(s(0))), X2067)\n\nX2067 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1290 [label="1290: quot(s(0), s(s(0)), s(s(s(0))), X2067), SCOPE: 66, CLAUSE: 1 | quot(s(0), s(s(0)), s(s(s(0))), X2067), SCOPE: 66, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(0))), X2067), SCOPE: 66, CLAUSE: 3\n\nX2067 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1291 [label="1291: quot(s(0), s(s(0)), s(s(s(0))), X2067), SCOPE: 66, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(0))), X2067), SCOPE: 66, CLAUSE: 3\n\nX2067 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1295 [label="1295: quot(s(0), s(s(0)), s(s(s(0))), X2067), SCOPE: 66, CLAUSE: 2\n\nX2067 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1296 [label="1296: quot(s(0), s(s(0)), s(s(s(0))), X2067), SCOPE: 66, CLAUSE: 3\n\nX2067 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1304 [label="1304: quot(0, s(0), s(s(s(0))), X2102)\n\nX2102 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1305 [label="1305: quot(0, s(0), s(s(s(0))), X2102), SCOPE: 67, CLAUSE: 1 | quot(0, s(0), s(s(s(0))), X2102), SCOPE: 67, CLAUSE: 2 | quot(0, s(0), s(s(s(0))), X2102), SCOPE: 67, CLAUSE: 3\n\nX2102 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1306 [label="1306: quot(0, s(0), s(s(s(0))), X2102), SCOPE: 67, CLAUSE: 1\n\nX2102 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1307 [label="1307: quot(0, s(0), s(s(s(0))), X2102), SCOPE: 67, CLAUSE: 2 | quot(0, s(0), s(s(s(0))), X2102), SCOPE: 67, CLAUSE: 3\n\nX2102 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1311 [label="1311: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1312 [label="1312: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1314 [label="1314: quot(0, s(0), s(s(s(0))), X2102), SCOPE: 67, CLAUSE: 3\n\nX2102 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1317 [label="1317: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1318 [label="1318: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1322 [label="1322: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1332 [label="U: quot(s(s(0)), s(s(0)), s(s(0)), X2139)\n\nX2139 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1333 [label="1333: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1337 [label="1337: quot(s(s(0)), s(s(0)), s(s(0)), X2139), SCOPE: 68, CLAUSE: 1 | quot(s(s(0)), s(s(0)), s(s(0)), X2139), SCOPE: 68, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(0)), X2139), SCOPE: 68, CLAUSE: 3\n\nX2139 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1340 [label="1340: quot(s(s(0)), s(s(0)), s(s(0)), X2139), SCOPE: 68, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(0)), X2139), SCOPE: 68, CLAUSE: 3\n\nX2139 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1344 [label="1344: quot(s(s(0)), s(s(0)), s(s(0)), X2139), SCOPE: 68, CLAUSE: 2\n\nX2139 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1345 [label="1345: quot(s(s(0)), s(s(0)), s(s(0)), X2139), SCOPE: 68, CLAUSE: 3\n\nX2139 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1352 [label="1352: quot(s(0), s(0), s(s(0)), X2178)\n\nX2178 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1356 [label="1356: quot(s(0), s(0), s(s(0)), X2178), SCOPE: 69, CLAUSE: 1 | quot(s(0), s(0), s(s(0)), X2178), SCOPE: 69, CLAUSE: 2 | quot(s(0), s(0), s(s(0)), X2178), SCOPE: 69, CLAUSE: 3\n\nX2178 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1358 [label="1358: quot(s(0), s(0), s(s(0)), X2178), SCOPE: 69, CLAUSE: 2 | quot(s(0), s(0), s(s(0)), X2178), SCOPE: 69, CLAUSE: 3\n\nX2178 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1363 [label="1363: quot(s(0), s(0), s(s(0)), X2178), SCOPE: 69, CLAUSE: 2\n\nX2178 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1364 [label="1364: quot(s(0), s(0), s(s(0)), X2178), SCOPE: 69, CLAUSE: 3\n\nX2178 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1371 [label="1371: quot(0, 0, s(s(0)), X2217)\n\nX2217 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1374 [label="1374: quot(0, 0, s(s(0)), X2217), SCOPE: 70, CLAUSE: 1 | quot(0, 0, s(s(0)), X2217), SCOPE: 70, CLAUSE: 2 | quot(0, 0, s(s(0)), X2217), SCOPE: 70, CLAUSE: 3\n\nX2217 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1375 [label="1375: quot(0, 0, s(s(0)), X2217), SCOPE: 70, CLAUSE: 2 | quot(0, 0, s(s(0)), X2217), SCOPE: 70, CLAUSE: 3\n\nX2217 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1379 [label="1379: quot(0, 0, s(s(0)), X2217), SCOPE: 70, CLAUSE: 3\n\nX2217 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1387 [label="1387: quot(0, s(s(0)), s(s(0)), X2241)\n\nX2241 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1393 [label="1393: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1395 [label="1395: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1398 [label="1398: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1401 [label="1401: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1402 [label="1402: times(T271, s(s(T269)), X1031)\n\nT269 is ground\nT271 is ground\nX1031 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1403 [label="1403: neq(s(s(s(s(T269)))), T407)\n\nT269 is ground\nT407 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1409 [label="1409: pr(s(s(s(s(T263)))), s(T263)), SCOPE: 71, CLAUSE: 5 | pr(s(s(s(s(T263)))), s(T263)), SCOPE: 71, CLAUSE: 6\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1411 [label="1411: pr(s(s(s(s(T263)))), s(T263)), SCOPE: 71, CLAUSE: 5\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1412 [label="1412: pr(s(s(s(s(T263)))), s(T263)), SCOPE: 71, CLAUSE: 6\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1413 [label="1413: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1414 [label="1414: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1415 [label="1415: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1419 [label="N19: ','(not_divides(s(s(T424)), s(s(s(s(s(T424)))))), pr(s(s(s(s(s(T424))))), s(T424)))\n\nT424 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1420 [label="1420: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1423 [label="N21: not_divides(s(s(T424)), s(s(s(s(s(T424))))))\n\nT424 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1424 [label="N23: pr(s(s(s(s(s(T424))))), s(T424))\n\nT424 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1425 [label="1425: not_divides(s(s(T424)), s(s(s(s(s(T424)))))), SCOPE: 72, CLAUSE: 7\n\nT424 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1431 [label="N22: ','(div(s(s(s(s(s(T430))))), s(s(T430)), X2295), ','(times(X2295, s(s(T430)), X2296), neq(s(s(s(s(s(T430))))), X2296)))\n\nT430 is ground\nX2295 is free\nX2296 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1434 [label="N25: div(s(s(s(s(s(T430))))), s(s(T430)), X2295)\n\nT430 is ground\nX2295 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1435 [label="N42: ','(times(T432, s(s(T430)), X2296), neq(s(s(s(s(s(T430))))), X2296))\n\nT430 is ground\nT432 is ground\nX2296 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1440 [label="1440: div(s(s(s(s(s(T430))))), s(s(T430)), X2295), SCOPE: 73, CLAUSE: 0\n\nT430 is ground\nX2295 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1448 [label="1448: quot(s(s(s(s(s(T436))))), s(s(T436)), s(s(T436)), X2320)\n\nT436 is ground\nX2320 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1451 [label="1451: quot(s(s(s(s(s(T436))))), s(s(T436)), s(s(T436)), X2320), SCOPE: 74, CLAUSE: 1 | quot(s(s(s(s(s(T436))))), s(s(T436)), s(s(T436)), X2320), SCOPE: 74, CLAUSE: 2 | quot(s(s(s(s(s(T436))))), s(s(T436)), s(s(T436)), X2320), SCOPE: 74, CLAUSE: 3\n\nT436 is ground\nX2320 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1452 [label="1452: quot(s(s(s(s(s(T436))))), s(s(T436)), s(s(T436)), X2320), SCOPE: 74, CLAUSE: 2 | quot(s(s(s(s(s(T436))))), s(s(T436)), s(s(T436)), X2320), SCOPE: 74, CLAUSE: 3\n\nT436 is ground\nX2320 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1459 [label="1459: quot(s(s(s(s(s(T436))))), s(s(T436)), s(s(T436)), X2320), SCOPE: 74, CLAUSE: 2\n\nT436 is ground\nX2320 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1460 [label="1460: quot(s(s(s(s(s(T436))))), s(s(T436)), s(s(T436)), X2320), SCOPE: 74, CLAUSE: 3\n\nT436 is ground\nX2320 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1469 [label="1469: quot(s(s(s(s(T441)))), s(T441), s(s(T441)), X2359)\n\nT441 is ground\nX2359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1471 [label="1471: quot(s(s(s(s(T441)))), s(T441), s(s(T441)), X2359), SCOPE: 75, CLAUSE: 1 | quot(s(s(s(s(T441)))), s(T441), s(s(T441)), X2359), SCOPE: 75, CLAUSE: 2 | quot(s(s(s(s(T441)))), s(T441), s(s(T441)), X2359), SCOPE: 75, CLAUSE: 3\n\nT441 is ground\nX2359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1472 [label="1472: quot(s(s(s(s(T441)))), s(T441), s(s(T441)), X2359), SCOPE: 75, CLAUSE: 2 | quot(s(s(s(s(T441)))), s(T441), s(s(T441)), X2359), SCOPE: 75, CLAUSE: 3\n\nT441 is ground\nX2359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1478 [label="1478: quot(s(s(s(s(T441)))), s(T441), s(s(T441)), X2359), SCOPE: 75, CLAUSE: 2\n\nT441 is ground\nX2359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1479 [label="1479: quot(s(s(s(s(T441)))), s(T441), s(s(T441)), X2359), SCOPE: 75, CLAUSE: 3\n\nT441 is ground\nX2359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1490 [label="1490: quot(s(s(s(T446))), T446, s(s(T446)), X2398)\n\nT446 is ground\nX2398 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1494 [label="1494: quot(s(s(s(T446))), T446, s(s(T446)), X2398), SCOPE: 76, CLAUSE: 1 | quot(s(s(s(T446))), T446, s(s(T446)), X2398), SCOPE: 76, CLAUSE: 2 | quot(s(s(s(T446))), T446, s(s(T446)), X2398), SCOPE: 76, CLAUSE: 3\n\nT446 is ground\nX2398 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1495 [label="1495: quot(s(s(s(T446))), T446, s(s(T446)), X2398), SCOPE: 76, CLAUSE: 2 | quot(s(s(s(T446))), T446, s(s(T446)), X2398), SCOPE: 76, CLAUSE: 3\n\nT446 is ground\nX2398 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1498 [label="1498: quot(s(s(s(T446))), T446, s(s(T446)), X2398), SCOPE: 76, CLAUSE: 2\n\nT446 is ground\nX2398 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1499 [label="1499: quot(s(s(s(T446))), T446, s(s(T446)), X2398), SCOPE: 76, CLAUSE: 3\n\nT446 is ground\nX2398 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1507 [label="1507: quot(s(s(s(T456))), T456, s(s(s(T456))), X2429)\n\nT456 is ground\nX2429 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1508 [label="1508: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1512 [label="1512: quot(s(s(s(T456))), T456, s(s(s(T456))), X2429), SCOPE: 77, CLAUSE: 1 | quot(s(s(s(T456))), T456, s(s(s(T456))), X2429), SCOPE: 77, CLAUSE: 2 | quot(s(s(s(T456))), T456, s(s(s(T456))), X2429), SCOPE: 77, CLAUSE: 3\n\nT456 is ground\nX2429 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1514 [label="1514: quot(s(s(s(T456))), T456, s(s(s(T456))), X2429), SCOPE: 77, CLAUSE: 2 | quot(s(s(s(T456))), T456, s(s(s(T456))), X2429), SCOPE: 77, CLAUSE: 3\n\nT456 is ground\nX2429 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1518 [label="1518: quot(s(s(s(T456))), T456, s(s(s(T456))), X2429), SCOPE: 77, CLAUSE: 2\n\nT456 is ground\nX2429 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1519 [label="1519: quot(s(s(s(T456))), T456, s(s(s(T456))), X2429), SCOPE: 77, CLAUSE: 3\n\nT456 is ground\nX2429 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1529 [label="1529: quot(s(s(s(T466))), T466, s(s(s(s(T466)))), X2460)\n\nT466 is ground\nX2460 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1530 [label="1530: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1534 [label="1534: quot(s(s(s(T466))), T466, s(s(s(s(T466)))), X2460), SCOPE: 78, CLAUSE: 1 | quot(s(s(s(T466))), T466, s(s(s(s(T466)))), X2460), SCOPE: 78, CLAUSE: 2 | quot(s(s(s(T466))), T466, s(s(s(s(T466)))), X2460), SCOPE: 78, CLAUSE: 3\n\nT466 is ground\nX2460 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1535 [label="1535: quot(s(s(s(T466))), T466, s(s(s(s(T466)))), X2460), SCOPE: 78, CLAUSE: 2 | quot(s(s(s(T466))), T466, s(s(s(s(T466)))), X2460), SCOPE: 78, CLAUSE: 3\n\nT466 is ground\nX2460 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1540 [label="1540: quot(s(s(s(T466))), T466, s(s(s(s(T466)))), X2460), SCOPE: 78, CLAUSE: 2\n\nT466 is ground\nX2460 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1541 [label="1541: quot(s(s(s(T466))), T466, s(s(s(s(T466)))), X2460), SCOPE: 78, CLAUSE: 3\n\nT466 is ground\nX2460 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1547 [label="1547: quot(s(s(s(T476))), T476, s(s(s(s(s(T476))))), X2491)\n\nT476 is ground\nX2491 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1548 [label="1548: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1549 [label="1549: quot(s(s(s(T476))), T476, s(s(s(s(s(T476))))), X2491), SCOPE: 79, CLAUSE: 1 | quot(s(s(s(T476))), T476, s(s(s(s(s(T476))))), X2491), SCOPE: 79, CLAUSE: 2 | quot(s(s(s(T476))), T476, s(s(s(s(s(T476))))), X2491), SCOPE: 79, CLAUSE: 3\n\nT476 is ground\nX2491 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1551 [label="1551: quot(s(s(s(T476))), T476, s(s(s(s(s(T476))))), X2491), SCOPE: 79, CLAUSE: 2 | quot(s(s(s(T476))), T476, s(s(s(s(s(T476))))), X2491), SCOPE: 79, CLAUSE: 3\n\nT476 is ground\nX2491 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1555 [label="1555: quot(s(s(s(T476))), T476, s(s(s(s(s(T476))))), X2491), SCOPE: 79, CLAUSE: 2\n\nT476 is ground\nX2491 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1556 [label="1556: quot(s(s(s(T476))), T476, s(s(s(s(s(T476))))), X2491), SCOPE: 79, CLAUSE: 3\n\nT476 is ground\nX2491 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1563 [label="1563: quot(s(s(s(T486))), T486, s(s(s(s(s(s(T486)))))), X2522)\n\nT486 is ground\nX2522 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1564 [label="1564: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1565 [label="1565: quot(s(s(s(T486))), T486, s(s(s(s(s(s(T486)))))), X2522), SCOPE: 80, CLAUSE: 1 | quot(s(s(s(T486))), T486, s(s(s(s(s(s(T486)))))), X2522), SCOPE: 80, CLAUSE: 2 | quot(s(s(s(T486))), T486, s(s(s(s(s(s(T486)))))), X2522), SCOPE: 80, CLAUSE: 3\n\nT486 is ground\nX2522 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1566 [label="1566: quot(s(s(s(T486))), T486, s(s(s(s(s(s(T486)))))), X2522), SCOPE: 80, CLAUSE: 2 | quot(s(s(s(T486))), T486, s(s(s(s(s(s(T486)))))), X2522), SCOPE: 80, CLAUSE: 3\n\nT486 is ground\nX2522 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1573 [label="1573: quot(s(s(s(T486))), T486, s(s(s(s(s(s(T486)))))), X2522), SCOPE: 80, CLAUSE: 2\n\nT486 is ground\nX2522 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1574 [label="1574: quot(s(s(s(T486))), T486, s(s(s(s(s(s(T486)))))), X2522), SCOPE: 80, CLAUSE: 3\n\nT486 is ground\nX2522 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1580 [label="1580: quot(s(s(s(T496))), T496, s(s(s(s(s(s(s(T496))))))), X2553)\n\nT496 is ground\nX2553 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1581 [label="1581: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1584 [label="1584: quot(s(s(s(T496))), T496, s(s(s(s(s(s(s(T496))))))), X2553), SCOPE: 81, CLAUSE: 1 | quot(s(s(s(T496))), T496, s(s(s(s(s(s(s(T496))))))), X2553), SCOPE: 81, CLAUSE: 2 | quot(s(s(s(T496))), T496, s(s(s(s(s(s(s(T496))))))), X2553), SCOPE: 81, CLAUSE: 3\n\nT496 is ground\nX2553 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1585 [label="1585: quot(s(s(s(T496))), T496, s(s(s(s(s(s(s(T496))))))), X2553), SCOPE: 81, CLAUSE: 2 | quot(s(s(s(T496))), T496, s(s(s(s(s(s(s(T496))))))), X2553), SCOPE: 81, CLAUSE: 3\n\nT496 is ground\nX2553 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1589 [label="1589: quot(s(s(s(T496))), T496, s(s(s(s(s(s(s(T496))))))), X2553), SCOPE: 81, CLAUSE: 2\n\nT496 is ground\nX2553 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1590 [label="1590: quot(s(s(s(T496))), T496, s(s(s(s(s(s(s(T496))))))), X2553), SCOPE: 81, CLAUSE: 3\n\nT496 is ground\nX2553 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1597 [label="1597: quot(s(s(s(T506))), T506, s(s(s(s(s(s(s(s(T506)))))))), X2584)\n\nT506 is ground\nX2584 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1598 [label="1598: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1601 [label="N: quot(s(s(s(T506))), T506, s(T507), X2584)\n\nT506 is ground\nT507 is ground\nX2584 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1606 [label="1606: quot(s(s(s(T506))), T506, s(T507), X2584), SCOPE: 82, CLAUSE: 1 | quot(s(s(s(T506))), T506, s(T507), X2584), SCOPE: 82, CLAUSE: 2 | quot(s(s(s(T506))), T506, s(T507), X2584), SCOPE: 82, CLAUSE: 3\n\nT506 is ground\nT507 is ground\nX2584 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1607 [label="1607: quot(s(s(s(T506))), T506, s(T507), X2584), SCOPE: 82, CLAUSE: 2 | quot(s(s(s(T506))), T506, s(T507), X2584), SCOPE: 82, CLAUSE: 3\n\nT506 is ground\nT507 is ground\nX2584 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1612 [label="1612: quot(s(s(s(T506))), T506, s(T507), X2584), SCOPE: 82, CLAUSE: 2\n\nT506 is ground\nT507 is ground\nX2584 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1613 [label="1613: quot(s(s(s(T506))), T506, s(T507), X2584), SCOPE: 82, CLAUSE: 3\n\nT506 is ground\nT507 is ground\nX2584 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1620 [label="1620: quot(s(s(s(T521))), T521, s(T522), X2619)\n\nT521 is ground\nT522 is ground\nX2619 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1621 [label="1621: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1630 [label="1630: quot(s(s(s(0))), s(T528), s(T528), X2635)\n\nT528 is ground\nX2635 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1631 [label="1631: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1632 [label="1632: quot(s(s(s(0))), s(T528), s(T528), X2635), SCOPE: 83, CLAUSE: 1 | quot(s(s(s(0))), s(T528), s(T528), X2635), SCOPE: 83, CLAUSE: 2 | quot(s(s(s(0))), s(T528), s(T528), X2635), SCOPE: 83, CLAUSE: 3\n\nT528 is ground\nX2635 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1633 [label="1633: quot(s(s(s(0))), s(T528), s(T528), X2635), SCOPE: 83, CLAUSE: 2 | quot(s(s(s(0))), s(T528), s(T528), X2635), SCOPE: 83, CLAUSE: 3\n\nT528 is ground\nX2635 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1642 [label="1642: quot(s(s(s(0))), s(T528), s(T528), X2635), SCOPE: 83, CLAUSE: 2\n\nT528 is ground\nX2635 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1643 [label="1643: quot(s(s(s(0))), s(T528), s(T528), X2635), SCOPE: 83, CLAUSE: 3\n\nT528 is ground\nX2635 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1648 [label="1648: quot(s(s(0)), T533, s(T533), X2674)\n\nT533 is ground\nX2674 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1653 [label="1653: quot(s(s(0)), T533, s(T533), X2674), SCOPE: 84, CLAUSE: 1 | quot(s(s(0)), T533, s(T533), X2674), SCOPE: 84, CLAUSE: 2 | quot(s(s(0)), T533, s(T533), X2674), SCOPE: 84, CLAUSE: 3\n\nT533 is ground\nX2674 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1654 [label="1654: quot(s(s(0)), T533, s(T533), X2674), SCOPE: 84, CLAUSE: 2 | quot(s(s(0)), T533, s(T533), X2674), SCOPE: 84, CLAUSE: 3\n\nT533 is ground\nX2674 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1659 [label="1659: quot(s(s(0)), T533, s(T533), X2674), SCOPE: 84, CLAUSE: 2\n\nT533 is ground\nX2674 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1660 [label="1660: quot(s(s(0)), T533, s(T533), X2674), SCOPE: 84, CLAUSE: 3\n\nT533 is ground\nX2674 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1666 [label="1666: quot(s(0), T538, s(s(T538)), X2705)\n\nT538 is ground\nX2705 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1667 [label="1667: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1670 [label="1670: quot(s(0), T538, s(s(T538)), X2705), SCOPE: 85, CLAUSE: 1 | quot(s(0), T538, s(s(T538)), X2705), SCOPE: 85, CLAUSE: 2 | quot(s(0), T538, s(s(T538)), X2705), SCOPE: 85, CLAUSE: 3\n\nT538 is ground\nX2705 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1671 [label="1671: quot(s(0), T538, s(s(T538)), X2705), SCOPE: 85, CLAUSE: 2 | quot(s(0), T538, s(s(T538)), X2705), SCOPE: 85, CLAUSE: 3\n\nT538 is ground\nX2705 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1676 [label="1676: quot(s(0), T538, s(s(T538)), X2705), SCOPE: 85, CLAUSE: 2\n\nT538 is ground\nX2705 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1677 [label="1677: quot(s(0), T538, s(s(T538)), X2705), SCOPE: 85, CLAUSE: 3\n\nT538 is ground\nX2705 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1682 [label="1682: quot(0, T543, s(s(s(T543))), X2736)\n\nT543 is ground\nX2736 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1683 [label="1683: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1688 [label="1688: quot(0, T543, s(s(s(T543))), X2736), SCOPE: 86, CLAUSE: 1 | quot(0, T543, s(s(s(T543))), X2736), SCOPE: 86, CLAUSE: 2 | quot(0, T543, s(s(s(T543))), X2736), SCOPE: 86, CLAUSE: 3\n\nT543 is ground\nX2736 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1689 [label="1689: quot(0, T543, s(s(s(T543))), X2736), SCOPE: 86, CLAUSE: 1\n\nT543 is ground\nX2736 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1690 [label="1690: quot(0, T543, s(s(s(T543))), X2736), SCOPE: 86, CLAUSE: 2 | quot(0, T543, s(s(s(T543))), X2736), SCOPE: 86, CLAUSE: 3\n\nT543 is ground\nX2736 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1693 [label="1693: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1694 [label="1694: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1695 [label="1695: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1699 [label="1699: quot(0, T543, s(s(s(T543))), X2736), SCOPE: 86, CLAUSE: 3\n\nT543 is ground\nX2736 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1702 [label="O: quot(0, s(s(s(0))), s(s(s(0))), X2766)\n\nX2766 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1703 [label="1703: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1704 [label="1704: quot(0, s(s(s(0))), s(s(s(0))), X2766), SCOPE: 87, CLAUSE: 1 | quot(0, s(s(s(0))), s(s(s(0))), X2766), SCOPE: 87, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(0))), X2766), SCOPE: 87, CLAUSE: 3\n\nX2766 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1706 [label="1706: quot(0, s(s(s(0))), s(s(s(0))), X2766), SCOPE: 87, CLAUSE: 1\n\nX2766 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1707 [label="1707: quot(0, s(s(s(0))), s(s(s(0))), X2766), SCOPE: 87, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(0))), X2766), SCOPE: 87, CLAUSE: 3\n\nX2766 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: quot(0, s(s(s(0))), s(s(s(0))), X2766), SCOPE: 87, CLAUSE: 3\n\nX2766 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1715 [label="1715: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1720 [label="1720: quot(s(0), s(s(0)), s(s(0)), X2797)\n\nX2797 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1721 [label="1721: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1728 [label="Q: quot(s(s(0)), s(0), s(0), X2813)\n\nX2813 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1729 [label="1729: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1732 [label="1732: quot(s(s(0)), s(0), s(0), X2813), SCOPE: 88, CLAUSE: 1 | quot(s(s(0)), s(0), s(0), X2813), SCOPE: 88, CLAUSE: 2 | quot(s(s(0)), s(0), s(0), X2813), SCOPE: 88, CLAUSE: 3\n\nX2813 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1735 [label="1735: quot(s(s(0)), s(0), s(0), X2813), SCOPE: 88, CLAUSE: 2 | quot(s(s(0)), s(0), s(0), X2813), SCOPE: 88, CLAUSE: 3\n\nX2813 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1741 [label="1741: quot(s(s(0)), s(0), s(0), X2813), SCOPE: 88, CLAUSE: 2\n\nX2813 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1742 [label="1742: quot(s(s(0)), s(0), s(0), X2813), SCOPE: 88, CLAUSE: 3\n\nX2813 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1758 [label="1758: quot(s(0), 0, s(0), X2852)\n\nX2852 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1764 [label="1764: quot(s(0), 0, s(0), X2852), SCOPE: 89, CLAUSE: 1 | quot(s(0), 0, s(0), X2852), SCOPE: 89, CLAUSE: 2 | quot(s(0), 0, s(0), X2852), SCOPE: 89, CLAUSE: 3\n\nX2852 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1767 [label="1767: quot(s(0), 0, s(0), X2852), SCOPE: 89, CLAUSE: 2 | quot(s(0), 0, s(0), X2852), SCOPE: 89, CLAUSE: 3\n\nX2852 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1770 [label="1770: quot(s(0), 0, s(0), X2852), SCOPE: 89, CLAUSE: 3\n\nX2852 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1778 [label="1778: quot(s(0), s(0), s(0), X2878)\n\nX2878 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1783 [label="1783: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1786 [label="1786: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1792 [label="1792: quot(s(s(s(0))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X2900)\n\nX2900 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1793 [label="1793: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1796 [label="1796: quot(s(s(s(0))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X2900), 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))))))), X2900), 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))))))), X2900), SCOPE: 90, CLAUSE: 3\n\nX2900 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1799 [label="1799: quot(s(s(s(0))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X2900), 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))))))), X2900), SCOPE: 90, CLAUSE: 3\n\nX2900 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1804 [label="1804: quot(s(s(s(0))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X2900), SCOPE: 90, CLAUSE: 2\n\nX2900 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1805 [label="1805: quot(s(s(s(0))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X2900), SCOPE: 90, CLAUSE: 3\n\nX2900 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1809 [label="1809: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2939)\n\nX2939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1812 [label="1812: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2939), SCOPE: 91, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2939), SCOPE: 91, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2939), SCOPE: 91, CLAUSE: 3\n\nX2939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1814 [label="1814: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2939), SCOPE: 91, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2939), SCOPE: 91, CLAUSE: 3\n\nX2939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1820 [label="1820: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2939), SCOPE: 91, CLAUSE: 2\n\nX2939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1821 [label="1821: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2939), SCOPE: 91, CLAUSE: 3\n\nX2939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1826 [label="1826: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2978)\n\nX2978 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1830 [label="1830: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2978), SCOPE: 92, CLAUSE: 1 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2978), SCOPE: 92, CLAUSE: 2 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2978), SCOPE: 92, CLAUSE: 3\n\nX2978 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1832 [label="1832: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2978), SCOPE: 92, CLAUSE: 2 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2978), SCOPE: 92, CLAUSE: 3\n\nX2978 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1837 [label="1837: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2978), SCOPE: 92, CLAUSE: 2\n\nX2978 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1838 [label="1838: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2978), SCOPE: 92, CLAUSE: 3\n\nX2978 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1842 [label="1842: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3013)\n\nX3013 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1846 [label="1846: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3013), SCOPE: 93, CLAUSE: 1 | quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3013), SCOPE: 93, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3013), SCOPE: 93, CLAUSE: 3\n\nX3013 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1849 [label="1849: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3013), SCOPE: 93, CLAUSE: 1\n\nX3013 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1850 [label="1850: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3013), SCOPE: 93, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3013), SCOPE: 93, CLAUSE: 3\n\nX3013 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1853 [label="1853: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1854 [label="1854: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1856 [label="1856: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3013), SCOPE: 93, CLAUSE: 3\n\nX3013 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1860 [label="1860: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1861 [label="1861: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1862 [label="1862: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1863 [label="1863: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1867 [label="1867: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3053)\n\nX3053 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1868 [label="1868: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1872 [label="1872: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3053), SCOPE: 94, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3053), SCOPE: 94, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3053), SCOPE: 94, CLAUSE: 3\n\nX3053 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1874 [label="1874: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3053), SCOPE: 94, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3053), SCOPE: 94, CLAUSE: 3\n\nX3053 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1880 [label="1880: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3053), SCOPE: 94, CLAUSE: 2\n\nX3053 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1881 [label="1881: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3053), SCOPE: 94, CLAUSE: 3\n\nX3053 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1884 [label="1884: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3092)\n\nX3092 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1890 [label="1890: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3092), SCOPE: 95, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3092), SCOPE: 95, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3092), SCOPE: 95, CLAUSE: 3\n\nX3092 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1891 [label="1891: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3092), SCOPE: 95, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3092), SCOPE: 95, CLAUSE: 3\n\nX3092 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1899 [label="1899: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3092), SCOPE: 95, CLAUSE: 2\n\nX3092 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1900 [label="1900: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3092), SCOPE: 95, CLAUSE: 3\n\nX3092 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1907 [label="1907: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3131)\n\nX3131 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1910 [label="1910: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3131), SCOPE: 96, CLAUSE: 1 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3131), SCOPE: 96, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3131), SCOPE: 96, CLAUSE: 3\n\nX3131 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1911 [label="1911: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3131), SCOPE: 96, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3131), SCOPE: 96, CLAUSE: 3\n\nX3131 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1916 [label="1916: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3131), SCOPE: 96, CLAUSE: 2\n\nX3131 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1917 [label="1917: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3131), SCOPE: 96, CLAUSE: 3\n\nX3131 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1927 [label="1927: quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3166)\n\nX3166 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1929 [label="1929: quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3166), SCOPE: 97, CLAUSE: 1 | quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3166), SCOPE: 97, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3166), SCOPE: 97, CLAUSE: 3\n\nX3166 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1932 [label="1932: quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3166), SCOPE: 97, CLAUSE: 1\n\nX3166 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1933 [label="1933: quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3166), SCOPE: 97, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3166), SCOPE: 97, CLAUSE: 3\n\nX3166 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1937 [label="1937: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1938 [label="1938: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1940 [label="1940: quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3166), SCOPE: 97, CLAUSE: 3\n\nX3166 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1941 [label="1941: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1942 [label="1942: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1943 [label="1943: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1947 [label="1947: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1950 [label="1950: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X3206)\n\nX3206 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1951 [label="1951: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1955 [label="1955: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X3206), SCOPE: 98, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X3206), SCOPE: 98, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X3206), SCOPE: 98, CLAUSE: 3\n\nX3206 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1956 [label="1956: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X3206), SCOPE: 98, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X3206), SCOPE: 98, CLAUSE: 3\n\nX3206 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1960 [label="1960: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X3206), SCOPE: 98, CLAUSE: 2\n\nX3206 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1961 [label="1961: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X3206), SCOPE: 98, CLAUSE: 3\n\nX3206 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1969 [label="1969: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X3245)\n\nX3245 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1973 [label="1973: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X3245), SCOPE: 99, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X3245), SCOPE: 99, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X3245), SCOPE: 99, CLAUSE: 3\n\nX3245 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1975 [label="1975: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X3245), SCOPE: 99, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X3245), SCOPE: 99, CLAUSE: 3\n\nX3245 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1980 [label="1980: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X3245), SCOPE: 99, CLAUSE: 2\n\nX3245 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1981 [label="1981: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X3245), SCOPE: 99, CLAUSE: 3\n\nX3245 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1988 [label="1988: quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X3284)\n\nX3284 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1990 [label="1990: quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X3284), SCOPE: 100, CLAUSE: 1 | quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X3284), SCOPE: 100, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X3284), SCOPE: 100, CLAUSE: 3\n\nX3284 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1993 [label="1993: quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X3284), SCOPE: 100, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X3284), SCOPE: 100, CLAUSE: 3\n\nX3284 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1997 [label="1997: quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X3284), SCOPE: 100, CLAUSE: 2\n\nX3284 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1998 [label="1998: quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X3284), SCOPE: 100, CLAUSE: 3\n\nX3284 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2009 [label="2009: quot(0, s(s(0)), s(s(s(s(s(0))))), X3319)\n\nX3319 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2010 [label="2010: quot(0, s(s(0)), s(s(s(s(s(0))))), X3319), SCOPE: 101, CLAUSE: 1 | quot(0, s(s(0)), s(s(s(s(s(0))))), X3319), SCOPE: 101, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(s(0))))), X3319), SCOPE: 101, CLAUSE: 3\n\nX3319 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2013 [label="2013: quot(0, s(s(0)), s(s(s(s(s(0))))), X3319), SCOPE: 101, CLAUSE: 1\n\nX3319 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2014 [label="2014: quot(0, s(s(0)), s(s(s(s(s(0))))), X3319), SCOPE: 101, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(s(0))))), X3319), SCOPE: 101, CLAUSE: 3\n\nX3319 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2017 [label="2017: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2018 [label="2018: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2020 [label="2020: quot(0, s(s(0)), s(s(s(s(s(0))))), X3319), SCOPE: 101, CLAUSE: 3\n\nX3319 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2022 [label="2022: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2023 [label="2023: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2024 [label="2024: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2026 [label="2026: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2031 [label="2031: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X3359)\n\nX3359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2032 [label="2032: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2033 [label="2033: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X3359), SCOPE: 102, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X3359), SCOPE: 102, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X3359), SCOPE: 102, CLAUSE: 3\n\nX3359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2035 [label="2035: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X3359), SCOPE: 102, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X3359), SCOPE: 102, CLAUSE: 3\n\nX3359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2040 [label="2040: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X3359), SCOPE: 102, CLAUSE: 2\n\nX3359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2041 [label="2041: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X3359), SCOPE: 102, CLAUSE: 3\n\nX3359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2048 [label="2048: quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X3398)\n\nX3398 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2054 [label="2054: quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X3398), SCOPE: 103, CLAUSE: 1 | quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X3398), SCOPE: 103, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X3398), SCOPE: 103, CLAUSE: 3\n\nX3398 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2056 [label="2056: quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X3398), SCOPE: 103, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X3398), SCOPE: 103, CLAUSE: 3\n\nX3398 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2061 [label="2061: quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X3398), SCOPE: 103, CLAUSE: 2\n\nX3398 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2062 [label="2062: quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X3398), SCOPE: 103, CLAUSE: 3\n\nX3398 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2068 [label="2068: quot(s(0), s(s(0)), s(s(s(s(0)))), X3437)\n\nX3437 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2071 [label="2071: quot(s(0), s(s(0)), s(s(s(s(0)))), X3437), SCOPE: 104, CLAUSE: 1 | quot(s(0), s(s(0)), s(s(s(s(0)))), X3437), SCOPE: 104, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(s(0)))), X3437), SCOPE: 104, CLAUSE: 3\n\nX3437 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2072 [label="2072: quot(s(0), s(s(0)), s(s(s(s(0)))), X3437), SCOPE: 104, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(s(0)))), X3437), SCOPE: 104, CLAUSE: 3\n\nX3437 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2078 [label="2078: quot(s(0), s(s(0)), s(s(s(s(0)))), X3437), SCOPE: 104, CLAUSE: 2\n\nX3437 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2079 [label="2079: quot(s(0), s(s(0)), s(s(s(s(0)))), X3437), SCOPE: 104, CLAUSE: 3\n\nX3437 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2088 [label="2088: quot(0, s(0), s(s(s(s(0)))), X3472)\n\nX3472 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2090 [label="2090: quot(0, s(0), s(s(s(s(0)))), X3472), SCOPE: 105, CLAUSE: 1 | quot(0, s(0), s(s(s(s(0)))), X3472), SCOPE: 105, CLAUSE: 2 | quot(0, s(0), s(s(s(s(0)))), X3472), SCOPE: 105, CLAUSE: 3\n\nX3472 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2094 [label="2094: quot(0, s(0), s(s(s(s(0)))), X3472), SCOPE: 105, CLAUSE: 1\n\nX3472 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2095 [label="2095: quot(0, s(0), s(s(s(s(0)))), X3472), SCOPE: 105, CLAUSE: 2 | quot(0, s(0), s(s(s(s(0)))), X3472), SCOPE: 105, CLAUSE: 3\n\nX3472 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2096 [label="2096: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2097 [label="2097: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2099 [label="2099: quot(0, s(0), s(s(s(s(0)))), X3472), SCOPE: 105, CLAUSE: 3\n\nX3472 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2102 [label="2102: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2103 [label="2103: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2104 [label="2104: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2105 [label="2105: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2109 [label="2109: quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X3512)\n\nX3512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2110 [label="2110: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2112 [label="2112: quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X3512), SCOPE: 106, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X3512), SCOPE: 106, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X3512), SCOPE: 106, CLAUSE: 3\n\nX3512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2113 [label="2113: quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X3512), SCOPE: 106, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X3512), SCOPE: 106, CLAUSE: 3\n\nX3512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2116 [label="2116: quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X3512), SCOPE: 106, CLAUSE: 2\n\nX3512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2117 [label="2117: quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X3512), SCOPE: 106, CLAUSE: 3\n\nX3512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2123 [label="2123: quot(s(s(0)), s(s(0)), s(s(s(0))), X3551)\n\nX3551 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2125 [label="2125: quot(s(s(0)), s(s(0)), s(s(s(0))), X3551), SCOPE: 107, CLAUSE: 1 | quot(s(s(0)), s(s(0)), s(s(s(0))), X3551), SCOPE: 107, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(s(0))), X3551), SCOPE: 107, CLAUSE: 3\n\nX3551 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2126 [label="2126: quot(s(s(0)), s(s(0)), s(s(s(0))), X3551), SCOPE: 107, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(s(0))), X3551), SCOPE: 107, CLAUSE: 3\n\nX3551 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2129 [label="2129: quot(s(s(0)), s(s(0)), s(s(s(0))), X3551), SCOPE: 107, CLAUSE: 2\n\nX3551 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2130 [label="2130: quot(s(s(0)), s(s(0)), s(s(s(0))), X3551), SCOPE: 107, CLAUSE: 3\n\nX3551 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2135 [label="2135: quot(s(0), s(0), s(s(s(0))), X3590)\n\nX3590 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2137 [label="2137: quot(s(0), s(0), s(s(s(0))), X3590), SCOPE: 108, CLAUSE: 1 | quot(s(0), s(0), s(s(s(0))), X3590), SCOPE: 108, CLAUSE: 2 | quot(s(0), s(0), s(s(s(0))), X3590), SCOPE: 108, CLAUSE: 3\n\nX3590 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2139 [label="2139: quot(s(0), s(0), s(s(s(0))), X3590), SCOPE: 108, CLAUSE: 2 | quot(s(0), s(0), s(s(s(0))), X3590), SCOPE: 108, CLAUSE: 3\n\nX3590 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2145 [label="2145: quot(s(0), s(0), s(s(s(0))), X3590), SCOPE: 108, CLAUSE: 2\n\nX3590 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2146 [label="2146: quot(s(0), s(0), s(s(s(0))), X3590), SCOPE: 108, CLAUSE: 3\n\nX3590 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2157 [label="2157: quot(0, 0, s(s(s(0))), X3629)\n\nX3629 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2163 [label="2163: quot(0, 0, s(s(s(0))), X3629), SCOPE: 109, CLAUSE: 1 | quot(0, 0, s(s(s(0))), X3629), SCOPE: 109, CLAUSE: 2 | quot(0, 0, s(s(s(0))), X3629), SCOPE: 109, CLAUSE: 3\n\nX3629 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2165 [label="2165: quot(0, 0, s(s(s(0))), X3629), SCOPE: 109, CLAUSE: 2 | quot(0, 0, s(s(s(0))), X3629), SCOPE: 109, CLAUSE: 3\n\nX3629 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2167 [label="2167: quot(0, 0, s(s(s(0))), X3629), SCOPE: 109, CLAUSE: 3\n\nX3629 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2172 [label="2172: quot(0, s(s(s(0))), s(s(s(0))), X3653)\n\nX3653 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2177 [label="2177: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2178 [label="2178: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2179 [label="2179: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2183 [label="N1: quot(s(s(s(0))), s(s(0)), s(s(0)), X3676)\n\nX3676 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2184 [label="2184: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2187 [label="2187: quot(s(s(s(0))), s(s(0)), s(s(0)), X3676), SCOPE: 110, CLAUSE: 1 | quot(s(s(s(0))), s(s(0)), s(s(0)), X3676), SCOPE: 110, CLAUSE: 2 | quot(s(s(s(0))), s(s(0)), s(s(0)), X3676), SCOPE: 110, CLAUSE: 3\n\nX3676 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2189 [label="2189: quot(s(s(s(0))), s(s(0)), s(s(0)), X3676), SCOPE: 110, CLAUSE: 2 | quot(s(s(s(0))), s(s(0)), s(s(0)), X3676), SCOPE: 110, CLAUSE: 3\n\nX3676 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2194 [label="2194: quot(s(s(s(0))), s(s(0)), s(s(0)), X3676), SCOPE: 110, CLAUSE: 2\n\nX3676 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2195 [label="2195: quot(s(s(s(0))), s(s(0)), s(s(0)), X3676), SCOPE: 110, CLAUSE: 3\n\nX3676 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2199 [label="2199: quot(s(s(0)), s(0), s(s(0)), X3715)\n\nX3715 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2202 [label="2202: quot(s(s(0)), s(0), s(s(0)), X3715), SCOPE: 111, CLAUSE: 1 | quot(s(s(0)), s(0), s(s(0)), X3715), SCOPE: 111, CLAUSE: 2 | quot(s(s(0)), s(0), s(s(0)), X3715), SCOPE: 111, CLAUSE: 3\n\nX3715 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2204 [label="2204: quot(s(s(0)), s(0), s(s(0)), X3715), SCOPE: 111, CLAUSE: 2 | quot(s(s(0)), s(0), s(s(0)), X3715), SCOPE: 111, CLAUSE: 3\n\nX3715 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2209 [label="2209: quot(s(s(0)), s(0), s(s(0)), X3715), SCOPE: 111, CLAUSE: 2\n\nX3715 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2210 [label="2210: quot(s(s(0)), s(0), s(s(0)), X3715), SCOPE: 111, CLAUSE: 3\n\nX3715 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2215 [label="2215: quot(s(0), 0, s(s(0)), X3754)\n\nX3754 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2219 [label="2219: quot(s(0), 0, s(s(0)), X3754), SCOPE: 112, CLAUSE: 1 | quot(s(0), 0, s(s(0)), X3754), SCOPE: 112, CLAUSE: 2 | quot(s(0), 0, s(s(0)), X3754), SCOPE: 112, CLAUSE: 3\n\nX3754 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2220 [label="2220: quot(s(0), 0, s(s(0)), X3754), SCOPE: 112, CLAUSE: 2 | quot(s(0), 0, s(s(0)), X3754), SCOPE: 112, CLAUSE: 3\n\nX3754 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2222 [label="2222: quot(s(0), 0, s(s(0)), X3754), SCOPE: 112, CLAUSE: 3\n\nX3754 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2228 [label="2228: quot(s(0), s(s(0)), s(s(0)), X3780)\n\nX3780 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2231 [label="2231: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2232 [label="2232: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2236 [label="2236: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2238 [label="2238: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2241 [label="2241: times(T432, s(s(T430)), X2296)\n\nT430 is ground\nT432 is ground\nX2296 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2242 [label="2242: neq(s(s(s(s(s(T430))))), T573)\n\nT430 is ground\nT573 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
2248 [label="2248: pr(s(s(s(s(s(T424))))), s(T424)), SCOPE: 113, CLAUSE: 5 | pr(s(s(s(s(s(T424))))), s(T424)), SCOPE: 113, CLAUSE: 6\n\nT424 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
2250 [label="2250: pr(s(s(s(s(s(T424))))), s(T424)), SCOPE: 113, CLAUSE: 5\n\nT424 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
2251 [label="2251: pr(s(s(s(s(s(T424))))), s(T424)), SCOPE: 113, CLAUSE: 6\n\nT424 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
2253 [label="2253: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2254 [label="2254: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2255 [label="2255: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2256 [label="N24: ','(not_divides(s(s(T590)), s(s(s(s(s(s(T590))))))), pr(s(s(s(s(s(s(T590)))))), s(T590)))\n\nT590 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
2257 [label="2257: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2261 [label="N26: not_divides(s(s(T590)), s(s(s(s(s(s(T590)))))))\n\nT590 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
2262 [label="N28: pr(s(s(s(s(s(s(T590)))))), s(T590))\n\nT590 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
2265 [label="2265: not_divides(s(s(T590)), s(s(s(s(s(s(T590))))))), SCOPE: 114, CLAUSE: 7\n\nT590 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
2268 [label="N27: ','(div(s(s(s(s(s(s(T596)))))), s(s(T596)), X3836), ','(times(X3836, s(s(T596)), X3837), neq(s(s(s(s(s(s(T596)))))), X3837)))\n\nT596 is ground\nX3836 is free\nX3837 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2269 [label="N30: div(s(s(s(s(s(s(T596)))))), s(s(T596)), X3836)\n\nT596 is ground\nX3836 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2270 [label="N43: ','(times(T598, s(s(T596)), X3837), neq(s(s(s(s(s(s(T596)))))), X3837))\n\nT596 is ground\nT598 is ground\nX3837 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2271 [label="2271: div(s(s(s(s(s(s(T596)))))), s(s(T596)), X3836), SCOPE: 115, CLAUSE: 0\n\nT596 is ground\nX3836 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2277 [label="2277: quot(s(s(s(s(s(s(T602)))))), s(s(T602)), s(s(T602)), X3861)\n\nT602 is ground\nX3861 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2279 [label="2279: quot(s(s(s(s(s(s(T602)))))), s(s(T602)), s(s(T602)), X3861), SCOPE: 116, CLAUSE: 1 | quot(s(s(s(s(s(s(T602)))))), s(s(T602)), s(s(T602)), X3861), SCOPE: 116, CLAUSE: 2 | quot(s(s(s(s(s(s(T602)))))), s(s(T602)), s(s(T602)), X3861), SCOPE: 116, CLAUSE: 3\n\nT602 is ground\nX3861 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2280 [label="2280: quot(s(s(s(s(s(s(T602)))))), s(s(T602)), s(s(T602)), X3861), SCOPE: 116, CLAUSE: 2 | quot(s(s(s(s(s(s(T602)))))), s(s(T602)), s(s(T602)), X3861), SCOPE: 116, CLAUSE: 3\n\nT602 is ground\nX3861 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2284 [label="2284: quot(s(s(s(s(s(s(T602)))))), s(s(T602)), s(s(T602)), X3861), SCOPE: 116, CLAUSE: 2\n\nT602 is ground\nX3861 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2285 [label="2285: quot(s(s(s(s(s(s(T602)))))), s(s(T602)), s(s(T602)), X3861), SCOPE: 116, CLAUSE: 3\n\nT602 is ground\nX3861 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2288 [label="2288: quot(s(s(s(s(s(T607))))), s(T607), s(s(T607)), X3900)\n\nT607 is ground\nX3900 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2291 [label="2291: quot(s(s(s(s(s(T607))))), s(T607), s(s(T607)), X3900), SCOPE: 117, CLAUSE: 1 | quot(s(s(s(s(s(T607))))), s(T607), s(s(T607)), X3900), SCOPE: 117, CLAUSE: 2 | quot(s(s(s(s(s(T607))))), s(T607), s(s(T607)), X3900), SCOPE: 117, CLAUSE: 3\n\nT607 is ground\nX3900 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2293 [label="2293: quot(s(s(s(s(s(T607))))), s(T607), s(s(T607)), X3900), SCOPE: 117, CLAUSE: 2 | quot(s(s(s(s(s(T607))))), s(T607), s(s(T607)), X3900), SCOPE: 117, CLAUSE: 3\n\nT607 is ground\nX3900 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2299 [label="2299: quot(s(s(s(s(s(T607))))), s(T607), s(s(T607)), X3900), SCOPE: 117, CLAUSE: 2\n\nT607 is ground\nX3900 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2300 [label="2300: quot(s(s(s(s(s(T607))))), s(T607), s(s(T607)), X3900), SCOPE: 117, CLAUSE: 3\n\nT607 is ground\nX3900 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2303 [label="2303: quot(s(s(s(s(T612)))), T612, s(s(T612)), X3939)\n\nT612 is ground\nX3939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2306 [label="2306: quot(s(s(s(s(T612)))), T612, s(s(T612)), X3939), SCOPE: 118, CLAUSE: 1 | quot(s(s(s(s(T612)))), T612, s(s(T612)), X3939), SCOPE: 118, CLAUSE: 2 | quot(s(s(s(s(T612)))), T612, s(s(T612)), X3939), SCOPE: 118, CLAUSE: 3\n\nT612 is ground\nX3939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2308 [label="2308: quot(s(s(s(s(T612)))), T612, s(s(T612)), X3939), SCOPE: 118, CLAUSE: 2 | quot(s(s(s(s(T612)))), T612, s(s(T612)), X3939), SCOPE: 118, CLAUSE: 3\n\nT612 is ground\nX3939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2315 [label="2315: quot(s(s(s(s(T612)))), T612, s(s(T612)), X3939), SCOPE: 118, CLAUSE: 2\n\nT612 is ground\nX3939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2316 [label="2316: quot(s(s(s(s(T612)))), T612, s(s(T612)), X3939), SCOPE: 118, CLAUSE: 3\n\nT612 is ground\nX3939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2325 [label="2325: quot(s(s(s(s(T622)))), T622, s(s(s(T622))), X3970)\n\nT622 is ground\nX3970 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2326 [label="2326: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2330 [label="2330: quot(s(s(s(s(T622)))), T622, s(s(s(T622))), X3970), SCOPE: 119, CLAUSE: 1 | quot(s(s(s(s(T622)))), T622, s(s(s(T622))), X3970), SCOPE: 119, CLAUSE: 2 | quot(s(s(s(s(T622)))), T622, s(s(s(T622))), X3970), SCOPE: 119, CLAUSE: 3\n\nT622 is ground\nX3970 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2333 [label="2333: quot(s(s(s(s(T622)))), T622, s(s(s(T622))), X3970), SCOPE: 119, CLAUSE: 2 | quot(s(s(s(s(T622)))), T622, s(s(s(T622))), X3970), SCOPE: 119, CLAUSE: 3\n\nT622 is ground\nX3970 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2336 [label="2336: quot(s(s(s(s(T622)))), T622, s(s(s(T622))), X3970), SCOPE: 119, CLAUSE: 2\n\nT622 is ground\nX3970 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2337 [label="2337: quot(s(s(s(s(T622)))), T622, s(s(s(T622))), X3970), SCOPE: 119, CLAUSE: 3\n\nT622 is ground\nX3970 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2342 [label="2342: quot(s(s(s(s(T632)))), T632, s(s(s(s(T632)))), X4001)\n\nT632 is ground\nX4001 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2343 [label="2343: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2345 [label="2345: quot(s(s(s(s(T632)))), T632, s(s(s(s(T632)))), X4001), SCOPE: 120, CLAUSE: 1 | quot(s(s(s(s(T632)))), T632, s(s(s(s(T632)))), X4001), SCOPE: 120, CLAUSE: 2 | quot(s(s(s(s(T632)))), T632, s(s(s(s(T632)))), X4001), SCOPE: 120, CLAUSE: 3\n\nT632 is ground\nX4001 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2346 [label="2346: quot(s(s(s(s(T632)))), T632, s(s(s(s(T632)))), X4001), SCOPE: 120, CLAUSE: 2 | quot(s(s(s(s(T632)))), T632, s(s(s(s(T632)))), X4001), SCOPE: 120, CLAUSE: 3\n\nT632 is ground\nX4001 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2351 [label="2351: quot(s(s(s(s(T632)))), T632, s(s(s(s(T632)))), X4001), SCOPE: 120, CLAUSE: 2\n\nT632 is ground\nX4001 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2352 [label="2352: quot(s(s(s(s(T632)))), T632, s(s(s(s(T632)))), X4001), SCOPE: 120, CLAUSE: 3\n\nT632 is ground\nX4001 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2357 [label="2357: quot(s(s(s(s(T642)))), T642, s(s(s(s(s(T642))))), X4032)\n\nT642 is ground\nX4032 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2358 [label="2358: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2362 [label="2362: quot(s(s(s(s(T642)))), T642, s(s(s(s(s(T642))))), X4032), SCOPE: 121, CLAUSE: 1 | quot(s(s(s(s(T642)))), T642, s(s(s(s(s(T642))))), X4032), SCOPE: 121, CLAUSE: 2 | quot(s(s(s(s(T642)))), T642, s(s(s(s(s(T642))))), X4032), SCOPE: 121, CLAUSE: 3\n\nT642 is ground\nX4032 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2363 [label="2363: quot(s(s(s(s(T642)))), T642, s(s(s(s(s(T642))))), X4032), SCOPE: 121, CLAUSE: 2 | quot(s(s(s(s(T642)))), T642, s(s(s(s(s(T642))))), X4032), SCOPE: 121, CLAUSE: 3\n\nT642 is ground\nX4032 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2368 [label="2368: quot(s(s(s(s(T642)))), T642, s(s(s(s(s(T642))))), X4032), SCOPE: 121, CLAUSE: 2\n\nT642 is ground\nX4032 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2369 [label="2369: quot(s(s(s(s(T642)))), T642, s(s(s(s(s(T642))))), X4032), SCOPE: 121, CLAUSE: 3\n\nT642 is ground\nX4032 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2372 [label="2372: quot(s(s(s(s(T652)))), T652, s(s(s(s(s(s(T652)))))), X4063)\n\nT652 is ground\nX4063 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2373 [label="2373: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2376 [label="2376: quot(s(s(s(s(T652)))), T652, s(s(s(s(s(s(T652)))))), X4063), SCOPE: 122, CLAUSE: 1 | quot(s(s(s(s(T652)))), T652, s(s(s(s(s(s(T652)))))), X4063), SCOPE: 122, CLAUSE: 2 | quot(s(s(s(s(T652)))), T652, s(s(s(s(s(s(T652)))))), X4063), SCOPE: 122, CLAUSE: 3\n\nT652 is ground\nX4063 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2378 [label="2378: quot(s(s(s(s(T652)))), T652, s(s(s(s(s(s(T652)))))), X4063), SCOPE: 122, CLAUSE: 2 | quot(s(s(s(s(T652)))), T652, s(s(s(s(s(s(T652)))))), X4063), SCOPE: 122, CLAUSE: 3\n\nT652 is ground\nX4063 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2382 [label="2382: quot(s(s(s(s(T652)))), T652, s(s(s(s(s(s(T652)))))), X4063), SCOPE: 122, CLAUSE: 2\n\nT652 is ground\nX4063 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2383 [label="2383: quot(s(s(s(s(T652)))), T652, s(s(s(s(s(s(T652)))))), X4063), SCOPE: 122, CLAUSE: 3\n\nT652 is ground\nX4063 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2388 [label="2388: quot(s(s(s(s(T662)))), T662, s(s(s(s(s(s(s(T662))))))), X4094)\n\nT662 is ground\nX4094 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2389 [label="2389: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2390 [label="2390: quot(s(s(s(s(T662)))), T662, s(s(s(s(s(s(s(T662))))))), X4094), SCOPE: 123, CLAUSE: 1 | quot(s(s(s(s(T662)))), T662, s(s(s(s(s(s(s(T662))))))), X4094), SCOPE: 123, CLAUSE: 2 | quot(s(s(s(s(T662)))), T662, s(s(s(s(s(s(s(T662))))))), X4094), SCOPE: 123, CLAUSE: 3\n\nT662 is ground\nX4094 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2392 [label="2392: quot(s(s(s(s(T662)))), T662, s(s(s(s(s(s(s(T662))))))), X4094), SCOPE: 123, CLAUSE: 2 | quot(s(s(s(s(T662)))), T662, s(s(s(s(s(s(s(T662))))))), X4094), SCOPE: 123, CLAUSE: 3\n\nT662 is ground\nX4094 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2395 [label="2395: quot(s(s(s(s(T662)))), T662, s(s(s(s(s(s(s(T662))))))), X4094), SCOPE: 123, CLAUSE: 2\n\nT662 is ground\nX4094 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2396 [label="2396: quot(s(s(s(s(T662)))), T662, s(s(s(s(s(s(s(T662))))))), X4094), SCOPE: 123, CLAUSE: 3\n\nT662 is ground\nX4094 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2402 [label="2402: quot(s(s(s(s(T672)))), T672, s(s(s(s(s(s(s(s(T672)))))))), X4125)\n\nT672 is ground\nX4125 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2403 [label="2403: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2408 [label="R: quot(s(s(s(s(T672)))), T672, s(T673), X4125)\n\nT672 is ground\nT673 is ground\nX4125 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2412 [label="2412: quot(s(s(s(s(T672)))), T672, s(T673), X4125), SCOPE: 124, CLAUSE: 1 | quot(s(s(s(s(T672)))), T672, s(T673), X4125), SCOPE: 124, CLAUSE: 2 | quot(s(s(s(s(T672)))), T672, s(T673), X4125), SCOPE: 124, CLAUSE: 3\n\nT672 is ground\nT673 is ground\nX4125 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2414 [label="2414: quot(s(s(s(s(T672)))), T672, s(T673), X4125), SCOPE: 124, CLAUSE: 2 | quot(s(s(s(s(T672)))), T672, s(T673), X4125), SCOPE: 124, CLAUSE: 3\n\nT672 is ground\nT673 is ground\nX4125 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2421 [label="2421: quot(s(s(s(s(T672)))), T672, s(T673), X4125), SCOPE: 124, CLAUSE: 2\n\nT672 is ground\nT673 is ground\nX4125 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2422 [label="2422: quot(s(s(s(s(T672)))), T672, s(T673), X4125), SCOPE: 124, CLAUSE: 3\n\nT672 is ground\nT673 is ground\nX4125 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2427 [label="2427: quot(s(s(s(s(T687)))), T687, s(T688), X4160)\n\nT687 is ground\nT688 is ground\nX4160 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2428 [label="2428: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2437 [label="2437: quot(s(s(s(s(0)))), s(T694), s(T694), X4176)\n\nT694 is ground\nX4176 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2438 [label="2438: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2441 [label="2441: quot(s(s(s(s(0)))), s(T694), s(T694), X4176), SCOPE: 125, CLAUSE: 1 | quot(s(s(s(s(0)))), s(T694), s(T694), X4176), SCOPE: 125, CLAUSE: 2 | quot(s(s(s(s(0)))), s(T694), s(T694), X4176), SCOPE: 125, CLAUSE: 3\n\nT694 is ground\nX4176 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2442 [label="2442: quot(s(s(s(s(0)))), s(T694), s(T694), X4176), SCOPE: 125, CLAUSE: 2 | quot(s(s(s(s(0)))), s(T694), s(T694), X4176), SCOPE: 125, CLAUSE: 3\n\nT694 is ground\nX4176 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2447 [label="2447: quot(s(s(s(s(0)))), s(T694), s(T694), X4176), SCOPE: 125, CLAUSE: 2\n\nT694 is ground\nX4176 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2448 [label="2448: quot(s(s(s(s(0)))), s(T694), s(T694), X4176), SCOPE: 125, CLAUSE: 3\n\nT694 is ground\nX4176 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2453 [label="2453: quot(s(s(s(0))), T699, s(T699), X4215)\n\nT699 is ground\nX4215 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2454 [label="2454: quot(s(s(s(0))), T699, s(T699), X4215), SCOPE: 126, CLAUSE: 1 | quot(s(s(s(0))), T699, s(T699), X4215), SCOPE: 126, CLAUSE: 2 | quot(s(s(s(0))), T699, s(T699), X4215), SCOPE: 126, CLAUSE: 3\n\nT699 is ground\nX4215 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2455 [label="2455: quot(s(s(s(0))), T699, s(T699), X4215), SCOPE: 126, CLAUSE: 2 | quot(s(s(s(0))), T699, s(T699), X4215), SCOPE: 126, CLAUSE: 3\n\nT699 is ground\nX4215 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2459 [label="2459: quot(s(s(s(0))), T699, s(T699), X4215), SCOPE: 126, CLAUSE: 2\n\nT699 is ground\nX4215 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2460 [label="2460: quot(s(s(s(0))), T699, s(T699), X4215), SCOPE: 126, CLAUSE: 3\n\nT699 is ground\nX4215 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2464 [label="2464: quot(s(s(0)), T704, s(s(T704)), X4246)\n\nT704 is ground\nX4246 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2465 [label="2465: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2470 [label="2470: quot(s(s(0)), T704, s(s(T704)), X4246), SCOPE: 127, CLAUSE: 1 | quot(s(s(0)), T704, s(s(T704)), X4246), SCOPE: 127, CLAUSE: 2 | quot(s(s(0)), T704, s(s(T704)), X4246), SCOPE: 127, CLAUSE: 3\n\nT704 is ground\nX4246 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2472 [label="2472: quot(s(s(0)), T704, s(s(T704)), X4246), SCOPE: 127, CLAUSE: 2 | quot(s(s(0)), T704, s(s(T704)), X4246), SCOPE: 127, CLAUSE: 3\n\nT704 is ground\nX4246 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2476 [label="2476: quot(s(s(0)), T704, s(s(T704)), X4246), SCOPE: 127, CLAUSE: 2\n\nT704 is ground\nX4246 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2477 [label="2477: quot(s(s(0)), T704, s(s(T704)), X4246), SCOPE: 127, CLAUSE: 3\n\nT704 is ground\nX4246 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2482 [label="2482: quot(s(0), T709, s(s(s(T709))), X4277)\n\nT709 is ground\nX4277 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2483 [label="2483: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2488 [label="2488: quot(s(0), T709, s(s(s(T709))), X4277), SCOPE: 128, CLAUSE: 1 | quot(s(0), T709, s(s(s(T709))), X4277), SCOPE: 128, CLAUSE: 2 | quot(s(0), T709, s(s(s(T709))), X4277), SCOPE: 128, CLAUSE: 3\n\nT709 is ground\nX4277 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2489 [label="2489: quot(s(0), T709, s(s(s(T709))), X4277), SCOPE: 128, CLAUSE: 2 | quot(s(0), T709, s(s(s(T709))), X4277), SCOPE: 128, CLAUSE: 3\n\nT709 is ground\nX4277 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2494 [label="2494: quot(s(0), T709, s(s(s(T709))), X4277), SCOPE: 128, CLAUSE: 2\n\nT709 is ground\nX4277 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2495 [label="2495: quot(s(0), T709, s(s(s(T709))), X4277), SCOPE: 128, CLAUSE: 3\n\nT709 is ground\nX4277 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2500 [label="2500: quot(0, T714, s(s(s(s(T714)))), X4308)\n\nT714 is ground\nX4308 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2501 [label="2501: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2505 [label="2505: quot(0, T714, s(s(s(s(T714)))), X4308), SCOPE: 129, CLAUSE: 1 | quot(0, T714, s(s(s(s(T714)))), X4308), SCOPE: 129, CLAUSE: 2 | quot(0, T714, s(s(s(s(T714)))), X4308), SCOPE: 129, CLAUSE: 3\n\nT714 is ground\nX4308 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2508 [label="2508: quot(0, T714, s(s(s(s(T714)))), X4308), SCOPE: 129, CLAUSE: 1\n\nT714 is ground\nX4308 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2509 [label="2509: quot(0, T714, s(s(s(s(T714)))), X4308), SCOPE: 129, CLAUSE: 2 | quot(0, T714, s(s(s(s(T714)))), X4308), SCOPE: 129, CLAUSE: 3\n\nT714 is ground\nX4308 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2511 [label="2511: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2512 [label="2512: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2513 [label="2513: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2514 [label="2514: quot(0, T714, s(s(s(s(T714)))), X4308), SCOPE: 129, CLAUSE: 3\n\nT714 is ground\nX4308 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2519 [label="S: quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X4338)\n\nX4338 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2520 [label="2520: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2523 [label="2523: quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X4338), SCOPE: 130, CLAUSE: 1 | quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X4338), SCOPE: 130, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X4338), SCOPE: 130, CLAUSE: 3\n\nX4338 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2524 [label="2524: quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X4338), SCOPE: 130, CLAUSE: 1\n\nX4338 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2525 [label="2525: quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X4338), SCOPE: 130, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X4338), SCOPE: 130, CLAUSE: 3\n\nX4338 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2530 [label="2530: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2531 [label="2531: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2533 [label="2533: quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X4338), SCOPE: 130, CLAUSE: 3\n\nX4338 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2535 [label="2535: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2536 [label="2536: quot(s(0), s(s(s(0))), s(s(s(0))), X4369)\n\nX4369 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2537 [label="2537: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2545 [label="2545: quot(s(s(0)), s(s(0)), s(s(0)), X4385)\n\nX4385 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2546 [label="2546: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2553 [label="V: quot(s(s(s(0))), s(0), s(0), X4401)\n\nX4401 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2554 [label="2554: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2556 [label="2556: quot(s(s(s(0))), s(0), s(0), X4401), SCOPE: 131, CLAUSE: 1 | quot(s(s(s(0))), s(0), s(0), X4401), SCOPE: 131, CLAUSE: 2 | quot(s(s(s(0))), s(0), s(0), X4401), SCOPE: 131, CLAUSE: 3\n\nX4401 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2557 [label="2557: quot(s(s(s(0))), s(0), s(0), X4401), SCOPE: 131, CLAUSE: 2 | quot(s(s(s(0))), s(0), s(0), X4401), SCOPE: 131, CLAUSE: 3\n\nX4401 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2562 [label="2562: quot(s(s(s(0))), s(0), s(0), X4401), SCOPE: 131, CLAUSE: 2\n\nX4401 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2563 [label="2563: quot(s(s(s(0))), s(0), s(0), X4401), SCOPE: 131, CLAUSE: 3\n\nX4401 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2570 [label="2570: quot(s(s(0)), 0, s(0), X4440)\n\nX4440 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2573 [label="2573: quot(s(s(0)), 0, s(0), X4440), SCOPE: 132, CLAUSE: 1 | quot(s(s(0)), 0, s(0), X4440), SCOPE: 132, CLAUSE: 2 | quot(s(s(0)), 0, s(0), X4440), SCOPE: 132, CLAUSE: 3\n\nX4440 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2577 [label="2577: quot(s(s(0)), 0, s(0), X4440), SCOPE: 132, CLAUSE: 2 | quot(s(s(0)), 0, s(0), X4440), SCOPE: 132, CLAUSE: 3\n\nX4440 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2579 [label="2579: quot(s(s(0)), 0, s(0), X4440), SCOPE: 132, CLAUSE: 3\n\nX4440 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2586 [label="2586: quot(s(s(0)), s(0), s(0), X4466)\n\nX4466 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2590 [label="2590: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2592 [label="2592: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2600 [label="2600: quot(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X4488)\n\nX4488 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2601 [label="2601: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2608 [label="2608: quot(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X4488), 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))))))), X4488), 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))))))), X4488), SCOPE: 133, CLAUSE: 3\n\nX4488 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2612 [label="2612: quot(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X4488), 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))))))), X4488), SCOPE: 133, CLAUSE: 3\n\nX4488 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2622 [label="2622: quot(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X4488), SCOPE: 133, CLAUSE: 2\n\nX4488 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2623 [label="2623: quot(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X4488), SCOPE: 133, CLAUSE: 3\n\nX4488 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2631 [label="2631: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X4527)\n\nX4527 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2638 [label="2638: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X4527), SCOPE: 134, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X4527), SCOPE: 134, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X4527), SCOPE: 134, CLAUSE: 3\n\nX4527 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2639 [label="2639: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X4527), SCOPE: 134, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X4527), SCOPE: 134, CLAUSE: 3\n\nX4527 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2646 [label="2646: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X4527), SCOPE: 134, CLAUSE: 2\n\nX4527 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2647 [label="2647: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X4527), SCOPE: 134, CLAUSE: 3\n\nX4527 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2654 [label="2654: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X4566)\n\nX4566 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2655 [label="2655: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X4566), SCOPE: 135, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X4566), SCOPE: 135, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X4566), SCOPE: 135, CLAUSE: 3\n\nX4566 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2660 [label="2660: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X4566), SCOPE: 135, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X4566), SCOPE: 135, CLAUSE: 3\n\nX4566 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2663 [label="2663: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X4566), SCOPE: 135, CLAUSE: 2\n\nX4566 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2664 [label="2664: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X4566), SCOPE: 135, CLAUSE: 3\n\nX4566 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2671 [label="2671: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X4605)\n\nX4605 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2673 [label="2673: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X4605), SCOPE: 136, CLAUSE: 1 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X4605), SCOPE: 136, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X4605), SCOPE: 136, CLAUSE: 3\n\nX4605 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2675 [label="2675: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X4605), SCOPE: 136, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X4605), SCOPE: 136, CLAUSE: 3\n\nX4605 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2681 [label="2681: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X4605), SCOPE: 136, CLAUSE: 2\n\nX4605 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2682 [label="2682: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X4605), SCOPE: 136, CLAUSE: 3\n\nX4605 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2686 [label="2686: quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X4640)\n\nX4640 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2689 [label="2689: quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X4640), SCOPE: 137, CLAUSE: 1 | quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X4640), SCOPE: 137, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X4640), SCOPE: 137, CLAUSE: 3\n\nX4640 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2692 [label="2692: quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X4640), SCOPE: 137, CLAUSE: 1\n\nX4640 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2693 [label="2693: quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X4640), SCOPE: 137, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X4640), SCOPE: 137, CLAUSE: 3\n\nX4640 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2694 [label="2694: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2695 [label="2695: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2700 [label="2700: quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X4640), SCOPE: 137, CLAUSE: 3\n\nX4640 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2701 [label="2701: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2702 [label="2702: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2704 [label="2704: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2706 [label="2706: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2707 [label="2707: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2713 [label="2713: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X4683)\n\nX4683 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2714 [label="2714: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2715 [label="2715: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X4683), SCOPE: 138, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X4683), SCOPE: 138, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X4683), SCOPE: 138, CLAUSE: 3\n\nX4683 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2719 [label="2719: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X4683), SCOPE: 138, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X4683), SCOPE: 138, CLAUSE: 3\n\nX4683 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2722 [label="2722: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X4683), SCOPE: 138, CLAUSE: 2\n\nX4683 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2723 [label="2723: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X4683), SCOPE: 138, CLAUSE: 3\n\nX4683 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2729 [label="2729: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X4722)\n\nX4722 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2731 [label="2731: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X4722), SCOPE: 139, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X4722), SCOPE: 139, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X4722), SCOPE: 139, CLAUSE: 3\n\nX4722 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2734 [label="2734: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X4722), SCOPE: 139, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X4722), SCOPE: 139, CLAUSE: 3\n\nX4722 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2737 [label="2737: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X4722), SCOPE: 139, CLAUSE: 2\n\nX4722 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2738 [label="2738: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X4722), SCOPE: 139, CLAUSE: 3\n\nX4722 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2744 [label="2744: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X4761)\n\nX4761 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2748 [label="2748: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X4761), SCOPE: 140, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X4761), SCOPE: 140, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X4761), SCOPE: 140, CLAUSE: 3\n\nX4761 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2749 [label="2749: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X4761), SCOPE: 140, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X4761), SCOPE: 140, CLAUSE: 3\n\nX4761 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2753 [label="2753: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X4761), SCOPE: 140, CLAUSE: 2\n\nX4761 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2754 [label="2754: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X4761), SCOPE: 140, CLAUSE: 3\n\nX4761 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2765 [label="2765: quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X4800)\n\nX4800 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2772 [label="2772: quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X4800), SCOPE: 141, CLAUSE: 1 | quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X4800), SCOPE: 141, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X4800), SCOPE: 141, CLAUSE: 3\n\nX4800 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2774 [label="2774: quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X4800), SCOPE: 141, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X4800), SCOPE: 141, CLAUSE: 3\n\nX4800 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2782 [label="2782: quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X4800), SCOPE: 141, CLAUSE: 2\n\nX4800 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2783 [label="2783: quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X4800), SCOPE: 141, CLAUSE: 3\n\nX4800 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2791 [label="2791: quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X4835)\n\nX4835 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2794 [label="2794: quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X4835), SCOPE: 142, CLAUSE: 1 | quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X4835), SCOPE: 142, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X4835), SCOPE: 142, CLAUSE: 3\n\nX4835 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2797 [label="2797: quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X4835), SCOPE: 142, CLAUSE: 1\n\nX4835 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2798 [label="2798: quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X4835), SCOPE: 142, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X4835), SCOPE: 142, CLAUSE: 3\n\nX4835 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2799 [label="2799: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2800 [label="2800: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2802 [label="2802: quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X4835), SCOPE: 142, CLAUSE: 3\n\nX4835 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2805 [label="2805: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2806 [label="2806: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2807 [label="2807: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2809 [label="2809: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2811 [label="2811: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2815 [label="2815: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4878)\n\nX4878 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2816 [label="2816: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2819 [label="2819: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4878), SCOPE: 143, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4878), SCOPE: 143, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4878), SCOPE: 143, CLAUSE: 3\n\nX4878 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2820 [label="2820: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4878), SCOPE: 143, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4878), SCOPE: 143, CLAUSE: 3\n\nX4878 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2826 [label="2826: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4878), SCOPE: 143, CLAUSE: 2\n\nX4878 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2827 [label="2827: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4878), SCOPE: 143, CLAUSE: 3\n\nX4878 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2833 [label="2833: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X4917)\n\nX4917 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2834 [label="2834: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X4917), SCOPE: 144, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X4917), SCOPE: 144, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X4917), SCOPE: 144, CLAUSE: 3\n\nX4917 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2838 [label="2838: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X4917), SCOPE: 144, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X4917), SCOPE: 144, CLAUSE: 3\n\nX4917 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2841 [label="2841: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X4917), SCOPE: 144, CLAUSE: 2\n\nX4917 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2842 [label="2842: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X4917), SCOPE: 144, CLAUSE: 3\n\nX4917 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2848 [label="2848: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X4956)\n\nX4956 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2852 [label="2852: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X4956), SCOPE: 145, CLAUSE: 1 | quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X4956), SCOPE: 145, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X4956), SCOPE: 145, CLAUSE: 3\n\nX4956 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2854 [label="2854: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X4956), SCOPE: 145, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X4956), SCOPE: 145, CLAUSE: 3\n\nX4956 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2860 [label="2860: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X4956), SCOPE: 145, CLAUSE: 2\n\nX4956 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2861 [label="2861: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X4956), SCOPE: 145, CLAUSE: 3\n\nX4956 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2874 [label="2874: quot(s(0), s(s(0)), s(s(s(s(s(0))))), X4995)\n\nX4995 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2879 [label="2879: quot(s(0), s(s(0)), s(s(s(s(s(0))))), X4995), SCOPE: 146, CLAUSE: 1 | quot(s(0), s(s(0)), s(s(s(s(s(0))))), X4995), SCOPE: 146, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(s(s(0))))), X4995), SCOPE: 146, CLAUSE: 3\n\nX4995 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2885 [label="2885: quot(s(0), s(s(0)), s(s(s(s(s(0))))), X4995), SCOPE: 146, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(s(s(0))))), X4995), SCOPE: 146, CLAUSE: 3\n\nX4995 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2889 [label="2889: quot(s(0), s(s(0)), s(s(s(s(s(0))))), X4995), SCOPE: 146, CLAUSE: 2\n\nX4995 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2890 [label="2890: quot(s(0), s(s(0)), s(s(s(s(s(0))))), X4995), SCOPE: 146, CLAUSE: 3\n\nX4995 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2896 [label="2896: quot(0, s(0), s(s(s(s(s(0))))), X5030)\n\nX5030 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2898 [label="2898: quot(0, s(0), s(s(s(s(s(0))))), X5030), SCOPE: 147, CLAUSE: 1 | quot(0, s(0), s(s(s(s(s(0))))), X5030), SCOPE: 147, CLAUSE: 2 | quot(0, s(0), s(s(s(s(s(0))))), X5030), SCOPE: 147, CLAUSE: 3\n\nX5030 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2900 [label="2900: quot(0, s(0), s(s(s(s(s(0))))), X5030), SCOPE: 147, CLAUSE: 1\n\nX5030 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2901 [label="2901: quot(0, s(0), s(s(s(s(s(0))))), X5030), SCOPE: 147, CLAUSE: 2 | quot(0, s(0), s(s(s(s(s(0))))), X5030), SCOPE: 147, CLAUSE: 3\n\nX5030 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2904 [label="2904: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2905 [label="2905: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2906 [label="2906: quot(0, s(0), s(s(s(s(s(0))))), X5030), SCOPE: 147, CLAUSE: 3\n\nX5030 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2907 [label="2907: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2911 [label="2911: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2913 [label="2913: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2914 [label="2914: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2915 [label="2915: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2919 [label="2919: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X5073)\n\nX5073 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2920 [label="2920: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
2923 [label="2923: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X5073), SCOPE: 148, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X5073), SCOPE: 148, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X5073), SCOPE: 148, CLAUSE: 3\n\nX5073 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2925 [label="2925: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X5073), SCOPE: 148, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X5073), SCOPE: 148, CLAUSE: 3\n\nX5073 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2930 [label="2930: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X5073), SCOPE: 148, CLAUSE: 2\n\nX5073 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2931 [label="2931: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X5073), SCOPE: 148, CLAUSE: 3\n\nX5073 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2936 [label="2936: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X5112)\n\nX5112 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2939 [label="2939: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X5112), SCOPE: 149, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X5112), SCOPE: 149, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X5112), SCOPE: 149, CLAUSE: 3\n\nX5112 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2940 [label="2940: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X5112), SCOPE: 149, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X5112), SCOPE: 149, CLAUSE: 3\n\nX5112 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2945 [label="2945: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X5112), SCOPE: 149, CLAUSE: 2\n\nX5112 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2946 [label="2946: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X5112), SCOPE: 149, CLAUSE: 3\n\nX5112 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2954 [label="2954: quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X5151)\n\nX5151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2956 [label="2956: quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X5151), SCOPE: 150, CLAUSE: 1 | quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X5151), SCOPE: 150, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X5151), SCOPE: 150, CLAUSE: 3\n\nX5151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2957 [label="2957: quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X5151), SCOPE: 150, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X5151), SCOPE: 150, CLAUSE: 3\n\nX5151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2965 [label="2965: quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X5151), SCOPE: 150, CLAUSE: 2\n\nX5151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2966 [label="2966: quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X5151), SCOPE: 150, CLAUSE: 3\n\nX5151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2978 [label="2978: quot(s(0), s(0), s(s(s(s(0)))), X5190)\n\nX5190 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2979 [label="2979: quot(s(0), s(0), s(s(s(s(0)))), X5190), SCOPE: 151, CLAUSE: 1 | quot(s(0), s(0), s(s(s(s(0)))), X5190), SCOPE: 151, CLAUSE: 2 | quot(s(0), s(0), s(s(s(s(0)))), X5190), SCOPE: 151, CLAUSE: 3\n\nX5190 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2982 [label="2982: quot(s(0), s(0), s(s(s(s(0)))), X5190), SCOPE: 151, CLAUSE: 2 | quot(s(0), s(0), s(s(s(s(0)))), X5190), SCOPE: 151, CLAUSE: 3\n\nX5190 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2989 [label="2989: quot(s(0), s(0), s(s(s(s(0)))), X5190), SCOPE: 151, CLAUSE: 2\n\nX5190 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2990 [label="2990: quot(s(0), s(0), s(s(s(s(0)))), X5190), SCOPE: 151, CLAUSE: 3\n\nX5190 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2995 [label="2995: quot(0, 0, s(s(s(s(0)))), X5229)\n\nX5229 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2996 [label="2996: quot(0, 0, s(s(s(s(0)))), X5229), SCOPE: 152, CLAUSE: 1 | quot(0, 0, s(s(s(s(0)))), X5229), SCOPE: 152, CLAUSE: 2 | quot(0, 0, s(s(s(s(0)))), X5229), SCOPE: 152, CLAUSE: 3\n\nX5229 is free", fontsize=16, style=filled, fillcolor=lightyellow];
2998 [label="2998: quot(0, 0, s(s(s(s(0)))), X5229), SCOPE: 152, CLAUSE: 2 | quot(0, 0, s(s(s(s(0)))), X5229), SCOPE: 152, CLAUSE: 3\n\nX5229 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3000 [label="3000: quot(0, 0, s(s(s(s(0)))), X5229), SCOPE: 152, CLAUSE: 3\n\nX5229 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3005 [label="3005: quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X5253)\n\nX5253 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3006 [label="3006: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3009 [label="3009: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3012 [label="3012: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3013 [label="3013: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3015 [label="3015: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X5279)\n\nX5279 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3016 [label="3016: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3018 [label="3018: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X5279), SCOPE: 153, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X5279), SCOPE: 153, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X5279), SCOPE: 153, CLAUSE: 3\n\nX5279 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3020 [label="3020: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X5279), SCOPE: 153, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X5279), SCOPE: 153, CLAUSE: 3\n\nX5279 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3026 [label="3026: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X5279), SCOPE: 153, CLAUSE: 2\n\nX5279 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3027 [label="3027: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X5279), SCOPE: 153, CLAUSE: 3\n\nX5279 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3031 [label="3031: quot(s(s(s(0))), s(s(0)), s(s(s(0))), X5318)\n\nX5318 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3035 [label="3035: quot(s(s(s(0))), s(s(0)), s(s(s(0))), X5318), SCOPE: 154, CLAUSE: 1 | quot(s(s(s(0))), s(s(0)), s(s(s(0))), X5318), SCOPE: 154, CLAUSE: 2 | quot(s(s(s(0))), s(s(0)), s(s(s(0))), X5318), SCOPE: 154, CLAUSE: 3\n\nX5318 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3036 [label="3036: quot(s(s(s(0))), s(s(0)), s(s(s(0))), X5318), SCOPE: 154, CLAUSE: 2 | quot(s(s(s(0))), s(s(0)), s(s(s(0))), X5318), SCOPE: 154, CLAUSE: 3\n\nX5318 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3041 [label="3041: quot(s(s(s(0))), s(s(0)), s(s(s(0))), X5318), SCOPE: 154, CLAUSE: 2\n\nX5318 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3042 [label="3042: quot(s(s(s(0))), s(s(0)), s(s(s(0))), X5318), SCOPE: 154, CLAUSE: 3\n\nX5318 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3045 [label="3045: quot(s(s(0)), s(0), s(s(s(0))), X5357)\n\nX5357 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3047 [label="3047: quot(s(s(0)), s(0), s(s(s(0))), X5357), SCOPE: 155, CLAUSE: 1 | quot(s(s(0)), s(0), s(s(s(0))), X5357), SCOPE: 155, CLAUSE: 2 | quot(s(s(0)), s(0), s(s(s(0))), X5357), SCOPE: 155, CLAUSE: 3\n\nX5357 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3049 [label="3049: quot(s(s(0)), s(0), s(s(s(0))), X5357), SCOPE: 155, CLAUSE: 2 | quot(s(s(0)), s(0), s(s(s(0))), X5357), SCOPE: 155, CLAUSE: 3\n\nX5357 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3055 [label="3055: quot(s(s(0)), s(0), s(s(s(0))), X5357), SCOPE: 155, CLAUSE: 2\n\nX5357 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3056 [label="3056: quot(s(s(0)), s(0), s(s(s(0))), X5357), SCOPE: 155, CLAUSE: 3\n\nX5357 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3063 [label="3063: quot(s(0), 0, s(s(s(0))), X5396)\n\nX5396 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3066 [label="3066: quot(s(0), 0, s(s(s(0))), X5396), SCOPE: 156, CLAUSE: 1 | quot(s(0), 0, s(s(s(0))), X5396), SCOPE: 156, CLAUSE: 2 | quot(s(0), 0, s(s(s(0))), X5396), SCOPE: 156, CLAUSE: 3\n\nX5396 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3067 [label="3067: quot(s(0), 0, s(s(s(0))), X5396), SCOPE: 156, CLAUSE: 2 | quot(s(0), 0, s(s(s(0))), X5396), SCOPE: 156, CLAUSE: 3\n\nX5396 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3072 [label="3072: quot(s(0), 0, s(s(s(0))), X5396), SCOPE: 156, CLAUSE: 3\n\nX5396 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3078 [label="3078: quot(s(0), s(s(s(0))), s(s(s(0))), X5422)\n\nX5422 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3082 [label="3082: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3084 [label="3084: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3085 [label="3085: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3089 [label="3089: quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X5447)\n\nX5447 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3091 [label="3091: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3093 [label="3093: quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X5447), SCOPE: 157, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X5447), SCOPE: 157, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X5447), SCOPE: 157, CLAUSE: 3\n\nX5447 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3094 [label="3094: quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X5447), SCOPE: 157, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X5447), SCOPE: 157, CLAUSE: 3\n\nX5447 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3099 [label="3099: quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X5447), SCOPE: 157, CLAUSE: 2\n\nX5447 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3100 [label="3100: quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X5447), SCOPE: 157, CLAUSE: 3\n\nX5447 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3107 [label="3107: quot(s(s(s(0))), s(0), s(s(0)), X5486)\n\nX5486 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3108 [label="3108: quot(s(s(s(0))), s(0), s(s(0)), X5486), SCOPE: 158, CLAUSE: 1 | quot(s(s(s(0))), s(0), s(s(0)), X5486), SCOPE: 158, CLAUSE: 2 | quot(s(s(s(0))), s(0), s(s(0)), X5486), SCOPE: 158, CLAUSE: 3\n\nX5486 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3109 [label="3109: quot(s(s(s(0))), s(0), s(s(0)), X5486), SCOPE: 158, CLAUSE: 2 | quot(s(s(s(0))), s(0), s(s(0)), X5486), SCOPE: 158, CLAUSE: 3\n\nX5486 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3114 [label="3114: quot(s(s(s(0))), s(0), s(s(0)), X5486), SCOPE: 158, CLAUSE: 2\n\nX5486 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3115 [label="3115: quot(s(s(s(0))), s(0), s(s(0)), X5486), SCOPE: 158, CLAUSE: 3\n\nX5486 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3122 [label="3122: quot(s(s(0)), 0, s(s(0)), X5525)\n\nX5525 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3124 [label="3124: quot(s(s(0)), 0, s(s(0)), X5525), SCOPE: 159, CLAUSE: 1 | quot(s(s(0)), 0, s(s(0)), X5525), SCOPE: 159, CLAUSE: 2 | quot(s(s(0)), 0, s(s(0)), X5525), SCOPE: 159, CLAUSE: 3\n\nX5525 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3125 [label="3125: quot(s(s(0)), 0, s(s(0)), X5525), SCOPE: 159, CLAUSE: 2 | quot(s(s(0)), 0, s(s(0)), X5525), SCOPE: 159, CLAUSE: 3\n\nX5525 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3126 [label="3126: quot(s(s(0)), 0, s(s(0)), X5525), SCOPE: 159, CLAUSE: 3\n\nX5525 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3132 [label="3132: quot(s(s(0)), s(s(0)), s(s(0)), X5551)\n\nX5551 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3136 [label="3136: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3137 [label="3137: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3141 [label="3141: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3142 [label="3142: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3145 [label="3145: times(T598, s(s(T596)), X3837)\n\nT596 is ground\nT598 is ground\nX3837 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3146 [label="3146: neq(s(s(s(s(s(s(T596)))))), T744)\n\nT596 is ground\nT744 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3154 [label="3154: pr(s(s(s(s(s(s(T590)))))), s(T590)), SCOPE: 160, CLAUSE: 5 | pr(s(s(s(s(s(s(T590)))))), s(T590)), SCOPE: 160, CLAUSE: 6\n\nT590 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3155 [label="3155: pr(s(s(s(s(s(s(T590)))))), s(T590)), SCOPE: 160, CLAUSE: 5\n\nT590 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3156 [label="3156: pr(s(s(s(s(s(s(T590)))))), s(T590)), SCOPE: 160, CLAUSE: 6\n\nT590 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3157 [label="3157: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3158 [label="3158: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3159 [label="3159: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3162 [label="N29: ','(not_divides(s(s(T761)), s(s(s(s(s(s(s(T761)))))))), pr(s(s(s(s(s(s(s(T761))))))), s(T761)))\n\nT761 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3163 [label="3163: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3165 [label="N31: not_divides(s(s(T761)), s(s(s(s(s(s(s(T761))))))))\n\nT761 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3166 [label="N33: pr(s(s(s(s(s(s(s(T761))))))), s(T761))\n\nT761 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3171 [label="3171: not_divides(s(s(T761)), s(s(s(s(s(s(s(T761)))))))), SCOPE: 161, CLAUSE: 7\n\nT761 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3174 [label="N32: ','(div(s(s(s(s(s(s(s(T767))))))), s(s(T767)), X5607), ','(times(X5607, s(s(T767)), X5608), neq(s(s(s(s(s(s(s(T767))))))), X5608)))\n\nT767 is ground\nX5607 is free\nX5608 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3176 [label="N35: div(s(s(s(s(s(s(s(T767))))))), s(s(T767)), X5607)\n\nT767 is ground\nX5607 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3177 [label="N44: ','(times(T769, s(s(T767)), X5608), neq(s(s(s(s(s(s(s(T767))))))), X5608))\n\nT767 is ground\nT769 is ground\nX5608 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3180 [label="3180: div(s(s(s(s(s(s(s(T767))))))), s(s(T767)), X5607), SCOPE: 162, CLAUSE: 0\n\nT767 is ground\nX5607 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3187 [label="3187: quot(s(s(s(s(s(s(s(T773))))))), s(s(T773)), s(s(T773)), X5632)\n\nT773 is ground\nX5632 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3188 [label="3188: quot(s(s(s(s(s(s(s(T773))))))), s(s(T773)), s(s(T773)), X5632), SCOPE: 163, CLAUSE: 1 | quot(s(s(s(s(s(s(s(T773))))))), s(s(T773)), s(s(T773)), X5632), SCOPE: 163, CLAUSE: 2 | quot(s(s(s(s(s(s(s(T773))))))), s(s(T773)), s(s(T773)), X5632), SCOPE: 163, CLAUSE: 3\n\nT773 is ground\nX5632 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3189 [label="3189: quot(s(s(s(s(s(s(s(T773))))))), s(s(T773)), s(s(T773)), X5632), SCOPE: 163, CLAUSE: 2 | quot(s(s(s(s(s(s(s(T773))))))), s(s(T773)), s(s(T773)), X5632), SCOPE: 163, CLAUSE: 3\n\nT773 is ground\nX5632 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3195 [label="3195: quot(s(s(s(s(s(s(s(T773))))))), s(s(T773)), s(s(T773)), X5632), SCOPE: 163, CLAUSE: 2\n\nT773 is ground\nX5632 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3196 [label="3196: quot(s(s(s(s(s(s(s(T773))))))), s(s(T773)), s(s(T773)), X5632), SCOPE: 163, CLAUSE: 3\n\nT773 is ground\nX5632 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3203 [label="3203: quot(s(s(s(s(s(s(T778)))))), s(T778), s(s(T778)), X5671)\n\nT778 is ground\nX5671 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3207 [label="3207: quot(s(s(s(s(s(s(T778)))))), s(T778), s(s(T778)), X5671), SCOPE: 164, CLAUSE: 1 | quot(s(s(s(s(s(s(T778)))))), s(T778), s(s(T778)), X5671), SCOPE: 164, CLAUSE: 2 | quot(s(s(s(s(s(s(T778)))))), s(T778), s(s(T778)), X5671), SCOPE: 164, CLAUSE: 3\n\nT778 is ground\nX5671 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3210 [label="3210: quot(s(s(s(s(s(s(T778)))))), s(T778), s(s(T778)), X5671), SCOPE: 164, CLAUSE: 2 | quot(s(s(s(s(s(s(T778)))))), s(T778), s(s(T778)), X5671), SCOPE: 164, CLAUSE: 3\n\nT778 is ground\nX5671 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3221 [label="3221: quot(s(s(s(s(s(s(T778)))))), s(T778), s(s(T778)), X5671), SCOPE: 164, CLAUSE: 2\n\nT778 is ground\nX5671 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3222 [label="3222: quot(s(s(s(s(s(s(T778)))))), s(T778), s(s(T778)), X5671), SCOPE: 164, CLAUSE: 3\n\nT778 is ground\nX5671 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3229 [label="3229: quot(s(s(s(s(s(T783))))), T783, s(s(T783)), X5710)\n\nT783 is ground\nX5710 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3236 [label="3236: quot(s(s(s(s(s(T783))))), T783, s(s(T783)), X5710), SCOPE: 165, CLAUSE: 1 | quot(s(s(s(s(s(T783))))), T783, s(s(T783)), X5710), SCOPE: 165, CLAUSE: 2 | quot(s(s(s(s(s(T783))))), T783, s(s(T783)), X5710), SCOPE: 165, CLAUSE: 3\n\nT783 is ground\nX5710 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3239 [label="3239: quot(s(s(s(s(s(T783))))), T783, s(s(T783)), X5710), SCOPE: 165, CLAUSE: 2 | quot(s(s(s(s(s(T783))))), T783, s(s(T783)), X5710), SCOPE: 165, CLAUSE: 3\n\nT783 is ground\nX5710 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3243 [label="3243: quot(s(s(s(s(s(T783))))), T783, s(s(T783)), X5710), SCOPE: 165, CLAUSE: 2\n\nT783 is ground\nX5710 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3244 [label="3244: quot(s(s(s(s(s(T783))))), T783, s(s(T783)), X5710), SCOPE: 165, CLAUSE: 3\n\nT783 is ground\nX5710 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3247 [label="3247: quot(s(s(s(s(s(T793))))), T793, s(s(s(T793))), X5741)\n\nT793 is ground\nX5741 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3248 [label="3248: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3254 [label="3254: quot(s(s(s(s(s(T793))))), T793, s(s(s(T793))), X5741), SCOPE: 166, CLAUSE: 1 | quot(s(s(s(s(s(T793))))), T793, s(s(s(T793))), X5741), SCOPE: 166, CLAUSE: 2 | quot(s(s(s(s(s(T793))))), T793, s(s(s(T793))), X5741), SCOPE: 166, CLAUSE: 3\n\nT793 is ground\nX5741 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3255 [label="3255: quot(s(s(s(s(s(T793))))), T793, s(s(s(T793))), X5741), SCOPE: 166, CLAUSE: 2 | quot(s(s(s(s(s(T793))))), T793, s(s(s(T793))), X5741), SCOPE: 166, CLAUSE: 3\n\nT793 is ground\nX5741 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3259 [label="3259: quot(s(s(s(s(s(T793))))), T793, s(s(s(T793))), X5741), SCOPE: 166, CLAUSE: 2\n\nT793 is ground\nX5741 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3260 [label="3260: quot(s(s(s(s(s(T793))))), T793, s(s(s(T793))), X5741), SCOPE: 166, CLAUSE: 3\n\nT793 is ground\nX5741 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3262 [label="3262: quot(s(s(s(s(s(T803))))), T803, s(s(s(s(T803)))), X5772)\n\nT803 is ground\nX5772 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3263 [label="3263: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3267 [label="3267: quot(s(s(s(s(s(T803))))), T803, s(s(s(s(T803)))), X5772), SCOPE: 167, CLAUSE: 1 | quot(s(s(s(s(s(T803))))), T803, s(s(s(s(T803)))), X5772), SCOPE: 167, CLAUSE: 2 | quot(s(s(s(s(s(T803))))), T803, s(s(s(s(T803)))), X5772), SCOPE: 167, CLAUSE: 3\n\nT803 is ground\nX5772 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3269 [label="3269: quot(s(s(s(s(s(T803))))), T803, s(s(s(s(T803)))), X5772), SCOPE: 167, CLAUSE: 2 | quot(s(s(s(s(s(T803))))), T803, s(s(s(s(T803)))), X5772), SCOPE: 167, CLAUSE: 3\n\nT803 is ground\nX5772 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3273 [label="3273: quot(s(s(s(s(s(T803))))), T803, s(s(s(s(T803)))), X5772), SCOPE: 167, CLAUSE: 2\n\nT803 is ground\nX5772 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3274 [label="3274: quot(s(s(s(s(s(T803))))), T803, s(s(s(s(T803)))), X5772), SCOPE: 167, CLAUSE: 3\n\nT803 is ground\nX5772 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3277 [label="3277: quot(s(s(s(s(s(T813))))), T813, s(s(s(s(s(T813))))), X5803)\n\nT813 is ground\nX5803 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3278 [label="3278: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3281 [label="3281: quot(s(s(s(s(s(T813))))), T813, s(s(s(s(s(T813))))), X5803), SCOPE: 168, CLAUSE: 1 | quot(s(s(s(s(s(T813))))), T813, s(s(s(s(s(T813))))), X5803), SCOPE: 168, CLAUSE: 2 | quot(s(s(s(s(s(T813))))), T813, s(s(s(s(s(T813))))), X5803), SCOPE: 168, CLAUSE: 3\n\nT813 is ground\nX5803 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3284 [label="3284: quot(s(s(s(s(s(T813))))), T813, s(s(s(s(s(T813))))), X5803), SCOPE: 168, CLAUSE: 2 | quot(s(s(s(s(s(T813))))), T813, s(s(s(s(s(T813))))), X5803), SCOPE: 168, CLAUSE: 3\n\nT813 is ground\nX5803 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3287 [label="3287: quot(s(s(s(s(s(T813))))), T813, s(s(s(s(s(T813))))), X5803), SCOPE: 168, CLAUSE: 2\n\nT813 is ground\nX5803 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3288 [label="3288: quot(s(s(s(s(s(T813))))), T813, s(s(s(s(s(T813))))), X5803), SCOPE: 168, CLAUSE: 3\n\nT813 is ground\nX5803 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3293 [label="3293: quot(s(s(s(s(s(T823))))), T823, s(s(s(s(s(s(T823)))))), X5834)\n\nT823 is ground\nX5834 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3294 [label="3294: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3298 [label="3298: quot(s(s(s(s(s(T823))))), T823, s(s(s(s(s(s(T823)))))), X5834), SCOPE: 169, CLAUSE: 1 | quot(s(s(s(s(s(T823))))), T823, s(s(s(s(s(s(T823)))))), X5834), SCOPE: 169, CLAUSE: 2 | quot(s(s(s(s(s(T823))))), T823, s(s(s(s(s(s(T823)))))), X5834), SCOPE: 169, CLAUSE: 3\n\nT823 is ground\nX5834 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3299 [label="3299: quot(s(s(s(s(s(T823))))), T823, s(s(s(s(s(s(T823)))))), X5834), SCOPE: 169, CLAUSE: 2 | quot(s(s(s(s(s(T823))))), T823, s(s(s(s(s(s(T823)))))), X5834), SCOPE: 169, CLAUSE: 3\n\nT823 is ground\nX5834 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3304 [label="3304: quot(s(s(s(s(s(T823))))), T823, s(s(s(s(s(s(T823)))))), X5834), SCOPE: 169, CLAUSE: 2\n\nT823 is ground\nX5834 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3305 [label="3305: quot(s(s(s(s(s(T823))))), T823, s(s(s(s(s(s(T823)))))), X5834), SCOPE: 169, CLAUSE: 3\n\nT823 is ground\nX5834 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3310 [label="3310: quot(s(s(s(s(s(T833))))), T833, s(s(s(s(s(s(s(T833))))))), X5865)\n\nT833 is ground\nX5865 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3311 [label="3311: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3316 [label="3316: quot(s(s(s(s(s(T833))))), T833, s(s(s(s(s(s(s(T833))))))), X5865), SCOPE: 170, CLAUSE: 1 | quot(s(s(s(s(s(T833))))), T833, s(s(s(s(s(s(s(T833))))))), X5865), SCOPE: 170, CLAUSE: 2 | quot(s(s(s(s(s(T833))))), T833, s(s(s(s(s(s(s(T833))))))), X5865), SCOPE: 170, CLAUSE: 3\n\nT833 is ground\nX5865 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3318 [label="3318: quot(s(s(s(s(s(T833))))), T833, s(s(s(s(s(s(s(T833))))))), X5865), SCOPE: 170, CLAUSE: 2 | quot(s(s(s(s(s(T833))))), T833, s(s(s(s(s(s(s(T833))))))), X5865), SCOPE: 170, CLAUSE: 3\n\nT833 is ground\nX5865 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3322 [label="3322: quot(s(s(s(s(s(T833))))), T833, s(s(s(s(s(s(s(T833))))))), X5865), SCOPE: 170, CLAUSE: 2\n\nT833 is ground\nX5865 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3323 [label="3323: quot(s(s(s(s(s(T833))))), T833, s(s(s(s(s(s(s(T833))))))), X5865), SCOPE: 170, CLAUSE: 3\n\nT833 is ground\nX5865 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3330 [label="3330: quot(s(s(s(s(s(T843))))), T843, s(s(s(s(s(s(s(s(T843)))))))), X5896)\n\nT843 is ground\nX5896 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3331 [label="3331: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3337 [label="W: quot(s(s(s(s(s(T843))))), T843, s(T844), X5896)\n\nT843 is ground\nT844 is ground\nX5896 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3343 [label="3343: quot(s(s(s(s(s(T843))))), T843, s(T844), X5896), SCOPE: 171, CLAUSE: 1 | quot(s(s(s(s(s(T843))))), T843, s(T844), X5896), SCOPE: 171, CLAUSE: 2 | quot(s(s(s(s(s(T843))))), T843, s(T844), X5896), SCOPE: 171, CLAUSE: 3\n\nT843 is ground\nT844 is ground\nX5896 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3344 [label="3344: quot(s(s(s(s(s(T843))))), T843, s(T844), X5896), SCOPE: 171, CLAUSE: 2 | quot(s(s(s(s(s(T843))))), T843, s(T844), X5896), SCOPE: 171, CLAUSE: 3\n\nT843 is ground\nT844 is ground\nX5896 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3348 [label="3348: quot(s(s(s(s(s(T843))))), T843, s(T844), X5896), SCOPE: 171, CLAUSE: 2\n\nT843 is ground\nT844 is ground\nX5896 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3349 [label="3349: quot(s(s(s(s(s(T843))))), T843, s(T844), X5896), SCOPE: 171, CLAUSE: 3\n\nT843 is ground\nT844 is ground\nX5896 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3356 [label="3356: quot(s(s(s(s(s(T858))))), T858, s(T859), X5931)\n\nT858 is ground\nT859 is ground\nX5931 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3357 [label="3357: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3363 [label="3363: quot(s(s(s(s(s(0))))), s(T865), s(T865), X5947)\n\nT865 is ground\nX5947 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3364 [label="3364: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3369 [label="3369: quot(s(s(s(s(s(0))))), s(T865), s(T865), X5947), SCOPE: 172, CLAUSE: 1 | quot(s(s(s(s(s(0))))), s(T865), s(T865), X5947), SCOPE: 172, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(T865), s(T865), X5947), SCOPE: 172, CLAUSE: 3\n\nT865 is ground\nX5947 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3370 [label="3370: quot(s(s(s(s(s(0))))), s(T865), s(T865), X5947), SCOPE: 172, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(T865), s(T865), X5947), SCOPE: 172, CLAUSE: 3\n\nT865 is ground\nX5947 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3375 [label="3375: quot(s(s(s(s(s(0))))), s(T865), s(T865), X5947), SCOPE: 172, CLAUSE: 2\n\nT865 is ground\nX5947 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3376 [label="3376: quot(s(s(s(s(s(0))))), s(T865), s(T865), X5947), SCOPE: 172, CLAUSE: 3\n\nT865 is ground\nX5947 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3383 [label="3383: quot(s(s(s(s(0)))), T870, s(T870), X5986)\n\nT870 is ground\nX5986 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3388 [label="3388: quot(s(s(s(s(0)))), T870, s(T870), X5986), SCOPE: 173, CLAUSE: 1 | quot(s(s(s(s(0)))), T870, s(T870), X5986), SCOPE: 173, CLAUSE: 2 | quot(s(s(s(s(0)))), T870, s(T870), X5986), SCOPE: 173, CLAUSE: 3\n\nT870 is ground\nX5986 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3390 [label="3390: quot(s(s(s(s(0)))), T870, s(T870), X5986), SCOPE: 173, CLAUSE: 2 | quot(s(s(s(s(0)))), T870, s(T870), X5986), SCOPE: 173, CLAUSE: 3\n\nT870 is ground\nX5986 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3395 [label="3395: quot(s(s(s(s(0)))), T870, s(T870), X5986), SCOPE: 173, CLAUSE: 2\n\nT870 is ground\nX5986 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3396 [label="3396: quot(s(s(s(s(0)))), T870, s(T870), X5986), SCOPE: 173, CLAUSE: 3\n\nT870 is ground\nX5986 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3400 [label="3400: quot(s(s(s(0))), T875, s(s(T875)), X6017)\n\nT875 is ground\nX6017 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3401 [label="3401: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3404 [label="3404: quot(s(s(s(0))), T875, s(s(T875)), X6017), SCOPE: 174, CLAUSE: 1 | quot(s(s(s(0))), T875, s(s(T875)), X6017), SCOPE: 174, CLAUSE: 2 | quot(s(s(s(0))), T875, s(s(T875)), X6017), SCOPE: 174, CLAUSE: 3\n\nT875 is ground\nX6017 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3405 [label="3405: quot(s(s(s(0))), T875, s(s(T875)), X6017), SCOPE: 174, CLAUSE: 2 | quot(s(s(s(0))), T875, s(s(T875)), X6017), SCOPE: 174, CLAUSE: 3\n\nT875 is ground\nX6017 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3410 [label="3410: quot(s(s(s(0))), T875, s(s(T875)), X6017), SCOPE: 174, CLAUSE: 2\n\nT875 is ground\nX6017 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3411 [label="3411: quot(s(s(s(0))), T875, s(s(T875)), X6017), SCOPE: 174, CLAUSE: 3\n\nT875 is ground\nX6017 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3414 [label="3414: quot(s(s(0)), T880, s(s(s(T880))), X6048)\n\nT880 is ground\nX6048 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3415 [label="3415: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3418 [label="3418: quot(s(s(0)), T880, s(s(s(T880))), X6048), SCOPE: 175, CLAUSE: 1 | quot(s(s(0)), T880, s(s(s(T880))), X6048), SCOPE: 175, CLAUSE: 2 | quot(s(s(0)), T880, s(s(s(T880))), X6048), SCOPE: 175, CLAUSE: 3\n\nT880 is ground\nX6048 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3420 [label="3420: quot(s(s(0)), T880, s(s(s(T880))), X6048), SCOPE: 175, CLAUSE: 2 | quot(s(s(0)), T880, s(s(s(T880))), X6048), SCOPE: 175, CLAUSE: 3\n\nT880 is ground\nX6048 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3424 [label="3424: quot(s(s(0)), T880, s(s(s(T880))), X6048), SCOPE: 175, CLAUSE: 2\n\nT880 is ground\nX6048 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3425 [label="3425: quot(s(s(0)), T880, s(s(s(T880))), X6048), SCOPE: 175, CLAUSE: 3\n\nT880 is ground\nX6048 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3432 [label="3432: quot(s(0), T885, s(s(s(s(T885)))), X6079)\n\nT885 is ground\nX6079 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3433 [label="3433: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3434 [label="3434: quot(s(0), T885, s(s(s(s(T885)))), X6079), SCOPE: 176, CLAUSE: 1 | quot(s(0), T885, s(s(s(s(T885)))), X6079), SCOPE: 176, CLAUSE: 2 | quot(s(0), T885, s(s(s(s(T885)))), X6079), SCOPE: 176, CLAUSE: 3\n\nT885 is ground\nX6079 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3436 [label="3436: quot(s(0), T885, s(s(s(s(T885)))), X6079), SCOPE: 176, CLAUSE: 2 | quot(s(0), T885, s(s(s(s(T885)))), X6079), SCOPE: 176, CLAUSE: 3\n\nT885 is ground\nX6079 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3439 [label="3439: quot(s(0), T885, s(s(s(s(T885)))), X6079), SCOPE: 176, CLAUSE: 2\n\nT885 is ground\nX6079 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3440 [label="3440: quot(s(0), T885, s(s(s(s(T885)))), X6079), SCOPE: 176, CLAUSE: 3\n\nT885 is ground\nX6079 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3446 [label="3446: quot(0, T890, s(s(s(s(s(T890))))), X6110)\n\nT890 is ground\nX6110 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3447 [label="3447: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3450 [label="3450: quot(0, T890, s(s(s(s(s(T890))))), X6110), SCOPE: 177, CLAUSE: 1 | quot(0, T890, s(s(s(s(s(T890))))), X6110), SCOPE: 177, CLAUSE: 2 | quot(0, T890, s(s(s(s(s(T890))))), X6110), SCOPE: 177, CLAUSE: 3\n\nT890 is ground\nX6110 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3453 [label="3453: quot(0, T890, s(s(s(s(s(T890))))), X6110), SCOPE: 177, CLAUSE: 1\n\nT890 is ground\nX6110 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3454 [label="3454: quot(0, T890, s(s(s(s(s(T890))))), X6110), SCOPE: 177, CLAUSE: 2 | quot(0, T890, s(s(s(s(s(T890))))), X6110), SCOPE: 177, CLAUSE: 3\n\nT890 is ground\nX6110 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3458 [label="3458: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3459 [label="3459: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3460 [label="3460: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3463 [label="3463: quot(0, T890, s(s(s(s(s(T890))))), X6110), SCOPE: 177, CLAUSE: 3\n\nT890 is ground\nX6110 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3469 [label="X: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6140)\n\nX6140 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3470 [label="3470: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3472 [label="3472: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6140), SCOPE: 178, CLAUSE: 1 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6140), SCOPE: 178, CLAUSE: 2 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6140), SCOPE: 178, CLAUSE: 3\n\nX6140 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3474 [label="3474: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6140), SCOPE: 178, CLAUSE: 1\n\nX6140 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3475 [label="3475: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6140), SCOPE: 178, CLAUSE: 2 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6140), SCOPE: 178, CLAUSE: 3\n\nX6140 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3479 [label="3479: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3480 [label="3480: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3483 [label="3483: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6140), SCOPE: 178, CLAUSE: 3\n\nX6140 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3485 [label="3485: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3490 [label="3490: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X6171)\n\nX6171 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3491 [label="3491: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3498 [label="3498: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X6187)\n\nX6187 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3499 [label="3499: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3508 [label="3508: quot(s(s(s(0))), s(s(0)), s(s(0)), X6203)\n\nX6203 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3509 [label="3509: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3518 [label="3518: quot(s(s(s(s(0)))), s(0), s(0), X6219)\n\nX6219 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3519 [label="3519: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3524 [label="3524: quot(s(s(s(s(0)))), s(0), s(0), X6219), SCOPE: 179, CLAUSE: 1 | quot(s(s(s(s(0)))), s(0), s(0), X6219), SCOPE: 179, CLAUSE: 2 | quot(s(s(s(s(0)))), s(0), s(0), X6219), SCOPE: 179, CLAUSE: 3\n\nX6219 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3527 [label="3527: quot(s(s(s(s(0)))), s(0), s(0), X6219), SCOPE: 179, CLAUSE: 2 | quot(s(s(s(s(0)))), s(0), s(0), X6219), SCOPE: 179, CLAUSE: 3\n\nX6219 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3535 [label="3535: quot(s(s(s(s(0)))), s(0), s(0), X6219), SCOPE: 179, CLAUSE: 2\n\nX6219 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3536 [label="3536: quot(s(s(s(s(0)))), s(0), s(0), X6219), SCOPE: 179, CLAUSE: 3\n\nX6219 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3546 [label="3546: quot(s(s(s(0))), 0, s(0), X6258)\n\nX6258 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3553 [label="3553: quot(s(s(s(0))), 0, s(0), X6258), SCOPE: 180, CLAUSE: 1 | quot(s(s(s(0))), 0, s(0), X6258), SCOPE: 180, CLAUSE: 2 | quot(s(s(s(0))), 0, s(0), X6258), SCOPE: 180, CLAUSE: 3\n\nX6258 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3554 [label="3554: quot(s(s(s(0))), 0, s(0), X6258), SCOPE: 180, CLAUSE: 2 | quot(s(s(s(0))), 0, s(0), X6258), SCOPE: 180, CLAUSE: 3\n\nX6258 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3555 [label="3555: quot(s(s(s(0))), 0, s(0), X6258), SCOPE: 180, CLAUSE: 3\n\nX6258 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3560 [label="3560: quot(s(s(s(0))), s(0), s(0), X6284)\n\nX6284 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3565 [label="3565: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3566 [label="3566: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3571 [label="3571: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X6306)\n\nX6306 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3572 [label="3572: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3575 [label="3575: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X6306), 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))))))), X6306), 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))))))), X6306), SCOPE: 181, CLAUSE: 3\n\nX6306 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3576 [label="3576: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X6306), 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))))))), X6306), SCOPE: 181, CLAUSE: 3\n\nX6306 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3583 [label="3583: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X6306), SCOPE: 181, CLAUSE: 2\n\nX6306 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3584 [label="3584: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X6306), SCOPE: 181, CLAUSE: 3\n\nX6306 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3589 [label="3589: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X6345)\n\nX6345 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3592 [label="3592: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X6345), 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))))))), X6345), 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))))))), X6345), SCOPE: 182, CLAUSE: 3\n\nX6345 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3594 [label="3594: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X6345), 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))))))), X6345), SCOPE: 182, CLAUSE: 3\n\nX6345 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3599 [label="3599: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X6345), SCOPE: 182, CLAUSE: 2\n\nX6345 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3600 [label="3600: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X6345), SCOPE: 182, CLAUSE: 3\n\nX6345 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3606 [label="3606: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X6384)\n\nX6384 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3609 [label="3609: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X6384), SCOPE: 183, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X6384), SCOPE: 183, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X6384), SCOPE: 183, CLAUSE: 3\n\nX6384 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3612 [label="3612: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X6384), SCOPE: 183, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X6384), SCOPE: 183, CLAUSE: 3\n\nX6384 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3617 [label="3617: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X6384), SCOPE: 183, CLAUSE: 2\n\nX6384 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3618 [label="3618: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X6384), SCOPE: 183, CLAUSE: 3\n\nX6384 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3622 [label="3622: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X6423)\n\nX6423 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3627 [label="3627: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X6423), SCOPE: 184, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X6423), SCOPE: 184, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X6423), SCOPE: 184, CLAUSE: 3\n\nX6423 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3628 [label="3628: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X6423), SCOPE: 184, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X6423), SCOPE: 184, CLAUSE: 3\n\nX6423 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3632 [label="3632: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X6423), SCOPE: 184, CLAUSE: 2\n\nX6423 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3633 [label="3633: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X6423), SCOPE: 184, CLAUSE: 3\n\nX6423 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3638 [label="3638: quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X6462)\n\nX6462 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3642 [label="3642: quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X6462), SCOPE: 185, CLAUSE: 1 | quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X6462), SCOPE: 185, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X6462), SCOPE: 185, CLAUSE: 3\n\nX6462 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3643 [label="3643: quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X6462), SCOPE: 185, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X6462), SCOPE: 185, CLAUSE: 3\n\nX6462 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3647 [label="3647: quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X6462), SCOPE: 185, CLAUSE: 2\n\nX6462 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3648 [label="3648: quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X6462), SCOPE: 185, CLAUSE: 3\n\nX6462 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3652 [label="3652: quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X6497)\n\nX6497 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3655 [label="3655: quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X6497), SCOPE: 186, CLAUSE: 1 | quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X6497), SCOPE: 186, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X6497), SCOPE: 186, CLAUSE: 3\n\nX6497 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3658 [label="3658: quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X6497), SCOPE: 186, CLAUSE: 1\n\nX6497 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3659 [label="3659: quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X6497), SCOPE: 186, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X6497), SCOPE: 186, CLAUSE: 3\n\nX6497 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3660 [label="3660: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3661 [label="3661: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3664 [label="3664: quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X6497), SCOPE: 186, CLAUSE: 3\n\nX6497 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3666 [label="3666: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3667 [label="3667: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3668 [label="3668: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3670 [label="3670: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3673 [label="3673: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3674 [label="3674: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3679 [label="3679: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X6543)\n\nX6543 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3680 [label="3680: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3683 [label="3683: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X6543), 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)))))), X6543), 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)))))), X6543), SCOPE: 187, CLAUSE: 3\n\nX6543 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3684 [label="3684: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X6543), 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)))))), X6543), SCOPE: 187, CLAUSE: 3\n\nX6543 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3688 [label="3688: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X6543), SCOPE: 187, CLAUSE: 2\n\nX6543 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3689 [label="3689: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X6543), SCOPE: 187, CLAUSE: 3\n\nX6543 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3699 [label="3699: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6582)\n\nX6582 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3703 [label="3703: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6582), SCOPE: 188, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6582), SCOPE: 188, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6582), SCOPE: 188, CLAUSE: 3\n\nX6582 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3704 [label="3704: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6582), SCOPE: 188, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6582), SCOPE: 188, CLAUSE: 3\n\nX6582 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3712 [label="3712: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6582), SCOPE: 188, CLAUSE: 2\n\nX6582 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3713 [label="3713: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6582), SCOPE: 188, CLAUSE: 3\n\nX6582 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3727 [label="3727: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6621)\n\nX6621 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3730 [label="3730: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6621), SCOPE: 189, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6621), SCOPE: 189, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6621), SCOPE: 189, CLAUSE: 3\n\nX6621 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3733 [label="3733: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6621), SCOPE: 189, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6621), SCOPE: 189, CLAUSE: 3\n\nX6621 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3736 [label="3736: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6621), SCOPE: 189, CLAUSE: 2\n\nX6621 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3737 [label="3737: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6621), SCOPE: 189, CLAUSE: 3\n\nX6621 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3743 [label="3743: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X6660)\n\nX6660 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3747 [label="3747: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X6660), SCOPE: 190, CLAUSE: 1 | quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X6660), SCOPE: 190, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X6660), SCOPE: 190, CLAUSE: 3\n\nX6660 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3750 [label="3750: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X6660), SCOPE: 190, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X6660), SCOPE: 190, CLAUSE: 3\n\nX6660 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3753 [label="3753: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X6660), SCOPE: 190, CLAUSE: 2\n\nX6660 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3754 [label="3754: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X6660), SCOPE: 190, CLAUSE: 3\n\nX6660 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3759 [label="3759: quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X6699)\n\nX6699 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3764 [label="3764: quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X6699), SCOPE: 191, CLAUSE: 1 | quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X6699), SCOPE: 191, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X6699), SCOPE: 191, CLAUSE: 3\n\nX6699 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3765 [label="3765: quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X6699), SCOPE: 191, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X6699), SCOPE: 191, CLAUSE: 3\n\nX6699 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3769 [label="3769: quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X6699), SCOPE: 191, CLAUSE: 2\n\nX6699 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3770 [label="3770: quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X6699), SCOPE: 191, CLAUSE: 3\n\nX6699 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3775 [label="3775: quot(0, s(0), s(s(s(s(s(s(0)))))), X6734)\n\nX6734 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3779 [label="3779: quot(0, s(0), s(s(s(s(s(s(0)))))), X6734), SCOPE: 192, CLAUSE: 1 | quot(0, s(0), s(s(s(s(s(s(0)))))), X6734), SCOPE: 192, CLAUSE: 2 | quot(0, s(0), s(s(s(s(s(s(0)))))), X6734), SCOPE: 192, CLAUSE: 3\n\nX6734 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3782 [label="3782: quot(0, s(0), s(s(s(s(s(s(0)))))), X6734), SCOPE: 192, CLAUSE: 1\n\nX6734 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3783 [label="3783: quot(0, s(0), s(s(s(s(s(s(0)))))), X6734), SCOPE: 192, CLAUSE: 2 | quot(0, s(0), s(s(s(s(s(s(0)))))), X6734), SCOPE: 192, CLAUSE: 3\n\nX6734 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3785 [label="3785: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3786 [label="3786: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3787 [label="3787: quot(0, s(0), s(s(s(s(s(s(0)))))), X6734), SCOPE: 192, CLAUSE: 3\n\nX6734 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3788 [label="3788: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3791 [label="3791: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3793 [label="3793: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3794 [label="3794: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3796 [label="3796: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3800 [label="3800: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3803 [label="3803: quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6780)\n\nX6780 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3804 [label="3804: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3808 [label="3808: quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6780), SCOPE: 193, CLAUSE: 1 | quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6780), SCOPE: 193, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6780), SCOPE: 193, CLAUSE: 3\n\nX6780 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3809 [label="3809: quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6780), SCOPE: 193, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6780), SCOPE: 193, CLAUSE: 3\n\nX6780 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3821 [label="3821: quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6780), SCOPE: 193, CLAUSE: 2\n\nX6780 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3822 [label="3822: quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6780), SCOPE: 193, CLAUSE: 3\n\nX6780 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3835 [label="3835: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6819)\n\nX6819 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3838 [label="3838: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6819), SCOPE: 194, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6819), SCOPE: 194, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6819), SCOPE: 194, CLAUSE: 3\n\nX6819 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3841 [label="3841: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6819), SCOPE: 194, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6819), SCOPE: 194, CLAUSE: 3\n\nX6819 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3846 [label="3846: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6819), SCOPE: 194, CLAUSE: 2\n\nX6819 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3847 [label="3847: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6819), SCOPE: 194, CLAUSE: 3\n\nX6819 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3853 [label="3853: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X6858)\n\nX6858 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3857 [label="3857: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X6858), SCOPE: 195, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X6858), SCOPE: 195, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X6858), SCOPE: 195, CLAUSE: 3\n\nX6858 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3858 [label="3858: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X6858), SCOPE: 195, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X6858), SCOPE: 195, CLAUSE: 3\n\nX6858 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3863 [label="3863: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X6858), SCOPE: 195, CLAUSE: 2\n\nX6858 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3864 [label="3864: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X6858), SCOPE: 195, CLAUSE: 3\n\nX6858 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3869 [label="3869: quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X6897)\n\nX6897 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3872 [label="3872: quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X6897), SCOPE: 196, CLAUSE: 1 | quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X6897), SCOPE: 196, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X6897), SCOPE: 196, CLAUSE: 3\n\nX6897 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3873 [label="3873: quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X6897), SCOPE: 196, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X6897), SCOPE: 196, CLAUSE: 3\n\nX6897 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3878 [label="3878: quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X6897), SCOPE: 196, CLAUSE: 2\n\nX6897 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3879 [label="3879: quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X6897), SCOPE: 196, CLAUSE: 3\n\nX6897 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3885 [label="3885: quot(s(0), s(0), s(s(s(s(s(0))))), X6936)\n\nX6936 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3887 [label="3887: quot(s(0), s(0), s(s(s(s(s(0))))), X6936), SCOPE: 197, CLAUSE: 1 | quot(s(0), s(0), s(s(s(s(s(0))))), X6936), SCOPE: 197, CLAUSE: 2 | quot(s(0), s(0), s(s(s(s(s(0))))), X6936), SCOPE: 197, CLAUSE: 3\n\nX6936 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3889 [label="3889: quot(s(0), s(0), s(s(s(s(s(0))))), X6936), SCOPE: 197, CLAUSE: 2 | quot(s(0), s(0), s(s(s(s(s(0))))), X6936), SCOPE: 197, CLAUSE: 3\n\nX6936 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3893 [label="3893: quot(s(0), s(0), s(s(s(s(s(0))))), X6936), SCOPE: 197, CLAUSE: 2\n\nX6936 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3894 [label="3894: quot(s(0), s(0), s(s(s(s(s(0))))), X6936), SCOPE: 197, CLAUSE: 3\n\nX6936 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3901 [label="3901: quot(0, 0, s(s(s(s(s(0))))), X6975)\n\nX6975 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3904 [label="3904: quot(0, 0, s(s(s(s(s(0))))), X6975), SCOPE: 198, CLAUSE: 1 | quot(0, 0, s(s(s(s(s(0))))), X6975), SCOPE: 198, CLAUSE: 2 | quot(0, 0, s(s(s(s(s(0))))), X6975), SCOPE: 198, CLAUSE: 3\n\nX6975 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3907 [label="3907: quot(0, 0, s(s(s(s(s(0))))), X6975), SCOPE: 198, CLAUSE: 2 | quot(0, 0, s(s(s(s(s(0))))), X6975), SCOPE: 198, CLAUSE: 3\n\nX6975 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3908 [label="3908: quot(0, 0, s(s(s(s(s(0))))), X6975), SCOPE: 198, CLAUSE: 3\n\nX6975 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3912 [label="3912: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6999)\n\nX6999 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3916 [label="3916: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3917 [label="3917: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3921 [label="3921: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3922 [label="3922: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3924 [label="3924: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3927 [label="3927: quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X7028)\n\nX7028 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3928 [label="3928: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3934 [label="3934: quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X7028), SCOPE: 199, CLAUSE: 1 | quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X7028), SCOPE: 199, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X7028), SCOPE: 199, CLAUSE: 3\n\nX7028 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3937 [label="3937: quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X7028), SCOPE: 199, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X7028), SCOPE: 199, CLAUSE: 3\n\nX7028 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3943 [label="3943: quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X7028), SCOPE: 199, CLAUSE: 2\n\nX7028 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3944 [label="3944: quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X7028), SCOPE: 199, CLAUSE: 3\n\nX7028 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3951 [label="3951: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X7067)\n\nX7067 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3954 [label="3954: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X7067), SCOPE: 200, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X7067), SCOPE: 200, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X7067), SCOPE: 200, CLAUSE: 3\n\nX7067 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3955 [label="3955: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X7067), SCOPE: 200, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X7067), SCOPE: 200, CLAUSE: 3\n\nX7067 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3959 [label="3959: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X7067), SCOPE: 200, CLAUSE: 2\n\nX7067 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3960 [label="3960: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X7067), SCOPE: 200, CLAUSE: 3\n\nX7067 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3968 [label="3968: quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X7106)\n\nX7106 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3971 [label="3971: quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X7106), SCOPE: 201, CLAUSE: 1 | quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X7106), SCOPE: 201, CLAUSE: 2 | quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X7106), SCOPE: 201, CLAUSE: 3\n\nX7106 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3972 [label="3972: quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X7106), SCOPE: 201, CLAUSE: 2 | quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X7106), SCOPE: 201, CLAUSE: 3\n\nX7106 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3975 [label="3975: quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X7106), SCOPE: 201, CLAUSE: 2\n\nX7106 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3976 [label="3976: quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X7106), SCOPE: 201, CLAUSE: 3\n\nX7106 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3983 [label="3983: quot(s(s(0)), s(0), s(s(s(s(0)))), X7145)\n\nX7145 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3986 [label="3986: quot(s(s(0)), s(0), s(s(s(s(0)))), X7145), SCOPE: 202, CLAUSE: 1 | quot(s(s(0)), s(0), s(s(s(s(0)))), X7145), SCOPE: 202, CLAUSE: 2 | quot(s(s(0)), s(0), s(s(s(s(0)))), X7145), SCOPE: 202, CLAUSE: 3\n\nX7145 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3987 [label="3987: quot(s(s(0)), s(0), s(s(s(s(0)))), X7145), SCOPE: 202, CLAUSE: 2 | quot(s(s(0)), s(0), s(s(s(s(0)))), X7145), SCOPE: 202, CLAUSE: 3\n\nX7145 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3991 [label="3991: quot(s(s(0)), s(0), s(s(s(s(0)))), X7145), SCOPE: 202, CLAUSE: 2\n\nX7145 is free", fontsize=16, style=filled, fillcolor=lightyellow];
3992 [label="3992: quot(s(s(0)), s(0), s(s(s(s(0)))), X7145), SCOPE: 202, CLAUSE: 3\n\nX7145 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4000 [label="4000: quot(s(0), 0, s(s(s(s(0)))), X7184)\n\nX7184 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4001 [label="4001: quot(s(0), 0, s(s(s(s(0)))), X7184), SCOPE: 203, CLAUSE: 1 | quot(s(0), 0, s(s(s(s(0)))), X7184), SCOPE: 203, CLAUSE: 2 | quot(s(0), 0, s(s(s(s(0)))), X7184), SCOPE: 203, CLAUSE: 3\n\nX7184 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4002 [label="4002: quot(s(0), 0, s(s(s(s(0)))), X7184), SCOPE: 203, CLAUSE: 2 | quot(s(0), 0, s(s(s(s(0)))), X7184), SCOPE: 203, CLAUSE: 3\n\nX7184 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4003 [label="4003: quot(s(0), 0, s(s(s(s(0)))), X7184), SCOPE: 203, CLAUSE: 3\n\nX7184 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4012 [label="4012: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X7210)\n\nX7210 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4013 [label="4013: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4015 [label="4015: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4017 [label="4017: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4018 [label="4018: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4027 [label="4027: quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X7238)\n\nX7238 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4028 [label="4028: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4031 [label="4031: quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X7238), SCOPE: 204, CLAUSE: 1 | quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X7238), SCOPE: 204, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X7238), SCOPE: 204, CLAUSE: 3\n\nX7238 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4032 [label="4032: quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X7238), SCOPE: 204, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X7238), SCOPE: 204, CLAUSE: 3\n\nX7238 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4039 [label="4039: quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X7238), SCOPE: 204, CLAUSE: 2\n\nX7238 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4040 [label="4040: quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X7238), SCOPE: 204, CLAUSE: 3\n\nX7238 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4045 [label="4045: quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X7277)\n\nX7277 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4048 [label="4048: quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X7277), SCOPE: 205, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X7277), SCOPE: 205, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X7277), SCOPE: 205, CLAUSE: 3\n\nX7277 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4049 [label="4049: quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X7277), SCOPE: 205, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X7277), SCOPE: 205, CLAUSE: 3\n\nX7277 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4054 [label="4054: quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X7277), SCOPE: 205, CLAUSE: 2\n\nX7277 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4055 [label="4055: quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X7277), SCOPE: 205, CLAUSE: 3\n\nX7277 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4060 [label="4060: quot(s(s(s(0))), s(0), s(s(s(0))), X7316)\n\nX7316 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4064 [label="4064: quot(s(s(s(0))), s(0), s(s(s(0))), X7316), SCOPE: 206, CLAUSE: 1 | quot(s(s(s(0))), s(0), s(s(s(0))), X7316), SCOPE: 206, CLAUSE: 2 | quot(s(s(s(0))), s(0), s(s(s(0))), X7316), SCOPE: 206, CLAUSE: 3\n\nX7316 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4067 [label="4067: quot(s(s(s(0))), s(0), s(s(s(0))), X7316), SCOPE: 206, CLAUSE: 2 | quot(s(s(s(0))), s(0), s(s(s(0))), X7316), SCOPE: 206, CLAUSE: 3\n\nX7316 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4073 [label="4073: quot(s(s(s(0))), s(0), s(s(s(0))), X7316), SCOPE: 206, CLAUSE: 2\n\nX7316 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4074 [label="4074: quot(s(s(s(0))), s(0), s(s(s(0))), X7316), SCOPE: 206, CLAUSE: 3\n\nX7316 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4078 [label="4078: quot(s(s(0)), 0, s(s(s(0))), X7355)\n\nX7355 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4083 [label="4083: quot(s(s(0)), 0, s(s(s(0))), X7355), SCOPE: 207, CLAUSE: 1 | quot(s(s(0)), 0, s(s(s(0))), X7355), SCOPE: 207, CLAUSE: 2 | quot(s(s(0)), 0, s(s(s(0))), X7355), SCOPE: 207, CLAUSE: 3\n\nX7355 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4085 [label="4085: quot(s(s(0)), 0, s(s(s(0))), X7355), SCOPE: 207, CLAUSE: 2 | quot(s(s(0)), 0, s(s(s(0))), X7355), SCOPE: 207, CLAUSE: 3\n\nX7355 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4086 [label="4086: quot(s(s(0)), 0, s(s(s(0))), X7355), SCOPE: 207, CLAUSE: 3\n\nX7355 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4090 [label="4090: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X7381)\n\nX7381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4096 [label="4096: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4097 [label="4097: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4100 [label="4100: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4107 [label="4107: quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X7406)\n\nX7406 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4108 [label="4108: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4109 [label="4109: quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X7406), SCOPE: 208, CLAUSE: 1 | quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X7406), SCOPE: 208, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X7406), SCOPE: 208, CLAUSE: 3\n\nX7406 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4112 [label="4112: quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X7406), SCOPE: 208, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X7406), SCOPE: 208, CLAUSE: 3\n\nX7406 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4115 [label="4115: quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X7406), SCOPE: 208, CLAUSE: 2\n\nX7406 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4116 [label="4116: quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X7406), SCOPE: 208, CLAUSE: 3\n\nX7406 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4123 [label="4123: quot(s(s(s(s(0)))), s(0), s(s(0)), X7445)\n\nX7445 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4128 [label="4128: quot(s(s(s(s(0)))), s(0), s(s(0)), X7445), SCOPE: 209, CLAUSE: 1 | quot(s(s(s(s(0)))), s(0), s(s(0)), X7445), SCOPE: 209, CLAUSE: 2 | quot(s(s(s(s(0)))), s(0), s(s(0)), X7445), SCOPE: 209, CLAUSE: 3\n\nX7445 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4129 [label="4129: quot(s(s(s(s(0)))), s(0), s(s(0)), X7445), SCOPE: 209, CLAUSE: 2 | quot(s(s(s(s(0)))), s(0), s(s(0)), X7445), SCOPE: 209, CLAUSE: 3\n\nX7445 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4132 [label="4132: quot(s(s(s(s(0)))), s(0), s(s(0)), X7445), SCOPE: 209, CLAUSE: 2\n\nX7445 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4133 [label="4133: quot(s(s(s(s(0)))), s(0), s(s(0)), X7445), SCOPE: 209, CLAUSE: 3\n\nX7445 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4140 [label="4140: quot(s(s(s(0))), 0, s(s(0)), X7484)\n\nX7484 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4142 [label="4142: quot(s(s(s(0))), 0, s(s(0)), X7484), SCOPE: 210, CLAUSE: 1 | quot(s(s(s(0))), 0, s(s(0)), X7484), SCOPE: 210, CLAUSE: 2 | quot(s(s(s(0))), 0, s(s(0)), X7484), SCOPE: 210, CLAUSE: 3\n\nX7484 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4145 [label="4145: quot(s(s(s(0))), 0, s(s(0)), X7484), SCOPE: 210, CLAUSE: 2 | quot(s(s(s(0))), 0, s(s(0)), X7484), SCOPE: 210, CLAUSE: 3\n\nX7484 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4148 [label="4148: quot(s(s(s(0))), 0, s(s(0)), X7484), SCOPE: 210, CLAUSE: 3\n\nX7484 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4156 [label="4156: quot(s(s(s(0))), s(s(0)), s(s(0)), X7510)\n\nX7510 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4165 [label="4165: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4167 [label="4167: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4172 [label="4172: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4176 [label="4176: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4178 [label="4178: times(T769, s(s(T767)), X5608)\n\nT767 is ground\nT769 is ground\nX5608 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4179 [label="4179: neq(s(s(s(s(s(s(s(T767))))))), T920)\n\nT767 is ground\nT920 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4186 [label="4186: pr(s(s(s(s(s(s(s(T761))))))), s(T761)), SCOPE: 211, CLAUSE: 5 | pr(s(s(s(s(s(s(s(T761))))))), s(T761)), SCOPE: 211, CLAUSE: 6\n\nT761 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4189 [label="4189: pr(s(s(s(s(s(s(s(T761))))))), s(T761)), SCOPE: 211, CLAUSE: 5\n\nT761 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4190 [label="4190: pr(s(s(s(s(s(s(s(T761))))))), s(T761)), SCOPE: 211, CLAUSE: 6\n\nT761 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4191 [label="4191: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4192 [label="4192: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4194 [label="4194: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4196 [label="4196: ','(not_divides(s(s(T937)), s(s(s(s(s(s(s(s(T937))))))))), pr(s(s(s(s(s(s(s(s(T937)))))))), s(T937)))\n\nT937 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4197 [label="4197: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4200 [label="N34: ','(not_divides(s(s(T937)), s(T939)), pr(s(T939), s(T937)))\n\nT937 is ground\nT939 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4203 [label="N36: not_divides(s(s(T937)), s(T939))\n\nT937 is ground\nT939 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4204 [label="N38: pr(s(T939), s(T937))\n\nT937 is ground\nT939 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4207 [label="4207: not_divides(s(s(T937)), s(T939)), SCOPE: 212, CLAUSE: 7\n\nT937 is ground\nT939 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4211 [label="N37: ','(div(s(T951), s(s(T950)), X7570), ','(times(X7570, s(s(T950)), X7571), neq(s(T951), X7571)))\n\nT950 is ground\nT951 is ground\nX7570 is free\nX7571 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4214 [label="N39: div(s(T951), s(s(T950)), X7570)\n\nT950 is ground\nT951 is ground\nX7570 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4215 [label="N45: ','(times(T954, s(s(T950)), X7571), neq(s(T951), X7571))\n\nT950 is ground\nT951 is ground\nT954 is ground\nX7571 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4218 [label="4218: div(s(T951), s(s(T950)), X7570), SCOPE: 213, CLAUSE: 0\n\nT950 is ground\nT951 is ground\nX7570 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4223 [label="4223: quot(s(T961), s(s(T962)), s(s(T962)), X7595)\n\nT961 is ground\nT962 is ground\nX7595 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4225 [label="4225: quot(s(T961), s(s(T962)), s(s(T962)), X7595), SCOPE: 214, CLAUSE: 1 | quot(s(T961), s(s(T962)), s(s(T962)), X7595), SCOPE: 214, CLAUSE: 2 | quot(s(T961), s(s(T962)), s(s(T962)), X7595), SCOPE: 214, CLAUSE: 3\n\nT961 is ground\nT962 is ground\nX7595 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4226 [label="4226: quot(s(T961), s(s(T962)), s(s(T962)), X7595), SCOPE: 214, CLAUSE: 2 | quot(s(T961), s(s(T962)), s(s(T962)), X7595), SCOPE: 214, CLAUSE: 3\n\nT961 is ground\nT962 is ground\nX7595 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4234 [label="4234: quot(s(T961), s(s(T962)), s(s(T962)), X7595), SCOPE: 214, CLAUSE: 2\n\nT961 is ground\nT962 is ground\nX7595 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4235 [label="4235: quot(s(T961), s(s(T962)), s(s(T962)), X7595), SCOPE: 214, CLAUSE: 3\n\nT961 is ground\nT962 is ground\nX7595 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4244 [label="4244: quot(T975, s(T976), s(s(T976)), X7634)\n\nT975 is ground\nT976 is ground\nX7634 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4249 [label="4249: quot(T975, s(T976), s(s(T976)), X7634), SCOPE: 215, CLAUSE: 1 | quot(T975, s(T976), s(s(T976)), X7634), SCOPE: 215, CLAUSE: 2 | quot(T975, s(T976), s(s(T976)), X7634), SCOPE: 215, CLAUSE: 3\n\nT975 is ground\nT976 is ground\nX7634 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4251 [label="4251: quot(T975, s(T976), s(s(T976)), X7634), SCOPE: 215, CLAUSE: 1\n\nT975 is ground\nT976 is ground\nX7634 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4252 [label="4252: quot(T975, s(T976), s(s(T976)), X7634), SCOPE: 215, CLAUSE: 2 | quot(T975, s(T976), s(s(T976)), X7634), SCOPE: 215, CLAUSE: 3\n\nT975 is ground\nT976 is ground\nX7634 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4260 [label="4260: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4261 [label="4261: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4262 [label="4262: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4268 [label="4268: quot(T975, s(T976), s(s(T976)), X7634), SCOPE: 215, CLAUSE: 2\n\nT975 is ground\nT976 is ground\nX7634 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4269 [label="4269: quot(T975, s(T976), s(s(T976)), X7634), SCOPE: 215, CLAUSE: 3\n\nT975 is ground\nT976 is ground\nX7634 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4277 [label="N3: quot(T992, T993, s(s(T993)), X7673)\n\nT992 is ground\nT993 is ground\nX7673 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4278 [label="4278: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4282 [label="4282: quot(T992, T993, s(s(T993)), X7673), SCOPE: 216, CLAUSE: 1 | quot(T992, T993, s(s(T993)), X7673), SCOPE: 216, CLAUSE: 2 | quot(T992, T993, s(s(T993)), X7673), SCOPE: 216, CLAUSE: 3\n\nT992 is ground\nT993 is ground\nX7673 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4285 [label="4285: quot(T992, T993, s(s(T993)), X7673), SCOPE: 216, CLAUSE: 1\n\nT992 is ground\nT993 is ground\nX7673 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4286 [label="4286: quot(T992, T993, s(s(T993)), X7673), SCOPE: 216, CLAUSE: 2 | quot(T992, T993, s(s(T993)), X7673), SCOPE: 216, CLAUSE: 3\n\nT992 is ground\nT993 is ground\nX7673 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4290 [label="4290: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4291 [label="4291: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4292 [label="4292: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4298 [label="4298: quot(T992, T993, s(s(T993)), X7673), SCOPE: 216, CLAUSE: 2\n\nT992 is ground\nT993 is ground\nX7673 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4299 [label="4299: quot(T992, T993, s(s(T993)), X7673), SCOPE: 216, CLAUSE: 3\n\nT992 is ground\nT993 is ground\nX7673 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4307 [label="4307: quot(T1009, T1010, s(s(s(T1010))), X7712)\n\nT1009 is ground\nT1010 is ground\nX7712 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4308 [label="4308: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4314 [label="4314: quot(T1009, T1010, s(s(s(T1010))), X7712), SCOPE: 217, CLAUSE: 1 | quot(T1009, T1010, s(s(s(T1010))), X7712), SCOPE: 217, CLAUSE: 2 | quot(T1009, T1010, s(s(s(T1010))), X7712), SCOPE: 217, CLAUSE: 3\n\nT1009 is ground\nT1010 is ground\nX7712 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4318 [label="4318: quot(T1009, T1010, s(s(s(T1010))), X7712), SCOPE: 217, CLAUSE: 1\n\nT1009 is ground\nT1010 is ground\nX7712 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4319 [label="4319: quot(T1009, T1010, s(s(s(T1010))), X7712), SCOPE: 217, CLAUSE: 2 | quot(T1009, T1010, s(s(s(T1010))), X7712), SCOPE: 217, CLAUSE: 3\n\nT1009 is ground\nT1010 is ground\nX7712 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4323 [label="4323: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4324 [label="4324: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4327 [label="4327: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4331 [label="4331: quot(T1009, T1010, s(s(s(T1010))), X7712), SCOPE: 217, CLAUSE: 2\n\nT1009 is ground\nT1010 is ground\nX7712 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4332 [label="4332: quot(T1009, T1010, s(s(s(T1010))), X7712), SCOPE: 217, CLAUSE: 3\n\nT1009 is ground\nT1010 is ground\nX7712 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4338 [label="4338: quot(T1026, T1027, s(s(s(s(T1027)))), X7751)\n\nT1026 is ground\nT1027 is ground\nX7751 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4339 [label="4339: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4347 [label="4347: quot(T1026, T1027, s(s(s(s(T1027)))), X7751), SCOPE: 218, CLAUSE: 1 | quot(T1026, T1027, s(s(s(s(T1027)))), X7751), SCOPE: 218, CLAUSE: 2 | quot(T1026, T1027, s(s(s(s(T1027)))), X7751), SCOPE: 218, CLAUSE: 3\n\nT1026 is ground\nT1027 is ground\nX7751 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4349 [label="4349: quot(T1026, T1027, s(s(s(s(T1027)))), X7751), SCOPE: 218, CLAUSE: 1\n\nT1026 is ground\nT1027 is ground\nX7751 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4350 [label="4350: quot(T1026, T1027, s(s(s(s(T1027)))), X7751), SCOPE: 218, CLAUSE: 2 | quot(T1026, T1027, s(s(s(s(T1027)))), X7751), SCOPE: 218, CLAUSE: 3\n\nT1026 is ground\nT1027 is ground\nX7751 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4355 [label="4355: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4356 [label="4356: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4357 [label="4357: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4363 [label="4363: quot(T1026, T1027, s(s(s(s(T1027)))), X7751), SCOPE: 218, CLAUSE: 2\n\nT1026 is ground\nT1027 is ground\nX7751 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4364 [label="4364: quot(T1026, T1027, s(s(s(s(T1027)))), X7751), SCOPE: 218, CLAUSE: 3\n\nT1026 is ground\nT1027 is ground\nX7751 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4372 [label="4372: quot(T1043, T1044, s(s(s(s(s(T1044))))), X7790)\n\nT1043 is ground\nT1044 is ground\nX7790 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4373 [label="4373: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4377 [label="4377: quot(T1043, T1044, s(s(s(s(s(T1044))))), X7790), SCOPE: 219, CLAUSE: 1 | quot(T1043, T1044, s(s(s(s(s(T1044))))), X7790), SCOPE: 219, CLAUSE: 2 | quot(T1043, T1044, s(s(s(s(s(T1044))))), X7790), SCOPE: 219, CLAUSE: 3\n\nT1043 is ground\nT1044 is ground\nX7790 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4381 [label="4381: quot(T1043, T1044, s(s(s(s(s(T1044))))), X7790), SCOPE: 219, CLAUSE: 1\n\nT1043 is ground\nT1044 is ground\nX7790 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4382 [label="4382: quot(T1043, T1044, s(s(s(s(s(T1044))))), X7790), SCOPE: 219, CLAUSE: 2 | quot(T1043, T1044, s(s(s(s(s(T1044))))), X7790), SCOPE: 219, CLAUSE: 3\n\nT1043 is ground\nT1044 is ground\nX7790 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4385 [label="4385: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4386 [label="4386: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4387 [label="4387: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4393 [label="4393: quot(T1043, T1044, s(s(s(s(s(T1044))))), X7790), SCOPE: 219, CLAUSE: 2\n\nT1043 is ground\nT1044 is ground\nX7790 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4394 [label="4394: quot(T1043, T1044, s(s(s(s(s(T1044))))), X7790), SCOPE: 219, CLAUSE: 3\n\nT1043 is ground\nT1044 is ground\nX7790 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4405 [label="4405: quot(T1060, T1061, s(s(s(s(s(s(T1061)))))), X7829)\n\nT1060 is ground\nT1061 is ground\nX7829 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4406 [label="4406: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4410 [label="4410: quot(T1060, T1061, s(s(s(s(s(s(T1061)))))), X7829), SCOPE: 220, CLAUSE: 1 | quot(T1060, T1061, s(s(s(s(s(s(T1061)))))), X7829), SCOPE: 220, CLAUSE: 2 | quot(T1060, T1061, s(s(s(s(s(s(T1061)))))), X7829), SCOPE: 220, CLAUSE: 3\n\nT1060 is ground\nT1061 is ground\nX7829 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4413 [label="4413: quot(T1060, T1061, s(s(s(s(s(s(T1061)))))), X7829), SCOPE: 220, CLAUSE: 1\n\nT1060 is ground\nT1061 is ground\nX7829 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4414 [label="4414: quot(T1060, T1061, s(s(s(s(s(s(T1061)))))), X7829), SCOPE: 220, CLAUSE: 2 | quot(T1060, T1061, s(s(s(s(s(s(T1061)))))), X7829), SCOPE: 220, CLAUSE: 3\n\nT1060 is ground\nT1061 is ground\nX7829 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4418 [label="4418: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4419 [label="4419: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4420 [label="4420: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4426 [label="4426: quot(T1060, T1061, s(s(s(s(s(s(T1061)))))), X7829), SCOPE: 220, CLAUSE: 2\n\nT1060 is ground\nT1061 is ground\nX7829 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4427 [label="4427: quot(T1060, T1061, s(s(s(s(s(s(T1061)))))), X7829), SCOPE: 220, CLAUSE: 3\n\nT1060 is ground\nT1061 is ground\nX7829 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4436 [label="4436: quot(T1077, T1078, s(s(s(s(s(s(s(T1078))))))), X7868)\n\nT1077 is ground\nT1078 is ground\nX7868 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4437 [label="4437: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4439 [label="4439: quot(T1077, T1078, s(s(s(s(s(s(s(T1078))))))), X7868), SCOPE: 221, CLAUSE: 1 | quot(T1077, T1078, s(s(s(s(s(s(s(T1078))))))), X7868), SCOPE: 221, CLAUSE: 2 | quot(T1077, T1078, s(s(s(s(s(s(s(T1078))))))), X7868), SCOPE: 221, CLAUSE: 3\n\nT1077 is ground\nT1078 is ground\nX7868 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4443 [label="4443: quot(T1077, T1078, s(s(s(s(s(s(s(T1078))))))), X7868), SCOPE: 221, CLAUSE: 1\n\nT1077 is ground\nT1078 is ground\nX7868 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4444 [label="4444: quot(T1077, T1078, s(s(s(s(s(s(s(T1078))))))), X7868), SCOPE: 221, CLAUSE: 2 | quot(T1077, T1078, s(s(s(s(s(s(s(T1078))))))), X7868), SCOPE: 221, CLAUSE: 3\n\nT1077 is ground\nT1078 is ground\nX7868 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4445 [label="4445: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4446 [label="4446: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4447 [label="4447: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4453 [label="4453: quot(T1077, T1078, s(s(s(s(s(s(s(T1078))))))), X7868), SCOPE: 221, CLAUSE: 2\n\nT1077 is ground\nT1078 is ground\nX7868 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4454 [label="4454: quot(T1077, T1078, s(s(s(s(s(s(s(T1078))))))), X7868), SCOPE: 221, CLAUSE: 3\n\nT1077 is ground\nT1078 is ground\nX7868 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4459 [label="4459: quot(T1094, T1095, s(s(s(s(s(s(s(s(T1095)))))))), X7907)\n\nT1094 is ground\nT1095 is ground\nX7907 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4460 [label="4460: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4465 [label="N2: quot(T1094, T1095, s(T1098), X7907)\n\nT1094 is ground\nT1095 is ground\nT1098 is ground\nX7907 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4469 [label="4469: quot(T1094, T1095, s(T1098), X7907), SCOPE: 222, CLAUSE: 1 | quot(T1094, T1095, s(T1098), X7907), SCOPE: 222, CLAUSE: 2 | quot(T1094, T1095, s(T1098), X7907), SCOPE: 222, CLAUSE: 3\n\nT1094 is ground\nT1095 is ground\nT1098 is ground\nX7907 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4470 [label="4470: quot(T1094, T1095, s(T1098), X7907), SCOPE: 222, CLAUSE: 1\n\nT1094 is ground\nT1095 is ground\nT1098 is ground\nX7907 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4471 [label="4471: quot(T1094, T1095, s(T1098), X7907), SCOPE: 222, CLAUSE: 2 | quot(T1094, T1095, s(T1098), X7907), SCOPE: 222, CLAUSE: 3\n\nT1094 is ground\nT1095 is ground\nT1098 is ground\nX7907 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4475 [label="4475: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4476 [label="4476: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4477 [label="4477: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4483 [label="4483: quot(T1094, T1095, s(T1098), X7907), SCOPE: 222, CLAUSE: 2\n\nT1094 is ground\nT1095 is ground\nT1098 is ground\nX7907 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4484 [label="4484: quot(T1094, T1095, s(T1098), X7907), SCOPE: 222, CLAUSE: 3\n\nT1094 is ground\nT1095 is ground\nT1098 is ground\nX7907 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4493 [label="4493: quot(T1125, T1126, s(T1127), X7950)\n\nT1125 is ground\nT1126 is ground\nT1127 is ground\nX7950 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4494 [label="4494: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4505 [label="4505: quot(T1136, s(T1137), s(T1137), X7966)\n\nT1136 is ground\nT1137 is ground\nX7966 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4506 [label="4506: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4511 [label="4511: quot(T1136, s(T1137), s(T1137), X7966), SCOPE: 223, CLAUSE: 1 | quot(T1136, s(T1137), s(T1137), X7966), SCOPE: 223, CLAUSE: 2 | quot(T1136, s(T1137), s(T1137), X7966), SCOPE: 223, CLAUSE: 3\n\nT1136 is ground\nT1137 is ground\nX7966 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4515 [label="4515: quot(T1136, s(T1137), s(T1137), X7966), SCOPE: 223, CLAUSE: 1\n\nT1136 is ground\nT1137 is ground\nX7966 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4516 [label="4516: quot(T1136, s(T1137), s(T1137), X7966), SCOPE: 223, CLAUSE: 2 | quot(T1136, s(T1137), s(T1137), X7966), SCOPE: 223, CLAUSE: 3\n\nT1136 is ground\nT1137 is ground\nX7966 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4521 [label="4521: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4522 [label="4522: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4523 [label="4523: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4526 [label="4526: quot(T1136, s(T1137), s(T1137), X7966), SCOPE: 223, CLAUSE: 2\n\nT1136 is ground\nT1137 is ground\nX7966 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4527 [label="4527: quot(T1136, s(T1137), s(T1137), X7966), SCOPE: 223, CLAUSE: 3\n\nT1136 is ground\nT1137 is ground\nX7966 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4533 [label="4533: quot(T1153, T1154, s(T1154), X8005)\n\nT1153 is ground\nT1154 is ground\nX8005 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4534 [label="4534: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4540 [label="4540: quot(T1153, T1154, s(T1154), X8005), SCOPE: 224, CLAUSE: 1 | quot(T1153, T1154, s(T1154), X8005), SCOPE: 224, CLAUSE: 2 | quot(T1153, T1154, s(T1154), X8005), SCOPE: 224, CLAUSE: 3\n\nT1153 is ground\nT1154 is ground\nX8005 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4544 [label="4544: quot(T1153, T1154, s(T1154), X8005), SCOPE: 224, CLAUSE: 1\n\nT1153 is ground\nT1154 is ground\nX8005 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4545 [label="4545: quot(T1153, T1154, s(T1154), X8005), SCOPE: 224, CLAUSE: 2 | quot(T1153, T1154, s(T1154), X8005), SCOPE: 224, CLAUSE: 3\n\nT1153 is ground\nT1154 is ground\nX8005 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4551 [label="4551: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4552 [label="4552: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4553 [label="4553: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4558 [label="4558: quot(T1153, T1154, s(T1154), X8005), SCOPE: 224, CLAUSE: 2\n\nT1153 is ground\nT1154 is ground\nX8005 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4559 [label="4559: quot(T1153, T1154, s(T1154), X8005), SCOPE: 224, CLAUSE: 3\n\nT1153 is ground\nT1154 is ground\nX8005 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4565 [label="4565: quot(T1170, T1171, s(s(T1171)), X8044)\n\nT1170 is ground\nT1171 is ground\nX8044 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4566 [label="4566: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4573 [label="N4: quot(T1176, s(0), s(0), X8060)\n\nT1176 is ground\nX8060 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4574 [label="4574: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4576 [label="4576: quot(T1176, s(0), s(0), X8060), SCOPE: 225, CLAUSE: 1 | quot(T1176, s(0), s(0), X8060), SCOPE: 225, CLAUSE: 2 | quot(T1176, s(0), s(0), X8060), SCOPE: 225, CLAUSE: 3\n\nT1176 is ground\nX8060 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4580 [label="4580: quot(T1176, s(0), s(0), X8060), SCOPE: 225, CLAUSE: 1\n\nT1176 is ground\nX8060 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4581 [label="4581: quot(T1176, s(0), s(0), X8060), SCOPE: 225, CLAUSE: 2 | quot(T1176, s(0), s(0), X8060), SCOPE: 225, CLAUSE: 3\n\nT1176 is ground\nX8060 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4583 [label="4583: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4584 [label="4584: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4585 [label="4585: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4594 [label="4594: quot(T1176, s(0), s(0), X8060), SCOPE: 225, CLAUSE: 2\n\nT1176 is ground\nX8060 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4595 [label="4595: quot(T1176, s(0), s(0), X8060), SCOPE: 225, CLAUSE: 3\n\nT1176 is ground\nX8060 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4604 [label="4604: quot(T1181, 0, s(0), X8099)\n\nT1181 is ground\nX8099 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4605 [label="4605: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4610 [label="4610: quot(T1181, 0, s(0), X8099), SCOPE: 226, CLAUSE: 1 | quot(T1181, 0, s(0), X8099), SCOPE: 226, CLAUSE: 2 | quot(T1181, 0, s(0), X8099), SCOPE: 226, CLAUSE: 3\n\nT1181 is ground\nX8099 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4611 [label="4611: quot(T1181, 0, s(0), X8099), SCOPE: 226, CLAUSE: 2 | quot(T1181, 0, s(0), X8099), SCOPE: 226, CLAUSE: 3\n\nT1181 is ground\nX8099 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4613 [label="4613: quot(T1181, 0, s(0), X8099), SCOPE: 226, CLAUSE: 3\n\nT1181 is ground\nX8099 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4626 [label="4626: quot(T1185, s(0), s(0), X8125)\n\nT1185 is ground\nX8125 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4630 [label="4630: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4631 [label="4631: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4639 [label="N5: quot(T1190, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8147)\n\nT1190 is ground\nX8147 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4640 [label="4640: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4646 [label="4646: quot(T1190, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8147), SCOPE: 227, CLAUSE: 1 | quot(T1190, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8147), SCOPE: 227, CLAUSE: 2 | quot(T1190, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8147), SCOPE: 227, CLAUSE: 3\n\nT1190 is ground\nX8147 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4650 [label="4650: quot(T1190, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8147), SCOPE: 227, CLAUSE: 1\n\nT1190 is ground\nX8147 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4651 [label="4651: quot(T1190, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8147), SCOPE: 227, CLAUSE: 2 | quot(T1190, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8147), SCOPE: 227, CLAUSE: 3\n\nT1190 is ground\nX8147 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4654 [label="4654: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4655 [label="4655: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4658 [label="4658: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4664 [label="4664: quot(T1190, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8147), SCOPE: 227, CLAUSE: 2\n\nT1190 is ground\nX8147 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4665 [label="4665: quot(T1190, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8147), SCOPE: 227, CLAUSE: 3\n\nT1190 is ground\nX8147 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4674 [label="4674: quot(T1195, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8186)\n\nT1195 is ground\nX8186 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4675 [label="4675: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4681 [label="4681: quot(T1195, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8186), SCOPE: 228, CLAUSE: 1 | quot(T1195, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8186), SCOPE: 228, CLAUSE: 2 | quot(T1195, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8186), SCOPE: 228, CLAUSE: 3\n\nT1195 is ground\nX8186 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4682 [label="4682: quot(T1195, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8186), SCOPE: 228, CLAUSE: 1\n\nT1195 is ground\nX8186 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4683 [label="4683: quot(T1195, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8186), SCOPE: 228, CLAUSE: 2 | quot(T1195, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8186), SCOPE: 228, CLAUSE: 3\n\nT1195 is ground\nX8186 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4689 [label="4689: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4690 [label="4690: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4691 [label="4691: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4695 [label="4695: quot(T1195, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8186), SCOPE: 228, CLAUSE: 2\n\nT1195 is ground\nX8186 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4696 [label="4696: quot(T1195, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8186), SCOPE: 228, CLAUSE: 3\n\nT1195 is ground\nX8186 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4707 [label="4707: quot(T1200, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8225)\n\nT1200 is ground\nX8225 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4708 [label="4708: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4714 [label="4714: quot(T1200, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8225), SCOPE: 229, CLAUSE: 1 | quot(T1200, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8225), SCOPE: 229, CLAUSE: 2 | quot(T1200, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8225), SCOPE: 229, CLAUSE: 3\n\nT1200 is ground\nX8225 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4715 [label="4715: quot(T1200, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8225), SCOPE: 229, CLAUSE: 1\n\nT1200 is ground\nX8225 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4716 [label="4716: quot(T1200, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8225), SCOPE: 229, CLAUSE: 2 | quot(T1200, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8225), SCOPE: 229, CLAUSE: 3\n\nT1200 is ground\nX8225 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4721 [label="4721: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4722 [label="4722: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4723 [label="4723: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4727 [label="4727: quot(T1200, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8225), SCOPE: 229, CLAUSE: 2\n\nT1200 is ground\nX8225 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4728 [label="4728: quot(T1200, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8225), SCOPE: 229, CLAUSE: 3\n\nT1200 is ground\nX8225 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4739 [label="4739: quot(T1205, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8264)\n\nT1205 is ground\nX8264 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4740 [label="4740: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4746 [label="4746: quot(T1205, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8264), SCOPE: 230, CLAUSE: 1 | quot(T1205, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8264), SCOPE: 230, CLAUSE: 2 | quot(T1205, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8264), SCOPE: 230, CLAUSE: 3\n\nT1205 is ground\nX8264 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4749 [label="4749: quot(T1205, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8264), SCOPE: 230, CLAUSE: 1\n\nT1205 is ground\nX8264 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4750 [label="4750: quot(T1205, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8264), SCOPE: 230, CLAUSE: 2 | quot(T1205, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8264), SCOPE: 230, CLAUSE: 3\n\nT1205 is ground\nX8264 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4752 [label="4752: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4753 [label="4753: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4754 [label="4754: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4762 [label="4762: quot(T1205, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8264), SCOPE: 230, CLAUSE: 2\n\nT1205 is ground\nX8264 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4763 [label="4763: quot(T1205, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8264), SCOPE: 230, CLAUSE: 3\n\nT1205 is ground\nX8264 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4772 [label="4772: quot(T1210, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8303)\n\nT1210 is ground\nX8303 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4773 [label="4773: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4778 [label="4778: quot(T1210, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8303), SCOPE: 231, CLAUSE: 1 | quot(T1210, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8303), SCOPE: 231, CLAUSE: 2 | quot(T1210, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8303), SCOPE: 231, CLAUSE: 3\n\nT1210 is ground\nX8303 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4781 [label="4781: quot(T1210, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8303), SCOPE: 231, CLAUSE: 1\n\nT1210 is ground\nX8303 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4782 [label="4782: quot(T1210, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8303), SCOPE: 231, CLAUSE: 2 | quot(T1210, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8303), SCOPE: 231, CLAUSE: 3\n\nT1210 is ground\nX8303 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4786 [label="4786: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4787 [label="4787: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4788 [label="4788: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4792 [label="4792: quot(T1210, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8303), SCOPE: 231, CLAUSE: 2\n\nT1210 is ground\nX8303 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4793 [label="4793: quot(T1210, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8303), SCOPE: 231, CLAUSE: 3\n\nT1210 is ground\nX8303 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4801 [label="4801: quot(T1215, s(s(0)), s(s(s(s(s(s(s(0))))))), X8342)\n\nT1215 is ground\nX8342 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4802 [label="4802: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4806 [label="4806: quot(T1215, s(s(0)), s(s(s(s(s(s(s(0))))))), X8342), SCOPE: 232, CLAUSE: 1 | quot(T1215, s(s(0)), s(s(s(s(s(s(s(0))))))), X8342), SCOPE: 232, CLAUSE: 2 | quot(T1215, s(s(0)), s(s(s(s(s(s(s(0))))))), X8342), SCOPE: 232, CLAUSE: 3\n\nT1215 is ground\nX8342 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4809 [label="4809: quot(T1215, s(s(0)), s(s(s(s(s(s(s(0))))))), X8342), SCOPE: 232, CLAUSE: 1\n\nT1215 is ground\nX8342 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4810 [label="4810: quot(T1215, s(s(0)), s(s(s(s(s(s(s(0))))))), X8342), SCOPE: 232, CLAUSE: 2 | quot(T1215, s(s(0)), s(s(s(s(s(s(s(0))))))), X8342), SCOPE: 232, CLAUSE: 3\n\nT1215 is ground\nX8342 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4815 [label="4815: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4816 [label="4816: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4817 [label="4817: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4823 [label="4823: quot(T1215, s(s(0)), s(s(s(s(s(s(s(0))))))), X8342), SCOPE: 232, CLAUSE: 2\n\nT1215 is ground\nX8342 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4824 [label="4824: quot(T1215, s(s(0)), s(s(s(s(s(s(s(0))))))), X8342), SCOPE: 232, CLAUSE: 3\n\nT1215 is ground\nX8342 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4833 [label="4833: quot(T1220, s(0), s(s(s(s(s(s(s(0))))))), X8381)\n\nT1220 is ground\nX8381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4834 [label="4834: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4837 [label="4837: quot(T1220, s(0), s(s(s(s(s(s(s(0))))))), X8381), SCOPE: 233, CLAUSE: 1 | quot(T1220, s(0), s(s(s(s(s(s(s(0))))))), X8381), SCOPE: 233, CLAUSE: 2 | quot(T1220, s(0), s(s(s(s(s(s(s(0))))))), X8381), SCOPE: 233, CLAUSE: 3\n\nT1220 is ground\nX8381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4843 [label="4843: quot(T1220, s(0), s(s(s(s(s(s(s(0))))))), X8381), SCOPE: 233, CLAUSE: 1\n\nT1220 is ground\nX8381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4844 [label="4844: quot(T1220, s(0), s(s(s(s(s(s(s(0))))))), X8381), SCOPE: 233, CLAUSE: 2 | quot(T1220, s(0), s(s(s(s(s(s(s(0))))))), X8381), SCOPE: 233, CLAUSE: 3\n\nT1220 is ground\nX8381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4846 [label="4846: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4847 [label="4847: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4848 [label="4848: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4856 [label="4856: quot(T1220, s(0), s(s(s(s(s(s(s(0))))))), X8381), SCOPE: 233, CLAUSE: 2\n\nT1220 is ground\nX8381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4857 [label="4857: quot(T1220, s(0), s(s(s(s(s(s(s(0))))))), X8381), SCOPE: 233, CLAUSE: 3\n\nT1220 is ground\nX8381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4865 [label="4865: quot(T1225, 0, s(s(s(s(s(s(s(0))))))), X8420)\n\nT1225 is ground\nX8420 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4866 [label="4866: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4872 [label="4872: quot(T1225, 0, s(s(s(s(s(s(s(0))))))), X8420), SCOPE: 234, CLAUSE: 1 | quot(T1225, 0, s(s(s(s(s(s(s(0))))))), X8420), SCOPE: 234, CLAUSE: 2 | quot(T1225, 0, s(s(s(s(s(s(s(0))))))), X8420), SCOPE: 234, CLAUSE: 3\n\nT1225 is ground\nX8420 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4874 [label="4874: quot(T1225, 0, s(s(s(s(s(s(s(0))))))), X8420), SCOPE: 234, CLAUSE: 2 | quot(T1225, 0, s(s(s(s(s(s(s(0))))))), X8420), SCOPE: 234, CLAUSE: 3\n\nT1225 is ground\nX8420 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4877 [label="4877: quot(T1225, 0, s(s(s(s(s(s(s(0))))))), X8420), SCOPE: 234, CLAUSE: 3\n\nT1225 is ground\nX8420 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4890 [label="4890: quot(T1229, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8446)\n\nT1229 is ground\nX8446 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4899 [label="4899: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4905 [label="4905: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4906 [label="4906: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4909 [label="4909: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4910 [label="4910: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4913 [label="4913: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4914 [label="4914: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4921 [label="N6: quot(T1239, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8483)\n\nT1239 is ground\nX8483 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4922 [label="4922: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4931 [label="4931: quot(T1239, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8483), SCOPE: 235, CLAUSE: 1 | quot(T1239, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8483), SCOPE: 235, CLAUSE: 2 | quot(T1239, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8483), SCOPE: 235, CLAUSE: 3\n\nT1239 is ground\nX8483 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4934 [label="4934: quot(T1239, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8483), SCOPE: 235, CLAUSE: 1\n\nT1239 is ground\nX8483 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4935 [label="4935: quot(T1239, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8483), SCOPE: 235, CLAUSE: 2 | quot(T1239, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8483), SCOPE: 235, CLAUSE: 3\n\nT1239 is ground\nX8483 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4938 [label="4938: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4939 [label="4939: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4940 [label="4940: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4943 [label="4943: quot(T1239, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8483), SCOPE: 235, CLAUSE: 2\n\nT1239 is ground\nX8483 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4944 [label="4944: quot(T1239, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8483), SCOPE: 235, CLAUSE: 3\n\nT1239 is ground\nX8483 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4956 [label="4956: quot(T1244, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8522)\n\nT1244 is ground\nX8522 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4957 [label="4957: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4961 [label="4961: quot(T1244, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8522), SCOPE: 236, CLAUSE: 1 | quot(T1244, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8522), SCOPE: 236, CLAUSE: 2 | quot(T1244, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8522), SCOPE: 236, CLAUSE: 3\n\nT1244 is ground\nX8522 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4966 [label="4966: quot(T1244, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8522), SCOPE: 236, CLAUSE: 1\n\nT1244 is ground\nX8522 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4967 [label="4967: quot(T1244, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8522), SCOPE: 236, CLAUSE: 2 | quot(T1244, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8522), SCOPE: 236, CLAUSE: 3\n\nT1244 is ground\nX8522 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4968 [label="4968: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4969 [label="4969: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4970 [label="4970: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4975 [label="4975: quot(T1244, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8522), SCOPE: 236, CLAUSE: 2\n\nT1244 is ground\nX8522 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4976 [label="4976: quot(T1244, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8522), SCOPE: 236, CLAUSE: 3\n\nT1244 is ground\nX8522 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4986 [label="4986: quot(T1249, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8561)\n\nT1249 is ground\nX8561 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4987 [label="4987: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4991 [label="4991: quot(T1249, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8561), SCOPE: 237, CLAUSE: 1 | quot(T1249, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8561), SCOPE: 237, CLAUSE: 2 | quot(T1249, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8561), SCOPE: 237, CLAUSE: 3\n\nT1249 is ground\nX8561 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4992 [label="4992: quot(T1249, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8561), SCOPE: 237, CLAUSE: 1\n\nT1249 is ground\nX8561 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4993 [label="4993: quot(T1249, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8561), SCOPE: 237, CLAUSE: 2 | quot(T1249, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8561), SCOPE: 237, CLAUSE: 3\n\nT1249 is ground\nX8561 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4999 [label="4999: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5000 [label="5000: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5001 [label="5001: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5008 [label="5008: quot(T1249, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8561), SCOPE: 237, CLAUSE: 2\n\nT1249 is ground\nX8561 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5009 [label="5009: quot(T1249, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8561), SCOPE: 237, CLAUSE: 3\n\nT1249 is ground\nX8561 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5014 [label="5014: quot(T1254, s(s(s(0))), s(s(s(s(s(s(0)))))), X8600)\n\nT1254 is ground\nX8600 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5015 [label="5015: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5022 [label="5022: quot(T1254, s(s(s(0))), s(s(s(s(s(s(0)))))), X8600), SCOPE: 238, CLAUSE: 1 | quot(T1254, s(s(s(0))), s(s(s(s(s(s(0)))))), X8600), SCOPE: 238, CLAUSE: 2 | quot(T1254, s(s(s(0))), s(s(s(s(s(s(0)))))), X8600), SCOPE: 238, CLAUSE: 3\n\nT1254 is ground\nX8600 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5024 [label="5024: quot(T1254, s(s(s(0))), s(s(s(s(s(s(0)))))), X8600), SCOPE: 238, CLAUSE: 1\n\nT1254 is ground\nX8600 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5025 [label="5025: quot(T1254, s(s(s(0))), s(s(s(s(s(s(0)))))), X8600), SCOPE: 238, CLAUSE: 2 | quot(T1254, s(s(s(0))), s(s(s(s(s(s(0)))))), X8600), SCOPE: 238, CLAUSE: 3\n\nT1254 is ground\nX8600 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5030 [label="5030: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5031 [label="5031: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5032 [label="5032: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5035 [label="5035: quot(T1254, s(s(s(0))), s(s(s(s(s(s(0)))))), X8600), SCOPE: 238, CLAUSE: 2\n\nT1254 is ground\nX8600 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5036 [label="5036: quot(T1254, s(s(s(0))), s(s(s(s(s(s(0)))))), X8600), SCOPE: 238, CLAUSE: 3\n\nT1254 is ground\nX8600 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5044 [label="5044: quot(T1259, s(s(0)), s(s(s(s(s(s(0)))))), X8639)\n\nT1259 is ground\nX8639 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5046 [label="5046: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5052 [label="5052: quot(T1259, s(s(0)), s(s(s(s(s(s(0)))))), X8639), SCOPE: 239, CLAUSE: 1 | quot(T1259, s(s(0)), s(s(s(s(s(s(0)))))), X8639), SCOPE: 239, CLAUSE: 2 | quot(T1259, s(s(0)), s(s(s(s(s(s(0)))))), X8639), SCOPE: 239, CLAUSE: 3\n\nT1259 is ground\nX8639 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5058 [label="5058: quot(T1259, s(s(0)), s(s(s(s(s(s(0)))))), X8639), SCOPE: 239, CLAUSE: 1\n\nT1259 is ground\nX8639 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5059 [label="5059: quot(T1259, s(s(0)), s(s(s(s(s(s(0)))))), X8639), SCOPE: 239, CLAUSE: 2 | quot(T1259, s(s(0)), s(s(s(s(s(s(0)))))), X8639), SCOPE: 239, CLAUSE: 3\n\nT1259 is ground\nX8639 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5060 [label="5060: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5061 [label="5061: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5062 [label="5062: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5067 [label="5067: quot(T1259, s(s(0)), s(s(s(s(s(s(0)))))), X8639), SCOPE: 239, CLAUSE: 2\n\nT1259 is ground\nX8639 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5068 [label="5068: quot(T1259, s(s(0)), s(s(s(s(s(s(0)))))), X8639), SCOPE: 239, CLAUSE: 3\n\nT1259 is ground\nX8639 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5077 [label="5077: quot(T1264, s(0), s(s(s(s(s(s(0)))))), X8678)\n\nT1264 is ground\nX8678 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5078 [label="5078: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5082 [label="5082: quot(T1264, s(0), s(s(s(s(s(s(0)))))), X8678), SCOPE: 240, CLAUSE: 1 | quot(T1264, s(0), s(s(s(s(s(s(0)))))), X8678), SCOPE: 240, CLAUSE: 2 | quot(T1264, s(0), s(s(s(s(s(s(0)))))), X8678), SCOPE: 240, CLAUSE: 3\n\nT1264 is ground\nX8678 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5088 [label="5088: quot(T1264, s(0), s(s(s(s(s(s(0)))))), X8678), SCOPE: 240, CLAUSE: 1\n\nT1264 is ground\nX8678 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5089 [label="5089: quot(T1264, s(0), s(s(s(s(s(s(0)))))), X8678), SCOPE: 240, CLAUSE: 2 | quot(T1264, s(0), s(s(s(s(s(s(0)))))), X8678), SCOPE: 240, CLAUSE: 3\n\nT1264 is ground\nX8678 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5090 [label="5090: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5091 [label="5091: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5092 [label="5092: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5097 [label="5097: quot(T1264, s(0), s(s(s(s(s(s(0)))))), X8678), SCOPE: 240, CLAUSE: 2\n\nT1264 is ground\nX8678 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5098 [label="5098: quot(T1264, s(0), s(s(s(s(s(s(0)))))), X8678), SCOPE: 240, CLAUSE: 3\n\nT1264 is ground\nX8678 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5107 [label="5107: quot(T1269, 0, s(s(s(s(s(s(0)))))), X8717)\n\nT1269 is ground\nX8717 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5108 [label="5108: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5114 [label="5114: quot(T1269, 0, s(s(s(s(s(s(0)))))), X8717), SCOPE: 241, CLAUSE: 1 | quot(T1269, 0, s(s(s(s(s(s(0)))))), X8717), SCOPE: 241, CLAUSE: 2 | quot(T1269, 0, s(s(s(s(s(s(0)))))), X8717), SCOPE: 241, CLAUSE: 3\n\nT1269 is ground\nX8717 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5115 [label="5115: quot(T1269, 0, s(s(s(s(s(s(0)))))), X8717), SCOPE: 241, CLAUSE: 2 | quot(T1269, 0, s(s(s(s(s(s(0)))))), X8717), SCOPE: 241, CLAUSE: 3\n\nT1269 is ground\nX8717 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5119 [label="5119: quot(T1269, 0, s(s(s(s(s(s(0)))))), X8717), SCOPE: 241, CLAUSE: 3\n\nT1269 is ground\nX8717 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5125 [label="5125: quot(T1273, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8743)\n\nT1273 is ground\nX8743 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5131 [label="5131: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5134 [label="5134: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5135 [label="5135: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5139 [label="5139: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5142 [label="5142: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5143 [label="5143: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5152 [label="N7: quot(T1282, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8777)\n\nT1282 is ground\nX8777 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5153 [label="5153: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5156 [label="5156: quot(T1282, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8777), SCOPE: 242, CLAUSE: 1 | quot(T1282, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8777), SCOPE: 242, CLAUSE: 2 | quot(T1282, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8777), SCOPE: 242, CLAUSE: 3\n\nT1282 is ground\nX8777 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5157 [label="5157: quot(T1282, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8777), SCOPE: 242, CLAUSE: 1\n\nT1282 is ground\nX8777 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5158 [label="5158: quot(T1282, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8777), SCOPE: 242, CLAUSE: 2 | quot(T1282, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8777), SCOPE: 242, CLAUSE: 3\n\nT1282 is ground\nX8777 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5161 [label="5161: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5162 [label="5162: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5163 [label="5163: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5170 [label="5170: quot(T1282, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8777), SCOPE: 242, CLAUSE: 2\n\nT1282 is ground\nX8777 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5171 [label="5171: quot(T1282, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8777), SCOPE: 242, CLAUSE: 3\n\nT1282 is ground\nX8777 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5180 [label="5180: quot(T1287, s(s(s(s(0)))), s(s(s(s(s(0))))), X8816)\n\nT1287 is ground\nX8816 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5181 [label="5181: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5184 [label="5184: quot(T1287, s(s(s(s(0)))), s(s(s(s(s(0))))), X8816), SCOPE: 243, CLAUSE: 1 | quot(T1287, s(s(s(s(0)))), s(s(s(s(s(0))))), X8816), SCOPE: 243, CLAUSE: 2 | quot(T1287, s(s(s(s(0)))), s(s(s(s(s(0))))), X8816), SCOPE: 243, CLAUSE: 3\n\nT1287 is ground\nX8816 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5186 [label="5186: quot(T1287, s(s(s(s(0)))), s(s(s(s(s(0))))), X8816), SCOPE: 243, CLAUSE: 1\n\nT1287 is ground\nX8816 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5187 [label="5187: quot(T1287, s(s(s(s(0)))), s(s(s(s(s(0))))), X8816), SCOPE: 243, CLAUSE: 2 | quot(T1287, s(s(s(s(0)))), s(s(s(s(s(0))))), X8816), SCOPE: 243, CLAUSE: 3\n\nT1287 is ground\nX8816 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5192 [label="5192: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5193 [label="5193: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5194 [label="5194: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5201 [label="5201: quot(T1287, s(s(s(s(0)))), s(s(s(s(s(0))))), X8816), SCOPE: 243, CLAUSE: 2\n\nT1287 is ground\nX8816 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5202 [label="5202: quot(T1287, s(s(s(s(0)))), s(s(s(s(s(0))))), X8816), SCOPE: 243, CLAUSE: 3\n\nT1287 is ground\nX8816 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5208 [label="5208: quot(T1292, s(s(s(0))), s(s(s(s(s(0))))), X8855)\n\nT1292 is ground\nX8855 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5209 [label="5209: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5212 [label="5212: quot(T1292, s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 244, CLAUSE: 1 | quot(T1292, s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 244, CLAUSE: 2 | quot(T1292, s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 244, CLAUSE: 3\n\nT1292 is ground\nX8855 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5216 [label="5216: quot(T1292, s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 244, CLAUSE: 1\n\nT1292 is ground\nX8855 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5217 [label="5217: quot(T1292, s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 244, CLAUSE: 2 | quot(T1292, s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 244, CLAUSE: 3\n\nT1292 is ground\nX8855 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5223 [label="5223: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5224 [label="5224: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5225 [label="5225: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5229 [label="5229: quot(T1292, s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 244, CLAUSE: 2\n\nT1292 is ground\nX8855 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5230 [label="5230: quot(T1292, s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 244, CLAUSE: 3\n\nT1292 is ground\nX8855 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5238 [label="5238: quot(T1297, s(s(0)), s(s(s(s(s(0))))), X8894)\n\nT1297 is ground\nX8894 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5239 [label="5239: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5244 [label="5244: quot(T1297, s(s(0)), s(s(s(s(s(0))))), X8894), SCOPE: 245, CLAUSE: 1 | quot(T1297, s(s(0)), s(s(s(s(s(0))))), X8894), SCOPE: 245, CLAUSE: 2 | quot(T1297, s(s(0)), s(s(s(s(s(0))))), X8894), SCOPE: 245, CLAUSE: 3\n\nT1297 is ground\nX8894 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5247 [label="5247: quot(T1297, s(s(0)), s(s(s(s(s(0))))), X8894), SCOPE: 245, CLAUSE: 1\n\nT1297 is ground\nX8894 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5248 [label="5248: quot(T1297, s(s(0)), s(s(s(s(s(0))))), X8894), SCOPE: 245, CLAUSE: 2 | quot(T1297, s(s(0)), s(s(s(s(s(0))))), X8894), SCOPE: 245, CLAUSE: 3\n\nT1297 is ground\nX8894 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5254 [label="5254: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5255 [label="5255: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5256 [label="5256: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5259 [label="5259: quot(T1297, s(s(0)), s(s(s(s(s(0))))), X8894), SCOPE: 245, CLAUSE: 2\n\nT1297 is ground\nX8894 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5260 [label="5260: quot(T1297, s(s(0)), s(s(s(s(s(0))))), X8894), SCOPE: 245, CLAUSE: 3\n\nT1297 is ground\nX8894 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5266 [label="5266: quot(T1302, s(0), s(s(s(s(s(0))))), X8933)\n\nT1302 is ground\nX8933 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5267 [label="5267: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5273 [label="5273: quot(T1302, s(0), s(s(s(s(s(0))))), X8933), SCOPE: 246, CLAUSE: 1 | quot(T1302, s(0), s(s(s(s(s(0))))), X8933), SCOPE: 246, CLAUSE: 2 | quot(T1302, s(0), s(s(s(s(s(0))))), X8933), SCOPE: 246, CLAUSE: 3\n\nT1302 is ground\nX8933 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5280 [label="5280: quot(T1302, s(0), s(s(s(s(s(0))))), X8933), SCOPE: 246, CLAUSE: 1\n\nT1302 is ground\nX8933 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5281 [label="5281: quot(T1302, s(0), s(s(s(s(s(0))))), X8933), SCOPE: 246, CLAUSE: 2 | quot(T1302, s(0), s(s(s(s(s(0))))), X8933), SCOPE: 246, CLAUSE: 3\n\nT1302 is ground\nX8933 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5282 [label="5282: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5283 [label="5283: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5284 [label="5284: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5289 [label="5289: quot(T1302, s(0), s(s(s(s(s(0))))), X8933), SCOPE: 246, CLAUSE: 2\n\nT1302 is ground\nX8933 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5290 [label="5290: quot(T1302, s(0), s(s(s(s(s(0))))), X8933), SCOPE: 246, CLAUSE: 3\n\nT1302 is ground\nX8933 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5298 [label="5298: quot(T1307, 0, s(s(s(s(s(0))))), X8972)\n\nT1307 is ground\nX8972 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5299 [label="5299: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5303 [label="5303: quot(T1307, 0, s(s(s(s(s(0))))), X8972), SCOPE: 247, CLAUSE: 1 | quot(T1307, 0, s(s(s(s(s(0))))), X8972), SCOPE: 247, CLAUSE: 2 | quot(T1307, 0, s(s(s(s(s(0))))), X8972), SCOPE: 247, CLAUSE: 3\n\nT1307 is ground\nX8972 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5304 [label="5304: quot(T1307, 0, s(s(s(s(s(0))))), X8972), SCOPE: 247, CLAUSE: 2 | quot(T1307, 0, s(s(s(s(s(0))))), X8972), SCOPE: 247, CLAUSE: 3\n\nT1307 is ground\nX8972 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5308 [label="5308: quot(T1307, 0, s(s(s(s(s(0))))), X8972), SCOPE: 247, CLAUSE: 3\n\nT1307 is ground\nX8972 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5315 [label="5315: quot(T1311, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8998)\n\nT1311 is ground\nX8998 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5319 [label="5319: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5320 [label="5320: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5322 [label="5322: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5325 [label="5325: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5328 [label="5328: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5338 [label="N8: quot(T1319, s(s(s(s(0)))), s(s(s(s(0)))), X9029)\n\nT1319 is ground\nX9029 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5339 [label="5339: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5344 [label="5344: quot(T1319, s(s(s(s(0)))), s(s(s(s(0)))), X9029), SCOPE: 248, CLAUSE: 1 | quot(T1319, s(s(s(s(0)))), s(s(s(s(0)))), X9029), SCOPE: 248, CLAUSE: 2 | quot(T1319, s(s(s(s(0)))), s(s(s(s(0)))), X9029), SCOPE: 248, CLAUSE: 3\n\nT1319 is ground\nX9029 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5345 [label="5345: quot(T1319, s(s(s(s(0)))), s(s(s(s(0)))), X9029), SCOPE: 248, CLAUSE: 1\n\nT1319 is ground\nX9029 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5346 [label="5346: quot(T1319, s(s(s(s(0)))), s(s(s(s(0)))), X9029), SCOPE: 248, CLAUSE: 2 | quot(T1319, s(s(s(s(0)))), s(s(s(s(0)))), X9029), SCOPE: 248, CLAUSE: 3\n\nT1319 is ground\nX9029 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5349 [label="5349: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5350 [label="5350: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5351 [label="5351: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5357 [label="5357: quot(T1319, s(s(s(s(0)))), s(s(s(s(0)))), X9029), SCOPE: 248, CLAUSE: 2\n\nT1319 is ground\nX9029 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5358 [label="5358: quot(T1319, s(s(s(s(0)))), s(s(s(s(0)))), X9029), SCOPE: 248, CLAUSE: 3\n\nT1319 is ground\nX9029 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5365 [label="5365: quot(T1324, s(s(s(0))), s(s(s(s(0)))), X9068)\n\nT1324 is ground\nX9068 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5366 [label="5366: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5370 [label="5370: quot(T1324, s(s(s(0))), s(s(s(s(0)))), X9068), SCOPE: 249, CLAUSE: 1 | quot(T1324, s(s(s(0))), s(s(s(s(0)))), X9068), SCOPE: 249, CLAUSE: 2 | quot(T1324, s(s(s(0))), s(s(s(s(0)))), X9068), SCOPE: 249, CLAUSE: 3\n\nT1324 is ground\nX9068 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5372 [label="5372: quot(T1324, s(s(s(0))), s(s(s(s(0)))), X9068), SCOPE: 249, CLAUSE: 1\n\nT1324 is ground\nX9068 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5373 [label="5373: quot(T1324, s(s(s(0))), s(s(s(s(0)))), X9068), SCOPE: 249, CLAUSE: 2 | quot(T1324, s(s(s(0))), s(s(s(s(0)))), X9068), SCOPE: 249, CLAUSE: 3\n\nT1324 is ground\nX9068 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5378 [label="5378: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5379 [label="5379: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5380 [label="5380: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5385 [label="5385: quot(T1324, s(s(s(0))), s(s(s(s(0)))), X9068), SCOPE: 249, CLAUSE: 2\n\nT1324 is ground\nX9068 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5386 [label="5386: quot(T1324, s(s(s(0))), s(s(s(s(0)))), X9068), SCOPE: 249, CLAUSE: 3\n\nT1324 is ground\nX9068 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5397 [label="5397: quot(T1329, s(s(0)), s(s(s(s(0)))), X9107)\n\nT1329 is ground\nX9107 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5398 [label="5398: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5402 [label="5402: quot(T1329, s(s(0)), s(s(s(s(0)))), X9107), SCOPE: 250, CLAUSE: 1 | quot(T1329, s(s(0)), s(s(s(s(0)))), X9107), SCOPE: 250, CLAUSE: 2 | quot(T1329, s(s(0)), s(s(s(s(0)))), X9107), SCOPE: 250, CLAUSE: 3\n\nT1329 is ground\nX9107 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5404 [label="5404: quot(T1329, s(s(0)), s(s(s(s(0)))), X9107), SCOPE: 250, CLAUSE: 1\n\nT1329 is ground\nX9107 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5405 [label="5405: quot(T1329, s(s(0)), s(s(s(s(0)))), X9107), SCOPE: 250, CLAUSE: 2 | quot(T1329, s(s(0)), s(s(s(s(0)))), X9107), SCOPE: 250, CLAUSE: 3\n\nT1329 is ground\nX9107 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5409 [label="5409: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5410 [label="5410: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5411 [label="5411: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5415 [label="5415: quot(T1329, s(s(0)), s(s(s(s(0)))), X9107), SCOPE: 250, CLAUSE: 2\n\nT1329 is ground\nX9107 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5416 [label="5416: quot(T1329, s(s(0)), s(s(s(s(0)))), X9107), SCOPE: 250, CLAUSE: 3\n\nT1329 is ground\nX9107 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5423 [label="5423: quot(T1334, s(0), s(s(s(s(0)))), X9146)\n\nT1334 is ground\nX9146 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5424 [label="5424: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5430 [label="5430: quot(T1334, s(0), s(s(s(s(0)))), X9146), SCOPE: 251, CLAUSE: 1 | quot(T1334, s(0), s(s(s(s(0)))), X9146), SCOPE: 251, CLAUSE: 2 | quot(T1334, s(0), s(s(s(s(0)))), X9146), SCOPE: 251, CLAUSE: 3\n\nT1334 is ground\nX9146 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5432 [label="5432: quot(T1334, s(0), s(s(s(s(0)))), X9146), SCOPE: 251, CLAUSE: 1\n\nT1334 is ground\nX9146 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5433 [label="5433: quot(T1334, s(0), s(s(s(s(0)))), X9146), SCOPE: 251, CLAUSE: 2 | quot(T1334, s(0), s(s(s(s(0)))), X9146), SCOPE: 251, CLAUSE: 3\n\nT1334 is ground\nX9146 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5436 [label="5436: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5437 [label="5437: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5438 [label="5438: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5442 [label="5442: quot(T1334, s(0), s(s(s(s(0)))), X9146), SCOPE: 251, CLAUSE: 2\n\nT1334 is ground\nX9146 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5443 [label="5443: quot(T1334, s(0), s(s(s(s(0)))), X9146), SCOPE: 251, CLAUSE: 3\n\nT1334 is ground\nX9146 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5454 [label="5454: quot(T1339, 0, s(s(s(s(0)))), X9185)\n\nT1339 is ground\nX9185 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5455 [label="5455: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5461 [label="5461: quot(T1339, 0, s(s(s(s(0)))), X9185), SCOPE: 252, CLAUSE: 1 | quot(T1339, 0, s(s(s(s(0)))), X9185), SCOPE: 252, CLAUSE: 2 | quot(T1339, 0, s(s(s(s(0)))), X9185), SCOPE: 252, CLAUSE: 3\n\nT1339 is ground\nX9185 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5462 [label="5462: quot(T1339, 0, s(s(s(s(0)))), X9185), SCOPE: 252, CLAUSE: 2 | quot(T1339, 0, s(s(s(s(0)))), X9185), SCOPE: 252, CLAUSE: 3\n\nT1339 is ground\nX9185 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5465 [label="5465: quot(T1339, 0, s(s(s(s(0)))), X9185), SCOPE: 252, CLAUSE: 3\n\nT1339 is ground\nX9185 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5473 [label="5473: quot(T1343, s(s(s(s(0)))), s(s(s(s(0)))), X9211)\n\nT1343 is ground\nX9211 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5479 [label="5479: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5480 [label="5480: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5484 [label="5484: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5485 [label="5485: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5489 [label="N9: quot(T1350, s(s(s(0))), s(s(s(0))), X9239)\n\nT1350 is ground\nX9239 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5490 [label="5490: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5495 [label="5495: quot(T1350, s(s(s(0))), s(s(s(0))), X9239), SCOPE: 253, CLAUSE: 1 | quot(T1350, s(s(s(0))), s(s(s(0))), X9239), SCOPE: 253, CLAUSE: 2 | quot(T1350, s(s(s(0))), s(s(s(0))), X9239), SCOPE: 253, CLAUSE: 3\n\nT1350 is ground\nX9239 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5498 [label="5498: quot(T1350, s(s(s(0))), s(s(s(0))), X9239), SCOPE: 253, CLAUSE: 1\n\nT1350 is ground\nX9239 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5499 [label="5499: quot(T1350, s(s(s(0))), s(s(s(0))), X9239), SCOPE: 253, CLAUSE: 2 | quot(T1350, s(s(s(0))), s(s(s(0))), X9239), SCOPE: 253, CLAUSE: 3\n\nT1350 is ground\nX9239 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5500 [label="5500: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5501 [label="5501: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5502 [label="5502: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5507 [label="5507: quot(T1350, s(s(s(0))), s(s(s(0))), X9239), SCOPE: 253, CLAUSE: 2\n\nT1350 is ground\nX9239 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5508 [label="5508: quot(T1350, s(s(s(0))), s(s(s(0))), X9239), SCOPE: 253, CLAUSE: 3\n\nT1350 is ground\nX9239 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5518 [label="5518: quot(T1355, s(s(0)), s(s(s(0))), X9278)\n\nT1355 is ground\nX9278 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5519 [label="5519: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5524 [label="5524: quot(T1355, s(s(0)), s(s(s(0))), X9278), SCOPE: 254, CLAUSE: 1 | quot(T1355, s(s(0)), s(s(s(0))), X9278), SCOPE: 254, CLAUSE: 2 | quot(T1355, s(s(0)), s(s(s(0))), X9278), SCOPE: 254, CLAUSE: 3\n\nT1355 is ground\nX9278 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5525 [label="5525: quot(T1355, s(s(0)), s(s(s(0))), X9278), SCOPE: 254, CLAUSE: 1\n\nT1355 is ground\nX9278 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5526 [label="5526: quot(T1355, s(s(0)), s(s(s(0))), X9278), SCOPE: 254, CLAUSE: 2 | quot(T1355, s(s(0)), s(s(s(0))), X9278), SCOPE: 254, CLAUSE: 3\n\nT1355 is ground\nX9278 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5530 [label="5530: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5531 [label="5531: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5532 [label="5532: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5541 [label="5541: quot(T1355, s(s(0)), s(s(s(0))), X9278), SCOPE: 254, CLAUSE: 2\n\nT1355 is ground\nX9278 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5542 [label="5542: quot(T1355, s(s(0)), s(s(s(0))), X9278), SCOPE: 254, CLAUSE: 3\n\nT1355 is ground\nX9278 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5548 [label="5548: quot(T1360, s(0), s(s(s(0))), X9317)\n\nT1360 is ground\nX9317 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5549 [label="5549: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5552 [label="5552: quot(T1360, s(0), s(s(s(0))), X9317), SCOPE: 255, CLAUSE: 1 | quot(T1360, s(0), s(s(s(0))), X9317), SCOPE: 255, CLAUSE: 2 | quot(T1360, s(0), s(s(s(0))), X9317), SCOPE: 255, CLAUSE: 3\n\nT1360 is ground\nX9317 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5553 [label="5553: quot(T1360, s(0), s(s(s(0))), X9317), SCOPE: 255, CLAUSE: 1\n\nT1360 is ground\nX9317 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5554 [label="5554: quot(T1360, s(0), s(s(s(0))), X9317), SCOPE: 255, CLAUSE: 2 | quot(T1360, s(0), s(s(s(0))), X9317), SCOPE: 255, CLAUSE: 3\n\nT1360 is ground\nX9317 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5555 [label="5555: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5556 [label="5556: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5557 [label="5557: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5558 [label="5558: quot(T1360, s(0), s(s(s(0))), X9317), SCOPE: 255, CLAUSE: 2\n\nT1360 is ground\nX9317 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5559 [label="5559: quot(T1360, s(0), s(s(s(0))), X9317), SCOPE: 255, CLAUSE: 3\n\nT1360 is ground\nX9317 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5562 [label="5562: quot(T1365, 0, s(s(s(0))), X9356)\n\nT1365 is ground\nX9356 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5563 [label="5563: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5564 [label="5564: quot(T1365, 0, s(s(s(0))), X9356), SCOPE: 256, CLAUSE: 1 | quot(T1365, 0, s(s(s(0))), X9356), SCOPE: 256, CLAUSE: 2 | quot(T1365, 0, s(s(s(0))), X9356), SCOPE: 256, CLAUSE: 3\n\nT1365 is ground\nX9356 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5565 [label="5565: quot(T1365, 0, s(s(s(0))), X9356), SCOPE: 256, CLAUSE: 2 | quot(T1365, 0, s(s(s(0))), X9356), SCOPE: 256, CLAUSE: 3\n\nT1365 is ground\nX9356 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5567 [label="5567: quot(T1365, 0, s(s(s(0))), X9356), SCOPE: 256, CLAUSE: 3\n\nT1365 is ground\nX9356 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5570 [label="5570: quot(T1369, s(s(s(0))), s(s(s(0))), X9382)\n\nT1369 is ground\nX9382 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5572 [label="5572: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5573 [label="5573: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5575 [label="5575: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5579 [label="N10: quot(T1375, s(s(0)), s(s(0)), X9407)\n\nT1375 is ground\nX9407 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5580 [label="5580: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5583 [label="5583: quot(T1375, s(s(0)), s(s(0)), X9407), SCOPE: 257, CLAUSE: 1 | quot(T1375, s(s(0)), s(s(0)), X9407), SCOPE: 257, CLAUSE: 2 | quot(T1375, s(s(0)), s(s(0)), X9407), SCOPE: 257, CLAUSE: 3\n\nT1375 is ground\nX9407 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5584 [label="5584: quot(T1375, s(s(0)), s(s(0)), X9407), SCOPE: 257, CLAUSE: 1\n\nT1375 is ground\nX9407 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5585 [label="5585: quot(T1375, s(s(0)), s(s(0)), X9407), SCOPE: 257, CLAUSE: 2 | quot(T1375, s(s(0)), s(s(0)), X9407), SCOPE: 257, CLAUSE: 3\n\nT1375 is ground\nX9407 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5589 [label="5589: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5590 [label="5590: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5591 [label="5591: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5597 [label="5597: quot(T1375, s(s(0)), s(s(0)), X9407), SCOPE: 257, CLAUSE: 2\n\nT1375 is ground\nX9407 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5598 [label="5598: quot(T1375, s(s(0)), s(s(0)), X9407), SCOPE: 257, CLAUSE: 3\n\nT1375 is ground\nX9407 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5599 [label="5599: quot(T1380, s(0), s(s(0)), X9446)\n\nT1380 is ground\nX9446 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5600 [label="5600: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5601 [label="5601: quot(T1380, s(0), s(s(0)), X9446), SCOPE: 258, CLAUSE: 1 | quot(T1380, s(0), s(s(0)), X9446), SCOPE: 258, CLAUSE: 2 | quot(T1380, s(0), s(s(0)), X9446), SCOPE: 258, CLAUSE: 3\n\nT1380 is ground\nX9446 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5602 [label="5602: quot(T1380, s(0), s(s(0)), X9446), SCOPE: 258, CLAUSE: 1\n\nT1380 is ground\nX9446 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5603 [label="5603: quot(T1380, s(0), s(s(0)), X9446), SCOPE: 258, CLAUSE: 2 | quot(T1380, s(0), s(s(0)), X9446), SCOPE: 258, CLAUSE: 3\n\nT1380 is ground\nX9446 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5604 [label="5604: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5605 [label="5605: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5606 [label="5606: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5607 [label="5607: quot(T1380, s(0), s(s(0)), X9446), SCOPE: 258, CLAUSE: 2\n\nT1380 is ground\nX9446 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5608 [label="5608: quot(T1380, s(0), s(s(0)), X9446), SCOPE: 258, CLAUSE: 3\n\nT1380 is ground\nX9446 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5609 [label="5609: quot(T1385, 0, s(s(0)), X9485)\n\nT1385 is ground\nX9485 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5610 [label="5610: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5611 [label="5611: quot(T1385, 0, s(s(0)), X9485), SCOPE: 259, CLAUSE: 1 | quot(T1385, 0, s(s(0)), X9485), SCOPE: 259, CLAUSE: 2 | quot(T1385, 0, s(s(0)), X9485), SCOPE: 259, CLAUSE: 3\n\nT1385 is ground\nX9485 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5612 [label="5612: quot(T1385, 0, s(s(0)), X9485), SCOPE: 259, CLAUSE: 2 | quot(T1385, 0, s(s(0)), X9485), SCOPE: 259, CLAUSE: 3\n\nT1385 is ground\nX9485 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5613 [label="5613: quot(T1385, 0, s(s(0)), X9485), SCOPE: 259, CLAUSE: 3\n\nT1385 is ground\nX9485 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5614 [label="5614: quot(T1389, s(s(0)), s(s(0)), X9511)\n\nT1389 is ground\nX9511 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5615 [label="5615: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5616 [label="5616: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5617 [label="5617: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5618 [label="5618: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5619 [label="5619: times(T954, s(s(T950)), X7571)\n\nT950 is ground\nT954 is ground\nX7571 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5620 [label="5620: neq(s(T951), T1396)\n\nT951 is ground\nT1396 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5621 [label="5621: pr(s(T939), s(T937)), SCOPE: 260, CLAUSE: 5 | pr(s(T939), s(T937)), SCOPE: 260, CLAUSE: 6\n\nT937 is ground\nT939 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5622 [label="5622: pr(s(T939), s(T937)), SCOPE: 260, CLAUSE: 5\n\nT937 is ground\nT939 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5623 [label="5623: pr(s(T939), s(T937)), SCOPE: 260, CLAUSE: 6\n\nT937 is ground\nT939 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5624 [label="5624: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5625 [label="5625: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5626 [label="5626: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5627 [label="5627: ','(not_divides(s(s(T1413)), s(T1412)), pr(s(T1412), s(T1413)))\n\nT1412 is ground\nT1413 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5628 [label="5628: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5629 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2 -> 5629 [arrowhead = none ];
5629 -> 6;

5630 [label="EVAL with clause\nprime(s(s(X2))) :- pr(s(s(X2)), s(X2)).\nand substitutionX2 -> T3,\nT1 -> s(s(T3))", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 5630 [arrowhead = none ];
5630 -> 9;

5631 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 5631 [arrowhead = none ];
5631 -> 12;

5632 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 5632 [arrowhead = none ];
5632 -> 13;

5633 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 5633 [arrowhead = none ];
5633 -> 16;

5634 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 5634 [arrowhead = none ];
5634 -> 18;

5635 [label="EVAL with clause\npr(X7, s(0)).\nand substitutionT3 -> 0,\nX7 -> s(s(0)),\nT8 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 5635 [arrowhead = none ];
5635 -> 20;

5636 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 5636 [arrowhead = none ];
5636 -> 22;

5637 [label="EVAL with clause\npr(X12, s(s(X13))) :- ','(not_divides(s(s(X13)), X12), pr(X12, s(X13))).\nand substitutionT3 -> s(T14),\nX12 -> s(s(s(T14))),\nX13 -> T14,\nT13 -> s(T14)", fontsize=14, style = filled, fillcolor = lightblue];
18 -> 5637 [arrowhead = none ];
5637 -> 30;

5638 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
18 -> 5638 [arrowhead = none ];
5638 -> 31;

5639 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 5639 [arrowhead = none ];
5639 -> 24;

5640 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
30 -> 5640 [arrowhead = none ];
5640 -> 48;

5641 [label="SPLIT 2\nnew knowledge:\nT14 is ground", fontsize=14, style = filled, fillcolor = violet];
30 -> 5641 [arrowhead = none ];
5641 -> 49;

5642 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
48 -> 5642 [arrowhead = none ];
5642 -> 50;

5643 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
49 -> 5643 [arrowhead = none ];
5643 -> 690;

5644 [label="ONLY EVAL with clause\nnot_divides(X32, X33) :- ','(div(X33, X32, X34), ','(times(X34, X32, X35), neq(X33, X35))).\nand substitutionT14 -> T20,\nX32 -> s(s(T20)),\nX33 -> s(s(s(T20)))", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 5644 [arrowhead = none ];
5644 -> 56;

5645 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
56 -> 5645 [arrowhead = none ];
5645 -> 57;

5646 [label="SPLIT 2\nnew knowledge:\nT20 is ground\nT22 is ground\nreplacements:X34 -> T22", fontsize=14, style = filled, fillcolor = violet];
56 -> 5646 [arrowhead = none ];
5646 -> 58;

5647 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
57 -> 5647 [arrowhead = none ];
5647 -> 63;

5648 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
58 -> 5648 [arrowhead = none ];
5648 -> 543;

5649 [label="SPLIT 2\nnew knowledge:\nT22 is ground\nT20 is ground\nT157 is ground\nreplacements:X35 -> T157", fontsize=14, style = filled, fillcolor = violet];
58 -> 5649 [arrowhead = none ];
5649 -> 545;

5650 [label="ONLY EVAL with clause\ndiv(X56, X57, X58) :- quot(X56, X57, X57, X58).\nand substitutionT20 -> T26,\nX56 -> s(s(s(T26))),\nX57 -> s(s(T26)),\nX34 -> X59,\nX58 -> X59", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 5650 [arrowhead = none ];
5650 -> 67;

5651 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
67 -> 5651 [arrowhead = none ];
5651 -> 69;

5652 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
69 -> 5652 [arrowhead = none ];
5652 -> 71;

5653 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
71 -> 5653 [arrowhead = none ];
5653 -> 72;

5654 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
71 -> 5654 [arrowhead = none ];
5654 -> 73;

5655 [label="ONLY EVAL with clause\nquot(s(X94), s(X95), X96, X97) :- quot(X94, X95, X96, X97).\nand substitutionT26 -> T31,\nX94 -> s(s(T31)),\nX95 -> s(T31),\nX96 -> s(s(T31)),\nX59 -> X98,\nX97 -> X98", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 5655 [arrowhead = none ];
5655 -> 91;

5656 [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 = lightgreen];
73 -> 5656 [arrowhead = none ];
5656 -> 539;

5657 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
91 -> 5657 [arrowhead = none ];
5657 -> 92;

5658 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
92 -> 5658 [arrowhead = none ];
5658 -> 93;

5659 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
93 -> 5659 [arrowhead = none ];
5659 -> 96;

5660 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
93 -> 5660 [arrowhead = none ];
5660 -> 97;

5661 [label="ONLY EVAL with clause\nquot(s(X133), s(X134), X135, X136) :- quot(X133, X134, X135, X136).\nand substitutionT31 -> T36,\nX133 -> s(T36),\nX134 -> T36,\nX135 -> s(s(T36)),\nX98 -> X137,\nX136 -> X137", fontsize=14, style = filled, fillcolor = lightblue];
96 -> 5661 [arrowhead = none ];
5661 -> 105;

5662 [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 = lightgreen];
97 -> 5662 [arrowhead = none ];
5662 -> 537;

5663 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
105 -> 5663 [arrowhead = none ];
5663 -> 107;

5664 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
107 -> 5664 [arrowhead = none ];
5664 -> 108;

5665 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
108 -> 5665 [arrowhead = none ];
5665 -> 113;

5666 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
108 -> 5666 [arrowhead = none ];
5666 -> 114;

5667 [label="EVAL with clause\nquot(s(X164), s(X165), X166, X167) :- quot(X164, X165, X166, X167).\nand substitutionT36 -> s(T46),\nX164 -> s(T46),\nX165 -> T46,\nT45 -> s(T46),\nX166 -> s(s(s(T46))),\nX137 -> X168,\nX167 -> X168", fontsize=14, style = filled, fillcolor = lightblue];
113 -> 5667 [arrowhead = none ];
5667 -> 121;

5668 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
113 -> 5668 [arrowhead = none ];
5668 -> 122;

5669 [label="EVAL with clause\nquot(X819, 0, s(X820), s(X821)) :- quot(X819, s(X820), s(X820), X821).\nand substitutionT36 -> 0,\nX819 -> s(0),\nT152 -> 0,\nX820 -> s(0),\nX821 -> X822,\nX137 -> s(X822)", fontsize=14, style = filled, fillcolor = lightblue];
114 -> 5669 [arrowhead = none ];
5669 -> 493;

5670 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
114 -> 5670 [arrowhead = none ];
5670 -> 494;

5671 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
121 -> 5671 [arrowhead = none ];
5671 -> 129;

5672 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 5672 [arrowhead = none ];
5672 -> 132;

5673 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
132 -> 5673 [arrowhead = none ];
5673 -> 133;

5674 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
132 -> 5674 [arrowhead = none ];
5674 -> 134;

5675 [label="EVAL with clause\nquot(s(X195), s(X196), X197, X198) :- quot(X195, X196, X197, X198).\nand substitutionT46 -> s(T56),\nX195 -> s(T56),\nX196 -> T56,\nT55 -> s(T56),\nX197 -> s(s(s(s(T56)))),\nX168 -> X199,\nX198 -> X199", fontsize=14, style = filled, fillcolor = lightblue];
133 -> 5675 [arrowhead = none ];
5675 -> 143;

5676 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
133 -> 5676 [arrowhead = none ];
5676 -> 144;

5677 [label="EVAL with clause\nquot(X750, 0, s(X751), s(X752)) :- quot(X750, s(X751), s(X751), X752).\nand substitutionT46 -> 0,\nX750 -> s(0),\nT149 -> 0,\nX751 -> s(s(0)),\nX752 -> X753,\nX168 -> s(X753)", fontsize=14, style = filled, fillcolor = lightblue];
134 -> 5677 [arrowhead = none ];
5677 -> 446;

5678 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
134 -> 5678 [arrowhead = none ];
5678 -> 447;

5679 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
143 -> 5679 [arrowhead = none ];
5679 -> 145;

5680 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
145 -> 5680 [arrowhead = none ];
5680 -> 154;

5681 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 5681 [arrowhead = none ];
5681 -> 157;

5682 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 5682 [arrowhead = none ];
5682 -> 158;

5683 [label="EVAL with clause\nquot(s(X226), s(X227), X228, X229) :- quot(X226, X227, X228, X229).\nand substitutionT56 -> s(T66),\nX226 -> s(T66),\nX227 -> T66,\nT65 -> s(T66),\nX228 -> s(s(s(s(s(T66))))),\nX199 -> X230,\nX229 -> X230", fontsize=14, style = filled, fillcolor = lightblue];
157 -> 5683 [arrowhead = none ];
5683 -> 163;

5684 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
157 -> 5684 [arrowhead = none ];
5684 -> 164;

5685 [label="EVAL with clause\nquot(X681, 0, s(X682), s(X683)) :- quot(X681, s(X682), s(X682), X683).\nand substitutionT56 -> 0,\nX681 -> s(0),\nT146 -> 0,\nX682 -> s(s(s(0))),\nX683 -> X684,\nX199 -> s(X684)", fontsize=14, style = filled, fillcolor = lightblue];
158 -> 5685 [arrowhead = none ];
5685 -> 401;

5686 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
158 -> 5686 [arrowhead = none ];
5686 -> 402;

5687 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
163 -> 5687 [arrowhead = none ];
5687 -> 166;

5688 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
166 -> 5688 [arrowhead = none ];
5688 -> 168;

5689 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
168 -> 5689 [arrowhead = none ];
5689 -> 169;

5690 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
168 -> 5690 [arrowhead = none ];
5690 -> 170;

5691 [label="EVAL with clause\nquot(s(X257), s(X258), X259, X260) :- quot(X257, X258, X259, X260).\nand substitutionT66 -> s(T76),\nX257 -> s(T76),\nX258 -> T76,\nT75 -> s(T76),\nX259 -> s(s(s(s(s(s(T76)))))),\nX230 -> X261,\nX260 -> X261", fontsize=14, style = filled, fillcolor = lightblue];
169 -> 5691 [arrowhead = none ];
5691 -> 173;

5692 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
169 -> 5692 [arrowhead = none ];
5692 -> 174;

5693 [label="EVAL with clause\nquot(X612, 0, s(X613), s(X614)) :- quot(X612, s(X613), s(X613), X614).\nand substitutionT66 -> 0,\nX612 -> s(0),\nT143 -> 0,\nX613 -> s(s(s(s(0)))),\nX614 -> X615,\nX230 -> s(X615)", fontsize=14, style = filled, fillcolor = lightblue];
170 -> 5693 [arrowhead = none ];
5693 -> 354;

5694 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
170 -> 5694 [arrowhead = none ];
5694 -> 355;

5695 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
173 -> 5695 [arrowhead = none ];
5695 -> 177;

5696 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
177 -> 5696 [arrowhead = none ];
5696 -> 178;

5697 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
178 -> 5697 [arrowhead = none ];
5697 -> 182;

5698 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
178 -> 5698 [arrowhead = none ];
5698 -> 183;

5699 [label="EVAL with clause\nquot(s(X288), s(X289), X290, X291) :- quot(X288, X289, X290, X291).\nand substitutionT76 -> s(T86),\nX288 -> s(T86),\nX289 -> T86,\nT85 -> s(T86),\nX290 -> s(s(s(s(s(s(s(T86))))))),\nX261 -> X292,\nX291 -> X292", fontsize=14, style = filled, fillcolor = lightblue];
182 -> 5699 [arrowhead = none ];
5699 -> 188;

5700 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
182 -> 5700 [arrowhead = none ];
5700 -> 189;

5701 [label="EVAL with clause\nquot(X543, 0, s(X544), s(X545)) :- quot(X543, s(X544), s(X544), X545).\nand substitutionT76 -> 0,\nX543 -> s(0),\nT140 -> 0,\nX544 -> s(s(s(s(s(0))))),\nX545 -> X546,\nX261 -> s(X546)", fontsize=14, style = filled, fillcolor = lightblue];
183 -> 5701 [arrowhead = none ];
5701 -> 308;

5702 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
183 -> 5702 [arrowhead = none ];
5702 -> 309;

5703 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
188 -> 5703 [arrowhead = none ];
5703 -> 192;

5704 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
192 -> 5704 [arrowhead = none ];
5704 -> 193;

5705 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
193 -> 5705 [arrowhead = none ];
5705 -> 196;

5706 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
193 -> 5706 [arrowhead = none ];
5706 -> 197;

5707 [label="EVAL with clause\nquot(s(X319), s(X320), X321, X322) :- quot(X319, X320, X321, X322).\nand substitutionT86 -> s(T96),\nX319 -> s(T96),\nX320 -> T96,\nT95 -> s(T96),\nX321 -> s(s(s(s(s(s(s(s(T96)))))))),\nX292 -> X323,\nX322 -> X323", fontsize=14, style = filled, fillcolor = lightblue];
196 -> 5707 [arrowhead = none ];
5707 -> 199;

5708 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
196 -> 5708 [arrowhead = none ];
5708 -> 201;

5709 [label="EVAL with clause\nquot(X474, 0, s(X475), s(X476)) :- quot(X474, s(X475), s(X475), X476).\nand substitutionT86 -> 0,\nX474 -> s(0),\nT137 -> 0,\nX475 -> s(s(s(s(s(s(0)))))),\nX476 -> X477,\nX292 -> s(X477)", fontsize=14, style = filled, fillcolor = lightblue];
197 -> 5709 [arrowhead = none ];
5709 -> 274;

5710 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
197 -> 5710 [arrowhead = none ];
5710 -> 275;

5711 [label="GENERALIZATION\nT97 <-- s(s(s(s(s(s(s(T96)))))))\n\nNew Knowledge:\nT97 is ground", fontsize=14, style = filled, fillcolor = violet];
199 -> 5711 [arrowhead = none ];
5711 -> 203;

5712 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
203 -> 5712 [arrowhead = none ];
5712 -> 205;

5713 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
205 -> 5713 [arrowhead = none ];
5713 -> 206;

5714 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
206 -> 5714 [arrowhead = none ];
5714 -> 209;

5715 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
206 -> 5715 [arrowhead = none ];
5715 -> 210;

5716 [label="EVAL with clause\nquot(s(X354), s(X355), X356, X357) :- quot(X354, X355, X356, X357).\nand substitutionT96 -> s(T111),\nX354 -> s(T111),\nX355 -> T111,\nT110 -> s(T111),\nT97 -> T112,\nX356 -> s(T112),\nX323 -> X358,\nX357 -> X358", fontsize=14, style = filled, fillcolor = lightblue];
209 -> 5716 [arrowhead = none ];
5716 -> 215;

5717 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
209 -> 5717 [arrowhead = none ];
5717 -> 216;

5718 [label="EVAL with clause\nquot(X371, 0, s(X372), s(X373)) :- quot(X371, s(X372), s(X372), X373).\nand substitutionT96 -> 0,\nX371 -> s(0),\nT117 -> 0,\nT97 -> T118,\nX372 -> T118,\nX373 -> X374,\nX323 -> s(X374)", fontsize=14, style = filled, fillcolor = lightblue];
210 -> 5718 [arrowhead = none ];
5718 -> 220;

5719 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
210 -> 5719 [arrowhead = none ];
5719 -> 221;

5720 [label="INSTANCE with matching:\nT96 -> T111\nT97 -> T112\nX323 -> X358", fontsize=14, style = filled, fillcolor = lightgrey];
215 -> 5720 [arrowhead = none , style=dashed];
5720 -> 203[style=dashed];

5721 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
220 -> 5721 [arrowhead = none ];
5721 -> 225;

5722 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
225 -> 5722 [arrowhead = none ];
5722 -> 230;

5723 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
230 -> 5723 [arrowhead = none ];
5723 -> 232;

5724 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
230 -> 5724 [arrowhead = none ];
5724 -> 233;

5725 [label="ONLY EVAL with clause\nquot(s(X409), s(X410), X411, X412) :- quot(X409, X410, X411, X412).\nand substitutionX409 -> 0,\nT118 -> T127,\nX410 -> T127,\nX411 -> s(T127),\nX374 -> X413,\nX412 -> X413", fontsize=14, style = filled, fillcolor = lightblue];
232 -> 5725 [arrowhead = none ];
5725 -> 237;

5726 [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 = lightgreen];
233 -> 5726 [arrowhead = none ];
5726 -> 271;

5727 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
237 -> 5727 [arrowhead = none ];
5727 -> 243;

5728 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
243 -> 5728 [arrowhead = none ];
5728 -> 246;

5729 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
243 -> 5729 [arrowhead = none ];
5729 -> 247;

5730 [label="EVAL with clause\nquot(0, s(X426), s(X427), 0).\nand substitutionX426 -> T134,\nT127 -> s(T134),\nX427 -> s(T134),\nX413 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
246 -> 5730 [arrowhead = none ];
5730 -> 250;

5731 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
246 -> 5731 [arrowhead = none ];
5731 -> 251;

5732 [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 = lightgreen];
247 -> 5732 [arrowhead = none ];
5732 -> 253;

5733 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
250 -> 5733 [arrowhead = none ];
5733 -> 252;

5734 [label="EVAL with clause\nquot(X440, 0, s(X441), s(X442)) :- quot(X440, s(X441), s(X441), X442).\nand substitutionX440 -> 0,\nT127 -> 0,\nX441 -> 0,\nX442 -> X443,\nX413 -> s(X443)", fontsize=14, style = filled, fillcolor = lightblue];
253 -> 5734 [arrowhead = none ];
5734 -> 258;

5735 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
253 -> 5735 [arrowhead = none ];
5735 -> 259;

5736 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
258 -> 5736 [arrowhead = none ];
5736 -> 262;

5737 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
262 -> 5737 [arrowhead = none ];
5737 -> 264;

5738 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
262 -> 5738 [arrowhead = none ];
5738 -> 266;

5739 [label="ONLY EVAL with clause\nquot(0, s(X454), s(X455), 0).\nand substitutionX454 -> 0,\nX455 -> 0,\nX443 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
264 -> 5739 [arrowhead = none ];
5739 -> 267;

5740 [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 = lightgreen];
266 -> 5740 [arrowhead = none ];
5740 -> 269;

5741 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
267 -> 5741 [arrowhead = none ];
5741 -> 268;

5742 [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 = lightgreen];
269 -> 5742 [arrowhead = none ];
5742 -> 270;

5743 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
274 -> 5743 [arrowhead = none ];
5743 -> 277;

5744 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
277 -> 5744 [arrowhead = none ];
5744 -> 278;

5745 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
278 -> 5745 [arrowhead = none ];
5745 -> 282;

5746 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
278 -> 5746 [arrowhead = none ];
5746 -> 283;

5747 [label="ONLY EVAL with clause\nquot(s(X508), s(X509), X510, X511) :- quot(X508, X509, X510, X511).\nand substitutionX508 -> 0,\nX509 -> s(s(s(s(s(s(0)))))),\nX510 -> s(s(s(s(s(s(s(0))))))),\nX477 -> X512,\nX511 -> X512", fontsize=14, style = filled, fillcolor = lightblue];
282 -> 5747 [arrowhead = none ];
5747 -> 292;

5748 [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 = lightgreen];
283 -> 5748 [arrowhead = none ];
5748 -> 305;

5749 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
292 -> 5749 [arrowhead = none ];
5749 -> 296;

5750 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
296 -> 5750 [arrowhead = none ];
5750 -> 297;

5751 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
296 -> 5751 [arrowhead = none ];
5751 -> 298;

5752 [label="ONLY EVAL with clause\nquot(0, s(X523), s(X524), 0).\nand substitutionX523 -> s(s(s(s(s(0))))),\nX524 -> s(s(s(s(s(s(0)))))),\nX512 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
297 -> 5752 [arrowhead = none ];
5752 -> 299;

5753 [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 = lightgreen];
298 -> 5753 [arrowhead = none ];
5753 -> 301;

5754 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
299 -> 5754 [arrowhead = none ];
5754 -> 300;

5755 [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 = lightgreen];
301 -> 5755 [arrowhead = none ];
5755 -> 304;

5756 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
308 -> 5756 [arrowhead = none ];
5756 -> 310;

5757 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
310 -> 5757 [arrowhead = none ];
5757 -> 313;

5758 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
313 -> 5758 [arrowhead = none ];
5758 -> 315;

5759 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
313 -> 5759 [arrowhead = none ];
5759 -> 316;

5760 [label="ONLY EVAL with clause\nquot(s(X577), s(X578), X579, X580) :- quot(X577, X578, X579, X580).\nand substitutionX577 -> 0,\nX578 -> s(s(s(s(s(0))))),\nX579 -> s(s(s(s(s(s(0)))))),\nX546 -> X581,\nX580 -> X581", fontsize=14, style = filled, fillcolor = lightblue];
315 -> 5760 [arrowhead = none ];
5760 -> 322;

5761 [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 = lightgreen];
316 -> 5761 [arrowhead = none ];
5761 -> 346;

5762 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
322 -> 5762 [arrowhead = none ];
5762 -> 329;

5763 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
329 -> 5763 [arrowhead = none ];
5763 -> 332;

5764 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
329 -> 5764 [arrowhead = none ];
5764 -> 333;

5765 [label="ONLY EVAL with clause\nquot(0, s(X592), s(X593), 0).\nand substitutionX592 -> s(s(s(s(0)))),\nX593 -> s(s(s(s(s(0))))),\nX581 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
332 -> 5765 [arrowhead = none ];
5765 -> 339;

5766 [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 = lightgreen];
333 -> 5766 [arrowhead = none ];
5766 -> 342;

5767 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
339 -> 5767 [arrowhead = none ];
5767 -> 340;

5768 [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 = lightgreen];
342 -> 5768 [arrowhead = none ];
5768 -> 343;

5769 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
354 -> 5769 [arrowhead = none ];
5769 -> 360;

5770 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
360 -> 5770 [arrowhead = none ];
5770 -> 361;

5771 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
361 -> 5771 [arrowhead = none ];
5771 -> 366;

5772 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
361 -> 5772 [arrowhead = none ];
5772 -> 367;

5773 [label="ONLY EVAL with clause\nquot(s(X646), s(X647), X648, X649) :- quot(X646, X647, X648, X649).\nand substitutionX646 -> 0,\nX647 -> s(s(s(s(0)))),\nX648 -> s(s(s(s(s(0))))),\nX615 -> X650,\nX649 -> X650", fontsize=14, style = filled, fillcolor = lightblue];
366 -> 5773 [arrowhead = none ];
5773 -> 371;

5774 [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 = lightgreen];
367 -> 5774 [arrowhead = none ];
5774 -> 396;

5775 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
371 -> 5775 [arrowhead = none ];
5775 -> 376;

5776 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
376 -> 5776 [arrowhead = none ];
5776 -> 380;

5777 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
376 -> 5777 [arrowhead = none ];
5777 -> 382;

5778 [label="ONLY EVAL with clause\nquot(0, s(X661), s(X662), 0).\nand substitutionX661 -> s(s(s(0))),\nX662 -> s(s(s(s(0)))),\nX650 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
380 -> 5778 [arrowhead = none ];
5778 -> 387;

5779 [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 = lightgreen];
382 -> 5779 [arrowhead = none ];
5779 -> 391;

5780 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
387 -> 5780 [arrowhead = none ];
5780 -> 388;

5781 [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 = lightgreen];
391 -> 5781 [arrowhead = none ];
5781 -> 393;

5782 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
401 -> 5782 [arrowhead = none ];
5782 -> 407;

5783 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
407 -> 5783 [arrowhead = none ];
5783 -> 410;

5784 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
410 -> 5784 [arrowhead = none ];
5784 -> 413;

5785 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
410 -> 5785 [arrowhead = none ];
5785 -> 414;

5786 [label="ONLY EVAL with clause\nquot(s(X715), s(X716), X717, X718) :- quot(X715, X716, X717, X718).\nand substitutionX715 -> 0,\nX716 -> s(s(s(0))),\nX717 -> s(s(s(s(0)))),\nX684 -> X719,\nX718 -> X719", fontsize=14, style = filled, fillcolor = lightblue];
413 -> 5786 [arrowhead = none ];
5786 -> 418;

5787 [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 = lightgreen];
414 -> 5787 [arrowhead = none ];
5787 -> 441;

5788 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
418 -> 5788 [arrowhead = none ];
5788 -> 424;

5789 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
424 -> 5789 [arrowhead = none ];
5789 -> 427;

5790 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
424 -> 5790 [arrowhead = none ];
5790 -> 428;

5791 [label="ONLY EVAL with clause\nquot(0, s(X730), s(X731), 0).\nand substitutionX730 -> s(s(0)),\nX731 -> s(s(s(0))),\nX719 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
427 -> 5791 [arrowhead = none ];
5791 -> 436;

5792 [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 = lightgreen];
428 -> 5792 [arrowhead = none ];
5792 -> 439;

5793 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
436 -> 5793 [arrowhead = none ];
5793 -> 437;

5794 [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 = lightgreen];
439 -> 5794 [arrowhead = none ];
5794 -> 440;

5795 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
446 -> 5795 [arrowhead = none ];
5795 -> 452;

5796 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
452 -> 5796 [arrowhead = none ];
5796 -> 453;

5797 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
453 -> 5797 [arrowhead = none ];
5797 -> 458;

5798 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
453 -> 5798 [arrowhead = none ];
5798 -> 459;

5799 [label="ONLY EVAL with clause\nquot(s(X784), s(X785), X786, X787) :- quot(X784, X785, X786, X787).\nand substitutionX784 -> 0,\nX785 -> s(s(0)),\nX786 -> s(s(s(0))),\nX753 -> X788,\nX787 -> X788", fontsize=14, style = filled, fillcolor = lightblue];
458 -> 5799 [arrowhead = none ];
5799 -> 462;

5800 [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 = lightgreen];
459 -> 5800 [arrowhead = none ];
5800 -> 488;

5801 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
462 -> 5801 [arrowhead = none ];
5801 -> 470;

5802 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
470 -> 5802 [arrowhead = none ];
5802 -> 475;

5803 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
470 -> 5803 [arrowhead = none ];
5803 -> 476;

5804 [label="ONLY EVAL with clause\nquot(0, s(X799), s(X800), 0).\nand substitutionX799 -> s(0),\nX800 -> s(s(0)),\nX788 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
475 -> 5804 [arrowhead = none ];
5804 -> 480;

5805 [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 = lightgreen];
476 -> 5805 [arrowhead = none ];
5805 -> 483;

5806 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
480 -> 5806 [arrowhead = none ];
5806 -> 481;

5807 [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 = lightgreen];
483 -> 5807 [arrowhead = none ];
5807 -> 487;

5808 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
493 -> 5808 [arrowhead = none ];
5808 -> 499;

5809 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
499 -> 5809 [arrowhead = none ];
5809 -> 500;

5810 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
500 -> 5810 [arrowhead = none ];
5810 -> 504;

5811 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
500 -> 5811 [arrowhead = none ];
5811 -> 505;

5812 [label="ONLY EVAL with clause\nquot(s(X853), s(X854), X855, X856) :- quot(X853, X854, X855, X856).\nand substitutionX853 -> 0,\nX854 -> s(0),\nX855 -> s(s(0)),\nX822 -> X857,\nX856 -> X857", fontsize=14, style = filled, fillcolor = lightblue];
504 -> 5812 [arrowhead = none ];
5812 -> 510;

5813 [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 = lightgreen];
505 -> 5813 [arrowhead = none ];
5813 -> 535;

5814 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
510 -> 5814 [arrowhead = none ];
5814 -> 517;

5815 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
517 -> 5815 [arrowhead = none ];
5815 -> 522;

5816 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
517 -> 5816 [arrowhead = none ];
5816 -> 523;

5817 [label="ONLY EVAL with clause\nquot(0, s(X868), s(X869), 0).\nand substitutionX868 -> 0,\nX869 -> s(0),\nX857 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
522 -> 5817 [arrowhead = none ];
5817 -> 526;

5818 [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 = lightgreen];
523 -> 5818 [arrowhead = none ];
5818 -> 530;

5819 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
526 -> 5819 [arrowhead = none ];
5819 -> 527;

5820 [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 = lightgreen];
530 -> 5820 [arrowhead = none ];
5820 -> 533;

5821 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
543 -> 5821 [arrowhead = none ];
5821 -> 550;

5822 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
545 -> 5822 [arrowhead = none ];
5822 -> 599;

5823 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
550 -> 5823 [arrowhead = none ];
5823 -> 552;

5824 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
550 -> 5824 [arrowhead = none ];
5824 -> 553;

5825 [label="EVAL with clause\ntimes(0, X894, 0).\nand substitutionT22 -> 0,\nT20 -> T164,\nX894 -> s(s(T164)),\nX35 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
552 -> 5825 [arrowhead = none ];
5825 -> 558;

5826 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
552 -> 5826 [arrowhead = none ];
5826 -> 559;

5827 [label="EVAL with clause\ntimes(s(X904), X905, X906) :- ','(times(X904, X905, X907), add(X907, X905, X906)).\nand substitutionX904 -> T169,\nT22 -> s(T169),\nT20 -> T170,\nX905 -> s(s(T170)),\nX35 -> X908,\nX906 -> X908", fontsize=14, style = filled, fillcolor = lightblue];
553 -> 5827 [arrowhead = none ];
5827 -> 567;

5828 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
553 -> 5828 [arrowhead = none ];
5828 -> 568;

5829 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
558 -> 5829 [arrowhead = none ];
5829 -> 561;

5830 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
567 -> 5830 [arrowhead = none ];
5830 -> 573;

5831 [label="SPLIT 2\nnew knowledge:\nT169 is ground\nT170 is ground\nT173 is ground\nreplacements:X907 -> T173", fontsize=14, style = filled, fillcolor = violet];
567 -> 5831 [arrowhead = none ];
5831 -> 574;

5832 [label="INSTANCE with matching:\nT22 -> T169\nT20 -> T170\nX35 -> X907", fontsize=14, style = filled, fillcolor = lightgrey];
573 -> 5832 [arrowhead = none , style=dashed];
5832 -> 543[style=dashed];

5833 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
574 -> 5833 [arrowhead = none ];
5833 -> 577;

5834 [label="BACKTRACK\nfor clause: add(X, 0, X)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
577 -> 5834 [arrowhead = none ];
5834 -> 578;

5835 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
578 -> 5835 [arrowhead = none ];
5835 -> 580;

5836 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
578 -> 5836 [arrowhead = none ];
5836 -> 581;

5837 [label="EVAL with clause\nadd(0, X920, X920).\nand substitutionT173 -> 0,\nT170 -> T183,\nX920 -> s(s(T183)),\nX908 -> s(s(T183))", fontsize=14, style = filled, fillcolor = lightblue];
580 -> 5837 [arrowhead = none ];
5837 -> 585;

5838 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
580 -> 5838 [arrowhead = none ];
5838 -> 586;

5839 [label="EVAL with clause\nadd(s(X929), X930, s(X931)) :- add(X929, X930, X931).\nand substitutionX929 -> T188,\nT173 -> s(T188),\nT170 -> T189,\nX930 -> s(s(T189)),\nX931 -> X932,\nX908 -> s(X932)", fontsize=14, style = filled, fillcolor = lightblue];
581 -> 5839 [arrowhead = none ];
5839 -> 593;

5840 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
581 -> 5840 [arrowhead = none ];
5840 -> 594;

5841 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
585 -> 5841 [arrowhead = none ];
5841 -> 587;

5842 [label="INSTANCE with matching:\nT173 -> T188\nT170 -> T189\nX908 -> X932", fontsize=14, style = filled, fillcolor = lightgrey];
593 -> 5842 [arrowhead = none , style=dashed];
5842 -> 574[style=dashed];

5843 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
599 -> 5843 [arrowhead = none ];
5843 -> 600;

5844 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
599 -> 5844 [arrowhead = none ];
5844 -> 601;

5845 [label="EVAL with clause\nneq(s(X941), 0).\nand substitutionT20 -> T198,\nX941 -> s(s(T198)),\nT157 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
600 -> 5845 [arrowhead = none ];
5845 -> 603;

5846 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
600 -> 5846 [arrowhead = none ];
5846 -> 604;

5847 [label="BACKTRACK\nfor clause: neq(0, s(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
601 -> 5847 [arrowhead = none ];
5847 -> 608;

5848 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
603 -> 5848 [arrowhead = none ];
5848 -> 607;

5849 [label="EVAL with clause\nneq(s(X947), s(X948)) :- neq(X947, X948).\nand substitutionT20 -> T203,\nX947 -> s(s(T203)),\nX948 -> T204,\nT157 -> s(T204)", fontsize=14, style = filled, fillcolor = lightblue];
608 -> 5849 [arrowhead = none ];
5849 -> 613;

5850 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
608 -> 5850 [arrowhead = none ];
5850 -> 614;

5851 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
613 -> 5851 [arrowhead = none ];
5851 -> 617;

5852 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
617 -> 5852 [arrowhead = none ];
5852 -> 619;

5853 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
617 -> 5853 [arrowhead = none ];
5853 -> 620;

5854 [label="EVAL with clause\nneq(s(X955), 0).\nand substitutionT203 -> T211,\nX955 -> s(T211),\nT204 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
619 -> 5854 [arrowhead = none ];
5854 -> 623;

5855 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
619 -> 5855 [arrowhead = none ];
5855 -> 624;

5856 [label="BACKTRACK\nfor clause: neq(0, s(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
620 -> 5856 [arrowhead = none ];
5856 -> 629;

5857 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
623 -> 5857 [arrowhead = none ];
5857 -> 626;

5858 [label="EVAL with clause\nneq(s(X961), s(X962)) :- neq(X961, X962).\nand substitutionT203 -> T216,\nX961 -> s(T216),\nX962 -> T217,\nT204 -> s(T217)", fontsize=14, style = filled, fillcolor = lightblue];
629 -> 5858 [arrowhead = none ];
5858 -> 633;

5859 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
629 -> 5859 [arrowhead = none ];
5859 -> 634;

5860 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
633 -> 5860 [arrowhead = none ];
5860 -> 639;

5861 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
639 -> 5861 [arrowhead = none ];
5861 -> 641;

5862 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
639 -> 5862 [arrowhead = none ];
5862 -> 642;

5863 [label="EVAL with clause\nneq(s(X969), 0).\nand substitutionT216 -> T224,\nX969 -> T224,\nT217 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
641 -> 5863 [arrowhead = none ];
5863 -> 645;

5864 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
641 -> 5864 [arrowhead = none ];
5864 -> 646;

5865 [label="BACKTRACK\nfor clause: neq(0, s(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
642 -> 5865 [arrowhead = none ];
5865 -> 648;

5866 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
645 -> 5866 [arrowhead = none ];
5866 -> 647;

5867 [label="EVAL with clause\nneq(s(X975), s(X976)) :- neq(X975, X976).\nand substitutionT216 -> T229,\nX975 -> T229,\nX976 -> T230,\nT217 -> s(T230)", fontsize=14, style = filled, fillcolor = lightblue];
648 -> 5867 [arrowhead = none ];
5867 -> 655;

5868 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
648 -> 5868 [arrowhead = none ];
5868 -> 656;

5869 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
655 -> 5869 [arrowhead = none ];
5869 -> 660;

5870 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
660 -> 5870 [arrowhead = none ];
5870 -> 663;

5871 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
660 -> 5871 [arrowhead = none ];
5871 -> 664;

5872 [label="EVAL with clause\nneq(s(X983), 0).\nand substitutionX983 -> T237,\nT229 -> s(T237),\nT230 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
663 -> 5872 [arrowhead = none ];
5872 -> 667;

5873 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
663 -> 5873 [arrowhead = none ];
5873 -> 668;

5874 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
664 -> 5874 [arrowhead = none ];
5874 -> 673;

5875 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
664 -> 5875 [arrowhead = none ];
5875 -> 674;

5876 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
667 -> 5876 [arrowhead = none ];
5876 -> 669;

5877 [label="EVAL with clause\nneq(0, s(X988)).\nand substitutionT229 -> 0,\nX988 -> T242,\nT230 -> s(T242)", fontsize=14, style = filled, fillcolor = lightblue];
673 -> 5877 [arrowhead = none ];
5877 -> 677;

5878 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
673 -> 5878 [arrowhead = none ];
5878 -> 678;

5879 [label="EVAL with clause\nneq(s(X993), s(X994)) :- neq(X993, X994).\nand substitutionX993 -> T247,\nT229 -> s(T247),\nX994 -> T248,\nT230 -> s(T248)", fontsize=14, style = filled, fillcolor = lightblue];
674 -> 5879 [arrowhead = none ];
5879 -> 683;

5880 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
674 -> 5880 [arrowhead = none ];
5880 -> 685;

5881 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
677 -> 5881 [arrowhead = none ];
5881 -> 679;

5882 [label="INSTANCE with matching:\nT229 -> T247\nT230 -> T248", fontsize=14, style = filled, fillcolor = lightgrey];
683 -> 5882 [arrowhead = none , style=dashed];
5882 -> 655[style=dashed];

5883 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
690 -> 5883 [arrowhead = none ];
5883 -> 694;

5884 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
690 -> 5884 [arrowhead = none ];
5884 -> 695;

5885 [label="EVAL with clause\npr(X1003, s(0)).\nand substitutionT14 -> 0,\nX1003 -> s(s(s(0))),\nT257 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
694 -> 5885 [arrowhead = none ];
5885 -> 699;

5886 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
694 -> 5886 [arrowhead = none ];
5886 -> 700;

5887 [label="EVAL with clause\npr(X1008, s(s(X1009))) :- ','(not_divides(s(s(X1009)), X1008), pr(X1008, s(X1009))).\nand substitutionT14 -> s(T263),\nX1008 -> s(s(s(s(T263)))),\nX1009 -> T263,\nT262 -> s(T263)", fontsize=14, style = filled, fillcolor = lightblue];
695 -> 5887 [arrowhead = none ];
5887 -> 707;

5888 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
695 -> 5888 [arrowhead = none ];
5888 -> 708;

5889 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
699 -> 5889 [arrowhead = none ];
5889 -> 701;

5890 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
707 -> 5890 [arrowhead = none ];
5890 -> 711;

5891 [label="SPLIT 2\nnew knowledge:\nT263 is ground", fontsize=14, style = filled, fillcolor = violet];
707 -> 5891 [arrowhead = none ];
5891 -> 712;

5892 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
711 -> 5892 [arrowhead = none ];
5892 -> 715;

5893 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
712 -> 5893 [arrowhead = none ];
5893 -> 1409;

5894 [label="ONLY EVAL with clause\nnot_divides(X1028, X1029) :- ','(div(X1029, X1028, X1030), ','(times(X1030, X1028, X1031), neq(X1029, X1031))).\nand substitutionT263 -> T269,\nX1028 -> s(s(T269)),\nX1029 -> s(s(s(s(T269))))", fontsize=14, style = filled, fillcolor = lightblue];
715 -> 5894 [arrowhead = none ];
5894 -> 720;

5895 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
720 -> 5895 [arrowhead = none ];
5895 -> 723;

5896 [label="SPLIT 2\nnew knowledge:\nT269 is ground\nT271 is ground\nreplacements:X1030 -> T271", fontsize=14, style = filled, fillcolor = violet];
720 -> 5896 [arrowhead = none ];
5896 -> 724;

5897 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
723 -> 5897 [arrowhead = none ];
5897 -> 728;

5898 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
724 -> 5898 [arrowhead = none ];
5898 -> 1402;

5899 [label="SPLIT 2\nnew knowledge:\nT271 is ground\nT269 is ground\nT407 is ground\nreplacements:X1031 -> T407", fontsize=14, style = filled, fillcolor = violet];
724 -> 5899 [arrowhead = none ];
5899 -> 1403;

5900 [label="ONLY EVAL with clause\ndiv(X1052, X1053, X1054) :- quot(X1052, X1053, X1053, X1054).\nand substitutionT269 -> T275,\nX1052 -> s(s(s(s(T275)))),\nX1053 -> s(s(T275)),\nX1030 -> X1055,\nX1054 -> X1055", fontsize=14, style = filled, fillcolor = lightblue];
728 -> 5900 [arrowhead = none ];
5900 -> 732;

5901 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
732 -> 5901 [arrowhead = none ];
5901 -> 734;

5902 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
734 -> 5902 [arrowhead = none ];
5902 -> 735;

5903 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
735 -> 5903 [arrowhead = none ];
5903 -> 745;

5904 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
735 -> 5904 [arrowhead = none ];
5904 -> 746;

5905 [label="ONLY EVAL with clause\nquot(s(X1090), s(X1091), X1092, X1093) :- quot(X1090, X1091, X1092, X1093).\nand substitutionT275 -> T280,\nX1090 -> s(s(s(T280))),\nX1091 -> s(T280),\nX1092 -> s(s(T280)),\nX1055 -> X1094,\nX1093 -> X1094", fontsize=14, style = filled, fillcolor = lightblue];
745 -> 5905 [arrowhead = none ];
5905 -> 749;

5906 [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 = lightgreen];
746 -> 5906 [arrowhead = none ];
5906 -> 1401;

5907 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
749 -> 5907 [arrowhead = none ];
5907 -> 751;

5908 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
751 -> 5908 [arrowhead = none ];
5908 -> 754;

5909 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
754 -> 5909 [arrowhead = none ];
5909 -> 760;

5910 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
754 -> 5910 [arrowhead = none ];
5910 -> 761;

5911 [label="ONLY EVAL with clause\nquot(s(X1129), s(X1130), X1131, X1132) :- quot(X1129, X1130, X1131, X1132).\nand substitutionT280 -> T285,\nX1129 -> s(s(T285)),\nX1130 -> T285,\nX1131 -> s(s(T285)),\nX1094 -> X1133,\nX1132 -> X1133", fontsize=14, style = filled, fillcolor = lightblue];
760 -> 5911 [arrowhead = none ];
5911 -> 768;

5912 [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 = lightgreen];
761 -> 5912 [arrowhead = none ];
5912 -> 1398;

5913 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
768 -> 5913 [arrowhead = none ];
5913 -> 772;

5914 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
772 -> 5914 [arrowhead = none ];
5914 -> 774;

5915 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
774 -> 5915 [arrowhead = none ];
5915 -> 779;

5916 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
774 -> 5916 [arrowhead = none ];
5916 -> 780;

5917 [label="EVAL with clause\nquot(s(X1160), s(X1161), X1162, X1163) :- quot(X1160, X1161, X1162, X1163).\nand substitutionT285 -> s(T295),\nX1160 -> s(s(T295)),\nX1161 -> T295,\nT294 -> s(T295),\nX1162 -> s(s(s(T295))),\nX1133 -> X1164,\nX1163 -> X1164", fontsize=14, style = filled, fillcolor = lightblue];
779 -> 5917 [arrowhead = none ];
5917 -> 783;

5918 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
779 -> 5918 [arrowhead = none ];
5918 -> 784;

5919 [label="EVAL with clause\nquot(X2136, 0, s(X2137), s(X2138)) :- quot(X2136, s(X2137), s(X2137), X2138).\nand substitutionT285 -> 0,\nX2136 -> s(s(0)),\nT402 -> 0,\nX2137 -> s(0),\nX2138 -> X2139,\nX1133 -> s(X2139)", fontsize=14, style = filled, fillcolor = lightblue];
780 -> 5919 [arrowhead = none ];
5919 -> 1332;

5920 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
780 -> 5920 [arrowhead = none ];
5920 -> 1333;

5921 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
783 -> 5921 [arrowhead = none ];
5921 -> 791;

5922 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
791 -> 5922 [arrowhead = none ];
5922 -> 794;

5923 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
794 -> 5923 [arrowhead = none ];
5923 -> 803;

5924 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
794 -> 5924 [arrowhead = none ];
5924 -> 804;

5925 [label="EVAL with clause\nquot(s(X1191), s(X1192), X1193, X1194) :- quot(X1191, X1192, X1193, X1194).\nand substitutionT295 -> s(T305),\nX1191 -> s(s(T305)),\nX1192 -> T305,\nT304 -> s(T305),\nX1193 -> s(s(s(s(T305)))),\nX1164 -> X1195,\nX1194 -> X1195", fontsize=14, style = filled, fillcolor = lightblue];
803 -> 5925 [arrowhead = none ];
5925 -> 808;

5926 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
803 -> 5926 [arrowhead = none ];
5926 -> 809;

5927 [label="EVAL with clause\nquot(X2025, 0, s(X2026), s(X2027)) :- quot(X2025, s(X2026), s(X2026), X2027).\nand substitutionT295 -> 0,\nX2025 -> s(s(0)),\nT399 -> 0,\nX2026 -> s(s(0)),\nX2027 -> X2028,\nX1164 -> s(X2028)", fontsize=14, style = filled, fillcolor = lightblue];
804 -> 5927 [arrowhead = none ];
5927 -> 1261;

5928 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
804 -> 5928 [arrowhead = none ];
5928 -> 1262;

5929 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
808 -> 5929 [arrowhead = none ];
5929 -> 812;

5930 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
812 -> 5930 [arrowhead = none ];
5930 -> 816;

5931 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
816 -> 5931 [arrowhead = none ];
5931 -> 819;

5932 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
816 -> 5932 [arrowhead = none ];
5932 -> 820;

5933 [label="EVAL with clause\nquot(s(X1222), s(X1223), X1224, X1225) :- quot(X1222, X1223, X1224, X1225).\nand substitutionT305 -> s(T315),\nX1222 -> s(s(T315)),\nX1223 -> T315,\nT314 -> s(T315),\nX1224 -> s(s(s(s(s(T315))))),\nX1195 -> X1226,\nX1225 -> X1226", fontsize=14, style = filled, fillcolor = lightblue];
819 -> 5933 [arrowhead = none ];
5933 -> 830;

5934 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
819 -> 5934 [arrowhead = none ];
5934 -> 831;

5935 [label="EVAL with clause\nquot(X1914, 0, s(X1915), s(X1916)) :- quot(X1914, s(X1915), s(X1915), X1916).\nand substitutionT305 -> 0,\nX1914 -> s(s(0)),\nT396 -> 0,\nX1915 -> s(s(s(0))),\nX1916 -> X1917,\nX1195 -> s(X1917)", fontsize=14, style = filled, fillcolor = lightblue];
820 -> 5935 [arrowhead = none ];
5935 -> 1194;

5936 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
820 -> 5936 [arrowhead = none ];
5936 -> 1195;

5937 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
830 -> 5937 [arrowhead = none ];
5937 -> 835;

5938 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
835 -> 5938 [arrowhead = none ];
5938 -> 838;

5939 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
838 -> 5939 [arrowhead = none ];
5939 -> 841;

5940 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
838 -> 5940 [arrowhead = none ];
5940 -> 842;

5941 [label="EVAL with clause\nquot(s(X1253), s(X1254), X1255, X1256) :- quot(X1253, X1254, X1255, X1256).\nand substitutionT315 -> s(T325),\nX1253 -> s(s(T325)),\nX1254 -> T325,\nT324 -> s(T325),\nX1255 -> s(s(s(s(s(s(T325)))))),\nX1226 -> X1257,\nX1256 -> X1257", fontsize=14, style = filled, fillcolor = lightblue];
841 -> 5941 [arrowhead = none ];
5941 -> 848;

5942 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
841 -> 5942 [arrowhead = none ];
5942 -> 849;

5943 [label="EVAL with clause\nquot(X1803, 0, s(X1804), s(X1805)) :- quot(X1803, s(X1804), s(X1804), X1805).\nand substitutionT315 -> 0,\nX1803 -> s(s(0)),\nT393 -> 0,\nX1804 -> s(s(s(s(0)))),\nX1805 -> X1806,\nX1226 -> s(X1806)", fontsize=14, style = filled, fillcolor = lightblue];
842 -> 5943 [arrowhead = none ];
5943 -> 1140;

5944 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
842 -> 5944 [arrowhead = none ];
5944 -> 1141;

5945 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
848 -> 5945 [arrowhead = none ];
5945 -> 855;

5946 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
855 -> 5946 [arrowhead = none ];
5946 -> 858;

5947 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
858 -> 5947 [arrowhead = none ];
5947 -> 863;

5948 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
858 -> 5948 [arrowhead = none ];
5948 -> 864;

5949 [label="EVAL with clause\nquot(s(X1284), s(X1285), X1286, X1287) :- quot(X1284, X1285, X1286, X1287).\nand substitutionT325 -> s(T335),\nX1284 -> s(s(T335)),\nX1285 -> T335,\nT334 -> s(T335),\nX1286 -> s(s(s(s(s(s(s(T335))))))),\nX1257 -> X1288,\nX1287 -> X1288", fontsize=14, style = filled, fillcolor = lightblue];
863 -> 5949 [arrowhead = none ];
5949 -> 865;

5950 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
863 -> 5950 [arrowhead = none ];
5950 -> 866;

5951 [label="EVAL with clause\nquot(X1692, 0, s(X1693), s(X1694)) :- quot(X1692, s(X1693), s(X1693), X1694).\nand substitutionT325 -> 0,\nX1692 -> s(s(0)),\nT390 -> 0,\nX1693 -> s(s(s(s(s(0))))),\nX1694 -> X1695,\nX1257 -> s(X1695)", fontsize=14, style = filled, fillcolor = lightblue];
864 -> 5951 [arrowhead = none ];
5951 -> 1073;

5952 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
864 -> 5952 [arrowhead = none ];
5952 -> 1074;

5953 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
865 -> 5953 [arrowhead = none ];
5953 -> 869;

5954 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
869 -> 5954 [arrowhead = none ];
5954 -> 874;

5955 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
874 -> 5955 [arrowhead = none ];
5955 -> 879;

5956 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
874 -> 5956 [arrowhead = none ];
5956 -> 880;

5957 [label="EVAL with clause\nquot(s(X1315), s(X1316), X1317, X1318) :- quot(X1315, X1316, X1317, X1318).\nand substitutionT335 -> s(T345),\nX1315 -> s(s(T345)),\nX1316 -> T345,\nT344 -> s(T345),\nX1317 -> s(s(s(s(s(s(s(s(T345)))))))),\nX1288 -> X1319,\nX1318 -> X1319", fontsize=14, style = filled, fillcolor = lightblue];
879 -> 5957 [arrowhead = none ];
5957 -> 884;

5958 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
879 -> 5958 [arrowhead = none ];
5958 -> 885;

5959 [label="EVAL with clause\nquot(X1581, 0, s(X1582), s(X1583)) :- quot(X1581, s(X1582), s(X1582), X1583).\nand substitutionT335 -> 0,\nX1581 -> s(s(0)),\nT387 -> 0,\nX1582 -> s(s(s(s(s(s(0)))))),\nX1583 -> X1584,\nX1288 -> s(X1584)", fontsize=14, style = filled, fillcolor = lightblue];
880 -> 5959 [arrowhead = none ];
5959 -> 1010;

5960 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
880 -> 5960 [arrowhead = none ];
5960 -> 1011;

5961 [label="GENERALIZATION\nT346 <-- s(s(s(s(s(s(s(T345)))))))\n\nNew Knowledge:\nT346 is ground", fontsize=14, style = filled, fillcolor = violet];
884 -> 5961 [arrowhead = none ];
5961 -> 888;

5962 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
888 -> 5962 [arrowhead = none ];
5962 -> 890;

5963 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
890 -> 5963 [arrowhead = none ];
5963 -> 892;

5964 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
892 -> 5964 [arrowhead = none ];
5964 -> 896;

5965 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
892 -> 5965 [arrowhead = none ];
5965 -> 897;

5966 [label="EVAL with clause\nquot(s(X1350), s(X1351), X1352, X1353) :- quot(X1350, X1351, X1352, X1353).\nand substitutionT345 -> s(T360),\nX1350 -> s(s(T360)),\nX1351 -> T360,\nT359 -> s(T360),\nT346 -> T361,\nX1352 -> s(T361),\nX1319 -> X1354,\nX1353 -> X1354", fontsize=14, style = filled, fillcolor = lightblue];
896 -> 5966 [arrowhead = none ];
5966 -> 900;

5967 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
896 -> 5967 [arrowhead = none ];
5967 -> 901;

5968 [label="EVAL with clause\nquot(X1367, 0, s(X1368), s(X1369)) :- quot(X1367, s(X1368), s(X1368), X1369).\nand substitutionT345 -> 0,\nX1367 -> s(s(0)),\nT366 -> 0,\nT346 -> T367,\nX1368 -> T367,\nX1369 -> X1370,\nX1319 -> s(X1370)", fontsize=14, style = filled, fillcolor = lightblue];
897 -> 5968 [arrowhead = none ];
5968 -> 905;

5969 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
897 -> 5969 [arrowhead = none ];
5969 -> 906;

5970 [label="INSTANCE with matching:\nT345 -> T360\nT346 -> T361\nX1319 -> X1354", fontsize=14, style = filled, fillcolor = lightgrey];
900 -> 5970 [arrowhead = none , style=dashed];
5970 -> 888[style=dashed];

5971 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
905 -> 5971 [arrowhead = none ];
5971 -> 907;

5972 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
907 -> 5972 [arrowhead = none ];
5972 -> 909;

5973 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
909 -> 5973 [arrowhead = none ];
5973 -> 912;

5974 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
909 -> 5974 [arrowhead = none ];
5974 -> 913;

5975 [label="ONLY EVAL with clause\nquot(s(X1405), s(X1406), X1407, X1408) :- quot(X1405, X1406, X1407, X1408).\nand substitutionX1405 -> s(0),\nT367 -> T372,\nX1406 -> T372,\nX1407 -> s(T372),\nX1370 -> X1409,\nX1408 -> X1409", fontsize=14, style = filled, fillcolor = lightblue];
912 -> 5975 [arrowhead = none ];
5975 -> 918;

5976 [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 = lightgreen];
913 -> 5976 [arrowhead = none ];
5976 -> 1003;

5977 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
918 -> 5977 [arrowhead = none ];
5977 -> 921;

5978 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
921 -> 5978 [arrowhead = none ];
5978 -> 922;

5979 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
922 -> 5979 [arrowhead = none ];
5979 -> 924;

5980 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
922 -> 5980 [arrowhead = none ];
5980 -> 925;

5981 [label="EVAL with clause\nquot(s(X1436), s(X1437), X1438, X1439) :- quot(X1436, X1437, X1438, X1439).\nand substitutionX1436 -> 0,\nX1437 -> T377,\nT372 -> s(T377),\nX1438 -> s(s(T377)),\nX1409 -> X1440,\nX1439 -> X1440", fontsize=14, style = filled, fillcolor = lightblue];
924 -> 5981 [arrowhead = none ];
5981 -> 928;

5982 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
924 -> 5982 [arrowhead = none ];
5982 -> 929;

5983 [label="EVAL with clause\nquot(X1498, 0, s(X1499), s(X1500)) :- quot(X1498, s(X1499), s(X1499), X1500).\nand substitutionX1498 -> s(0),\nT372 -> 0,\nX1499 -> 0,\nX1500 -> X1501,\nX1409 -> s(X1501)", fontsize=14, style = filled, fillcolor = lightblue];
925 -> 5983 [arrowhead = none ];
5983 -> 960;

5984 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
925 -> 5984 [arrowhead = none ];
5984 -> 961;

5985 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
928 -> 5985 [arrowhead = none ];
5985 -> 932;

5986 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
932 -> 5986 [arrowhead = none ];
5986 -> 933;

5987 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
932 -> 5987 [arrowhead = none ];
5987 -> 934;

5988 [label="EVAL with clause\nquot(0, s(X1453), s(X1454), 0).\nand substitutionX1453 -> T384,\nT377 -> s(T384),\nX1454 -> s(s(T384)),\nX1440 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
933 -> 5988 [arrowhead = none ];
5988 -> 937;

5989 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
933 -> 5989 [arrowhead = none ];
5989 -> 938;

5990 [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 = lightgreen];
934 -> 5990 [arrowhead = none ];
5990 -> 940;

5991 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
937 -> 5991 [arrowhead = none ];
5991 -> 939;

5992 [label="EVAL with clause\nquot(X1467, 0, s(X1468), s(X1469)) :- quot(X1467, s(X1468), s(X1468), X1469).\nand substitutionX1467 -> 0,\nT377 -> 0,\nX1468 -> s(0),\nX1469 -> X1470,\nX1440 -> s(X1470)", fontsize=14, style = filled, fillcolor = lightblue];
940 -> 5992 [arrowhead = none ];
5992 -> 943;

5993 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
940 -> 5993 [arrowhead = none ];
5993 -> 944;

5994 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
943 -> 5994 [arrowhead = none ];
5994 -> 945;

5995 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
945 -> 5995 [arrowhead = none ];
5995 -> 948;

5996 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
945 -> 5996 [arrowhead = none ];
5996 -> 949;

5997 [label="ONLY EVAL with clause\nquot(0, s(X1481), s(X1482), 0).\nand substitutionX1481 -> s(0),\nX1482 -> s(0),\nX1470 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
948 -> 5997 [arrowhead = none ];
5997 -> 952;

5998 [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 = lightgreen];
949 -> 5998 [arrowhead = none ];
5998 -> 954;

5999 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
952 -> 5999 [arrowhead = none ];
5999 -> 953;

6000 [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 = lightgreen];
954 -> 6000 [arrowhead = none ];
6000 -> 955;

6001 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
960 -> 6001 [arrowhead = none ];
6001 -> 962;

6002 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
962 -> 6002 [arrowhead = none ];
6002 -> 964;

6003 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
964 -> 6003 [arrowhead = none ];
6003 -> 971;

6004 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
964 -> 6004 [arrowhead = none ];
6004 -> 972;

6005 [label="ONLY EVAL with clause\nquot(s(X1536), s(X1537), X1538, X1539) :- quot(X1536, X1537, X1538, X1539).\nand substitutionX1536 -> 0,\nX1537 -> 0,\nX1538 -> s(0),\nX1501 -> X1540,\nX1539 -> X1540", fontsize=14, style = filled, fillcolor = lightblue];
971 -> 6005 [arrowhead = none ];
6005 -> 979;

6006 [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 = lightgreen];
972 -> 6006 [arrowhead = none ];
6006 -> 999;

6007 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
979 -> 6007 [arrowhead = none ];
6007 -> 983;

6008 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
983 -> 6008 [arrowhead = none ];
6008 -> 985;

6009 [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 = lightgreen];
985 -> 6009 [arrowhead = none ];
6009 -> 987;

6010 [label="ONLY EVAL with clause\nquot(X1561, 0, s(X1562), s(X1563)) :- quot(X1561, s(X1562), s(X1562), X1563).\nand substitutionX1561 -> 0,\nX1562 -> 0,\nX1563 -> X1564,\nX1540 -> s(X1564)", fontsize=14, style = filled, fillcolor = lightblue];
987 -> 6010 [arrowhead = none ];
6010 -> 996;

6011 [label="INSTANCE with matching:\nX443 -> X1564", fontsize=14, style = filled, fillcolor = lightgrey];
996 -> 6011 [arrowhead = none , style=dashed];
6011 -> 258[style=dashed];

6012 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1010 -> 6012 [arrowhead = none ];
6012 -> 1015;

6013 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1015 -> 6013 [arrowhead = none ];
6013 -> 1019;

6014 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1019 -> 6014 [arrowhead = none ];
6014 -> 1024;

6015 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1019 -> 6015 [arrowhead = none ];
6015 -> 1025;

6016 [label="ONLY EVAL with clause\nquot(s(X1619), s(X1620), X1621, X1622) :- quot(X1619, X1620, X1621, X1622).\nand substitutionX1619 -> s(0),\nX1620 -> s(s(s(s(s(s(0)))))),\nX1621 -> s(s(s(s(s(s(s(0))))))),\nX1584 -> X1623,\nX1622 -> X1623", fontsize=14, style = filled, fillcolor = lightblue];
1024 -> 6016 [arrowhead = none ];
6016 -> 1034;

6017 [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 = lightgreen];
1025 -> 6017 [arrowhead = none ];
6017 -> 1068;

6018 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1034 -> 6018 [arrowhead = none ];
6018 -> 1036;

6019 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1036 -> 6019 [arrowhead = none ];
6019 -> 1037;

6020 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1037 -> 6020 [arrowhead = none ];
6020 -> 1041;

6021 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1037 -> 6021 [arrowhead = none ];
6021 -> 1042;

6022 [label="ONLY EVAL with clause\nquot(s(X1654), s(X1655), X1656, X1657) :- quot(X1654, X1655, X1656, X1657).\nand substitutionX1654 -> 0,\nX1655 -> s(s(s(s(s(0))))),\nX1656 -> s(s(s(s(s(s(s(0))))))),\nX1623 -> X1658,\nX1657 -> X1658", fontsize=14, style = filled, fillcolor = lightblue];
1041 -> 6022 [arrowhead = none ];
6022 -> 1050;

6023 [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 = lightgreen];
1042 -> 6023 [arrowhead = none ];
6023 -> 1067;

6024 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1050 -> 6024 [arrowhead = none ];
6024 -> 1052;

6025 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1052 -> 6025 [arrowhead = none ];
6025 -> 1053;

6026 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1052 -> 6026 [arrowhead = none ];
6026 -> 1054;

6027 [label="ONLY EVAL with clause\nquot(0, s(X1669), s(X1670), 0).\nand substitutionX1669 -> s(s(s(s(0)))),\nX1670 -> s(s(s(s(s(s(0)))))),\nX1658 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1053 -> 6027 [arrowhead = none ];
6027 -> 1059;

6028 [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 = lightgreen];
1054 -> 6028 [arrowhead = none ];
6028 -> 1061;

6029 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1059 -> 6029 [arrowhead = none ];
6029 -> 1060;

6030 [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 = lightgreen];
1061 -> 6030 [arrowhead = none ];
6030 -> 1064;

6031 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1073 -> 6031 [arrowhead = none ];
6031 -> 1078;

6032 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1078 -> 6032 [arrowhead = none ];
6032 -> 1079;

6033 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1079 -> 6033 [arrowhead = none ];
6033 -> 1083;

6034 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1079 -> 6034 [arrowhead = none ];
6034 -> 1084;

6035 [label="ONLY EVAL with clause\nquot(s(X1730), s(X1731), X1732, X1733) :- quot(X1730, X1731, X1732, X1733).\nand substitutionX1730 -> s(0),\nX1731 -> s(s(s(s(s(0))))),\nX1732 -> s(s(s(s(s(s(0)))))),\nX1695 -> X1734,\nX1733 -> X1734", fontsize=14, style = filled, fillcolor = lightblue];
1083 -> 6035 [arrowhead = none ];
6035 -> 1089;

6036 [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 = lightgreen];
1084 -> 6036 [arrowhead = none ];
6036 -> 1131;

6037 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1089 -> 6037 [arrowhead = none ];
6037 -> 1095;

6038 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1095 -> 6038 [arrowhead = none ];
6038 -> 1096;

6039 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1096 -> 6039 [arrowhead = none ];
6039 -> 1103;

6040 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1096 -> 6040 [arrowhead = none ];
6040 -> 1104;

6041 [label="ONLY EVAL with clause\nquot(s(X1765), s(X1766), X1767, X1768) :- quot(X1765, X1766, X1767, X1768).\nand substitutionX1765 -> 0,\nX1766 -> s(s(s(s(0)))),\nX1767 -> s(s(s(s(s(s(0)))))),\nX1734 -> X1769,\nX1768 -> X1769", fontsize=14, style = filled, fillcolor = lightblue];
1103 -> 6041 [arrowhead = none ];
6041 -> 1110;

6042 [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 = lightgreen];
1104 -> 6042 [arrowhead = none ];
6042 -> 1130;

6043 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1110 -> 6043 [arrowhead = none ];
6043 -> 1114;

6044 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1114 -> 6044 [arrowhead = none ];
6044 -> 1117;

6045 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1114 -> 6045 [arrowhead = none ];
6045 -> 1118;

6046 [label="ONLY EVAL with clause\nquot(0, s(X1780), s(X1781), 0).\nand substitutionX1780 -> s(s(s(0))),\nX1781 -> s(s(s(s(s(0))))),\nX1769 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1117 -> 6046 [arrowhead = none ];
6046 -> 1120;

6047 [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 = lightgreen];
1118 -> 6047 [arrowhead = none ];
6047 -> 1124;

6048 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1120 -> 6048 [arrowhead = none ];
6048 -> 1122;

6049 [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 = lightgreen];
1124 -> 6049 [arrowhead = none ];
6049 -> 1128;

6050 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1140 -> 6050 [arrowhead = none ];
6050 -> 1142;

6051 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1142 -> 6051 [arrowhead = none ];
6051 -> 1143;

6052 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1143 -> 6052 [arrowhead = none ];
6052 -> 1150;

6053 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1143 -> 6053 [arrowhead = none ];
6053 -> 1151;

6054 [label="ONLY EVAL with clause\nquot(s(X1841), s(X1842), X1843, X1844) :- quot(X1841, X1842, X1843, X1844).\nand substitutionX1841 -> s(0),\nX1842 -> s(s(s(s(0)))),\nX1843 -> s(s(s(s(s(0))))),\nX1806 -> X1845,\nX1844 -> X1845", fontsize=14, style = filled, fillcolor = lightblue];
1150 -> 6054 [arrowhead = none ];
6054 -> 1157;

6055 [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 = lightgreen];
1151 -> 6055 [arrowhead = none ];
6055 -> 1187;

6056 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1157 -> 6056 [arrowhead = none ];
6056 -> 1160;

6057 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1160 -> 6057 [arrowhead = none ];
6057 -> 1161;

6058 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1161 -> 6058 [arrowhead = none ];
6058 -> 1165;

6059 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1161 -> 6059 [arrowhead = none ];
6059 -> 1166;

6060 [label="ONLY EVAL with clause\nquot(s(X1876), s(X1877), X1878, X1879) :- quot(X1876, X1877, X1878, X1879).\nand substitutionX1876 -> 0,\nX1877 -> s(s(s(0))),\nX1878 -> s(s(s(s(s(0))))),\nX1845 -> X1880,\nX1879 -> X1880", fontsize=14, style = filled, fillcolor = lightblue];
1165 -> 6060 [arrowhead = none ];
6060 -> 1171;

6061 [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 = lightgreen];
1166 -> 6061 [arrowhead = none ];
6061 -> 1185;

6062 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1171 -> 6062 [arrowhead = none ];
6062 -> 1176;

6063 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1176 -> 6063 [arrowhead = none ];
6063 -> 1177;

6064 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1176 -> 6064 [arrowhead = none ];
6064 -> 1178;

6065 [label="ONLY EVAL with clause\nquot(0, s(X1891), s(X1892), 0).\nand substitutionX1891 -> s(s(0)),\nX1892 -> s(s(s(s(0)))),\nX1880 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1177 -> 6065 [arrowhead = none ];
6065 -> 1179;

6066 [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 = lightgreen];
1178 -> 6066 [arrowhead = none ];
6066 -> 1182;

6067 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1179 -> 6067 [arrowhead = none ];
6067 -> 1180;

6068 [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 = lightgreen];
1182 -> 6068 [arrowhead = none ];
6068 -> 1183;

6069 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1194 -> 6069 [arrowhead = none ];
6069 -> 1198;

6070 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1198 -> 6070 [arrowhead = none ];
6070 -> 1200;

6071 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1200 -> 6071 [arrowhead = none ];
6071 -> 1208;

6072 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1200 -> 6072 [arrowhead = none ];
6072 -> 1209;

6073 [label="ONLY EVAL with clause\nquot(s(X1952), s(X1953), X1954, X1955) :- quot(X1952, X1953, X1954, X1955).\nand substitutionX1952 -> s(0),\nX1953 -> s(s(s(0))),\nX1954 -> s(s(s(s(0)))),\nX1917 -> X1956,\nX1955 -> X1956", fontsize=14, style = filled, fillcolor = lightblue];
1208 -> 6073 [arrowhead = none ];
6073 -> 1220;

6074 [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 = lightgreen];
1209 -> 6074 [arrowhead = none ];
6074 -> 1254;

6075 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1220 -> 6075 [arrowhead = none ];
6075 -> 1223;

6076 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1223 -> 6076 [arrowhead = none ];
6076 -> 1225;

6077 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1225 -> 6077 [arrowhead = none ];
6077 -> 1229;

6078 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1225 -> 6078 [arrowhead = none ];
6078 -> 1230;

6079 [label="ONLY EVAL with clause\nquot(s(X1987), s(X1988), X1989, X1990) :- quot(X1987, X1988, X1989, X1990).\nand substitutionX1987 -> 0,\nX1988 -> s(s(0)),\nX1989 -> s(s(s(s(0)))),\nX1956 -> X1991,\nX1990 -> X1991", fontsize=14, style = filled, fillcolor = lightblue];
1229 -> 6079 [arrowhead = none ];
6079 -> 1236;

6080 [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 = lightgreen];
1230 -> 6080 [arrowhead = none ];
6080 -> 1251;

6081 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1236 -> 6081 [arrowhead = none ];
6081 -> 1239;

6082 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1239 -> 6082 [arrowhead = none ];
6082 -> 1241;

6083 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1239 -> 6083 [arrowhead = none ];
6083 -> 1242;

6084 [label="ONLY EVAL with clause\nquot(0, s(X2002), s(X2003), 0).\nand substitutionX2002 -> s(0),\nX2003 -> s(s(s(0))),\nX1991 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1241 -> 6084 [arrowhead = none ];
6084 -> 1247;

6085 [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 = lightgreen];
1242 -> 6085 [arrowhead = none ];
6085 -> 1249;

6086 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1247 -> 6086 [arrowhead = none ];
6086 -> 1248;

6087 [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 = lightgreen];
1249 -> 6087 [arrowhead = none ];
6087 -> 1250;

6088 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1261 -> 6088 [arrowhead = none ];
6088 -> 1269;

6089 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1269 -> 6089 [arrowhead = none ];
6089 -> 1271;

6090 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1271 -> 6090 [arrowhead = none ];
6090 -> 1279;

6091 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1271 -> 6091 [arrowhead = none ];
6091 -> 1280;

6092 [label="ONLY EVAL with clause\nquot(s(X2063), s(X2064), X2065, X2066) :- quot(X2063, X2064, X2065, X2066).\nand substitutionX2063 -> s(0),\nX2064 -> s(s(0)),\nX2065 -> s(s(s(0))),\nX2028 -> X2067,\nX2066 -> X2067", fontsize=14, style = filled, fillcolor = lightblue];
1279 -> 6092 [arrowhead = none ];
6092 -> 1287;

6093 [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 = lightgreen];
1280 -> 6093 [arrowhead = none ];
6093 -> 1322;

6094 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1287 -> 6094 [arrowhead = none ];
6094 -> 1290;

6095 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1290 -> 6095 [arrowhead = none ];
6095 -> 1291;

6096 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1291 -> 6096 [arrowhead = none ];
6096 -> 1295;

6097 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1291 -> 6097 [arrowhead = none ];
6097 -> 1296;

6098 [label="ONLY EVAL with clause\nquot(s(X2098), s(X2099), X2100, X2101) :- quot(X2098, X2099, X2100, X2101).\nand substitutionX2098 -> 0,\nX2099 -> s(0),\nX2100 -> s(s(s(0))),\nX2067 -> X2102,\nX2101 -> X2102", fontsize=14, style = filled, fillcolor = lightblue];
1295 -> 6098 [arrowhead = none ];
6098 -> 1304;

6099 [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 = lightgreen];
1296 -> 6099 [arrowhead = none ];
6099 -> 1318;

6100 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1304 -> 6100 [arrowhead = none ];
6100 -> 1305;

6101 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1305 -> 6101 [arrowhead = none ];
6101 -> 1306;

6102 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1305 -> 6102 [arrowhead = none ];
6102 -> 1307;

6103 [label="ONLY EVAL with clause\nquot(0, s(X2113), s(X2114), 0).\nand substitutionX2113 -> 0,\nX2114 -> s(s(0)),\nX2102 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1306 -> 6103 [arrowhead = none ];
6103 -> 1311;

6104 [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 = lightgreen];
1307 -> 6104 [arrowhead = none ];
6104 -> 1314;

6105 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1311 -> 6105 [arrowhead = none ];
6105 -> 1312;

6106 [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 = lightgreen];
1314 -> 6106 [arrowhead = none ];
6106 -> 1317;

6107 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1332 -> 6107 [arrowhead = none ];
6107 -> 1337;

6108 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1337 -> 6108 [arrowhead = none ];
6108 -> 1340;

6109 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1340 -> 6109 [arrowhead = none ];
6109 -> 1344;

6110 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1340 -> 6110 [arrowhead = none ];
6110 -> 1345;

6111 [label="ONLY EVAL with clause\nquot(s(X2174), s(X2175), X2176, X2177) :- quot(X2174, X2175, X2176, X2177).\nand substitutionX2174 -> s(0),\nX2175 -> s(0),\nX2176 -> s(s(0)),\nX2139 -> X2178,\nX2177 -> X2178", fontsize=14, style = filled, fillcolor = lightblue];
1344 -> 6111 [arrowhead = none ];
6111 -> 1352;

6112 [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 = lightgreen];
1345 -> 6112 [arrowhead = none ];
6112 -> 1395;

6113 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1352 -> 6113 [arrowhead = none ];
6113 -> 1356;

6114 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1356 -> 6114 [arrowhead = none ];
6114 -> 1358;

6115 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1358 -> 6115 [arrowhead = none ];
6115 -> 1363;

6116 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1358 -> 6116 [arrowhead = none ];
6116 -> 1364;

6117 [label="ONLY EVAL with clause\nquot(s(X2213), s(X2214), X2215, X2216) :- quot(X2213, X2214, X2215, X2216).\nand substitutionX2213 -> 0,\nX2214 -> 0,\nX2215 -> s(s(0)),\nX2178 -> X2217,\nX2216 -> X2217", fontsize=14, style = filled, fillcolor = lightblue];
1363 -> 6117 [arrowhead = none ];
6117 -> 1371;

6118 [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 = lightgreen];
1364 -> 6118 [arrowhead = none ];
6118 -> 1393;

6119 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1371 -> 6119 [arrowhead = none ];
6119 -> 1374;

6120 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1374 -> 6120 [arrowhead = none ];
6120 -> 1375;

6121 [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 = lightgreen];
1375 -> 6121 [arrowhead = none ];
6121 -> 1379;

6122 [label="ONLY EVAL with clause\nquot(X2238, 0, s(X2239), s(X2240)) :- quot(X2238, s(X2239), s(X2239), X2240).\nand substitutionX2238 -> 0,\nX2239 -> s(0),\nX2240 -> X2241,\nX2217 -> s(X2241)", fontsize=14, style = filled, fillcolor = lightblue];
1379 -> 6122 [arrowhead = none ];
6122 -> 1387;

6123 [label="INSTANCE with matching:\nX1470 -> X2241", fontsize=14, style = filled, fillcolor = lightgrey];
1387 -> 6123 [arrowhead = none , style=dashed];
6123 -> 943[style=dashed];

6124 [label="INSTANCE with matching:\nT22 -> T271\nT20 -> T269\nX35 -> X1031", fontsize=14, style = filled, fillcolor = lightgrey];
1402 -> 6124 [arrowhead = none , style=dashed];
6124 -> 543[style=dashed];

6125 [label="INSTANCE with matching:\nT20 -> s(T269)\nT157 -> T407", fontsize=14, style = filled, fillcolor = lightgrey];
1403 -> 6125 [arrowhead = none , style=dashed];
6125 -> 545[style=dashed];

6126 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1409 -> 6126 [arrowhead = none ];
6126 -> 1411;

6127 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1409 -> 6127 [arrowhead = none ];
6127 -> 1412;

6128 [label="EVAL with clause\npr(X2268, s(0)).\nand substitutionT263 -> 0,\nX2268 -> s(s(s(s(0)))),\nT418 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1411 -> 6128 [arrowhead = none ];
6128 -> 1413;

6129 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1411 -> 6129 [arrowhead = none ];
6129 -> 1414;

6130 [label="EVAL with clause\npr(X2273, s(s(X2274))) :- ','(not_divides(s(s(X2274)), X2273), pr(X2273, s(X2274))).\nand substitutionT263 -> s(T424),\nX2273 -> s(s(s(s(s(T424))))),\nX2274 -> T424,\nT423 -> s(T424)", fontsize=14, style = filled, fillcolor = lightblue];
1412 -> 6130 [arrowhead = none ];
6130 -> 1419;

6131 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1412 -> 6131 [arrowhead = none ];
6131 -> 1420;

6132 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1413 -> 6132 [arrowhead = none ];
6132 -> 1415;

6133 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1419 -> 6133 [arrowhead = none ];
6133 -> 1423;

6134 [label="SPLIT 2\nnew knowledge:\nT424 is ground", fontsize=14, style = filled, fillcolor = violet];
1419 -> 6134 [arrowhead = none ];
6134 -> 1424;

6135 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1423 -> 6135 [arrowhead = none ];
6135 -> 1425;

6136 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1424 -> 6136 [arrowhead = none ];
6136 -> 2248;

6137 [label="ONLY EVAL with clause\nnot_divides(X2293, X2294) :- ','(div(X2294, X2293, X2295), ','(times(X2295, X2293, X2296), neq(X2294, X2296))).\nand substitutionT424 -> T430,\nX2293 -> s(s(T430)),\nX2294 -> s(s(s(s(s(T430)))))", fontsize=14, style = filled, fillcolor = lightblue];
1425 -> 6137 [arrowhead = none ];
6137 -> 1431;

6138 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1431 -> 6138 [arrowhead = none ];
6138 -> 1434;

6139 [label="SPLIT 2\nnew knowledge:\nT430 is ground\nT432 is ground\nreplacements:X2295 -> T432", fontsize=14, style = filled, fillcolor = violet];
1431 -> 6139 [arrowhead = none ];
6139 -> 1435;

6140 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1434 -> 6140 [arrowhead = none ];
6140 -> 1440;

6141 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1435 -> 6141 [arrowhead = none ];
6141 -> 2241;

6142 [label="SPLIT 2\nnew knowledge:\nT432 is ground\nT430 is ground\nT573 is ground\nreplacements:X2296 -> T573", fontsize=14, style = filled, fillcolor = violet];
1435 -> 6142 [arrowhead = none ];
6142 -> 2242;

6143 [label="ONLY EVAL with clause\ndiv(X2317, X2318, X2319) :- quot(X2317, X2318, X2318, X2319).\nand substitutionT430 -> T436,\nX2317 -> s(s(s(s(s(T436))))),\nX2318 -> s(s(T436)),\nX2295 -> X2320,\nX2319 -> X2320", fontsize=14, style = filled, fillcolor = lightblue];
1440 -> 6143 [arrowhead = none ];
6143 -> 1448;

6144 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1448 -> 6144 [arrowhead = none ];
6144 -> 1451;

6145 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1451 -> 6145 [arrowhead = none ];
6145 -> 1452;

6146 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1452 -> 6146 [arrowhead = none ];
6146 -> 1459;

6147 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1452 -> 6147 [arrowhead = none ];
6147 -> 1460;

6148 [label="ONLY EVAL with clause\nquot(s(X2355), s(X2356), X2357, X2358) :- quot(X2355, X2356, X2357, X2358).\nand substitutionT436 -> T441,\nX2355 -> s(s(s(s(T441)))),\nX2356 -> s(T441),\nX2357 -> s(s(T441)),\nX2320 -> X2359,\nX2358 -> X2359", fontsize=14, style = filled, fillcolor = lightblue];
1459 -> 6148 [arrowhead = none ];
6148 -> 1469;

6149 [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 = lightgreen];
1460 -> 6149 [arrowhead = none ];
6149 -> 2238;

6150 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1469 -> 6150 [arrowhead = none ];
6150 -> 1471;

6151 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1471 -> 6151 [arrowhead = none ];
6151 -> 1472;

6152 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1472 -> 6152 [arrowhead = none ];
6152 -> 1478;

6153 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1472 -> 6153 [arrowhead = none ];
6153 -> 1479;

6154 [label="ONLY EVAL with clause\nquot(s(X2394), s(X2395), X2396, X2397) :- quot(X2394, X2395, X2396, X2397).\nand substitutionT441 -> T446,\nX2394 -> s(s(s(T446))),\nX2395 -> T446,\nX2396 -> s(s(T446)),\nX2359 -> X2398,\nX2397 -> X2398", fontsize=14, style = filled, fillcolor = lightblue];
1478 -> 6154 [arrowhead = none ];
6154 -> 1490;

6155 [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 = lightgreen];
1479 -> 6155 [arrowhead = none ];
6155 -> 2236;

6156 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1490 -> 6156 [arrowhead = none ];
6156 -> 1494;

6157 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1494 -> 6157 [arrowhead = none ];
6157 -> 1495;

6158 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1495 -> 6158 [arrowhead = none ];
6158 -> 1498;

6159 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1495 -> 6159 [arrowhead = none ];
6159 -> 1499;

6160 [label="EVAL with clause\nquot(s(X2425), s(X2426), X2427, X2428) :- quot(X2425, X2426, X2427, X2428).\nand substitutionT446 -> s(T456),\nX2425 -> s(s(s(T456))),\nX2426 -> T456,\nT455 -> s(T456),\nX2427 -> s(s(s(T456))),\nX2398 -> X2429,\nX2428 -> X2429", fontsize=14, style = filled, fillcolor = lightblue];
1498 -> 6160 [arrowhead = none ];
6160 -> 1507;

6161 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1498 -> 6161 [arrowhead = none ];
6161 -> 1508;

6162 [label="EVAL with clause\nquot(X3673, 0, s(X3674), s(X3675)) :- quot(X3673, s(X3674), s(X3674), X3675).\nand substitutionT446 -> 0,\nX3673 -> s(s(s(0))),\nT568 -> 0,\nX3674 -> s(0),\nX3675 -> X3676,\nX2398 -> s(X3676)", fontsize=14, style = filled, fillcolor = lightblue];
1499 -> 6162 [arrowhead = none ];
6162 -> 2183;

6163 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1499 -> 6163 [arrowhead = none ];
6163 -> 2184;

6164 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1507 -> 6164 [arrowhead = none ];
6164 -> 1512;

6165 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1512 -> 6165 [arrowhead = none ];
6165 -> 1514;

6166 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1514 -> 6166 [arrowhead = none ];
6166 -> 1518;

6167 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1514 -> 6167 [arrowhead = none ];
6167 -> 1519;

6168 [label="EVAL with clause\nquot(s(X2456), s(X2457), X2458, X2459) :- quot(X2456, X2457, X2458, X2459).\nand substitutionT456 -> s(T466),\nX2456 -> s(s(s(T466))),\nX2457 -> T466,\nT465 -> s(T466),\nX2458 -> s(s(s(s(T466)))),\nX2429 -> X2460,\nX2459 -> X2460", fontsize=14, style = filled, fillcolor = lightblue];
1518 -> 6168 [arrowhead = none ];
6168 -> 1529;

6169 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1518 -> 6169 [arrowhead = none ];
6169 -> 1530;

6170 [label="EVAL with clause\nquot(X3509, 0, s(X3510), s(X3511)) :- quot(X3509, s(X3510), s(X3510), X3511).\nand substitutionT456 -> 0,\nX3509 -> s(s(s(0))),\nT565 -> 0,\nX3510 -> s(s(0)),\nX3511 -> X3512,\nX2429 -> s(X3512)", fontsize=14, style = filled, fillcolor = lightblue];
1519 -> 6170 [arrowhead = none ];
6170 -> 2109;

6171 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1519 -> 6171 [arrowhead = none ];
6171 -> 2110;

6172 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1529 -> 6172 [arrowhead = none ];
6172 -> 1534;

6173 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1534 -> 6173 [arrowhead = none ];
6173 -> 1535;

6174 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1535 -> 6174 [arrowhead = none ];
6174 -> 1540;

6175 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1535 -> 6175 [arrowhead = none ];
6175 -> 1541;

6176 [label="EVAL with clause\nquot(s(X2487), s(X2488), X2489, X2490) :- quot(X2487, X2488, X2489, X2490).\nand substitutionT466 -> s(T476),\nX2487 -> s(s(s(T476))),\nX2488 -> T476,\nT475 -> s(T476),\nX2489 -> s(s(s(s(s(T476))))),\nX2460 -> X2491,\nX2490 -> X2491", fontsize=14, style = filled, fillcolor = lightblue];
1540 -> 6176 [arrowhead = none ];
6176 -> 1547;

6177 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1540 -> 6177 [arrowhead = none ];
6177 -> 1548;

6178 [label="EVAL with clause\nquot(X3356, 0, s(X3357), s(X3358)) :- quot(X3356, s(X3357), s(X3357), X3358).\nand substitutionT466 -> 0,\nX3356 -> s(s(s(0))),\nT562 -> 0,\nX3357 -> s(s(s(0))),\nX3358 -> X3359,\nX2460 -> s(X3359)", fontsize=14, style = filled, fillcolor = lightblue];
1541 -> 6178 [arrowhead = none ];
6178 -> 2031;

6179 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1541 -> 6179 [arrowhead = none ];
6179 -> 2032;

6180 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1547 -> 6180 [arrowhead = none ];
6180 -> 1549;

6181 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1549 -> 6181 [arrowhead = none ];
6181 -> 1551;

6182 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1551 -> 6182 [arrowhead = none ];
6182 -> 1555;

6183 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1551 -> 6183 [arrowhead = none ];
6183 -> 1556;

6184 [label="EVAL with clause\nquot(s(X2518), s(X2519), X2520, X2521) :- quot(X2518, X2519, X2520, X2521).\nand substitutionT476 -> s(T486),\nX2518 -> s(s(s(T486))),\nX2519 -> T486,\nT485 -> s(T486),\nX2520 -> s(s(s(s(s(s(T486)))))),\nX2491 -> X2522,\nX2521 -> X2522", fontsize=14, style = filled, fillcolor = lightblue];
1555 -> 6184 [arrowhead = none ];
6184 -> 1563;

6185 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1555 -> 6185 [arrowhead = none ];
6185 -> 1564;

6186 [label="EVAL with clause\nquot(X3203, 0, s(X3204), s(X3205)) :- quot(X3203, s(X3204), s(X3204), X3205).\nand substitutionT476 -> 0,\nX3203 -> s(s(s(0))),\nT559 -> 0,\nX3204 -> s(s(s(s(0)))),\nX3205 -> X3206,\nX2491 -> s(X3206)", fontsize=14, style = filled, fillcolor = lightblue];
1556 -> 6186 [arrowhead = none ];
6186 -> 1950;

6187 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1556 -> 6187 [arrowhead = none ];
6187 -> 1951;

6188 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1563 -> 6188 [arrowhead = none ];
6188 -> 1565;

6189 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1565 -> 6189 [arrowhead = none ];
6189 -> 1566;

6190 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1566 -> 6190 [arrowhead = none ];
6190 -> 1573;

6191 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1566 -> 6191 [arrowhead = none ];
6191 -> 1574;

6192 [label="EVAL with clause\nquot(s(X2549), s(X2550), X2551, X2552) :- quot(X2549, X2550, X2551, X2552).\nand substitutionT486 -> s(T496),\nX2549 -> s(s(s(T496))),\nX2550 -> T496,\nT495 -> s(T496),\nX2551 -> s(s(s(s(s(s(s(T496))))))),\nX2522 -> X2553,\nX2552 -> X2553", fontsize=14, style = filled, fillcolor = lightblue];
1573 -> 6192 [arrowhead = none ];
6192 -> 1580;

6193 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1573 -> 6193 [arrowhead = none ];
6193 -> 1581;

6194 [label="EVAL with clause\nquot(X3050, 0, s(X3051), s(X3052)) :- quot(X3050, s(X3051), s(X3051), X3052).\nand substitutionT486 -> 0,\nX3050 -> s(s(s(0))),\nT556 -> 0,\nX3051 -> s(s(s(s(s(0))))),\nX3052 -> X3053,\nX2522 -> s(X3053)", fontsize=14, style = filled, fillcolor = lightblue];
1574 -> 6194 [arrowhead = none ];
6194 -> 1867;

6195 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1574 -> 6195 [arrowhead = none ];
6195 -> 1868;

6196 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1580 -> 6196 [arrowhead = none ];
6196 -> 1584;

6197 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1584 -> 6197 [arrowhead = none ];
6197 -> 1585;

6198 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1585 -> 6198 [arrowhead = none ];
6198 -> 1589;

6199 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1585 -> 6199 [arrowhead = none ];
6199 -> 1590;

6200 [label="EVAL with clause\nquot(s(X2580), s(X2581), X2582, X2583) :- quot(X2580, X2581, X2582, X2583).\nand substitutionT496 -> s(T506),\nX2580 -> s(s(s(T506))),\nX2581 -> T506,\nT505 -> s(T506),\nX2582 -> s(s(s(s(s(s(s(s(T506)))))))),\nX2553 -> X2584,\nX2583 -> X2584", fontsize=14, style = filled, fillcolor = lightblue];
1589 -> 6200 [arrowhead = none ];
6200 -> 1597;

6201 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1589 -> 6201 [arrowhead = none ];
6201 -> 1598;

6202 [label="EVAL with clause\nquot(X2897, 0, s(X2898), s(X2899)) :- quot(X2897, s(X2898), s(X2898), X2899).\nand substitutionT496 -> 0,\nX2897 -> s(s(s(0))),\nT553 -> 0,\nX2898 -> s(s(s(s(s(s(0)))))),\nX2899 -> X2900,\nX2553 -> s(X2900)", fontsize=14, style = filled, fillcolor = lightblue];
1590 -> 6202 [arrowhead = none ];
6202 -> 1792;

6203 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1590 -> 6203 [arrowhead = none ];
6203 -> 1793;

6204 [label="GENERALIZATION\nT507 <-- s(s(s(s(s(s(s(T506)))))))\n\nNew Knowledge:\nT507 is ground", fontsize=14, style = filled, fillcolor = violet];
1597 -> 6204 [arrowhead = none ];
6204 -> 1601;

6205 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1601 -> 6205 [arrowhead = none ];
6205 -> 1606;

6206 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1606 -> 6206 [arrowhead = none ];
6206 -> 1607;

6207 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1607 -> 6207 [arrowhead = none ];
6207 -> 1612;

6208 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1607 -> 6208 [arrowhead = none ];
6208 -> 1613;

6209 [label="EVAL with clause\nquot(s(X2615), s(X2616), X2617, X2618) :- quot(X2615, X2616, X2617, X2618).\nand substitutionT506 -> s(T521),\nX2615 -> s(s(s(T521))),\nX2616 -> T521,\nT520 -> s(T521),\nT507 -> T522,\nX2617 -> s(T522),\nX2584 -> X2619,\nX2618 -> X2619", fontsize=14, style = filled, fillcolor = lightblue];
1612 -> 6209 [arrowhead = none ];
6209 -> 1620;

6210 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1612 -> 6210 [arrowhead = none ];
6210 -> 1621;

6211 [label="EVAL with clause\nquot(X2632, 0, s(X2633), s(X2634)) :- quot(X2632, s(X2633), s(X2633), X2634).\nand substitutionT506 -> 0,\nX2632 -> s(s(s(0))),\nT527 -> 0,\nT507 -> T528,\nX2633 -> T528,\nX2634 -> X2635,\nX2584 -> s(X2635)", fontsize=14, style = filled, fillcolor = lightblue];
1613 -> 6211 [arrowhead = none ];
6211 -> 1630;

6212 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1613 -> 6212 [arrowhead = none ];
6212 -> 1631;

6213 [label="INSTANCE with matching:\nT506 -> T521\nT507 -> T522\nX2584 -> X2619", fontsize=14, style = filled, fillcolor = lightgrey];
1620 -> 6213 [arrowhead = none , style=dashed];
6213 -> 1601[style=dashed];

6214 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1630 -> 6214 [arrowhead = none ];
6214 -> 1632;

6215 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1632 -> 6215 [arrowhead = none ];
6215 -> 1633;

6216 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1633 -> 6216 [arrowhead = none ];
6216 -> 1642;

6217 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1633 -> 6217 [arrowhead = none ];
6217 -> 1643;

6218 [label="ONLY EVAL with clause\nquot(s(X2670), s(X2671), X2672, X2673) :- quot(X2670, X2671, X2672, X2673).\nand substitutionX2670 -> s(s(0)),\nT528 -> T533,\nX2671 -> T533,\nX2672 -> s(T533),\nX2635 -> X2674,\nX2673 -> X2674", fontsize=14, style = filled, fillcolor = lightblue];
1642 -> 6218 [arrowhead = none ];
6218 -> 1648;

6219 [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 = lightgreen];
1643 -> 6219 [arrowhead = none ];
6219 -> 1786;

6220 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1648 -> 6220 [arrowhead = none ];
6220 -> 1653;

6221 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1653 -> 6221 [arrowhead = none ];
6221 -> 1654;

6222 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1654 -> 6222 [arrowhead = none ];
6222 -> 1659;

6223 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1654 -> 6223 [arrowhead = none ];
6223 -> 1660;

6224 [label="EVAL with clause\nquot(s(X2701), s(X2702), X2703, X2704) :- quot(X2701, X2702, X2703, X2704).\nand substitutionX2701 -> s(0),\nX2702 -> T538,\nT533 -> s(T538),\nX2703 -> s(s(T538)),\nX2674 -> X2705,\nX2704 -> X2705", fontsize=14, style = filled, fillcolor = lightblue];
1659 -> 6224 [arrowhead = none ];
6224 -> 1666;

6225 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1659 -> 6225 [arrowhead = none ];
6225 -> 1667;

6226 [label="EVAL with clause\nquot(X2810, 0, s(X2811), s(X2812)) :- quot(X2810, s(X2811), s(X2811), X2812).\nand substitutionX2810 -> s(s(0)),\nT533 -> 0,\nX2811 -> 0,\nX2812 -> X2813,\nX2674 -> s(X2813)", fontsize=14, style = filled, fillcolor = lightblue];
1660 -> 6226 [arrowhead = none ];
6226 -> 1728;

6227 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1660 -> 6227 [arrowhead = none ];
6227 -> 1729;

6228 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1666 -> 6228 [arrowhead = none ];
6228 -> 1670;

6229 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1670 -> 6229 [arrowhead = none ];
6229 -> 1671;

6230 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1671 -> 6230 [arrowhead = none ];
6230 -> 1676;

6231 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1671 -> 6231 [arrowhead = none ];
6231 -> 1677;

6232 [label="EVAL with clause\nquot(s(X2732), s(X2733), X2734, X2735) :- quot(X2732, X2733, X2734, X2735).\nand substitutionX2732 -> 0,\nX2733 -> T543,\nT538 -> s(T543),\nX2734 -> s(s(s(T543))),\nX2705 -> X2736,\nX2735 -> X2736", fontsize=14, style = filled, fillcolor = lightblue];
1676 -> 6232 [arrowhead = none ];
6232 -> 1682;

6233 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1676 -> 6233 [arrowhead = none ];
6233 -> 1683;

6234 [label="EVAL with clause\nquot(X2794, 0, s(X2795), s(X2796)) :- quot(X2794, s(X2795), s(X2795), X2796).\nand substitutionX2794 -> s(0),\nT538 -> 0,\nX2795 -> s(0),\nX2796 -> X2797,\nX2705 -> s(X2797)", fontsize=14, style = filled, fillcolor = lightblue];
1677 -> 6234 [arrowhead = none ];
6234 -> 1720;

6235 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1677 -> 6235 [arrowhead = none ];
6235 -> 1721;

6236 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1682 -> 6236 [arrowhead = none ];
6236 -> 1688;

6237 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1688 -> 6237 [arrowhead = none ];
6237 -> 1689;

6238 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1688 -> 6238 [arrowhead = none ];
6238 -> 1690;

6239 [label="EVAL with clause\nquot(0, s(X2749), s(X2750), 0).\nand substitutionX2749 -> T550,\nT543 -> s(T550),\nX2750 -> s(s(s(T550))),\nX2736 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1689 -> 6239 [arrowhead = none ];
6239 -> 1693;

6240 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1689 -> 6240 [arrowhead = none ];
6240 -> 1694;

6241 [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 = lightgreen];
1690 -> 6241 [arrowhead = none ];
6241 -> 1699;

6242 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1693 -> 6242 [arrowhead = none ];
6242 -> 1695;

6243 [label="EVAL with clause\nquot(X2763, 0, s(X2764), s(X2765)) :- quot(X2763, s(X2764), s(X2764), X2765).\nand substitutionX2763 -> 0,\nT543 -> 0,\nX2764 -> s(s(0)),\nX2765 -> X2766,\nX2736 -> s(X2766)", fontsize=14, style = filled, fillcolor = lightblue];
1699 -> 6243 [arrowhead = none ];
6243 -> 1702;

6244 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1699 -> 6244 [arrowhead = none ];
6244 -> 1703;

6245 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1702 -> 6245 [arrowhead = none ];
6245 -> 1704;

6246 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1704 -> 6246 [arrowhead = none ];
6246 -> 1706;

6247 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1704 -> 6247 [arrowhead = none ];
6247 -> 1707;

6248 [label="ONLY EVAL with clause\nquot(0, s(X2777), s(X2778), 0).\nand substitutionX2777 -> s(s(0)),\nX2778 -> s(s(0)),\nX2766 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1706 -> 6248 [arrowhead = none ];
6248 -> 1712;

6249 [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 = lightgreen];
1707 -> 6249 [arrowhead = none ];
6249 -> 1714;

6250 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1712 -> 6250 [arrowhead = none ];
6250 -> 1713;

6251 [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 = lightgreen];
1714 -> 6251 [arrowhead = none ];
6251 -> 1715;

6252 [label="INSTANCE with matching:\nX822 -> X2797", fontsize=14, style = filled, fillcolor = lightgrey];
1720 -> 6252 [arrowhead = none , style=dashed];
6252 -> 493[style=dashed];

6253 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1728 -> 6253 [arrowhead = none ];
6253 -> 1732;

6254 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1732 -> 6254 [arrowhead = none ];
6254 -> 1735;

6255 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1735 -> 6255 [arrowhead = none ];
6255 -> 1741;

6256 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1735 -> 6256 [arrowhead = none ];
6256 -> 1742;

6257 [label="ONLY EVAL with clause\nquot(s(X2848), s(X2849), X2850, X2851) :- quot(X2848, X2849, X2850, X2851).\nand substitutionX2848 -> s(0),\nX2849 -> 0,\nX2850 -> s(0),\nX2813 -> X2852,\nX2851 -> X2852", fontsize=14, style = filled, fillcolor = lightblue];
1741 -> 6257 [arrowhead = none ];
6257 -> 1758;

6258 [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 = lightgreen];
1742 -> 6258 [arrowhead = none ];
6258 -> 1783;

6259 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1758 -> 6259 [arrowhead = none ];
6259 -> 1764;

6260 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1764 -> 6260 [arrowhead = none ];
6260 -> 1767;

6261 [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 = lightgreen];
1767 -> 6261 [arrowhead = none ];
6261 -> 1770;

6262 [label="ONLY EVAL with clause\nquot(X2875, 0, s(X2876), s(X2877)) :- quot(X2875, s(X2876), s(X2876), X2877).\nand substitutionX2875 -> s(0),\nX2876 -> 0,\nX2877 -> X2878,\nX2852 -> s(X2878)", fontsize=14, style = filled, fillcolor = lightblue];
1770 -> 6262 [arrowhead = none ];
6262 -> 1778;

6263 [label="INSTANCE with matching:\nX1501 -> X2878", fontsize=14, style = filled, fillcolor = lightgrey];
1778 -> 6263 [arrowhead = none , style=dashed];
6263 -> 960[style=dashed];

6264 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1792 -> 6264 [arrowhead = none ];
6264 -> 1796;

6265 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1796 -> 6265 [arrowhead = none ];
6265 -> 1799;

6266 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1799 -> 6266 [arrowhead = none ];
6266 -> 1804;

6267 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1799 -> 6267 [arrowhead = none ];
6267 -> 1805;

6268 [label="ONLY EVAL with clause\nquot(s(X2935), s(X2936), X2937, X2938) :- quot(X2935, X2936, X2937, X2938).\nand substitutionX2935 -> s(s(0)),\nX2936 -> s(s(s(s(s(s(0)))))),\nX2937 -> s(s(s(s(s(s(s(0))))))),\nX2900 -> X2939,\nX2938 -> X2939", fontsize=14, style = filled, fillcolor = lightblue];
1804 -> 6268 [arrowhead = none ];
6268 -> 1809;

6269 [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 = lightgreen];
1805 -> 6269 [arrowhead = none ];
6269 -> 1863;

6270 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1809 -> 6270 [arrowhead = none ];
6270 -> 1812;

6271 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1812 -> 6271 [arrowhead = none ];
6271 -> 1814;

6272 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1814 -> 6272 [arrowhead = none ];
6272 -> 1820;

6273 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1814 -> 6273 [arrowhead = none ];
6273 -> 1821;

6274 [label="ONLY EVAL with clause\nquot(s(X2974), s(X2975), X2976, X2977) :- quot(X2974, X2975, X2976, X2977).\nand substitutionX2974 -> s(0),\nX2975 -> s(s(s(s(s(0))))),\nX2976 -> s(s(s(s(s(s(s(0))))))),\nX2939 -> X2978,\nX2977 -> X2978", fontsize=14, style = filled, fillcolor = lightblue];
1820 -> 6274 [arrowhead = none ];
6274 -> 1826;

6275 [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 = lightgreen];
1821 -> 6275 [arrowhead = none ];
6275 -> 1862;

6276 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1826 -> 6276 [arrowhead = none ];
6276 -> 1830;

6277 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1830 -> 6277 [arrowhead = none ];
6277 -> 1832;

6278 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1832 -> 6278 [arrowhead = none ];
6278 -> 1837;

6279 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1832 -> 6279 [arrowhead = none ];
6279 -> 1838;

6280 [label="ONLY EVAL with clause\nquot(s(X3009), s(X3010), X3011, X3012) :- quot(X3009, X3010, X3011, X3012).\nand substitutionX3009 -> 0,\nX3010 -> s(s(s(s(0)))),\nX3011 -> s(s(s(s(s(s(s(0))))))),\nX2978 -> X3013,\nX3012 -> X3013", fontsize=14, style = filled, fillcolor = lightblue];
1837 -> 6280 [arrowhead = none ];
6280 -> 1842;

6281 [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 = lightgreen];
1838 -> 6281 [arrowhead = none ];
6281 -> 1861;

6282 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1842 -> 6282 [arrowhead = none ];
6282 -> 1846;

6283 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1846 -> 6283 [arrowhead = none ];
6283 -> 1849;

6284 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1846 -> 6284 [arrowhead = none ];
6284 -> 1850;

6285 [label="ONLY EVAL with clause\nquot(0, s(X3024), s(X3025), 0).\nand substitutionX3024 -> s(s(s(0))),\nX3025 -> s(s(s(s(s(s(0)))))),\nX3013 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1849 -> 6285 [arrowhead = none ];
6285 -> 1853;

6286 [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 = lightgreen];
1850 -> 6286 [arrowhead = none ];
6286 -> 1856;

6287 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1853 -> 6287 [arrowhead = none ];
6287 -> 1854;

6288 [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 = lightgreen];
1856 -> 6288 [arrowhead = none ];
6288 -> 1860;

6289 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1867 -> 6289 [arrowhead = none ];
6289 -> 1872;

6290 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1872 -> 6290 [arrowhead = none ];
6290 -> 1874;

6291 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1874 -> 6291 [arrowhead = none ];
6291 -> 1880;

6292 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1874 -> 6292 [arrowhead = none ];
6292 -> 1881;

6293 [label="ONLY EVAL with clause\nquot(s(X3088), s(X3089), X3090, X3091) :- quot(X3088, X3089, X3090, X3091).\nand substitutionX3088 -> s(s(0)),\nX3089 -> s(s(s(s(s(0))))),\nX3090 -> s(s(s(s(s(s(0)))))),\nX3053 -> X3092,\nX3091 -> X3092", fontsize=14, style = filled, fillcolor = lightblue];
1880 -> 6293 [arrowhead = none ];
6293 -> 1884;

6294 [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 = lightgreen];
1881 -> 6294 [arrowhead = none ];
6294 -> 1947;

6295 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1884 -> 6295 [arrowhead = none ];
6295 -> 1890;

6296 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1890 -> 6296 [arrowhead = none ];
6296 -> 1891;

6297 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1891 -> 6297 [arrowhead = none ];
6297 -> 1899;

6298 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1891 -> 6298 [arrowhead = none ];
6298 -> 1900;

6299 [label="ONLY EVAL with clause\nquot(s(X3127), s(X3128), X3129, X3130) :- quot(X3127, X3128, X3129, X3130).\nand substitutionX3127 -> s(0),\nX3128 -> s(s(s(s(0)))),\nX3129 -> s(s(s(s(s(s(0)))))),\nX3092 -> X3131,\nX3130 -> X3131", fontsize=14, style = filled, fillcolor = lightblue];
1899 -> 6299 [arrowhead = none ];
6299 -> 1907;

6300 [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 = lightgreen];
1900 -> 6300 [arrowhead = none ];
6300 -> 1943;

6301 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1907 -> 6301 [arrowhead = none ];
6301 -> 1910;

6302 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1910 -> 6302 [arrowhead = none ];
6302 -> 1911;

6303 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1911 -> 6303 [arrowhead = none ];
6303 -> 1916;

6304 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1911 -> 6304 [arrowhead = none ];
6304 -> 1917;

6305 [label="ONLY EVAL with clause\nquot(s(X3162), s(X3163), X3164, X3165) :- quot(X3162, X3163, X3164, X3165).\nand substitutionX3162 -> 0,\nX3163 -> s(s(s(0))),\nX3164 -> s(s(s(s(s(s(0)))))),\nX3131 -> X3166,\nX3165 -> X3166", fontsize=14, style = filled, fillcolor = lightblue];
1916 -> 6305 [arrowhead = none ];
6305 -> 1927;

6306 [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 = lightgreen];
1917 -> 6306 [arrowhead = none ];
6306 -> 1942;

6307 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1927 -> 6307 [arrowhead = none ];
6307 -> 1929;

6308 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1929 -> 6308 [arrowhead = none ];
6308 -> 1932;

6309 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1929 -> 6309 [arrowhead = none ];
6309 -> 1933;

6310 [label="ONLY EVAL with clause\nquot(0, s(X3177), s(X3178), 0).\nand substitutionX3177 -> s(s(0)),\nX3178 -> s(s(s(s(s(0))))),\nX3166 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1932 -> 6310 [arrowhead = none ];
6310 -> 1937;

6311 [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 = lightgreen];
1933 -> 6311 [arrowhead = none ];
6311 -> 1940;

6312 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1937 -> 6312 [arrowhead = none ];
6312 -> 1938;

6313 [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 = lightgreen];
1940 -> 6313 [arrowhead = none ];
6313 -> 1941;

6314 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1950 -> 6314 [arrowhead = none ];
6314 -> 1955;

6315 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1955 -> 6315 [arrowhead = none ];
6315 -> 1956;

6316 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1956 -> 6316 [arrowhead = none ];
6316 -> 1960;

6317 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1956 -> 6317 [arrowhead = none ];
6317 -> 1961;

6318 [label="ONLY EVAL with clause\nquot(s(X3241), s(X3242), X3243, X3244) :- quot(X3241, X3242, X3243, X3244).\nand substitutionX3241 -> s(s(0)),\nX3242 -> s(s(s(s(0)))),\nX3243 -> s(s(s(s(s(0))))),\nX3206 -> X3245,\nX3244 -> X3245", fontsize=14, style = filled, fillcolor = lightblue];
1960 -> 6318 [arrowhead = none ];
6318 -> 1969;

6319 [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 = lightgreen];
1961 -> 6319 [arrowhead = none ];
6319 -> 2026;

6320 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1969 -> 6320 [arrowhead = none ];
6320 -> 1973;

6321 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1973 -> 6321 [arrowhead = none ];
6321 -> 1975;

6322 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1975 -> 6322 [arrowhead = none ];
6322 -> 1980;

6323 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1975 -> 6323 [arrowhead = none ];
6323 -> 1981;

6324 [label="ONLY EVAL with clause\nquot(s(X3280), s(X3281), X3282, X3283) :- quot(X3280, X3281, X3282, X3283).\nand substitutionX3280 -> s(0),\nX3281 -> s(s(s(0))),\nX3282 -> s(s(s(s(s(0))))),\nX3245 -> X3284,\nX3283 -> X3284", fontsize=14, style = filled, fillcolor = lightblue];
1980 -> 6324 [arrowhead = none ];
6324 -> 1988;

6325 [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 = lightgreen];
1981 -> 6325 [arrowhead = none ];
6325 -> 2024;

6326 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1988 -> 6326 [arrowhead = none ];
6326 -> 1990;

6327 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1990 -> 6327 [arrowhead = none ];
6327 -> 1993;

6328 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1993 -> 6328 [arrowhead = none ];
6328 -> 1997;

6329 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1993 -> 6329 [arrowhead = none ];
6329 -> 1998;

6330 [label="ONLY EVAL with clause\nquot(s(X3315), s(X3316), X3317, X3318) :- quot(X3315, X3316, X3317, X3318).\nand substitutionX3315 -> 0,\nX3316 -> s(s(0)),\nX3317 -> s(s(s(s(s(0))))),\nX3284 -> X3319,\nX3318 -> X3319", fontsize=14, style = filled, fillcolor = lightblue];
1997 -> 6330 [arrowhead = none ];
6330 -> 2009;

6331 [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 = lightgreen];
1998 -> 6331 [arrowhead = none ];
6331 -> 2023;

6332 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2009 -> 6332 [arrowhead = none ];
6332 -> 2010;

6333 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2010 -> 6333 [arrowhead = none ];
6333 -> 2013;

6334 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2010 -> 6334 [arrowhead = none ];
6334 -> 2014;

6335 [label="ONLY EVAL with clause\nquot(0, s(X3330), s(X3331), 0).\nand substitutionX3330 -> s(0),\nX3331 -> s(s(s(s(0)))),\nX3319 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
2013 -> 6335 [arrowhead = none ];
6335 -> 2017;

6336 [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 = lightgreen];
2014 -> 6336 [arrowhead = none ];
6336 -> 2020;

6337 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
2017 -> 6337 [arrowhead = none ];
6337 -> 2018;

6338 [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 = lightgreen];
2020 -> 6338 [arrowhead = none ];
6338 -> 2022;

6339 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2031 -> 6339 [arrowhead = none ];
6339 -> 2033;

6340 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2033 -> 6340 [arrowhead = none ];
6340 -> 2035;

6341 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2035 -> 6341 [arrowhead = none ];
6341 -> 2040;

6342 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2035 -> 6342 [arrowhead = none ];
6342 -> 2041;

6343 [label="ONLY EVAL with clause\nquot(s(X3394), s(X3395), X3396, X3397) :- quot(X3394, X3395, X3396, X3397).\nand substitutionX3394 -> s(s(0)),\nX3395 -> s(s(s(0))),\nX3396 -> s(s(s(s(0)))),\nX3359 -> X3398,\nX3397 -> X3398", fontsize=14, style = filled, fillcolor = lightblue];
2040 -> 6343 [arrowhead = none ];
6343 -> 2048;

6344 [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 = lightgreen];
2041 -> 6344 [arrowhead = none ];
6344 -> 2105;

6345 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2048 -> 6345 [arrowhead = none ];
6345 -> 2054;

6346 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2054 -> 6346 [arrowhead = none ];
6346 -> 2056;

6347 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2056 -> 6347 [arrowhead = none ];
6347 -> 2061;

6348 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2056 -> 6348 [arrowhead = none ];
6348 -> 2062;

6349 [label="ONLY EVAL with clause\nquot(s(X3433), s(X3434), X3435, X3436) :- quot(X3433, X3434, X3435, X3436).\nand substitutionX3433 -> s(0),\nX3434 -> s(s(0)),\nX3435 -> s(s(s(s(0)))),\nX3398 -> X3437,\nX3436 -> X3437", fontsize=14, style = filled, fillcolor = lightblue];
2061 -> 6349 [arrowhead = none ];
6349 -> 2068;

6350 [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 = lightgreen];
2062 -> 6350 [arrowhead = none ];
6350 -> 2104;

6351 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2068 -> 6351 [arrowhead = none ];
6351 -> 2071;

6352 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2071 -> 6352 [arrowhead = none ];
6352 -> 2072;

6353 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2072 -> 6353 [arrowhead = none ];
6353 -> 2078;

6354 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2072 -> 6354 [arrowhead = none ];
6354 -> 2079;

6355 [label="ONLY EVAL with clause\nquot(s(X3468), s(X3469), X3470, X3471) :- quot(X3468, X3469, X3470, X3471).\nand substitutionX3468 -> 0,\nX3469 -> s(0),\nX3470 -> s(s(s(s(0)))),\nX3437 -> X3472,\nX3471 -> X3472", fontsize=14, style = filled, fillcolor = lightblue];
2078 -> 6355 [arrowhead = none ];
6355 -> 2088;

6356 [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 = lightgreen];
2079 -> 6356 [arrowhead = none ];
6356 -> 2103;

6357 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2088 -> 6357 [arrowhead = none ];
6357 -> 2090;

6358 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2090 -> 6358 [arrowhead = none ];
6358 -> 2094;

6359 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2090 -> 6359 [arrowhead = none ];
6359 -> 2095;

6360 [label="ONLY EVAL with clause\nquot(0, s(X3483), s(X3484), 0).\nand substitutionX3483 -> 0,\nX3484 -> s(s(s(0))),\nX3472 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
2094 -> 6360 [arrowhead = none ];
6360 -> 2096;

6361 [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 = lightgreen];
2095 -> 6361 [arrowhead = none ];
6361 -> 2099;

6362 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
2096 -> 6362 [arrowhead = none ];
6362 -> 2097;

6363 [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 = lightgreen];
2099 -> 6363 [arrowhead = none ];
6363 -> 2102;

6364 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2109 -> 6364 [arrowhead = none ];
6364 -> 2112;

6365 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2112 -> 6365 [arrowhead = none ];
6365 -> 2113;

6366 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2113 -> 6366 [arrowhead = none ];
6366 -> 2116;

6367 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2113 -> 6367 [arrowhead = none ];
6367 -> 2117;

6368 [label="ONLY EVAL with clause\nquot(s(X3547), s(X3548), X3549, X3550) :- quot(X3547, X3548, X3549, X3550).\nand substitutionX3547 -> s(s(0)),\nX3548 -> s(s(0)),\nX3549 -> s(s(s(0))),\nX3512 -> X3551,\nX3550 -> X3551", fontsize=14, style = filled, fillcolor = lightblue];
2116 -> 6368 [arrowhead = none ];
6368 -> 2123;

6369 [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 = lightgreen];
2117 -> 6369 [arrowhead = none ];
6369 -> 2179;

6370 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2123 -> 6370 [arrowhead = none ];
6370 -> 2125;

6371 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2125 -> 6371 [arrowhead = none ];
6371 -> 2126;

6372 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2126 -> 6372 [arrowhead = none ];
6372 -> 2129;

6373 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2126 -> 6373 [arrowhead = none ];
6373 -> 2130;

6374 [label="ONLY EVAL with clause\nquot(s(X3586), s(X3587), X3588, X3589) :- quot(X3586, X3587, X3588, X3589).\nand substitutionX3586 -> s(0),\nX3587 -> s(0),\nX3588 -> s(s(s(0))),\nX3551 -> X3590,\nX3589 -> X3590", fontsize=14, style = filled, fillcolor = lightblue];
2129 -> 6374 [arrowhead = none ];
6374 -> 2135;

6375 [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 = lightgreen];
2130 -> 6375 [arrowhead = none ];
6375 -> 2178;

6376 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2135 -> 6376 [arrowhead = none ];
6376 -> 2137;

6377 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2137 -> 6377 [arrowhead = none ];
6377 -> 2139;

6378 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2139 -> 6378 [arrowhead = none ];
6378 -> 2145;

6379 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2139 -> 6379 [arrowhead = none ];
6379 -> 2146;

6380 [label="ONLY EVAL with clause\nquot(s(X3625), s(X3626), X3627, X3628) :- quot(X3625, X3626, X3627, X3628).\nand substitutionX3625 -> 0,\nX3626 -> 0,\nX3627 -> s(s(s(0))),\nX3590 -> X3629,\nX3628 -> X3629", fontsize=14, style = filled, fillcolor = lightblue];
2145 -> 6380 [arrowhead = none ];
6380 -> 2157;

6381 [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 = lightgreen];
2146 -> 6381 [arrowhead = none ];
6381 -> 2177;

6382 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2157 -> 6382 [arrowhead = none ];
6382 -> 2163;

6383 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2163 -> 6383 [arrowhead = none ];
6383 -> 2165;

6384 [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 = lightgreen];
2165 -> 6384 [arrowhead = none ];
6384 -> 2167;

6385 [label="ONLY EVAL with clause\nquot(X3650, 0, s(X3651), s(X3652)) :- quot(X3650, s(X3651), s(X3651), X3652).\nand substitutionX3650 -> 0,\nX3651 -> s(s(0)),\nX3652 -> X3653,\nX3629 -> s(X3653)", fontsize=14, style = filled, fillcolor = lightblue];
2167 -> 6385 [arrowhead = none ];
6385 -> 2172;

6386 [label="INSTANCE with matching:\nX2766 -> X3653", fontsize=14, style = filled, fillcolor = lightgrey];
2172 -> 6386 [arrowhead = none , style=dashed];
6386 -> 1702[style=dashed];

6387 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2183 -> 6387 [arrowhead = none ];
6387 -> 2187;

6388 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2187 -> 6388 [arrowhead = none ];
6388 -> 2189;

6389 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2189 -> 6389 [arrowhead = none ];
6389 -> 2194;

6390 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2189 -> 6390 [arrowhead = none ];
6390 -> 2195;

6391 [label="ONLY EVAL with clause\nquot(s(X3711), s(X3712), X3713, X3714) :- quot(X3711, X3712, X3713, X3714).\nand substitutionX3711 -> s(s(0)),\nX3712 -> s(0),\nX3713 -> s(s(0)),\nX3676 -> X3715,\nX3714 -> X3715", fontsize=14, style = filled, fillcolor = lightblue];
2194 -> 6391 [arrowhead = none ];
6391 -> 2199;

6392 [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 = lightgreen];
2195 -> 6392 [arrowhead = none ];
6392 -> 2232;

6393 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2199 -> 6393 [arrowhead = none ];
6393 -> 2202;

6394 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2202 -> 6394 [arrowhead = none ];
6394 -> 2204;

6395 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2204 -> 6395 [arrowhead = none ];
6395 -> 2209;

6396 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2204 -> 6396 [arrowhead = none ];
6396 -> 2210;

6397 [label="ONLY EVAL with clause\nquot(s(X3750), s(X3751), X3752, X3753) :- quot(X3750, X3751, X3752, X3753).\nand substitutionX3750 -> s(0),\nX3751 -> 0,\nX3752 -> s(s(0)),\nX3715 -> X3754,\nX3753 -> X3754", fontsize=14, style = filled, fillcolor = lightblue];
2209 -> 6397 [arrowhead = none ];
6397 -> 2215;

6398 [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 = lightgreen];
2210 -> 6398 [arrowhead = none ];
6398 -> 2231;

6399 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2215 -> 6399 [arrowhead = none ];
6399 -> 2219;

6400 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2219 -> 6400 [arrowhead = none ];
6400 -> 2220;

6401 [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 = lightgreen];
2220 -> 6401 [arrowhead = none ];
6401 -> 2222;

6402 [label="ONLY EVAL with clause\nquot(X3777, 0, s(X3778), s(X3779)) :- quot(X3777, s(X3778), s(X3778), X3779).\nand substitutionX3777 -> s(0),\nX3778 -> s(0),\nX3779 -> X3780,\nX3754 -> s(X3780)", fontsize=14, style = filled, fillcolor = lightblue];
2222 -> 6402 [arrowhead = none ];
6402 -> 2228;

6403 [label="INSTANCE with matching:\nX822 -> X3780", fontsize=14, style = filled, fillcolor = lightgrey];
2228 -> 6403 [arrowhead = none , style=dashed];
6403 -> 493[style=dashed];

6404 [label="INSTANCE with matching:\nT22 -> T432\nT20 -> T430\nX35 -> X2296", fontsize=14, style = filled, fillcolor = lightgrey];
2241 -> 6404 [arrowhead = none , style=dashed];
6404 -> 543[style=dashed];

6405 [label="INSTANCE with matching:\nT20 -> s(s(T430))\nT157 -> T573", fontsize=14, style = filled, fillcolor = lightgrey];
2242 -> 6405 [arrowhead = none , style=dashed];
6405 -> 545[style=dashed];

6406 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2248 -> 6406 [arrowhead = none ];
6406 -> 2250;

6407 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2248 -> 6407 [arrowhead = none ];
6407 -> 2251;

6408 [label="EVAL with clause\npr(X3809, s(0)).\nand substitutionT424 -> 0,\nX3809 -> s(s(s(s(s(0))))),\nT584 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
2250 -> 6408 [arrowhead = none ];
6408 -> 2253;

6409 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2250 -> 6409 [arrowhead = none ];
6409 -> 2254;

6410 [label="EVAL with clause\npr(X3814, s(s(X3815))) :- ','(not_divides(s(s(X3815)), X3814), pr(X3814, s(X3815))).\nand substitutionT424 -> s(T590),\nX3814 -> s(s(s(s(s(s(T590)))))),\nX3815 -> T590,\nT589 -> s(T590)", fontsize=14, style = filled, fillcolor = lightblue];
2251 -> 6410 [arrowhead = none ];
6410 -> 2256;

6411 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2251 -> 6411 [arrowhead = none ];
6411 -> 2257;

6412 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
2253 -> 6412 [arrowhead = none ];
6412 -> 2255;

6413 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
2256 -> 6413 [arrowhead = none ];
6413 -> 2261;

6414 [label="SPLIT 2\nnew knowledge:\nT590 is ground", fontsize=14, style = filled, fillcolor = violet];
2256 -> 6414 [arrowhead = none ];
6414 -> 2262;

6415 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2261 -> 6415 [arrowhead = none ];
6415 -> 2265;

6416 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2262 -> 6416 [arrowhead = none ];
6416 -> 3154;

6417 [label="ONLY EVAL with clause\nnot_divides(X3834, X3835) :- ','(div(X3835, X3834, X3836), ','(times(X3836, X3834, X3837), neq(X3835, X3837))).\nand substitutionT590 -> T596,\nX3834 -> s(s(T596)),\nX3835 -> s(s(s(s(s(s(T596))))))", fontsize=14, style = filled, fillcolor = lightblue];
2265 -> 6417 [arrowhead = none ];
6417 -> 2268;

6418 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
2268 -> 6418 [arrowhead = none ];
6418 -> 2269;

6419 [label="SPLIT 2\nnew knowledge:\nT596 is ground\nT598 is ground\nreplacements:X3836 -> T598", fontsize=14, style = filled, fillcolor = violet];
2268 -> 6419 [arrowhead = none ];
6419 -> 2270;

6420 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2269 -> 6420 [arrowhead = none ];
6420 -> 2271;

6421 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
2270 -> 6421 [arrowhead = none ];
6421 -> 3145;

6422 [label="SPLIT 2\nnew knowledge:\nT598 is ground\nT596 is ground\nT744 is ground\nreplacements:X3837 -> T744", fontsize=14, style = filled, fillcolor = violet];
2270 -> 6422 [arrowhead = none ];
6422 -> 3146;

6423 [label="ONLY EVAL with clause\ndiv(X3858, X3859, X3860) :- quot(X3858, X3859, X3859, X3860).\nand substitutionT596 -> T602,\nX3858 -> s(s(s(s(s(s(T602)))))),\nX3859 -> s(s(T602)),\nX3836 -> X3861,\nX3860 -> X3861", fontsize=14, style = filled, fillcolor = lightblue];
2271 -> 6423 [arrowhead = none ];
6423 -> 2277;

6424 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2277 -> 6424 [arrowhead = none ];
6424 -> 2279;

6425 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2279 -> 6425 [arrowhead = none ];
6425 -> 2280;

6426 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2280 -> 6426 [arrowhead = none ];
6426 -> 2284;

6427 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2280 -> 6427 [arrowhead = none ];
6427 -> 2285;

6428 [label="ONLY EVAL with clause\nquot(s(X3896), s(X3897), X3898, X3899) :- quot(X3896, X3897, X3898, X3899).\nand substitutionT602 -> T607,\nX3896 -> s(s(s(s(s(T607))))),\nX3897 -> s(T607),\nX3898 -> s(s(T607)),\nX3861 -> X3900,\nX3899 -> X3900", fontsize=14, style = filled, fillcolor = lightblue];
2284 -> 6428 [arrowhead = none ];
6428 -> 2288;

6429 [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 = lightgreen];
2285 -> 6429 [arrowhead = none ];
6429 -> 3142;

6430 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2288 -> 6430 [arrowhead = none ];
6430 -> 2291;

6431 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2291 -> 6431 [arrowhead = none ];
6431 -> 2293;

6432 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2293 -> 6432 [arrowhead = none ];
6432 -> 2299;

6433 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2293 -> 6433 [arrowhead = none ];
6433 -> 2300;

6434 [label="ONLY EVAL with clause\nquot(s(X3935), s(X3936), X3937, X3938) :- quot(X3935, X3936, X3937, X3938).\nand substitutionT607 -> T612,\nX3935 -> s(s(s(s(T612)))),\nX3936 -> T612,\nX3937 -> s(s(T612)),\nX3900 -> X3939,\nX3938 -> X3939", fontsize=14, style = filled, fillcolor = lightblue];
2299 -> 6434 [arrowhead = none ];
6434 -> 2303;

6435 [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 = lightgreen];
2300 -> 6435 [arrowhead = none ];
6435 -> 3141;

6436 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2303 -> 6436 [arrowhead = none ];
6436 -> 2306;

6437 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2306 -> 6437 [arrowhead = none ];
6437 -> 2308;

6438 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2308 -> 6438 [arrowhead = none ];
6438 -> 2315;

6439 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2308 -> 6439 [arrowhead = none ];
6439 -> 2316;

6440 [label="EVAL with clause\nquot(s(X3966), s(X3967), X3968, X3969) :- quot(X3966, X3967, X3968, X3969).\nand substitutionT612 -> s(T622),\nX3966 -> s(s(s(s(T622)))),\nX3967 -> T622,\nT621 -> s(T622),\nX3968 -> s(s(s(T622))),\nX3939 -> X3970,\nX3969 -> X3970", fontsize=14, style = filled, fillcolor = lightblue];
2315 -> 6440 [arrowhead = none ];
6440 -> 2325;

6441 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2315 -> 6441 [arrowhead = none ];
6441 -> 2326;

6442 [label="EVAL with clause\nquot(X5444, 0, s(X5445), s(X5446)) :- quot(X5444, s(X5445), s(X5445), X5446).\nand substitutionT612 -> 0,\nX5444 -> s(s(s(s(0)))),\nT739 -> 0,\nX5445 -> s(0),\nX5446 -> X5447,\nX3939 -> s(X5447)", fontsize=14, style = filled, fillcolor = lightblue];
2316 -> 6442 [arrowhead = none ];
6442 -> 3089;

6443 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2316 -> 6443 [arrowhead = none ];
6443 -> 3091;

6444 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2325 -> 6444 [arrowhead = none ];
6444 -> 2330;

6445 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2330 -> 6445 [arrowhead = none ];
6445 -> 2333;

6446 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2333 -> 6446 [arrowhead = none ];
6446 -> 2336;

6447 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2333 -> 6447 [arrowhead = none ];
6447 -> 2337;

6448 [label="EVAL with clause\nquot(s(X3997), s(X3998), X3999, X4000) :- quot(X3997, X3998, X3999, X4000).\nand substitutionT622 -> s(T632),\nX3997 -> s(s(s(s(T632)))),\nX3998 -> T632,\nT631 -> s(T632),\nX3999 -> s(s(s(s(T632)))),\nX3970 -> X4001,\nX4000 -> X4001", fontsize=14, style = filled, fillcolor = lightblue];
2336 -> 6448 [arrowhead = none ];
6448 -> 2342;

6449 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2336 -> 6449 [arrowhead = none ];
6449 -> 2343;

6450 [label="EVAL with clause\nquot(X5276, 0, s(X5277), s(X5278)) :- quot(X5276, s(X5277), s(X5277), X5278).\nand substitutionT622 -> 0,\nX5276 -> s(s(s(s(0)))),\nT736 -> 0,\nX5277 -> s(s(0)),\nX5278 -> X5279,\nX3970 -> s(X5279)", fontsize=14, style = filled, fillcolor = lightblue];
2337 -> 6450 [arrowhead = none ];
6450 -> 3015;

6451 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2337 -> 6451 [arrowhead = none ];
6451 -> 3016;

6452 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2342 -> 6452 [arrowhead = none ];
6452 -> 2345;

6453 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2345 -> 6453 [arrowhead = none ];
6453 -> 2346;

6454 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2346 -> 6454 [arrowhead = none ];
6454 -> 2351;

6455 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2346 -> 6455 [arrowhead = none ];
6455 -> 2352;

6456 [label="EVAL with clause\nquot(s(X4028), s(X4029), X4030, X4031) :- quot(X4028, X4029, X4030, X4031).\nand substitutionT632 -> s(T642),\nX4028 -> s(s(s(s(T642)))),\nX4029 -> T642,\nT641 -> s(T642),\nX4030 -> s(s(s(s(s(T642))))),\nX4001 -> X4032,\nX4031 -> X4032", fontsize=14, style = filled, fillcolor = lightblue];
2351 -> 6456 [arrowhead = none ];
6456 -> 2357;

6457 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2351 -> 6457 [arrowhead = none ];
6457 -> 2358;

6458 [label="EVAL with clause\nquot(X5070, 0, s(X5071), s(X5072)) :- quot(X5070, s(X5071), s(X5071), X5072).\nand substitutionT632 -> 0,\nX5070 -> s(s(s(s(0)))),\nT733 -> 0,\nX5071 -> s(s(s(0))),\nX5072 -> X5073,\nX4001 -> s(X5073)", fontsize=14, style = filled, fillcolor = lightblue];
2352 -> 6458 [arrowhead = none ];
6458 -> 2919;

6459 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2352 -> 6459 [arrowhead = none ];
6459 -> 2920;

6460 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2357 -> 6460 [arrowhead = none ];
6460 -> 2362;

6461 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2362 -> 6461 [arrowhead = none ];
6461 -> 2363;

6462 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2363 -> 6462 [arrowhead = none ];
6462 -> 2368;

6463 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2363 -> 6463 [arrowhead = none ];
6463 -> 2369;

6464 [label="EVAL with clause\nquot(s(X4059), s(X4060), X4061, X4062) :- quot(X4059, X4060, X4061, X4062).\nand substitutionT642 -> s(T652),\nX4059 -> s(s(s(s(T652)))),\nX4060 -> T652,\nT651 -> s(T652),\nX4061 -> s(s(s(s(s(s(T652)))))),\nX4032 -> X4063,\nX4062 -> X4063", fontsize=14, style = filled, fillcolor = lightblue];
2368 -> 6464 [arrowhead = none ];
6464 -> 2372;

6465 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2368 -> 6465 [arrowhead = none ];
6465 -> 2373;

6466 [label="EVAL with clause\nquot(X4875, 0, s(X4876), s(X4877)) :- quot(X4875, s(X4876), s(X4876), X4877).\nand substitutionT642 -> 0,\nX4875 -> s(s(s(s(0)))),\nT730 -> 0,\nX4876 -> s(s(s(s(0)))),\nX4877 -> X4878,\nX4032 -> s(X4878)", fontsize=14, style = filled, fillcolor = lightblue];
2369 -> 6466 [arrowhead = none ];
6466 -> 2815;

6467 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2369 -> 6467 [arrowhead = none ];
6467 -> 2816;

6468 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2372 -> 6468 [arrowhead = none ];
6468 -> 2376;

6469 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2376 -> 6469 [arrowhead = none ];
6469 -> 2378;

6470 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2378 -> 6470 [arrowhead = none ];
6470 -> 2382;

6471 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2378 -> 6471 [arrowhead = none ];
6471 -> 2383;

6472 [label="EVAL with clause\nquot(s(X4090), s(X4091), X4092, X4093) :- quot(X4090, X4091, X4092, X4093).\nand substitutionT652 -> s(T662),\nX4090 -> s(s(s(s(T662)))),\nX4091 -> T662,\nT661 -> s(T662),\nX4092 -> s(s(s(s(s(s(s(T662))))))),\nX4063 -> X4094,\nX4093 -> X4094", fontsize=14, style = filled, fillcolor = lightblue];
2382 -> 6472 [arrowhead = none ];
6472 -> 2388;

6473 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2382 -> 6473 [arrowhead = none ];
6473 -> 2389;

6474 [label="EVAL with clause\nquot(X4680, 0, s(X4681), s(X4682)) :- quot(X4680, s(X4681), s(X4681), X4682).\nand substitutionT652 -> 0,\nX4680 -> s(s(s(s(0)))),\nT727 -> 0,\nX4681 -> s(s(s(s(s(0))))),\nX4682 -> X4683,\nX4063 -> s(X4683)", fontsize=14, style = filled, fillcolor = lightblue];
2383 -> 6474 [arrowhead = none ];
6474 -> 2713;

6475 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2383 -> 6475 [arrowhead = none ];
6475 -> 2714;

6476 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2388 -> 6476 [arrowhead = none ];
6476 -> 2390;

6477 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2390 -> 6477 [arrowhead = none ];
6477 -> 2392;

6478 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2392 -> 6478 [arrowhead = none ];
6478 -> 2395;

6479 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2392 -> 6479 [arrowhead = none ];
6479 -> 2396;

6480 [label="EVAL with clause\nquot(s(X4121), s(X4122), X4123, X4124) :- quot(X4121, X4122, X4123, X4124).\nand substitutionT662 -> s(T672),\nX4121 -> s(s(s(s(T672)))),\nX4122 -> T672,\nT671 -> s(T672),\nX4123 -> s(s(s(s(s(s(s(s(T672)))))))),\nX4094 -> X4125,\nX4124 -> X4125", fontsize=14, style = filled, fillcolor = lightblue];
2395 -> 6480 [arrowhead = none ];
6480 -> 2402;

6481 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2395 -> 6481 [arrowhead = none ];
6481 -> 2403;

6482 [label="EVAL with clause\nquot(X4485, 0, s(X4486), s(X4487)) :- quot(X4485, s(X4486), s(X4486), X4487).\nand substitutionT662 -> 0,\nX4485 -> s(s(s(s(0)))),\nT724 -> 0,\nX4486 -> s(s(s(s(s(s(0)))))),\nX4487 -> X4488,\nX4094 -> s(X4488)", fontsize=14, style = filled, fillcolor = lightblue];
2396 -> 6482 [arrowhead = none ];
6482 -> 2600;

6483 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2396 -> 6483 [arrowhead = none ];
6483 -> 2601;

6484 [label="GENERALIZATION\nT673 <-- s(s(s(s(s(s(s(T672)))))))\n\nNew Knowledge:\nT673 is ground", fontsize=14, style = filled, fillcolor = violet];
2402 -> 6484 [arrowhead = none ];
6484 -> 2408;

6485 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2408 -> 6485 [arrowhead = none ];
6485 -> 2412;

6486 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2412 -> 6486 [arrowhead = none ];
6486 -> 2414;

6487 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2414 -> 6487 [arrowhead = none ];
6487 -> 2421;

6488 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2414 -> 6488 [arrowhead = none ];
6488 -> 2422;

6489 [label="EVAL with clause\nquot(s(X4156), s(X4157), X4158, X4159) :- quot(X4156, X4157, X4158, X4159).\nand substitutionT672 -> s(T687),\nX4156 -> s(s(s(s(T687)))),\nX4157 -> T687,\nT686 -> s(T687),\nT673 -> T688,\nX4158 -> s(T688),\nX4125 -> X4160,\nX4159 -> X4160", fontsize=14, style = filled, fillcolor = lightblue];
2421 -> 6489 [arrowhead = none ];
6489 -> 2427;

6490 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2421 -> 6490 [arrowhead = none ];
6490 -> 2428;

6491 [label="EVAL with clause\nquot(X4173, 0, s(X4174), s(X4175)) :- quot(X4173, s(X4174), s(X4174), X4175).\nand substitutionT672 -> 0,\nX4173 -> s(s(s(s(0)))),\nT693 -> 0,\nT673 -> T694,\nX4174 -> T694,\nX4175 -> X4176,\nX4125 -> s(X4176)", fontsize=14, style = filled, fillcolor = lightblue];
2422 -> 6491 [arrowhead = none ];
6491 -> 2437;

6492 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2422 -> 6492 [arrowhead = none ];
6492 -> 2438;

6493 [label="INSTANCE with matching:\nT672 -> T687\nT673 -> T688\nX4125 -> X4160", fontsize=14, style = filled, fillcolor = lightgrey];
2427 -> 6493 [arrowhead = none , style=dashed];
6493 -> 2408[style=dashed];

6494 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2437 -> 6494 [arrowhead = none ];
6494 -> 2441;

6495 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2441 -> 6495 [arrowhead = none ];
6495 -> 2442;

6496 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2442 -> 6496 [arrowhead = none ];
6496 -> 2447;

6497 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2442 -> 6497 [arrowhead = none ];
6497 -> 2448;

6498 [label="ONLY EVAL with clause\nquot(s(X4211), s(X4212), X4213, X4214) :- quot(X4211, X4212, X4213, X4214).\nand substitutionX4211 -> s(s(s(0))),\nT694 -> T699,\nX4212 -> T699,\nX4213 -> s(T699),\nX4176 -> X4215,\nX4214 -> X4215", fontsize=14, style = filled, fillcolor = lightblue];
2447 -> 6498 [arrowhead = none ];
6498 -> 2453;

6499 [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 = lightgreen];
2448 -> 6499 [arrowhead = none ];
6499 -> 2592;

6500 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2453 -> 6500 [arrowhead = none ];
6500 -> 2454;

6501 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2454 -> 6501 [arrowhead = none ];
6501 -> 2455;

6502 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2455 -> 6502 [arrowhead = none ];
6502 -> 2459;

6503 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2455 -> 6503 [arrowhead = none ];
6503 -> 2460;

6504 [label="EVAL with clause\nquot(s(X4242), s(X4243), X4244, X4245) :- quot(X4242, X4243, X4244, X4245).\nand substitutionX4242 -> s(s(0)),\nX4243 -> T704,\nT699 -> s(T704),\nX4244 -> s(s(T704)),\nX4215 -> X4246,\nX4245 -> X4246", fontsize=14, style = filled, fillcolor = lightblue];
2459 -> 6504 [arrowhead = none ];
6504 -> 2464;

6505 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2459 -> 6505 [arrowhead = none ];
6505 -> 2465;

6506 [label="EVAL with clause\nquot(X4398, 0, s(X4399), s(X4400)) :- quot(X4398, s(X4399), s(X4399), X4400).\nand substitutionX4398 -> s(s(s(0))),\nT699 -> 0,\nX4399 -> 0,\nX4400 -> X4401,\nX4215 -> s(X4401)", fontsize=14, style = filled, fillcolor = lightblue];
2460 -> 6506 [arrowhead = none ];
6506 -> 2553;

6507 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2460 -> 6507 [arrowhead = none ];
6507 -> 2554;

6508 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2464 -> 6508 [arrowhead = none ];
6508 -> 2470;

6509 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2470 -> 6509 [arrowhead = none ];
6509 -> 2472;

6510 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2472 -> 6510 [arrowhead = none ];
6510 -> 2476;

6511 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2472 -> 6511 [arrowhead = none ];
6511 -> 2477;

6512 [label="EVAL with clause\nquot(s(X4273), s(X4274), X4275, X4276) :- quot(X4273, X4274, X4275, X4276).\nand substitutionX4273 -> s(0),\nX4274 -> T709,\nT704 -> s(T709),\nX4275 -> s(s(s(T709))),\nX4246 -> X4277,\nX4276 -> X4277", fontsize=14, style = filled, fillcolor = lightblue];
2476 -> 6512 [arrowhead = none ];
6512 -> 2482;

6513 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2476 -> 6513 [arrowhead = none ];
6513 -> 2483;

6514 [label="EVAL with clause\nquot(X4382, 0, s(X4383), s(X4384)) :- quot(X4382, s(X4383), s(X4383), X4384).\nand substitutionX4382 -> s(s(0)),\nT704 -> 0,\nX4383 -> s(0),\nX4384 -> X4385,\nX4246 -> s(X4385)", fontsize=14, style = filled, fillcolor = lightblue];
2477 -> 6514 [arrowhead = none ];
6514 -> 2545;

6515 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2477 -> 6515 [arrowhead = none ];
6515 -> 2546;

6516 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2482 -> 6516 [arrowhead = none ];
6516 -> 2488;

6517 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2488 -> 6517 [arrowhead = none ];
6517 -> 2489;

6518 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2489 -> 6518 [arrowhead = none ];
6518 -> 2494;

6519 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2489 -> 6519 [arrowhead = none ];
6519 -> 2495;

6520 [label="EVAL with clause\nquot(s(X4304), s(X4305), X4306, X4307) :- quot(X4304, X4305, X4306, X4307).\nand substitutionX4304 -> 0,\nX4305 -> T714,\nT709 -> s(T714),\nX4306 -> s(s(s(s(T714)))),\nX4277 -> X4308,\nX4307 -> X4308", fontsize=14, style = filled, fillcolor = lightblue];
2494 -> 6520 [arrowhead = none ];
6520 -> 2500;

6521 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2494 -> 6521 [arrowhead = none ];
6521 -> 2501;

6522 [label="EVAL with clause\nquot(X4366, 0, s(X4367), s(X4368)) :- quot(X4366, s(X4367), s(X4367), X4368).\nand substitutionX4366 -> s(0),\nT709 -> 0,\nX4367 -> s(s(0)),\nX4368 -> X4369,\nX4277 -> s(X4369)", fontsize=14, style = filled, fillcolor = lightblue];
2495 -> 6522 [arrowhead = none ];
6522 -> 2536;

6523 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2495 -> 6523 [arrowhead = none ];
6523 -> 2537;

6524 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2500 -> 6524 [arrowhead = none ];
6524 -> 2505;

6525 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2505 -> 6525 [arrowhead = none ];
6525 -> 2508;

6526 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2505 -> 6526 [arrowhead = none ];
6526 -> 2509;

6527 [label="EVAL with clause\nquot(0, s(X4321), s(X4322), 0).\nand substitutionX4321 -> T721,\nT714 -> s(T721),\nX4322 -> s(s(s(s(T721)))),\nX4308 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
2508 -> 6527 [arrowhead = none ];
6527 -> 2511;

6528 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2508 -> 6528 [arrowhead = none ];
6528 -> 2512;

6529 [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 = lightgreen];
2509 -> 6529 [arrowhead = none ];
6529 -> 2514;

6530 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
2511 -> 6530 [arrowhead = none ];
6530 -> 2513;

6531 [label="EVAL with clause\nquot(X4335, 0, s(X4336), s(X4337)) :- quot(X4335, s(X4336), s(X4336), X4337).\nand substitutionX4335 -> 0,\nT714 -> 0,\nX4336 -> s(s(s(0))),\nX4337 -> X4338,\nX4308 -> s(X4338)", fontsize=14, style = filled, fillcolor = lightblue];
2514 -> 6531 [arrowhead = none ];
6531 -> 2519;

6532 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2514 -> 6532 [arrowhead = none ];
6532 -> 2520;

6533 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2519 -> 6533 [arrowhead = none ];
6533 -> 2523;

6534 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2523 -> 6534 [arrowhead = none ];
6534 -> 2524;

6535 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2523 -> 6535 [arrowhead = none ];
6535 -> 2525;

6536 [label="ONLY EVAL with clause\nquot(0, s(X4349), s(X4350), 0).\nand substitutionX4349 -> s(s(s(0))),\nX4350 -> s(s(s(0))),\nX4338 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
2524 -> 6536 [arrowhead = none ];
6536 -> 2530;

6537 [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 = lightgreen];
2525 -> 6537 [arrowhead = none ];
6537 -> 2533;

6538 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
2530 -> 6538 [arrowhead = none ];
6538 -> 2531;

6539 [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 = lightgreen];
2533 -> 6539 [arrowhead = none ];
6539 -> 2535;

6540 [label="INSTANCE with matching:\nX753 -> X4369", fontsize=14, style = filled, fillcolor = lightgrey];
2536 -> 6540 [arrowhead = none , style=dashed];
6540 -> 446[style=dashed];

6541 [label="INSTANCE with matching:\nX2139 -> X4385", fontsize=14, style = filled, fillcolor = lightgrey];
2545 -> 6541 [arrowhead = none , style=dashed];
6541 -> 1332[style=dashed];

6542 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2553 -> 6542 [arrowhead = none ];
6542 -> 2556;

6543 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2556 -> 6543 [arrowhead = none ];
6543 -> 2557;

6544 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2557 -> 6544 [arrowhead = none ];
6544 -> 2562;

6545 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2557 -> 6545 [arrowhead = none ];
6545 -> 2563;

6546 [label="ONLY EVAL with clause\nquot(s(X4436), s(X4437), X4438, X4439) :- quot(X4436, X4437, X4438, X4439).\nand substitutionX4436 -> s(s(0)),\nX4437 -> 0,\nX4438 -> s(0),\nX4401 -> X4440,\nX4439 -> X4440", fontsize=14, style = filled, fillcolor = lightblue];
2562 -> 6546 [arrowhead = none ];
6546 -> 2570;

6547 [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 = lightgreen];
2563 -> 6547 [arrowhead = none ];
6547 -> 2590;

6548 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2570 -> 6548 [arrowhead = none ];
6548 -> 2573;

6549 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2573 -> 6549 [arrowhead = none ];
6549 -> 2577;

6550 [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 = lightgreen];
2577 -> 6550 [arrowhead = none ];
6550 -> 2579;

6551 [label="ONLY EVAL with clause\nquot(X4463, 0, s(X4464), s(X4465)) :- quot(X4463, s(X4464), s(X4464), X4465).\nand substitutionX4463 -> s(s(0)),\nX4464 -> 0,\nX4465 -> X4466,\nX4440 -> s(X4466)", fontsize=14, style = filled, fillcolor = lightblue];
2579 -> 6551 [arrowhead = none ];
6551 -> 2586;

6552 [label="INSTANCE with matching:\nX2813 -> X4466", fontsize=14, style = filled, fillcolor = lightgrey];
2586 -> 6552 [arrowhead = none , style=dashed];
6552 -> 1728[style=dashed];

6553 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2600 -> 6553 [arrowhead = none ];
6553 -> 2608;

6554 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2608 -> 6554 [arrowhead = none ];
6554 -> 2612;

6555 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2612 -> 6555 [arrowhead = none ];
6555 -> 2622;

6556 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2612 -> 6556 [arrowhead = none ];
6556 -> 2623;

6557 [label="ONLY EVAL with clause\nquot(s(X4523), s(X4524), X4525, X4526) :- quot(X4523, X4524, X4525, X4526).\nand substitutionX4523 -> s(s(s(0))),\nX4524 -> s(s(s(s(s(s(0)))))),\nX4525 -> s(s(s(s(s(s(s(0))))))),\nX4488 -> X4527,\nX4526 -> X4527", fontsize=14, style = filled, fillcolor = lightblue];
2622 -> 6557 [arrowhead = none ];
6557 -> 2631;

6558 [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 = lightgreen];
2623 -> 6558 [arrowhead = none ];
6558 -> 2707;

6559 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2631 -> 6559 [arrowhead = none ];
6559 -> 2638;

6560 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2638 -> 6560 [arrowhead = none ];
6560 -> 2639;

6561 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2639 -> 6561 [arrowhead = none ];
6561 -> 2646;

6562 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2639 -> 6562 [arrowhead = none ];
6562 -> 2647;

6563 [label="ONLY EVAL with clause\nquot(s(X4562), s(X4563), X4564, X4565) :- quot(X4562, X4563, X4564, X4565).\nand substitutionX4562 -> s(s(0)),\nX4563 -> s(s(s(s(s(0))))),\nX4564 -> s(s(s(s(s(s(s(0))))))),\nX4527 -> X4566,\nX4565 -> X4566", fontsize=14, style = filled, fillcolor = lightblue];
2646 -> 6563 [arrowhead = none ];
6563 -> 2654;

6564 [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 = lightgreen];
2647 -> 6564 [arrowhead = none ];
6564 -> 2706;

6565 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2654 -> 6565 [arrowhead = none ];
6565 -> 2655;

6566 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2655 -> 6566 [arrowhead = none ];
6566 -> 2660;

6567 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2660 -> 6567 [arrowhead = none ];
6567 -> 2663;

6568 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2660 -> 6568 [arrowhead = none ];
6568 -> 2664;

6569 [label="ONLY EVAL with clause\nquot(s(X4601), s(X4602), X4603, X4604) :- quot(X4601, X4602, X4603, X4604).\nand substitutionX4601 -> s(0),\nX4602 -> s(s(s(s(0)))),\nX4603 -> s(s(s(s(s(s(s(0))))))),\nX4566 -> X4605,\nX4604 -> X4605", fontsize=14, style = filled, fillcolor = lightblue];
2663 -> 6569 [arrowhead = none ];
6569 -> 2671;

6570 [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 = lightgreen];
2664 -> 6570 [arrowhead = none ];
6570 -> 2704;

6571 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2671 -> 6571 [arrowhead = none ];
6571 -> 2673;

6572 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2673 -> 6572 [arrowhead = none ];
6572 -> 2675;

6573 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2675 -> 6573 [arrowhead = none ];
6573 -> 2681;

6574 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2675 -> 6574 [arrowhead = none ];
6574 -> 2682;

6575 [label="ONLY EVAL with clause\nquot(s(X4636), s(X4637), X4638, X4639) :- quot(X4636, X4637, X4638, X4639).\nand substitutionX4636 -> 0,\nX4637 -> s(s(s(0))),\nX4638 -> s(s(s(s(s(s(s(0))))))),\nX4605 -> X4640,\nX4639 -> X4640", fontsize=14, style = filled, fillcolor = lightblue];
2681 -> 6575 [arrowhead = none ];
6575 -> 2686;

6576 [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 = lightgreen];
2682 -> 6576 [arrowhead = none ];
6576 -> 2702;

6577 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2686 -> 6577 [arrowhead = none ];
6577 -> 2689;

6578 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2689 -> 6578 [arrowhead = none ];
6578 -> 2692;

6579 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2689 -> 6579 [arrowhead = none ];
6579 -> 2693;

6580 [label="ONLY EVAL with clause\nquot(0, s(X4651), s(X4652), 0).\nand substitutionX4651 -> s(s(0)),\nX4652 -> s(s(s(s(s(s(0)))))),\nX4640 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
2692 -> 6580 [arrowhead = none ];
6580 -> 2694;

6581 [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 = lightgreen];
2693 -> 6581 [arrowhead = none ];
6581 -> 2700;

6582 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
2694 -> 6582 [arrowhead = none ];
6582 -> 2695;

6583 [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 = lightgreen];
2700 -> 6583 [arrowhead = none ];
6583 -> 2701;

6584 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2713 -> 6584 [arrowhead = none ];
6584 -> 2715;

6585 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2715 -> 6585 [arrowhead = none ];
6585 -> 2719;

6586 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2719 -> 6586 [arrowhead = none ];
6586 -> 2722;

6587 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2719 -> 6587 [arrowhead = none ];
6587 -> 2723;

6588 [label="ONLY EVAL with clause\nquot(s(X4718), s(X4719), X4720, X4721) :- quot(X4718, X4719, X4720, X4721).\nand substitutionX4718 -> s(s(s(0))),\nX4719 -> s(s(s(s(s(0))))),\nX4720 -> s(s(s(s(s(s(0)))))),\nX4683 -> X4722,\nX4721 -> X4722", fontsize=14, style = filled, fillcolor = lightblue];
2722 -> 6588 [arrowhead = none ];
6588 -> 2729;

6589 [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 = lightgreen];
2723 -> 6589 [arrowhead = none ];
6589 -> 2811;

6590 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2729 -> 6590 [arrowhead = none ];
6590 -> 2731;

6591 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2731 -> 6591 [arrowhead = none ];
6591 -> 2734;

6592 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2734 -> 6592 [arrowhead = none ];
6592 -> 2737;

6593 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2734 -> 6593 [arrowhead = none ];
6593 -> 2738;

6594 [label="ONLY EVAL with clause\nquot(s(X4757), s(X4758), X4759, X4760) :- quot(X4757, X4758, X4759, X4760).\nand substitutionX4757 -> s(s(0)),\nX4758 -> s(s(s(s(0)))),\nX4759 -> s(s(s(s(s(s(0)))))),\nX4722 -> X4761,\nX4760 -> X4761", fontsize=14, style = filled, fillcolor = lightblue];
2737 -> 6594 [arrowhead = none ];
6594 -> 2744;

6595 [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 = lightgreen];
2738 -> 6595 [arrowhead = none ];
6595 -> 2809;

6596 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2744 -> 6596 [arrowhead = none ];
6596 -> 2748;

6597 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2748 -> 6597 [arrowhead = none ];
6597 -> 2749;

6598 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2749 -> 6598 [arrowhead = none ];
6598 -> 2753;

6599 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2749 -> 6599 [arrowhead = none ];
6599 -> 2754;

6600 [label="ONLY EVAL with clause\nquot(s(X4796), s(X4797), X4798, X4799) :- quot(X4796, X4797, X4798, X4799).\nand substitutionX4796 -> s(0),\nX4797 -> s(s(s(0))),\nX4798 -> s(s(s(s(s(s(0)))))),\nX4761 -> X4800,\nX4799 -> X4800", fontsize=14, style = filled, fillcolor = lightblue];
2753 -> 6600 [arrowhead = none ];
6600 -> 2765;

6601 [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 = lightgreen];
2754 -> 6601 [arrowhead = none ];
6601 -> 2807;

6602 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2765 -> 6602 [arrowhead = none ];
6602 -> 2772;

6603 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2772 -> 6603 [arrowhead = none ];
6603 -> 2774;

6604 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2774 -> 6604 [arrowhead = none ];
6604 -> 2782;

6605 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2774 -> 6605 [arrowhead = none ];
6605 -> 2783;

6606 [label="ONLY EVAL with clause\nquot(s(X4831), s(X4832), X4833, X4834) :- quot(X4831, X4832, X4833, X4834).\nand substitutionX4831 -> 0,\nX4832 -> s(s(0)),\nX4833 -> s(s(s(s(s(s(0)))))),\nX4800 -> X4835,\nX4834 -> X4835", fontsize=14, style = filled, fillcolor = lightblue];
2782 -> 6606 [arrowhead = none ];
6606 -> 2791;

6607 [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 = lightgreen];
2783 -> 6607 [arrowhead = none ];
6607 -> 2806;

6608 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2791 -> 6608 [arrowhead = none ];
6608 -> 2794;

6609 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2794 -> 6609 [arrowhead = none ];
6609 -> 2797;

6610 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2794 -> 6610 [arrowhead = none ];
6610 -> 2798;

6611 [label="ONLY EVAL with clause\nquot(0, s(X4846), s(X4847), 0).\nand substitutionX4846 -> s(0),\nX4847 -> s(s(s(s(s(0))))),\nX4835 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
2797 -> 6611 [arrowhead = none ];
6611 -> 2799;

6612 [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 = lightgreen];
2798 -> 6612 [arrowhead = none ];
6612 -> 2802;

6613 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
2799 -> 6613 [arrowhead = none ];
6613 -> 2800;

6614 [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 = lightgreen];
2802 -> 6614 [arrowhead = none ];
6614 -> 2805;

6615 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2815 -> 6615 [arrowhead = none ];
6615 -> 2819;

6616 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2819 -> 6616 [arrowhead = none ];
6616 -> 2820;

6617 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2820 -> 6617 [arrowhead = none ];
6617 -> 2826;

6618 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2820 -> 6618 [arrowhead = none ];
6618 -> 2827;

6619 [label="ONLY EVAL with clause\nquot(s(X4913), s(X4914), X4915, X4916) :- quot(X4913, X4914, X4915, X4916).\nand substitutionX4913 -> s(s(s(0))),\nX4914 -> s(s(s(s(0)))),\nX4915 -> s(s(s(s(s(0))))),\nX4878 -> X4917,\nX4916 -> X4917", fontsize=14, style = filled, fillcolor = lightblue];
2826 -> 6619 [arrowhead = none ];
6619 -> 2833;

6620 [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 = lightgreen];
2827 -> 6620 [arrowhead = none ];
6620 -> 2915;

6621 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2833 -> 6621 [arrowhead = none ];
6621 -> 2834;

6622 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2834 -> 6622 [arrowhead = none ];
6622 -> 2838;

6623 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2838 -> 6623 [arrowhead = none ];
6623 -> 2841;

6624 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2838 -> 6624 [arrowhead = none ];
6624 -> 2842;

6625 [label="ONLY EVAL with clause\nquot(s(X4952), s(X4953), X4954, X4955) :- quot(X4952, X4953, X4954, X4955).\nand substitutionX4952 -> s(s(0)),\nX4953 -> s(s(s(0))),\nX4954 -> s(s(s(s(s(0))))),\nX4917 -> X4956,\nX4955 -> X4956", fontsize=14, style = filled, fillcolor = lightblue];
2841 -> 6625 [arrowhead = none ];
6625 -> 2848;

6626 [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 = lightgreen];
2842 -> 6626 [arrowhead = none ];
6626 -> 2914;

6627 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2848 -> 6627 [arrowhead = none ];
6627 -> 2852;

6628 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2852 -> 6628 [arrowhead = none ];
6628 -> 2854;

6629 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2854 -> 6629 [arrowhead = none ];
6629 -> 2860;

6630 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2854 -> 6630 [arrowhead = none ];
6630 -> 2861;

6631 [label="ONLY EVAL with clause\nquot(s(X4991), s(X4992), X4993, X4994) :- quot(X4991, X4992, X4993, X4994).\nand substitutionX4991 -> s(0),\nX4992 -> s(s(0)),\nX4993 -> s(s(s(s(s(0))))),\nX4956 -> X4995,\nX4994 -> X4995", fontsize=14, style = filled, fillcolor = lightblue];
2860 -> 6631 [arrowhead = none ];
6631 -> 2874;

6632 [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 = lightgreen];
2861 -> 6632 [arrowhead = none ];
6632 -> 2913;

6633 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2874 -> 6633 [arrowhead = none ];
6633 -> 2879;

6634 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2879 -> 6634 [arrowhead = none ];
6634 -> 2885;

6635 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2885 -> 6635 [arrowhead = none ];
6635 -> 2889;

6636 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2885 -> 6636 [arrowhead = none ];
6636 -> 2890;

6637 [label="ONLY EVAL with clause\nquot(s(X5026), s(X5027), X5028, X5029) :- quot(X5026, X5027, X5028, X5029).\nand substitutionX5026 -> 0,\nX5027 -> s(0),\nX5028 -> s(s(s(s(s(0))))),\nX4995 -> X5030,\nX5029 -> X5030", fontsize=14, style = filled, fillcolor = lightblue];
2889 -> 6637 [arrowhead = none ];
6637 -> 2896;

6638 [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 = lightgreen];
2890 -> 6638 [arrowhead = none ];
6638 -> 2911;

6639 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2896 -> 6639 [arrowhead = none ];
6639 -> 2898;

6640 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2898 -> 6640 [arrowhead = none ];
6640 -> 2900;

6641 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2898 -> 6641 [arrowhead = none ];
6641 -> 2901;

6642 [label="ONLY EVAL with clause\nquot(0, s(X5041), s(X5042), 0).\nand substitutionX5041 -> 0,\nX5042 -> s(s(s(s(0)))),\nX5030 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
2900 -> 6642 [arrowhead = none ];
6642 -> 2904;

6643 [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 = lightgreen];
2901 -> 6643 [arrowhead = none ];
6643 -> 2906;

6644 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
2904 -> 6644 [arrowhead = none ];
6644 -> 2905;

6645 [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 = lightgreen];
2906 -> 6645 [arrowhead = none ];
6645 -> 2907;

6646 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2919 -> 6646 [arrowhead = none ];
6646 -> 2923;

6647 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2923 -> 6647 [arrowhead = none ];
6647 -> 2925;

6648 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2925 -> 6648 [arrowhead = none ];
6648 -> 2930;

6649 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2925 -> 6649 [arrowhead = none ];
6649 -> 2931;

6650 [label="ONLY EVAL with clause\nquot(s(X5108), s(X5109), X5110, X5111) :- quot(X5108, X5109, X5110, X5111).\nand substitutionX5108 -> s(s(s(0))),\nX5109 -> s(s(s(0))),\nX5110 -> s(s(s(s(0)))),\nX5073 -> X5112,\nX5111 -> X5112", fontsize=14, style = filled, fillcolor = lightblue];
2930 -> 6650 [arrowhead = none ];
6650 -> 2936;

6651 [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 = lightgreen];
2931 -> 6651 [arrowhead = none ];
6651 -> 3013;

6652 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2936 -> 6652 [arrowhead = none ];
6652 -> 2939;

6653 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2939 -> 6653 [arrowhead = none ];
6653 -> 2940;

6654 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2940 -> 6654 [arrowhead = none ];
6654 -> 2945;

6655 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2940 -> 6655 [arrowhead = none ];
6655 -> 2946;

6656 [label="ONLY EVAL with clause\nquot(s(X5147), s(X5148), X5149, X5150) :- quot(X5147, X5148, X5149, X5150).\nand substitutionX5147 -> s(s(0)),\nX5148 -> s(s(0)),\nX5149 -> s(s(s(s(0)))),\nX5112 -> X5151,\nX5150 -> X5151", fontsize=14, style = filled, fillcolor = lightblue];
2945 -> 6656 [arrowhead = none ];
6656 -> 2954;

6657 [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 = lightgreen];
2946 -> 6657 [arrowhead = none ];
6657 -> 3012;

6658 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2954 -> 6658 [arrowhead = none ];
6658 -> 2956;

6659 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2956 -> 6659 [arrowhead = none ];
6659 -> 2957;

6660 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2957 -> 6660 [arrowhead = none ];
6660 -> 2965;

6661 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2957 -> 6661 [arrowhead = none ];
6661 -> 2966;

6662 [label="ONLY EVAL with clause\nquot(s(X5186), s(X5187), X5188, X5189) :- quot(X5186, X5187, X5188, X5189).\nand substitutionX5186 -> s(0),\nX5187 -> s(0),\nX5188 -> s(s(s(s(0)))),\nX5151 -> X5190,\nX5189 -> X5190", fontsize=14, style = filled, fillcolor = lightblue];
2965 -> 6662 [arrowhead = none ];
6662 -> 2978;

6663 [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 = lightgreen];
2966 -> 6663 [arrowhead = none ];
6663 -> 3009;

6664 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2978 -> 6664 [arrowhead = none ];
6664 -> 2979;

6665 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2979 -> 6665 [arrowhead = none ];
6665 -> 2982;

6666 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2982 -> 6666 [arrowhead = none ];
6666 -> 2989;

6667 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2982 -> 6667 [arrowhead = none ];
6667 -> 2990;

6668 [label="ONLY EVAL with clause\nquot(s(X5225), s(X5226), X5227, X5228) :- quot(X5225, X5226, X5227, X5228).\nand substitutionX5225 -> 0,\nX5226 -> 0,\nX5227 -> s(s(s(s(0)))),\nX5190 -> X5229,\nX5228 -> X5229", fontsize=14, style = filled, fillcolor = lightblue];
2989 -> 6668 [arrowhead = none ];
6668 -> 2995;

6669 [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 = lightgreen];
2990 -> 6669 [arrowhead = none ];
6669 -> 3006;

6670 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2995 -> 6670 [arrowhead = none ];
6670 -> 2996;

6671 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
2996 -> 6671 [arrowhead = none ];
6671 -> 2998;

6672 [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 = lightgreen];
2998 -> 6672 [arrowhead = none ];
6672 -> 3000;

6673 [label="ONLY EVAL with clause\nquot(X5250, 0, s(X5251), s(X5252)) :- quot(X5250, s(X5251), s(X5251), X5252).\nand substitutionX5250 -> 0,\nX5251 -> s(s(s(0))),\nX5252 -> X5253,\nX5229 -> s(X5253)", fontsize=14, style = filled, fillcolor = lightblue];
3000 -> 6673 [arrowhead = none ];
6673 -> 3005;

6674 [label="INSTANCE with matching:\nX4338 -> X5253", fontsize=14, style = filled, fillcolor = lightgrey];
3005 -> 6674 [arrowhead = none , style=dashed];
6674 -> 2519[style=dashed];

6675 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3015 -> 6675 [arrowhead = none ];
6675 -> 3018;

6676 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3018 -> 6676 [arrowhead = none ];
6676 -> 3020;

6677 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3020 -> 6677 [arrowhead = none ];
6677 -> 3026;

6678 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3020 -> 6678 [arrowhead = none ];
6678 -> 3027;

6679 [label="ONLY EVAL with clause\nquot(s(X5314), s(X5315), X5316, X5317) :- quot(X5314, X5315, X5316, X5317).\nand substitutionX5314 -> s(s(s(0))),\nX5315 -> s(s(0)),\nX5316 -> s(s(s(0))),\nX5279 -> X5318,\nX5317 -> X5318", fontsize=14, style = filled, fillcolor = lightblue];
3026 -> 6679 [arrowhead = none ];
6679 -> 3031;

6680 [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 = lightgreen];
3027 -> 6680 [arrowhead = none ];
6680 -> 3085;

6681 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3031 -> 6681 [arrowhead = none ];
6681 -> 3035;

6682 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3035 -> 6682 [arrowhead = none ];
6682 -> 3036;

6683 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3036 -> 6683 [arrowhead = none ];
6683 -> 3041;

6684 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3036 -> 6684 [arrowhead = none ];
6684 -> 3042;

6685 [label="ONLY EVAL with clause\nquot(s(X5353), s(X5354), X5355, X5356) :- quot(X5353, X5354, X5355, X5356).\nand substitutionX5353 -> s(s(0)),\nX5354 -> s(0),\nX5355 -> s(s(s(0))),\nX5318 -> X5357,\nX5356 -> X5357", fontsize=14, style = filled, fillcolor = lightblue];
3041 -> 6685 [arrowhead = none ];
6685 -> 3045;

6686 [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 = lightgreen];
3042 -> 6686 [arrowhead = none ];
6686 -> 3084;

6687 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3045 -> 6687 [arrowhead = none ];
6687 -> 3047;

6688 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3047 -> 6688 [arrowhead = none ];
6688 -> 3049;

6689 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3049 -> 6689 [arrowhead = none ];
6689 -> 3055;

6690 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3049 -> 6690 [arrowhead = none ];
6690 -> 3056;

6691 [label="ONLY EVAL with clause\nquot(s(X5392), s(X5393), X5394, X5395) :- quot(X5392, X5393, X5394, X5395).\nand substitutionX5392 -> s(0),\nX5393 -> 0,\nX5394 -> s(s(s(0))),\nX5357 -> X5396,\nX5395 -> X5396", fontsize=14, style = filled, fillcolor = lightblue];
3055 -> 6691 [arrowhead = none ];
6691 -> 3063;

6692 [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 = lightgreen];
3056 -> 6692 [arrowhead = none ];
6692 -> 3082;

6693 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3063 -> 6693 [arrowhead = none ];
6693 -> 3066;

6694 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3066 -> 6694 [arrowhead = none ];
6694 -> 3067;

6695 [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 = lightgreen];
3067 -> 6695 [arrowhead = none ];
6695 -> 3072;

6696 [label="ONLY EVAL with clause\nquot(X5419, 0, s(X5420), s(X5421)) :- quot(X5419, s(X5420), s(X5420), X5421).\nand substitutionX5419 -> s(0),\nX5420 -> s(s(0)),\nX5421 -> X5422,\nX5396 -> s(X5422)", fontsize=14, style = filled, fillcolor = lightblue];
3072 -> 6696 [arrowhead = none ];
6696 -> 3078;

6697 [label="INSTANCE with matching:\nX753 -> X5422", fontsize=14, style = filled, fillcolor = lightgrey];
3078 -> 6697 [arrowhead = none , style=dashed];
6697 -> 446[style=dashed];

6698 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3089 -> 6698 [arrowhead = none ];
6698 -> 3093;

6699 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3093 -> 6699 [arrowhead = none ];
6699 -> 3094;

6700 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3094 -> 6700 [arrowhead = none ];
6700 -> 3099;

6701 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3094 -> 6701 [arrowhead = none ];
6701 -> 3100;

6702 [label="ONLY EVAL with clause\nquot(s(X5482), s(X5483), X5484, X5485) :- quot(X5482, X5483, X5484, X5485).\nand substitutionX5482 -> s(s(s(0))),\nX5483 -> s(0),\nX5484 -> s(s(0)),\nX5447 -> X5486,\nX5485 -> X5486", fontsize=14, style = filled, fillcolor = lightblue];
3099 -> 6702 [arrowhead = none ];
6702 -> 3107;

6703 [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 = lightgreen];
3100 -> 6703 [arrowhead = none ];
6703 -> 3137;

6704 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3107 -> 6704 [arrowhead = none ];
6704 -> 3108;

6705 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3108 -> 6705 [arrowhead = none ];
6705 -> 3109;

6706 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3109 -> 6706 [arrowhead = none ];
6706 -> 3114;

6707 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3109 -> 6707 [arrowhead = none ];
6707 -> 3115;

6708 [label="ONLY EVAL with clause\nquot(s(X5521), s(X5522), X5523, X5524) :- quot(X5521, X5522, X5523, X5524).\nand substitutionX5521 -> s(s(0)),\nX5522 -> 0,\nX5523 -> s(s(0)),\nX5486 -> X5525,\nX5524 -> X5525", fontsize=14, style = filled, fillcolor = lightblue];
3114 -> 6708 [arrowhead = none ];
6708 -> 3122;

6709 [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 = lightgreen];
3115 -> 6709 [arrowhead = none ];
6709 -> 3136;

6710 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3122 -> 6710 [arrowhead = none ];
6710 -> 3124;

6711 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3124 -> 6711 [arrowhead = none ];
6711 -> 3125;

6712 [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 = lightgreen];
3125 -> 6712 [arrowhead = none ];
6712 -> 3126;

6713 [label="ONLY EVAL with clause\nquot(X5548, 0, s(X5549), s(X5550)) :- quot(X5548, s(X5549), s(X5549), X5550).\nand substitutionX5548 -> s(s(0)),\nX5549 -> s(0),\nX5550 -> X5551,\nX5525 -> s(X5551)", fontsize=14, style = filled, fillcolor = lightblue];
3126 -> 6713 [arrowhead = none ];
6713 -> 3132;

6714 [label="INSTANCE with matching:\nX2139 -> X5551", fontsize=14, style = filled, fillcolor = lightgrey];
3132 -> 6714 [arrowhead = none , style=dashed];
6714 -> 1332[style=dashed];

6715 [label="INSTANCE with matching:\nT22 -> T598\nT20 -> T596\nX35 -> X3837", fontsize=14, style = filled, fillcolor = lightgrey];
3145 -> 6715 [arrowhead = none , style=dashed];
6715 -> 543[style=dashed];

6716 [label="INSTANCE with matching:\nT20 -> s(s(s(T596)))\nT157 -> T744", fontsize=14, style = filled, fillcolor = lightgrey];
3146 -> 6716 [arrowhead = none , style=dashed];
6716 -> 545[style=dashed];

6717 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3154 -> 6717 [arrowhead = none ];
6717 -> 3155;

6718 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3154 -> 6718 [arrowhead = none ];
6718 -> 3156;

6719 [label="EVAL with clause\npr(X5580, s(0)).\nand substitutionT590 -> 0,\nX5580 -> s(s(s(s(s(s(0)))))),\nT755 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
3155 -> 6719 [arrowhead = none ];
6719 -> 3157;

6720 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3155 -> 6720 [arrowhead = none ];
6720 -> 3158;

6721 [label="EVAL with clause\npr(X5585, s(s(X5586))) :- ','(not_divides(s(s(X5586)), X5585), pr(X5585, s(X5586))).\nand substitutionT590 -> s(T761),\nX5585 -> s(s(s(s(s(s(s(T761))))))),\nX5586 -> T761,\nT760 -> s(T761)", fontsize=14, style = filled, fillcolor = lightblue];
3156 -> 6721 [arrowhead = none ];
6721 -> 3162;

6722 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3156 -> 6722 [arrowhead = none ];
6722 -> 3163;

6723 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3157 -> 6723 [arrowhead = none ];
6723 -> 3159;

6724 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
3162 -> 6724 [arrowhead = none ];
6724 -> 3165;

6725 [label="SPLIT 2\nnew knowledge:\nT761 is ground", fontsize=14, style = filled, fillcolor = violet];
3162 -> 6725 [arrowhead = none ];
6725 -> 3166;

6726 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3165 -> 6726 [arrowhead = none ];
6726 -> 3171;

6727 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3166 -> 6727 [arrowhead = none ];
6727 -> 4186;

6728 [label="ONLY EVAL with clause\nnot_divides(X5605, X5606) :- ','(div(X5606, X5605, X5607), ','(times(X5607, X5605, X5608), neq(X5606, X5608))).\nand substitutionT761 -> T767,\nX5605 -> s(s(T767)),\nX5606 -> s(s(s(s(s(s(s(T767)))))))", fontsize=14, style = filled, fillcolor = lightblue];
3171 -> 6728 [arrowhead = none ];
6728 -> 3174;

6729 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
3174 -> 6729 [arrowhead = none ];
6729 -> 3176;

6730 [label="SPLIT 2\nnew knowledge:\nT767 is ground\nT769 is ground\nreplacements:X5607 -> T769", fontsize=14, style = filled, fillcolor = violet];
3174 -> 6730 [arrowhead = none ];
6730 -> 3177;

6731 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3176 -> 6731 [arrowhead = none ];
6731 -> 3180;

6732 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
3177 -> 6732 [arrowhead = none ];
6732 -> 4178;

6733 [label="SPLIT 2\nnew knowledge:\nT769 is ground\nT767 is ground\nT920 is ground\nreplacements:X5608 -> T920", fontsize=14, style = filled, fillcolor = violet];
3177 -> 6733 [arrowhead = none ];
6733 -> 4179;

6734 [label="ONLY EVAL with clause\ndiv(X5629, X5630, X5631) :- quot(X5629, X5630, X5630, X5631).\nand substitutionT767 -> T773,\nX5629 -> s(s(s(s(s(s(s(T773))))))),\nX5630 -> s(s(T773)),\nX5607 -> X5632,\nX5631 -> X5632", fontsize=14, style = filled, fillcolor = lightblue];
3180 -> 6734 [arrowhead = none ];
6734 -> 3187;

6735 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3187 -> 6735 [arrowhead = none ];
6735 -> 3188;

6736 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3188 -> 6736 [arrowhead = none ];
6736 -> 3189;

6737 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3189 -> 6737 [arrowhead = none ];
6737 -> 3195;

6738 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3189 -> 6738 [arrowhead = none ];
6738 -> 3196;

6739 [label="ONLY EVAL with clause\nquot(s(X5667), s(X5668), X5669, X5670) :- quot(X5667, X5668, X5669, X5670).\nand substitutionT773 -> T778,\nX5667 -> s(s(s(s(s(s(T778)))))),\nX5668 -> s(T778),\nX5669 -> s(s(T778)),\nX5632 -> X5671,\nX5670 -> X5671", fontsize=14, style = filled, fillcolor = lightblue];
3195 -> 6739 [arrowhead = none ];
6739 -> 3203;

6740 [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 = lightgreen];
3196 -> 6740 [arrowhead = none ];
6740 -> 4176;

6741 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3203 -> 6741 [arrowhead = none ];
6741 -> 3207;

6742 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3207 -> 6742 [arrowhead = none ];
6742 -> 3210;

6743 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3210 -> 6743 [arrowhead = none ];
6743 -> 3221;

6744 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3210 -> 6744 [arrowhead = none ];
6744 -> 3222;

6745 [label="ONLY EVAL with clause\nquot(s(X5706), s(X5707), X5708, X5709) :- quot(X5706, X5707, X5708, X5709).\nand substitutionT778 -> T783,\nX5706 -> s(s(s(s(s(T783))))),\nX5707 -> T783,\nX5708 -> s(s(T783)),\nX5671 -> X5710,\nX5709 -> X5710", fontsize=14, style = filled, fillcolor = lightblue];
3221 -> 6745 [arrowhead = none ];
6745 -> 3229;

6746 [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 = lightgreen];
3222 -> 6746 [arrowhead = none ];
6746 -> 4172;

6747 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3229 -> 6747 [arrowhead = none ];
6747 -> 3236;

6748 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3236 -> 6748 [arrowhead = none ];
6748 -> 3239;

6749 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3239 -> 6749 [arrowhead = none ];
6749 -> 3243;

6750 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3239 -> 6750 [arrowhead = none ];
6750 -> 3244;

6751 [label="EVAL with clause\nquot(s(X5737), s(X5738), X5739, X5740) :- quot(X5737, X5738, X5739, X5740).\nand substitutionT783 -> s(T793),\nX5737 -> s(s(s(s(s(T793))))),\nX5738 -> T793,\nT792 -> s(T793),\nX5739 -> s(s(s(T793))),\nX5710 -> X5741,\nX5740 -> X5741", fontsize=14, style = filled, fillcolor = lightblue];
3243 -> 6751 [arrowhead = none ];
6751 -> 3247;

6752 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3243 -> 6752 [arrowhead = none ];
6752 -> 3248;

6753 [label="EVAL with clause\nquot(X7403, 0, s(X7404), s(X7405)) :- quot(X7403, s(X7404), s(X7404), X7405).\nand substitutionT783 -> 0,\nX7403 -> s(s(s(s(s(0))))),\nT915 -> 0,\nX7404 -> s(0),\nX7405 -> X7406,\nX5710 -> s(X7406)", fontsize=14, style = filled, fillcolor = lightblue];
3244 -> 6753 [arrowhead = none ];
6753 -> 4107;

6754 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3244 -> 6754 [arrowhead = none ];
6754 -> 4108;

6755 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3247 -> 6755 [arrowhead = none ];
6755 -> 3254;

6756 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3254 -> 6756 [arrowhead = none ];
6756 -> 3255;

6757 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3255 -> 6757 [arrowhead = none ];
6757 -> 3259;

6758 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3255 -> 6758 [arrowhead = none ];
6758 -> 3260;

6759 [label="EVAL with clause\nquot(s(X5768), s(X5769), X5770, X5771) :- quot(X5768, X5769, X5770, X5771).\nand substitutionT793 -> s(T803),\nX5768 -> s(s(s(s(s(T803))))),\nX5769 -> T803,\nT802 -> s(T803),\nX5770 -> s(s(s(s(T803)))),\nX5741 -> X5772,\nX5771 -> X5772", fontsize=14, style = filled, fillcolor = lightblue];
3259 -> 6759 [arrowhead = none ];
6759 -> 3262;

6760 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3259 -> 6760 [arrowhead = none ];
6760 -> 3263;

6761 [label="EVAL with clause\nquot(X7235, 0, s(X7236), s(X7237)) :- quot(X7235, s(X7236), s(X7236), X7237).\nand substitutionT793 -> 0,\nX7235 -> s(s(s(s(s(0))))),\nT912 -> 0,\nX7236 -> s(s(0)),\nX7237 -> X7238,\nX5741 -> s(X7238)", fontsize=14, style = filled, fillcolor = lightblue];
3260 -> 6761 [arrowhead = none ];
6761 -> 4027;

6762 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3260 -> 6762 [arrowhead = none ];
6762 -> 4028;

6763 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3262 -> 6763 [arrowhead = none ];
6763 -> 3267;

6764 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3267 -> 6764 [arrowhead = none ];
6764 -> 3269;

6765 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3269 -> 6765 [arrowhead = none ];
6765 -> 3273;

6766 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3269 -> 6766 [arrowhead = none ];
6766 -> 3274;

6767 [label="EVAL with clause\nquot(s(X5799), s(X5800), X5801, X5802) :- quot(X5799, X5800, X5801, X5802).\nand substitutionT803 -> s(T813),\nX5799 -> s(s(s(s(s(T813))))),\nX5800 -> T813,\nT812 -> s(T813),\nX5801 -> s(s(s(s(s(T813))))),\nX5772 -> X5803,\nX5802 -> X5803", fontsize=14, style = filled, fillcolor = lightblue];
3273 -> 6767 [arrowhead = none ];
6767 -> 3277;

6768 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3273 -> 6768 [arrowhead = none ];
6768 -> 3278;

6769 [label="EVAL with clause\nquot(X7025, 0, s(X7026), s(X7027)) :- quot(X7025, s(X7026), s(X7026), X7027).\nand substitutionT803 -> 0,\nX7025 -> s(s(s(s(s(0))))),\nT909 -> 0,\nX7026 -> s(s(s(0))),\nX7027 -> X7028,\nX5772 -> s(X7028)", fontsize=14, style = filled, fillcolor = lightblue];
3274 -> 6769 [arrowhead = none ];
6769 -> 3927;

6770 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3274 -> 6770 [arrowhead = none ];
6770 -> 3928;

6771 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3277 -> 6771 [arrowhead = none ];
6771 -> 3281;

6772 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3281 -> 6772 [arrowhead = none ];
6772 -> 3284;

6773 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3284 -> 6773 [arrowhead = none ];
6773 -> 3287;

6774 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3284 -> 6774 [arrowhead = none ];
6774 -> 3288;

6775 [label="EVAL with clause\nquot(s(X5830), s(X5831), X5832, X5833) :- quot(X5830, X5831, X5832, X5833).\nand substitutionT813 -> s(T823),\nX5830 -> s(s(s(s(s(T823))))),\nX5831 -> T823,\nT822 -> s(T823),\nX5832 -> s(s(s(s(s(s(T823)))))),\nX5803 -> X5834,\nX5833 -> X5834", fontsize=14, style = filled, fillcolor = lightblue];
3287 -> 6775 [arrowhead = none ];
6775 -> 3293;

6776 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3287 -> 6776 [arrowhead = none ];
6776 -> 3294;

6777 [label="EVAL with clause\nquot(X6777, 0, s(X6778), s(X6779)) :- quot(X6777, s(X6778), s(X6778), X6779).\nand substitutionT813 -> 0,\nX6777 -> s(s(s(s(s(0))))),\nT906 -> 0,\nX6778 -> s(s(s(s(0)))),\nX6779 -> X6780,\nX5803 -> s(X6780)", fontsize=14, style = filled, fillcolor = lightblue];
3288 -> 6777 [arrowhead = none ];
6777 -> 3803;

6778 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3288 -> 6778 [arrowhead = none ];
6778 -> 3804;

6779 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3293 -> 6779 [arrowhead = none ];
6779 -> 3298;

6780 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3298 -> 6780 [arrowhead = none ];
6780 -> 3299;

6781 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3299 -> 6781 [arrowhead = none ];
6781 -> 3304;

6782 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3299 -> 6782 [arrowhead = none ];
6782 -> 3305;

6783 [label="EVAL with clause\nquot(s(X5861), s(X5862), X5863, X5864) :- quot(X5861, X5862, X5863, X5864).\nand substitutionT823 -> s(T833),\nX5861 -> s(s(s(s(s(T833))))),\nX5862 -> T833,\nT832 -> s(T833),\nX5863 -> s(s(s(s(s(s(s(T833))))))),\nX5834 -> X5865,\nX5864 -> X5865", fontsize=14, style = filled, fillcolor = lightblue];
3304 -> 6783 [arrowhead = none ];
6783 -> 3310;

6784 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3304 -> 6784 [arrowhead = none ];
6784 -> 3311;

6785 [label="EVAL with clause\nquot(X6540, 0, s(X6541), s(X6542)) :- quot(X6540, s(X6541), s(X6541), X6542).\nand substitutionT823 -> 0,\nX6540 -> s(s(s(s(s(0))))),\nT903 -> 0,\nX6541 -> s(s(s(s(s(0))))),\nX6542 -> X6543,\nX5834 -> s(X6543)", fontsize=14, style = filled, fillcolor = lightblue];
3305 -> 6785 [arrowhead = none ];
6785 -> 3679;

6786 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3305 -> 6786 [arrowhead = none ];
6786 -> 3680;

6787 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3310 -> 6787 [arrowhead = none ];
6787 -> 3316;

6788 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3316 -> 6788 [arrowhead = none ];
6788 -> 3318;

6789 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3318 -> 6789 [arrowhead = none ];
6789 -> 3322;

6790 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3318 -> 6790 [arrowhead = none ];
6790 -> 3323;

6791 [label="EVAL with clause\nquot(s(X5892), s(X5893), X5894, X5895) :- quot(X5892, X5893, X5894, X5895).\nand substitutionT833 -> s(T843),\nX5892 -> s(s(s(s(s(T843))))),\nX5893 -> T843,\nT842 -> s(T843),\nX5894 -> s(s(s(s(s(s(s(s(T843)))))))),\nX5865 -> X5896,\nX5895 -> X5896", fontsize=14, style = filled, fillcolor = lightblue];
3322 -> 6791 [arrowhead = none ];
6791 -> 3330;

6792 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3322 -> 6792 [arrowhead = none ];
6792 -> 3331;

6793 [label="EVAL with clause\nquot(X6303, 0, s(X6304), s(X6305)) :- quot(X6303, s(X6304), s(X6304), X6305).\nand substitutionT833 -> 0,\nX6303 -> s(s(s(s(s(0))))),\nT900 -> 0,\nX6304 -> s(s(s(s(s(s(0)))))),\nX6305 -> X6306,\nX5865 -> s(X6306)", fontsize=14, style = filled, fillcolor = lightblue];
3323 -> 6793 [arrowhead = none ];
6793 -> 3571;

6794 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3323 -> 6794 [arrowhead = none ];
6794 -> 3572;

6795 [label="GENERALIZATION\nT844 <-- s(s(s(s(s(s(s(T843)))))))\n\nNew Knowledge:\nT844 is ground", fontsize=14, style = filled, fillcolor = violet];
3330 -> 6795 [arrowhead = none ];
6795 -> 3337;

6796 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3337 -> 6796 [arrowhead = none ];
6796 -> 3343;

6797 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3343 -> 6797 [arrowhead = none ];
6797 -> 3344;

6798 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3344 -> 6798 [arrowhead = none ];
6798 -> 3348;

6799 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3344 -> 6799 [arrowhead = none ];
6799 -> 3349;

6800 [label="EVAL with clause\nquot(s(X5927), s(X5928), X5929, X5930) :- quot(X5927, X5928, X5929, X5930).\nand substitutionT843 -> s(T858),\nX5927 -> s(s(s(s(s(T858))))),\nX5928 -> T858,\nT857 -> s(T858),\nT844 -> T859,\nX5929 -> s(T859),\nX5896 -> X5931,\nX5930 -> X5931", fontsize=14, style = filled, fillcolor = lightblue];
3348 -> 6800 [arrowhead = none ];
6800 -> 3356;

6801 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3348 -> 6801 [arrowhead = none ];
6801 -> 3357;

6802 [label="EVAL with clause\nquot(X5944, 0, s(X5945), s(X5946)) :- quot(X5944, s(X5945), s(X5945), X5946).\nand substitutionT843 -> 0,\nX5944 -> s(s(s(s(s(0))))),\nT864 -> 0,\nT844 -> T865,\nX5945 -> T865,\nX5946 -> X5947,\nX5896 -> s(X5947)", fontsize=14, style = filled, fillcolor = lightblue];
3349 -> 6802 [arrowhead = none ];
6802 -> 3363;

6803 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3349 -> 6803 [arrowhead = none ];
6803 -> 3364;

6804 [label="INSTANCE with matching:\nT843 -> T858\nT844 -> T859\nX5896 -> X5931", fontsize=14, style = filled, fillcolor = lightgrey];
3356 -> 6804 [arrowhead = none , style=dashed];
6804 -> 3337[style=dashed];

6805 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3363 -> 6805 [arrowhead = none ];
6805 -> 3369;

6806 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3369 -> 6806 [arrowhead = none ];
6806 -> 3370;

6807 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3370 -> 6807 [arrowhead = none ];
6807 -> 3375;

6808 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3370 -> 6808 [arrowhead = none ];
6808 -> 3376;

6809 [label="ONLY EVAL with clause\nquot(s(X5982), s(X5983), X5984, X5985) :- quot(X5982, X5983, X5984, X5985).\nand substitutionX5982 -> s(s(s(s(0)))),\nT865 -> T870,\nX5983 -> T870,\nX5984 -> s(T870),\nX5947 -> X5986,\nX5985 -> X5986", fontsize=14, style = filled, fillcolor = lightblue];
3375 -> 6809 [arrowhead = none ];
6809 -> 3383;

6810 [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 = lightgreen];
3376 -> 6810 [arrowhead = none ];
6810 -> 3566;

6811 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3383 -> 6811 [arrowhead = none ];
6811 -> 3388;

6812 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3388 -> 6812 [arrowhead = none ];
6812 -> 3390;

6813 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3390 -> 6813 [arrowhead = none ];
6813 -> 3395;

6814 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3390 -> 6814 [arrowhead = none ];
6814 -> 3396;

6815 [label="EVAL with clause\nquot(s(X6013), s(X6014), X6015, X6016) :- quot(X6013, X6014, X6015, X6016).\nand substitutionX6013 -> s(s(s(0))),\nX6014 -> T875,\nT870 -> s(T875),\nX6015 -> s(s(T875)),\nX5986 -> X6017,\nX6016 -> X6017", fontsize=14, style = filled, fillcolor = lightblue];
3395 -> 6815 [arrowhead = none ];
6815 -> 3400;

6816 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3395 -> 6816 [arrowhead = none ];
6816 -> 3401;

6817 [label="EVAL with clause\nquot(X6216, 0, s(X6217), s(X6218)) :- quot(X6216, s(X6217), s(X6217), X6218).\nand substitutionX6216 -> s(s(s(s(0)))),\nT870 -> 0,\nX6217 -> 0,\nX6218 -> X6219,\nX5986 -> s(X6219)", fontsize=14, style = filled, fillcolor = lightblue];
3396 -> 6817 [arrowhead = none ];
6817 -> 3518;

6818 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3396 -> 6818 [arrowhead = none ];
6818 -> 3519;

6819 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3400 -> 6819 [arrowhead = none ];
6819 -> 3404;

6820 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3404 -> 6820 [arrowhead = none ];
6820 -> 3405;

6821 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3405 -> 6821 [arrowhead = none ];
6821 -> 3410;

6822 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3405 -> 6822 [arrowhead = none ];
6822 -> 3411;

6823 [label="EVAL with clause\nquot(s(X6044), s(X6045), X6046, X6047) :- quot(X6044, X6045, X6046, X6047).\nand substitutionX6044 -> s(s(0)),\nX6045 -> T880,\nT875 -> s(T880),\nX6046 -> s(s(s(T880))),\nX6017 -> X6048,\nX6047 -> X6048", fontsize=14, style = filled, fillcolor = lightblue];
3410 -> 6823 [arrowhead = none ];
6823 -> 3414;

6824 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3410 -> 6824 [arrowhead = none ];
6824 -> 3415;

6825 [label="EVAL with clause\nquot(X6200, 0, s(X6201), s(X6202)) :- quot(X6200, s(X6201), s(X6201), X6202).\nand substitutionX6200 -> s(s(s(0))),\nT875 -> 0,\nX6201 -> s(0),\nX6202 -> X6203,\nX6017 -> s(X6203)", fontsize=14, style = filled, fillcolor = lightblue];
3411 -> 6825 [arrowhead = none ];
6825 -> 3508;

6826 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3411 -> 6826 [arrowhead = none ];
6826 -> 3509;

6827 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3414 -> 6827 [arrowhead = none ];
6827 -> 3418;

6828 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3418 -> 6828 [arrowhead = none ];
6828 -> 3420;

6829 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3420 -> 6829 [arrowhead = none ];
6829 -> 3424;

6830 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3420 -> 6830 [arrowhead = none ];
6830 -> 3425;

6831 [label="EVAL with clause\nquot(s(X6075), s(X6076), X6077, X6078) :- quot(X6075, X6076, X6077, X6078).\nand substitutionX6075 -> s(0),\nX6076 -> T885,\nT880 -> s(T885),\nX6077 -> s(s(s(s(T885)))),\nX6048 -> X6079,\nX6078 -> X6079", fontsize=14, style = filled, fillcolor = lightblue];
3424 -> 6831 [arrowhead = none ];
6831 -> 3432;

6832 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3424 -> 6832 [arrowhead = none ];
6832 -> 3433;

6833 [label="EVAL with clause\nquot(X6184, 0, s(X6185), s(X6186)) :- quot(X6184, s(X6185), s(X6185), X6186).\nand substitutionX6184 -> s(s(0)),\nT880 -> 0,\nX6185 -> s(s(0)),\nX6186 -> X6187,\nX6048 -> s(X6187)", fontsize=14, style = filled, fillcolor = lightblue];
3425 -> 6833 [arrowhead = none ];
6833 -> 3498;

6834 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3425 -> 6834 [arrowhead = none ];
6834 -> 3499;

6835 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3432 -> 6835 [arrowhead = none ];
6835 -> 3434;

6836 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3434 -> 6836 [arrowhead = none ];
6836 -> 3436;

6837 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3436 -> 6837 [arrowhead = none ];
6837 -> 3439;

6838 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3436 -> 6838 [arrowhead = none ];
6838 -> 3440;

6839 [label="EVAL with clause\nquot(s(X6106), s(X6107), X6108, X6109) :- quot(X6106, X6107, X6108, X6109).\nand substitutionX6106 -> 0,\nX6107 -> T890,\nT885 -> s(T890),\nX6108 -> s(s(s(s(s(T890))))),\nX6079 -> X6110,\nX6109 -> X6110", fontsize=14, style = filled, fillcolor = lightblue];
3439 -> 6839 [arrowhead = none ];
6839 -> 3446;

6840 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3439 -> 6840 [arrowhead = none ];
6840 -> 3447;

6841 [label="EVAL with clause\nquot(X6168, 0, s(X6169), s(X6170)) :- quot(X6168, s(X6169), s(X6169), X6170).\nand substitutionX6168 -> s(0),\nT885 -> 0,\nX6169 -> s(s(s(0))),\nX6170 -> X6171,\nX6079 -> s(X6171)", fontsize=14, style = filled, fillcolor = lightblue];
3440 -> 6841 [arrowhead = none ];
6841 -> 3490;

6842 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3440 -> 6842 [arrowhead = none ];
6842 -> 3491;

6843 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3446 -> 6843 [arrowhead = none ];
6843 -> 3450;

6844 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3450 -> 6844 [arrowhead = none ];
6844 -> 3453;

6845 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3450 -> 6845 [arrowhead = none ];
6845 -> 3454;

6846 [label="EVAL with clause\nquot(0, s(X6123), s(X6124), 0).\nand substitutionX6123 -> T897,\nT890 -> s(T897),\nX6124 -> s(s(s(s(s(T897))))),\nX6110 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
3453 -> 6846 [arrowhead = none ];
6846 -> 3458;

6847 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3453 -> 6847 [arrowhead = none ];
6847 -> 3459;

6848 [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 = lightgreen];
3454 -> 6848 [arrowhead = none ];
6848 -> 3463;

6849 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3458 -> 6849 [arrowhead = none ];
6849 -> 3460;

6850 [label="EVAL with clause\nquot(X6137, 0, s(X6138), s(X6139)) :- quot(X6137, s(X6138), s(X6138), X6139).\nand substitutionX6137 -> 0,\nT890 -> 0,\nX6138 -> s(s(s(s(0)))),\nX6139 -> X6140,\nX6110 -> s(X6140)", fontsize=14, style = filled, fillcolor = lightblue];
3463 -> 6850 [arrowhead = none ];
6850 -> 3469;

6851 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3463 -> 6851 [arrowhead = none ];
6851 -> 3470;

6852 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3469 -> 6852 [arrowhead = none ];
6852 -> 3472;

6853 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3472 -> 6853 [arrowhead = none ];
6853 -> 3474;

6854 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3472 -> 6854 [arrowhead = none ];
6854 -> 3475;

6855 [label="ONLY EVAL with clause\nquot(0, s(X6151), s(X6152), 0).\nand substitutionX6151 -> s(s(s(s(0)))),\nX6152 -> s(s(s(s(0)))),\nX6140 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
3474 -> 6855 [arrowhead = none ];
6855 -> 3479;

6856 [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 = lightgreen];
3475 -> 6856 [arrowhead = none ];
6856 -> 3483;

6857 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3479 -> 6857 [arrowhead = none ];
6857 -> 3480;

6858 [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 = lightgreen];
3483 -> 6858 [arrowhead = none ];
6858 -> 3485;

6859 [label="INSTANCE with matching:\nX684 -> X6171", fontsize=14, style = filled, fillcolor = lightgrey];
3490 -> 6859 [arrowhead = none , style=dashed];
6859 -> 401[style=dashed];

6860 [label="INSTANCE with matching:\nX2028 -> X6187", fontsize=14, style = filled, fillcolor = lightgrey];
3498 -> 6860 [arrowhead = none , style=dashed];
6860 -> 1261[style=dashed];

6861 [label="INSTANCE with matching:\nX3676 -> X6203", fontsize=14, style = filled, fillcolor = lightgrey];
3508 -> 6861 [arrowhead = none , style=dashed];
6861 -> 2183[style=dashed];

6862 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3518 -> 6862 [arrowhead = none ];
6862 -> 3524;

6863 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3524 -> 6863 [arrowhead = none ];
6863 -> 3527;

6864 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3527 -> 6864 [arrowhead = none ];
6864 -> 3535;

6865 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3527 -> 6865 [arrowhead = none ];
6865 -> 3536;

6866 [label="ONLY EVAL with clause\nquot(s(X6254), s(X6255), X6256, X6257) :- quot(X6254, X6255, X6256, X6257).\nand substitutionX6254 -> s(s(s(0))),\nX6255 -> 0,\nX6256 -> s(0),\nX6219 -> X6258,\nX6257 -> X6258", fontsize=14, style = filled, fillcolor = lightblue];
3535 -> 6866 [arrowhead = none ];
6866 -> 3546;

6867 [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 = lightgreen];
3536 -> 6867 [arrowhead = none ];
6867 -> 3565;

6868 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3546 -> 6868 [arrowhead = none ];
6868 -> 3553;

6869 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3553 -> 6869 [arrowhead = none ];
6869 -> 3554;

6870 [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 = lightgreen];
3554 -> 6870 [arrowhead = none ];
6870 -> 3555;

6871 [label="ONLY EVAL with clause\nquot(X6281, 0, s(X6282), s(X6283)) :- quot(X6281, s(X6282), s(X6282), X6283).\nand substitutionX6281 -> s(s(s(0))),\nX6282 -> 0,\nX6283 -> X6284,\nX6258 -> s(X6284)", fontsize=14, style = filled, fillcolor = lightblue];
3555 -> 6871 [arrowhead = none ];
6871 -> 3560;

6872 [label="INSTANCE with matching:\nX4401 -> X6284", fontsize=14, style = filled, fillcolor = lightgrey];
3560 -> 6872 [arrowhead = none , style=dashed];
6872 -> 2553[style=dashed];

6873 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3571 -> 6873 [arrowhead = none ];
6873 -> 3575;

6874 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3575 -> 6874 [arrowhead = none ];
6874 -> 3576;

6875 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3576 -> 6875 [arrowhead = none ];
6875 -> 3583;

6876 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3576 -> 6876 [arrowhead = none ];
6876 -> 3584;

6877 [label="ONLY EVAL with clause\nquot(s(X6341), s(X6342), X6343, X6344) :- quot(X6341, X6342, X6343, X6344).\nand substitutionX6341 -> s(s(s(s(0)))),\nX6342 -> s(s(s(s(s(s(0)))))),\nX6343 -> s(s(s(s(s(s(s(0))))))),\nX6306 -> X6345,\nX6344 -> X6345", fontsize=14, style = filled, fillcolor = lightblue];
3583 -> 6877 [arrowhead = none ];
6877 -> 3589;

6878 [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 = lightgreen];
3584 -> 6878 [arrowhead = none ];
6878 -> 3674;

6879 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3589 -> 6879 [arrowhead = none ];
6879 -> 3592;

6880 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3592 -> 6880 [arrowhead = none ];
6880 -> 3594;

6881 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3594 -> 6881 [arrowhead = none ];
6881 -> 3599;

6882 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3594 -> 6882 [arrowhead = none ];
6882 -> 3600;

6883 [label="ONLY EVAL with clause\nquot(s(X6380), s(X6381), X6382, X6383) :- quot(X6380, X6381, X6382, X6383).\nand substitutionX6380 -> s(s(s(0))),\nX6381 -> s(s(s(s(s(0))))),\nX6382 -> s(s(s(s(s(s(s(0))))))),\nX6345 -> X6384,\nX6383 -> X6384", fontsize=14, style = filled, fillcolor = lightblue];
3599 -> 6883 [arrowhead = none ];
6883 -> 3606;

6884 [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 = lightgreen];
3600 -> 6884 [arrowhead = none ];
6884 -> 3673;

6885 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3606 -> 6885 [arrowhead = none ];
6885 -> 3609;

6886 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3609 -> 6886 [arrowhead = none ];
6886 -> 3612;

6887 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3612 -> 6887 [arrowhead = none ];
6887 -> 3617;

6888 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3612 -> 6888 [arrowhead = none ];
6888 -> 3618;

6889 [label="ONLY EVAL with clause\nquot(s(X6419), s(X6420), X6421, X6422) :- quot(X6419, X6420, X6421, X6422).\nand substitutionX6419 -> s(s(0)),\nX6420 -> s(s(s(s(0)))),\nX6421 -> s(s(s(s(s(s(s(0))))))),\nX6384 -> X6423,\nX6422 -> X6423", fontsize=14, style = filled, fillcolor = lightblue];
3617 -> 6889 [arrowhead = none ];
6889 -> 3622;

6890 [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 = lightgreen];
3618 -> 6890 [arrowhead = none ];
6890 -> 3670;

6891 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3622 -> 6891 [arrowhead = none ];
6891 -> 3627;

6892 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3627 -> 6892 [arrowhead = none ];
6892 -> 3628;

6893 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3628 -> 6893 [arrowhead = none ];
6893 -> 3632;

6894 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3628 -> 6894 [arrowhead = none ];
6894 -> 3633;

6895 [label="ONLY EVAL with clause\nquot(s(X6458), s(X6459), X6460, X6461) :- quot(X6458, X6459, X6460, X6461).\nand substitutionX6458 -> s(0),\nX6459 -> s(s(s(0))),\nX6460 -> s(s(s(s(s(s(s(0))))))),\nX6423 -> X6462,\nX6461 -> X6462", fontsize=14, style = filled, fillcolor = lightblue];
3632 -> 6895 [arrowhead = none ];
6895 -> 3638;

6896 [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 = lightgreen];
3633 -> 6896 [arrowhead = none ];
6896 -> 3668;

6897 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3638 -> 6897 [arrowhead = none ];
6897 -> 3642;

6898 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3642 -> 6898 [arrowhead = none ];
6898 -> 3643;

6899 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3643 -> 6899 [arrowhead = none ];
6899 -> 3647;

6900 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3643 -> 6900 [arrowhead = none ];
6900 -> 3648;

6901 [label="ONLY EVAL with clause\nquot(s(X6493), s(X6494), X6495, X6496) :- quot(X6493, X6494, X6495, X6496).\nand substitutionX6493 -> 0,\nX6494 -> s(s(0)),\nX6495 -> s(s(s(s(s(s(s(0))))))),\nX6462 -> X6497,\nX6496 -> X6497", fontsize=14, style = filled, fillcolor = lightblue];
3647 -> 6901 [arrowhead = none ];
6901 -> 3652;

6902 [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 = lightgreen];
3648 -> 6902 [arrowhead = none ];
6902 -> 3667;

6903 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3652 -> 6903 [arrowhead = none ];
6903 -> 3655;

6904 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3655 -> 6904 [arrowhead = none ];
6904 -> 3658;

6905 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3655 -> 6905 [arrowhead = none ];
6905 -> 3659;

6906 [label="ONLY EVAL with clause\nquot(0, s(X6508), s(X6509), 0).\nand substitutionX6508 -> s(0),\nX6509 -> s(s(s(s(s(s(0)))))),\nX6497 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
3658 -> 6906 [arrowhead = none ];
6906 -> 3660;

6907 [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 = lightgreen];
3659 -> 6907 [arrowhead = none ];
6907 -> 3664;

6908 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3660 -> 6908 [arrowhead = none ];
6908 -> 3661;

6909 [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 = lightgreen];
3664 -> 6909 [arrowhead = none ];
6909 -> 3666;

6910 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3679 -> 6910 [arrowhead = none ];
6910 -> 3683;

6911 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3683 -> 6911 [arrowhead = none ];
6911 -> 3684;

6912 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3684 -> 6912 [arrowhead = none ];
6912 -> 3688;

6913 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3684 -> 6913 [arrowhead = none ];
6913 -> 3689;

6914 [label="ONLY EVAL with clause\nquot(s(X6578), s(X6579), X6580, X6581) :- quot(X6578, X6579, X6580, X6581).\nand substitutionX6578 -> s(s(s(s(0)))),\nX6579 -> s(s(s(s(s(0))))),\nX6580 -> s(s(s(s(s(s(0)))))),\nX6543 -> X6582,\nX6581 -> X6582", fontsize=14, style = filled, fillcolor = lightblue];
3688 -> 6914 [arrowhead = none ];
6914 -> 3699;

6915 [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 = lightgreen];
3689 -> 6915 [arrowhead = none ];
6915 -> 3800;

6916 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3699 -> 6916 [arrowhead = none ];
6916 -> 3703;

6917 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3703 -> 6917 [arrowhead = none ];
6917 -> 3704;

6918 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3704 -> 6918 [arrowhead = none ];
6918 -> 3712;

6919 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3704 -> 6919 [arrowhead = none ];
6919 -> 3713;

6920 [label="ONLY EVAL with clause\nquot(s(X6617), s(X6618), X6619, X6620) :- quot(X6617, X6618, X6619, X6620).\nand substitutionX6617 -> s(s(s(0))),\nX6618 -> s(s(s(s(0)))),\nX6619 -> s(s(s(s(s(s(0)))))),\nX6582 -> X6621,\nX6620 -> X6621", fontsize=14, style = filled, fillcolor = lightblue];
3712 -> 6920 [arrowhead = none ];
6920 -> 3727;

6921 [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 = lightgreen];
3713 -> 6921 [arrowhead = none ];
6921 -> 3796;

6922 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3727 -> 6922 [arrowhead = none ];
6922 -> 3730;

6923 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3730 -> 6923 [arrowhead = none ];
6923 -> 3733;

6924 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3733 -> 6924 [arrowhead = none ];
6924 -> 3736;

6925 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3733 -> 6925 [arrowhead = none ];
6925 -> 3737;

6926 [label="ONLY EVAL with clause\nquot(s(X6656), s(X6657), X6658, X6659) :- quot(X6656, X6657, X6658, X6659).\nand substitutionX6656 -> s(s(0)),\nX6657 -> s(s(s(0))),\nX6658 -> s(s(s(s(s(s(0)))))),\nX6621 -> X6660,\nX6659 -> X6660", fontsize=14, style = filled, fillcolor = lightblue];
3736 -> 6926 [arrowhead = none ];
6926 -> 3743;

6927 [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 = lightgreen];
3737 -> 6927 [arrowhead = none ];
6927 -> 3794;

6928 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3743 -> 6928 [arrowhead = none ];
6928 -> 3747;

6929 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3747 -> 6929 [arrowhead = none ];
6929 -> 3750;

6930 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3750 -> 6930 [arrowhead = none ];
6930 -> 3753;

6931 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3750 -> 6931 [arrowhead = none ];
6931 -> 3754;

6932 [label="ONLY EVAL with clause\nquot(s(X6695), s(X6696), X6697, X6698) :- quot(X6695, X6696, X6697, X6698).\nand substitutionX6695 -> s(0),\nX6696 -> s(s(0)),\nX6697 -> s(s(s(s(s(s(0)))))),\nX6660 -> X6699,\nX6698 -> X6699", fontsize=14, style = filled, fillcolor = lightblue];
3753 -> 6932 [arrowhead = none ];
6932 -> 3759;

6933 [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 = lightgreen];
3754 -> 6933 [arrowhead = none ];
6933 -> 3793;

6934 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3759 -> 6934 [arrowhead = none ];
6934 -> 3764;

6935 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3764 -> 6935 [arrowhead = none ];
6935 -> 3765;

6936 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3765 -> 6936 [arrowhead = none ];
6936 -> 3769;

6937 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3765 -> 6937 [arrowhead = none ];
6937 -> 3770;

6938 [label="ONLY EVAL with clause\nquot(s(X6730), s(X6731), X6732, X6733) :- quot(X6730, X6731, X6732, X6733).\nand substitutionX6730 -> 0,\nX6731 -> s(0),\nX6732 -> s(s(s(s(s(s(0)))))),\nX6699 -> X6734,\nX6733 -> X6734", fontsize=14, style = filled, fillcolor = lightblue];
3769 -> 6938 [arrowhead = none ];
6938 -> 3775;

6939 [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 = lightgreen];
3770 -> 6939 [arrowhead = none ];
6939 -> 3791;

6940 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3775 -> 6940 [arrowhead = none ];
6940 -> 3779;

6941 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3779 -> 6941 [arrowhead = none ];
6941 -> 3782;

6942 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3779 -> 6942 [arrowhead = none ];
6942 -> 3783;

6943 [label="ONLY EVAL with clause\nquot(0, s(X6745), s(X6746), 0).\nand substitutionX6745 -> 0,\nX6746 -> s(s(s(s(s(0))))),\nX6734 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
3782 -> 6943 [arrowhead = none ];
6943 -> 3785;

6944 [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 = lightgreen];
3783 -> 6944 [arrowhead = none ];
6944 -> 3787;

6945 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3785 -> 6945 [arrowhead = none ];
6945 -> 3786;

6946 [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 = lightgreen];
3787 -> 6946 [arrowhead = none ];
6946 -> 3788;

6947 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3803 -> 6947 [arrowhead = none ];
6947 -> 3808;

6948 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3808 -> 6948 [arrowhead = none ];
6948 -> 3809;

6949 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3809 -> 6949 [arrowhead = none ];
6949 -> 3821;

6950 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3809 -> 6950 [arrowhead = none ];
6950 -> 3822;

6951 [label="ONLY EVAL with clause\nquot(s(X6815), s(X6816), X6817, X6818) :- quot(X6815, X6816, X6817, X6818).\nand substitutionX6815 -> s(s(s(s(0)))),\nX6816 -> s(s(s(s(0)))),\nX6817 -> s(s(s(s(s(0))))),\nX6780 -> X6819,\nX6818 -> X6819", fontsize=14, style = filled, fillcolor = lightblue];
3821 -> 6951 [arrowhead = none ];
6951 -> 3835;

6952 [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 = lightgreen];
3822 -> 6952 [arrowhead = none ];
6952 -> 3924;

6953 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3835 -> 6953 [arrowhead = none ];
6953 -> 3838;

6954 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3838 -> 6954 [arrowhead = none ];
6954 -> 3841;

6955 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3841 -> 6955 [arrowhead = none ];
6955 -> 3846;

6956 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3841 -> 6956 [arrowhead = none ];
6956 -> 3847;

6957 [label="ONLY EVAL with clause\nquot(s(X6854), s(X6855), X6856, X6857) :- quot(X6854, X6855, X6856, X6857).\nand substitutionX6854 -> s(s(s(0))),\nX6855 -> s(s(s(0))),\nX6856 -> s(s(s(s(s(0))))),\nX6819 -> X6858,\nX6857 -> X6858", fontsize=14, style = filled, fillcolor = lightblue];
3846 -> 6957 [arrowhead = none ];
6957 -> 3853;

6958 [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 = lightgreen];
3847 -> 6958 [arrowhead = none ];
6958 -> 3922;

6959 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3853 -> 6959 [arrowhead = none ];
6959 -> 3857;

6960 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3857 -> 6960 [arrowhead = none ];
6960 -> 3858;

6961 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3858 -> 6961 [arrowhead = none ];
6961 -> 3863;

6962 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3858 -> 6962 [arrowhead = none ];
6962 -> 3864;

6963 [label="ONLY EVAL with clause\nquot(s(X6893), s(X6894), X6895, X6896) :- quot(X6893, X6894, X6895, X6896).\nand substitutionX6893 -> s(s(0)),\nX6894 -> s(s(0)),\nX6895 -> s(s(s(s(s(0))))),\nX6858 -> X6897,\nX6896 -> X6897", fontsize=14, style = filled, fillcolor = lightblue];
3863 -> 6963 [arrowhead = none ];
6963 -> 3869;

6964 [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 = lightgreen];
3864 -> 6964 [arrowhead = none ];
6964 -> 3921;

6965 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3869 -> 6965 [arrowhead = none ];
6965 -> 3872;

6966 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3872 -> 6966 [arrowhead = none ];
6966 -> 3873;

6967 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3873 -> 6967 [arrowhead = none ];
6967 -> 3878;

6968 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3873 -> 6968 [arrowhead = none ];
6968 -> 3879;

6969 [label="ONLY EVAL with clause\nquot(s(X6932), s(X6933), X6934, X6935) :- quot(X6932, X6933, X6934, X6935).\nand substitutionX6932 -> s(0),\nX6933 -> s(0),\nX6934 -> s(s(s(s(s(0))))),\nX6897 -> X6936,\nX6935 -> X6936", fontsize=14, style = filled, fillcolor = lightblue];
3878 -> 6969 [arrowhead = none ];
6969 -> 3885;

6970 [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 = lightgreen];
3879 -> 6970 [arrowhead = none ];
6970 -> 3917;

6971 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3885 -> 6971 [arrowhead = none ];
6971 -> 3887;

6972 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3887 -> 6972 [arrowhead = none ];
6972 -> 3889;

6973 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3889 -> 6973 [arrowhead = none ];
6973 -> 3893;

6974 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3889 -> 6974 [arrowhead = none ];
6974 -> 3894;

6975 [label="ONLY EVAL with clause\nquot(s(X6971), s(X6972), X6973, X6974) :- quot(X6971, X6972, X6973, X6974).\nand substitutionX6971 -> 0,\nX6972 -> 0,\nX6973 -> s(s(s(s(s(0))))),\nX6936 -> X6975,\nX6974 -> X6975", fontsize=14, style = filled, fillcolor = lightblue];
3893 -> 6975 [arrowhead = none ];
6975 -> 3901;

6976 [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 = lightgreen];
3894 -> 6976 [arrowhead = none ];
6976 -> 3916;

6977 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3901 -> 6977 [arrowhead = none ];
6977 -> 3904;

6978 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3904 -> 6978 [arrowhead = none ];
6978 -> 3907;

6979 [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 = lightgreen];
3907 -> 6979 [arrowhead = none ];
6979 -> 3908;

6980 [label="ONLY EVAL with clause\nquot(X6996, 0, s(X6997), s(X6998)) :- quot(X6996, s(X6997), s(X6997), X6998).\nand substitutionX6996 -> 0,\nX6997 -> s(s(s(s(0)))),\nX6998 -> X6999,\nX6975 -> s(X6999)", fontsize=14, style = filled, fillcolor = lightblue];
3908 -> 6980 [arrowhead = none ];
6980 -> 3912;

6981 [label="INSTANCE with matching:\nX6140 -> X6999", fontsize=14, style = filled, fillcolor = lightgrey];
3912 -> 6981 [arrowhead = none , style=dashed];
6981 -> 3469[style=dashed];

6982 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3927 -> 6982 [arrowhead = none ];
6982 -> 3934;

6983 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3934 -> 6983 [arrowhead = none ];
6983 -> 3937;

6984 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3937 -> 6984 [arrowhead = none ];
6984 -> 3943;

6985 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3937 -> 6985 [arrowhead = none ];
6985 -> 3944;

6986 [label="ONLY EVAL with clause\nquot(s(X7063), s(X7064), X7065, X7066) :- quot(X7063, X7064, X7065, X7066).\nand substitutionX7063 -> s(s(s(s(0)))),\nX7064 -> s(s(s(0))),\nX7065 -> s(s(s(s(0)))),\nX7028 -> X7067,\nX7066 -> X7067", fontsize=14, style = filled, fillcolor = lightblue];
3943 -> 6986 [arrowhead = none ];
6986 -> 3951;

6987 [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 = lightgreen];
3944 -> 6987 [arrowhead = none ];
6987 -> 4018;

6988 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3951 -> 6988 [arrowhead = none ];
6988 -> 3954;

6989 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3954 -> 6989 [arrowhead = none ];
6989 -> 3955;

6990 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3955 -> 6990 [arrowhead = none ];
6990 -> 3959;

6991 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3955 -> 6991 [arrowhead = none ];
6991 -> 3960;

6992 [label="ONLY EVAL with clause\nquot(s(X7102), s(X7103), X7104, X7105) :- quot(X7102, X7103, X7104, X7105).\nand substitutionX7102 -> s(s(s(0))),\nX7103 -> s(s(0)),\nX7104 -> s(s(s(s(0)))),\nX7067 -> X7106,\nX7105 -> X7106", fontsize=14, style = filled, fillcolor = lightblue];
3959 -> 6992 [arrowhead = none ];
6992 -> 3968;

6993 [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 = lightgreen];
3960 -> 6993 [arrowhead = none ];
6993 -> 4017;

6994 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3968 -> 6994 [arrowhead = none ];
6994 -> 3971;

6995 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3971 -> 6995 [arrowhead = none ];
6995 -> 3972;

6996 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3972 -> 6996 [arrowhead = none ];
6996 -> 3975;

6997 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3972 -> 6997 [arrowhead = none ];
6997 -> 3976;

6998 [label="ONLY EVAL with clause\nquot(s(X7141), s(X7142), X7143, X7144) :- quot(X7141, X7142, X7143, X7144).\nand substitutionX7141 -> s(s(0)),\nX7142 -> s(0),\nX7143 -> s(s(s(s(0)))),\nX7106 -> X7145,\nX7144 -> X7145", fontsize=14, style = filled, fillcolor = lightblue];
3975 -> 6998 [arrowhead = none ];
6998 -> 3983;

6999 [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 = lightgreen];
3976 -> 6999 [arrowhead = none ];
6999 -> 4015;

7000 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3983 -> 7000 [arrowhead = none ];
7000 -> 3986;

7001 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
3986 -> 7001 [arrowhead = none ];
7001 -> 3987;

7002 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3987 -> 7002 [arrowhead = none ];
7002 -> 3991;

7003 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
3987 -> 7003 [arrowhead = none ];
7003 -> 3992;

7004 [label="ONLY EVAL with clause\nquot(s(X7180), s(X7181), X7182, X7183) :- quot(X7180, X7181, X7182, X7183).\nand substitutionX7180 -> s(0),\nX7181 -> 0,\nX7182 -> s(s(s(s(0)))),\nX7145 -> X7184,\nX7183 -> X7184", fontsize=14, style = filled, fillcolor = lightblue];
3991 -> 7004 [arrowhead = none ];
7004 -> 4000;

7005 [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 = lightgreen];
3992 -> 7005 [arrowhead = none ];
7005 -> 4013;

7006 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4000 -> 7006 [arrowhead = none ];
7006 -> 4001;

7007 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
4001 -> 7007 [arrowhead = none ];
7007 -> 4002;

7008 [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 = lightgreen];
4002 -> 7008 [arrowhead = none ];
7008 -> 4003;

7009 [label="ONLY EVAL with clause\nquot(X7207, 0, s(X7208), s(X7209)) :- quot(X7207, s(X7208), s(X7208), X7209).\nand substitutionX7207 -> s(0),\nX7208 -> s(s(s(0))),\nX7209 -> X7210,\nX7184 -> s(X7210)", fontsize=14, style = filled, fillcolor = lightblue];
4003 -> 7009 [arrowhead = none ];
7009 -> 4012;

7010 [label="INSTANCE with matching:\nX684 -> X7210", fontsize=14, style = filled, fillcolor = lightgrey];
4012 -> 7010 [arrowhead = none , style=dashed];
7010 -> 401[style=dashed];

7011 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4027 -> 7011 [arrowhead = none ];
7011 -> 4031;

7012 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
4031 -> 7012 [arrowhead = none ];
7012 -> 4032;

7013 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4032 -> 7013 [arrowhead = none ];
7013 -> 4039;

7014 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4032 -> 7014 [arrowhead = none ];
7014 -> 4040;

7015 [label="ONLY EVAL with clause\nquot(s(X7273), s(X7274), X7275, X7276) :- quot(X7273, X7274, X7275, X7276).\nand substitutionX7273 -> s(s(s(s(0)))),\nX7274 -> s(s(0)),\nX7275 -> s(s(s(0))),\nX7238 -> X7277,\nX7276 -> X7277", fontsize=14, style = filled, fillcolor = lightblue];
4039 -> 7015 [arrowhead = none ];
7015 -> 4045;

7016 [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 = lightgreen];
4040 -> 7016 [arrowhead = none ];
7016 -> 4100;

7017 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4045 -> 7017 [arrowhead = none ];
7017 -> 4048;

7018 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
4048 -> 7018 [arrowhead = none ];
7018 -> 4049;

7019 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4049 -> 7019 [arrowhead = none ];
7019 -> 4054;

7020 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4049 -> 7020 [arrowhead = none ];
7020 -> 4055;

7021 [label="ONLY EVAL with clause\nquot(s(X7312), s(X7313), X7314, X7315) :- quot(X7312, X7313, X7314, X7315).\nand substitutionX7312 -> s(s(s(0))),\nX7313 -> s(0),\nX7314 -> s(s(s(0))),\nX7277 -> X7316,\nX7315 -> X7316", fontsize=14, style = filled, fillcolor = lightblue];
4054 -> 7021 [arrowhead = none ];
7021 -> 4060;

7022 [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 = lightgreen];
4055 -> 7022 [arrowhead = none ];
7022 -> 4097;

7023 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4060 -> 7023 [arrowhead = none ];
7023 -> 4064;

7024 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
4064 -> 7024 [arrowhead = none ];
7024 -> 4067;

7025 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4067 -> 7025 [arrowhead = none ];
7025 -> 4073;

7026 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4067 -> 7026 [arrowhead = none ];
7026 -> 4074;

7027 [label="ONLY EVAL with clause\nquot(s(X7351), s(X7352), X7353, X7354) :- quot(X7351, X7352, X7353, X7354).\nand substitutionX7351 -> s(s(0)),\nX7352 -> 0,\nX7353 -> s(s(s(0))),\nX7316 -> X7355,\nX7354 -> X7355", fontsize=14, style = filled, fillcolor = lightblue];
4073 -> 7027 [arrowhead = none ];
7027 -> 4078;

7028 [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 = lightgreen];
4074 -> 7028 [arrowhead = none ];
7028 -> 4096;

7029 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4078 -> 7029 [arrowhead = none ];
7029 -> 4083;

7030 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
4083 -> 7030 [arrowhead = none ];
7030 -> 4085;

7031 [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 = lightgreen];
4085 -> 7031 [arrowhead = none ];
7031 -> 4086;

7032 [label="ONLY EVAL with clause\nquot(X7378, 0, s(X7379), s(X7380)) :- quot(X7378, s(X7379), s(X7379), X7380).\nand substitutionX7378 -> s(s(0)),\nX7379 -> s(s(0)),\nX7380 -> X7381,\nX7355 -> s(X7381)", fontsize=14, style = filled, fillcolor = lightblue];
4086 -> 7032 [arrowhead = none ];
7032 -> 4090;

7033 [label="INSTANCE with matching:\nX2028 -> X7381", fontsize=14, style = filled, fillcolor = lightgrey];
4090 -> 7033 [arrowhead = none , style=dashed];
7033 -> 1261[style=dashed];

7034 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4107 -> 7034 [arrowhead = none ];
7034 -> 4109;

7035 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
4109 -> 7035 [arrowhead = none ];
7035 -> 4112;

7036 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4112 -> 7036 [arrowhead = none ];
7036 -> 4115;

7037 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4112 -> 7037 [arrowhead = none ];
7037 -> 4116;

7038 [label="ONLY EVAL with clause\nquot(s(X7441), s(X7442), X7443, X7444) :- quot(X7441, X7442, X7443, X7444).\nand substitutionX7441 -> s(s(s(s(0)))),\nX7442 -> s(0),\nX7443 -> s(s(0)),\nX7406 -> X7445,\nX7444 -> X7445", fontsize=14, style = filled, fillcolor = lightblue];
4115 -> 7038 [arrowhead = none ];
7038 -> 4123;

7039 [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 = lightgreen];
4116 -> 7039 [arrowhead = none ];
7039 -> 4167;

7040 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4123 -> 7040 [arrowhead = none ];
7040 -> 4128;

7041 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
4128 -> 7041 [arrowhead = none ];
7041 -> 4129;

7042 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4129 -> 7042 [arrowhead = none ];
7042 -> 4132;

7043 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4129 -> 7043 [arrowhead = none ];
7043 -> 4133;

7044 [label="ONLY EVAL with clause\nquot(s(X7480), s(X7481), X7482, X7483) :- quot(X7480, X7481, X7482, X7483).\nand substitutionX7480 -> s(s(s(0))),\nX7481 -> 0,\nX7482 -> s(s(0)),\nX7445 -> X7484,\nX7483 -> X7484", fontsize=14, style = filled, fillcolor = lightblue];
4132 -> 7044 [arrowhead = none ];
7044 -> 4140;

7045 [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 = lightgreen];
4133 -> 7045 [arrowhead = none ];
7045 -> 4165;

7046 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4140 -> 7046 [arrowhead = none ];
7046 -> 4142;

7047 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
4142 -> 7047 [arrowhead = none ];
7047 -> 4145;

7048 [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 = lightgreen];
4145 -> 7048 [arrowhead = none ];
7048 -> 4148;

7049 [label="ONLY EVAL with clause\nquot(X7507, 0, s(X7508), s(X7509)) :- quot(X7507, s(X7508), s(X7508), X7509).\nand substitutionX7507 -> s(s(s(0))),\nX7508 -> s(0),\nX7509 -> X7510,\nX7484 -> s(X7510)", fontsize=14, style = filled, fillcolor = lightblue];
4148 -> 7049 [arrowhead = none ];
7049 -> 4156;

7050 [label="INSTANCE with matching:\nX3676 -> X7510", fontsize=14, style = filled, fillcolor = lightgrey];
4156 -> 7050 [arrowhead = none , style=dashed];
7050 -> 2183[style=dashed];

7051 [label="INSTANCE with matching:\nT22 -> T769\nT20 -> T767\nX35 -> X5608", fontsize=14, style = filled, fillcolor = lightgrey];
4178 -> 7051 [arrowhead = none , style=dashed];
7051 -> 543[style=dashed];

7052 [label="INSTANCE with matching:\nT20 -> s(s(s(s(T767))))\nT157 -> T920", fontsize=14, style = filled, fillcolor = lightgrey];
4179 -> 7052 [arrowhead = none , style=dashed];
7052 -> 545[style=dashed];

7053 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4186 -> 7053 [arrowhead = none ];
7053 -> 4189;

7054 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4186 -> 7054 [arrowhead = none ];
7054 -> 4190;

7055 [label="EVAL with clause\npr(X7539, s(0)).\nand substitutionT761 -> 0,\nX7539 -> s(s(s(s(s(s(s(0))))))),\nT931 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4189 -> 7055 [arrowhead = none ];
7055 -> 4191;

7056 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4189 -> 7056 [arrowhead = none ];
7056 -> 4192;

7057 [label="EVAL with clause\npr(X7544, s(s(X7545))) :- ','(not_divides(s(s(X7545)), X7544), pr(X7544, s(X7545))).\nand substitutionT761 -> s(T937),\nX7544 -> s(s(s(s(s(s(s(s(T937)))))))),\nX7545 -> T937,\nT936 -> s(T937)", fontsize=14, style = filled, fillcolor = lightblue];
4190 -> 7057 [arrowhead = none ];
7057 -> 4196;

7058 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4190 -> 7058 [arrowhead = none ];
7058 -> 4197;

7059 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4191 -> 7059 [arrowhead = none ];
7059 -> 4194;

7060 [label="GENERALIZATION\nT939 <-- s(s(s(s(s(s(s(T937)))))))\n\nNew Knowledge:\nT939 is ground", fontsize=14, style = filled, fillcolor = violet];
4196 -> 7060 [arrowhead = none ];
7060 -> 4200;

7061 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
4200 -> 7061 [arrowhead = none ];
7061 -> 4203;

7062 [label="SPLIT 2\nnew knowledge:\nT937 is ground\nT939 is ground", fontsize=14, style = filled, fillcolor = violet];
4200 -> 7062 [arrowhead = none ];
7062 -> 4204;

7063 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4203 -> 7063 [arrowhead = none ];
7063 -> 4207;

7064 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4204 -> 7064 [arrowhead = none ];
7064 -> 5621;

7065 [label="ONLY EVAL with clause\nnot_divides(X7568, X7569) :- ','(div(X7569, X7568, X7570), ','(times(X7570, X7568, X7571), neq(X7569, X7571))).\nand substitutionT937 -> T950,\nX7568 -> s(s(T950)),\nT939 -> T951,\nX7569 -> s(T951)", fontsize=14, style = filled, fillcolor = lightblue];
4207 -> 7065 [arrowhead = none ];
7065 -> 4211;

7066 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
4211 -> 7066 [arrowhead = none ];
7066 -> 4214;

7067 [label="SPLIT 2\nnew knowledge:\nT951 is ground\nT950 is ground\nT954 is ground\nreplacements:X7570 -> T954", fontsize=14, style = filled, fillcolor = violet];
4211 -> 7067 [arrowhead = none ];
7067 -> 4215;

7068 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4214 -> 7068 [arrowhead = none ];
7068 -> 4218;

7069 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
4215 -> 7069 [arrowhead = none ];
7069 -> 5619;

7070 [label="SPLIT 2\nnew knowledge:\nT954 is ground\nT950 is ground\nT1396 is ground\nreplacements:X7571 -> T1396", fontsize=14, style = filled, fillcolor = violet];
4215 -> 7070 [arrowhead = none ];
7070 -> 5620;

7071 [label="ONLY EVAL with clause\ndiv(X7592, X7593, X7594) :- quot(X7592, X7593, X7593, X7594).\nand substitutionT951 -> T961,\nX7592 -> s(T961),\nT950 -> T962,\nX7593 -> s(s(T962)),\nX7570 -> X7595,\nX7594 -> X7595", fontsize=14, style = filled, fillcolor = lightblue];
4218 -> 7071 [arrowhead = none ];
7071 -> 4223;

7072 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4223 -> 7072 [arrowhead = none ];
7072 -> 4225;

7073 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
4225 -> 7073 [arrowhead = none ];
7073 -> 4226;

7074 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4226 -> 7074 [arrowhead = none ];
7074 -> 4234;

7075 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4226 -> 7075 [arrowhead = none ];
7075 -> 4235;

7076 [label="ONLY EVAL with clause\nquot(s(X7630), s(X7631), X7632, X7633) :- quot(X7630, X7631, X7632, X7633).\nand substitutionT961 -> T975,\nX7630 -> T975,\nT962 -> T976,\nX7631 -> s(T976),\nX7632 -> s(s(T976)),\nX7595 -> X7634,\nX7633 -> X7634", fontsize=14, style = filled, fillcolor = lightblue];
4234 -> 7076 [arrowhead = none ];
7076 -> 4244;

7077 [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 = lightgreen];
4235 -> 7077 [arrowhead = none ];
7077 -> 5618;

7078 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4244 -> 7078 [arrowhead = none ];
7078 -> 4249;

7079 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4249 -> 7079 [arrowhead = none ];
7079 -> 4251;

7080 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4249 -> 7080 [arrowhead = none ];
7080 -> 4252;

7081 [label="EVAL with clause\nquot(0, s(X7647), s(X7648), 0).\nand substitutionT975 -> 0,\nT976 -> T983,\nX7647 -> T983,\nX7648 -> s(T983),\nX7634 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4251 -> 7081 [arrowhead = none ];
7081 -> 4260;

7082 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4251 -> 7082 [arrowhead = none ];
7082 -> 4261;

7083 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4252 -> 7083 [arrowhead = none ];
7083 -> 4268;

7084 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4252 -> 7084 [arrowhead = none ];
7084 -> 4269;

7085 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4260 -> 7085 [arrowhead = none ];
7085 -> 4262;

7086 [label="EVAL with clause\nquot(s(X7669), s(X7670), X7671, X7672) :- quot(X7669, X7670, X7671, X7672).\nand substitutionX7669 -> T992,\nT975 -> s(T992),\nT976 -> T993,\nX7670 -> T993,\nX7671 -> s(s(T993)),\nX7634 -> X7673,\nX7672 -> X7673", fontsize=14, style = filled, fillcolor = lightblue];
4268 -> 7086 [arrowhead = none ];
7086 -> 4277;

7087 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4268 -> 7087 [arrowhead = none ];
7087 -> 4278;

7088 [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 = lightgreen];
4269 -> 7088 [arrowhead = none ];
7088 -> 5617;

7089 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4277 -> 7089 [arrowhead = none ];
7089 -> 4282;

7090 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4282 -> 7090 [arrowhead = none ];
7090 -> 4285;

7091 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4282 -> 7091 [arrowhead = none ];
7091 -> 4286;

7092 [label="EVAL with clause\nquot(0, s(X7686), s(X7687), 0).\nand substitutionT992 -> 0,\nX7686 -> T1000,\nT993 -> s(T1000),\nX7687 -> s(s(T1000)),\nX7673 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4285 -> 7092 [arrowhead = none ];
7092 -> 4290;

7093 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4285 -> 7093 [arrowhead = none ];
7093 -> 4291;

7094 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4286 -> 7094 [arrowhead = none ];
7094 -> 4298;

7095 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4286 -> 7095 [arrowhead = none ];
7095 -> 4299;

7096 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4290 -> 7096 [arrowhead = none ];
7096 -> 4292;

7097 [label="EVAL with clause\nquot(s(X7708), s(X7709), X7710, X7711) :- quot(X7708, X7709, X7710, X7711).\nand substitutionX7708 -> T1009,\nT992 -> s(T1009),\nX7709 -> T1010,\nT993 -> s(T1010),\nX7710 -> s(s(s(T1010))),\nX7673 -> X7712,\nX7711 -> X7712", fontsize=14, style = filled, fillcolor = lightblue];
4298 -> 7097 [arrowhead = none ];
7097 -> 4307;

7098 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4298 -> 7098 [arrowhead = none ];
7098 -> 4308;

7099 [label="EVAL with clause\nquot(X9404, 0, s(X9405), s(X9406)) :- quot(X9404, s(X9405), s(X9405), X9406).\nand substitutionT992 -> T1375,\nX9404 -> T1375,\nT993 -> 0,\nX9405 -> s(0),\nX9406 -> X9407,\nX7673 -> s(X9407)", fontsize=14, style = filled, fillcolor = lightblue];
4299 -> 7099 [arrowhead = none ];
7099 -> 5579;

7100 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4299 -> 7100 [arrowhead = none ];
7100 -> 5580;

7101 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4307 -> 7101 [arrowhead = none ];
7101 -> 4314;

7102 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4314 -> 7102 [arrowhead = none ];
7102 -> 4318;

7103 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4314 -> 7103 [arrowhead = none ];
7103 -> 4319;

7104 [label="EVAL with clause\nquot(0, s(X7725), s(X7726), 0).\nand substitutionT1009 -> 0,\nX7725 -> T1017,\nT1010 -> s(T1017),\nX7726 -> s(s(s(T1017))),\nX7712 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4318 -> 7104 [arrowhead = none ];
7104 -> 4323;

7105 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4318 -> 7105 [arrowhead = none ];
7105 -> 4324;

7106 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4319 -> 7106 [arrowhead = none ];
7106 -> 4331;

7107 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4319 -> 7107 [arrowhead = none ];
7107 -> 4332;

7108 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4323 -> 7108 [arrowhead = none ];
7108 -> 4327;

7109 [label="EVAL with clause\nquot(s(X7747), s(X7748), X7749, X7750) :- quot(X7747, X7748, X7749, X7750).\nand substitutionX7747 -> T1026,\nT1009 -> s(T1026),\nX7748 -> T1027,\nT1010 -> s(T1027),\nX7749 -> s(s(s(s(T1027)))),\nX7712 -> X7751,\nX7750 -> X7751", fontsize=14, style = filled, fillcolor = lightblue];
4331 -> 7109 [arrowhead = none ];
7109 -> 4338;

7110 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4331 -> 7110 [arrowhead = none ];
7110 -> 4339;

7111 [label="EVAL with clause\nquot(X9236, 0, s(X9237), s(X9238)) :- quot(X9236, s(X9237), s(X9237), X9238).\nand substitutionT1009 -> T1350,\nX9236 -> T1350,\nT1010 -> 0,\nX9237 -> s(s(0)),\nX9238 -> X9239,\nX7712 -> s(X9239)", fontsize=14, style = filled, fillcolor = lightblue];
4332 -> 7111 [arrowhead = none ];
7111 -> 5489;

7112 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4332 -> 7112 [arrowhead = none ];
7112 -> 5490;

7113 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4338 -> 7113 [arrowhead = none ];
7113 -> 4347;

7114 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4347 -> 7114 [arrowhead = none ];
7114 -> 4349;

7115 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4347 -> 7115 [arrowhead = none ];
7115 -> 4350;

7116 [label="EVAL with clause\nquot(0, s(X7764), s(X7765), 0).\nand substitutionT1026 -> 0,\nX7764 -> T1034,\nT1027 -> s(T1034),\nX7765 -> s(s(s(s(T1034)))),\nX7751 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4349 -> 7116 [arrowhead = none ];
7116 -> 4355;

7117 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4349 -> 7117 [arrowhead = none ];
7117 -> 4356;

7118 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4350 -> 7118 [arrowhead = none ];
7118 -> 4363;

7119 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4350 -> 7119 [arrowhead = none ];
7119 -> 4364;

7120 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4355 -> 7120 [arrowhead = none ];
7120 -> 4357;

7121 [label="EVAL with clause\nquot(s(X7786), s(X7787), X7788, X7789) :- quot(X7786, X7787, X7788, X7789).\nand substitutionX7786 -> T1043,\nT1026 -> s(T1043),\nX7787 -> T1044,\nT1027 -> s(T1044),\nX7788 -> s(s(s(s(s(T1044))))),\nX7751 -> X7790,\nX7789 -> X7790", fontsize=14, style = filled, fillcolor = lightblue];
4363 -> 7121 [arrowhead = none ];
7121 -> 4372;

7122 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4363 -> 7122 [arrowhead = none ];
7122 -> 4373;

7123 [label="EVAL with clause\nquot(X9026, 0, s(X9027), s(X9028)) :- quot(X9026, s(X9027), s(X9027), X9028).\nand substitutionT1026 -> T1319,\nX9026 -> T1319,\nT1027 -> 0,\nX9027 -> s(s(s(0))),\nX9028 -> X9029,\nX7751 -> s(X9029)", fontsize=14, style = filled, fillcolor = lightblue];
4364 -> 7123 [arrowhead = none ];
7123 -> 5338;

7124 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4364 -> 7124 [arrowhead = none ];
7124 -> 5339;

7125 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4372 -> 7125 [arrowhead = none ];
7125 -> 4377;

7126 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4377 -> 7126 [arrowhead = none ];
7126 -> 4381;

7127 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4377 -> 7127 [arrowhead = none ];
7127 -> 4382;

7128 [label="EVAL with clause\nquot(0, s(X7803), s(X7804), 0).\nand substitutionT1043 -> 0,\nX7803 -> T1051,\nT1044 -> s(T1051),\nX7804 -> s(s(s(s(s(T1051))))),\nX7790 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4381 -> 7128 [arrowhead = none ];
7128 -> 4385;

7129 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4381 -> 7129 [arrowhead = none ];
7129 -> 4386;

7130 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4382 -> 7130 [arrowhead = none ];
7130 -> 4393;

7131 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4382 -> 7131 [arrowhead = none ];
7131 -> 4394;

7132 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4385 -> 7132 [arrowhead = none ];
7132 -> 4387;

7133 [label="EVAL with clause\nquot(s(X7825), s(X7826), X7827, X7828) :- quot(X7825, X7826, X7827, X7828).\nand substitutionX7825 -> T1060,\nT1043 -> s(T1060),\nX7826 -> T1061,\nT1044 -> s(T1061),\nX7827 -> s(s(s(s(s(s(T1061)))))),\nX7790 -> X7829,\nX7828 -> X7829", fontsize=14, style = filled, fillcolor = lightblue];
4393 -> 7133 [arrowhead = none ];
7133 -> 4405;

7134 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4393 -> 7134 [arrowhead = none ];
7134 -> 4406;

7135 [label="EVAL with clause\nquot(X8774, 0, s(X8775), s(X8776)) :- quot(X8774, s(X8775), s(X8775), X8776).\nand substitutionT1043 -> T1282,\nX8774 -> T1282,\nT1044 -> 0,\nX8775 -> s(s(s(s(0)))),\nX8776 -> X8777,\nX7790 -> s(X8777)", fontsize=14, style = filled, fillcolor = lightblue];
4394 -> 7135 [arrowhead = none ];
7135 -> 5152;

7136 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4394 -> 7136 [arrowhead = none ];
7136 -> 5153;

7137 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4405 -> 7137 [arrowhead = none ];
7137 -> 4410;

7138 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4410 -> 7138 [arrowhead = none ];
7138 -> 4413;

7139 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4410 -> 7139 [arrowhead = none ];
7139 -> 4414;

7140 [label="EVAL with clause\nquot(0, s(X7842), s(X7843), 0).\nand substitutionT1060 -> 0,\nX7842 -> T1068,\nT1061 -> s(T1068),\nX7843 -> s(s(s(s(s(s(T1068)))))),\nX7829 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4413 -> 7140 [arrowhead = none ];
7140 -> 4418;

7141 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4413 -> 7141 [arrowhead = none ];
7141 -> 4419;

7142 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4414 -> 7142 [arrowhead = none ];
7142 -> 4426;

7143 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4414 -> 7143 [arrowhead = none ];
7143 -> 4427;

7144 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4418 -> 7144 [arrowhead = none ];
7144 -> 4420;

7145 [label="EVAL with clause\nquot(s(X7864), s(X7865), X7866, X7867) :- quot(X7864, X7865, X7866, X7867).\nand substitutionX7864 -> T1077,\nT1060 -> s(T1077),\nX7865 -> T1078,\nT1061 -> s(T1078),\nX7866 -> s(s(s(s(s(s(s(T1078))))))),\nX7829 -> X7868,\nX7867 -> X7868", fontsize=14, style = filled, fillcolor = lightblue];
4426 -> 7145 [arrowhead = none ];
7145 -> 4436;

7146 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4426 -> 7146 [arrowhead = none ];
7146 -> 4437;

7147 [label="EVAL with clause\nquot(X8480, 0, s(X8481), s(X8482)) :- quot(X8480, s(X8481), s(X8481), X8482).\nand substitutionT1060 -> T1239,\nX8480 -> T1239,\nT1061 -> 0,\nX8481 -> s(s(s(s(s(0))))),\nX8482 -> X8483,\nX7829 -> s(X8483)", fontsize=14, style = filled, fillcolor = lightblue];
4427 -> 7147 [arrowhead = none ];
7147 -> 4921;

7148 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4427 -> 7148 [arrowhead = none ];
7148 -> 4922;

7149 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4436 -> 7149 [arrowhead = none ];
7149 -> 4439;

7150 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4439 -> 7150 [arrowhead = none ];
7150 -> 4443;

7151 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4439 -> 7151 [arrowhead = none ];
7151 -> 4444;

7152 [label="EVAL with clause\nquot(0, s(X7881), s(X7882), 0).\nand substitutionT1077 -> 0,\nX7881 -> T1085,\nT1078 -> s(T1085),\nX7882 -> s(s(s(s(s(s(s(T1085))))))),\nX7868 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4443 -> 7152 [arrowhead = none ];
7152 -> 4445;

7153 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4443 -> 7153 [arrowhead = none ];
7153 -> 4446;

7154 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4444 -> 7154 [arrowhead = none ];
7154 -> 4453;

7155 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4444 -> 7155 [arrowhead = none ];
7155 -> 4454;

7156 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4445 -> 7156 [arrowhead = none ];
7156 -> 4447;

7157 [label="EVAL with clause\nquot(s(X7903), s(X7904), X7905, X7906) :- quot(X7903, X7904, X7905, X7906).\nand substitutionX7903 -> T1094,\nT1077 -> s(T1094),\nX7904 -> T1095,\nT1078 -> s(T1095),\nX7905 -> s(s(s(s(s(s(s(s(T1095)))))))),\nX7868 -> X7907,\nX7906 -> X7907", fontsize=14, style = filled, fillcolor = lightblue];
4453 -> 7157 [arrowhead = none ];
7157 -> 4459;

7158 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4453 -> 7158 [arrowhead = none ];
7158 -> 4460;

7159 [label="EVAL with clause\nquot(X8144, 0, s(X8145), s(X8146)) :- quot(X8144, s(X8145), s(X8145), X8146).\nand substitutionT1077 -> T1190,\nX8144 -> T1190,\nT1078 -> 0,\nX8145 -> s(s(s(s(s(s(0)))))),\nX8146 -> X8147,\nX7868 -> s(X8147)", fontsize=14, style = filled, fillcolor = lightblue];
4454 -> 7159 [arrowhead = none ];
7159 -> 4639;

7160 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4454 -> 7160 [arrowhead = none ];
7160 -> 4640;

7161 [label="GENERALIZATION\nT1098 <-- s(s(s(s(s(s(s(T1095)))))))\n\nNew Knowledge:\nT1098 is ground", fontsize=14, style = filled, fillcolor = violet];
4459 -> 7161 [arrowhead = none ];
7161 -> 4465;

7162 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4465 -> 7162 [arrowhead = none ];
7162 -> 4469;

7163 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4469 -> 7163 [arrowhead = none ];
7163 -> 4470;

7164 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4469 -> 7164 [arrowhead = none ];
7164 -> 4471;

7165 [label="EVAL with clause\nquot(0, s(X7924), s(X7925), 0).\nand substitutionT1094 -> 0,\nX7924 -> T1111,\nT1095 -> s(T1111),\nT1098 -> T1112,\nX7925 -> T1112,\nX7907 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4470 -> 7165 [arrowhead = none ];
7165 -> 4475;

7166 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4470 -> 7166 [arrowhead = none ];
7166 -> 4476;

7167 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4471 -> 7167 [arrowhead = none ];
7167 -> 4483;

7168 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4471 -> 7168 [arrowhead = none ];
7168 -> 4484;

7169 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4475 -> 7169 [arrowhead = none ];
7169 -> 4477;

7170 [label="EVAL with clause\nquot(s(X7946), s(X7947), X7948, X7949) :- quot(X7946, X7947, X7948, X7949).\nand substitutionX7946 -> T1125,\nT1094 -> s(T1125),\nX7947 -> T1126,\nT1095 -> s(T1126),\nT1098 -> T1127,\nX7948 -> s(T1127),\nX7907 -> X7950,\nX7949 -> X7950", fontsize=14, style = filled, fillcolor = lightblue];
4483 -> 7170 [arrowhead = none ];
7170 -> 4493;

7171 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4483 -> 7171 [arrowhead = none ];
7171 -> 4494;

7172 [label="EVAL with clause\nquot(X7963, 0, s(X7964), s(X7965)) :- quot(X7963, s(X7964), s(X7964), X7965).\nand substitutionT1094 -> T1136,\nX7963 -> T1136,\nT1095 -> 0,\nT1098 -> T1137,\nX7964 -> T1137,\nX7965 -> X7966,\nX7907 -> s(X7966)", fontsize=14, style = filled, fillcolor = lightblue];
4484 -> 7172 [arrowhead = none ];
7172 -> 4505;

7173 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4484 -> 7173 [arrowhead = none ];
7173 -> 4506;

7174 [label="INSTANCE with matching:\nT1094 -> T1125\nT1095 -> T1126\nT1098 -> T1127\nX7907 -> X7950", fontsize=14, style = filled, fillcolor = lightgrey];
4493 -> 7174 [arrowhead = none , style=dashed];
7174 -> 4465[style=dashed];

7175 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4505 -> 7175 [arrowhead = none ];
7175 -> 4511;

7176 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4511 -> 7176 [arrowhead = none ];
7176 -> 4515;

7177 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4511 -> 7177 [arrowhead = none ];
7177 -> 4516;

7178 [label="EVAL with clause\nquot(0, s(X7979), s(X7980), 0).\nand substitutionT1136 -> 0,\nT1137 -> T1144,\nX7979 -> T1144,\nX7980 -> T1144,\nX7966 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4515 -> 7178 [arrowhead = none ];
7178 -> 4521;

7179 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4515 -> 7179 [arrowhead = none ];
7179 -> 4522;

7180 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4516 -> 7180 [arrowhead = none ];
7180 -> 4526;

7181 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4516 -> 7181 [arrowhead = none ];
7181 -> 4527;

7182 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4521 -> 7182 [arrowhead = none ];
7182 -> 4523;

7183 [label="EVAL with clause\nquot(s(X8001), s(X8002), X8003, X8004) :- quot(X8001, X8002, X8003, X8004).\nand substitutionX8001 -> T1153,\nT1136 -> s(T1153),\nT1137 -> T1154,\nX8002 -> T1154,\nX8003 -> s(T1154),\nX7966 -> X8005,\nX8004 -> X8005", fontsize=14, style = filled, fillcolor = lightblue];
4526 -> 7183 [arrowhead = none ];
7183 -> 4533;

7184 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4526 -> 7184 [arrowhead = none ];
7184 -> 4534;

7185 [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 = lightgreen];
4527 -> 7185 [arrowhead = none ];
7185 -> 4631;

7186 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4533 -> 7186 [arrowhead = none ];
7186 -> 4540;

7187 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4540 -> 7187 [arrowhead = none ];
7187 -> 4544;

7188 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4540 -> 7188 [arrowhead = none ];
7188 -> 4545;

7189 [label="EVAL with clause\nquot(0, s(X8018), s(X8019), 0).\nand substitutionT1153 -> 0,\nX8018 -> T1161,\nT1154 -> s(T1161),\nX8019 -> s(T1161),\nX8005 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4544 -> 7189 [arrowhead = none ];
7189 -> 4551;

7190 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4544 -> 7190 [arrowhead = none ];
7190 -> 4552;

7191 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4545 -> 7191 [arrowhead = none ];
7191 -> 4558;

7192 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4545 -> 7192 [arrowhead = none ];
7192 -> 4559;

7193 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4551 -> 7193 [arrowhead = none ];
7193 -> 4553;

7194 [label="EVAL with clause\nquot(s(X8040), s(X8041), X8042, X8043) :- quot(X8040, X8041, X8042, X8043).\nand substitutionX8040 -> T1170,\nT1153 -> s(T1170),\nX8041 -> T1171,\nT1154 -> s(T1171),\nX8042 -> s(s(T1171)),\nX8005 -> X8044,\nX8043 -> X8044", fontsize=14, style = filled, fillcolor = lightblue];
4558 -> 7194 [arrowhead = none ];
7194 -> 4565;

7195 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4558 -> 7195 [arrowhead = none ];
7195 -> 4566;

7196 [label="EVAL with clause\nquot(X8057, 0, s(X8058), s(X8059)) :- quot(X8057, s(X8058), s(X8058), X8059).\nand substitutionT1153 -> T1176,\nX8057 -> T1176,\nT1154 -> 0,\nX8058 -> 0,\nX8059 -> X8060,\nX8005 -> s(X8060)", fontsize=14, style = filled, fillcolor = lightblue];
4559 -> 7196 [arrowhead = none ];
7196 -> 4573;

7197 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4559 -> 7197 [arrowhead = none ];
7197 -> 4574;

7198 [label="INSTANCE with matching:\nT992 -> T1170\nT993 -> T1171\nX7673 -> X8044", fontsize=14, style = filled, fillcolor = lightgrey];
4565 -> 7198 [arrowhead = none , style=dashed];
7198 -> 4277[style=dashed];

7199 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4573 -> 7199 [arrowhead = none ];
7199 -> 4576;

7200 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4576 -> 7200 [arrowhead = none ];
7200 -> 4580;

7201 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4576 -> 7201 [arrowhead = none ];
7201 -> 4581;

7202 [label="EVAL with clause\nquot(0, s(X8073), s(X8074), 0).\nand substitutionT1176 -> 0,\nX8073 -> 0,\nX8074 -> 0,\nX8060 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4580 -> 7202 [arrowhead = none ];
7202 -> 4583;

7203 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4580 -> 7203 [arrowhead = none ];
7203 -> 4584;

7204 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4581 -> 7204 [arrowhead = none ];
7204 -> 4594;

7205 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4581 -> 7205 [arrowhead = none ];
7205 -> 4595;

7206 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4583 -> 7206 [arrowhead = none ];
7206 -> 4585;

7207 [label="EVAL with clause\nquot(s(X8095), s(X8096), X8097, X8098) :- quot(X8095, X8096, X8097, X8098).\nand substitutionX8095 -> T1181,\nT1176 -> s(T1181),\nX8096 -> 0,\nX8097 -> s(0),\nX8060 -> X8099,\nX8098 -> X8099", fontsize=14, style = filled, fillcolor = lightblue];
4594 -> 7207 [arrowhead = none ];
7207 -> 4604;

7208 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4594 -> 7208 [arrowhead = none ];
7208 -> 4605;

7209 [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 = lightgreen];
4595 -> 7209 [arrowhead = none ];
7209 -> 4630;

7210 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4604 -> 7210 [arrowhead = none ];
7210 -> 4610;

7211 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
4610 -> 7211 [arrowhead = none ];
7211 -> 4611;

7212 [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 = lightgreen];
4611 -> 7212 [arrowhead = none ];
7212 -> 4613;

7213 [label="ONLY EVAL with clause\nquot(X8122, 0, s(X8123), s(X8124)) :- quot(X8122, s(X8123), s(X8123), X8124).\nand substitutionT1181 -> T1185,\nX8122 -> T1185,\nX8123 -> 0,\nX8124 -> X8125,\nX8099 -> s(X8125)", fontsize=14, style = filled, fillcolor = lightblue];
4613 -> 7213 [arrowhead = none ];
7213 -> 4626;

7214 [label="INSTANCE with matching:\nT1176 -> T1185\nX8060 -> X8125", fontsize=14, style = filled, fillcolor = lightgrey];
4626 -> 7214 [arrowhead = none , style=dashed];
7214 -> 4573[style=dashed];

7215 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4639 -> 7215 [arrowhead = none ];
7215 -> 4646;

7216 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4646 -> 7216 [arrowhead = none ];
7216 -> 4650;

7217 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4646 -> 7217 [arrowhead = none ];
7217 -> 4651;

7218 [label="EVAL with clause\nquot(0, s(X8160), s(X8161), 0).\nand substitutionT1190 -> 0,\nX8160 -> s(s(s(s(s(s(0)))))),\nX8161 -> s(s(s(s(s(s(0)))))),\nX8147 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4650 -> 7218 [arrowhead = none ];
7218 -> 4654;

7219 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4650 -> 7219 [arrowhead = none ];
7219 -> 4655;

7220 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4651 -> 7220 [arrowhead = none ];
7220 -> 4664;

7221 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4651 -> 7221 [arrowhead = none ];
7221 -> 4665;

7222 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4654 -> 7222 [arrowhead = none ];
7222 -> 4658;

7223 [label="EVAL with clause\nquot(s(X8182), s(X8183), X8184, X8185) :- quot(X8182, X8183, X8184, X8185).\nand substitutionX8182 -> T1195,\nT1190 -> s(T1195),\nX8183 -> s(s(s(s(s(s(0)))))),\nX8184 -> s(s(s(s(s(s(s(0))))))),\nX8147 -> X8186,\nX8185 -> X8186", fontsize=14, style = filled, fillcolor = lightblue];
4664 -> 7223 [arrowhead = none ];
7223 -> 4674;

7224 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4664 -> 7224 [arrowhead = none ];
7224 -> 4675;

7225 [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 = lightgreen];
4665 -> 7225 [arrowhead = none ];
7225 -> 4914;

7226 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4674 -> 7226 [arrowhead = none ];
7226 -> 4681;

7227 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4681 -> 7227 [arrowhead = none ];
7227 -> 4682;

7228 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4681 -> 7228 [arrowhead = none ];
7228 -> 4683;

7229 [label="EVAL with clause\nquot(0, s(X8199), s(X8200), 0).\nand substitutionT1195 -> 0,\nX8199 -> s(s(s(s(s(0))))),\nX8200 -> s(s(s(s(s(s(0)))))),\nX8186 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4682 -> 7229 [arrowhead = none ];
7229 -> 4689;

7230 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4682 -> 7230 [arrowhead = none ];
7230 -> 4690;

7231 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4683 -> 7231 [arrowhead = none ];
7231 -> 4695;

7232 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4683 -> 7232 [arrowhead = none ];
7232 -> 4696;

7233 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4689 -> 7233 [arrowhead = none ];
7233 -> 4691;

7234 [label="EVAL with clause\nquot(s(X8221), s(X8222), X8223, X8224) :- quot(X8221, X8222, X8223, X8224).\nand substitutionX8221 -> T1200,\nT1195 -> s(T1200),\nX8222 -> s(s(s(s(s(0))))),\nX8223 -> s(s(s(s(s(s(s(0))))))),\nX8186 -> X8225,\nX8224 -> X8225", fontsize=14, style = filled, fillcolor = lightblue];
4695 -> 7234 [arrowhead = none ];
7234 -> 4707;

7235 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4695 -> 7235 [arrowhead = none ];
7235 -> 4708;

7236 [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 = lightgreen];
4696 -> 7236 [arrowhead = none ];
7236 -> 4913;

7237 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4707 -> 7237 [arrowhead = none ];
7237 -> 4714;

7238 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4714 -> 7238 [arrowhead = none ];
7238 -> 4715;

7239 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4714 -> 7239 [arrowhead = none ];
7239 -> 4716;

7240 [label="EVAL with clause\nquot(0, s(X8238), s(X8239), 0).\nand substitutionT1200 -> 0,\nX8238 -> s(s(s(s(0)))),\nX8239 -> s(s(s(s(s(s(0)))))),\nX8225 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4715 -> 7240 [arrowhead = none ];
7240 -> 4721;

7241 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4715 -> 7241 [arrowhead = none ];
7241 -> 4722;

7242 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4716 -> 7242 [arrowhead = none ];
7242 -> 4727;

7243 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4716 -> 7243 [arrowhead = none ];
7243 -> 4728;

7244 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4721 -> 7244 [arrowhead = none ];
7244 -> 4723;

7245 [label="EVAL with clause\nquot(s(X8260), s(X8261), X8262, X8263) :- quot(X8260, X8261, X8262, X8263).\nand substitutionX8260 -> T1205,\nT1200 -> s(T1205),\nX8261 -> s(s(s(s(0)))),\nX8262 -> s(s(s(s(s(s(s(0))))))),\nX8225 -> X8264,\nX8263 -> X8264", fontsize=14, style = filled, fillcolor = lightblue];
4727 -> 7245 [arrowhead = none ];
7245 -> 4739;

7246 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4727 -> 7246 [arrowhead = none ];
7246 -> 4740;

7247 [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 = lightgreen];
4728 -> 7247 [arrowhead = none ];
7247 -> 4910;

7248 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4739 -> 7248 [arrowhead = none ];
7248 -> 4746;

7249 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4746 -> 7249 [arrowhead = none ];
7249 -> 4749;

7250 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4746 -> 7250 [arrowhead = none ];
7250 -> 4750;

7251 [label="EVAL with clause\nquot(0, s(X8277), s(X8278), 0).\nand substitutionT1205 -> 0,\nX8277 -> s(s(s(0))),\nX8278 -> s(s(s(s(s(s(0)))))),\nX8264 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4749 -> 7251 [arrowhead = none ];
7251 -> 4752;

7252 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4749 -> 7252 [arrowhead = none ];
7252 -> 4753;

7253 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4750 -> 7253 [arrowhead = none ];
7253 -> 4762;

7254 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4750 -> 7254 [arrowhead = none ];
7254 -> 4763;

7255 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4752 -> 7255 [arrowhead = none ];
7255 -> 4754;

7256 [label="EVAL with clause\nquot(s(X8299), s(X8300), X8301, X8302) :- quot(X8299, X8300, X8301, X8302).\nand substitutionX8299 -> T1210,\nT1205 -> s(T1210),\nX8300 -> s(s(s(0))),\nX8301 -> s(s(s(s(s(s(s(0))))))),\nX8264 -> X8303,\nX8302 -> X8303", fontsize=14, style = filled, fillcolor = lightblue];
4762 -> 7256 [arrowhead = none ];
7256 -> 4772;

7257 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4762 -> 7257 [arrowhead = none ];
7257 -> 4773;

7258 [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 = lightgreen];
4763 -> 7258 [arrowhead = none ];
7258 -> 4909;

7259 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4772 -> 7259 [arrowhead = none ];
7259 -> 4778;

7260 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4778 -> 7260 [arrowhead = none ];
7260 -> 4781;

7261 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4778 -> 7261 [arrowhead = none ];
7261 -> 4782;

7262 [label="EVAL with clause\nquot(0, s(X8316), s(X8317), 0).\nand substitutionT1210 -> 0,\nX8316 -> s(s(0)),\nX8317 -> s(s(s(s(s(s(0)))))),\nX8303 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4781 -> 7262 [arrowhead = none ];
7262 -> 4786;

7263 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4781 -> 7263 [arrowhead = none ];
7263 -> 4787;

7264 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4782 -> 7264 [arrowhead = none ];
7264 -> 4792;

7265 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4782 -> 7265 [arrowhead = none ];
7265 -> 4793;

7266 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4786 -> 7266 [arrowhead = none ];
7266 -> 4788;

7267 [label="EVAL with clause\nquot(s(X8338), s(X8339), X8340, X8341) :- quot(X8338, X8339, X8340, X8341).\nand substitutionX8338 -> T1215,\nT1210 -> s(T1215),\nX8339 -> s(s(0)),\nX8340 -> s(s(s(s(s(s(s(0))))))),\nX8303 -> X8342,\nX8341 -> X8342", fontsize=14, style = filled, fillcolor = lightblue];
4792 -> 7267 [arrowhead = none ];
7267 -> 4801;

7268 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4792 -> 7268 [arrowhead = none ];
7268 -> 4802;

7269 [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 = lightgreen];
4793 -> 7269 [arrowhead = none ];
7269 -> 4906;

7270 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4801 -> 7270 [arrowhead = none ];
7270 -> 4806;

7271 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4806 -> 7271 [arrowhead = none ];
7271 -> 4809;

7272 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4806 -> 7272 [arrowhead = none ];
7272 -> 4810;

7273 [label="EVAL with clause\nquot(0, s(X8355), s(X8356), 0).\nand substitutionT1215 -> 0,\nX8355 -> s(0),\nX8356 -> s(s(s(s(s(s(0)))))),\nX8342 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4809 -> 7273 [arrowhead = none ];
7273 -> 4815;

7274 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4809 -> 7274 [arrowhead = none ];
7274 -> 4816;

7275 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4810 -> 7275 [arrowhead = none ];
7275 -> 4823;

7276 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4810 -> 7276 [arrowhead = none ];
7276 -> 4824;

7277 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4815 -> 7277 [arrowhead = none ];
7277 -> 4817;

7278 [label="EVAL with clause\nquot(s(X8377), s(X8378), X8379, X8380) :- quot(X8377, X8378, X8379, X8380).\nand substitutionX8377 -> T1220,\nT1215 -> s(T1220),\nX8378 -> s(0),\nX8379 -> s(s(s(s(s(s(s(0))))))),\nX8342 -> X8381,\nX8380 -> X8381", fontsize=14, style = filled, fillcolor = lightblue];
4823 -> 7278 [arrowhead = none ];
7278 -> 4833;

7279 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4823 -> 7279 [arrowhead = none ];
7279 -> 4834;

7280 [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 = lightgreen];
4824 -> 7280 [arrowhead = none ];
7280 -> 4905;

7281 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4833 -> 7281 [arrowhead = none ];
7281 -> 4837;

7282 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4837 -> 7282 [arrowhead = none ];
7282 -> 4843;

7283 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4837 -> 7283 [arrowhead = none ];
7283 -> 4844;

7284 [label="EVAL with clause\nquot(0, s(X8394), s(X8395), 0).\nand substitutionT1220 -> 0,\nX8394 -> 0,\nX8395 -> s(s(s(s(s(s(0)))))),\nX8381 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4843 -> 7284 [arrowhead = none ];
7284 -> 4846;

7285 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4843 -> 7285 [arrowhead = none ];
7285 -> 4847;

7286 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4844 -> 7286 [arrowhead = none ];
7286 -> 4856;

7287 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4844 -> 7287 [arrowhead = none ];
7287 -> 4857;

7288 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4846 -> 7288 [arrowhead = none ];
7288 -> 4848;

7289 [label="EVAL with clause\nquot(s(X8416), s(X8417), X8418, X8419) :- quot(X8416, X8417, X8418, X8419).\nand substitutionX8416 -> T1225,\nT1220 -> s(T1225),\nX8417 -> 0,\nX8418 -> s(s(s(s(s(s(s(0))))))),\nX8381 -> X8420,\nX8419 -> X8420", fontsize=14, style = filled, fillcolor = lightblue];
4856 -> 7289 [arrowhead = none ];
7289 -> 4865;

7290 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4856 -> 7290 [arrowhead = none ];
7290 -> 4866;

7291 [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 = lightgreen];
4857 -> 7291 [arrowhead = none ];
7291 -> 4899;

7292 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4865 -> 7292 [arrowhead = none ];
7292 -> 4872;

7293 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
4872 -> 7293 [arrowhead = none ];
7293 -> 4874;

7294 [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 = lightgreen];
4874 -> 7294 [arrowhead = none ];
7294 -> 4877;

7295 [label="ONLY EVAL with clause\nquot(X8443, 0, s(X8444), s(X8445)) :- quot(X8443, s(X8444), s(X8444), X8445).\nand substitutionT1225 -> T1229,\nX8443 -> T1229,\nX8444 -> s(s(s(s(s(s(0)))))),\nX8445 -> X8446,\nX8420 -> s(X8446)", fontsize=14, style = filled, fillcolor = lightblue];
4877 -> 7295 [arrowhead = none ];
7295 -> 4890;

7296 [label="INSTANCE with matching:\nT1190 -> T1229\nX8147 -> X8446", fontsize=14, style = filled, fillcolor = lightgrey];
4890 -> 7296 [arrowhead = none , style=dashed];
7296 -> 4639[style=dashed];

7297 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4921 -> 7297 [arrowhead = none ];
7297 -> 4931;

7298 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4931 -> 7298 [arrowhead = none ];
7298 -> 4934;

7299 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4931 -> 7299 [arrowhead = none ];
7299 -> 4935;

7300 [label="EVAL with clause\nquot(0, s(X8496), s(X8497), 0).\nand substitutionT1239 -> 0,\nX8496 -> s(s(s(s(s(0))))),\nX8497 -> s(s(s(s(s(0))))),\nX8483 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4934 -> 7300 [arrowhead = none ];
7300 -> 4938;

7301 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4934 -> 7301 [arrowhead = none ];
7301 -> 4939;

7302 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4935 -> 7302 [arrowhead = none ];
7302 -> 4943;

7303 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4935 -> 7303 [arrowhead = none ];
7303 -> 4944;

7304 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4938 -> 7304 [arrowhead = none ];
7304 -> 4940;

7305 [label="EVAL with clause\nquot(s(X8518), s(X8519), X8520, X8521) :- quot(X8518, X8519, X8520, X8521).\nand substitutionX8518 -> T1244,\nT1239 -> s(T1244),\nX8519 -> s(s(s(s(s(0))))),\nX8520 -> s(s(s(s(s(s(0)))))),\nX8483 -> X8522,\nX8521 -> X8522", fontsize=14, style = filled, fillcolor = lightblue];
4943 -> 7305 [arrowhead = none ];
7305 -> 4956;

7306 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4943 -> 7306 [arrowhead = none ];
7306 -> 4957;

7307 [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 = lightgreen];
4944 -> 7307 [arrowhead = none ];
7307 -> 5143;

7308 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4956 -> 7308 [arrowhead = none ];
7308 -> 4961;

7309 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4961 -> 7309 [arrowhead = none ];
7309 -> 4966;

7310 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4961 -> 7310 [arrowhead = none ];
7310 -> 4967;

7311 [label="EVAL with clause\nquot(0, s(X8535), s(X8536), 0).\nand substitutionT1244 -> 0,\nX8535 -> s(s(s(s(0)))),\nX8536 -> s(s(s(s(s(0))))),\nX8522 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4966 -> 7311 [arrowhead = none ];
7311 -> 4968;

7312 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4966 -> 7312 [arrowhead = none ];
7312 -> 4969;

7313 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4967 -> 7313 [arrowhead = none ];
7313 -> 4975;

7314 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4967 -> 7314 [arrowhead = none ];
7314 -> 4976;

7315 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4968 -> 7315 [arrowhead = none ];
7315 -> 4970;

7316 [label="EVAL with clause\nquot(s(X8557), s(X8558), X8559, X8560) :- quot(X8557, X8558, X8559, X8560).\nand substitutionX8557 -> T1249,\nT1244 -> s(T1249),\nX8558 -> s(s(s(s(0)))),\nX8559 -> s(s(s(s(s(s(0)))))),\nX8522 -> X8561,\nX8560 -> X8561", fontsize=14, style = filled, fillcolor = lightblue];
4975 -> 7316 [arrowhead = none ];
7316 -> 4986;

7317 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4975 -> 7317 [arrowhead = none ];
7317 -> 4987;

7318 [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 = lightgreen];
4976 -> 7318 [arrowhead = none ];
7318 -> 5142;

7319 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4986 -> 7319 [arrowhead = none ];
7319 -> 4991;

7320 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4991 -> 7320 [arrowhead = none ];
7320 -> 4992;

7321 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4991 -> 7321 [arrowhead = none ];
7321 -> 4993;

7322 [label="EVAL with clause\nquot(0, s(X8574), s(X8575), 0).\nand substitutionT1249 -> 0,\nX8574 -> s(s(s(0))),\nX8575 -> s(s(s(s(s(0))))),\nX8561 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4992 -> 7322 [arrowhead = none ];
7322 -> 4999;

7323 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4992 -> 7323 [arrowhead = none ];
7323 -> 5000;

7324 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4993 -> 7324 [arrowhead = none ];
7324 -> 5008;

7325 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4993 -> 7325 [arrowhead = none ];
7325 -> 5009;

7326 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
4999 -> 7326 [arrowhead = none ];
7326 -> 5001;

7327 [label="EVAL with clause\nquot(s(X8596), s(X8597), X8598, X8599) :- quot(X8596, X8597, X8598, X8599).\nand substitutionX8596 -> T1254,\nT1249 -> s(T1254),\nX8597 -> s(s(s(0))),\nX8598 -> s(s(s(s(s(s(0)))))),\nX8561 -> X8600,\nX8599 -> X8600", fontsize=14, style = filled, fillcolor = lightblue];
5008 -> 7327 [arrowhead = none ];
7327 -> 5014;

7328 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5008 -> 7328 [arrowhead = none ];
7328 -> 5015;

7329 [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 = lightgreen];
5009 -> 7329 [arrowhead = none ];
7329 -> 5139;

7330 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5014 -> 7330 [arrowhead = none ];
7330 -> 5022;

7331 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5022 -> 7331 [arrowhead = none ];
7331 -> 5024;

7332 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5022 -> 7332 [arrowhead = none ];
7332 -> 5025;

7333 [label="EVAL with clause\nquot(0, s(X8613), s(X8614), 0).\nand substitutionT1254 -> 0,\nX8613 -> s(s(0)),\nX8614 -> s(s(s(s(s(0))))),\nX8600 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5024 -> 7333 [arrowhead = none ];
7333 -> 5030;

7334 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5024 -> 7334 [arrowhead = none ];
7334 -> 5031;

7335 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5025 -> 7335 [arrowhead = none ];
7335 -> 5035;

7336 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5025 -> 7336 [arrowhead = none ];
7336 -> 5036;

7337 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5030 -> 7337 [arrowhead = none ];
7337 -> 5032;

7338 [label="EVAL with clause\nquot(s(X8635), s(X8636), X8637, X8638) :- quot(X8635, X8636, X8637, X8638).\nand substitutionX8635 -> T1259,\nT1254 -> s(T1259),\nX8636 -> s(s(0)),\nX8637 -> s(s(s(s(s(s(0)))))),\nX8600 -> X8639,\nX8638 -> X8639", fontsize=14, style = filled, fillcolor = lightblue];
5035 -> 7338 [arrowhead = none ];
7338 -> 5044;

7339 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5035 -> 7339 [arrowhead = none ];
7339 -> 5046;

7340 [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 = lightgreen];
5036 -> 7340 [arrowhead = none ];
7340 -> 5135;

7341 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5044 -> 7341 [arrowhead = none ];
7341 -> 5052;

7342 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5052 -> 7342 [arrowhead = none ];
7342 -> 5058;

7343 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5052 -> 7343 [arrowhead = none ];
7343 -> 5059;

7344 [label="EVAL with clause\nquot(0, s(X8652), s(X8653), 0).\nand substitutionT1259 -> 0,\nX8652 -> s(0),\nX8653 -> s(s(s(s(s(0))))),\nX8639 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5058 -> 7344 [arrowhead = none ];
7344 -> 5060;

7345 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5058 -> 7345 [arrowhead = none ];
7345 -> 5061;

7346 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5059 -> 7346 [arrowhead = none ];
7346 -> 5067;

7347 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5059 -> 7347 [arrowhead = none ];
7347 -> 5068;

7348 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5060 -> 7348 [arrowhead = none ];
7348 -> 5062;

7349 [label="EVAL with clause\nquot(s(X8674), s(X8675), X8676, X8677) :- quot(X8674, X8675, X8676, X8677).\nand substitutionX8674 -> T1264,\nT1259 -> s(T1264),\nX8675 -> s(0),\nX8676 -> s(s(s(s(s(s(0)))))),\nX8639 -> X8678,\nX8677 -> X8678", fontsize=14, style = filled, fillcolor = lightblue];
5067 -> 7349 [arrowhead = none ];
7349 -> 5077;

7350 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5067 -> 7350 [arrowhead = none ];
7350 -> 5078;

7351 [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 = lightgreen];
5068 -> 7351 [arrowhead = none ];
7351 -> 5134;

7352 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5077 -> 7352 [arrowhead = none ];
7352 -> 5082;

7353 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5082 -> 7353 [arrowhead = none ];
7353 -> 5088;

7354 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5082 -> 7354 [arrowhead = none ];
7354 -> 5089;

7355 [label="EVAL with clause\nquot(0, s(X8691), s(X8692), 0).\nand substitutionT1264 -> 0,\nX8691 -> 0,\nX8692 -> s(s(s(s(s(0))))),\nX8678 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5088 -> 7355 [arrowhead = none ];
7355 -> 5090;

7356 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5088 -> 7356 [arrowhead = none ];
7356 -> 5091;

7357 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5089 -> 7357 [arrowhead = none ];
7357 -> 5097;

7358 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5089 -> 7358 [arrowhead = none ];
7358 -> 5098;

7359 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5090 -> 7359 [arrowhead = none ];
7359 -> 5092;

7360 [label="EVAL with clause\nquot(s(X8713), s(X8714), X8715, X8716) :- quot(X8713, X8714, X8715, X8716).\nand substitutionX8713 -> T1269,\nT1264 -> s(T1269),\nX8714 -> 0,\nX8715 -> s(s(s(s(s(s(0)))))),\nX8678 -> X8717,\nX8716 -> X8717", fontsize=14, style = filled, fillcolor = lightblue];
5097 -> 7360 [arrowhead = none ];
7360 -> 5107;

7361 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5097 -> 7361 [arrowhead = none ];
7361 -> 5108;

7362 [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 = lightgreen];
5098 -> 7362 [arrowhead = none ];
7362 -> 5131;

7363 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5107 -> 7363 [arrowhead = none ];
7363 -> 5114;

7364 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
5114 -> 7364 [arrowhead = none ];
7364 -> 5115;

7365 [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 = lightgreen];
5115 -> 7365 [arrowhead = none ];
7365 -> 5119;

7366 [label="ONLY EVAL with clause\nquot(X8740, 0, s(X8741), s(X8742)) :- quot(X8740, s(X8741), s(X8741), X8742).\nand substitutionT1269 -> T1273,\nX8740 -> T1273,\nX8741 -> s(s(s(s(s(0))))),\nX8742 -> X8743,\nX8717 -> s(X8743)", fontsize=14, style = filled, fillcolor = lightblue];
5119 -> 7366 [arrowhead = none ];
7366 -> 5125;

7367 [label="INSTANCE with matching:\nT1239 -> T1273\nX8483 -> X8743", fontsize=14, style = filled, fillcolor = lightgrey];
5125 -> 7367 [arrowhead = none , style=dashed];
7367 -> 4921[style=dashed];

7368 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5152 -> 7368 [arrowhead = none ];
7368 -> 5156;

7369 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5156 -> 7369 [arrowhead = none ];
7369 -> 5157;

7370 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5156 -> 7370 [arrowhead = none ];
7370 -> 5158;

7371 [label="EVAL with clause\nquot(0, s(X8790), s(X8791), 0).\nand substitutionT1282 -> 0,\nX8790 -> s(s(s(s(0)))),\nX8791 -> s(s(s(s(0)))),\nX8777 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5157 -> 7371 [arrowhead = none ];
7371 -> 5161;

7372 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5157 -> 7372 [arrowhead = none ];
7372 -> 5162;

7373 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5158 -> 7373 [arrowhead = none ];
7373 -> 5170;

7374 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5158 -> 7374 [arrowhead = none ];
7374 -> 5171;

7375 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5161 -> 7375 [arrowhead = none ];
7375 -> 5163;

7376 [label="EVAL with clause\nquot(s(X8812), s(X8813), X8814, X8815) :- quot(X8812, X8813, X8814, X8815).\nand substitutionX8812 -> T1287,\nT1282 -> s(T1287),\nX8813 -> s(s(s(s(0)))),\nX8814 -> s(s(s(s(s(0))))),\nX8777 -> X8816,\nX8815 -> X8816", fontsize=14, style = filled, fillcolor = lightblue];
5170 -> 7376 [arrowhead = none ];
7376 -> 5180;

7377 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5170 -> 7377 [arrowhead = none ];
7377 -> 5181;

7378 [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 = lightgreen];
5171 -> 7378 [arrowhead = none ];
7378 -> 5328;

7379 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5180 -> 7379 [arrowhead = none ];
7379 -> 5184;

7380 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5184 -> 7380 [arrowhead = none ];
7380 -> 5186;

7381 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5184 -> 7381 [arrowhead = none ];
7381 -> 5187;

7382 [label="EVAL with clause\nquot(0, s(X8829), s(X8830), 0).\nand substitutionT1287 -> 0,\nX8829 -> s(s(s(0))),\nX8830 -> s(s(s(s(0)))),\nX8816 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5186 -> 7382 [arrowhead = none ];
7382 -> 5192;

7383 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5186 -> 7383 [arrowhead = none ];
7383 -> 5193;

7384 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5187 -> 7384 [arrowhead = none ];
7384 -> 5201;

7385 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5187 -> 7385 [arrowhead = none ];
7385 -> 5202;

7386 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5192 -> 7386 [arrowhead = none ];
7386 -> 5194;

7387 [label="EVAL with clause\nquot(s(X8851), s(X8852), X8853, X8854) :- quot(X8851, X8852, X8853, X8854).\nand substitutionX8851 -> T1292,\nT1287 -> s(T1292),\nX8852 -> s(s(s(0))),\nX8853 -> s(s(s(s(s(0))))),\nX8816 -> X8855,\nX8854 -> X8855", fontsize=14, style = filled, fillcolor = lightblue];
5201 -> 7387 [arrowhead = none ];
7387 -> 5208;

7388 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5201 -> 7388 [arrowhead = none ];
7388 -> 5209;

7389 [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 = lightgreen];
5202 -> 7389 [arrowhead = none ];
7389 -> 5325;

7390 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5208 -> 7390 [arrowhead = none ];
7390 -> 5212;

7391 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5212 -> 7391 [arrowhead = none ];
7391 -> 5216;

7392 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5212 -> 7392 [arrowhead = none ];
7392 -> 5217;

7393 [label="EVAL with clause\nquot(0, s(X8868), s(X8869), 0).\nand substitutionT1292 -> 0,\nX8868 -> s(s(0)),\nX8869 -> s(s(s(s(0)))),\nX8855 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5216 -> 7393 [arrowhead = none ];
7393 -> 5223;

7394 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5216 -> 7394 [arrowhead = none ];
7394 -> 5224;

7395 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5217 -> 7395 [arrowhead = none ];
7395 -> 5229;

7396 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5217 -> 7396 [arrowhead = none ];
7396 -> 5230;

7397 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5223 -> 7397 [arrowhead = none ];
7397 -> 5225;

7398 [label="EVAL with clause\nquot(s(X8890), s(X8891), X8892, X8893) :- quot(X8890, X8891, X8892, X8893).\nand substitutionX8890 -> T1297,\nT1292 -> s(T1297),\nX8891 -> s(s(0)),\nX8892 -> s(s(s(s(s(0))))),\nX8855 -> X8894,\nX8893 -> X8894", fontsize=14, style = filled, fillcolor = lightblue];
5229 -> 7398 [arrowhead = none ];
7398 -> 5238;

7399 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5229 -> 7399 [arrowhead = none ];
7399 -> 5239;

7400 [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 = lightgreen];
5230 -> 7400 [arrowhead = none ];
7400 -> 5322;

7401 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5238 -> 7401 [arrowhead = none ];
7401 -> 5244;

7402 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5244 -> 7402 [arrowhead = none ];
7402 -> 5247;

7403 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5244 -> 7403 [arrowhead = none ];
7403 -> 5248;

7404 [label="EVAL with clause\nquot(0, s(X8907), s(X8908), 0).\nand substitutionT1297 -> 0,\nX8907 -> s(0),\nX8908 -> s(s(s(s(0)))),\nX8894 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5247 -> 7404 [arrowhead = none ];
7404 -> 5254;

7405 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5247 -> 7405 [arrowhead = none ];
7405 -> 5255;

7406 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5248 -> 7406 [arrowhead = none ];
7406 -> 5259;

7407 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5248 -> 7407 [arrowhead = none ];
7407 -> 5260;

7408 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5254 -> 7408 [arrowhead = none ];
7408 -> 5256;

7409 [label="EVAL with clause\nquot(s(X8929), s(X8930), X8931, X8932) :- quot(X8929, X8930, X8931, X8932).\nand substitutionX8929 -> T1302,\nT1297 -> s(T1302),\nX8930 -> s(0),\nX8931 -> s(s(s(s(s(0))))),\nX8894 -> X8933,\nX8932 -> X8933", fontsize=14, style = filled, fillcolor = lightblue];
5259 -> 7409 [arrowhead = none ];
7409 -> 5266;

7410 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5259 -> 7410 [arrowhead = none ];
7410 -> 5267;

7411 [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 = lightgreen];
5260 -> 7411 [arrowhead = none ];
7411 -> 5320;

7412 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5266 -> 7412 [arrowhead = none ];
7412 -> 5273;

7413 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5273 -> 7413 [arrowhead = none ];
7413 -> 5280;

7414 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5273 -> 7414 [arrowhead = none ];
7414 -> 5281;

7415 [label="EVAL with clause\nquot(0, s(X8946), s(X8947), 0).\nand substitutionT1302 -> 0,\nX8946 -> 0,\nX8947 -> s(s(s(s(0)))),\nX8933 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5280 -> 7415 [arrowhead = none ];
7415 -> 5282;

7416 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5280 -> 7416 [arrowhead = none ];
7416 -> 5283;

7417 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5281 -> 7417 [arrowhead = none ];
7417 -> 5289;

7418 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5281 -> 7418 [arrowhead = none ];
7418 -> 5290;

7419 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5282 -> 7419 [arrowhead = none ];
7419 -> 5284;

7420 [label="EVAL with clause\nquot(s(X8968), s(X8969), X8970, X8971) :- quot(X8968, X8969, X8970, X8971).\nand substitutionX8968 -> T1307,\nT1302 -> s(T1307),\nX8969 -> 0,\nX8970 -> s(s(s(s(s(0))))),\nX8933 -> X8972,\nX8971 -> X8972", fontsize=14, style = filled, fillcolor = lightblue];
5289 -> 7420 [arrowhead = none ];
7420 -> 5298;

7421 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5289 -> 7421 [arrowhead = none ];
7421 -> 5299;

7422 [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 = lightgreen];
5290 -> 7422 [arrowhead = none ];
7422 -> 5319;

7423 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5298 -> 7423 [arrowhead = none ];
7423 -> 5303;

7424 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
5303 -> 7424 [arrowhead = none ];
7424 -> 5304;

7425 [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 = lightgreen];
5304 -> 7425 [arrowhead = none ];
7425 -> 5308;

7426 [label="ONLY EVAL with clause\nquot(X8995, 0, s(X8996), s(X8997)) :- quot(X8995, s(X8996), s(X8996), X8997).\nand substitutionT1307 -> T1311,\nX8995 -> T1311,\nX8996 -> s(s(s(s(0)))),\nX8997 -> X8998,\nX8972 -> s(X8998)", fontsize=14, style = filled, fillcolor = lightblue];
5308 -> 7426 [arrowhead = none ];
7426 -> 5315;

7427 [label="INSTANCE with matching:\nT1282 -> T1311\nX8777 -> X8998", fontsize=14, style = filled, fillcolor = lightgrey];
5315 -> 7427 [arrowhead = none , style=dashed];
7427 -> 5152[style=dashed];

7428 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5338 -> 7428 [arrowhead = none ];
7428 -> 5344;

7429 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5344 -> 7429 [arrowhead = none ];
7429 -> 5345;

7430 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5344 -> 7430 [arrowhead = none ];
7430 -> 5346;

7431 [label="EVAL with clause\nquot(0, s(X9042), s(X9043), 0).\nand substitutionT1319 -> 0,\nX9042 -> s(s(s(0))),\nX9043 -> s(s(s(0))),\nX9029 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5345 -> 7431 [arrowhead = none ];
7431 -> 5349;

7432 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5345 -> 7432 [arrowhead = none ];
7432 -> 5350;

7433 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5346 -> 7433 [arrowhead = none ];
7433 -> 5357;

7434 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5346 -> 7434 [arrowhead = none ];
7434 -> 5358;

7435 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5349 -> 7435 [arrowhead = none ];
7435 -> 5351;

7436 [label="EVAL with clause\nquot(s(X9064), s(X9065), X9066, X9067) :- quot(X9064, X9065, X9066, X9067).\nand substitutionX9064 -> T1324,\nT1319 -> s(T1324),\nX9065 -> s(s(s(0))),\nX9066 -> s(s(s(s(0)))),\nX9029 -> X9068,\nX9067 -> X9068", fontsize=14, style = filled, fillcolor = lightblue];
5357 -> 7436 [arrowhead = none ];
7436 -> 5365;

7437 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5357 -> 7437 [arrowhead = none ];
7437 -> 5366;

7438 [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 = lightgreen];
5358 -> 7438 [arrowhead = none ];
7438 -> 5485;

7439 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5365 -> 7439 [arrowhead = none ];
7439 -> 5370;

7440 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5370 -> 7440 [arrowhead = none ];
7440 -> 5372;

7441 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5370 -> 7441 [arrowhead = none ];
7441 -> 5373;

7442 [label="EVAL with clause\nquot(0, s(X9081), s(X9082), 0).\nand substitutionT1324 -> 0,\nX9081 -> s(s(0)),\nX9082 -> s(s(s(0))),\nX9068 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5372 -> 7442 [arrowhead = none ];
7442 -> 5378;

7443 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5372 -> 7443 [arrowhead = none ];
7443 -> 5379;

7444 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5373 -> 7444 [arrowhead = none ];
7444 -> 5385;

7445 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5373 -> 7445 [arrowhead = none ];
7445 -> 5386;

7446 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5378 -> 7446 [arrowhead = none ];
7446 -> 5380;

7447 [label="EVAL with clause\nquot(s(X9103), s(X9104), X9105, X9106) :- quot(X9103, X9104, X9105, X9106).\nand substitutionX9103 -> T1329,\nT1324 -> s(T1329),\nX9104 -> s(s(0)),\nX9105 -> s(s(s(s(0)))),\nX9068 -> X9107,\nX9106 -> X9107", fontsize=14, style = filled, fillcolor = lightblue];
5385 -> 7447 [arrowhead = none ];
7447 -> 5397;

7448 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5385 -> 7448 [arrowhead = none ];
7448 -> 5398;

7449 [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 = lightgreen];
5386 -> 7449 [arrowhead = none ];
7449 -> 5484;

7450 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5397 -> 7450 [arrowhead = none ];
7450 -> 5402;

7451 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5402 -> 7451 [arrowhead = none ];
7451 -> 5404;

7452 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5402 -> 7452 [arrowhead = none ];
7452 -> 5405;

7453 [label="EVAL with clause\nquot(0, s(X9120), s(X9121), 0).\nand substitutionT1329 -> 0,\nX9120 -> s(0),\nX9121 -> s(s(s(0))),\nX9107 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5404 -> 7453 [arrowhead = none ];
7453 -> 5409;

7454 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5404 -> 7454 [arrowhead = none ];
7454 -> 5410;

7455 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5405 -> 7455 [arrowhead = none ];
7455 -> 5415;

7456 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5405 -> 7456 [arrowhead = none ];
7456 -> 5416;

7457 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5409 -> 7457 [arrowhead = none ];
7457 -> 5411;

7458 [label="EVAL with clause\nquot(s(X9142), s(X9143), X9144, X9145) :- quot(X9142, X9143, X9144, X9145).\nand substitutionX9142 -> T1334,\nT1329 -> s(T1334),\nX9143 -> s(0),\nX9144 -> s(s(s(s(0)))),\nX9107 -> X9146,\nX9145 -> X9146", fontsize=14, style = filled, fillcolor = lightblue];
5415 -> 7458 [arrowhead = none ];
7458 -> 5423;

7459 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5415 -> 7459 [arrowhead = none ];
7459 -> 5424;

7460 [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 = lightgreen];
5416 -> 7460 [arrowhead = none ];
7460 -> 5480;

7461 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5423 -> 7461 [arrowhead = none ];
7461 -> 5430;

7462 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5430 -> 7462 [arrowhead = none ];
7462 -> 5432;

7463 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5430 -> 7463 [arrowhead = none ];
7463 -> 5433;

7464 [label="EVAL with clause\nquot(0, s(X9159), s(X9160), 0).\nand substitutionT1334 -> 0,\nX9159 -> 0,\nX9160 -> s(s(s(0))),\nX9146 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5432 -> 7464 [arrowhead = none ];
7464 -> 5436;

7465 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5432 -> 7465 [arrowhead = none ];
7465 -> 5437;

7466 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5433 -> 7466 [arrowhead = none ];
7466 -> 5442;

7467 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5433 -> 7467 [arrowhead = none ];
7467 -> 5443;

7468 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5436 -> 7468 [arrowhead = none ];
7468 -> 5438;

7469 [label="EVAL with clause\nquot(s(X9181), s(X9182), X9183, X9184) :- quot(X9181, X9182, X9183, X9184).\nand substitutionX9181 -> T1339,\nT1334 -> s(T1339),\nX9182 -> 0,\nX9183 -> s(s(s(s(0)))),\nX9146 -> X9185,\nX9184 -> X9185", fontsize=14, style = filled, fillcolor = lightblue];
5442 -> 7469 [arrowhead = none ];
7469 -> 5454;

7470 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5442 -> 7470 [arrowhead = none ];
7470 -> 5455;

7471 [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 = lightgreen];
5443 -> 7471 [arrowhead = none ];
7471 -> 5479;

7472 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5454 -> 7472 [arrowhead = none ];
7472 -> 5461;

7473 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
5461 -> 7473 [arrowhead = none ];
7473 -> 5462;

7474 [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 = lightgreen];
5462 -> 7474 [arrowhead = none ];
7474 -> 5465;

7475 [label="ONLY EVAL with clause\nquot(X9208, 0, s(X9209), s(X9210)) :- quot(X9208, s(X9209), s(X9209), X9210).\nand substitutionT1339 -> T1343,\nX9208 -> T1343,\nX9209 -> s(s(s(0))),\nX9210 -> X9211,\nX9185 -> s(X9211)", fontsize=14, style = filled, fillcolor = lightblue];
5465 -> 7475 [arrowhead = none ];
7475 -> 5473;

7476 [label="INSTANCE with matching:\nT1319 -> T1343\nX9029 -> X9211", fontsize=14, style = filled, fillcolor = lightgrey];
5473 -> 7476 [arrowhead = none , style=dashed];
7476 -> 5338[style=dashed];

7477 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5489 -> 7477 [arrowhead = none ];
7477 -> 5495;

7478 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5495 -> 7478 [arrowhead = none ];
7478 -> 5498;

7479 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5495 -> 7479 [arrowhead = none ];
7479 -> 5499;

7480 [label="EVAL with clause\nquot(0, s(X9252), s(X9253), 0).\nand substitutionT1350 -> 0,\nX9252 -> s(s(0)),\nX9253 -> s(s(0)),\nX9239 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5498 -> 7480 [arrowhead = none ];
7480 -> 5500;

7481 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5498 -> 7481 [arrowhead = none ];
7481 -> 5501;

7482 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5499 -> 7482 [arrowhead = none ];
7482 -> 5507;

7483 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5499 -> 7483 [arrowhead = none ];
7483 -> 5508;

7484 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5500 -> 7484 [arrowhead = none ];
7484 -> 5502;

7485 [label="EVAL with clause\nquot(s(X9274), s(X9275), X9276, X9277) :- quot(X9274, X9275, X9276, X9277).\nand substitutionX9274 -> T1355,\nT1350 -> s(T1355),\nX9275 -> s(s(0)),\nX9276 -> s(s(s(0))),\nX9239 -> X9278,\nX9277 -> X9278", fontsize=14, style = filled, fillcolor = lightblue];
5507 -> 7485 [arrowhead = none ];
7485 -> 5518;

7486 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5507 -> 7486 [arrowhead = none ];
7486 -> 5519;

7487 [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 = lightgreen];
5508 -> 7487 [arrowhead = none ];
7487 -> 5575;

7488 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5518 -> 7488 [arrowhead = none ];
7488 -> 5524;

7489 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5524 -> 7489 [arrowhead = none ];
7489 -> 5525;

7490 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5524 -> 7490 [arrowhead = none ];
7490 -> 5526;

7491 [label="EVAL with clause\nquot(0, s(X9291), s(X9292), 0).\nand substitutionT1355 -> 0,\nX9291 -> s(0),\nX9292 -> s(s(0)),\nX9278 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5525 -> 7491 [arrowhead = none ];
7491 -> 5530;

7492 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5525 -> 7492 [arrowhead = none ];
7492 -> 5531;

7493 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5526 -> 7493 [arrowhead = none ];
7493 -> 5541;

7494 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5526 -> 7494 [arrowhead = none ];
7494 -> 5542;

7495 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5530 -> 7495 [arrowhead = none ];
7495 -> 5532;

7496 [label="EVAL with clause\nquot(s(X9313), s(X9314), X9315, X9316) :- quot(X9313, X9314, X9315, X9316).\nand substitutionX9313 -> T1360,\nT1355 -> s(T1360),\nX9314 -> s(0),\nX9315 -> s(s(s(0))),\nX9278 -> X9317,\nX9316 -> X9317", fontsize=14, style = filled, fillcolor = lightblue];
5541 -> 7496 [arrowhead = none ];
7496 -> 5548;

7497 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5541 -> 7497 [arrowhead = none ];
7497 -> 5549;

7498 [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 = lightgreen];
5542 -> 7498 [arrowhead = none ];
7498 -> 5573;

7499 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5548 -> 7499 [arrowhead = none ];
7499 -> 5552;

7500 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5552 -> 7500 [arrowhead = none ];
7500 -> 5553;

7501 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5552 -> 7501 [arrowhead = none ];
7501 -> 5554;

7502 [label="EVAL with clause\nquot(0, s(X9330), s(X9331), 0).\nand substitutionT1360 -> 0,\nX9330 -> 0,\nX9331 -> s(s(0)),\nX9317 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5553 -> 7502 [arrowhead = none ];
7502 -> 5555;

7503 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5553 -> 7503 [arrowhead = none ];
7503 -> 5556;

7504 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5554 -> 7504 [arrowhead = none ];
7504 -> 5558;

7505 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5554 -> 7505 [arrowhead = none ];
7505 -> 5559;

7506 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5555 -> 7506 [arrowhead = none ];
7506 -> 5557;

7507 [label="EVAL with clause\nquot(s(X9352), s(X9353), X9354, X9355) :- quot(X9352, X9353, X9354, X9355).\nand substitutionX9352 -> T1365,\nT1360 -> s(T1365),\nX9353 -> 0,\nX9354 -> s(s(s(0))),\nX9317 -> X9356,\nX9355 -> X9356", fontsize=14, style = filled, fillcolor = lightblue];
5558 -> 7507 [arrowhead = none ];
7507 -> 5562;

7508 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5558 -> 7508 [arrowhead = none ];
7508 -> 5563;

7509 [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 = lightgreen];
5559 -> 7509 [arrowhead = none ];
7509 -> 5572;

7510 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5562 -> 7510 [arrowhead = none ];
7510 -> 5564;

7511 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
5564 -> 7511 [arrowhead = none ];
7511 -> 5565;

7512 [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 = lightgreen];
5565 -> 7512 [arrowhead = none ];
7512 -> 5567;

7513 [label="ONLY EVAL with clause\nquot(X9379, 0, s(X9380), s(X9381)) :- quot(X9379, s(X9380), s(X9380), X9381).\nand substitutionT1365 -> T1369,\nX9379 -> T1369,\nX9380 -> s(s(0)),\nX9381 -> X9382,\nX9356 -> s(X9382)", fontsize=14, style = filled, fillcolor = lightblue];
5567 -> 7513 [arrowhead = none ];
7513 -> 5570;

7514 [label="INSTANCE with matching:\nT1350 -> T1369\nX9239 -> X9382", fontsize=14, style = filled, fillcolor = lightgrey];
5570 -> 7514 [arrowhead = none , style=dashed];
7514 -> 5489[style=dashed];

7515 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5579 -> 7515 [arrowhead = none ];
7515 -> 5583;

7516 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5583 -> 7516 [arrowhead = none ];
7516 -> 5584;

7517 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5583 -> 7517 [arrowhead = none ];
7517 -> 5585;

7518 [label="EVAL with clause\nquot(0, s(X9420), s(X9421), 0).\nand substitutionT1375 -> 0,\nX9420 -> s(0),\nX9421 -> s(0),\nX9407 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5584 -> 7518 [arrowhead = none ];
7518 -> 5589;

7519 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5584 -> 7519 [arrowhead = none ];
7519 -> 5590;

7520 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5585 -> 7520 [arrowhead = none ];
7520 -> 5597;

7521 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5585 -> 7521 [arrowhead = none ];
7521 -> 5598;

7522 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5589 -> 7522 [arrowhead = none ];
7522 -> 5591;

7523 [label="EVAL with clause\nquot(s(X9442), s(X9443), X9444, X9445) :- quot(X9442, X9443, X9444, X9445).\nand substitutionX9442 -> T1380,\nT1375 -> s(T1380),\nX9443 -> s(0),\nX9444 -> s(s(0)),\nX9407 -> X9446,\nX9445 -> X9446", fontsize=14, style = filled, fillcolor = lightblue];
5597 -> 7523 [arrowhead = none ];
7523 -> 5599;

7524 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5597 -> 7524 [arrowhead = none ];
7524 -> 5600;

7525 [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 = lightgreen];
5598 -> 7525 [arrowhead = none ];
7525 -> 5616;

7526 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5599 -> 7526 [arrowhead = none ];
7526 -> 5601;

7527 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5601 -> 7527 [arrowhead = none ];
7527 -> 5602;

7528 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5601 -> 7528 [arrowhead = none ];
7528 -> 5603;

7529 [label="EVAL with clause\nquot(0, s(X9459), s(X9460), 0).\nand substitutionT1380 -> 0,\nX9459 -> 0,\nX9460 -> s(0),\nX9446 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5602 -> 7529 [arrowhead = none ];
7529 -> 5604;

7530 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5602 -> 7530 [arrowhead = none ];
7530 -> 5605;

7531 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5603 -> 7531 [arrowhead = none ];
7531 -> 5607;

7532 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5603 -> 7532 [arrowhead = none ];
7532 -> 5608;

7533 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5604 -> 7533 [arrowhead = none ];
7533 -> 5606;

7534 [label="EVAL with clause\nquot(s(X9481), s(X9482), X9483, X9484) :- quot(X9481, X9482, X9483, X9484).\nand substitutionX9481 -> T1385,\nT1380 -> s(T1385),\nX9482 -> 0,\nX9483 -> s(s(0)),\nX9446 -> X9485,\nX9484 -> X9485", fontsize=14, style = filled, fillcolor = lightblue];
5607 -> 7534 [arrowhead = none ];
7534 -> 5609;

7535 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5607 -> 7535 [arrowhead = none ];
7535 -> 5610;

7536 [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 = lightgreen];
5608 -> 7536 [arrowhead = none ];
7536 -> 5615;

7537 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5609 -> 7537 [arrowhead = none ];
7537 -> 5611;

7538 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
5611 -> 7538 [arrowhead = none ];
7538 -> 5612;

7539 [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 = lightgreen];
5612 -> 7539 [arrowhead = none ];
7539 -> 5613;

7540 [label="ONLY EVAL with clause\nquot(X9508, 0, s(X9509), s(X9510)) :- quot(X9508, s(X9509), s(X9509), X9510).\nand substitutionT1385 -> T1389,\nX9508 -> T1389,\nX9509 -> s(0),\nX9510 -> X9511,\nX9485 -> s(X9511)", fontsize=14, style = filled, fillcolor = lightblue];
5613 -> 7540 [arrowhead = none ];
7540 -> 5614;

7541 [label="INSTANCE with matching:\nT1375 -> T1389\nX9407 -> X9511", fontsize=14, style = filled, fillcolor = lightgrey];
5614 -> 7541 [arrowhead = none , style=dashed];
7541 -> 5579[style=dashed];

7542 [label="INSTANCE with matching:\nT22 -> T954\nT20 -> T950\nX35 -> X7571", fontsize=14, style = filled, fillcolor = lightgrey];
5619 -> 7542 [arrowhead = none , style=dashed];
7542 -> 543[style=dashed];

7543 [label="INSTANCE with matching:\nT216 -> T951\nT217 -> T1396", fontsize=14, style = filled, fillcolor = lightgrey];
5620 -> 7543 [arrowhead = none , style=dashed];
7543 -> 633[style=dashed];

7544 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5621 -> 7544 [arrowhead = none ];
7544 -> 5622;

7545 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5621 -> 7545 [arrowhead = none ];
7545 -> 5623;

7546 [label="EVAL with clause\npr(X9540, s(0)).\nand substitutionT939 -> T1407,\nX9540 -> s(T1407),\nT937 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5622 -> 7546 [arrowhead = none ];
7546 -> 5624;

7547 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5622 -> 7547 [arrowhead = none ];
7547 -> 5625;

7548 [label="EVAL with clause\npr(X9545, s(s(X9546))) :- ','(not_divides(s(s(X9546)), X9545), pr(X9545, s(X9546))).\nand substitutionT939 -> T1412,\nX9545 -> s(T1412),\nX9546 -> T1413,\nT937 -> s(T1413)", fontsize=14, style = filled, fillcolor = lightblue];
5623 -> 7548 [arrowhead = none ];
7548 -> 5627;

7549 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5623 -> 7549 [arrowhead = none ];
7549 -> 5628;

7550 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5624 -> 7550 [arrowhead = none ];
7550 -> 5626;

7551 [label="INSTANCE with matching:\nT937 -> T1413\nT939 -> T1412", fontsize=14, style = filled, fillcolor = lightgrey];
5627 -> 7551 [arrowhead = none , style=dashed];
7551 -> 4200[style=dashed];

}

(2) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(3) 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:

PRIMEA_IN_G(s(s(s(T14)))) → U1_G(T14, pB_in_g(T14))
PRIMEA_IN_G(s(s(s(T14)))) → PB_IN_G(T14)
PB_IN_G(T14) → U81_G(T14, not_dividesN11_in_g(T14))
PB_IN_G(T14) → NOT_DIVIDESN11_IN_G(T14)
NOT_DIVIDESN11_IN_G(T20) → U49_G(T20, pN12_in_gaa(T20, X34, X35))
NOT_DIVIDESN11_IN_G(T20) → PN12_IN_GAA(T20, X34, X35)
PN12_IN_GAA(T20, T22, X35) → U83_GAA(T20, T22, X35, divN15_in_ga(T20, T22))
PN12_IN_GAA(T20, T22, X35) → DIVN15_IN_GA(T20, T22)
DIVN15_IN_GA(s(s(s(s(s(s(T96)))))), X323) → U51_GA(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
DIVN15_IN_GA(s(s(s(s(s(s(T96)))))), X323) → QUOTC_IN_GGA(T96, s(s(s(s(s(s(s(T96))))))), X323)
QUOTC_IN_GGA(s(T111), T112, X358) → U2_GGA(T111, T112, X358, quotC_in_gga(T111, T112, X358))
QUOTC_IN_GGA(s(T111), T112, X358) → QUOTC_IN_GGA(T111, T112, X358)
QUOTC_IN_GGA(0, 0, s(s(X443))) → U3_GGA(X443, quotD_in_a(X443))
QUOTC_IN_GGA(0, 0, s(s(X443))) → QUOTD_IN_A(X443)
DIVN15_IN_GA(s(s(0)), s(X684)) → U52_GA(X684, quotY_in_a(X684))
DIVN15_IN_GA(s(s(0)), s(X684)) → QUOTY_IN_A(X684)
DIVN15_IN_GA(s(0), s(X753)) → U53_GA(X753, quotT_in_a(X753))
DIVN15_IN_GA(s(0), s(X753)) → QUOTT_IN_A(X753)
DIVN15_IN_GA(0, s(X822)) → U54_GA(X822, quotP_in_a(X822))
DIVN15_IN_GA(0, s(X822)) → QUOTP_IN_A(X822)
U83_GAA(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_GAA(T20, T22, X35, pN40_in_gga(T22, T20, X35))
U83_GAA(T20, T22, X35, divN15_out_ga(T20, T22)) → PN40_IN_GGA(T22, T20, X35)
PN40_IN_GGA(T22, T20, T157) → U85_GGA(T22, T20, T157, timesE_in_gga(T22, T20, T157))
PN40_IN_GGA(T22, T20, T157) → TIMESE_IN_GGA(T22, T20, T157)
TIMESE_IN_GGA(s(T169), T170, X908) → U4_GGA(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
TIMESE_IN_GGA(s(T169), T170, X908) → PF_IN_GGAA(T169, T170, X907, X908)
PF_IN_GGAA(T169, T170, T173, X908) → U87_GGAA(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
PF_IN_GGAA(T169, T170, T173, X908) → TIMESE_IN_GGA(T169, T170, T173)
U87_GGAA(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_GGAA(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
U87_GGAA(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → ADDG_IN_GGA(T173, T170, X908)
ADDG_IN_GGA(s(T188), T189, s(X932)) → U5_GGA(T188, T189, X932, addG_in_gga(T188, T189, X932))
ADDG_IN_GGA(s(T188), T189, s(X932)) → ADDG_IN_GGA(T188, T189, X932)
U85_GGA(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_GGA(T22, T20, T157, neqL_in_gg(T20, T157))
U85_GGA(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → NEQL_IN_GG(T20, T157)
NEQL_IN_GG(T216, s(s(T217))) → U10_GG(T216, T217, neqM_in_gg(T216, T217))
NEQL_IN_GG(T216, s(s(T217))) → NEQM_IN_GG(T216, T217)
NEQM_IN_GG(T229, s(T230)) → U48_GG(T229, T230, neqH_in_gg(T229, T230))
NEQM_IN_GG(T229, s(T230)) → NEQH_IN_GG(T229, T230)
NEQH_IN_GG(s(T247), s(T248)) → U6_GG(T247, T248, neqH_in_gg(T247, T248))
NEQH_IN_GG(s(T247), s(T248)) → NEQH_IN_GG(T247, T248)
U81_G(T14, not_dividesN11_out_g(T14)) → U82_G(T14, prN13_in_g(T14))
U81_G(T14, not_dividesN11_out_g(T14)) → PRN13_IN_G(T14)
PRN13_IN_G(s(T263)) → U50_G(T263, pN14_in_g(T263))
PRN13_IN_G(s(T263)) → PN14_IN_G(T263)
PN14_IN_G(T263) → U89_G(T263, not_dividesN16_in_g(T263))
PN14_IN_G(T263) → NOT_DIVIDESN16_IN_G(T263)
NOT_DIVIDESN16_IN_G(T269) → U55_G(T269, pN17_in_gaa(T269, X1030, X1031))
NOT_DIVIDESN16_IN_G(T269) → PN17_IN_GAA(T269, X1030, X1031)
PN17_IN_GAA(T269, T271, X1031) → U91_GAA(T269, T271, X1031, divN20_in_ga(T269, T271))
PN17_IN_GAA(T269, T271, X1031) → DIVN20_IN_GA(T269, T271)
DIVN20_IN_GA(s(s(s(s(s(s(T345)))))), X1319) → U57_GA(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
DIVN20_IN_GA(s(s(s(s(s(s(T345)))))), X1319) → QUOTI_IN_GGA(T345, s(s(s(s(s(s(s(T345))))))), X1319)
QUOTI_IN_GGA(s(T360), T361, X1354) → U7_GGA(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
QUOTI_IN_GGA(s(T360), T361, X1354) → QUOTI_IN_GGA(T360, T361, X1354)
QUOTI_IN_GGA(0, s(0), s(s(X1470))) → U8_GGA(X1470, quotJ_in_a(X1470))
QUOTI_IN_GGA(0, s(0), s(s(X1470))) → QUOTJ_IN_A(X1470)
QUOTI_IN_GGA(0, 0, s(s(X1501))) → U9_GGA(X1501, quotK_in_a(X1501))
QUOTI_IN_GGA(0, 0, s(s(X1501))) → QUOTK_IN_A(X1501)
QUOTK_IN_A(s(X1564)) → U15_A(X1564, quotD_in_a(X1564))
QUOTK_IN_A(s(X1564)) → QUOTD_IN_A(X1564)
DIVN20_IN_GA(s(0), s(X2028)) → U58_GA(X2028, quotZ_in_a(X2028))
DIVN20_IN_GA(s(0), s(X2028)) → QUOTZ_IN_A(X2028)
DIVN20_IN_GA(0, s(X2139)) → U59_GA(X2139, quotU_in_a(X2139))
DIVN20_IN_GA(0, s(X2139)) → QUOTU_IN_A(X2139)
QUOTU_IN_A(s(X2241)) → U21_A(X2241, quotJ_in_a(X2241))
QUOTU_IN_A(s(X2241)) → QUOTJ_IN_A(X2241)
U91_GAA(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_GAA(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
U91_GAA(T269, T271, X1031, divN20_out_ga(T269, T271)) → PN41_IN_GGA(T271, T269, X1031)
PN41_IN_GGA(T271, T269, T407) → U93_GGA(T271, T269, T407, timesE_in_gga(T271, T269, T407))
PN41_IN_GGA(T271, T269, T407) → TIMESE_IN_GGA(T271, T269, T407)
U93_GGA(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_GGA(T271, T269, T407, neqL_in_gg(s(T269), T407))
U93_GGA(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → NEQL_IN_GG(s(T269), T407)
U89_G(T263, not_dividesN16_out_g(T263)) → U90_G(T263, prN18_in_g(T263))
U89_G(T263, not_dividesN16_out_g(T263)) → PRN18_IN_G(T263)
PRN18_IN_G(s(T424)) → U56_G(T424, pN19_in_g(T424))
PRN18_IN_G(s(T424)) → PN19_IN_G(T424)
PN19_IN_G(T424) → U95_G(T424, not_dividesN21_in_g(T424))
PN19_IN_G(T424) → NOT_DIVIDESN21_IN_G(T424)
NOT_DIVIDESN21_IN_G(T430) → U60_G(T430, pN22_in_gaa(T430, X2295, X2296))
NOT_DIVIDESN21_IN_G(T430) → PN22_IN_GAA(T430, X2295, X2296)
PN22_IN_GAA(T430, T432, X2296) → U97_GAA(T430, T432, X2296, divN25_in_ga(T430, T432))
PN22_IN_GAA(T430, T432, X2296) → DIVN25_IN_GA(T430, T432)
DIVN25_IN_GA(s(s(s(s(s(s(T506)))))), X2584) → U62_GA(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
DIVN25_IN_GA(s(s(s(s(s(s(T506)))))), X2584) → QUOTN_IN_GGA(T506, s(s(s(s(s(s(s(T506))))))), X2584)
QUOTN_IN_GGA(s(T521), T522, X2619) → U11_GGA(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
QUOTN_IN_GGA(s(T521), T522, X2619) → QUOTN_IN_GGA(T521, T522, X2619)
QUOTN_IN_GGA(0, s(s(0)), s(s(X2766))) → U12_GGA(X2766, quotO_in_a(X2766))
QUOTN_IN_GGA(0, s(s(0)), s(s(X2766))) → QUOTO_IN_A(X2766)
QUOTN_IN_GGA(0, s(0), s(s(X2797))) → U13_GGA(X2797, quotP_in_a(X2797))
QUOTN_IN_GGA(0, s(0), s(s(X2797))) → QUOTP_IN_A(X2797)
QUOTN_IN_GGA(0, 0, s(s(X2813))) → U14_GGA(X2813, quotQ_in_a(X2813))
QUOTN_IN_GGA(0, 0, s(s(X2813))) → QUOTQ_IN_A(X2813)
QUOTQ_IN_A(s(X2878)) → U22_A(X2878, quotK_in_a(X2878))
QUOTQ_IN_A(s(X2878)) → QUOTK_IN_A(X2878)
DIVN25_IN_GA(s(0), s(s(X3653))) → U63_GA(X3653, quotO_in_a(X3653))
DIVN25_IN_GA(s(0), s(s(X3653))) → QUOTO_IN_A(X3653)
DIVN25_IN_GA(0, s(X3676)) → U64_GA(X3676, quotN1_in_a(X3676))
DIVN25_IN_GA(0, s(X3676)) → QUOTN1_IN_A(X3676)
QUOTN1_IN_A(s(X3780)) → U29_A(X3780, quotP_in_a(X3780))
QUOTN1_IN_A(s(X3780)) → QUOTP_IN_A(X3780)
U97_GAA(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_GAA(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
U97_GAA(T430, T432, X2296, divN25_out_ga(T430, T432)) → PN42_IN_GGA(T432, T430, X2296)
PN42_IN_GGA(T432, T430, T573) → U99_GGA(T432, T430, T573, timesE_in_gga(T432, T430, T573))
PN42_IN_GGA(T432, T430, T573) → TIMESE_IN_GGA(T432, T430, T573)
U99_GGA(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_GGA(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U99_GGA(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → NEQL_IN_GG(s(s(T430)), T573)
U95_G(T424, not_dividesN21_out_g(T424)) → U96_G(T424, prN23_in_g(T424))
U95_G(T424, not_dividesN21_out_g(T424)) → PRN23_IN_G(T424)
PRN23_IN_G(s(T590)) → U61_G(T590, pN24_in_g(T590))
PRN23_IN_G(s(T590)) → PN24_IN_G(T590)
PN24_IN_G(T590) → U101_G(T590, not_dividesN26_in_g(T590))
PN24_IN_G(T590) → NOT_DIVIDESN26_IN_G(T590)
NOT_DIVIDESN26_IN_G(T596) → U65_G(T596, pN27_in_gaa(T596, X3836, X3837))
NOT_DIVIDESN26_IN_G(T596) → PN27_IN_GAA(T596, X3836, X3837)
PN27_IN_GAA(T596, T598, X3837) → U103_GAA(T596, T598, X3837, divN30_in_ga(T596, T598))
PN27_IN_GAA(T596, T598, X3837) → DIVN30_IN_GA(T596, T598)
DIVN30_IN_GA(s(s(s(s(s(s(T672)))))), X4125) → U67_GA(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
DIVN30_IN_GA(s(s(s(s(s(s(T672)))))), X4125) → QUOTR_IN_GGA(T672, s(s(s(s(s(s(s(T672))))))), X4125)
QUOTR_IN_GGA(s(T687), T688, X4160) → U16_GGA(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
QUOTR_IN_GGA(s(T687), T688, X4160) → QUOTR_IN_GGA(T687, T688, X4160)
QUOTR_IN_GGA(0, s(s(s(0))), s(s(X4338))) → U17_GGA(X4338, quotS_in_a(X4338))
QUOTR_IN_GGA(0, s(s(s(0))), s(s(X4338))) → QUOTS_IN_A(X4338)
QUOTR_IN_GGA(0, s(s(0)), s(s(X4369))) → U18_GGA(X4369, quotT_in_a(X4369))
QUOTR_IN_GGA(0, s(s(0)), s(s(X4369))) → QUOTT_IN_A(X4369)
QUOTR_IN_GGA(0, s(0), s(s(X4385))) → U19_GGA(X4385, quotU_in_a(X4385))
QUOTR_IN_GGA(0, s(0), s(s(X4385))) → QUOTU_IN_A(X4385)
QUOTR_IN_GGA(0, 0, s(s(X4401))) → U20_GGA(X4401, quotV_in_a(X4401))
QUOTR_IN_GGA(0, 0, s(s(X4401))) → QUOTV_IN_A(X4401)
QUOTV_IN_A(s(X4466)) → U30_A(X4466, quotQ_in_a(X4466))
QUOTV_IN_A(s(X4466)) → QUOTQ_IN_A(X4466)
DIVN30_IN_GA(s(s(0)), s(s(X5253))) → U68_GA(X5253, quotS_in_a(X5253))
DIVN30_IN_GA(s(s(0)), s(s(X5253))) → QUOTS_IN_A(X5253)
DIVN30_IN_GA(s(0), s(s(X5422))) → U69_GA(X5422, quotT_in_a(X5422))
DIVN30_IN_GA(s(0), s(s(X5422))) → QUOTT_IN_A(X5422)
DIVN30_IN_GA(0, s(s(X5551))) → U70_GA(X5551, quotU_in_a(X5551))
DIVN30_IN_GA(0, s(s(X5551))) → QUOTU_IN_A(X5551)
U103_GAA(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_GAA(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
U103_GAA(T596, T598, X3837, divN30_out_ga(T596, T598)) → PN43_IN_GGA(T598, T596, X3837)
PN43_IN_GGA(T598, T596, T744) → U105_GGA(T598, T596, T744, timesE_in_gga(T598, T596, T744))
PN43_IN_GGA(T598, T596, T744) → TIMESE_IN_GGA(T598, T596, T744)
U105_GGA(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_GGA(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U105_GGA(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → NEQL_IN_GG(s(s(s(T596))), T744)
U101_G(T590, not_dividesN26_out_g(T590)) → U102_G(T590, prN28_in_g(T590))
U101_G(T590, not_dividesN26_out_g(T590)) → PRN28_IN_G(T590)
PRN28_IN_G(s(T761)) → U66_G(T761, pN29_in_g(T761))
PRN28_IN_G(s(T761)) → PN29_IN_G(T761)
PN29_IN_G(T761) → U107_G(T761, not_dividesN31_in_g(T761))
PN29_IN_G(T761) → NOT_DIVIDESN31_IN_G(T761)
NOT_DIVIDESN31_IN_G(T767) → U71_G(T767, pN32_in_gaa(T767, X5607, X5608))
NOT_DIVIDESN31_IN_G(T767) → PN32_IN_GAA(T767, X5607, X5608)
PN32_IN_GAA(T767, T769, X5608) → U109_GAA(T767, T769, X5608, divN35_in_ga(T767, T769))
PN32_IN_GAA(T767, T769, X5608) → DIVN35_IN_GA(T767, T769)
DIVN35_IN_GA(s(s(s(s(s(s(T843)))))), X5896) → U73_GA(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
DIVN35_IN_GA(s(s(s(s(s(s(T843)))))), X5896) → QUOTW_IN_GGA(T843, s(s(s(s(s(s(s(T843))))))), X5896)
QUOTW_IN_GGA(s(T858), T859, X5931) → U23_GGA(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
QUOTW_IN_GGA(s(T858), T859, X5931) → QUOTW_IN_GGA(T858, T859, X5931)
QUOTW_IN_GGA(0, s(s(s(s(0)))), s(s(X6140))) → U24_GGA(X6140, quotX_in_a(X6140))
QUOTW_IN_GGA(0, s(s(s(s(0)))), s(s(X6140))) → QUOTX_IN_A(X6140)
QUOTW_IN_GGA(0, s(s(s(0))), s(s(X6171))) → U25_GGA(X6171, quotY_in_a(X6171))
QUOTW_IN_GGA(0, s(s(s(0))), s(s(X6171))) → QUOTY_IN_A(X6171)
QUOTW_IN_GGA(0, s(s(0)), s(s(X6187))) → U26_GGA(X6187, quotZ_in_a(X6187))
QUOTW_IN_GGA(0, s(s(0)), s(s(X6187))) → QUOTZ_IN_A(X6187)
QUOTW_IN_GGA(0, s(0), s(s(X6203))) → U27_GGA(X6203, quotN1_in_a(X6203))
QUOTW_IN_GGA(0, s(0), s(s(X6203))) → QUOTN1_IN_A(X6203)
QUOTW_IN_GGA(0, 0, s(s(s(X6284)))) → U28_GGA(X6284, quotV_in_a(X6284))
QUOTW_IN_GGA(0, 0, s(s(s(X6284)))) → QUOTV_IN_A(X6284)
DIVN35_IN_GA(s(s(s(0))), s(s(X6999))) → U74_GA(X6999, quotX_in_a(X6999))
DIVN35_IN_GA(s(s(s(0))), s(s(X6999))) → QUOTX_IN_A(X6999)
DIVN35_IN_GA(s(s(0)), s(s(X7210))) → U75_GA(X7210, quotY_in_a(X7210))
DIVN35_IN_GA(s(s(0)), s(s(X7210))) → QUOTY_IN_A(X7210)
DIVN35_IN_GA(s(0), s(s(X7381))) → U76_GA(X7381, quotZ_in_a(X7381))
DIVN35_IN_GA(s(0), s(s(X7381))) → QUOTZ_IN_A(X7381)
DIVN35_IN_GA(0, s(s(X7510))) → U77_GA(X7510, quotN1_in_a(X7510))
DIVN35_IN_GA(0, s(s(X7510))) → QUOTN1_IN_A(X7510)
U109_GAA(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_GAA(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
U109_GAA(T767, T769, X5608, divN35_out_ga(T767, T769)) → PN44_IN_GGA(T769, T767, X5608)
PN44_IN_GGA(T769, T767, T920) → U111_GGA(T769, T767, T920, timesE_in_gga(T769, T767, T920))
PN44_IN_GGA(T769, T767, T920) → TIMESE_IN_GGA(T769, T767, T920)
U111_GGA(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_GGA(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U111_GGA(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → NEQL_IN_GG(s(s(s(s(T767)))), T920)
U107_G(T761, not_dividesN31_out_g(T761)) → U108_G(T761, prN33_in_g(T761))
U107_G(T761, not_dividesN31_out_g(T761)) → PRN33_IN_G(T761)
PRN33_IN_G(s(T937)) → U72_G(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
PRN33_IN_G(s(T937)) → PN34_IN_GG(T937, s(s(s(s(s(s(s(T937))))))))
PN34_IN_GG(T937, T939) → U113_GG(T937, T939, not_dividesN36_in_gg(T937, T939))
PN34_IN_GG(T937, T939) → NOT_DIVIDESN36_IN_GG(T937, T939)
NOT_DIVIDESN36_IN_GG(T950, T951) → U78_GG(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
NOT_DIVIDESN36_IN_GG(T950, T951) → PN37_IN_GGAA(T951, T950, X7570, X7571)
PN37_IN_GGAA(T951, T950, T954, X7571) → U115_GGAA(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
PN37_IN_GGAA(T951, T950, T954, X7571) → DIVN39_IN_GGA(T951, T950, T954)
DIVN39_IN_GGA(s(T992), T993, X7673) → U80_GGA(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
DIVN39_IN_GGA(s(T992), T993, X7673) → QUOTN3_IN_GGA(T992, T993, X7673)
QUOTN3_IN_GGA(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_GGA(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
QUOTN3_IN_GGA(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → QUOTN2_IN_GGGA(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)
QUOTN2_IN_GGGA(s(T1125), s(T1126), T1127, X7950) → U31_GGGA(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
QUOTN2_IN_GGGA(s(T1125), s(T1126), T1127, X7950) → QUOTN2_IN_GGGA(T1125, T1126, T1127, X7950)
QUOTN2_IN_GGGA(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_GGGA(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
QUOTN2_IN_GGGA(s(s(T1170)), 0, s(T1171), s(X8044)) → QUOTN3_IN_GGA(T1170, T1171, X8044)
QUOTN3_IN_GGA(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_GGA(T1190, X8147, quotN5_in_ga(T1190, X8147))
QUOTN3_IN_GGA(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → QUOTN5_IN_GA(T1190, X8147)
QUOTN5_IN_GA(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_GA(T1229, X8446, quotN5_in_ga(T1229, X8446))
QUOTN5_IN_GA(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → QUOTN5_IN_GA(T1229, X8446)
QUOTN3_IN_GGA(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_GGA(T1239, X8483, quotN6_in_ga(T1239, X8483))
QUOTN3_IN_GGA(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → QUOTN6_IN_GA(T1239, X8483)
QUOTN6_IN_GA(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_GA(T1273, X8743, quotN6_in_ga(T1273, X8743))
QUOTN6_IN_GA(s(s(s(s(s(s(T1273)))))), s(X8743)) → QUOTN6_IN_GA(T1273, X8743)
QUOTN3_IN_GGA(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_GGA(T1282, X8777, quotN7_in_ga(T1282, X8777))
QUOTN3_IN_GGA(s(s(s(T1282))), s(s(s(0))), s(X8777)) → QUOTN7_IN_GA(T1282, X8777)
QUOTN7_IN_GA(s(s(s(s(s(T1311))))), s(X8998)) → U44_GA(T1311, X8998, quotN7_in_ga(T1311, X8998))
QUOTN7_IN_GA(s(s(s(s(s(T1311))))), s(X8998)) → QUOTN7_IN_GA(T1311, X8998)
QUOTN3_IN_GGA(s(s(T1319)), s(s(0)), s(X9029)) → U38_GGA(T1319, X9029, quotN8_in_ga(T1319, X9029))
QUOTN3_IN_GGA(s(s(T1319)), s(s(0)), s(X9029)) → QUOTN8_IN_GA(T1319, X9029)
QUOTN8_IN_GA(s(s(s(s(T1343)))), s(X9211)) → U45_GA(T1343, X9211, quotN8_in_ga(T1343, X9211))
QUOTN8_IN_GA(s(s(s(s(T1343)))), s(X9211)) → QUOTN8_IN_GA(T1343, X9211)
QUOTN3_IN_GGA(s(T1350), s(0), s(X9239)) → U39_GGA(T1350, X9239, quotN9_in_ga(T1350, X9239))
QUOTN3_IN_GGA(s(T1350), s(0), s(X9239)) → QUOTN9_IN_GA(T1350, X9239)
QUOTN9_IN_GA(s(s(s(T1369))), s(X9382)) → U46_GA(T1369, X9382, quotN9_in_ga(T1369, X9382))
QUOTN9_IN_GA(s(s(s(T1369))), s(X9382)) → QUOTN9_IN_GA(T1369, X9382)
QUOTN3_IN_GGA(T1375, 0, s(X9407)) → U40_GGA(T1375, X9407, quotN10_in_ga(T1375, X9407))
QUOTN3_IN_GGA(T1375, 0, s(X9407)) → QUOTN10_IN_GA(T1375, X9407)
QUOTN10_IN_GA(s(s(T1389)), s(X9511)) → U47_GA(T1389, X9511, quotN10_in_ga(T1389, X9511))
QUOTN10_IN_GA(s(s(T1389)), s(X9511)) → QUOTN10_IN_GA(T1389, X9511)
QUOTN2_IN_GGGA(s(T1176), 0, 0, s(s(X8060))) → U33_GGGA(T1176, X8060, quotN4_in_ga(T1176, X8060))
QUOTN2_IN_GGGA(s(T1176), 0, 0, s(s(X8060))) → QUOTN4_IN_GA(T1176, X8060)
QUOTN4_IN_GA(s(T1185), s(X8125)) → U41_GA(T1185, X8125, quotN4_in_ga(T1185, X8125))
QUOTN4_IN_GA(s(T1185), s(X8125)) → QUOTN4_IN_GA(T1185, X8125)
U115_GGAA(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_GGAA(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
U115_GGAA(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → PN45_IN_GGAG(T954, T950, X7571, T951)
PN45_IN_GGAG(T954, T950, T1396, T951) → U117_GGAG(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
PN45_IN_GGAG(T954, T950, T1396, T951) → TIMESE_IN_GGA(T954, T950, T1396)
U117_GGAG(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_GGAG(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U117_GGAG(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → NEQM_IN_GG(T951, T1396)
U113_GG(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_GG(T937, T939, prN38_in_gg(T939, T937))
U113_GG(T937, T939, not_dividesN36_out_gg(T937, T939)) → PRN38_IN_GG(T939, T937)
PRN38_IN_GG(T1412, s(T1413)) → U79_GG(T1412, T1413, pN34_in_gg(T1413, T1412))
PRN38_IN_GG(T1412, s(T1413)) → PN34_IN_GG(T1413, T1412)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

The argument filtering Pi contains the following mapping:
primeA_in_g(x1) = primeA_in_g(x1)
s(x1) = s(x1)
0 = 0
primeA_out_g(x1) = primeA_out_g(x1)
U1_g(x1, x2) = U1_g(x1, x2)
pB_in_g(x1) = pB_in_g(x1)
U81_g(x1, x2) = U81_g(x1, x2)
not_dividesN11_in_g(x1) = not_dividesN11_in_g(x1)
U49_g(x1, x2) = U49_g(x1, x2)
pN12_in_gaa(x1, x2, x3) = pN12_in_gaa(x1)
U83_gaa(x1, x2, x3, x4) = U83_gaa(x1, x4)
divN15_in_ga(x1, x2) = divN15_in_ga(x1)
U51_ga(x1, x2, x3) = U51_ga(x1, x3)
quotC_in_gga(x1, x2, x3) = quotC_in_gga(x1, x2)
U2_gga(x1, x2, x3, x4) = U2_gga(x1, x2, x4)
quotC_out_gga(x1, x2, x3) = quotC_out_gga(x1, x2, x3)
U3_gga(x1, x2) = U3_gga(x2)
quotD_in_a(x1) = quotD_in_a
quotD_out_a(x1) = quotD_out_a(x1)
divN15_out_ga(x1, x2) = divN15_out_ga(x1, x2)
U52_ga(x1, x2) = U52_ga(x2)
quotY_in_a(x1) = quotY_in_a
quotY_out_a(x1) = quotY_out_a(x1)
U53_ga(x1, x2) = U53_ga(x2)
quotT_in_a(x1) = quotT_in_a
quotT_out_a(x1) = quotT_out_a(x1)
U54_ga(x1, x2) = U54_ga(x2)
quotP_in_a(x1) = quotP_in_a
quotP_out_a(x1) = quotP_out_a(x1)
U84_gaa(x1, x2, x3, x4) = U84_gaa(x1, x2, x4)
pN40_in_gga(x1, x2, x3) = pN40_in_gga(x1, x2)
U85_gga(x1, x2, x3, x4) = U85_gga(x1, x2, x4)
timesE_in_gga(x1, x2, x3) = timesE_in_gga(x1, x2)
timesE_out_gga(x1, x2, x3) = timesE_out_gga(x1, x2, x3)
U4_gga(x1, x2, x3, x4) = U4_gga(x1, x2, x4)
pF_in_ggaa(x1, x2, x3, x4) = pF_in_ggaa(x1, x2)
U87_ggaa(x1, x2, x3, x4, x5) = U87_ggaa(x1, x2, x5)
U88_ggaa(x1, x2, x3, x4, x5) = U88_ggaa(x1, x2, x3, x5)
addG_in_gga(x1, x2, x3) = addG_in_gga(x1, x2)
addG_out_gga(x1, x2, x3) = addG_out_gga(x1, x2, x3)
U5_gga(x1, x2, x3, x4) = U5_gga(x1, x2, x4)
pF_out_ggaa(x1, x2, x3, x4) = pF_out_ggaa(x1, x2, x3, x4)
U86_gga(x1, x2, x3, x4) = U86_gga(x1, x2, x3, x4)
neqL_in_gg(x1, x2) = neqL_in_gg(x1, x2)
neqL_out_gg(x1, x2) = neqL_out_gg(x1, x2)
U10_gg(x1, x2, x3) = U10_gg(x1, x2, x3)
neqM_in_gg(x1, x2) = neqM_in_gg(x1, x2)
neqM_out_gg(x1, x2) = neqM_out_gg(x1, x2)
U48_gg(x1, x2, x3) = U48_gg(x1, x2, x3)
neqH_in_gg(x1, x2) = neqH_in_gg(x1, x2)
neqH_out_gg(x1, x2) = neqH_out_gg(x1, x2)
U6_gg(x1, x2, x3) = U6_gg(x1, x2, x3)
pN40_out_gga(x1, x2, x3) = pN40_out_gga(x1, x2, x3)
pN12_out_gaa(x1, x2, x3) = pN12_out_gaa(x1, x2, x3)
not_dividesN11_out_g(x1) = not_dividesN11_out_g(x1)
U82_g(x1, x2) = U82_g(x1, x2)
prN13_in_g(x1) = prN13_in_g(x1)
prN13_out_g(x1) = prN13_out_g(x1)
U50_g(x1, x2) = U50_g(x1, x2)
pN14_in_g(x1) = pN14_in_g(x1)
U89_g(x1, x2) = U89_g(x1, x2)
not_dividesN16_in_g(x1) = not_dividesN16_in_g(x1)
U55_g(x1, x2) = U55_g(x1, x2)
pN17_in_gaa(x1, x2, x3) = pN17_in_gaa(x1)
U91_gaa(x1, x2, x3, x4) = U91_gaa(x1, x4)
divN20_in_ga(x1, x2) = divN20_in_ga(x1)
U57_ga(x1, x2, x3) = U57_ga(x1, x3)
quotI_in_gga(x1, x2, x3) = quotI_in_gga(x1, x2)
U7_gga(x1, x2, x3, x4) = U7_gga(x1, x2, x4)
quotI_out_gga(x1, x2, x3) = quotI_out_gga(x1, x2, x3)
U8_gga(x1, x2) = U8_gga(x2)
quotJ_in_a(x1) = quotJ_in_a
quotJ_out_a(x1) = quotJ_out_a(x1)
U9_gga(x1, x2) = U9_gga(x2)
quotK_in_a(x1) = quotK_in_a
U15_a(x1, x2) = U15_a(x2)
quotK_out_a(x1) = quotK_out_a(x1)
divN20_out_ga(x1, x2) = divN20_out_ga(x1, x2)
U58_ga(x1, x2) = U58_ga(x2)
quotZ_in_a(x1) = quotZ_in_a
quotZ_out_a(x1) = quotZ_out_a(x1)
U59_ga(x1, x2) = U59_ga(x2)
quotU_in_a(x1) = quotU_in_a
U21_a(x1, x2) = U21_a(x2)
quotU_out_a(x1) = quotU_out_a(x1)
U92_gaa(x1, x2, x3, x4) = U92_gaa(x1, x2, x4)
pN41_in_gga(x1, x2, x3) = pN41_in_gga(x1, x2)
U93_gga(x1, x2, x3, x4) = U93_gga(x1, x2, x4)
U94_gga(x1, x2, x3, x4) = U94_gga(x1, x2, x3, x4)
pN41_out_gga(x1, x2, x3) = pN41_out_gga(x1, x2, x3)
pN17_out_gaa(x1, x2, x3) = pN17_out_gaa(x1, x2, x3)
not_dividesN16_out_g(x1) = not_dividesN16_out_g(x1)
U90_g(x1, x2) = U90_g(x1, x2)
prN18_in_g(x1) = prN18_in_g(x1)
prN18_out_g(x1) = prN18_out_g(x1)
U56_g(x1, x2) = U56_g(x1, x2)
pN19_in_g(x1) = pN19_in_g(x1)
U95_g(x1, x2) = U95_g(x1, x2)
not_dividesN21_in_g(x1) = not_dividesN21_in_g(x1)
U60_g(x1, x2) = U60_g(x1, x2)
pN22_in_gaa(x1, x2, x3) = pN22_in_gaa(x1)
U97_gaa(x1, x2, x3, x4) = U97_gaa(x1, x4)
divN25_in_ga(x1, x2) = divN25_in_ga(x1)
U62_ga(x1, x2, x3) = U62_ga(x1, x3)
quotN_in_gga(x1, x2, x3) = quotN_in_gga(x1, x2)
U11_gga(x1, x2, x3, x4) = U11_gga(x1, x2, x4)
quotN_out_gga(x1, x2, x3) = quotN_out_gga(x1, x2, x3)
U12_gga(x1, x2) = U12_gga(x2)
quotO_in_a(x1) = quotO_in_a
quotO_out_a(x1) = quotO_out_a(x1)
U13_gga(x1, x2) = U13_gga(x2)
U14_gga(x1, x2) = U14_gga(x2)
quotQ_in_a(x1) = quotQ_in_a
U22_a(x1, x2) = U22_a(x2)
quotQ_out_a(x1) = quotQ_out_a(x1)
divN25_out_ga(x1, x2) = divN25_out_ga(x1, x2)
U63_ga(x1, x2) = U63_ga(x2)
U64_ga(x1, x2) = U64_ga(x2)
quotN1_in_a(x1) = quotN1_in_a
U29_a(x1, x2) = U29_a(x2)
quotN1_out_a(x1) = quotN1_out_a(x1)
U98_gaa(x1, x2, x3, x4) = U98_gaa(x1, x2, x4)
pN42_in_gga(x1, x2, x3) = pN42_in_gga(x1, x2)
U99_gga(x1, x2, x3, x4) = U99_gga(x1, x2, x4)
U100_gga(x1, x2, x3, x4) = U100_gga(x1, x2, x3, x4)
pN42_out_gga(x1, x2, x3) = pN42_out_gga(x1, x2, x3)
pN22_out_gaa(x1, x2, x3) = pN22_out_gaa(x1, x2, x3)
not_dividesN21_out_g(x1) = not_dividesN21_out_g(x1)
U96_g(x1, x2) = U96_g(x1, x2)
prN23_in_g(x1) = prN23_in_g(x1)
prN23_out_g(x1) = prN23_out_g(x1)
U61_g(x1, x2) = U61_g(x1, x2)
pN24_in_g(x1) = pN24_in_g(x1)
U101_g(x1, x2) = U101_g(x1, x2)
not_dividesN26_in_g(x1) = not_dividesN26_in_g(x1)
U65_g(x1, x2) = U65_g(x1, x2)
pN27_in_gaa(x1, x2, x3) = pN27_in_gaa(x1)
U103_gaa(x1, x2, x3, x4) = U103_gaa(x1, x4)
divN30_in_ga(x1, x2) = divN30_in_ga(x1)
U67_ga(x1, x2, x3) = U67_ga(x1, x3)
quotR_in_gga(x1, x2, x3) = quotR_in_gga(x1, x2)
U16_gga(x1, x2, x3, x4) = U16_gga(x1, x2, x4)
quotR_out_gga(x1, x2, x3) = quotR_out_gga(x1, x2, x3)
U17_gga(x1, x2) = U17_gga(x2)
quotS_in_a(x1) = quotS_in_a
quotS_out_a(x1) = quotS_out_a(x1)
U18_gga(x1, x2) = U18_gga(x2)
U19_gga(x1, x2) = U19_gga(x2)
U20_gga(x1, x2) = U20_gga(x2)
quotV_in_a(x1) = quotV_in_a
U30_a(x1, x2) = U30_a(x2)
quotV_out_a(x1) = quotV_out_a(x1)
divN30_out_ga(x1, x2) = divN30_out_ga(x1, x2)
U68_ga(x1, x2) = U68_ga(x2)
U69_ga(x1, x2) = U69_ga(x2)
U70_ga(x1, x2) = U70_ga(x2)
U104_gaa(x1, x2, x3, x4) = U104_gaa(x1, x2, x4)
pN43_in_gga(x1, x2, x3) = pN43_in_gga(x1, x2)
U105_gga(x1, x2, x3, x4) = U105_gga(x1, x2, x4)
U106_gga(x1, x2, x3, x4) = U106_gga(x1, x2, x3, x4)
pN43_out_gga(x1, x2, x3) = pN43_out_gga(x1, x2, x3)
pN27_out_gaa(x1, x2, x3) = pN27_out_gaa(x1, x2, x3)
not_dividesN26_out_g(x1) = not_dividesN26_out_g(x1)
U102_g(x1, x2) = U102_g(x1, x2)
prN28_in_g(x1) = prN28_in_g(x1)
prN28_out_g(x1) = prN28_out_g(x1)
U66_g(x1, x2) = U66_g(x1, x2)
pN29_in_g(x1) = pN29_in_g(x1)
U107_g(x1, x2) = U107_g(x1, x2)
not_dividesN31_in_g(x1) = not_dividesN31_in_g(x1)
U71_g(x1, x2) = U71_g(x1, x2)
pN32_in_gaa(x1, x2, x3) = pN32_in_gaa(x1)
U109_gaa(x1, x2, x3, x4) = U109_gaa(x1, x4)
divN35_in_ga(x1, x2) = divN35_in_ga(x1)
U73_ga(x1, x2, x3) = U73_ga(x1, x3)
quotW_in_gga(x1, x2, x3) = quotW_in_gga(x1, x2)
U23_gga(x1, x2, x3, x4) = U23_gga(x1, x2, x4)
quotW_out_gga(x1, x2, x3) = quotW_out_gga(x1, x2, x3)
U24_gga(x1, x2) = U24_gga(x2)
quotX_in_a(x1) = quotX_in_a
quotX_out_a(x1) = quotX_out_a(x1)
U25_gga(x1, x2) = U25_gga(x2)
U26_gga(x1, x2) = U26_gga(x2)
U27_gga(x1, x2) = U27_gga(x2)
U28_gga(x1, x2) = U28_gga(x2)
divN35_out_ga(x1, x2) = divN35_out_ga(x1, x2)
U74_ga(x1, x2) = U74_ga(x2)
U75_ga(x1, x2) = U75_ga(x2)
U76_ga(x1, x2) = U76_ga(x2)
U77_ga(x1, x2) = U77_ga(x2)
U110_gaa(x1, x2, x3, x4) = U110_gaa(x1, x2, x4)
pN44_in_gga(x1, x2, x3) = pN44_in_gga(x1, x2)
U111_gga(x1, x2, x3, x4) = U111_gga(x1, x2, x4)
U112_gga(x1, x2, x3, x4) = U112_gga(x1, x2, x3, x4)
pN44_out_gga(x1, x2, x3) = pN44_out_gga(x1, x2, x3)
pN32_out_gaa(x1, x2, x3) = pN32_out_gaa(x1, x2, x3)
not_dividesN31_out_g(x1) = not_dividesN31_out_g(x1)
U108_g(x1, x2) = U108_g(x1, x2)
prN33_in_g(x1) = prN33_in_g(x1)
prN33_out_g(x1) = prN33_out_g(x1)
U72_g(x1, x2) = U72_g(x1, x2)
pN34_in_gg(x1, x2) = pN34_in_gg(x1, x2)
U113_gg(x1, x2, x3) = U113_gg(x1, x2, x3)
not_dividesN36_in_gg(x1, x2) = not_dividesN36_in_gg(x1, x2)
U78_gg(x1, x2, x3) = U78_gg(x1, x2, x3)
pN37_in_ggaa(x1, x2, x3, x4) = pN37_in_ggaa(x1, x2)
U115_ggaa(x1, x2, x3, x4, x5) = U115_ggaa(x1, x2, x5)
divN39_in_gga(x1, x2, x3) = divN39_in_gga(x1, x2)
divN39_out_gga(x1, x2, x3) = divN39_out_gga(x1, x2, x3)
U80_gga(x1, x2, x3, x4) = U80_gga(x1, x2, x4)
quotN3_in_gga(x1, x2, x3) = quotN3_in_gga(x1, x2)
quotN3_out_gga(x1, x2, x3) = quotN3_out_gga(x1, x2, x3)
U34_gga(x1, x2, x3, x4) = U34_gga(x1, x2, x4)
quotN2_in_ggga(x1, x2, x3, x4) = quotN2_in_ggga(x1, x2, x3)
quotN2_out_ggga(x1, x2, x3, x4) = quotN2_out_ggga(x1, x2, x3, x4)
U31_ggga(x1, x2, x3, x4, x5) = U31_ggga(x1, x2, x3, x5)
U32_ggga(x1, x2, x3, x4) = U32_ggga(x1, x2, x4)
U35_gga(x1, x2, x3) = U35_gga(x1, x3)
quotN5_in_ga(x1, x2) = quotN5_in_ga(x1)
quotN5_out_ga(x1, x2) = quotN5_out_ga(x1, x2)
U42_ga(x1, x2, x3) = U42_ga(x1, x3)
U36_gga(x1, x2, x3) = U36_gga(x1, x3)
quotN6_in_ga(x1, x2) = quotN6_in_ga(x1)
quotN6_out_ga(x1, x2) = quotN6_out_ga(x1, x2)
U43_ga(x1, x2, x3) = U43_ga(x1, x3)
U37_gga(x1, x2, x3) = U37_gga(x1, x3)
quotN7_in_ga(x1, x2) = quotN7_in_ga(x1)
quotN7_out_ga(x1, x2) = quotN7_out_ga(x1, x2)
U44_ga(x1, x2, x3) = U44_ga(x1, x3)
U38_gga(x1, x2, x3) = U38_gga(x1, x3)
quotN8_in_ga(x1, x2) = quotN8_in_ga(x1)
quotN8_out_ga(x1, x2) = quotN8_out_ga(x1, x2)
U45_ga(x1, x2, x3) = U45_ga(x1, x3)
U39_gga(x1, x2, x3) = U39_gga(x1, x3)
quotN9_in_ga(x1, x2) = quotN9_in_ga(x1)
quotN9_out_ga(x1, x2) = quotN9_out_ga(x1, x2)
U46_ga(x1, x2, x3) = U46_ga(x1, x3)
U40_gga(x1, x2, x3) = U40_gga(x1, x3)
quotN10_in_ga(x1, x2) = quotN10_in_ga(x1)
quotN10_out_ga(x1, x2) = quotN10_out_ga(x1, x2)
U47_ga(x1, x2, x3) = U47_ga(x1, x3)
U33_ggga(x1, x2, x3) = U33_ggga(x1, x3)
quotN4_in_ga(x1, x2) = quotN4_in_ga(x1)
quotN4_out_ga(x1, x2) = quotN4_out_ga(x1, x2)
U41_ga(x1, x2, x3) = U41_ga(x1, x3)
U116_ggaa(x1, x2, x3, x4, x5) = U116_ggaa(x1, x2, x3, x5)
pN45_in_ggag(x1, x2, x3, x4) = pN45_in_ggag(x1, x2, x4)
U117_ggag(x1, x2, x3, x4, x5) = U117_ggag(x1, x2, x4, x5)
U118_ggag(x1, x2, x3, x4, x5) = U118_ggag(x1, x2, x3, x4, x5)
pN45_out_ggag(x1, x2, x3, x4) = pN45_out_ggag(x1, x2, x3, x4)
pN37_out_ggaa(x1, x2, x3, x4) = pN37_out_ggaa(x1, x2, x3, x4)
not_dividesN36_out_gg(x1, x2) = not_dividesN36_out_gg(x1, x2)
U114_gg(x1, x2, x3) = U114_gg(x1, x2, x3)
prN38_in_gg(x1, x2) = prN38_in_gg(x1, x2)
prN38_out_gg(x1, x2) = prN38_out_gg(x1, x2)
U79_gg(x1, x2, x3) = U79_gg(x1, x2, x3)
pN34_out_gg(x1, x2) = pN34_out_gg(x1, x2)
pN29_out_g(x1) = pN29_out_g(x1)
pN24_out_g(x1) = pN24_out_g(x1)
pN19_out_g(x1) = pN19_out_g(x1)
pN14_out_g(x1) = pN14_out_g(x1)
pB_out_g(x1) = pB_out_g(x1)
PRIMEA_IN_G(x1) = PRIMEA_IN_G(x1)
U1_G(x1, x2) = U1_G(x1, x2)
PB_IN_G(x1) = PB_IN_G(x1)
U81_G(x1, x2) = U81_G(x1, x2)
NOT_DIVIDESN11_IN_G(x1) = NOT_DIVIDESN11_IN_G(x1)
U49_G(x1, x2) = U49_G(x1, x2)
PN12_IN_GAA(x1, x2, x3) = PN12_IN_GAA(x1)
U83_GAA(x1, x2, x3, x4) = U83_GAA(x1, x4)
DIVN15_IN_GA(x1, x2) = DIVN15_IN_GA(x1)
U51_GA(x1, x2, x3) = U51_GA(x1, x3)
QUOTC_IN_GGA(x1, x2, x3) = QUOTC_IN_GGA(x1, x2)
U2_GGA(x1, x2, x3, x4) = U2_GGA(x1, x2, x4)
U3_GGA(x1, x2) = U3_GGA(x2)
QUOTD_IN_A(x1) = QUOTD_IN_A
U52_GA(x1, x2) = U52_GA(x2)
QUOTY_IN_A(x1) = QUOTY_IN_A
U53_GA(x1, x2) = U53_GA(x2)
QUOTT_IN_A(x1) = QUOTT_IN_A
U54_GA(x1, x2) = U54_GA(x2)
QUOTP_IN_A(x1) = QUOTP_IN_A
U84_GAA(x1, x2, x3, x4) = U84_GAA(x1, x2, x4)
PN40_IN_GGA(x1, x2, x3) = PN40_IN_GGA(x1, x2)
U85_GGA(x1, x2, x3, x4) = U85_GGA(x1, x2, x4)
TIMESE_IN_GGA(x1, x2, x3) = TIMESE_IN_GGA(x1, x2)
U4_GGA(x1, x2, x3, x4) = U4_GGA(x1, x2, x4)
PF_IN_GGAA(x1, x2, x3, x4) = PF_IN_GGAA(x1, x2)
U87_GGAA(x1, x2, x3, x4, x5) = U87_GGAA(x1, x2, x5)
U88_GGAA(x1, x2, x3, x4, x5) = U88_GGAA(x1, x2, x3, x5)
ADDG_IN_GGA(x1, x2, x3) = ADDG_IN_GGA(x1, x2)
U5_GGA(x1, x2, x3, x4) = U5_GGA(x1, x2, x4)
U86_GGA(x1, x2, x3, x4) = U86_GGA(x1, x2, x3, x4)
NEQL_IN_GG(x1, x2) = NEQL_IN_GG(x1, x2)
U10_GG(x1, x2, x3) = U10_GG(x1, x2, x3)
NEQM_IN_GG(x1, x2) = NEQM_IN_GG(x1, x2)
U48_GG(x1, x2, x3) = U48_GG(x1, x2, x3)
NEQH_IN_GG(x1, x2) = NEQH_IN_GG(x1, x2)
U6_GG(x1, x2, x3) = U6_GG(x1, x2, x3)
U82_G(x1, x2) = U82_G(x1, x2)
PRN13_IN_G(x1) = PRN13_IN_G(x1)
U50_G(x1, x2) = U50_G(x1, x2)
PN14_IN_G(x1) = PN14_IN_G(x1)
U89_G(x1, x2) = U89_G(x1, x2)
NOT_DIVIDESN16_IN_G(x1) = NOT_DIVIDESN16_IN_G(x1)
U55_G(x1, x2) = U55_G(x1, x2)
PN17_IN_GAA(x1, x2, x3) = PN17_IN_GAA(x1)
U91_GAA(x1, x2, x3, x4) = U91_GAA(x1, x4)
DIVN20_IN_GA(x1, x2) = DIVN20_IN_GA(x1)
U57_GA(x1, x2, x3) = U57_GA(x1, x3)
QUOTI_IN_GGA(x1, x2, x3) = QUOTI_IN_GGA(x1, x2)
U7_GGA(x1, x2, x3, x4) = U7_GGA(x1, x2, x4)
U8_GGA(x1, x2) = U8_GGA(x2)
QUOTJ_IN_A(x1) = QUOTJ_IN_A
U9_GGA(x1, x2) = U9_GGA(x2)
QUOTK_IN_A(x1) = QUOTK_IN_A
U15_A(x1, x2) = U15_A(x2)
U58_GA(x1, x2) = U58_GA(x2)
QUOTZ_IN_A(x1) = QUOTZ_IN_A
U59_GA(x1, x2) = U59_GA(x2)
QUOTU_IN_A(x1) = QUOTU_IN_A
U21_A(x1, x2) = U21_A(x2)
U92_GAA(x1, x2, x3, x4) = U92_GAA(x1, x2, x4)
PN41_IN_GGA(x1, x2, x3) = PN41_IN_GGA(x1, x2)
U93_GGA(x1, x2, x3, x4) = U93_GGA(x1, x2, x4)
U94_GGA(x1, x2, x3, x4) = U94_GGA(x1, x2, x3, x4)
U90_G(x1, x2) = U90_G(x1, x2)
PRN18_IN_G(x1) = PRN18_IN_G(x1)
U56_G(x1, x2) = U56_G(x1, x2)
PN19_IN_G(x1) = PN19_IN_G(x1)
U95_G(x1, x2) = U95_G(x1, x2)
NOT_DIVIDESN21_IN_G(x1) = NOT_DIVIDESN21_IN_G(x1)
U60_G(x1, x2) = U60_G(x1, x2)
PN22_IN_GAA(x1, x2, x3) = PN22_IN_GAA(x1)
U97_GAA(x1, x2, x3, x4) = U97_GAA(x1, x4)
DIVN25_IN_GA(x1, x2) = DIVN25_IN_GA(x1)
U62_GA(x1, x2, x3) = U62_GA(x1, x3)
QUOTN_IN_GGA(x1, x2, x3) = QUOTN_IN_GGA(x1, x2)
U11_GGA(x1, x2, x3, x4) = U11_GGA(x1, x2, x4)
U12_GGA(x1, x2) = U12_GGA(x2)
QUOTO_IN_A(x1) = QUOTO_IN_A
U13_GGA(x1, x2) = U13_GGA(x2)
U14_GGA(x1, x2) = U14_GGA(x2)
QUOTQ_IN_A(x1) = QUOTQ_IN_A
U22_A(x1, x2) = U22_A(x2)
U63_GA(x1, x2) = U63_GA(x2)
U64_GA(x1, x2) = U64_GA(x2)
QUOTN1_IN_A(x1) = QUOTN1_IN_A
U29_A(x1, x2) = U29_A(x2)
U98_GAA(x1, x2, x3, x4) = U98_GAA(x1, x2, x4)
PN42_IN_GGA(x1, x2, x3) = PN42_IN_GGA(x1, x2)
U99_GGA(x1, x2, x3, x4) = U99_GGA(x1, x2, x4)
U100_GGA(x1, x2, x3, x4) = U100_GGA(x1, x2, x3, x4)
U96_G(x1, x2) = U96_G(x1, x2)
PRN23_IN_G(x1) = PRN23_IN_G(x1)
U61_G(x1, x2) = U61_G(x1, x2)
PN24_IN_G(x1) = PN24_IN_G(x1)
U101_G(x1, x2) = U101_G(x1, x2)
NOT_DIVIDESN26_IN_G(x1) = NOT_DIVIDESN26_IN_G(x1)
U65_G(x1, x2) = U65_G(x1, x2)
PN27_IN_GAA(x1, x2, x3) = PN27_IN_GAA(x1)
U103_GAA(x1, x2, x3, x4) = U103_GAA(x1, x4)
DIVN30_IN_GA(x1, x2) = DIVN30_IN_GA(x1)
U67_GA(x1, x2, x3) = U67_GA(x1, x3)
QUOTR_IN_GGA(x1, x2, x3) = QUOTR_IN_GGA(x1, x2)
U16_GGA(x1, x2, x3, x4) = U16_GGA(x1, x2, x4)
U17_GGA(x1, x2) = U17_GGA(x2)
QUOTS_IN_A(x1) = QUOTS_IN_A
U18_GGA(x1, x2) = U18_GGA(x2)
U19_GGA(x1, x2) = U19_GGA(x2)
U20_GGA(x1, x2) = U20_GGA(x2)
QUOTV_IN_A(x1) = QUOTV_IN_A
U30_A(x1, x2) = U30_A(x2)
U68_GA(x1, x2) = U68_GA(x2)
U69_GA(x1, x2) = U69_GA(x2)
U70_GA(x1, x2) = U70_GA(x2)
U104_GAA(x1, x2, x3, x4) = U104_GAA(x1, x2, x4)
PN43_IN_GGA(x1, x2, x3) = PN43_IN_GGA(x1, x2)
U105_GGA(x1, x2, x3, x4) = U105_GGA(x1, x2, x4)
U106_GGA(x1, x2, x3, x4) = U106_GGA(x1, x2, x3, x4)
U102_G(x1, x2) = U102_G(x1, x2)
PRN28_IN_G(x1) = PRN28_IN_G(x1)
U66_G(x1, x2) = U66_G(x1, x2)
PN29_IN_G(x1) = PN29_IN_G(x1)
U107_G(x1, x2) = U107_G(x1, x2)
NOT_DIVIDESN31_IN_G(x1) = NOT_DIVIDESN31_IN_G(x1)
U71_G(x1, x2) = U71_G(x1, x2)
PN32_IN_GAA(x1, x2, x3) = PN32_IN_GAA(x1)
U109_GAA(x1, x2, x3, x4) = U109_GAA(x1, x4)
DIVN35_IN_GA(x1, x2) = DIVN35_IN_GA(x1)
U73_GA(x1, x2, x3) = U73_GA(x1, x3)
QUOTW_IN_GGA(x1, x2, x3) = QUOTW_IN_GGA(x1, x2)
U23_GGA(x1, x2, x3, x4) = U23_GGA(x1, x2, x4)
U24_GGA(x1, x2) = U24_GGA(x2)
QUOTX_IN_A(x1) = QUOTX_IN_A
U25_GGA(x1, x2) = U25_GGA(x2)
U26_GGA(x1, x2) = U26_GGA(x2)
U27_GGA(x1, x2) = U27_GGA(x2)
U28_GGA(x1, x2) = U28_GGA(x2)
U74_GA(x1, x2) = U74_GA(x2)
U75_GA(x1, x2) = U75_GA(x2)
U76_GA(x1, x2) = U76_GA(x2)
U77_GA(x1, x2) = U77_GA(x2)
U110_GAA(x1, x2, x3, x4) = U110_GAA(x1, x2, x4)
PN44_IN_GGA(x1, x2, x3) = PN44_IN_GGA(x1, x2)
U111_GGA(x1, x2, x3, x4) = U111_GGA(x1, x2, x4)
U112_GGA(x1, x2, x3, x4) = U112_GGA(x1, x2, x3, x4)
U108_G(x1, x2) = U108_G(x1, x2)
PRN33_IN_G(x1) = PRN33_IN_G(x1)
U72_G(x1, x2) = U72_G(x1, x2)
PN34_IN_GG(x1, x2) = PN34_IN_GG(x1, x2)
U113_GG(x1, x2, x3) = U113_GG(x1, x2, x3)
NOT_DIVIDESN36_IN_GG(x1, x2) = NOT_DIVIDESN36_IN_GG(x1, x2)
U78_GG(x1, x2, x3) = U78_GG(x1, x2, x3)
PN37_IN_GGAA(x1, x2, x3, x4) = PN37_IN_GGAA(x1, x2)
U115_GGAA(x1, x2, x3, x4, x5) = U115_GGAA(x1, x2, x5)
DIVN39_IN_GGA(x1, x2, x3) = DIVN39_IN_GGA(x1, x2)
U80_GGA(x1, x2, x3, x4) = U80_GGA(x1, x2, x4)
QUOTN3_IN_GGA(x1, x2, x3) = QUOTN3_IN_GGA(x1, x2)
U34_GGA(x1, x2, x3, x4) = U34_GGA(x1, x2, x4)
QUOTN2_IN_GGGA(x1, x2, x3, x4) = QUOTN2_IN_GGGA(x1, x2, x3)
U31_GGGA(x1, x2, x3, x4, x5) = U31_GGGA(x1, x2, x3, x5)
U32_GGGA(x1, x2, x3, x4) = U32_GGGA(x1, x2, x4)
U35_GGA(x1, x2, x3) = U35_GGA(x1, x3)
QUOTN5_IN_GA(x1, x2) = QUOTN5_IN_GA(x1)
U42_GA(x1, x2, x3) = U42_GA(x1, x3)
U36_GGA(x1, x2, x3) = U36_GGA(x1, x3)
QUOTN6_IN_GA(x1, x2) = QUOTN6_IN_GA(x1)
U43_GA(x1, x2, x3) = U43_GA(x1, x3)
U37_GGA(x1, x2, x3) = U37_GGA(x1, x3)
QUOTN7_IN_GA(x1, x2) = QUOTN7_IN_GA(x1)
U44_GA(x1, x2, x3) = U44_GA(x1, x3)
U38_GGA(x1, x2, x3) = U38_GGA(x1, x3)
QUOTN8_IN_GA(x1, x2) = QUOTN8_IN_GA(x1)
U45_GA(x1, x2, x3) = U45_GA(x1, x3)
U39_GGA(x1, x2, x3) = U39_GGA(x1, x3)
QUOTN9_IN_GA(x1, x2) = QUOTN9_IN_GA(x1)
U46_GA(x1, x2, x3) = U46_GA(x1, x3)
U40_GGA(x1, x2, x3) = U40_GGA(x1, x3)
QUOTN10_IN_GA(x1, x2) = QUOTN10_IN_GA(x1)
U47_GA(x1, x2, x3) = U47_GA(x1, x3)
U33_GGGA(x1, x2, x3) = U33_GGGA(x1, x3)
QUOTN4_IN_GA(x1, x2) = QUOTN4_IN_GA(x1)
U41_GA(x1, x2, x3) = U41_GA(x1, x3)
U116_GGAA(x1, x2, x3, x4, x5) = U116_GGAA(x1, x2, x3, x5)
PN45_IN_GGAG(x1, x2, x3, x4) = PN45_IN_GGAG(x1, x2, x4)
U117_GGAG(x1, x2, x3, x4, x5) = U117_GGAG(x1, x2, x4, x5)
U118_GGAG(x1, x2, x3, x4, x5) = U118_GGAG(x1, x2, x3, x4, x5)
U114_GG(x1, x2, x3) = U114_GG(x1, x2, x3)
PRN38_IN_GG(x1, x2) = PRN38_IN_GG(x1, x2)
U79_GG(x1, x2, x3) = U79_GG(x1, x2, x3)

We have to consider all (P,R,Pi)-chains

(4) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

PRIMEA_IN_G(s(s(s(T14)))) → U1_G(T14, pB_in_g(T14))
PRIMEA_IN_G(s(s(s(T14)))) → PB_IN_G(T14)
PB_IN_G(T14) → U81_G(T14, not_dividesN11_in_g(T14))
PB_IN_G(T14) → NOT_DIVIDESN11_IN_G(T14)
NOT_DIVIDESN11_IN_G(T20) → U49_G(T20, pN12_in_gaa(T20, X34, X35))
NOT_DIVIDESN11_IN_G(T20) → PN12_IN_GAA(T20, X34, X35)
PN12_IN_GAA(T20, T22, X35) → U83_GAA(T20, T22, X35, divN15_in_ga(T20, T22))
PN12_IN_GAA(T20, T22, X35) → DIVN15_IN_GA(T20, T22)
DIVN15_IN_GA(s(s(s(s(s(s(T96)))))), X323) → U51_GA(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
DIVN15_IN_GA(s(s(s(s(s(s(T96)))))), X323) → QUOTC_IN_GGA(T96, s(s(s(s(s(s(s(T96))))))), X323)
QUOTC_IN_GGA(s(T111), T112, X358) → U2_GGA(T111, T112, X358, quotC_in_gga(T111, T112, X358))
QUOTC_IN_GGA(s(T111), T112, X358) → QUOTC_IN_GGA(T111, T112, X358)
QUOTC_IN_GGA(0, 0, s(s(X443))) → U3_GGA(X443, quotD_in_a(X443))
QUOTC_IN_GGA(0, 0, s(s(X443))) → QUOTD_IN_A(X443)
DIVN15_IN_GA(s(s(0)), s(X684)) → U52_GA(X684, quotY_in_a(X684))
DIVN15_IN_GA(s(s(0)), s(X684)) → QUOTY_IN_A(X684)
DIVN15_IN_GA(s(0), s(X753)) → U53_GA(X753, quotT_in_a(X753))
DIVN15_IN_GA(s(0), s(X753)) → QUOTT_IN_A(X753)
DIVN15_IN_GA(0, s(X822)) → U54_GA(X822, quotP_in_a(X822))
DIVN15_IN_GA(0, s(X822)) → QUOTP_IN_A(X822)
U83_GAA(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_GAA(T20, T22, X35, pN40_in_gga(T22, T20, X35))
U83_GAA(T20, T22, X35, divN15_out_ga(T20, T22)) → PN40_IN_GGA(T22, T20, X35)
PN40_IN_GGA(T22, T20, T157) → U85_GGA(T22, T20, T157, timesE_in_gga(T22, T20, T157))
PN40_IN_GGA(T22, T20, T157) → TIMESE_IN_GGA(T22, T20, T157)
TIMESE_IN_GGA(s(T169), T170, X908) → U4_GGA(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
TIMESE_IN_GGA(s(T169), T170, X908) → PF_IN_GGAA(T169, T170, X907, X908)
PF_IN_GGAA(T169, T170, T173, X908) → U87_GGAA(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
PF_IN_GGAA(T169, T170, T173, X908) → TIMESE_IN_GGA(T169, T170, T173)
U87_GGAA(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_GGAA(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
U87_GGAA(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → ADDG_IN_GGA(T173, T170, X908)
ADDG_IN_GGA(s(T188), T189, s(X932)) → U5_GGA(T188, T189, X932, addG_in_gga(T188, T189, X932))
ADDG_IN_GGA(s(T188), T189, s(X932)) → ADDG_IN_GGA(T188, T189, X932)
U85_GGA(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_GGA(T22, T20, T157, neqL_in_gg(T20, T157))
U85_GGA(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → NEQL_IN_GG(T20, T157)
NEQL_IN_GG(T216, s(s(T217))) → U10_GG(T216, T217, neqM_in_gg(T216, T217))
NEQL_IN_GG(T216, s(s(T217))) → NEQM_IN_GG(T216, T217)
NEQM_IN_GG(T229, s(T230)) → U48_GG(T229, T230, neqH_in_gg(T229, T230))
NEQM_IN_GG(T229, s(T230)) → NEQH_IN_GG(T229, T230)
NEQH_IN_GG(s(T247), s(T248)) → U6_GG(T247, T248, neqH_in_gg(T247, T248))
NEQH_IN_GG(s(T247), s(T248)) → NEQH_IN_GG(T247, T248)
U81_G(T14, not_dividesN11_out_g(T14)) → U82_G(T14, prN13_in_g(T14))
U81_G(T14, not_dividesN11_out_g(T14)) → PRN13_IN_G(T14)
PRN13_IN_G(s(T263)) → U50_G(T263, pN14_in_g(T263))
PRN13_IN_G(s(T263)) → PN14_IN_G(T263)
PN14_IN_G(T263) → U89_G(T263, not_dividesN16_in_g(T263))
PN14_IN_G(T263) → NOT_DIVIDESN16_IN_G(T263)
NOT_DIVIDESN16_IN_G(T269) → U55_G(T269, pN17_in_gaa(T269, X1030, X1031))
NOT_DIVIDESN16_IN_G(T269) → PN17_IN_GAA(T269, X1030, X1031)
PN17_IN_GAA(T269, T271, X1031) → U91_GAA(T269, T271, X1031, divN20_in_ga(T269, T271))
PN17_IN_GAA(T269, T271, X1031) → DIVN20_IN_GA(T269, T271)
DIVN20_IN_GA(s(s(s(s(s(s(T345)))))), X1319) → U57_GA(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
DIVN20_IN_GA(s(s(s(s(s(s(T345)))))), X1319) → QUOTI_IN_GGA(T345, s(s(s(s(s(s(s(T345))))))), X1319)
QUOTI_IN_GGA(s(T360), T361, X1354) → U7_GGA(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
QUOTI_IN_GGA(s(T360), T361, X1354) → QUOTI_IN_GGA(T360, T361, X1354)
QUOTI_IN_GGA(0, s(0), s(s(X1470))) → U8_GGA(X1470, quotJ_in_a(X1470))
QUOTI_IN_GGA(0, s(0), s(s(X1470))) → QUOTJ_IN_A(X1470)
QUOTI_IN_GGA(0, 0, s(s(X1501))) → U9_GGA(X1501, quotK_in_a(X1501))
QUOTI_IN_GGA(0, 0, s(s(X1501))) → QUOTK_IN_A(X1501)
QUOTK_IN_A(s(X1564)) → U15_A(X1564, quotD_in_a(X1564))
QUOTK_IN_A(s(X1564)) → QUOTD_IN_A(X1564)
DIVN20_IN_GA(s(0), s(X2028)) → U58_GA(X2028, quotZ_in_a(X2028))
DIVN20_IN_GA(s(0), s(X2028)) → QUOTZ_IN_A(X2028)
DIVN20_IN_GA(0, s(X2139)) → U59_GA(X2139, quotU_in_a(X2139))
DIVN20_IN_GA(0, s(X2139)) → QUOTU_IN_A(X2139)
QUOTU_IN_A(s(X2241)) → U21_A(X2241, quotJ_in_a(X2241))
QUOTU_IN_A(s(X2241)) → QUOTJ_IN_A(X2241)
U91_GAA(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_GAA(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
U91_GAA(T269, T271, X1031, divN20_out_ga(T269, T271)) → PN41_IN_GGA(T271, T269, X1031)
PN41_IN_GGA(T271, T269, T407) → U93_GGA(T271, T269, T407, timesE_in_gga(T271, T269, T407))
PN41_IN_GGA(T271, T269, T407) → TIMESE_IN_GGA(T271, T269, T407)
U93_GGA(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_GGA(T271, T269, T407, neqL_in_gg(s(T269), T407))
U93_GGA(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → NEQL_IN_GG(s(T269), T407)
U89_G(T263, not_dividesN16_out_g(T263)) → U90_G(T263, prN18_in_g(T263))
U89_G(T263, not_dividesN16_out_g(T263)) → PRN18_IN_G(T263)
PRN18_IN_G(s(T424)) → U56_G(T424, pN19_in_g(T424))
PRN18_IN_G(s(T424)) → PN19_IN_G(T424)
PN19_IN_G(T424) → U95_G(T424, not_dividesN21_in_g(T424))
PN19_IN_G(T424) → NOT_DIVIDESN21_IN_G(T424)
NOT_DIVIDESN21_IN_G(T430) → U60_G(T430, pN22_in_gaa(T430, X2295, X2296))
NOT_DIVIDESN21_IN_G(T430) → PN22_IN_GAA(T430, X2295, X2296)
PN22_IN_GAA(T430, T432, X2296) → U97_GAA(T430, T432, X2296, divN25_in_ga(T430, T432))
PN22_IN_GAA(T430, T432, X2296) → DIVN25_IN_GA(T430, T432)
DIVN25_IN_GA(s(s(s(s(s(s(T506)))))), X2584) → U62_GA(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
DIVN25_IN_GA(s(s(s(s(s(s(T506)))))), X2584) → QUOTN_IN_GGA(T506, s(s(s(s(s(s(s(T506))))))), X2584)
QUOTN_IN_GGA(s(T521), T522, X2619) → U11_GGA(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
QUOTN_IN_GGA(s(T521), T522, X2619) → QUOTN_IN_GGA(T521, T522, X2619)
QUOTN_IN_GGA(0, s(s(0)), s(s(X2766))) → U12_GGA(X2766, quotO_in_a(X2766))
QUOTN_IN_GGA(0, s(s(0)), s(s(X2766))) → QUOTO_IN_A(X2766)
QUOTN_IN_GGA(0, s(0), s(s(X2797))) → U13_GGA(X2797, quotP_in_a(X2797))
QUOTN_IN_GGA(0, s(0), s(s(X2797))) → QUOTP_IN_A(X2797)
QUOTN_IN_GGA(0, 0, s(s(X2813))) → U14_GGA(X2813, quotQ_in_a(X2813))
QUOTN_IN_GGA(0, 0, s(s(X2813))) → QUOTQ_IN_A(X2813)
QUOTQ_IN_A(s(X2878)) → U22_A(X2878, quotK_in_a(X2878))
QUOTQ_IN_A(s(X2878)) → QUOTK_IN_A(X2878)
DIVN25_IN_GA(s(0), s(s(X3653))) → U63_GA(X3653, quotO_in_a(X3653))
DIVN25_IN_GA(s(0), s(s(X3653))) → QUOTO_IN_A(X3653)
DIVN25_IN_GA(0, s(X3676)) → U64_GA(X3676, quotN1_in_a(X3676))
DIVN25_IN_GA(0, s(X3676)) → QUOTN1_IN_A(X3676)
QUOTN1_IN_A(s(X3780)) → U29_A(X3780, quotP_in_a(X3780))
QUOTN1_IN_A(s(X3780)) → QUOTP_IN_A(X3780)
U97_GAA(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_GAA(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
U97_GAA(T430, T432, X2296, divN25_out_ga(T430, T432)) → PN42_IN_GGA(T432, T430, X2296)
PN42_IN_GGA(T432, T430, T573) → U99_GGA(T432, T430, T573, timesE_in_gga(T432, T430, T573))
PN42_IN_GGA(T432, T430, T573) → TIMESE_IN_GGA(T432, T430, T573)
U99_GGA(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_GGA(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U99_GGA(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → NEQL_IN_GG(s(s(T430)), T573)
U95_G(T424, not_dividesN21_out_g(T424)) → U96_G(T424, prN23_in_g(T424))
U95_G(T424, not_dividesN21_out_g(T424)) → PRN23_IN_G(T424)
PRN23_IN_G(s(T590)) → U61_G(T590, pN24_in_g(T590))
PRN23_IN_G(s(T590)) → PN24_IN_G(T590)
PN24_IN_G(T590) → U101_G(T590, not_dividesN26_in_g(T590))
PN24_IN_G(T590) → NOT_DIVIDESN26_IN_G(T590)
NOT_DIVIDESN26_IN_G(T596) → U65_G(T596, pN27_in_gaa(T596, X3836, X3837))
NOT_DIVIDESN26_IN_G(T596) → PN27_IN_GAA(T596, X3836, X3837)
PN27_IN_GAA(T596, T598, X3837) → U103_GAA(T596, T598, X3837, divN30_in_ga(T596, T598))
PN27_IN_GAA(T596, T598, X3837) → DIVN30_IN_GA(T596, T598)
DIVN30_IN_GA(s(s(s(s(s(s(T672)))))), X4125) → U67_GA(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
DIVN30_IN_GA(s(s(s(s(s(s(T672)))))), X4125) → QUOTR_IN_GGA(T672, s(s(s(s(s(s(s(T672))))))), X4125)
QUOTR_IN_GGA(s(T687), T688, X4160) → U16_GGA(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
QUOTR_IN_GGA(s(T687), T688, X4160) → QUOTR_IN_GGA(T687, T688, X4160)
QUOTR_IN_GGA(0, s(s(s(0))), s(s(X4338))) → U17_GGA(X4338, quotS_in_a(X4338))
QUOTR_IN_GGA(0, s(s(s(0))), s(s(X4338))) → QUOTS_IN_A(X4338)
QUOTR_IN_GGA(0, s(s(0)), s(s(X4369))) → U18_GGA(X4369, quotT_in_a(X4369))
QUOTR_IN_GGA(0, s(s(0)), s(s(X4369))) → QUOTT_IN_A(X4369)
QUOTR_IN_GGA(0, s(0), s(s(X4385))) → U19_GGA(X4385, quotU_in_a(X4385))
QUOTR_IN_GGA(0, s(0), s(s(X4385))) → QUOTU_IN_A(X4385)
QUOTR_IN_GGA(0, 0, s(s(X4401))) → U20_GGA(X4401, quotV_in_a(X4401))
QUOTR_IN_GGA(0, 0, s(s(X4401))) → QUOTV_IN_A(X4401)
QUOTV_IN_A(s(X4466)) → U30_A(X4466, quotQ_in_a(X4466))
QUOTV_IN_A(s(X4466)) → QUOTQ_IN_A(X4466)
DIVN30_IN_GA(s(s(0)), s(s(X5253))) → U68_GA(X5253, quotS_in_a(X5253))
DIVN30_IN_GA(s(s(0)), s(s(X5253))) → QUOTS_IN_A(X5253)
DIVN30_IN_GA(s(0), s(s(X5422))) → U69_GA(X5422, quotT_in_a(X5422))
DIVN30_IN_GA(s(0), s(s(X5422))) → QUOTT_IN_A(X5422)
DIVN30_IN_GA(0, s(s(X5551))) → U70_GA(X5551, quotU_in_a(X5551))
DIVN30_IN_GA(0, s(s(X5551))) → QUOTU_IN_A(X5551)
U103_GAA(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_GAA(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
U103_GAA(T596, T598, X3837, divN30_out_ga(T596, T598)) → PN43_IN_GGA(T598, T596, X3837)
PN43_IN_GGA(T598, T596, T744) → U105_GGA(T598, T596, T744, timesE_in_gga(T598, T596, T744))
PN43_IN_GGA(T598, T596, T744) → TIMESE_IN_GGA(T598, T596, T744)
U105_GGA(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_GGA(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U105_GGA(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → NEQL_IN_GG(s(s(s(T596))), T744)
U101_G(T590, not_dividesN26_out_g(T590)) → U102_G(T590, prN28_in_g(T590))
U101_G(T590, not_dividesN26_out_g(T590)) → PRN28_IN_G(T590)
PRN28_IN_G(s(T761)) → U66_G(T761, pN29_in_g(T761))
PRN28_IN_G(s(T761)) → PN29_IN_G(T761)
PN29_IN_G(T761) → U107_G(T761, not_dividesN31_in_g(T761))
PN29_IN_G(T761) → NOT_DIVIDESN31_IN_G(T761)
NOT_DIVIDESN31_IN_G(T767) → U71_G(T767, pN32_in_gaa(T767, X5607, X5608))
NOT_DIVIDESN31_IN_G(T767) → PN32_IN_GAA(T767, X5607, X5608)
PN32_IN_GAA(T767, T769, X5608) → U109_GAA(T767, T769, X5608, divN35_in_ga(T767, T769))
PN32_IN_GAA(T767, T769, X5608) → DIVN35_IN_GA(T767, T769)
DIVN35_IN_GA(s(s(s(s(s(s(T843)))))), X5896) → U73_GA(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
DIVN35_IN_GA(s(s(s(s(s(s(T843)))))), X5896) → QUOTW_IN_GGA(T843, s(s(s(s(s(s(s(T843))))))), X5896)
QUOTW_IN_GGA(s(T858), T859, X5931) → U23_GGA(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
QUOTW_IN_GGA(s(T858), T859, X5931) → QUOTW_IN_GGA(T858, T859, X5931)
QUOTW_IN_GGA(0, s(s(s(s(0)))), s(s(X6140))) → U24_GGA(X6140, quotX_in_a(X6140))
QUOTW_IN_GGA(0, s(s(s(s(0)))), s(s(X6140))) → QUOTX_IN_A(X6140)
QUOTW_IN_GGA(0, s(s(s(0))), s(s(X6171))) → U25_GGA(X6171, quotY_in_a(X6171))
QUOTW_IN_GGA(0, s(s(s(0))), s(s(X6171))) → QUOTY_IN_A(X6171)
QUOTW_IN_GGA(0, s(s(0)), s(s(X6187))) → U26_GGA(X6187, quotZ_in_a(X6187))
QUOTW_IN_GGA(0, s(s(0)), s(s(X6187))) → QUOTZ_IN_A(X6187)
QUOTW_IN_GGA(0, s(0), s(s(X6203))) → U27_GGA(X6203, quotN1_in_a(X6203))
QUOTW_IN_GGA(0, s(0), s(s(X6203))) → QUOTN1_IN_A(X6203)
QUOTW_IN_GGA(0, 0, s(s(s(X6284)))) → U28_GGA(X6284, quotV_in_a(X6284))
QUOTW_IN_GGA(0, 0, s(s(s(X6284)))) → QUOTV_IN_A(X6284)
DIVN35_IN_GA(s(s(s(0))), s(s(X6999))) → U74_GA(X6999, quotX_in_a(X6999))
DIVN35_IN_GA(s(s(s(0))), s(s(X6999))) → QUOTX_IN_A(X6999)
DIVN35_IN_GA(s(s(0)), s(s(X7210))) → U75_GA(X7210, quotY_in_a(X7210))
DIVN35_IN_GA(s(s(0)), s(s(X7210))) → QUOTY_IN_A(X7210)
DIVN35_IN_GA(s(0), s(s(X7381))) → U76_GA(X7381, quotZ_in_a(X7381))
DIVN35_IN_GA(s(0), s(s(X7381))) → QUOTZ_IN_A(X7381)
DIVN35_IN_GA(0, s(s(X7510))) → U77_GA(X7510, quotN1_in_a(X7510))
DIVN35_IN_GA(0, s(s(X7510))) → QUOTN1_IN_A(X7510)
U109_GAA(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_GAA(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
U109_GAA(T767, T769, X5608, divN35_out_ga(T767, T769)) → PN44_IN_GGA(T769, T767, X5608)
PN44_IN_GGA(T769, T767, T920) → U111_GGA(T769, T767, T920, timesE_in_gga(T769, T767, T920))
PN44_IN_GGA(T769, T767, T920) → TIMESE_IN_GGA(T769, T767, T920)
U111_GGA(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_GGA(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U111_GGA(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → NEQL_IN_GG(s(s(s(s(T767)))), T920)
U107_G(T761, not_dividesN31_out_g(T761)) → U108_G(T761, prN33_in_g(T761))
U107_G(T761, not_dividesN31_out_g(T761)) → PRN33_IN_G(T761)
PRN33_IN_G(s(T937)) → U72_G(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
PRN33_IN_G(s(T937)) → PN34_IN_GG(T937, s(s(s(s(s(s(s(T937))))))))
PN34_IN_GG(T937, T939) → U113_GG(T937, T939, not_dividesN36_in_gg(T937, T939))
PN34_IN_GG(T937, T939) → NOT_DIVIDESN36_IN_GG(T937, T939)
NOT_DIVIDESN36_IN_GG(T950, T951) → U78_GG(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
NOT_DIVIDESN36_IN_GG(T950, T951) → PN37_IN_GGAA(T951, T950, X7570, X7571)
PN37_IN_GGAA(T951, T950, T954, X7571) → U115_GGAA(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
PN37_IN_GGAA(T951, T950, T954, X7571) → DIVN39_IN_GGA(T951, T950, T954)
DIVN39_IN_GGA(s(T992), T993, X7673) → U80_GGA(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
DIVN39_IN_GGA(s(T992), T993, X7673) → QUOTN3_IN_GGA(T992, T993, X7673)
QUOTN3_IN_GGA(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_GGA(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
QUOTN3_IN_GGA(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → QUOTN2_IN_GGGA(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)
QUOTN2_IN_GGGA(s(T1125), s(T1126), T1127, X7950) → U31_GGGA(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
QUOTN2_IN_GGGA(s(T1125), s(T1126), T1127, X7950) → QUOTN2_IN_GGGA(T1125, T1126, T1127, X7950)
QUOTN2_IN_GGGA(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_GGGA(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
QUOTN2_IN_GGGA(s(s(T1170)), 0, s(T1171), s(X8044)) → QUOTN3_IN_GGA(T1170, T1171, X8044)
QUOTN3_IN_GGA(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_GGA(T1190, X8147, quotN5_in_ga(T1190, X8147))
QUOTN3_IN_GGA(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → QUOTN5_IN_GA(T1190, X8147)
QUOTN5_IN_GA(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_GA(T1229, X8446, quotN5_in_ga(T1229, X8446))
QUOTN5_IN_GA(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → QUOTN5_IN_GA(T1229, X8446)
QUOTN3_IN_GGA(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_GGA(T1239, X8483, quotN6_in_ga(T1239, X8483))
QUOTN3_IN_GGA(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → QUOTN6_IN_GA(T1239, X8483)
QUOTN6_IN_GA(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_GA(T1273, X8743, quotN6_in_ga(T1273, X8743))
QUOTN6_IN_GA(s(s(s(s(s(s(T1273)))))), s(X8743)) → QUOTN6_IN_GA(T1273, X8743)
QUOTN3_IN_GGA(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_GGA(T1282, X8777, quotN7_in_ga(T1282, X8777))
QUOTN3_IN_GGA(s(s(s(T1282))), s(s(s(0))), s(X8777)) → QUOTN7_IN_GA(T1282, X8777)
QUOTN7_IN_GA(s(s(s(s(s(T1311))))), s(X8998)) → U44_GA(T1311, X8998, quotN7_in_ga(T1311, X8998))
QUOTN7_IN_GA(s(s(s(s(s(T1311))))), s(X8998)) → QUOTN7_IN_GA(T1311, X8998)
QUOTN3_IN_GGA(s(s(T1319)), s(s(0)), s(X9029)) → U38_GGA(T1319, X9029, quotN8_in_ga(T1319, X9029))
QUOTN3_IN_GGA(s(s(T1319)), s(s(0)), s(X9029)) → QUOTN8_IN_GA(T1319, X9029)
QUOTN8_IN_GA(s(s(s(s(T1343)))), s(X9211)) → U45_GA(T1343, X9211, quotN8_in_ga(T1343, X9211))
QUOTN8_IN_GA(s(s(s(s(T1343)))), s(X9211)) → QUOTN8_IN_GA(T1343, X9211)
QUOTN3_IN_GGA(s(T1350), s(0), s(X9239)) → U39_GGA(T1350, X9239, quotN9_in_ga(T1350, X9239))
QUOTN3_IN_GGA(s(T1350), s(0), s(X9239)) → QUOTN9_IN_GA(T1350, X9239)
QUOTN9_IN_GA(s(s(s(T1369))), s(X9382)) → U46_GA(T1369, X9382, quotN9_in_ga(T1369, X9382))
QUOTN9_IN_GA(s(s(s(T1369))), s(X9382)) → QUOTN9_IN_GA(T1369, X9382)
QUOTN3_IN_GGA(T1375, 0, s(X9407)) → U40_GGA(T1375, X9407, quotN10_in_ga(T1375, X9407))
QUOTN3_IN_GGA(T1375, 0, s(X9407)) → QUOTN10_IN_GA(T1375, X9407)
QUOTN10_IN_GA(s(s(T1389)), s(X9511)) → U47_GA(T1389, X9511, quotN10_in_ga(T1389, X9511))
QUOTN10_IN_GA(s(s(T1389)), s(X9511)) → QUOTN10_IN_GA(T1389, X9511)
QUOTN2_IN_GGGA(s(T1176), 0, 0, s(s(X8060))) → U33_GGGA(T1176, X8060, quotN4_in_ga(T1176, X8060))
QUOTN2_IN_GGGA(s(T1176), 0, 0, s(s(X8060))) → QUOTN4_IN_GA(T1176, X8060)
QUOTN4_IN_GA(s(T1185), s(X8125)) → U41_GA(T1185, X8125, quotN4_in_ga(T1185, X8125))
QUOTN4_IN_GA(s(T1185), s(X8125)) → QUOTN4_IN_GA(T1185, X8125)
U115_GGAA(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_GGAA(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
U115_GGAA(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → PN45_IN_GGAG(T954, T950, X7571, T951)
PN45_IN_GGAG(T954, T950, T1396, T951) → U117_GGAG(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
PN45_IN_GGAG(T954, T950, T1396, T951) → TIMESE_IN_GGA(T954, T950, T1396)
U117_GGAG(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_GGAG(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U117_GGAG(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → NEQM_IN_GG(T951, T1396)
U113_GG(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_GG(T937, T939, prN38_in_gg(T939, T937))
U113_GG(T937, T939, not_dividesN36_out_gg(T937, T939)) → PRN38_IN_GG(T939, T937)
PRN38_IN_GG(T1412, s(T1413)) → U79_GG(T1412, T1413, pN34_in_gg(T1413, T1412))
PRN38_IN_GG(T1412, s(T1413)) → PN34_IN_GG(T1413, T1412)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 17 SCCs with 214 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN4_IN_GA(s(T1185), s(X8125)) → QUOTN4_IN_GA(T1185, X8125)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(8) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(9) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN4_IN_GA(s(T1185), s(X8125)) → QUOTN4_IN_GA(T1185, X8125)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTN4_IN_GA(x1, x2) = QUOTN4_IN_GA(x1)

We have to consider all (P,R,Pi)-chains

(10) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(11) Obligation:

Q DP problem:
The TRS P consists of the following rules:

QUOTN4_IN_GA(s(T1185)) → QUOTN4_IN_GA(T1185)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(12) 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:

QUOTN4_IN_GA(s(T1185)) → QUOTN4_IN_GA(T1185)
The graph contains the following edges 1 > 1

(13) YES

(14) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN10_IN_GA(s(s(T1389)), s(X9511)) → QUOTN10_IN_GA(T1389, X9511)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(15) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(16) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN10_IN_GA(s(s(T1389)), s(X9511)) → QUOTN10_IN_GA(T1389, X9511)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTN10_IN_GA(x1, x2) = QUOTN10_IN_GA(x1)

We have to consider all (P,R,Pi)-chains

(17) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(18) Obligation:

Q DP problem:
The TRS P consists of the following rules:

QUOTN10_IN_GA(s(s(T1389))) → QUOTN10_IN_GA(T1389)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(19) 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:

QUOTN10_IN_GA(s(s(T1389))) → QUOTN10_IN_GA(T1389)
The graph contains the following edges 1 > 1

(20) YES

(21) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN9_IN_GA(s(s(s(T1369))), s(X9382)) → QUOTN9_IN_GA(T1369, X9382)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(22) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(23) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN9_IN_GA(s(s(s(T1369))), s(X9382)) → QUOTN9_IN_GA(T1369, X9382)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTN9_IN_GA(x1, x2) = QUOTN9_IN_GA(x1)

We have to consider all (P,R,Pi)-chains

(24) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(25) Obligation:

Q DP problem:
The TRS P consists of the following rules:

QUOTN9_IN_GA(s(s(s(T1369)))) → QUOTN9_IN_GA(T1369)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(26) 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:

QUOTN9_IN_GA(s(s(s(T1369)))) → QUOTN9_IN_GA(T1369)
The graph contains the following edges 1 > 1

(27) YES

(28) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN8_IN_GA(s(s(s(s(T1343)))), s(X9211)) → QUOTN8_IN_GA(T1343, X9211)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(29) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(30) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN8_IN_GA(s(s(s(s(T1343)))), s(X9211)) → QUOTN8_IN_GA(T1343, X9211)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTN8_IN_GA(x1, x2) = QUOTN8_IN_GA(x1)

We have to consider all (P,R,Pi)-chains

(31) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(32) Obligation:

Q DP problem:
The TRS P consists of the following rules:

QUOTN8_IN_GA(s(s(s(s(T1343))))) → QUOTN8_IN_GA(T1343)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(33) 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:

QUOTN8_IN_GA(s(s(s(s(T1343))))) → QUOTN8_IN_GA(T1343)
The graph contains the following edges 1 > 1

(34) YES

(35) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN7_IN_GA(s(s(s(s(s(T1311))))), s(X8998)) → QUOTN7_IN_GA(T1311, X8998)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(36) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(37) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN7_IN_GA(s(s(s(s(s(T1311))))), s(X8998)) → QUOTN7_IN_GA(T1311, X8998)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTN7_IN_GA(x1, x2) = QUOTN7_IN_GA(x1)

We have to consider all (P,R,Pi)-chains

(38) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(39) Obligation:

Q DP problem:
The TRS P consists of the following rules:

QUOTN7_IN_GA(s(s(s(s(s(T1311)))))) → QUOTN7_IN_GA(T1311)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(40) 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:

QUOTN7_IN_GA(s(s(s(s(s(T1311)))))) → QUOTN7_IN_GA(T1311)
The graph contains the following edges 1 > 1

(41) YES

(42) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN6_IN_GA(s(s(s(s(s(s(T1273)))))), s(X8743)) → QUOTN6_IN_GA(T1273, X8743)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(43) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(44) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN6_IN_GA(s(s(s(s(s(s(T1273)))))), s(X8743)) → QUOTN6_IN_GA(T1273, X8743)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTN6_IN_GA(x1, x2) = QUOTN6_IN_GA(x1)

We have to consider all (P,R,Pi)-chains

(45) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(46) Obligation:

Q DP problem:
The TRS P consists of the following rules:

QUOTN6_IN_GA(s(s(s(s(s(s(T1273))))))) → QUOTN6_IN_GA(T1273)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(47) 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:

QUOTN6_IN_GA(s(s(s(s(s(s(T1273))))))) → QUOTN6_IN_GA(T1273)
The graph contains the following edges 1 > 1

(48) YES

(49) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN5_IN_GA(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → QUOTN5_IN_GA(T1229, X8446)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(50) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(51) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN5_IN_GA(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → QUOTN5_IN_GA(T1229, X8446)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTN5_IN_GA(x1, x2) = QUOTN5_IN_GA(x1)

We have to consider all (P,R,Pi)-chains

(52) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(53) Obligation:

Q DP problem:
The TRS P consists of the following rules:

QUOTN5_IN_GA(s(s(s(s(s(s(s(T1229)))))))) → QUOTN5_IN_GA(T1229)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(54) 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:

QUOTN5_IN_GA(s(s(s(s(s(s(s(T1229)))))))) → QUOTN5_IN_GA(T1229)
The graph contains the following edges 1 > 1

(55) YES

(56) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN3_IN_GGA(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → QUOTN2_IN_GGGA(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)
QUOTN2_IN_GGGA(s(T1125), s(T1126), T1127, X7950) → QUOTN2_IN_GGGA(T1125, T1126, T1127, X7950)
QUOTN2_IN_GGGA(s(s(T1170)), 0, s(T1171), s(X8044)) → QUOTN3_IN_GGA(T1170, T1171, X8044)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(57) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(58) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN3_IN_GGA(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → QUOTN2_IN_GGGA(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)
QUOTN2_IN_GGGA(s(T1125), s(T1126), T1127, X7950) → QUOTN2_IN_GGGA(T1125, T1126, T1127, X7950)
QUOTN2_IN_GGGA(s(s(T1170)), 0, s(T1171), s(X8044)) → QUOTN3_IN_GGA(T1170, T1171, X8044)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
0 = 0
QUOTN3_IN_GGA(x1, x2, x3) = QUOTN3_IN_GGA(x1, x2)
QUOTN2_IN_GGGA(x1, x2, x3, x4) = QUOTN2_IN_GGGA(x1, x2, x3)

We have to consider all (P,R,Pi)-chains

(59) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(60) Obligation:

Q DP problem:
The TRS P consists of the following rules:

QUOTN3_IN_GGA(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095))))))) → QUOTN2_IN_GGGA(T1094, T1095, s(s(s(s(s(s(s(T1095))))))))
QUOTN2_IN_GGGA(s(T1125), s(T1126), T1127) → QUOTN2_IN_GGGA(T1125, T1126, T1127)
QUOTN2_IN_GGGA(s(s(T1170)), 0, s(T1171)) → QUOTN3_IN_GGA(T1170, T1171)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(61) 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:

QUOTN2_IN_GGGA(s(s(T1170)), 0, s(T1171)) → QUOTN3_IN_GGA(T1170, T1171)
The graph contains the following edges 1 > 1, 3 > 2
QUOTN2_IN_GGGA(s(T1125), s(T1126), T1127) → QUOTN2_IN_GGGA(T1125, T1126, T1127)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
QUOTN3_IN_GGA(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095))))))) → QUOTN2_IN_GGGA(T1094, T1095, s(s(s(s(s(s(s(T1095))))))))
The graph contains the following edges 1 > 1, 2 > 2

(62) YES

(63) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTW_IN_GGA(s(T858), T859, X5931) → QUOTW_IN_GGA(T858, T859, X5931)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(64) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(65) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTW_IN_GGA(s(T858), T859, X5931) → QUOTW_IN_GGA(T858, T859, X5931)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTW_IN_GGA(x1, x2, x3) = QUOTW_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(66) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(67) Obligation:

Q DP problem:
The TRS P consists of the following rules:

QUOTW_IN_GGA(s(T858), T859) → QUOTW_IN_GGA(T858, T859)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(68) 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:

QUOTW_IN_GGA(s(T858), T859) → QUOTW_IN_GGA(T858, T859)
The graph contains the following edges 1 > 1, 2 >= 2

(69) YES

(70) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTR_IN_GGA(s(T687), T688, X4160) → QUOTR_IN_GGA(T687, T688, X4160)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(71) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(72) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTR_IN_GGA(s(T687), T688, X4160) → QUOTR_IN_GGA(T687, T688, X4160)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTR_IN_GGA(x1, x2, x3) = QUOTR_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(73) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(74) Obligation:

Q DP problem:
The TRS P consists of the following rules:

QUOTR_IN_GGA(s(T687), T688) → QUOTR_IN_GGA(T687, T688)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(75) 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:

QUOTR_IN_GGA(s(T687), T688) → QUOTR_IN_GGA(T687, T688)
The graph contains the following edges 1 > 1, 2 >= 2

(76) YES

(77) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN_IN_GGA(s(T521), T522, X2619) → QUOTN_IN_GGA(T521, T522, X2619)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(78) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(79) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTN_IN_GGA(s(T521), T522, X2619) → QUOTN_IN_GGA(T521, T522, X2619)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTN_IN_GGA(x1, x2, x3) = QUOTN_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(80) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(81) Obligation:

Q DP problem:
The TRS P consists of the following rules:

QUOTN_IN_GGA(s(T521), T522) → QUOTN_IN_GGA(T521, T522)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(82) 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:

QUOTN_IN_GGA(s(T521), T522) → QUOTN_IN_GGA(T521, T522)
The graph contains the following edges 1 > 1, 2 >= 2

(83) YES

(84) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTI_IN_GGA(s(T360), T361, X1354) → QUOTI_IN_GGA(T360, T361, X1354)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(85) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(86) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTI_IN_GGA(s(T360), T361, X1354) → QUOTI_IN_GGA(T360, T361, X1354)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTI_IN_GGA(x1, x2, x3) = QUOTI_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(87) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(88) Obligation:

Q DP problem:
The TRS P consists of the following rules:

QUOTI_IN_GGA(s(T360), T361) → QUOTI_IN_GGA(T360, T361)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(89) 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:

QUOTI_IN_GGA(s(T360), T361) → QUOTI_IN_GGA(T360, T361)
The graph contains the following edges 1 > 1, 2 >= 2

(90) YES

(91) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

NEQH_IN_GG(s(T247), s(T248)) → NEQH_IN_GG(T247, T248)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(92) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(93) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

NEQH_IN_GG(s(T247), s(T248)) → NEQH_IN_GG(T247, T248)

R is empty.
Pi is empty.
We have to consider all (P,R,Pi)-chains

(94) PiDPToQDPProof (EQUIVALENT transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(95) Obligation:

Q DP problem:
The TRS P consists of the following rules:

NEQH_IN_GG(s(T247), s(T248)) → NEQH_IN_GG(T247, T248)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(96) 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:

NEQH_IN_GG(s(T247), s(T248)) → NEQH_IN_GG(T247, T248)
The graph contains the following edges 1 > 1, 2 > 2

(97) YES

(98) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ADDG_IN_GGA(s(T188), T189, s(X932)) → ADDG_IN_GGA(T188, T189, X932)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(99) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(100) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ADDG_IN_GGA(s(T188), T189, s(X932)) → ADDG_IN_GGA(T188, T189, X932)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
ADDG_IN_GGA(x1, x2, x3) = ADDG_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(101) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(102) Obligation:

Q DP problem:
The TRS P consists of the following rules:

ADDG_IN_GGA(s(T188), T189) → ADDG_IN_GGA(T188, T189)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(103) 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:

ADDG_IN_GGA(s(T188), T189) → ADDG_IN_GGA(T188, T189)
The graph contains the following edges 1 > 1, 2 >= 2

(104) YES

(105) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

TIMESE_IN_GGA(s(T169), T170, X908) → PF_IN_GGAA(T169, T170, X907, X908)
PF_IN_GGAA(T169, T170, T173, X908) → TIMESE_IN_GGA(T169, T170, T173)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(106) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(107) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

TIMESE_IN_GGA(s(T169), T170, X908) → PF_IN_GGAA(T169, T170, X907, X908)
PF_IN_GGAA(T169, T170, T173, X908) → TIMESE_IN_GGA(T169, T170, T173)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
TIMESE_IN_GGA(x1, x2, x3) = TIMESE_IN_GGA(x1, x2)
PF_IN_GGAA(x1, x2, x3, x4) = PF_IN_GGAA(x1, x2)

We have to consider all (P,R,Pi)-chains

(108) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(109) Obligation:

Q DP problem:
The TRS P consists of the following rules:

TIMESE_IN_GGA(s(T169), T170) → PF_IN_GGAA(T169, T170)
PF_IN_GGAA(T169, T170) → TIMESE_IN_GGA(T169, T170)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(110) 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:

PF_IN_GGAA(T169, T170) → TIMESE_IN_GGA(T169, T170)
The graph contains the following edges 1 >= 1, 2 >= 2
TIMESE_IN_GGA(s(T169), T170) → PF_IN_GGAA(T169, T170)
The graph contains the following edges 1 > 1, 2 >= 2

(111) YES

(112) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

PN34_IN_GG(T937, T939) → U113_GG(T937, T939, not_dividesN36_in_gg(T937, T939))
U113_GG(T937, T939, not_dividesN36_out_gg(T937, T939)) → PRN38_IN_GG(T939, T937)
PRN38_IN_GG(T1412, s(T1413)) → PN34_IN_GG(T1413, T1412)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(113) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(114) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

PN34_IN_GG(T937, T939) → U113_GG(T937, T939, not_dividesN36_in_gg(T937, T939))
U113_GG(T937, T939, not_dividesN36_out_gg(T937, T939)) → PRN38_IN_GG(T939, T937)
PRN38_IN_GG(T1412, s(T1413)) → PN34_IN_GG(T1413, T1412)

The TRS R consists of the following rules:

not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))

The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
0 = 0
timesE_in_gga(x1, x2, x3) = timesE_in_gga(x1, x2)
timesE_out_gga(x1, x2, x3) = timesE_out_gga(x1, x2, x3)
U4_gga(x1, x2, x3, x4) = U4_gga(x1, x2, x4)
pF_in_ggaa(x1, x2, x3, x4) = pF_in_ggaa(x1, x2)
U87_ggaa(x1, x2, x3, x4, x5) = U87_ggaa(x1, x2, x5)
U88_ggaa(x1, x2, x3, x4, x5) = U88_ggaa(x1, x2, x3, x5)
addG_in_gga(x1, x2, x3) = addG_in_gga(x1, x2)
addG_out_gga(x1, x2, x3) = addG_out_gga(x1, x2, x3)
U5_gga(x1, x2, x3, x4) = U5_gga(x1, x2, x4)
pF_out_ggaa(x1, x2, x3, x4) = pF_out_ggaa(x1, x2, x3, x4)
neqM_in_gg(x1, x2) = neqM_in_gg(x1, x2)
neqM_out_gg(x1, x2) = neqM_out_gg(x1, x2)
U48_gg(x1, x2, x3) = U48_gg(x1, x2, x3)
neqH_in_gg(x1, x2) = neqH_in_gg(x1, x2)
neqH_out_gg(x1, x2) = neqH_out_gg(x1, x2)
U6_gg(x1, x2, x3) = U6_gg(x1, x2, x3)
not_dividesN36_in_gg(x1, x2) = not_dividesN36_in_gg(x1, x2)
U78_gg(x1, x2, x3) = U78_gg(x1, x2, x3)
pN37_in_ggaa(x1, x2, x3, x4) = pN37_in_ggaa(x1, x2)
U115_ggaa(x1, x2, x3, x4, x5) = U115_ggaa(x1, x2, x5)
divN39_in_gga(x1, x2, x3) = divN39_in_gga(x1, x2)
divN39_out_gga(x1, x2, x3) = divN39_out_gga(x1, x2, x3)
U80_gga(x1, x2, x3, x4) = U80_gga(x1, x2, x4)
quotN3_in_gga(x1, x2, x3) = quotN3_in_gga(x1, x2)
quotN3_out_gga(x1, x2, x3) = quotN3_out_gga(x1, x2, x3)
U34_gga(x1, x2, x3, x4) = U34_gga(x1, x2, x4)
quotN2_in_ggga(x1, x2, x3, x4) = quotN2_in_ggga(x1, x2, x3)
quotN2_out_ggga(x1, x2, x3, x4) = quotN2_out_ggga(x1, x2, x3, x4)
U31_ggga(x1, x2, x3, x4, x5) = U31_ggga(x1, x2, x3, x5)
U32_ggga(x1, x2, x3, x4) = U32_ggga(x1, x2, x4)
U35_gga(x1, x2, x3) = U35_gga(x1, x3)
quotN5_in_ga(x1, x2) = quotN5_in_ga(x1)
quotN5_out_ga(x1, x2) = quotN5_out_ga(x1, x2)
U42_ga(x1, x2, x3) = U42_ga(x1, x3)
U36_gga(x1, x2, x3) = U36_gga(x1, x3)
quotN6_in_ga(x1, x2) = quotN6_in_ga(x1)
quotN6_out_ga(x1, x2) = quotN6_out_ga(x1, x2)
U43_ga(x1, x2, x3) = U43_ga(x1, x3)
U37_gga(x1, x2, x3) = U37_gga(x1, x3)
quotN7_in_ga(x1, x2) = quotN7_in_ga(x1)
quotN7_out_ga(x1, x2) = quotN7_out_ga(x1, x2)
U44_ga(x1, x2, x3) = U44_ga(x1, x3)
U38_gga(x1, x2, x3) = U38_gga(x1, x3)
quotN8_in_ga(x1, x2) = quotN8_in_ga(x1)
quotN8_out_ga(x1, x2) = quotN8_out_ga(x1, x2)
U45_ga(x1, x2, x3) = U45_ga(x1, x3)
U39_gga(x1, x2, x3) = U39_gga(x1, x3)
quotN9_in_ga(x1, x2) = quotN9_in_ga(x1)
quotN9_out_ga(x1, x2) = quotN9_out_ga(x1, x2)
U46_ga(x1, x2, x3) = U46_ga(x1, x3)
U40_gga(x1, x2, x3) = U40_gga(x1, x3)
quotN10_in_ga(x1, x2) = quotN10_in_ga(x1)
quotN10_out_ga(x1, x2) = quotN10_out_ga(x1, x2)
U47_ga(x1, x2, x3) = U47_ga(x1, x3)
U33_ggga(x1, x2, x3) = U33_ggga(x1, x3)
quotN4_in_ga(x1, x2) = quotN4_in_ga(x1)
quotN4_out_ga(x1, x2) = quotN4_out_ga(x1, x2)
U41_ga(x1, x2, x3) = U41_ga(x1, x3)
U116_ggaa(x1, x2, x3, x4, x5) = U116_ggaa(x1, x2, x3, x5)
pN45_in_ggag(x1, x2, x3, x4) = pN45_in_ggag(x1, x2, x4)
U117_ggag(x1, x2, x3, x4, x5) = U117_ggag(x1, x2, x4, x5)
U118_ggag(x1, x2, x3, x4, x5) = U118_ggag(x1, x2, x3, x4, x5)
pN45_out_ggag(x1, x2, x3, x4) = pN45_out_ggag(x1, x2, x3, x4)
pN37_out_ggaa(x1, x2, x3, x4) = pN37_out_ggaa(x1, x2, x3, x4)
not_dividesN36_out_gg(x1, x2) = not_dividesN36_out_gg(x1, x2)
PN34_IN_GG(x1, x2) = PN34_IN_GG(x1, x2)
U113_GG(x1, x2, x3) = U113_GG(x1, x2, x3)
PRN38_IN_GG(x1, x2) = PRN38_IN_GG(x1, x2)

We have to consider all (P,R,Pi)-chains

(115) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(116) Obligation:

Q DP problem:
The TRS P consists of the following rules:

PN34_IN_GG(T937, T939) → U113_GG(T937, T939, not_dividesN36_in_gg(T937, T939))
U113_GG(T937, T939, not_dividesN36_out_gg(T937, T939)) → PRN38_IN_GG(T939, T937)
PRN38_IN_GG(T1412, s(T1413)) → PN34_IN_GG(T1413, T1412)

The TRS R consists of the following rules:

not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950))
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
pN37_in_ggaa(T951, T950) → U115_ggaa(T951, T950, divN39_in_gga(T951, T950))
U115_ggaa(T951, T950, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, pN45_in_ggag(T954, T950, T951))
divN39_in_gga(0, T983) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993) → U80_gga(T992, T993, quotN3_in_gga(T992, T993))
U116_ggaa(T951, T950, T954, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U80_gga(T992, T993, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
pN45_in_ggag(T954, T950, T951) → U117_ggag(T954, T950, T951, timesE_in_gga(T954, T950))
quotN3_in_gga(0, s(T1000)) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017))) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034)))) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051))))) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068)))))) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085))))))) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095))))))) → U34_gga(T1094, T1095, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095)))))))))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0)))))) → U35_gga(T1190, quotN5_in_ga(T1190))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0))))) → U36_gga(T1239, quotN6_in_ga(T1239))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0)))) → U37_gga(T1282, quotN7_in_ga(T1282))
quotN3_in_gga(s(s(T1319)), s(s(0))) → U38_gga(T1319, quotN8_in_ga(T1319))
quotN3_in_gga(s(T1350), s(0)) → U39_gga(T1350, quotN9_in_ga(T1350))
quotN3_in_gga(T1375, 0) → U40_gga(T1375, quotN10_in_ga(T1375))
U117_ggag(T954, T950, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U34_gga(T1094, T1095, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U35_gga(T1190, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
U36_gga(T1239, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
U37_gga(T1282, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
U38_gga(T1319, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
U39_gga(T1350, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
U40_gga(T1375, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
timesE_in_gga(0, T164) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170) → U4_gga(T169, T170, pF_in_ggaa(T169, T170))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
quotN2_in_ggga(0, s(T1111), T1112) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127) → U31_ggga(T1125, T1126, T1127, quotN2_in_ggga(T1125, T1126, T1127))
quotN2_in_ggga(0, 0, T1144) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171)) → U32_ggga(T1170, T1171, quotN3_in_gga(T1170, T1171))
quotN5_in_ga(0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0)) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0))) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0)))) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0))))) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0)))))) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0))))))) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229)))))))) → U42_ga(T1229, quotN5_in_ga(T1229))
quotN6_in_ga(0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0)) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0))) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0)))) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0))))) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0)))))) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273))))))) → U43_ga(T1273, quotN6_in_ga(T1273))
quotN7_in_ga(0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0)) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0))) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0)))) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0))))) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311)))))) → U44_ga(T1311, quotN7_in_ga(T1311))
quotN8_in_ga(0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0)) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0))) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0)))) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343))))) → U45_ga(T1343, quotN8_in_ga(T1343))
quotN9_in_ga(0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0)) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0))) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369)))) → U46_ga(T1369, quotN9_in_ga(T1369))
quotN10_in_ga(0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0)) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389))) → U47_ga(T1389, quotN10_in_ga(T1389))
U4_gga(T169, T170, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
U31_ggga(T1125, T1126, T1127, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U32_ggga(T1170, T1171, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
U42_ga(T1229, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U43_ga(T1273, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U44_ga(T1311, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U45_ga(T1343, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U46_ga(T1369, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U47_ga(T1389, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
pF_in_ggaa(T169, T170) → U87_ggaa(T169, T170, timesE_in_gga(T169, T170))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
quotN2_in_ggga(s(T1176), 0, 0) → U33_ggga(T1176, quotN4_in_ga(T1176))
U87_ggaa(T169, T170, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, addG_in_gga(T173, T170))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U33_ggga(T1176, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U88_ggaa(T169, T170, T173, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
quotN4_in_ga(0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185)) → U41_ga(T1185, quotN4_in_ga(T1185))
addG_in_gga(0, T183) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189) → U5_gga(T188, T189, addG_in_gga(T188, T189))
U41_ga(T1185, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U5_gga(T188, T189, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))

The set Q consists of the following terms:

not_dividesN36_in_gg(x0, x1)
U78_gg(x0, x1, x2)
pN37_in_ggaa(x0, x1)
U115_ggaa(x0, x1, x2)
divN39_in_gga(x0, x1)
U116_ggaa(x0, x1, x2, x3)
U80_gga(x0, x1, x2)
pN45_in_ggag(x0, x1, x2)
quotN3_in_gga(x0, x1)
U117_ggag(x0, x1, x2, x3)
U34_gga(x0, x1, x2)
U35_gga(x0, x1)
U36_gga(x0, x1)
U37_gga(x0, x1)
U38_gga(x0, x1)
U39_gga(x0, x1)
U40_gga(x0, x1)
timesE_in_gga(x0, x1)
U118_ggag(x0, x1, x2, x3, x4)
quotN2_in_ggga(x0, x1, x2)
quotN5_in_ga(x0)
quotN6_in_ga(x0)
quotN7_in_ga(x0)
quotN8_in_ga(x0)
quotN9_in_ga(x0)
quotN10_in_ga(x0)
U4_gga(x0, x1, x2)
neqM_in_gg(x0, x1)
U31_ggga(x0, x1, x2, x3)
U32_ggga(x0, x1, x2)
U42_ga(x0, x1)
U43_ga(x0, x1)
U44_ga(x0, x1)
U45_ga(x0, x1)
U46_ga(x0, x1)
U47_ga(x0, x1)
pF_in_ggaa(x0, x1)
U48_gg(x0, x1, x2)
U87_ggaa(x0, x1, x2)
neqH_in_gg(x0, x1)
U33_ggga(x0, x1)
U88_ggaa(x0, x1, x2, x3)
U6_gg(x0, x1, x2)
quotN4_in_ga(x0)
addG_in_gga(x0, x1)
U41_ga(x0, x1)
U5_gga(x0, x1, x2)

We have to consider all (P,Q,R)-chains.

(117) 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:

U113_GG(T937, T939, not_dividesN36_out_gg(T937, T939)) → PRN38_IN_GG(T939, T937)
The graph contains the following edges 2 >= 1, 3 > 1, 1 >= 2, 3 > 2
PRN38_IN_GG(T1412, s(T1413)) → PN34_IN_GG(T1413, T1412)
The graph contains the following edges 2 > 1, 1 >= 2
PN34_IN_GG(T937, T939) → U113_GG(T937, T939, not_dividesN36_in_gg(T937, T939))
The graph contains the following edges 1 >= 1, 2 >= 2

(118) YES

(119) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTC_IN_GGA(s(T111), T112, X358) → QUOTC_IN_GGA(T111, T112, X358)

The TRS R consists of the following rules:

primeA_in_g(s(s(0))) → primeA_out_g(s(s(0)))
primeA_in_g(s(s(s(T14)))) → U1_g(T14, pB_in_g(T14))
pB_in_g(T14) → U81_g(T14, not_dividesN11_in_g(T14))
not_dividesN11_in_g(T20) → U49_g(T20, pN12_in_gaa(T20, X34, X35))
pN12_in_gaa(T20, T22, X35) → U83_gaa(T20, T22, X35, divN15_in_ga(T20, T22))
divN15_in_ga(s(s(s(s(s(s(T96)))))), X323) → U51_ga(T96, X323, quotC_in_gga(T96, s(s(s(s(s(s(s(T96))))))), X323))
quotC_in_gga(s(T111), T112, X358) → U2_gga(T111, T112, X358, quotC_in_gga(T111, T112, X358))
quotC_in_gga(0, s(T134), s(0)) → quotC_out_gga(0, s(T134), s(0))
quotC_in_gga(0, 0, s(s(X443))) → U3_gga(X443, quotD_in_a(X443))
quotD_in_a(0) → quotD_out_a(0)
U3_gga(X443, quotD_out_a(X443)) → quotC_out_gga(0, 0, s(s(X443)))
U2_gga(T111, T112, X358, quotC_out_gga(T111, T112, X358)) → quotC_out_gga(s(T111), T112, X358)
U51_ga(T96, X323, quotC_out_gga(T96, s(s(s(s(s(s(s(T96))))))), X323)) → divN15_out_ga(s(s(s(s(s(s(T96)))))), X323)
divN15_in_ga(s(s(s(s(s(0))))), s(0)) → divN15_out_ga(s(s(s(s(s(0))))), s(0))
divN15_in_ga(s(s(s(s(0)))), s(0)) → divN15_out_ga(s(s(s(s(0)))), s(0))
divN15_in_ga(s(s(s(0))), s(0)) → divN15_out_ga(s(s(s(0))), s(0))
divN15_in_ga(s(s(0)), s(X684)) → U52_ga(X684, quotY_in_a(X684))
quotY_in_a(0) → quotY_out_a(0)
U52_ga(X684, quotY_out_a(X684)) → divN15_out_ga(s(s(0)), s(X684))
divN15_in_ga(s(0), s(X753)) → U53_ga(X753, quotT_in_a(X753))
quotT_in_a(0) → quotT_out_a(0)
U53_ga(X753, quotT_out_a(X753)) → divN15_out_ga(s(0), s(X753))
divN15_in_ga(0, s(X822)) → U54_ga(X822, quotP_in_a(X822))
quotP_in_a(0) → quotP_out_a(0)
U54_ga(X822, quotP_out_a(X822)) → divN15_out_ga(0, s(X822))
U83_gaa(T20, T22, X35, divN15_out_ga(T20, T22)) → U84_gaa(T20, T22, X35, pN40_in_gga(T22, T20, X35))
pN40_in_gga(T22, T20, T157) → U85_gga(T22, T20, T157, timesE_in_gga(T22, T20, T157))
timesE_in_gga(0, T164, 0) → timesE_out_gga(0, T164, 0)
timesE_in_gga(s(T169), T170, X908) → U4_gga(T169, T170, X908, pF_in_ggaa(T169, T170, X907, X908))
pF_in_ggaa(T169, T170, T173, X908) → U87_ggaa(T169, T170, T173, X908, timesE_in_gga(T169, T170, T173))
U87_ggaa(T169, T170, T173, X908, timesE_out_gga(T169, T170, T173)) → U88_ggaa(T169, T170, T173, X908, addG_in_gga(T173, T170, X908))
addG_in_gga(0, T183, s(s(T183))) → addG_out_gga(0, T183, s(s(T183)))
addG_in_gga(s(T188), T189, s(X932)) → U5_gga(T188, T189, X932, addG_in_gga(T188, T189, X932))
U5_gga(T188, T189, X932, addG_out_gga(T188, T189, X932)) → addG_out_gga(s(T188), T189, s(X932))
U88_ggaa(T169, T170, T173, X908, addG_out_gga(T173, T170, X908)) → pF_out_ggaa(T169, T170, T173, X908)
U4_gga(T169, T170, X908, pF_out_ggaa(T169, T170, X907, X908)) → timesE_out_gga(s(T169), T170, X908)
U85_gga(T22, T20, T157, timesE_out_gga(T22, T20, T157)) → U86_gga(T22, T20, T157, neqL_in_gg(T20, T157))
neqL_in_gg(T198, 0) → neqL_out_gg(T198, 0)
neqL_in_gg(T211, s(0)) → neqL_out_gg(T211, s(0))
neqL_in_gg(T216, s(s(T217))) → U10_gg(T216, T217, neqM_in_gg(T216, T217))
neqM_in_gg(T224, 0) → neqM_out_gg(T224, 0)
neqM_in_gg(T229, s(T230)) → U48_gg(T229, T230, neqH_in_gg(T229, T230))
neqH_in_gg(s(T237), 0) → neqH_out_gg(s(T237), 0)
neqH_in_gg(0, s(T242)) → neqH_out_gg(0, s(T242))
neqH_in_gg(s(T247), s(T248)) → U6_gg(T247, T248, neqH_in_gg(T247, T248))
U6_gg(T247, T248, neqH_out_gg(T247, T248)) → neqH_out_gg(s(T247), s(T248))
U48_gg(T229, T230, neqH_out_gg(T229, T230)) → neqM_out_gg(T229, s(T230))
U10_gg(T216, T217, neqM_out_gg(T216, T217)) → neqL_out_gg(T216, s(s(T217)))
U86_gga(T22, T20, T157, neqL_out_gg(T20, T157)) → pN40_out_gga(T22, T20, T157)
U84_gaa(T20, T22, X35, pN40_out_gga(T22, T20, X35)) → pN12_out_gaa(T20, T22, X35)
U49_g(T20, pN12_out_gaa(T20, X34, X35)) → not_dividesN11_out_g(T20)
U81_g(T14, not_dividesN11_out_g(T14)) → U82_g(T14, prN13_in_g(T14))
prN13_in_g(0) → prN13_out_g(0)
prN13_in_g(s(T263)) → U50_g(T263, pN14_in_g(T263))
pN14_in_g(T263) → U89_g(T263, not_dividesN16_in_g(T263))
not_dividesN16_in_g(T269) → U55_g(T269, pN17_in_gaa(T269, X1030, X1031))
pN17_in_gaa(T269, T271, X1031) → U91_gaa(T269, T271, X1031, divN20_in_ga(T269, T271))
divN20_in_ga(s(s(s(s(s(s(T345)))))), X1319) → U57_ga(T345, X1319, quotI_in_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319))
quotI_in_gga(s(T360), T361, X1354) → U7_gga(T360, T361, X1354, quotI_in_gga(T360, T361, X1354))
quotI_in_gga(0, s(s(T384)), s(0)) → quotI_out_gga(0, s(s(T384)), s(0))
quotI_in_gga(0, s(0), s(s(X1470))) → U8_gga(X1470, quotJ_in_a(X1470))
quotJ_in_a(0) → quotJ_out_a(0)
U8_gga(X1470, quotJ_out_a(X1470)) → quotI_out_gga(0, s(0), s(s(X1470)))
quotI_in_gga(0, 0, s(s(X1501))) → U9_gga(X1501, quotK_in_a(X1501))
quotK_in_a(s(X1564)) → U15_a(X1564, quotD_in_a(X1564))
U15_a(X1564, quotD_out_a(X1564)) → quotK_out_a(s(X1564))
U9_gga(X1501, quotK_out_a(X1501)) → quotI_out_gga(0, 0, s(s(X1501)))
U7_gga(T360, T361, X1354, quotI_out_gga(T360, T361, X1354)) → quotI_out_gga(s(T360), T361, X1354)
U57_ga(T345, X1319, quotI_out_gga(T345, s(s(s(s(s(s(s(T345))))))), X1319)) → divN20_out_ga(s(s(s(s(s(s(T345)))))), X1319)
divN20_in_ga(s(s(s(s(s(0))))), s(0)) → divN20_out_ga(s(s(s(s(s(0))))), s(0))
divN20_in_ga(s(s(s(s(0)))), s(0)) → divN20_out_ga(s(s(s(s(0)))), s(0))
divN20_in_ga(s(s(s(0))), s(0)) → divN20_out_ga(s(s(s(0))), s(0))
divN20_in_ga(s(s(0)), s(0)) → divN20_out_ga(s(s(0)), s(0))
divN20_in_ga(s(0), s(X2028)) → U58_ga(X2028, quotZ_in_a(X2028))
quotZ_in_a(0) → quotZ_out_a(0)
U58_ga(X2028, quotZ_out_a(X2028)) → divN20_out_ga(s(0), s(X2028))
divN20_in_ga(0, s(X2139)) → U59_ga(X2139, quotU_in_a(X2139))
quotU_in_a(s(X2241)) → U21_a(X2241, quotJ_in_a(X2241))
U21_a(X2241, quotJ_out_a(X2241)) → quotU_out_a(s(X2241))
U59_ga(X2139, quotU_out_a(X2139)) → divN20_out_ga(0, s(X2139))
U91_gaa(T269, T271, X1031, divN20_out_ga(T269, T271)) → U92_gaa(T269, T271, X1031, pN41_in_gga(T271, T269, X1031))
pN41_in_gga(T271, T269, T407) → U93_gga(T271, T269, T407, timesE_in_gga(T271, T269, T407))
U93_gga(T271, T269, T407, timesE_out_gga(T271, T269, T407)) → U94_gga(T271, T269, T407, neqL_in_gg(s(T269), T407))
U94_gga(T271, T269, T407, neqL_out_gg(s(T269), T407)) → pN41_out_gga(T271, T269, T407)
U92_gaa(T269, T271, X1031, pN41_out_gga(T271, T269, X1031)) → pN17_out_gaa(T269, T271, X1031)
U55_g(T269, pN17_out_gaa(T269, X1030, X1031)) → not_dividesN16_out_g(T269)
U89_g(T263, not_dividesN16_out_g(T263)) → U90_g(T263, prN18_in_g(T263))
prN18_in_g(0) → prN18_out_g(0)
prN18_in_g(s(T424)) → U56_g(T424, pN19_in_g(T424))
pN19_in_g(T424) → U95_g(T424, not_dividesN21_in_g(T424))
not_dividesN21_in_g(T430) → U60_g(T430, pN22_in_gaa(T430, X2295, X2296))
pN22_in_gaa(T430, T432, X2296) → U97_gaa(T430, T432, X2296, divN25_in_ga(T430, T432))
divN25_in_ga(s(s(s(s(s(s(T506)))))), X2584) → U62_ga(T506, X2584, quotN_in_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584))
quotN_in_gga(s(T521), T522, X2619) → U11_gga(T521, T522, X2619, quotN_in_gga(T521, T522, X2619))
quotN_in_gga(0, s(s(s(T550))), s(0)) → quotN_out_gga(0, s(s(s(T550))), s(0))
quotN_in_gga(0, s(s(0)), s(s(X2766))) → U12_gga(X2766, quotO_in_a(X2766))
quotO_in_a(0) → quotO_out_a(0)
U12_gga(X2766, quotO_out_a(X2766)) → quotN_out_gga(0, s(s(0)), s(s(X2766)))
quotN_in_gga(0, s(0), s(s(X2797))) → U13_gga(X2797, quotP_in_a(X2797))
U13_gga(X2797, quotP_out_a(X2797)) → quotN_out_gga(0, s(0), s(s(X2797)))
quotN_in_gga(0, 0, s(s(X2813))) → U14_gga(X2813, quotQ_in_a(X2813))
quotQ_in_a(s(X2878)) → U22_a(X2878, quotK_in_a(X2878))
U22_a(X2878, quotK_out_a(X2878)) → quotQ_out_a(s(X2878))
U14_gga(X2813, quotQ_out_a(X2813)) → quotN_out_gga(0, 0, s(s(X2813)))
U11_gga(T521, T522, X2619, quotN_out_gga(T521, T522, X2619)) → quotN_out_gga(s(T521), T522, X2619)
U62_ga(T506, X2584, quotN_out_gga(T506, s(s(s(s(s(s(s(T506))))))), X2584)) → divN25_out_ga(s(s(s(s(s(s(T506)))))), X2584)
divN25_in_ga(s(s(s(s(s(0))))), s(0)) → divN25_out_ga(s(s(s(s(s(0))))), s(0))
divN25_in_ga(s(s(s(s(0)))), s(0)) → divN25_out_ga(s(s(s(s(0)))), s(0))
divN25_in_ga(s(s(s(0))), s(0)) → divN25_out_ga(s(s(s(0))), s(0))
divN25_in_ga(s(s(0)), s(0)) → divN25_out_ga(s(s(0)), s(0))
divN25_in_ga(s(0), s(s(X3653))) → U63_ga(X3653, quotO_in_a(X3653))
U63_ga(X3653, quotO_out_a(X3653)) → divN25_out_ga(s(0), s(s(X3653)))
divN25_in_ga(0, s(X3676)) → U64_ga(X3676, quotN1_in_a(X3676))
quotN1_in_a(s(X3780)) → U29_a(X3780, quotP_in_a(X3780))
U29_a(X3780, quotP_out_a(X3780)) → quotN1_out_a(s(X3780))
U64_ga(X3676, quotN1_out_a(X3676)) → divN25_out_ga(0, s(X3676))
U97_gaa(T430, T432, X2296, divN25_out_ga(T430, T432)) → U98_gaa(T430, T432, X2296, pN42_in_gga(T432, T430, X2296))
pN42_in_gga(T432, T430, T573) → U99_gga(T432, T430, T573, timesE_in_gga(T432, T430, T573))
U99_gga(T432, T430, T573, timesE_out_gga(T432, T430, T573)) → U100_gga(T432, T430, T573, neqL_in_gg(s(s(T430)), T573))
U100_gga(T432, T430, T573, neqL_out_gg(s(s(T430)), T573)) → pN42_out_gga(T432, T430, T573)
U98_gaa(T430, T432, X2296, pN42_out_gga(T432, T430, X2296)) → pN22_out_gaa(T430, T432, X2296)
U60_g(T430, pN22_out_gaa(T430, X2295, X2296)) → not_dividesN21_out_g(T430)
U95_g(T424, not_dividesN21_out_g(T424)) → U96_g(T424, prN23_in_g(T424))
prN23_in_g(0) → prN23_out_g(0)
prN23_in_g(s(T590)) → U61_g(T590, pN24_in_g(T590))
pN24_in_g(T590) → U101_g(T590, not_dividesN26_in_g(T590))
not_dividesN26_in_g(T596) → U65_g(T596, pN27_in_gaa(T596, X3836, X3837))
pN27_in_gaa(T596, T598, X3837) → U103_gaa(T596, T598, X3837, divN30_in_ga(T596, T598))
divN30_in_ga(s(s(s(s(s(s(T672)))))), X4125) → U67_ga(T672, X4125, quotR_in_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125))
quotR_in_gga(s(T687), T688, X4160) → U16_gga(T687, T688, X4160, quotR_in_gga(T687, T688, X4160))
quotR_in_gga(0, s(s(s(s(T721)))), s(0)) → quotR_out_gga(0, s(s(s(s(T721)))), s(0))
quotR_in_gga(0, s(s(s(0))), s(s(X4338))) → U17_gga(X4338, quotS_in_a(X4338))
quotS_in_a(0) → quotS_out_a(0)
U17_gga(X4338, quotS_out_a(X4338)) → quotR_out_gga(0, s(s(s(0))), s(s(X4338)))
quotR_in_gga(0, s(s(0)), s(s(X4369))) → U18_gga(X4369, quotT_in_a(X4369))
U18_gga(X4369, quotT_out_a(X4369)) → quotR_out_gga(0, s(s(0)), s(s(X4369)))
quotR_in_gga(0, s(0), s(s(X4385))) → U19_gga(X4385, quotU_in_a(X4385))
U19_gga(X4385, quotU_out_a(X4385)) → quotR_out_gga(0, s(0), s(s(X4385)))
quotR_in_gga(0, 0, s(s(X4401))) → U20_gga(X4401, quotV_in_a(X4401))
quotV_in_a(s(X4466)) → U30_a(X4466, quotQ_in_a(X4466))
U30_a(X4466, quotQ_out_a(X4466)) → quotV_out_a(s(X4466))
U20_gga(X4401, quotV_out_a(X4401)) → quotR_out_gga(0, 0, s(s(X4401)))
U16_gga(T687, T688, X4160, quotR_out_gga(T687, T688, X4160)) → quotR_out_gga(s(T687), T688, X4160)
U67_ga(T672, X4125, quotR_out_gga(T672, s(s(s(s(s(s(s(T672))))))), X4125)) → divN30_out_ga(s(s(s(s(s(s(T672)))))), X4125)
divN30_in_ga(s(s(s(s(s(0))))), s(0)) → divN30_out_ga(s(s(s(s(s(0))))), s(0))
divN30_in_ga(s(s(s(s(0)))), s(0)) → divN30_out_ga(s(s(s(s(0)))), s(0))
divN30_in_ga(s(s(s(0))), s(0)) → divN30_out_ga(s(s(s(0))), s(0))
divN30_in_ga(s(s(0)), s(s(X5253))) → U68_ga(X5253, quotS_in_a(X5253))
U68_ga(X5253, quotS_out_a(X5253)) → divN30_out_ga(s(s(0)), s(s(X5253)))
divN30_in_ga(s(0), s(s(X5422))) → U69_ga(X5422, quotT_in_a(X5422))
U69_ga(X5422, quotT_out_a(X5422)) → divN30_out_ga(s(0), s(s(X5422)))
divN30_in_ga(0, s(s(X5551))) → U70_ga(X5551, quotU_in_a(X5551))
U70_ga(X5551, quotU_out_a(X5551)) → divN30_out_ga(0, s(s(X5551)))
U103_gaa(T596, T598, X3837, divN30_out_ga(T596, T598)) → U104_gaa(T596, T598, X3837, pN43_in_gga(T598, T596, X3837))
pN43_in_gga(T598, T596, T744) → U105_gga(T598, T596, T744, timesE_in_gga(T598, T596, T744))
U105_gga(T598, T596, T744, timesE_out_gga(T598, T596, T744)) → U106_gga(T598, T596, T744, neqL_in_gg(s(s(s(T596))), T744))
U106_gga(T598, T596, T744, neqL_out_gg(s(s(s(T596))), T744)) → pN43_out_gga(T598, T596, T744)
U104_gaa(T596, T598, X3837, pN43_out_gga(T598, T596, X3837)) → pN27_out_gaa(T596, T598, X3837)
U65_g(T596, pN27_out_gaa(T596, X3836, X3837)) → not_dividesN26_out_g(T596)
U101_g(T590, not_dividesN26_out_g(T590)) → U102_g(T590, prN28_in_g(T590))
prN28_in_g(0) → prN28_out_g(0)
prN28_in_g(s(T761)) → U66_g(T761, pN29_in_g(T761))
pN29_in_g(T761) → U107_g(T761, not_dividesN31_in_g(T761))
not_dividesN31_in_g(T767) → U71_g(T767, pN32_in_gaa(T767, X5607, X5608))
pN32_in_gaa(T767, T769, X5608) → U109_gaa(T767, T769, X5608, divN35_in_ga(T767, T769))
divN35_in_ga(s(s(s(s(s(s(T843)))))), X5896) → U73_ga(T843, X5896, quotW_in_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896))
quotW_in_gga(s(T858), T859, X5931) → U23_gga(T858, T859, X5931, quotW_in_gga(T858, T859, X5931))
quotW_in_gga(0, s(s(s(s(s(T897))))), s(0)) → quotW_out_gga(0, s(s(s(s(s(T897))))), s(0))
quotW_in_gga(0, s(s(s(s(0)))), s(s(X6140))) → U24_gga(X6140, quotX_in_a(X6140))
quotX_in_a(0) → quotX_out_a(0)
U24_gga(X6140, quotX_out_a(X6140)) → quotW_out_gga(0, s(s(s(s(0)))), s(s(X6140)))
quotW_in_gga(0, s(s(s(0))), s(s(X6171))) → U25_gga(X6171, quotY_in_a(X6171))
U25_gga(X6171, quotY_out_a(X6171)) → quotW_out_gga(0, s(s(s(0))), s(s(X6171)))
quotW_in_gga(0, s(s(0)), s(s(X6187))) → U26_gga(X6187, quotZ_in_a(X6187))
U26_gga(X6187, quotZ_out_a(X6187)) → quotW_out_gga(0, s(s(0)), s(s(X6187)))
quotW_in_gga(0, s(0), s(s(X6203))) → U27_gga(X6203, quotN1_in_a(X6203))
U27_gga(X6203, quotN1_out_a(X6203)) → quotW_out_gga(0, s(0), s(s(X6203)))
quotW_in_gga(0, 0, s(s(s(X6284)))) → U28_gga(X6284, quotV_in_a(X6284))
U28_gga(X6284, quotV_out_a(X6284)) → quotW_out_gga(0, 0, s(s(s(X6284))))
U23_gga(T858, T859, X5931, quotW_out_gga(T858, T859, X5931)) → quotW_out_gga(s(T858), T859, X5931)
U73_ga(T843, X5896, quotW_out_gga(T843, s(s(s(s(s(s(s(T843))))))), X5896)) → divN35_out_ga(s(s(s(s(s(s(T843)))))), X5896)
divN35_in_ga(s(s(s(s(s(0))))), s(0)) → divN35_out_ga(s(s(s(s(s(0))))), s(0))
divN35_in_ga(s(s(s(s(0)))), s(0)) → divN35_out_ga(s(s(s(s(0)))), s(0))
divN35_in_ga(s(s(s(0))), s(s(X6999))) → U74_ga(X6999, quotX_in_a(X6999))
U74_ga(X6999, quotX_out_a(X6999)) → divN35_out_ga(s(s(s(0))), s(s(X6999)))
divN35_in_ga(s(s(0)), s(s(X7210))) → U75_ga(X7210, quotY_in_a(X7210))
U75_ga(X7210, quotY_out_a(X7210)) → divN35_out_ga(s(s(0)), s(s(X7210)))
divN35_in_ga(s(0), s(s(X7381))) → U76_ga(X7381, quotZ_in_a(X7381))
U76_ga(X7381, quotZ_out_a(X7381)) → divN35_out_ga(s(0), s(s(X7381)))
divN35_in_ga(0, s(s(X7510))) → U77_ga(X7510, quotN1_in_a(X7510))
U77_ga(X7510, quotN1_out_a(X7510)) → divN35_out_ga(0, s(s(X7510)))
U109_gaa(T767, T769, X5608, divN35_out_ga(T767, T769)) → U110_gaa(T767, T769, X5608, pN44_in_gga(T769, T767, X5608))
pN44_in_gga(T769, T767, T920) → U111_gga(T769, T767, T920, timesE_in_gga(T769, T767, T920))
U111_gga(T769, T767, T920, timesE_out_gga(T769, T767, T920)) → U112_gga(T769, T767, T920, neqL_in_gg(s(s(s(s(T767)))), T920))
U112_gga(T769, T767, T920, neqL_out_gg(s(s(s(s(T767)))), T920)) → pN44_out_gga(T769, T767, T920)
U110_gaa(T767, T769, X5608, pN44_out_gga(T769, T767, X5608)) → pN32_out_gaa(T767, T769, X5608)
U71_g(T767, pN32_out_gaa(T767, X5607, X5608)) → not_dividesN31_out_g(T767)
U107_g(T761, not_dividesN31_out_g(T761)) → U108_g(T761, prN33_in_g(T761))
prN33_in_g(0) → prN33_out_g(0)
prN33_in_g(s(T937)) → U72_g(T937, pN34_in_gg(T937, s(s(s(s(s(s(s(T937)))))))))
pN34_in_gg(T937, T939) → U113_gg(T937, T939, not_dividesN36_in_gg(T937, T939))
not_dividesN36_in_gg(T950, T951) → U78_gg(T950, T951, pN37_in_ggaa(T951, T950, X7570, X7571))
pN37_in_ggaa(T951, T950, T954, X7571) → U115_ggaa(T951, T950, T954, X7571, divN39_in_gga(T951, T950, T954))
divN39_in_gga(0, T983, 0) → divN39_out_gga(0, T983, 0)
divN39_in_gga(s(T992), T993, X7673) → U80_gga(T992, T993, X7673, quotN3_in_gga(T992, T993, X7673))
quotN3_in_gga(0, s(T1000), 0) → quotN3_out_gga(0, s(T1000), 0)
quotN3_in_gga(s(0), s(s(T1017)), 0) → quotN3_out_gga(s(0), s(s(T1017)), 0)
quotN3_in_gga(s(s(0)), s(s(s(T1034))), 0) → quotN3_out_gga(s(s(0)), s(s(s(T1034))), 0)
quotN3_in_gga(s(s(s(0))), s(s(s(s(T1051)))), 0) → quotN3_out_gga(s(s(s(0))), s(s(s(s(T1051)))), 0)
quotN3_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0) → quotN3_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1068))))), 0)
quotN3_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0) → quotN3_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1085)))))), 0)
quotN3_in_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907) → U34_gga(T1094, T1095, X7907, quotN2_in_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907))
quotN2_in_ggga(0, s(T1111), T1112, 0) → quotN2_out_ggga(0, s(T1111), T1112, 0)
quotN2_in_ggga(s(T1125), s(T1126), T1127, X7950) → U31_ggga(T1125, T1126, T1127, X7950, quotN2_in_ggga(T1125, T1126, T1127, X7950))
quotN2_in_ggga(0, 0, T1144, s(0)) → quotN2_out_ggga(0, 0, T1144, s(0))
quotN2_in_ggga(s(0), 0, s(T1161), s(0)) → quotN2_out_ggga(s(0), 0, s(T1161), s(0))
quotN2_in_ggga(s(s(T1170)), 0, s(T1171), s(X8044)) → U32_ggga(T1170, T1171, X8044, quotN3_in_gga(T1170, T1171, X8044))
quotN3_in_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147)) → U35_gga(T1190, X8147, quotN5_in_ga(T1190, X8147))
quotN5_in_ga(0, 0) → quotN5_out_ga(0, 0)
quotN5_in_ga(s(0), 0) → quotN5_out_ga(s(0), 0)
quotN5_in_ga(s(s(0)), 0) → quotN5_out_ga(s(s(0)), 0)
quotN5_in_ga(s(s(s(0))), 0) → quotN5_out_ga(s(s(s(0))), 0)
quotN5_in_ga(s(s(s(s(0)))), 0) → quotN5_out_ga(s(s(s(s(0)))), 0)
quotN5_in_ga(s(s(s(s(s(0))))), 0) → quotN5_out_ga(s(s(s(s(s(0))))), 0)
quotN5_in_ga(s(s(s(s(s(s(0)))))), 0) → quotN5_out_ga(s(s(s(s(s(s(0)))))), 0)
quotN5_in_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446)) → U42_ga(T1229, X8446, quotN5_in_ga(T1229, X8446))
U42_ga(T1229, X8446, quotN5_out_ga(T1229, X8446)) → quotN5_out_ga(s(s(s(s(s(s(s(T1229))))))), s(X8446))
U35_gga(T1190, X8147, quotN5_out_ga(T1190, X8147)) → quotN3_out_gga(s(s(s(s(s(T1190))))), s(s(s(s(s(0))))), s(X8147))
quotN3_in_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483)) → U36_gga(T1239, X8483, quotN6_in_ga(T1239, X8483))
quotN6_in_ga(0, 0) → quotN6_out_ga(0, 0)
quotN6_in_ga(s(0), 0) → quotN6_out_ga(s(0), 0)
quotN6_in_ga(s(s(0)), 0) → quotN6_out_ga(s(s(0)), 0)
quotN6_in_ga(s(s(s(0))), 0) → quotN6_out_ga(s(s(s(0))), 0)
quotN6_in_ga(s(s(s(s(0)))), 0) → quotN6_out_ga(s(s(s(s(0)))), 0)
quotN6_in_ga(s(s(s(s(s(0))))), 0) → quotN6_out_ga(s(s(s(s(s(0))))), 0)
quotN6_in_ga(s(s(s(s(s(s(T1273)))))), s(X8743)) → U43_ga(T1273, X8743, quotN6_in_ga(T1273, X8743))
U43_ga(T1273, X8743, quotN6_out_ga(T1273, X8743)) → quotN6_out_ga(s(s(s(s(s(s(T1273)))))), s(X8743))
U36_gga(T1239, X8483, quotN6_out_ga(T1239, X8483)) → quotN3_out_gga(s(s(s(s(T1239)))), s(s(s(s(0)))), s(X8483))
quotN3_in_gga(s(s(s(T1282))), s(s(s(0))), s(X8777)) → U37_gga(T1282, X8777, quotN7_in_ga(T1282, X8777))
quotN7_in_ga(0, 0) → quotN7_out_ga(0, 0)
quotN7_in_ga(s(0), 0) → quotN7_out_ga(s(0), 0)
quotN7_in_ga(s(s(0)), 0) → quotN7_out_ga(s(s(0)), 0)
quotN7_in_ga(s(s(s(0))), 0) → quotN7_out_ga(s(s(s(0))), 0)
quotN7_in_ga(s(s(s(s(0)))), 0) → quotN7_out_ga(s(s(s(s(0)))), 0)
quotN7_in_ga(s(s(s(s(s(T1311))))), s(X8998)) → U44_ga(T1311, X8998, quotN7_in_ga(T1311, X8998))
U44_ga(T1311, X8998, quotN7_out_ga(T1311, X8998)) → quotN7_out_ga(s(s(s(s(s(T1311))))), s(X8998))
U37_gga(T1282, X8777, quotN7_out_ga(T1282, X8777)) → quotN3_out_gga(s(s(s(T1282))), s(s(s(0))), s(X8777))
quotN3_in_gga(s(s(T1319)), s(s(0)), s(X9029)) → U38_gga(T1319, X9029, quotN8_in_ga(T1319, X9029))
quotN8_in_ga(0, 0) → quotN8_out_ga(0, 0)
quotN8_in_ga(s(0), 0) → quotN8_out_ga(s(0), 0)
quotN8_in_ga(s(s(0)), 0) → quotN8_out_ga(s(s(0)), 0)
quotN8_in_ga(s(s(s(0))), 0) → quotN8_out_ga(s(s(s(0))), 0)
quotN8_in_ga(s(s(s(s(T1343)))), s(X9211)) → U45_ga(T1343, X9211, quotN8_in_ga(T1343, X9211))
U45_ga(T1343, X9211, quotN8_out_ga(T1343, X9211)) → quotN8_out_ga(s(s(s(s(T1343)))), s(X9211))
U38_gga(T1319, X9029, quotN8_out_ga(T1319, X9029)) → quotN3_out_gga(s(s(T1319)), s(s(0)), s(X9029))
quotN3_in_gga(s(T1350), s(0), s(X9239)) → U39_gga(T1350, X9239, quotN9_in_ga(T1350, X9239))
quotN9_in_ga(0, 0) → quotN9_out_ga(0, 0)
quotN9_in_ga(s(0), 0) → quotN9_out_ga(s(0), 0)
quotN9_in_ga(s(s(0)), 0) → quotN9_out_ga(s(s(0)), 0)
quotN9_in_ga(s(s(s(T1369))), s(X9382)) → U46_ga(T1369, X9382, quotN9_in_ga(T1369, X9382))
U46_ga(T1369, X9382, quotN9_out_ga(T1369, X9382)) → quotN9_out_ga(s(s(s(T1369))), s(X9382))
U39_gga(T1350, X9239, quotN9_out_ga(T1350, X9239)) → quotN3_out_gga(s(T1350), s(0), s(X9239))
quotN3_in_gga(T1375, 0, s(X9407)) → U40_gga(T1375, X9407, quotN10_in_ga(T1375, X9407))
quotN10_in_ga(0, 0) → quotN10_out_ga(0, 0)
quotN10_in_ga(s(0), 0) → quotN10_out_ga(s(0), 0)
quotN10_in_ga(s(s(T1389)), s(X9511)) → U47_ga(T1389, X9511, quotN10_in_ga(T1389, X9511))
U47_ga(T1389, X9511, quotN10_out_ga(T1389, X9511)) → quotN10_out_ga(s(s(T1389)), s(X9511))
U40_gga(T1375, X9407, quotN10_out_ga(T1375, X9407)) → quotN3_out_gga(T1375, 0, s(X9407))
U32_ggga(T1170, T1171, X8044, quotN3_out_gga(T1170, T1171, X8044)) → quotN2_out_ggga(s(s(T1170)), 0, s(T1171), s(X8044))
quotN2_in_ggga(s(T1176), 0, 0, s(s(X8060))) → U33_ggga(T1176, X8060, quotN4_in_ga(T1176, X8060))
quotN4_in_ga(0, 0) → quotN4_out_ga(0, 0)
quotN4_in_ga(s(T1185), s(X8125)) → U41_ga(T1185, X8125, quotN4_in_ga(T1185, X8125))
U41_ga(T1185, X8125, quotN4_out_ga(T1185, X8125)) → quotN4_out_ga(s(T1185), s(X8125))
U33_ggga(T1176, X8060, quotN4_out_ga(T1176, X8060)) → quotN2_out_ggga(s(T1176), 0, 0, s(s(X8060)))
U31_ggga(T1125, T1126, T1127, X7950, quotN2_out_ggga(T1125, T1126, T1127, X7950)) → quotN2_out_ggga(s(T1125), s(T1126), T1127, X7950)
U34_gga(T1094, T1095, X7907, quotN2_out_ggga(T1094, T1095, s(s(s(s(s(s(s(T1095))))))), X7907)) → quotN3_out_gga(s(s(s(s(s(s(T1094)))))), s(s(s(s(s(s(T1095)))))), X7907)
U80_gga(T992, T993, X7673, quotN3_out_gga(T992, T993, X7673)) → divN39_out_gga(s(T992), T993, X7673)
U115_ggaa(T951, T950, T954, X7571, divN39_out_gga(T951, T950, T954)) → U116_ggaa(T951, T950, T954, X7571, pN45_in_ggag(T954, T950, X7571, T951))
pN45_in_ggag(T954, T950, T1396, T951) → U117_ggag(T954, T950, T1396, T951, timesE_in_gga(T954, T950, T1396))
U117_ggag(T954, T950, T1396, T951, timesE_out_gga(T954, T950, T1396)) → U118_ggag(T954, T950, T1396, T951, neqM_in_gg(T951, T1396))
U118_ggag(T954, T950, T1396, T951, neqM_out_gg(T951, T1396)) → pN45_out_ggag(T954, T950, T1396, T951)
U116_ggaa(T951, T950, T954, X7571, pN45_out_ggag(T954, T950, X7571, T951)) → pN37_out_ggaa(T951, T950, T954, X7571)
U78_gg(T950, T951, pN37_out_ggaa(T951, T950, X7570, X7571)) → not_dividesN36_out_gg(T950, T951)
U113_gg(T937, T939, not_dividesN36_out_gg(T937, T939)) → U114_gg(T937, T939, prN38_in_gg(T939, T937))
prN38_in_gg(T1407, 0) → prN38_out_gg(T1407, 0)
prN38_in_gg(T1412, s(T1413)) → U79_gg(T1412, T1413, pN34_in_gg(T1413, T1412))
U79_gg(T1412, T1413, pN34_out_gg(T1413, T1412)) → prN38_out_gg(T1412, s(T1413))
U114_gg(T937, T939, prN38_out_gg(T939, T937)) → pN34_out_gg(T937, T939)
U72_g(T937, pN34_out_gg(T937, s(s(s(s(s(s(s(T937))))))))) → prN33_out_g(s(T937))
U108_g(T761, prN33_out_g(T761)) → pN29_out_g(T761)
U66_g(T761, pN29_out_g(T761)) → prN28_out_g(s(T761))
U102_g(T590, prN28_out_g(T590)) → pN24_out_g(T590)
U61_g(T590, pN24_out_g(T590)) → prN23_out_g(s(T590))
U96_g(T424, prN23_out_g(T424)) → pN19_out_g(T424)
U56_g(T424, pN19_out_g(T424)) → prN18_out_g(s(T424))
U90_g(T263, prN18_out_g(T263)) → pN14_out_g(T263)
U50_g(T263, pN14_out_g(T263)) → prN13_out_g(s(T263))
U82_g(T14, prN13_out_g(T14)) → pB_out_g(T14)
U1_g(T14, pB_out_g(T14)) → primeA_out_g(s(s(s(T14))))

(120) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(121) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTC_IN_GGA(s(T111), T112, X358) → QUOTC_IN_GGA(T111, T112, X358)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTC_IN_GGA(x1, x2, x3) = QUOTC_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(122) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(123) Obligation:

Q DP problem:
The TRS P consists of the following rules:

QUOTC_IN_GGA(s(T111), T112) → QUOTC_IN_GGA(T111, T112)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(124) 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:

QUOTC_IN_GGA(s(T111), T112) → QUOTC_IN_GGA(T111, T112)
The graph contains the following edges 1 > 1, 2 >= 2