Left Termination proof of /tmp/tmpxPQxtL/quot.pl

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

0 Prolog

↳1 PrologToPiTRSViaGraphTransformerProof (⇒, 1272 ms)

↳2 PiTRS

↳3 DependencyPairsProof (⇔, 894 ms)

↳4 PiDP

↳5 DependencyGraphProof (⇔, 221 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

(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).

Query: div(g,g,a)

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

Transformed Prolog program to (Pi-)TRS.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
3 [label="A: div(T1, T2, T3)\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
4 [label="4: div(T1, T2, T3), SCOPE: 1, CLAUSE: 0\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="B: quot(T7, T8, T8, T10)\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 1 | quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 2 | quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 3\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 1\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 2 | quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 3\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 2\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 3\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: quot(T28, T29, s(T29), T31)\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 1 | quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 2 | quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 3\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 1\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 2 | quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 3\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 2\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 3\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: quot(T51, T52, s(s(T52)), T54)\n\nT51 is ground\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 1 | quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 2 | quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 3\n\nT51 is ground\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 1\n\nT51 is ground\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 2 | quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 3\n\nT51 is ground\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 2\n\nT51 is ground\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 3\n\nT51 is ground\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: quot(T74, T75, s(s(s(T75))), T77)\n\nT74 is ground\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 1 | quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 2 | quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 3\n\nT74 is ground\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 1\n\nT74 is ground\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 2 | quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 3\n\nT74 is ground\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 2\n\nT74 is ground\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 3\n\nT74 is ground\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: quot(T97, T98, s(s(s(s(T98)))), T100)\n\nT97 is ground\nT98 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 1 | quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 2 | quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 3\n\nT97 is ground\nT98 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 1\n\nT97 is ground\nT98 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 2 | quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 3\n\nT97 is ground\nT98 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 2\n\nT97 is ground\nT98 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 3\n\nT97 is ground\nT98 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: quot(T120, T121, s(s(s(s(s(T121))))), T123)\n\nT120 is ground\nT121 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 1 | quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 2 | quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 3\n\nT120 is ground\nT121 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 1\n\nT120 is ground\nT121 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 2 | quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 3\n\nT120 is ground\nT121 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 2\n\nT120 is ground\nT121 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 3\n\nT120 is ground\nT121 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: quot(T143, T144, s(s(s(s(s(s(T144)))))), T146)\n\nT143 is ground\nT144 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 1 | quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 2 | quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 3\n\nT143 is ground\nT144 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 1\n\nT143 is ground\nT144 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 2 | quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 3\n\nT143 is ground\nT144 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 2\n\nT143 is ground\nT144 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 3\n\nT143 is ground\nT144 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169)\n\nT166 is ground\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 1 | quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 2 | quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 3\n\nT166 is ground\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 1\n\nT166 is ground\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 2 | quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 3\n\nT166 is ground\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
246 [label="246: quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 2\n\nT166 is ground\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="248: quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 3\n\nT166 is ground\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
255 [label="255: quot(T189, T190, s(s(s(s(s(s(s(s(T190)))))))), T192)\n\nT189 is ground\nT190 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
256 [label="256: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
261 [label="C: quot(T189, T190, s(T195), T192)\n\nT189 is ground\nT190 is ground\nT195 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="270: quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 1 | quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 2 | quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 3\n\nT189 is ground\nT190 is ground\nT195 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
271 [label="271: quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 1\n\nT189 is ground\nT190 is ground\nT195 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
272 [label="272: quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 2 | quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 3\n\nT189 is ground\nT190 is ground\nT195 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
285 [label="285: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
286 [label="286: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
288 [label="288: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
289 [label="289: quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 2\n\nT189 is ground\nT190 is ground\nT195 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
290 [label="290: quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 3\n\nT189 is ground\nT190 is ground\nT195 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
303 [label="303: quot(T226, T227, s(T228), T230)\n\nT226 is ground\nT227 is ground\nT228 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
304 [label="304: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
307 [label="307: quot(T241, s(T242), s(T242), T244)\n\nT241 is ground\nT242 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
308 [label="308: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
323 [label="D: quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253)\n\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
324 [label="324: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
328 [label="328: quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 1 | quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 2 | quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 3\n\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
340 [label="340: quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 1\n\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
343 [label="343: quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 2 | quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 3\n\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
345 [label="345: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
347 [label="347: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
348 [label="348: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
352 [label="352: quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 2\n\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
353 [label="353: quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 3\n\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
357 [label="357: quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264)\n\nT262 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
358 [label="358: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
361 [label="361: quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 1 | quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 2 | quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 3\n\nT262 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
362 [label="362: quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 1\n\nT262 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
363 [label="363: quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 2 | quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 3\n\nT262 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
368 [label="368: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
369 [label="369: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
370 [label="370: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
371 [label="371: quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 2\n\nT262 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
372 [label="372: quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 3\n\nT262 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
379 [label="379: quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275)\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
381 [label="381: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
386 [label="386: quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 1 | quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 2 | quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 3\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
387 [label="387: quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 1\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
388 [label="388: quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 2 | quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 3\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
389 [label="389: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
390 [label="390: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
391 [label="391: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
397 [label="397: quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 2\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
398 [label="398: quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 3\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
404 [label="404: quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286)\n\nT284 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
405 [label="405: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
427 [label="427: quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 1 | quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 2 | quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 3\n\nT284 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
429 [label="429: quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 1\n\nT284 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
430 [label="430: quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 2 | quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 3\n\nT284 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
439 [label="439: true\n\n", 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];
445 [label="445: quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 2\n\nT284 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
446 [label="446: quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 3\n\nT284 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
468 [label="468: quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297)\n\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
469 [label="469: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
475 [label="475: quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 1 | quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 2 | quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 3\n\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
479 [label="479: quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 1\n\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
480 [label="480: quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 2 | quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 3\n\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
483 [label="483: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
484 [label="484: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
485 [label="485: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
504 [label="504: quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 2\n\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
505 [label="505: quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 3\n\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
511 [label="511: quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308)\n\nT306 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
512 [label="512: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
523 [label="523: quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 1 | quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 2 | quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 3\n\nT306 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
528 [label="528: quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 1\n\nT306 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
529 [label="529: quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 2 | quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 3\n\nT306 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
531 [label="531: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
532 [label="532: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
533 [label="533: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
538 [label="538: quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 2\n\nT306 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
539 [label="539: quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 3\n\nT306 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
554 [label="554: quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319)\n\nT317 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
555 [label="555: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
561 [label="561: quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 1 | quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 2 | quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 3\n\nT317 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
562 [label="562: quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 1\n\nT317 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
563 [label="563: quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 2 | quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 3\n\nT317 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
564 [label="564: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
566 [label="566: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
568 [label="568: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
569 [label="569: quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 2\n\nT317 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
570 [label="570: quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 3\n\nT317 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
571 [label="571: quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330)\n\nT328 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
572 [label="572: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
579 [label="579: quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330), SCOPE: 18, CLAUSE: 1 | quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330), SCOPE: 18, CLAUSE: 2 | quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330), SCOPE: 18, CLAUSE: 3\n\nT328 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
580 [label="580: quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330), SCOPE: 18, CLAUSE: 2 | quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330), SCOPE: 18, CLAUSE: 3\n\nT328 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
584 [label="584: quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330), SCOPE: 18, CLAUSE: 3\n\nT328 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
587 [label="587: quot(T336, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T338)\n\nT336 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
588 [label="588: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
591 [label="591: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
595 [label="595: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
596 [label="596: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
597 [label="597: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
600 [label="600: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
601 [label="601: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
602 [label="602: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
607 [label="E: quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352)\n\nT350 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
608 [label="608: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
615 [label="615: quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 1 | quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 2 | quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 3\n\nT350 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
616 [label="616: quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 1\n\nT350 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
617 [label="617: quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 2 | quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 3\n\nT350 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
619 [label="619: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
620 [label="620: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
621 [label="621: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
624 [label="624: quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 2\n\nT350 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
625 [label="625: quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 3\n\nT350 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
626 [label="626: quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363)\n\nT361 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
627 [label="627: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
633 [label="633: quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 1 | quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 2 | quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 3\n\nT361 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
639 [label="639: quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 1\n\nT361 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
640 [label="640: quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 2 | quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 3\n\nT361 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
641 [label="641: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
642 [label="642: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
643 [label="643: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
648 [label="648: quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 2\n\nT361 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
649 [label="649: quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 3\n\nT361 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
656 [label="656: quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374)\n\nT372 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
657 [label="657: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
661 [label="661: quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 1 | quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 2 | quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 3\n\nT372 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
667 [label="667: quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 1\n\nT372 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
668 [label="668: quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 2 | quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 3\n\nT372 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
669 [label="669: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
670 [label="670: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
671 [label="671: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
677 [label="677: quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 2\n\nT372 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
678 [label="678: quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 3\n\nT372 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
684 [label="684: quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385)\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
685 [label="685: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
691 [label="691: quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 1 | quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 2 | quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 3\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
695 [label="695: quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 1\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
696 [label="696: quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 2 | quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 3\n\nT383 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];
704 [label="704: quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 2\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
705 [label="705: quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 3\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
714 [label="714: quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396)\n\nT394 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
715 [label="715: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
721 [label="721: quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 1 | quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 2 | quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 3\n\nT394 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
725 [label="725: quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 1\n\nT394 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
726 [label="726: quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 2 | quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 3\n\nT394 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
727 [label="727: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
728 [label="728: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
729 [label="729: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
734 [label="734: quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 2\n\nT394 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
735 [label="735: quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 3\n\nT394 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
739 [label="739: quot(T405, s(0), s(s(s(s(s(s(0)))))), T407)\n\nT405 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
741 [label="741: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
749 [label="749: quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 1 | quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 2 | quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 3\n\nT405 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
750 [label="750: quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 1\n\nT405 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
751 [label="751: quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 2 | quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 3\n\nT405 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
757 [label="757: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
758 [label="758: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
759 [label="759: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
762 [label="762: quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 2\n\nT405 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
763 [label="763: quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 3\n\nT405 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
768 [label="768: quot(T416, 0, s(s(s(s(s(s(0)))))), T418)\n\nT416 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
769 [label="769: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
775 [label="775: quot(T416, 0, s(s(s(s(s(s(0)))))), T418), SCOPE: 25, CLAUSE: 1 | quot(T416, 0, s(s(s(s(s(s(0)))))), T418), SCOPE: 25, CLAUSE: 2 | quot(T416, 0, s(s(s(s(s(s(0)))))), T418), SCOPE: 25, CLAUSE: 3\n\nT416 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
777 [label="777: quot(T416, 0, s(s(s(s(s(s(0)))))), T418), SCOPE: 25, CLAUSE: 2 | quot(T416, 0, s(s(s(s(s(s(0)))))), T418), SCOPE: 25, CLAUSE: 3\n\nT416 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
781 [label="781: quot(T416, 0, s(s(s(s(s(s(0)))))), T418), SCOPE: 25, CLAUSE: 3\n\nT416 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
786 [label="786: quot(T424, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T426)\n\nT424 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
787 [label="787: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
790 [label="790: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
792 [label="792: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
796 [label="796: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
798 [label="798: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
800 [label="800: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
802 [label="802: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
807 [label="F: quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439)\n\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
808 [label="808: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
813 [label="813: quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 1 | quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 2 | quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 3\n\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
818 [label="818: quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 1\n\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
819 [label="819: quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 2 | quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 3\n\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
823 [label="823: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
824 [label="824: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
825 [label="825: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
830 [label="830: quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 2\n\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
831 [label="831: quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 3\n\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
833 [label="833: quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450)\n\nT448 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
834 [label="834: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
837 [label="837: quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 1 | quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 2 | quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 3\n\nT448 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
839 [label="839: quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 1\n\nT448 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
840 [label="840: quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 2 | quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 3\n\nT448 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
842 [label="842: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
843 [label="843: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
844 [label="844: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
845 [label="845: quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 2\n\nT448 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
846 [label="846: quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 3\n\nT448 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
855 [label="855: quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461)\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
856 [label="856: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
860 [label="860: quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 1 | quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 2 | quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 3\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
861 [label="861: quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 1\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
862 [label="862: quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 2 | quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 3\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
864 [label="864: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
865 [label="865: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
866 [label="866: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
869 [label="869: quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 2\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
870 [label="870: quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 3\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
879 [label="879: quot(T470, s(s(0)), s(s(s(s(s(0))))), T472)\n\nT470 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
881 [label="881: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
886 [label="886: quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 1 | quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 2 | quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 3\n\nT470 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
887 [label="887: quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 1\n\nT470 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
888 [label="888: quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 2 | quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 3\n\nT470 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
890 [label="890: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
891 [label="891: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
892 [label="892: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
898 [label="898: quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 2\n\nT470 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
899 [label="899: quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 3\n\nT470 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
906 [label="906: quot(T481, s(0), s(s(s(s(s(0))))), T483)\n\nT481 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
907 [label="907: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
919 [label="919: quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 1 | quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 2 | quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 3\n\nT481 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
923 [label="923: quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 1\n\nT481 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
924 [label="924: quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 2 | quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 3\n\nT481 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
925 [label="925: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
926 [label="926: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
927 [label="927: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
943 [label="943: quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 2\n\nT481 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
944 [label="944: quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 3\n\nT481 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
949 [label="949: quot(T492, 0, s(s(s(s(s(0))))), T494)\n\nT492 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
950 [label="950: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
955 [label="955: quot(T492, 0, s(s(s(s(s(0))))), T494), SCOPE: 31, CLAUSE: 1 | quot(T492, 0, s(s(s(s(s(0))))), T494), SCOPE: 31, CLAUSE: 2 | quot(T492, 0, s(s(s(s(s(0))))), T494), SCOPE: 31, CLAUSE: 3\n\nT492 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
957 [label="957: quot(T492, 0, s(s(s(s(s(0))))), T494), SCOPE: 31, CLAUSE: 2 | quot(T492, 0, s(s(s(s(s(0))))), T494), SCOPE: 31, CLAUSE: 3\n\nT492 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
960 [label="960: quot(T492, 0, s(s(s(s(s(0))))), T494), SCOPE: 31, CLAUSE: 3\n\nT492 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
967 [label="967: quot(T500, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T502)\n\nT500 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
968 [label="968: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
973 [label="973: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
975 [label="975: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
978 [label="978: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
979 [label="979: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
983 [label="983: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
988 [label="G: quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514)\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
989 [label="989: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
993 [label="993: quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 1 | quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 2 | quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 3\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
999 [label="999: quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 1\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1000 [label="1000: quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 2 | quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 3\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1001 [label="1001: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1002 [label="1002: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1003 [label="1003: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1009 [label="1009: quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 2\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1010 [label="1010: quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 3\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1018 [label="1018: quot(T523, s(s(s(0))), s(s(s(s(0)))), T525)\n\nT523 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1019 [label="1019: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1030 [label="1030: quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 1 | quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 2 | quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 3\n\nT523 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1031 [label="1031: quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 1\n\nT523 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1032 [label="1032: quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 2 | quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 3\n\nT523 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1037 [label="1037: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1041 [label="1041: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1042 [label="1042: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1043 [label="1043: quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 2\n\nT523 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1044 [label="1044: quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 3\n\nT523 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1059 [label="1059: quot(T534, s(s(0)), s(s(s(s(0)))), T536)\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1060 [label="1060: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1069 [label="1069: quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 1 | quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 2 | quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 3\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1070 [label="1070: quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 1\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1071 [label="1071: quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 2 | quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 3\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1081 [label="1081: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1082 [label="1082: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1083 [label="1083: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1088 [label="1088: quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 2\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1089 [label="1089: quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 3\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1095 [label="1095: quot(T545, s(0), s(s(s(s(0)))), T547)\n\nT545 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1096 [label="1096: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1101 [label="1101: quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 1 | quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 2 | quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 3\n\nT545 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1106 [label="1106: quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 1\n\nT545 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1107 [label="1107: quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 2 | quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 3\n\nT545 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1111 [label="1111: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1112 [label="1112: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1113 [label="1113: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1116 [label="1116: quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 2\n\nT545 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1118 [label="1118: quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 3\n\nT545 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1123 [label="1123: quot(T556, 0, s(s(s(s(0)))), T558)\n\nT556 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1124 [label="1124: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1130 [label="1130: quot(T556, 0, s(s(s(s(0)))), T558), SCOPE: 36, CLAUSE: 1 | quot(T556, 0, s(s(s(s(0)))), T558), SCOPE: 36, CLAUSE: 2 | quot(T556, 0, s(s(s(s(0)))), T558), SCOPE: 36, CLAUSE: 3\n\nT556 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1131 [label="1131: quot(T556, 0, s(s(s(s(0)))), T558), SCOPE: 36, CLAUSE: 2 | quot(T556, 0, s(s(s(s(0)))), T558), SCOPE: 36, CLAUSE: 3\n\nT556 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1135 [label="1135: quot(T556, 0, s(s(s(s(0)))), T558), SCOPE: 36, CLAUSE: 3\n\nT556 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1141 [label="1141: quot(T564, s(s(s(s(0)))), s(s(s(s(0)))), T566)\n\nT564 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1142 [label="1142: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1147 [label="1147: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1149 [label="1149: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1150 [label="1150: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1153 [label="1153: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1159 [label="H: quot(T575, s(s(s(0))), s(s(s(0))), T577)\n\nT575 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1160 [label="1160: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1165 [label="1165: quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 1 | quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 2 | quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 3\n\nT575 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1167 [label="1167: quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 1\n\nT575 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1168 [label="1168: quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 2 | quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 3\n\nT575 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1171 [label="1171: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1172 [label="1172: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1173 [label="1173: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1177 [label="1177: quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 2\n\nT575 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1178 [label="1178: quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 3\n\nT575 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1184 [label="1184: quot(T586, s(s(0)), s(s(s(0))), T588)\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1185 [label="1185: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1188 [label="1188: quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 1 | quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 2 | quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 3\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1192 [label="1192: quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 1\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1193 [label="1193: quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 2 | quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 3\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1195 [label="1195: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1197 [label="1197: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1198 [label="1198: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1202 [label="1202: quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 2\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1203 [label="1203: quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 3\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1212 [label="1212: quot(T597, s(0), s(s(s(0))), T599)\n\nT597 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1213 [label="1213: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1219 [label="1219: quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 1 | quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 2 | quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 3\n\nT597 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1220 [label="1220: quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 1\n\nT597 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1221 [label="1221: quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 2 | quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 3\n\nT597 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1226 [label="1226: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1227 [label="1227: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1228 [label="1228: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1230 [label="1230: quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 2\n\nT597 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1231 [label="1231: quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 3\n\nT597 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1240 [label="1240: quot(T608, 0, s(s(s(0))), T610)\n\nT608 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1241 [label="1241: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1246 [label="1246: quot(T608, 0, s(s(s(0))), T610), SCOPE: 40, CLAUSE: 1 | quot(T608, 0, s(s(s(0))), T610), SCOPE: 40, CLAUSE: 2 | quot(T608, 0, s(s(s(0))), T610), SCOPE: 40, CLAUSE: 3\n\nT608 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1250 [label="1250: quot(T608, 0, s(s(s(0))), T610), SCOPE: 40, CLAUSE: 2 | quot(T608, 0, s(s(s(0))), T610), SCOPE: 40, CLAUSE: 3\n\nT608 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1251 [label="1251: quot(T608, 0, s(s(s(0))), T610), SCOPE: 40, CLAUSE: 3\n\nT608 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1256 [label="1256: quot(T616, s(s(s(0))), s(s(s(0))), T618)\n\nT616 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1257 [label="1257: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1262 [label="1262: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1264 [label="1264: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1265 [label="1265: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1271 [label="I: quot(T626, s(s(0)), s(s(0)), T628)\n\nT626 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1272 [label="1272: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1275 [label="1275: quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 1 | quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 2 | quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 3\n\nT626 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1278 [label="1278: quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 1\n\nT626 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1279 [label="1279: quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 2 | quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 3\n\nT626 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1281 [label="1281: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1282 [label="1282: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1283 [label="1283: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1287 [label="1287: quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 2\n\nT626 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1288 [label="1288: quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 3\n\nT626 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1295 [label="1295: quot(T637, s(0), s(s(0)), T639)\n\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1296 [label="1296: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1302 [label="1302: quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 1 | quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 2 | quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 3\n\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1308 [label="1308: quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 1\n\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1309 [label="1309: quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 2 | quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 3\n\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1310 [label="1310: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1311 [label="1311: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1312 [label="1312: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1317 [label="1317: quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 2\n\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1318 [label="1318: quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 3\n\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1323 [label="1323: quot(T648, 0, s(s(0)), T650)\n\nT648 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1324 [label="1324: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1328 [label="1328: quot(T648, 0, s(s(0)), T650), SCOPE: 43, CLAUSE: 1 | quot(T648, 0, s(s(0)), T650), SCOPE: 43, CLAUSE: 2 | quot(T648, 0, s(s(0)), T650), SCOPE: 43, CLAUSE: 3\n\nT648 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1330 [label="1330: quot(T648, 0, s(s(0)), T650), SCOPE: 43, CLAUSE: 2 | quot(T648, 0, s(s(0)), T650), SCOPE: 43, CLAUSE: 3\n\nT648 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1333 [label="1333: quot(T648, 0, s(s(0)), T650), SCOPE: 43, CLAUSE: 3\n\nT648 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1337 [label="1337: quot(T656, s(s(0)), s(s(0)), T658)\n\nT656 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1338 [label="1338: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1342 [label="1342: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1343 [label="1343: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1344 [label="J: quot(T665, s(0), s(0), T667)\n\nT665 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1345 [label="1345: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1346 [label="1346: quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 1 | quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 2 | quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 3\n\nT665 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1347 [label="1347: quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 1\n\nT665 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1348 [label="1348: quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 2 | quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 3\n\nT665 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1349 [label="1349: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1350 [label="1350: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1351 [label="1351: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1352 [label="1352: quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 2\n\nT665 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1353 [label="1353: quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 3\n\nT665 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1354 [label="1354: quot(T676, 0, s(0), T678)\n\nT676 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1355 [label="1355: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1356 [label="1356: quot(T676, 0, s(0), T678), SCOPE: 45, CLAUSE: 1 | quot(T676, 0, s(0), T678), SCOPE: 45, CLAUSE: 2 | quot(T676, 0, s(0), T678), SCOPE: 45, CLAUSE: 3\n\nT676 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1357 [label="1357: quot(T676, 0, s(0), T678), SCOPE: 45, CLAUSE: 2 | quot(T676, 0, s(0), T678), SCOPE: 45, CLAUSE: 3\n\nT676 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1358 [label="1358: quot(T676, 0, s(0), T678), SCOPE: 45, CLAUSE: 3\n\nT676 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1359 [label="1359: quot(T684, s(0), s(0), T686)\n\nT684 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1360 [label="1360: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1361 [label="1361: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1362 [label="1362: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1363 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 1363 [arrowhead = none ];
1363 -> 4;

1364 [label="ONLY EVAL with clause\ndiv(X4, X5, X6) :- quot(X4, X5, X5, X6).\nand substitutionT1 -> T7,\nX4 -> T7,\nT2 -> T8,\nX5 -> T8,\nT3 -> T10,\nX6 -> T10,\nT9 -> T10", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 1364 [arrowhead = none ];
1364 -> 8;

1365 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
8 -> 1365 [arrowhead = none ];
1365 -> 11;

1366 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 1366 [arrowhead = none ];
1366 -> 12;

1367 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 1367 [arrowhead = none ];
1367 -> 14;

1368 [label="EVAL with clause\nquot(0, s(X15), s(X16), 0).\nand substitutionT7 -> 0,\nX15 -> T15,\nT8 -> s(T15),\nX16 -> T15,\nT10 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 1368 [arrowhead = none ];
1368 -> 17;

1369 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 1369 [arrowhead = none ];
1369 -> 19;

1370 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 1370 [arrowhead = none ];
1370 -> 28;

1371 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 1371 [arrowhead = none ];
1371 -> 29;

1372 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 1372 [arrowhead = none ];
1372 -> 21;

1373 [label="EVAL with clause\nquot(s(X33), s(X34), X35, X36) :- quot(X33, X34, X35, X36).\nand substitutionX33 -> T28,\nT7 -> s(T28),\nX34 -> T29,\nT8 -> s(T29),\nX35 -> s(T29),\nT10 -> T31,\nX36 -> T31,\nT30 -> T31", fontsize=14, style = filled, fillcolor = lightblue];
28 -> 1373 [arrowhead = none ];
1373 -> 34;

1374 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
28 -> 1374 [arrowhead = none ];
1374 -> 35;

1375 [label="BACKTRACK\nfor 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];
29 -> 1375 [arrowhead = none ];
1375 -> 1362;

1376 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
34 -> 1376 [arrowhead = none ];
1376 -> 37;

1377 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
37 -> 1377 [arrowhead = none ];
1377 -> 39;

1378 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
37 -> 1378 [arrowhead = none ];
1378 -> 41;

1379 [label="EVAL with clause\nquot(0, s(X49), s(X50), 0).\nand substitutionT28 -> 0,\nX49 -> T38,\nT29 -> s(T38),\nX50 -> s(T38),\nT31 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 1379 [arrowhead = none ];
1379 -> 52;

1380 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
39 -> 1380 [arrowhead = none ];
1380 -> 53;

1381 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
41 -> 1381 [arrowhead = none ];
1381 -> 64;

1382 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
41 -> 1382 [arrowhead = none ];
1382 -> 65;

1383 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
52 -> 1383 [arrowhead = none ];
1383 -> 54;

1384 [label="EVAL with clause\nquot(s(X67), s(X68), X69, X70) :- quot(X67, X68, X69, X70).\nand substitutionX67 -> T51,\nT28 -> s(T51),\nX68 -> T52,\nT29 -> s(T52),\nX69 -> s(s(T52)),\nT31 -> T54,\nX70 -> T54,\nT53 -> T54", fontsize=14, style = filled, fillcolor = lightblue];
64 -> 1384 [arrowhead = none ];
1384 -> 71;

1385 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
64 -> 1385 [arrowhead = none ];
1385 -> 72;

1386 [label="EVAL with clause\nquot(X1527, 0, s(X1528), s(X1529)) :- quot(X1527, s(X1528), s(X1528), X1529).\nand substitutionT28 -> T665,\nX1527 -> T665,\nT29 -> 0,\nX1528 -> 0,\nX1529 -> T667,\nT31 -> s(T667),\nT666 -> T667", fontsize=14, style = filled, fillcolor = lightblue];
65 -> 1386 [arrowhead = none ];
1386 -> 1344;

1387 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
65 -> 1387 [arrowhead = none ];
1387 -> 1345;

1388 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
71 -> 1388 [arrowhead = none ];
1388 -> 77;

1389 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 1389 [arrowhead = none ];
1389 -> 80;

1390 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 1390 [arrowhead = none ];
1390 -> 82;

1391 [label="EVAL with clause\nquot(0, s(X83), s(X84), 0).\nand substitutionT51 -> 0,\nX83 -> T61,\nT52 -> s(T61),\nX84 -> s(s(T61)),\nT54 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 1391 [arrowhead = none ];
1391 -> 87;

1392 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
80 -> 1392 [arrowhead = none ];
1392 -> 88;

1393 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
82 -> 1393 [arrowhead = none ];
1393 -> 92;

1394 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
82 -> 1394 [arrowhead = none ];
1394 -> 93;

1395 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
87 -> 1395 [arrowhead = none ];
1395 -> 89;

1396 [label="EVAL with clause\nquot(s(X101), s(X102), X103, X104) :- quot(X101, X102, X103, X104).\nand substitutionX101 -> T74,\nT51 -> s(T74),\nX102 -> T75,\nT52 -> s(T75),\nX103 -> s(s(s(T75))),\nT54 -> T77,\nX104 -> T77,\nT76 -> T77", fontsize=14, style = filled, fillcolor = lightblue];
92 -> 1396 [arrowhead = none ];
1396 -> 97;

1397 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
92 -> 1397 [arrowhead = none ];
1397 -> 98;

1398 [label="EVAL with clause\nquot(X1421, 0, s(X1422), s(X1423)) :- quot(X1421, s(X1422), s(X1422), X1423).\nand substitutionT51 -> T626,\nX1421 -> T626,\nT52 -> 0,\nX1422 -> s(0),\nX1423 -> T628,\nT54 -> s(T628),\nT627 -> T628", fontsize=14, style = filled, fillcolor = lightblue];
93 -> 1398 [arrowhead = none ];
1398 -> 1271;

1399 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
93 -> 1399 [arrowhead = none ];
1399 -> 1272;

1400 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
97 -> 1400 [arrowhead = none ];
1400 -> 104;

1401 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
104 -> 1401 [arrowhead = none ];
1401 -> 107;

1402 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
104 -> 1402 [arrowhead = none ];
1402 -> 108;

1403 [label="EVAL with clause\nquot(0, s(X117), s(X118), 0).\nand substitutionT74 -> 0,\nX117 -> T84,\nT75 -> s(T84),\nX118 -> s(s(s(T84))),\nT77 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
107 -> 1403 [arrowhead = none ];
1403 -> 111;

1404 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
107 -> 1404 [arrowhead = none ];
1404 -> 112;

1405 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
108 -> 1405 [arrowhead = none ];
1405 -> 116;

1406 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
108 -> 1406 [arrowhead = none ];
1406 -> 117;

1407 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
111 -> 1407 [arrowhead = none ];
1407 -> 113;

1408 [label="EVAL with clause\nquot(s(X135), s(X136), X137, X138) :- quot(X135, X136, X137, X138).\nand substitutionX135 -> T97,\nT74 -> s(T97),\nX136 -> T98,\nT75 -> s(T98),\nX137 -> s(s(s(s(T98)))),\nT77 -> T100,\nX138 -> T100,\nT99 -> T100", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 1408 [arrowhead = none ];
1408 -> 119;

1409 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
116 -> 1409 [arrowhead = none ];
1409 -> 121;

1410 [label="EVAL with clause\nquot(X1278, 0, s(X1279), s(X1280)) :- quot(X1278, s(X1279), s(X1279), X1280).\nand substitutionT74 -> T575,\nX1278 -> T575,\nT75 -> 0,\nX1279 -> s(s(0)),\nX1280 -> T577,\nT77 -> s(T577),\nT576 -> T577", fontsize=14, style = filled, fillcolor = lightblue];
117 -> 1410 [arrowhead = none ];
1410 -> 1159;

1411 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
117 -> 1411 [arrowhead = none ];
1411 -> 1160;

1412 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
119 -> 1412 [arrowhead = none ];
1412 -> 129;

1413 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
129 -> 1413 [arrowhead = none ];
1413 -> 131;

1414 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
129 -> 1414 [arrowhead = none ];
1414 -> 132;

1415 [label="EVAL with clause\nquot(0, s(X151), s(X152), 0).\nand substitutionT97 -> 0,\nX151 -> T107,\nT98 -> s(T107),\nX152 -> s(s(s(s(T107)))),\nT100 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 1415 [arrowhead = none ];
1415 -> 137;

1416 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
131 -> 1416 [arrowhead = none ];
1416 -> 138;

1417 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
132 -> 1417 [arrowhead = none ];
1417 -> 142;

1418 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
132 -> 1418 [arrowhead = none ];
1418 -> 143;

1419 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
137 -> 1419 [arrowhead = none ];
1419 -> 139;

1420 [label="EVAL with clause\nquot(s(X169), s(X170), X171, X172) :- quot(X169, X170, X171, X172).\nand substitutionX169 -> T120,\nT97 -> s(T120),\nX170 -> T121,\nT98 -> s(T121),\nX171 -> s(s(s(s(s(T121))))),\nT100 -> T123,\nX172 -> T123,\nT122 -> T123", fontsize=14, style = filled, fillcolor = lightblue];
142 -> 1420 [arrowhead = none ];
1420 -> 147;

1421 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
142 -> 1421 [arrowhead = none ];
1421 -> 148;

1422 [label="EVAL with clause\nquot(X1098, 0, s(X1099), s(X1100)) :- quot(X1098, s(X1099), s(X1099), X1100).\nand substitutionT97 -> T512,\nX1098 -> T512,\nT98 -> 0,\nX1099 -> s(s(s(0))),\nX1100 -> T514,\nT100 -> s(T514),\nT513 -> T514", fontsize=14, style = filled, fillcolor = lightblue];
143 -> 1422 [arrowhead = none ];
1422 -> 988;

1423 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
143 -> 1423 [arrowhead = none ];
1423 -> 989;

1424 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
147 -> 1424 [arrowhead = none ];
1424 -> 154;

1425 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 1425 [arrowhead = none ];
1425 -> 157;

1426 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 1426 [arrowhead = none ];
1426 -> 158;

1427 [label="EVAL with clause\nquot(0, s(X185), s(X186), 0).\nand substitutionT120 -> 0,\nX185 -> T130,\nT121 -> s(T130),\nX186 -> s(s(s(s(s(T130))))),\nT123 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
157 -> 1427 [arrowhead = none ];
1427 -> 164;

1428 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
157 -> 1428 [arrowhead = none ];
1428 -> 165;

1429 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
158 -> 1429 [arrowhead = none ];
1429 -> 169;

1430 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
158 -> 1430 [arrowhead = none ];
1430 -> 170;

1431 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
164 -> 1431 [arrowhead = none ];
1431 -> 166;

1432 [label="EVAL with clause\nquot(s(X203), s(X204), X205, X206) :- quot(X203, X204, X205, X206).\nand substitutionX203 -> T143,\nT120 -> s(T143),\nX204 -> T144,\nT121 -> s(T144),\nX205 -> s(s(s(s(s(s(T144)))))),\nT123 -> T146,\nX206 -> T146,\nT145 -> T146", fontsize=14, style = filled, fillcolor = lightblue];
169 -> 1432 [arrowhead = none ];
1432 -> 182;

1433 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
169 -> 1433 [arrowhead = none ];
1433 -> 185;

1434 [label="EVAL with clause\nquot(X881, 0, s(X882), s(X883)) :- quot(X881, s(X882), s(X882), X883).\nand substitutionT120 -> T437,\nX881 -> T437,\nT121 -> 0,\nX882 -> s(s(s(s(0)))),\nX883 -> T439,\nT123 -> s(T439),\nT438 -> T439", fontsize=14, style = filled, fillcolor = lightblue];
170 -> 1434 [arrowhead = none ];
1434 -> 807;

1435 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
170 -> 1435 [arrowhead = none ];
1435 -> 808;

1436 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
182 -> 1436 [arrowhead = none ];
1436 -> 186;

1437 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
186 -> 1437 [arrowhead = none ];
1437 -> 189;

1438 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
186 -> 1438 [arrowhead = none ];
1438 -> 190;

1439 [label="EVAL with clause\nquot(0, s(X219), s(X220), 0).\nand substitutionT143 -> 0,\nX219 -> T153,\nT144 -> s(T153),\nX220 -> s(s(s(s(s(s(T153)))))),\nT146 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
189 -> 1439 [arrowhead = none ];
1439 -> 193;

1440 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
189 -> 1440 [arrowhead = none ];
1440 -> 194;

1441 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
190 -> 1441 [arrowhead = none ];
1441 -> 199;

1442 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
190 -> 1442 [arrowhead = none ];
1442 -> 200;

1443 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
193 -> 1443 [arrowhead = none ];
1443 -> 195;

1444 [label="EVAL with clause\nquot(s(X237), s(X238), X239, X240) :- quot(X237, X238, X239, X240).\nand substitutionX237 -> T166,\nT143 -> s(T166),\nX238 -> T167,\nT144 -> s(T167),\nX239 -> s(s(s(s(s(s(s(T167))))))),\nT146 -> T169,\nX240 -> T169,\nT168 -> T169", fontsize=14, style = filled, fillcolor = lightblue];
199 -> 1444 [arrowhead = none ];
1444 -> 204;

1445 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
199 -> 1445 [arrowhead = none ];
1445 -> 206;

1446 [label="EVAL with clause\nquot(X627, 0, s(X628), s(X629)) :- quot(X627, s(X628), s(X628), X629).\nand substitutionT143 -> T350,\nX627 -> T350,\nT144 -> 0,\nX628 -> s(s(s(s(s(0))))),\nX629 -> T352,\nT146 -> s(T352),\nT351 -> T352", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 1446 [arrowhead = none ];
1446 -> 607;

1447 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
200 -> 1447 [arrowhead = none ];
1447 -> 608;

1448 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
204 -> 1448 [arrowhead = none ];
1448 -> 211;

1449 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
211 -> 1449 [arrowhead = none ];
1449 -> 225;

1450 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
211 -> 1450 [arrowhead = none ];
1450 -> 226;

1451 [label="EVAL with clause\nquot(0, s(X253), s(X254), 0).\nand substitutionT166 -> 0,\nX253 -> T176,\nT167 -> s(T176),\nX254 -> s(s(s(s(s(s(s(T176))))))),\nT169 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
225 -> 1451 [arrowhead = none ];
1451 -> 230;

1452 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
225 -> 1452 [arrowhead = none ];
1452 -> 232;

1453 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
226 -> 1453 [arrowhead = none ];
1453 -> 246;

1454 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
226 -> 1454 [arrowhead = none ];
1454 -> 248;

1455 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
230 -> 1455 [arrowhead = none ];
1455 -> 233;

1456 [label="EVAL with clause\nquot(s(X271), s(X272), X273, X274) :- quot(X271, X272, X273, X274).\nand substitutionX271 -> T189,\nT166 -> s(T189),\nX272 -> T190,\nT167 -> s(T190),\nX273 -> s(s(s(s(s(s(s(s(T190)))))))),\nT169 -> T192,\nX274 -> T192,\nT191 -> T192", fontsize=14, style = filled, fillcolor = lightblue];
246 -> 1456 [arrowhead = none ];
1456 -> 255;

1457 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
246 -> 1457 [arrowhead = none ];
1457 -> 256;

1458 [label="EVAL with clause\nquot(X336, 0, s(X337), s(X338)) :- quot(X336, s(X337), s(X337), X338).\nand substitutionT166 -> T251,\nX336 -> T251,\nT167 -> 0,\nX337 -> s(s(s(s(s(s(0)))))),\nX338 -> T253,\nT169 -> s(T253),\nT252 -> T253", fontsize=14, style = filled, fillcolor = lightblue];
248 -> 1458 [arrowhead = none ];
1458 -> 323;

1459 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
248 -> 1459 [arrowhead = none ];
1459 -> 324;

1460 [label="GENERALIZATION\nT195 <-- s(s(s(s(s(s(s(T190)))))))\n\nNew Knowledge:\nT195 is ground", fontsize=14, style = filled, fillcolor = violet];
255 -> 1460 [arrowhead = none ];
1460 -> 261;

1461 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
261 -> 1461 [arrowhead = none ];
1461 -> 270;

1462 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
270 -> 1462 [arrowhead = none ];
1462 -> 271;

1463 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
270 -> 1463 [arrowhead = none ];
1463 -> 272;

1464 [label="EVAL with clause\nquot(0, s(X291), s(X292), 0).\nand substitutionT189 -> 0,\nX291 -> T208,\nT190 -> s(T208),\nT195 -> T209,\nX292 -> T209,\nT192 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
271 -> 1464 [arrowhead = none ];
1464 -> 285;

1465 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
271 -> 1465 [arrowhead = none ];
1465 -> 286;

1466 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
272 -> 1466 [arrowhead = none ];
1466 -> 289;

1467 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
272 -> 1467 [arrowhead = none ];
1467 -> 290;

1468 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
285 -> 1468 [arrowhead = none ];
1468 -> 288;

1469 [label="EVAL with clause\nquot(s(X309), s(X310), X311, X312) :- quot(X309, X310, X311, X312).\nand substitutionX309 -> T226,\nT189 -> s(T226),\nX310 -> T227,\nT190 -> s(T227),\nT195 -> T228,\nX311 -> s(T228),\nT192 -> T230,\nX312 -> T230,\nT229 -> T230", fontsize=14, style = filled, fillcolor = lightblue];
289 -> 1469 [arrowhead = none ];
1469 -> 303;

1470 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
289 -> 1470 [arrowhead = none ];
1470 -> 304;

1471 [label="EVAL with clause\nquot(X323, 0, s(X324), s(X325)) :- quot(X323, s(X324), s(X324), X325).\nand substitutionT189 -> T241,\nX323 -> T241,\nT190 -> 0,\nT195 -> T242,\nX324 -> T242,\nX325 -> T244,\nT192 -> s(T244),\nT243 -> T244", fontsize=14, style = filled, fillcolor = lightblue];
290 -> 1471 [arrowhead = none ];
1471 -> 307;

1472 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
290 -> 1472 [arrowhead = none ];
1472 -> 308;

1473 [label="INSTANCE with matching:\nT189 -> T226\nT190 -> T227\nT195 -> T228\nT192 -> T230", fontsize=14, style = filled, fillcolor = lightgrey];
303 -> 1473 [arrowhead = none , style=dashed];
1473 -> 261[style=dashed];

1474 [label="INSTANCE with matching:\nT7 -> T241\nT8 -> s(T242)\nT10 -> T244", fontsize=14, style = filled, fillcolor = lightgrey];
307 -> 1474 [arrowhead = none , style=dashed];
1474 -> 8[style=dashed];

1475 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
323 -> 1475 [arrowhead = none ];
1475 -> 328;

1476 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
328 -> 1476 [arrowhead = none ];
1476 -> 340;

1477 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
328 -> 1477 [arrowhead = none ];
1477 -> 343;

1478 [label="EVAL with clause\nquot(0, s(X351), s(X352), 0).\nand substitutionT251 -> 0,\nX351 -> s(s(s(s(s(s(0)))))),\nX352 -> s(s(s(s(s(s(0)))))),\nT253 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
340 -> 1478 [arrowhead = none ];
1478 -> 345;

1479 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
340 -> 1479 [arrowhead = none ];
1479 -> 347;

1480 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
343 -> 1480 [arrowhead = none ];
1480 -> 352;

1481 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
343 -> 1481 [arrowhead = none ];
1481 -> 353;

1482 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
345 -> 1482 [arrowhead = none ];
1482 -> 348;

1483 [label="EVAL with clause\nquot(s(X369), s(X370), X371, X372) :- quot(X369, X370, X371, X372).\nand substitutionX369 -> T262,\nT251 -> s(T262),\nX370 -> s(s(s(s(s(s(0)))))),\nX371 -> s(s(s(s(s(s(s(0))))))),\nT253 -> T264,\nX372 -> T264,\nT263 -> T264", fontsize=14, style = filled, fillcolor = lightblue];
352 -> 1483 [arrowhead = none ];
1483 -> 357;

1484 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
352 -> 1484 [arrowhead = none ];
1484 -> 358;

1485 [label="BACKTRACK\nfor 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];
353 -> 1485 [arrowhead = none ];
1485 -> 602;

1486 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
357 -> 1486 [arrowhead = none ];
1486 -> 361;

1487 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
361 -> 1487 [arrowhead = none ];
1487 -> 362;

1488 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
361 -> 1488 [arrowhead = none ];
1488 -> 363;

1489 [label="EVAL with clause\nquot(0, s(X385), s(X386), 0).\nand substitutionT262 -> 0,\nX385 -> s(s(s(s(s(0))))),\nX386 -> s(s(s(s(s(s(0)))))),\nT264 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
362 -> 1489 [arrowhead = none ];
1489 -> 368;

1490 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
362 -> 1490 [arrowhead = none ];
1490 -> 369;

1491 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
363 -> 1491 [arrowhead = none ];
1491 -> 371;

1492 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
363 -> 1492 [arrowhead = none ];
1492 -> 372;

1493 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
368 -> 1493 [arrowhead = none ];
1493 -> 370;

1494 [label="EVAL with clause\nquot(s(X403), s(X404), X405, X406) :- quot(X403, X404, X405, X406).\nand substitutionX403 -> T273,\nT262 -> s(T273),\nX404 -> s(s(s(s(s(0))))),\nX405 -> s(s(s(s(s(s(s(0))))))),\nT264 -> T275,\nX406 -> T275,\nT274 -> T275", fontsize=14, style = filled, fillcolor = lightblue];
371 -> 1494 [arrowhead = none ];
1494 -> 379;

1495 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
371 -> 1495 [arrowhead = none ];
1495 -> 381;

1496 [label="BACKTRACK\nfor 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];
372 -> 1496 [arrowhead = none ];
1496 -> 601;

1497 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
379 -> 1497 [arrowhead = none ];
1497 -> 386;

1498 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
386 -> 1498 [arrowhead = none ];
1498 -> 387;

1499 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
386 -> 1499 [arrowhead = none ];
1499 -> 388;

1500 [label="EVAL with clause\nquot(0, s(X419), s(X420), 0).\nand substitutionT273 -> 0,\nX419 -> s(s(s(s(0)))),\nX420 -> s(s(s(s(s(s(0)))))),\nT275 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
387 -> 1500 [arrowhead = none ];
1500 -> 389;

1501 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
387 -> 1501 [arrowhead = none ];
1501 -> 390;

1502 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
388 -> 1502 [arrowhead = none ];
1502 -> 397;

1503 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
388 -> 1503 [arrowhead = none ];
1503 -> 398;

1504 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
389 -> 1504 [arrowhead = none ];
1504 -> 391;

1505 [label="EVAL with clause\nquot(s(X437), s(X438), X439, X440) :- quot(X437, X438, X439, X440).\nand substitutionX437 -> T284,\nT273 -> s(T284),\nX438 -> s(s(s(s(0)))),\nX439 -> s(s(s(s(s(s(s(0))))))),\nT275 -> T286,\nX440 -> T286,\nT285 -> T286", fontsize=14, style = filled, fillcolor = lightblue];
397 -> 1505 [arrowhead = none ];
1505 -> 404;

1506 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
397 -> 1506 [arrowhead = none ];
1506 -> 405;

1507 [label="BACKTRACK\nfor 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];
398 -> 1507 [arrowhead = none ];
1507 -> 600;

1508 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
404 -> 1508 [arrowhead = none ];
1508 -> 427;

1509 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
427 -> 1509 [arrowhead = none ];
1509 -> 429;

1510 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
427 -> 1510 [arrowhead = none ];
1510 -> 430;

1511 [label="EVAL with clause\nquot(0, s(X453), s(X454), 0).\nand substitutionT284 -> 0,\nX453 -> s(s(s(0))),\nX454 -> s(s(s(s(s(s(0)))))),\nT286 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
429 -> 1511 [arrowhead = none ];
1511 -> 439;

1512 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
429 -> 1512 [arrowhead = none ];
1512 -> 440;

1513 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
430 -> 1513 [arrowhead = none ];
1513 -> 445;

1514 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
430 -> 1514 [arrowhead = none ];
1514 -> 446;

1515 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
439 -> 1515 [arrowhead = none ];
1515 -> 441;

1516 [label="EVAL with clause\nquot(s(X471), s(X472), X473, X474) :- quot(X471, X472, X473, X474).\nand substitutionX471 -> T295,\nT284 -> s(T295),\nX472 -> s(s(s(0))),\nX473 -> s(s(s(s(s(s(s(0))))))),\nT286 -> T297,\nX474 -> T297,\nT296 -> T297", fontsize=14, style = filled, fillcolor = lightblue];
445 -> 1516 [arrowhead = none ];
1516 -> 468;

1517 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
445 -> 1517 [arrowhead = none ];
1517 -> 469;

1518 [label="BACKTRACK\nfor 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];
446 -> 1518 [arrowhead = none ];
1518 -> 597;

1519 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
468 -> 1519 [arrowhead = none ];
1519 -> 475;

1520 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
475 -> 1520 [arrowhead = none ];
1520 -> 479;

1521 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
475 -> 1521 [arrowhead = none ];
1521 -> 480;

1522 [label="EVAL with clause\nquot(0, s(X487), s(X488), 0).\nand substitutionT295 -> 0,\nX487 -> s(s(0)),\nX488 -> s(s(s(s(s(s(0)))))),\nT297 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
479 -> 1522 [arrowhead = none ];
1522 -> 483;

1523 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
479 -> 1523 [arrowhead = none ];
1523 -> 484;

1524 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
480 -> 1524 [arrowhead = none ];
1524 -> 504;

1525 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
480 -> 1525 [arrowhead = none ];
1525 -> 505;

1526 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
483 -> 1526 [arrowhead = none ];
1526 -> 485;

1527 [label="EVAL with clause\nquot(s(X505), s(X506), X507, X508) :- quot(X505, X506, X507, X508).\nand substitutionX505 -> T306,\nT295 -> s(T306),\nX506 -> s(s(0)),\nX507 -> s(s(s(s(s(s(s(0))))))),\nT297 -> T308,\nX508 -> T308,\nT307 -> T308", fontsize=14, style = filled, fillcolor = lightblue];
504 -> 1527 [arrowhead = none ];
1527 -> 511;

1528 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
504 -> 1528 [arrowhead = none ];
1528 -> 512;

1529 [label="BACKTRACK\nfor 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 -> 1529 [arrowhead = none ];
1529 -> 596;

1530 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
511 -> 1530 [arrowhead = none ];
1530 -> 523;

1531 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
523 -> 1531 [arrowhead = none ];
1531 -> 528;

1532 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
523 -> 1532 [arrowhead = none ];
1532 -> 529;

1533 [label="EVAL with clause\nquot(0, s(X521), s(X522), 0).\nand substitutionT306 -> 0,\nX521 -> s(0),\nX522 -> s(s(s(s(s(s(0)))))),\nT308 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
528 -> 1533 [arrowhead = none ];
1533 -> 531;

1534 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
528 -> 1534 [arrowhead = none ];
1534 -> 532;

1535 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
529 -> 1535 [arrowhead = none ];
1535 -> 538;

1536 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
529 -> 1536 [arrowhead = none ];
1536 -> 539;

1537 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
531 -> 1537 [arrowhead = none ];
1537 -> 533;

1538 [label="EVAL with clause\nquot(s(X539), s(X540), X541, X542) :- quot(X539, X540, X541, X542).\nand substitutionX539 -> T317,\nT306 -> s(T317),\nX540 -> s(0),\nX541 -> s(s(s(s(s(s(s(0))))))),\nT308 -> T319,\nX542 -> T319,\nT318 -> T319", fontsize=14, style = filled, fillcolor = lightblue];
538 -> 1538 [arrowhead = none ];
1538 -> 554;

1539 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
538 -> 1539 [arrowhead = none ];
1539 -> 555;

1540 [label="BACKTRACK\nfor 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];
539 -> 1540 [arrowhead = none ];
1540 -> 595;

1541 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
554 -> 1541 [arrowhead = none ];
1541 -> 561;

1542 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
561 -> 1542 [arrowhead = none ];
1542 -> 562;

1543 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
561 -> 1543 [arrowhead = none ];
1543 -> 563;

1544 [label="EVAL with clause\nquot(0, s(X555), s(X556), 0).\nand substitutionT317 -> 0,\nX555 -> 0,\nX556 -> s(s(s(s(s(s(0)))))),\nT319 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
562 -> 1544 [arrowhead = none ];
1544 -> 564;

1545 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
562 -> 1545 [arrowhead = none ];
1545 -> 566;

1546 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
563 -> 1546 [arrowhead = none ];
1546 -> 569;

1547 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
563 -> 1547 [arrowhead = none ];
1547 -> 570;

1548 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
564 -> 1548 [arrowhead = none ];
1548 -> 568;

1549 [label="EVAL with clause\nquot(s(X573), s(X574), X575, X576) :- quot(X573, X574, X575, X576).\nand substitutionX573 -> T328,\nT317 -> s(T328),\nX574 -> 0,\nX575 -> s(s(s(s(s(s(s(0))))))),\nT319 -> T330,\nX576 -> T330,\nT329 -> T330", fontsize=14, style = filled, fillcolor = lightblue];
569 -> 1549 [arrowhead = none ];
1549 -> 571;

1550 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
569 -> 1550 [arrowhead = none ];
1550 -> 572;

1551 [label="BACKTRACK\nfor 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];
570 -> 1551 [arrowhead = none ];
1551 -> 591;

1552 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
571 -> 1552 [arrowhead = none ];
1552 -> 579;

1553 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
579 -> 1553 [arrowhead = none ];
1553 -> 580;

1554 [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];
580 -> 1554 [arrowhead = none ];
1554 -> 584;

1555 [label="EVAL with clause\nquot(X593, 0, s(X594), s(X595)) :- quot(X593, s(X594), s(X594), X595).\nand substitutionT328 -> T336,\nX593 -> T336,\nX594 -> s(s(s(s(s(s(0)))))),\nX595 -> T338,\nT330 -> s(T338),\nT337 -> T338", fontsize=14, style = filled, fillcolor = lightblue];
584 -> 1555 [arrowhead = none ];
1555 -> 587;

1556 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
584 -> 1556 [arrowhead = none ];
1556 -> 588;

1557 [label="INSTANCE with matching:\nT251 -> T336\nT253 -> T338", fontsize=14, style = filled, fillcolor = lightgrey];
587 -> 1557 [arrowhead = none , style=dashed];
1557 -> 323[style=dashed];

1558 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
607 -> 1558 [arrowhead = none ];
1558 -> 615;

1559 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
615 -> 1559 [arrowhead = none ];
1559 -> 616;

1560 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
615 -> 1560 [arrowhead = none ];
1560 -> 617;

1561 [label="EVAL with clause\nquot(0, s(X642), s(X643), 0).\nand substitutionT350 -> 0,\nX642 -> s(s(s(s(s(0))))),\nX643 -> s(s(s(s(s(0))))),\nT352 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
616 -> 1561 [arrowhead = none ];
1561 -> 619;

1562 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
616 -> 1562 [arrowhead = none ];
1562 -> 620;

1563 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
617 -> 1563 [arrowhead = none ];
1563 -> 624;

1564 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
617 -> 1564 [arrowhead = none ];
1564 -> 625;

1565 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
619 -> 1565 [arrowhead = none ];
1565 -> 621;

1566 [label="EVAL with clause\nquot(s(X660), s(X661), X662, X663) :- quot(X660, X661, X662, X663).\nand substitutionX660 -> T361,\nT350 -> s(T361),\nX661 -> s(s(s(s(s(0))))),\nX662 -> s(s(s(s(s(s(0)))))),\nT352 -> T363,\nX663 -> T363,\nT362 -> T363", fontsize=14, style = filled, fillcolor = lightblue];
624 -> 1566 [arrowhead = none ];
1566 -> 626;

1567 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
624 -> 1567 [arrowhead = none ];
1567 -> 627;

1568 [label="BACKTRACK\nfor 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];
625 -> 1568 [arrowhead = none ];
1568 -> 802;

1569 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
626 -> 1569 [arrowhead = none ];
1569 -> 633;

1570 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
633 -> 1570 [arrowhead = none ];
1570 -> 639;

1571 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
633 -> 1571 [arrowhead = none ];
1571 -> 640;

1572 [label="EVAL with clause\nquot(0, s(X676), s(X677), 0).\nand substitutionT361 -> 0,\nX676 -> s(s(s(s(0)))),\nX677 -> s(s(s(s(s(0))))),\nT363 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
639 -> 1572 [arrowhead = none ];
1572 -> 641;

1573 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
639 -> 1573 [arrowhead = none ];
1573 -> 642;

1574 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
640 -> 1574 [arrowhead = none ];
1574 -> 648;

1575 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
640 -> 1575 [arrowhead = none ];
1575 -> 649;

1576 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
641 -> 1576 [arrowhead = none ];
1576 -> 643;

1577 [label="EVAL with clause\nquot(s(X694), s(X695), X696, X697) :- quot(X694, X695, X696, X697).\nand substitutionX694 -> T372,\nT361 -> s(T372),\nX695 -> s(s(s(s(0)))),\nX696 -> s(s(s(s(s(s(0)))))),\nT363 -> T374,\nX697 -> T374,\nT373 -> T374", fontsize=14, style = filled, fillcolor = lightblue];
648 -> 1577 [arrowhead = none ];
1577 -> 656;

1578 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
648 -> 1578 [arrowhead = none ];
1578 -> 657;

1579 [label="BACKTRACK\nfor 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];
649 -> 1579 [arrowhead = none ];
1579 -> 800;

1580 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
656 -> 1580 [arrowhead = none ];
1580 -> 661;

1581 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
661 -> 1581 [arrowhead = none ];
1581 -> 667;

1582 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
661 -> 1582 [arrowhead = none ];
1582 -> 668;

1583 [label="EVAL with clause\nquot(0, s(X710), s(X711), 0).\nand substitutionT372 -> 0,\nX710 -> s(s(s(0))),\nX711 -> s(s(s(s(s(0))))),\nT374 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
667 -> 1583 [arrowhead = none ];
1583 -> 669;

1584 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
667 -> 1584 [arrowhead = none ];
1584 -> 670;

1585 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
668 -> 1585 [arrowhead = none ];
1585 -> 677;

1586 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
668 -> 1586 [arrowhead = none ];
1586 -> 678;

1587 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
669 -> 1587 [arrowhead = none ];
1587 -> 671;

1588 [label="EVAL with clause\nquot(s(X728), s(X729), X730, X731) :- quot(X728, X729, X730, X731).\nand substitutionX728 -> T383,\nT372 -> s(T383),\nX729 -> s(s(s(0))),\nX730 -> s(s(s(s(s(s(0)))))),\nT374 -> T385,\nX731 -> T385,\nT384 -> T385", fontsize=14, style = filled, fillcolor = lightblue];
677 -> 1588 [arrowhead = none ];
1588 -> 684;

1589 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
677 -> 1589 [arrowhead = none ];
1589 -> 685;

1590 [label="BACKTRACK\nfor 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];
678 -> 1590 [arrowhead = none ];
1590 -> 798;

1591 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
684 -> 1591 [arrowhead = none ];
1591 -> 691;

1592 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
691 -> 1592 [arrowhead = none ];
1592 -> 695;

1593 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
691 -> 1593 [arrowhead = none ];
1593 -> 696;

1594 [label="EVAL with clause\nquot(0, s(X744), s(X745), 0).\nand substitutionT383 -> 0,\nX744 -> s(s(0)),\nX745 -> s(s(s(s(s(0))))),\nT385 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
695 -> 1594 [arrowhead = none ];
1594 -> 699;

1595 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
695 -> 1595 [arrowhead = none ];
1595 -> 700;

1596 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
696 -> 1596 [arrowhead = none ];
1596 -> 704;

1597 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
696 -> 1597 [arrowhead = none ];
1597 -> 705;

1598 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
699 -> 1598 [arrowhead = none ];
1598 -> 701;

1599 [label="EVAL with clause\nquot(s(X762), s(X763), X764, X765) :- quot(X762, X763, X764, X765).\nand substitutionX762 -> T394,\nT383 -> s(T394),\nX763 -> s(s(0)),\nX764 -> s(s(s(s(s(s(0)))))),\nT385 -> T396,\nX765 -> T396,\nT395 -> T396", fontsize=14, style = filled, fillcolor = lightblue];
704 -> 1599 [arrowhead = none ];
1599 -> 714;

1600 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
704 -> 1600 [arrowhead = none ];
1600 -> 715;

1601 [label="BACKTRACK\nfor 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];
705 -> 1601 [arrowhead = none ];
1601 -> 796;

1602 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
714 -> 1602 [arrowhead = none ];
1602 -> 721;

1603 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
721 -> 1603 [arrowhead = none ];
1603 -> 725;

1604 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
721 -> 1604 [arrowhead = none ];
1604 -> 726;

1605 [label="EVAL with clause\nquot(0, s(X778), s(X779), 0).\nand substitutionT394 -> 0,\nX778 -> s(0),\nX779 -> s(s(s(s(s(0))))),\nT396 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
725 -> 1605 [arrowhead = none ];
1605 -> 727;

1606 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
725 -> 1606 [arrowhead = none ];
1606 -> 728;

1607 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
726 -> 1607 [arrowhead = none ];
1607 -> 734;

1608 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
726 -> 1608 [arrowhead = none ];
1608 -> 735;

1609 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
727 -> 1609 [arrowhead = none ];
1609 -> 729;

1610 [label="EVAL with clause\nquot(s(X796), s(X797), X798, X799) :- quot(X796, X797, X798, X799).\nand substitutionX796 -> T405,\nT394 -> s(T405),\nX797 -> s(0),\nX798 -> s(s(s(s(s(s(0)))))),\nT396 -> T407,\nX799 -> T407,\nT406 -> T407", fontsize=14, style = filled, fillcolor = lightblue];
734 -> 1610 [arrowhead = none ];
1610 -> 739;

1611 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
734 -> 1611 [arrowhead = none ];
1611 -> 741;

1612 [label="BACKTRACK\nfor 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];
735 -> 1612 [arrowhead = none ];
1612 -> 792;

1613 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
739 -> 1613 [arrowhead = none ];
1613 -> 749;

1614 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
749 -> 1614 [arrowhead = none ];
1614 -> 750;

1615 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
749 -> 1615 [arrowhead = none ];
1615 -> 751;

1616 [label="EVAL with clause\nquot(0, s(X812), s(X813), 0).\nand substitutionT405 -> 0,\nX812 -> 0,\nX813 -> s(s(s(s(s(0))))),\nT407 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
750 -> 1616 [arrowhead = none ];
1616 -> 757;

1617 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
750 -> 1617 [arrowhead = none ];
1617 -> 758;

1618 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
751 -> 1618 [arrowhead = none ];
1618 -> 762;

1619 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
751 -> 1619 [arrowhead = none ];
1619 -> 763;

1620 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
757 -> 1620 [arrowhead = none ];
1620 -> 759;

1621 [label="EVAL with clause\nquot(s(X830), s(X831), X832, X833) :- quot(X830, X831, X832, X833).\nand substitutionX830 -> T416,\nT405 -> s(T416),\nX831 -> 0,\nX832 -> s(s(s(s(s(s(0)))))),\nT407 -> T418,\nX833 -> T418,\nT417 -> T418", fontsize=14, style = filled, fillcolor = lightblue];
762 -> 1621 [arrowhead = none ];
1621 -> 768;

1622 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
762 -> 1622 [arrowhead = none ];
1622 -> 769;

1623 [label="BACKTRACK\nfor 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];
763 -> 1623 [arrowhead = none ];
1623 -> 790;

1624 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
768 -> 1624 [arrowhead = none ];
1624 -> 775;

1625 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
775 -> 1625 [arrowhead = none ];
1625 -> 777;

1626 [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];
777 -> 1626 [arrowhead = none ];
1626 -> 781;

1627 [label="EVAL with clause\nquot(X850, 0, s(X851), s(X852)) :- quot(X850, s(X851), s(X851), X852).\nand substitutionT416 -> T424,\nX850 -> T424,\nX851 -> s(s(s(s(s(0))))),\nX852 -> T426,\nT418 -> s(T426),\nT425 -> T426", fontsize=14, style = filled, fillcolor = lightblue];
781 -> 1627 [arrowhead = none ];
1627 -> 786;

1628 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
781 -> 1628 [arrowhead = none ];
1628 -> 787;

1629 [label="INSTANCE with matching:\nT350 -> T424\nT352 -> T426", fontsize=14, style = filled, fillcolor = lightgrey];
786 -> 1629 [arrowhead = none , style=dashed];
1629 -> 607[style=dashed];

1630 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
807 -> 1630 [arrowhead = none ];
1630 -> 813;

1631 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
813 -> 1631 [arrowhead = none ];
1631 -> 818;

1632 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
813 -> 1632 [arrowhead = none ];
1632 -> 819;

1633 [label="EVAL with clause\nquot(0, s(X896), s(X897), 0).\nand substitutionT437 -> 0,\nX896 -> s(s(s(s(0)))),\nX897 -> s(s(s(s(0)))),\nT439 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
818 -> 1633 [arrowhead = none ];
1633 -> 823;

1634 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
818 -> 1634 [arrowhead = none ];
1634 -> 824;

1635 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
819 -> 1635 [arrowhead = none ];
1635 -> 830;

1636 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
819 -> 1636 [arrowhead = none ];
1636 -> 831;

1637 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
823 -> 1637 [arrowhead = none ];
1637 -> 825;

1638 [label="EVAL with clause\nquot(s(X914), s(X915), X916, X917) :- quot(X914, X915, X916, X917).\nand substitutionX914 -> T448,\nT437 -> s(T448),\nX915 -> s(s(s(s(0)))),\nX916 -> s(s(s(s(s(0))))),\nT439 -> T450,\nX917 -> T450,\nT449 -> T450", fontsize=14, style = filled, fillcolor = lightblue];
830 -> 1638 [arrowhead = none ];
1638 -> 833;

1639 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
830 -> 1639 [arrowhead = none ];
1639 -> 834;

1640 [label="BACKTRACK\nfor 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];
831 -> 1640 [arrowhead = none ];
1640 -> 983;

1641 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
833 -> 1641 [arrowhead = none ];
1641 -> 837;

1642 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
837 -> 1642 [arrowhead = none ];
1642 -> 839;

1643 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
837 -> 1643 [arrowhead = none ];
1643 -> 840;

1644 [label="EVAL with clause\nquot(0, s(X930), s(X931), 0).\nand substitutionT448 -> 0,\nX930 -> s(s(s(0))),\nX931 -> s(s(s(s(0)))),\nT450 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
839 -> 1644 [arrowhead = none ];
1644 -> 842;

1645 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
839 -> 1645 [arrowhead = none ];
1645 -> 843;

1646 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
840 -> 1646 [arrowhead = none ];
1646 -> 845;

1647 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
840 -> 1647 [arrowhead = none ];
1647 -> 846;

1648 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
842 -> 1648 [arrowhead = none ];
1648 -> 844;

1649 [label="EVAL with clause\nquot(s(X948), s(X949), X950, X951) :- quot(X948, X949, X950, X951).\nand substitutionX948 -> T459,\nT448 -> s(T459),\nX949 -> s(s(s(0))),\nX950 -> s(s(s(s(s(0))))),\nT450 -> T461,\nX951 -> T461,\nT460 -> T461", fontsize=14, style = filled, fillcolor = lightblue];
845 -> 1649 [arrowhead = none ];
1649 -> 855;

1650 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
845 -> 1650 [arrowhead = none ];
1650 -> 856;

1651 [label="BACKTRACK\nfor 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];
846 -> 1651 [arrowhead = none ];
1651 -> 979;

1652 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
855 -> 1652 [arrowhead = none ];
1652 -> 860;

1653 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
860 -> 1653 [arrowhead = none ];
1653 -> 861;

1654 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
860 -> 1654 [arrowhead = none ];
1654 -> 862;

1655 [label="EVAL with clause\nquot(0, s(X964), s(X965), 0).\nand substitutionT459 -> 0,\nX964 -> s(s(0)),\nX965 -> s(s(s(s(0)))),\nT461 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
861 -> 1655 [arrowhead = none ];
1655 -> 864;

1656 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
861 -> 1656 [arrowhead = none ];
1656 -> 865;

1657 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
862 -> 1657 [arrowhead = none ];
1657 -> 869;

1658 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
862 -> 1658 [arrowhead = none ];
1658 -> 870;

1659 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
864 -> 1659 [arrowhead = none ];
1659 -> 866;

1660 [label="EVAL with clause\nquot(s(X982), s(X983), X984, X985) :- quot(X982, X983, X984, X985).\nand substitutionX982 -> T470,\nT459 -> s(T470),\nX983 -> s(s(0)),\nX984 -> s(s(s(s(s(0))))),\nT461 -> T472,\nX985 -> T472,\nT471 -> T472", fontsize=14, style = filled, fillcolor = lightblue];
869 -> 1660 [arrowhead = none ];
1660 -> 879;

1661 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
869 -> 1661 [arrowhead = none ];
1661 -> 881;

1662 [label="BACKTRACK\nfor 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];
870 -> 1662 [arrowhead = none ];
1662 -> 978;

1663 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
879 -> 1663 [arrowhead = none ];
1663 -> 886;

1664 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
886 -> 1664 [arrowhead = none ];
1664 -> 887;

1665 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
886 -> 1665 [arrowhead = none ];
1665 -> 888;

1666 [label="EVAL with clause\nquot(0, s(X998), s(X999), 0).\nand substitutionT470 -> 0,\nX998 -> s(0),\nX999 -> s(s(s(s(0)))),\nT472 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
887 -> 1666 [arrowhead = none ];
1666 -> 890;

1667 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
887 -> 1667 [arrowhead = none ];
1667 -> 891;

1668 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
888 -> 1668 [arrowhead = none ];
1668 -> 898;

1669 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
888 -> 1669 [arrowhead = none ];
1669 -> 899;

1670 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
890 -> 1670 [arrowhead = none ];
1670 -> 892;

1671 [label="EVAL with clause\nquot(s(X1016), s(X1017), X1018, X1019) :- quot(X1016, X1017, X1018, X1019).\nand substitutionX1016 -> T481,\nT470 -> s(T481),\nX1017 -> s(0),\nX1018 -> s(s(s(s(s(0))))),\nT472 -> T483,\nX1019 -> T483,\nT482 -> T483", fontsize=14, style = filled, fillcolor = lightblue];
898 -> 1671 [arrowhead = none ];
1671 -> 906;

1672 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
898 -> 1672 [arrowhead = none ];
1672 -> 907;

1673 [label="BACKTRACK\nfor 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];
899 -> 1673 [arrowhead = none ];
1673 -> 975;

1674 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
906 -> 1674 [arrowhead = none ];
1674 -> 919;

1675 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
919 -> 1675 [arrowhead = none ];
1675 -> 923;

1676 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
919 -> 1676 [arrowhead = none ];
1676 -> 924;

1677 [label="EVAL with clause\nquot(0, s(X1032), s(X1033), 0).\nand substitutionT481 -> 0,\nX1032 -> 0,\nX1033 -> s(s(s(s(0)))),\nT483 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
923 -> 1677 [arrowhead = none ];
1677 -> 925;

1678 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
923 -> 1678 [arrowhead = none ];
1678 -> 926;

1679 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
924 -> 1679 [arrowhead = none ];
1679 -> 943;

1680 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
924 -> 1680 [arrowhead = none ];
1680 -> 944;

1681 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
925 -> 1681 [arrowhead = none ];
1681 -> 927;

1682 [label="EVAL with clause\nquot(s(X1050), s(X1051), X1052, X1053) :- quot(X1050, X1051, X1052, X1053).\nand substitutionX1050 -> T492,\nT481 -> s(T492),\nX1051 -> 0,\nX1052 -> s(s(s(s(s(0))))),\nT483 -> T494,\nX1053 -> T494,\nT493 -> T494", fontsize=14, style = filled, fillcolor = lightblue];
943 -> 1682 [arrowhead = none ];
1682 -> 949;

1683 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
943 -> 1683 [arrowhead = none ];
1683 -> 950;

1684 [label="BACKTRACK\nfor 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];
944 -> 1684 [arrowhead = none ];
1684 -> 973;

1685 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
949 -> 1685 [arrowhead = none ];
1685 -> 955;

1686 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
955 -> 1686 [arrowhead = none ];
1686 -> 957;

1687 [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];
957 -> 1687 [arrowhead = none ];
1687 -> 960;

1688 [label="EVAL with clause\nquot(X1070, 0, s(X1071), s(X1072)) :- quot(X1070, s(X1071), s(X1071), X1072).\nand substitutionT492 -> T500,\nX1070 -> T500,\nX1071 -> s(s(s(s(0)))),\nX1072 -> T502,\nT494 -> s(T502),\nT501 -> T502", fontsize=14, style = filled, fillcolor = lightblue];
960 -> 1688 [arrowhead = none ];
1688 -> 967;

1689 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
960 -> 1689 [arrowhead = none ];
1689 -> 968;

1690 [label="INSTANCE with matching:\nT437 -> T500\nT439 -> T502", fontsize=14, style = filled, fillcolor = lightgrey];
967 -> 1690 [arrowhead = none , style=dashed];
1690 -> 807[style=dashed];

1691 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
988 -> 1691 [arrowhead = none ];
1691 -> 993;

1692 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
993 -> 1692 [arrowhead = none ];
1692 -> 999;

1693 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
993 -> 1693 [arrowhead = none ];
1693 -> 1000;

1694 [label="EVAL with clause\nquot(0, s(X1113), s(X1114), 0).\nand substitutionT512 -> 0,\nX1113 -> s(s(s(0))),\nX1114 -> s(s(s(0))),\nT514 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
999 -> 1694 [arrowhead = none ];
1694 -> 1001;

1695 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
999 -> 1695 [arrowhead = none ];
1695 -> 1002;

1696 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1000 -> 1696 [arrowhead = none ];
1696 -> 1009;

1697 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1000 -> 1697 [arrowhead = none ];
1697 -> 1010;

1698 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1001 -> 1698 [arrowhead = none ];
1698 -> 1003;

1699 [label="EVAL with clause\nquot(s(X1131), s(X1132), X1133, X1134) :- quot(X1131, X1132, X1133, X1134).\nand substitutionX1131 -> T523,\nT512 -> s(T523),\nX1132 -> s(s(s(0))),\nX1133 -> s(s(s(s(0)))),\nT514 -> T525,\nX1134 -> T525,\nT524 -> T525", fontsize=14, style = filled, fillcolor = lightblue];
1009 -> 1699 [arrowhead = none ];
1699 -> 1018;

1700 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1009 -> 1700 [arrowhead = none ];
1700 -> 1019;

1701 [label="BACKTRACK\nfor 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];
1010 -> 1701 [arrowhead = none ];
1701 -> 1153;

1702 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1018 -> 1702 [arrowhead = none ];
1702 -> 1030;

1703 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1030 -> 1703 [arrowhead = none ];
1703 -> 1031;

1704 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1030 -> 1704 [arrowhead = none ];
1704 -> 1032;

1705 [label="EVAL with clause\nquot(0, s(X1147), s(X1148), 0).\nand substitutionT523 -> 0,\nX1147 -> s(s(0)),\nX1148 -> s(s(s(0))),\nT525 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1031 -> 1705 [arrowhead = none ];
1705 -> 1037;

1706 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1031 -> 1706 [arrowhead = none ];
1706 -> 1041;

1707 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1032 -> 1707 [arrowhead = none ];
1707 -> 1043;

1708 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1032 -> 1708 [arrowhead = none ];
1708 -> 1044;

1709 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1037 -> 1709 [arrowhead = none ];
1709 -> 1042;

1710 [label="EVAL with clause\nquot(s(X1165), s(X1166), X1167, X1168) :- quot(X1165, X1166, X1167, X1168).\nand substitutionX1165 -> T534,\nT523 -> s(T534),\nX1166 -> s(s(0)),\nX1167 -> s(s(s(s(0)))),\nT525 -> T536,\nX1168 -> T536,\nT535 -> T536", fontsize=14, style = filled, fillcolor = lightblue];
1043 -> 1710 [arrowhead = none ];
1710 -> 1059;

1711 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1043 -> 1711 [arrowhead = none ];
1711 -> 1060;

1712 [label="BACKTRACK\nfor 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];
1044 -> 1712 [arrowhead = none ];
1712 -> 1150;

1713 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1059 -> 1713 [arrowhead = none ];
1713 -> 1069;

1714 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1069 -> 1714 [arrowhead = none ];
1714 -> 1070;

1715 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1069 -> 1715 [arrowhead = none ];
1715 -> 1071;

1716 [label="EVAL with clause\nquot(0, s(X1181), s(X1182), 0).\nand substitutionT534 -> 0,\nX1181 -> s(0),\nX1182 -> s(s(s(0))),\nT536 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1070 -> 1716 [arrowhead = none ];
1716 -> 1081;

1717 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1070 -> 1717 [arrowhead = none ];
1717 -> 1082;

1718 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1071 -> 1718 [arrowhead = none ];
1718 -> 1088;

1719 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1071 -> 1719 [arrowhead = none ];
1719 -> 1089;

1720 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1081 -> 1720 [arrowhead = none ];
1720 -> 1083;

1721 [label="EVAL with clause\nquot(s(X1199), s(X1200), X1201, X1202) :- quot(X1199, X1200, X1201, X1202).\nand substitutionX1199 -> T545,\nT534 -> s(T545),\nX1200 -> s(0),\nX1201 -> s(s(s(s(0)))),\nT536 -> T547,\nX1202 -> T547,\nT546 -> T547", fontsize=14, style = filled, fillcolor = lightblue];
1088 -> 1721 [arrowhead = none ];
1721 -> 1095;

1722 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1088 -> 1722 [arrowhead = none ];
1722 -> 1096;

1723 [label="BACKTRACK\nfor 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];
1089 -> 1723 [arrowhead = none ];
1723 -> 1149;

1724 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1095 -> 1724 [arrowhead = none ];
1724 -> 1101;

1725 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1101 -> 1725 [arrowhead = none ];
1725 -> 1106;

1726 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1101 -> 1726 [arrowhead = none ];
1726 -> 1107;

1727 [label="EVAL with clause\nquot(0, s(X1215), s(X1216), 0).\nand substitutionT545 -> 0,\nX1215 -> 0,\nX1216 -> s(s(s(0))),\nT547 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1106 -> 1727 [arrowhead = none ];
1727 -> 1111;

1728 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1106 -> 1728 [arrowhead = none ];
1728 -> 1112;

1729 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1107 -> 1729 [arrowhead = none ];
1729 -> 1116;

1730 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1107 -> 1730 [arrowhead = none ];
1730 -> 1118;

1731 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1111 -> 1731 [arrowhead = none ];
1731 -> 1113;

1732 [label="EVAL with clause\nquot(s(X1233), s(X1234), X1235, X1236) :- quot(X1233, X1234, X1235, X1236).\nand substitutionX1233 -> T556,\nT545 -> s(T556),\nX1234 -> 0,\nX1235 -> s(s(s(s(0)))),\nT547 -> T558,\nX1236 -> T558,\nT557 -> T558", fontsize=14, style = filled, fillcolor = lightblue];
1116 -> 1732 [arrowhead = none ];
1732 -> 1123;

1733 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1116 -> 1733 [arrowhead = none ];
1733 -> 1124;

1734 [label="BACKTRACK\nfor 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];
1118 -> 1734 [arrowhead = none ];
1734 -> 1147;

1735 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1123 -> 1735 [arrowhead = none ];
1735 -> 1130;

1736 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1130 -> 1736 [arrowhead = none ];
1736 -> 1131;

1737 [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];
1131 -> 1737 [arrowhead = none ];
1737 -> 1135;

1738 [label="EVAL with clause\nquot(X1253, 0, s(X1254), s(X1255)) :- quot(X1253, s(X1254), s(X1254), X1255).\nand substitutionT556 -> T564,\nX1253 -> T564,\nX1254 -> s(s(s(0))),\nX1255 -> T566,\nT558 -> s(T566),\nT565 -> T566", fontsize=14, style = filled, fillcolor = lightblue];
1135 -> 1738 [arrowhead = none ];
1738 -> 1141;

1739 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1135 -> 1739 [arrowhead = none ];
1739 -> 1142;

1740 [label="INSTANCE with matching:\nT512 -> T564\nT514 -> T566", fontsize=14, style = filled, fillcolor = lightgrey];
1141 -> 1740 [arrowhead = none , style=dashed];
1740 -> 988[style=dashed];

1741 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1159 -> 1741 [arrowhead = none ];
1741 -> 1165;

1742 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1165 -> 1742 [arrowhead = none ];
1742 -> 1167;

1743 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1165 -> 1743 [arrowhead = none ];
1743 -> 1168;

1744 [label="EVAL with clause\nquot(0, s(X1293), s(X1294), 0).\nand substitutionT575 -> 0,\nX1293 -> s(s(0)),\nX1294 -> s(s(0)),\nT577 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1167 -> 1744 [arrowhead = none ];
1744 -> 1171;

1745 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1167 -> 1745 [arrowhead = none ];
1745 -> 1172;

1746 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1168 -> 1746 [arrowhead = none ];
1746 -> 1177;

1747 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1168 -> 1747 [arrowhead = none ];
1747 -> 1178;

1748 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1171 -> 1748 [arrowhead = none ];
1748 -> 1173;

1749 [label="EVAL with clause\nquot(s(X1311), s(X1312), X1313, X1314) :- quot(X1311, X1312, X1313, X1314).\nand substitutionX1311 -> T586,\nT575 -> s(T586),\nX1312 -> s(s(0)),\nX1313 -> s(s(s(0))),\nT577 -> T588,\nX1314 -> T588,\nT587 -> T588", fontsize=14, style = filled, fillcolor = lightblue];
1177 -> 1749 [arrowhead = none ];
1749 -> 1184;

1750 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1177 -> 1750 [arrowhead = none ];
1750 -> 1185;

1751 [label="BACKTRACK\nfor 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];
1178 -> 1751 [arrowhead = none ];
1751 -> 1265;

1752 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1184 -> 1752 [arrowhead = none ];
1752 -> 1188;

1753 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1188 -> 1753 [arrowhead = none ];
1753 -> 1192;

1754 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1188 -> 1754 [arrowhead = none ];
1754 -> 1193;

1755 [label="EVAL with clause\nquot(0, s(X1327), s(X1328), 0).\nand substitutionT586 -> 0,\nX1327 -> s(0),\nX1328 -> s(s(0)),\nT588 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1192 -> 1755 [arrowhead = none ];
1755 -> 1195;

1756 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1192 -> 1756 [arrowhead = none ];
1756 -> 1197;

1757 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1193 -> 1757 [arrowhead = none ];
1757 -> 1202;

1758 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1193 -> 1758 [arrowhead = none ];
1758 -> 1203;

1759 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1195 -> 1759 [arrowhead = none ];
1759 -> 1198;

1760 [label="EVAL with clause\nquot(s(X1345), s(X1346), X1347, X1348) :- quot(X1345, X1346, X1347, X1348).\nand substitutionX1345 -> T597,\nT586 -> s(T597),\nX1346 -> s(0),\nX1347 -> s(s(s(0))),\nT588 -> T599,\nX1348 -> T599,\nT598 -> T599", fontsize=14, style = filled, fillcolor = lightblue];
1202 -> 1760 [arrowhead = none ];
1760 -> 1212;

1761 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1202 -> 1761 [arrowhead = none ];
1761 -> 1213;

1762 [label="BACKTRACK\nfor 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];
1203 -> 1762 [arrowhead = none ];
1762 -> 1264;

1763 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1212 -> 1763 [arrowhead = none ];
1763 -> 1219;

1764 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1219 -> 1764 [arrowhead = none ];
1764 -> 1220;

1765 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1219 -> 1765 [arrowhead = none ];
1765 -> 1221;

1766 [label="EVAL with clause\nquot(0, s(X1361), s(X1362), 0).\nand substitutionT597 -> 0,\nX1361 -> 0,\nX1362 -> s(s(0)),\nT599 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1220 -> 1766 [arrowhead = none ];
1766 -> 1226;

1767 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1220 -> 1767 [arrowhead = none ];
1767 -> 1227;

1768 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1221 -> 1768 [arrowhead = none ];
1768 -> 1230;

1769 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1221 -> 1769 [arrowhead = none ];
1769 -> 1231;

1770 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1226 -> 1770 [arrowhead = none ];
1770 -> 1228;

1771 [label="EVAL with clause\nquot(s(X1379), s(X1380), X1381, X1382) :- quot(X1379, X1380, X1381, X1382).\nand substitutionX1379 -> T608,\nT597 -> s(T608),\nX1380 -> 0,\nX1381 -> s(s(s(0))),\nT599 -> T610,\nX1382 -> T610,\nT609 -> T610", fontsize=14, style = filled, fillcolor = lightblue];
1230 -> 1771 [arrowhead = none ];
1771 -> 1240;

1772 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1230 -> 1772 [arrowhead = none ];
1772 -> 1241;

1773 [label="BACKTRACK\nfor 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];
1231 -> 1773 [arrowhead = none ];
1773 -> 1262;

1774 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1240 -> 1774 [arrowhead = none ];
1774 -> 1246;

1775 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1246 -> 1775 [arrowhead = none ];
1775 -> 1250;

1776 [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];
1250 -> 1776 [arrowhead = none ];
1776 -> 1251;

1777 [label="EVAL with clause\nquot(X1399, 0, s(X1400), s(X1401)) :- quot(X1399, s(X1400), s(X1400), X1401).\nand substitutionT608 -> T616,\nX1399 -> T616,\nX1400 -> s(s(0)),\nX1401 -> T618,\nT610 -> s(T618),\nT617 -> T618", fontsize=14, style = filled, fillcolor = lightblue];
1251 -> 1777 [arrowhead = none ];
1777 -> 1256;

1778 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1251 -> 1778 [arrowhead = none ];
1778 -> 1257;

1779 [label="INSTANCE with matching:\nT575 -> T616\nT577 -> T618", fontsize=14, style = filled, fillcolor = lightgrey];
1256 -> 1779 [arrowhead = none , style=dashed];
1779 -> 1159[style=dashed];

1780 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1271 -> 1780 [arrowhead = none ];
1780 -> 1275;

1781 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1275 -> 1781 [arrowhead = none ];
1781 -> 1278;

1782 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1275 -> 1782 [arrowhead = none ];
1782 -> 1279;

1783 [label="EVAL with clause\nquot(0, s(X1436), s(X1437), 0).\nand substitutionT626 -> 0,\nX1436 -> s(0),\nX1437 -> s(0),\nT628 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1278 -> 1783 [arrowhead = none ];
1783 -> 1281;

1784 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1278 -> 1784 [arrowhead = none ];
1784 -> 1282;

1785 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1279 -> 1785 [arrowhead = none ];
1785 -> 1287;

1786 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1279 -> 1786 [arrowhead = none ];
1786 -> 1288;

1787 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1281 -> 1787 [arrowhead = none ];
1787 -> 1283;

1788 [label="EVAL with clause\nquot(s(X1454), s(X1455), X1456, X1457) :- quot(X1454, X1455, X1456, X1457).\nand substitutionX1454 -> T637,\nT626 -> s(T637),\nX1455 -> s(0),\nX1456 -> s(s(0)),\nT628 -> T639,\nX1457 -> T639,\nT638 -> T639", fontsize=14, style = filled, fillcolor = lightblue];
1287 -> 1788 [arrowhead = none ];
1788 -> 1295;

1789 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1287 -> 1789 [arrowhead = none ];
1789 -> 1296;

1790 [label="BACKTRACK\nfor 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];
1288 -> 1790 [arrowhead = none ];
1790 -> 1343;

1791 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1295 -> 1791 [arrowhead = none ];
1791 -> 1302;

1792 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1302 -> 1792 [arrowhead = none ];
1792 -> 1308;

1793 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1302 -> 1793 [arrowhead = none ];
1793 -> 1309;

1794 [label="EVAL with clause\nquot(0, s(X1470), s(X1471), 0).\nand substitutionT637 -> 0,\nX1470 -> 0,\nX1471 -> s(0),\nT639 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1308 -> 1794 [arrowhead = none ];
1794 -> 1310;

1795 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1308 -> 1795 [arrowhead = none ];
1795 -> 1311;

1796 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1309 -> 1796 [arrowhead = none ];
1796 -> 1317;

1797 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1309 -> 1797 [arrowhead = none ];
1797 -> 1318;

1798 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1310 -> 1798 [arrowhead = none ];
1798 -> 1312;

1799 [label="EVAL with clause\nquot(s(X1488), s(X1489), X1490, X1491) :- quot(X1488, X1489, X1490, X1491).\nand substitutionX1488 -> T648,\nT637 -> s(T648),\nX1489 -> 0,\nX1490 -> s(s(0)),\nT639 -> T650,\nX1491 -> T650,\nT649 -> T650", fontsize=14, style = filled, fillcolor = lightblue];
1317 -> 1799 [arrowhead = none ];
1799 -> 1323;

1800 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1317 -> 1800 [arrowhead = none ];
1800 -> 1324;

1801 [label="BACKTRACK\nfor 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];
1318 -> 1801 [arrowhead = none ];
1801 -> 1342;

1802 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1323 -> 1802 [arrowhead = none ];
1802 -> 1328;

1803 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1328 -> 1803 [arrowhead = none ];
1803 -> 1330;

1804 [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];
1330 -> 1804 [arrowhead = none ];
1804 -> 1333;

1805 [label="EVAL with clause\nquot(X1508, 0, s(X1509), s(X1510)) :- quot(X1508, s(X1509), s(X1509), X1510).\nand substitutionT648 -> T656,\nX1508 -> T656,\nX1509 -> s(0),\nX1510 -> T658,\nT650 -> s(T658),\nT657 -> T658", fontsize=14, style = filled, fillcolor = lightblue];
1333 -> 1805 [arrowhead = none ];
1805 -> 1337;

1806 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1333 -> 1806 [arrowhead = none ];
1806 -> 1338;

1807 [label="INSTANCE with matching:\nT626 -> T656\nT628 -> T658", fontsize=14, style = filled, fillcolor = lightgrey];
1337 -> 1807 [arrowhead = none , style=dashed];
1807 -> 1271[style=dashed];

1808 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1344 -> 1808 [arrowhead = none ];
1808 -> 1346;

1809 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1346 -> 1809 [arrowhead = none ];
1809 -> 1347;

1810 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1346 -> 1810 [arrowhead = none ];
1810 -> 1348;

1811 [label="EVAL with clause\nquot(0, s(X1542), s(X1543), 0).\nand substitutionT665 -> 0,\nX1542 -> 0,\nX1543 -> 0,\nT667 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1347 -> 1811 [arrowhead = none ];
1811 -> 1349;

1812 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1347 -> 1812 [arrowhead = none ];
1812 -> 1350;

1813 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1348 -> 1813 [arrowhead = none ];
1813 -> 1352;

1814 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1348 -> 1814 [arrowhead = none ];
1814 -> 1353;

1815 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1349 -> 1815 [arrowhead = none ];
1815 -> 1351;

1816 [label="EVAL with clause\nquot(s(X1560), s(X1561), X1562, X1563) :- quot(X1560, X1561, X1562, X1563).\nand substitutionX1560 -> T676,\nT665 -> s(T676),\nX1561 -> 0,\nX1562 -> s(0),\nT667 -> T678,\nX1563 -> T678,\nT677 -> T678", fontsize=14, style = filled, fillcolor = lightblue];
1352 -> 1816 [arrowhead = none ];
1816 -> 1354;

1817 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1352 -> 1817 [arrowhead = none ];
1817 -> 1355;

1818 [label="BACKTRACK\nfor 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];
1353 -> 1818 [arrowhead = none ];
1818 -> 1361;

1819 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1354 -> 1819 [arrowhead = none ];
1819 -> 1356;

1820 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1356 -> 1820 [arrowhead = none ];
1820 -> 1357;

1821 [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];
1357 -> 1821 [arrowhead = none ];
1821 -> 1358;

1822 [label="EVAL with clause\nquot(X1580, 0, s(X1581), s(X1582)) :- quot(X1580, s(X1581), s(X1581), X1582).\nand substitutionT676 -> T684,\nX1580 -> T684,\nX1581 -> 0,\nX1582 -> T686,\nT678 -> s(T686),\nT685 -> T686", fontsize=14, style = filled, fillcolor = lightblue];
1358 -> 1822 [arrowhead = none ];
1822 -> 1359;

1823 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1358 -> 1823 [arrowhead = none ];
1823 -> 1360;

1824 [label="INSTANCE with matching:\nT665 -> T684\nT667 -> T686", fontsize=14, style = filled, fillcolor = lightgrey];
1359 -> 1824 [arrowhead = none , style=dashed];
1824 -> 1344[style=dashed];

}

(2) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

divA_in_gga(T7, T8, T10) → U1_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U4_gga(T189, T190, T192, quotC_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotC_in_ggga(0, s(T208), T209, 0) → quotC_out_ggga(0, s(T208), T209, 0)
quotC_in_ggga(s(T226), s(T227), T228, T230) → U2_ggga(T226, T227, T228, T230, quotC_in_ggga(T226, T227, T228, T230))
quotC_in_ggga(T241, 0, T242, s(T244)) → U3_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U5_gga(T251, T253, quotD_in_ga(T251, T253))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(0)))))), 0) → quotD_out_ga(s(s(s(s(s(s(0)))))), 0)
quotD_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U12_ga(T336, T338, quotD_in_ga(T336, T338))
U12_ga(T336, T338, quotD_out_ga(T336, T338)) → quotD_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U5_gga(T251, T253, quotD_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U6_gga(T350, T352, quotE_in_ga(T350, T352))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(0))))), 0) → quotE_out_ga(s(s(s(s(s(0))))), 0)
quotE_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U13_ga(T424, T426, quotE_in_ga(T424, T426))
U13_ga(T424, T426, quotE_out_ga(T424, T426)) → quotE_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U6_gga(T350, T352, quotE_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U7_gga(T437, T439, quotF_in_ga(T437, T439))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(0)))), 0) → quotF_out_ga(s(s(s(s(0)))), 0)
quotF_in_ga(s(s(s(s(s(T500))))), s(T502)) → U14_ga(T500, T502, quotF_in_ga(T500, T502))
U14_ga(T500, T502, quotF_out_ga(T500, T502)) → quotF_out_ga(s(s(s(s(s(T500))))), s(T502))
U7_gga(T437, T439, quotF_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U8_gga(T512, T514, quotG_in_ga(T512, T514))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(0))), 0) → quotG_out_ga(s(s(s(0))), 0)
quotG_in_ga(s(s(s(s(T564)))), s(T566)) → U15_ga(T564, T566, quotG_in_ga(T564, T566))
U15_ga(T564, T566, quotG_out_ga(T564, T566)) → quotG_out_ga(s(s(s(s(T564)))), s(T566))
U8_gga(T512, T514, quotG_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U9_gga(T575, T577, quotH_in_ga(T575, T577))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(0)), 0) → quotH_out_ga(s(s(0)), 0)
quotH_in_ga(s(s(s(T616))), s(T618)) → U16_ga(T616, T618, quotH_in_ga(T616, T618))
U16_ga(T616, T618, quotH_out_ga(T616, T618)) → quotH_out_ga(s(s(s(T616))), s(T618))
U9_gga(T575, T577, quotH_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U10_gga(T626, T628, quotI_in_ga(T626, T628))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(0), 0) → quotI_out_ga(s(0), 0)
quotI_in_ga(s(s(T656)), s(T658)) → U17_ga(T656, T658, quotI_in_ga(T656, T658))
U17_ga(T656, T658, quotI_out_ga(T656, T658)) → quotI_out_ga(s(s(T656)), s(T658))
U10_gga(T626, T628, quotI_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U11_gga(T665, T667, quotJ_in_ga(T665, T667))
quotJ_in_ga(0, 0) → quotJ_out_ga(0, 0)
quotJ_in_ga(s(T684), s(T686)) → U18_ga(T684, T686, quotJ_in_ga(T684, T686))
U18_ga(T684, T686, quotJ_out_ga(T684, T686)) → quotJ_out_ga(s(T684), s(T686))
U11_gga(T665, T667, quotJ_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U3_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotC_out_ggga(T241, 0, T242, s(T244))
U2_ggga(T226, T227, T228, T230, quotC_out_ggga(T226, T227, T228, T230)) → quotC_out_ggga(s(T226), s(T227), T228, T230)
U4_gga(T189, T190, T192, quotC_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U1_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divA_out_gga(T7, T8, T10)

(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:

DIVA_IN_GGA(T7, T8, T10) → U1_GGA(T7, T8, T10, quotB_in_gga(T7, T8, T10))
DIVA_IN_GGA(T7, T8, T10) → QUOTB_IN_GGA(T7, T8, T10)
QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U4_GGA(T189, T190, T192, quotC_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → QUOTC_IN_GGGA(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)
QUOTC_IN_GGGA(s(T226), s(T227), T228, T230) → U2_GGGA(T226, T227, T228, T230, quotC_in_ggga(T226, T227, T228, T230))
QUOTC_IN_GGGA(s(T226), s(T227), T228, T230) → QUOTC_IN_GGGA(T226, T227, T228, T230)
QUOTC_IN_GGGA(T241, 0, T242, s(T244)) → U3_GGGA(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
QUOTC_IN_GGGA(T241, 0, T242, s(T244)) → QUOTB_IN_GGA(T241, s(T242), T244)
QUOTB_IN_GGA(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U5_GGA(T251, T253, quotD_in_ga(T251, T253))
QUOTB_IN_GGA(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → QUOTD_IN_GA(T251, T253)
QUOTD_IN_GA(s(s(s(s(s(s(s(T336))))))), s(T338)) → U12_GA(T336, T338, quotD_in_ga(T336, T338))
QUOTD_IN_GA(s(s(s(s(s(s(s(T336))))))), s(T338)) → QUOTD_IN_GA(T336, T338)
QUOTB_IN_GGA(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U6_GGA(T350, T352, quotE_in_ga(T350, T352))
QUOTB_IN_GGA(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → QUOTE_IN_GA(T350, T352)
QUOTE_IN_GA(s(s(s(s(s(s(T424)))))), s(T426)) → U13_GA(T424, T426, quotE_in_ga(T424, T426))
QUOTE_IN_GA(s(s(s(s(s(s(T424)))))), s(T426)) → QUOTE_IN_GA(T424, T426)
QUOTB_IN_GGA(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U7_GGA(T437, T439, quotF_in_ga(T437, T439))
QUOTB_IN_GGA(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → QUOTF_IN_GA(T437, T439)
QUOTF_IN_GA(s(s(s(s(s(T500))))), s(T502)) → U14_GA(T500, T502, quotF_in_ga(T500, T502))
QUOTF_IN_GA(s(s(s(s(s(T500))))), s(T502)) → QUOTF_IN_GA(T500, T502)
QUOTB_IN_GGA(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U8_GGA(T512, T514, quotG_in_ga(T512, T514))
QUOTB_IN_GGA(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → QUOTG_IN_GA(T512, T514)
QUOTG_IN_GA(s(s(s(s(T564)))), s(T566)) → U15_GA(T564, T566, quotG_in_ga(T564, T566))
QUOTG_IN_GA(s(s(s(s(T564)))), s(T566)) → QUOTG_IN_GA(T564, T566)
QUOTB_IN_GGA(s(s(s(T575))), s(s(s(0))), s(T577)) → U9_GGA(T575, T577, quotH_in_ga(T575, T577))
QUOTB_IN_GGA(s(s(s(T575))), s(s(s(0))), s(T577)) → QUOTH_IN_GA(T575, T577)
QUOTH_IN_GA(s(s(s(T616))), s(T618)) → U16_GA(T616, T618, quotH_in_ga(T616, T618))
QUOTH_IN_GA(s(s(s(T616))), s(T618)) → QUOTH_IN_GA(T616, T618)
QUOTB_IN_GGA(s(s(T626)), s(s(0)), s(T628)) → U10_GGA(T626, T628, quotI_in_ga(T626, T628))
QUOTB_IN_GGA(s(s(T626)), s(s(0)), s(T628)) → QUOTI_IN_GA(T626, T628)
QUOTI_IN_GA(s(s(T656)), s(T658)) → U17_GA(T656, T658, quotI_in_ga(T656, T658))
QUOTI_IN_GA(s(s(T656)), s(T658)) → QUOTI_IN_GA(T656, T658)
QUOTB_IN_GGA(s(T665), s(0), s(T667)) → U11_GGA(T665, T667, quotJ_in_ga(T665, T667))
QUOTB_IN_GGA(s(T665), s(0), s(T667)) → QUOTJ_IN_GA(T665, T667)
QUOTJ_IN_GA(s(T684), s(T686)) → U18_GA(T684, T686, quotJ_in_ga(T684, T686))
QUOTJ_IN_GA(s(T684), s(T686)) → QUOTJ_IN_GA(T684, T686)

The TRS R consists of the following rules:

divA_in_gga(T7, T8, T10) → U1_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U4_gga(T189, T190, T192, quotC_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotC_in_ggga(0, s(T208), T209, 0) → quotC_out_ggga(0, s(T208), T209, 0)
quotC_in_ggga(s(T226), s(T227), T228, T230) → U2_ggga(T226, T227, T228, T230, quotC_in_ggga(T226, T227, T228, T230))
quotC_in_ggga(T241, 0, T242, s(T244)) → U3_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U5_gga(T251, T253, quotD_in_ga(T251, T253))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(0)))))), 0) → quotD_out_ga(s(s(s(s(s(s(0)))))), 0)
quotD_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U12_ga(T336, T338, quotD_in_ga(T336, T338))
U12_ga(T336, T338, quotD_out_ga(T336, T338)) → quotD_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U5_gga(T251, T253, quotD_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U6_gga(T350, T352, quotE_in_ga(T350, T352))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(0))))), 0) → quotE_out_ga(s(s(s(s(s(0))))), 0)
quotE_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U13_ga(T424, T426, quotE_in_ga(T424, T426))
U13_ga(T424, T426, quotE_out_ga(T424, T426)) → quotE_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U6_gga(T350, T352, quotE_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U7_gga(T437, T439, quotF_in_ga(T437, T439))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(0)))), 0) → quotF_out_ga(s(s(s(s(0)))), 0)
quotF_in_ga(s(s(s(s(s(T500))))), s(T502)) → U14_ga(T500, T502, quotF_in_ga(T500, T502))
U14_ga(T500, T502, quotF_out_ga(T500, T502)) → quotF_out_ga(s(s(s(s(s(T500))))), s(T502))
U7_gga(T437, T439, quotF_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U8_gga(T512, T514, quotG_in_ga(T512, T514))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(0))), 0) → quotG_out_ga(s(s(s(0))), 0)
quotG_in_ga(s(s(s(s(T564)))), s(T566)) → U15_ga(T564, T566, quotG_in_ga(T564, T566))
U15_ga(T564, T566, quotG_out_ga(T564, T566)) → quotG_out_ga(s(s(s(s(T564)))), s(T566))
U8_gga(T512, T514, quotG_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U9_gga(T575, T577, quotH_in_ga(T575, T577))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(0)), 0) → quotH_out_ga(s(s(0)), 0)
quotH_in_ga(s(s(s(T616))), s(T618)) → U16_ga(T616, T618, quotH_in_ga(T616, T618))
U16_ga(T616, T618, quotH_out_ga(T616, T618)) → quotH_out_ga(s(s(s(T616))), s(T618))
U9_gga(T575, T577, quotH_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U10_gga(T626, T628, quotI_in_ga(T626, T628))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(0), 0) → quotI_out_ga(s(0), 0)
quotI_in_ga(s(s(T656)), s(T658)) → U17_ga(T656, T658, quotI_in_ga(T656, T658))
U17_ga(T656, T658, quotI_out_ga(T656, T658)) → quotI_out_ga(s(s(T656)), s(T658))
U10_gga(T626, T628, quotI_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U11_gga(T665, T667, quotJ_in_ga(T665, T667))
quotJ_in_ga(0, 0) → quotJ_out_ga(0, 0)
quotJ_in_ga(s(T684), s(T686)) → U18_ga(T684, T686, quotJ_in_ga(T684, T686))
U18_ga(T684, T686, quotJ_out_ga(T684, T686)) → quotJ_out_ga(s(T684), s(T686))
U11_gga(T665, T667, quotJ_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U3_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotC_out_ggga(T241, 0, T242, s(T244))
U2_ggga(T226, T227, T228, T230, quotC_out_ggga(T226, T227, T228, T230)) → quotC_out_ggga(s(T226), s(T227), T228, T230)
U4_gga(T189, T190, T192, quotC_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U1_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divA_out_gga(T7, T8, T10)

The argument filtering Pi contains the following mapping:
divA_in_gga(x1, x2, x3) = divA_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4) = U1_gga(x1, x2, x4)
quotB_in_gga(x1, x2, x3) = quotB_in_gga(x1, x2)
0 = 0
s(x1) = s(x1)
quotB_out_gga(x1, x2, x3) = quotB_out_gga(x1, x2, x3)
U4_gga(x1, x2, x3, x4) = U4_gga(x1, x2, x4)
quotC_in_ggga(x1, x2, x3, x4) = quotC_in_ggga(x1, x2, x3)
quotC_out_ggga(x1, x2, x3, x4) = quotC_out_ggga(x1, x2, x3, x4)
U2_ggga(x1, x2, x3, x4, x5) = U2_ggga(x1, x2, x3, x5)
U3_ggga(x1, x2, x3, x4) = U3_ggga(x1, x2, x4)
U5_gga(x1, x2, x3) = U5_gga(x1, x3)
quotD_in_ga(x1, x2) = quotD_in_ga(x1)
quotD_out_ga(x1, x2) = quotD_out_ga(x1, x2)
U12_ga(x1, x2, x3) = U12_ga(x1, x3)
U6_gga(x1, x2, x3) = U6_gga(x1, x3)
quotE_in_ga(x1, x2) = quotE_in_ga(x1)
quotE_out_ga(x1, x2) = quotE_out_ga(x1, x2)
U13_ga(x1, x2, x3) = U13_ga(x1, x3)
U7_gga(x1, x2, x3) = U7_gga(x1, x3)
quotF_in_ga(x1, x2) = quotF_in_ga(x1)
quotF_out_ga(x1, x2) = quotF_out_ga(x1, x2)
U14_ga(x1, x2, x3) = U14_ga(x1, x3)
U8_gga(x1, x2, x3) = U8_gga(x1, x3)
quotG_in_ga(x1, x2) = quotG_in_ga(x1)
quotG_out_ga(x1, x2) = quotG_out_ga(x1, x2)
U15_ga(x1, x2, x3) = U15_ga(x1, x3)
U9_gga(x1, x2, x3) = U9_gga(x1, x3)
quotH_in_ga(x1, x2) = quotH_in_ga(x1)
quotH_out_ga(x1, x2) = quotH_out_ga(x1, x2)
U16_ga(x1, x2, x3) = U16_ga(x1, x3)
U10_gga(x1, x2, x3) = U10_gga(x1, x3)
quotI_in_ga(x1, x2) = quotI_in_ga(x1)
quotI_out_ga(x1, x2) = quotI_out_ga(x1, x2)
U17_ga(x1, x2, x3) = U17_ga(x1, x3)
U11_gga(x1, x2, x3) = U11_gga(x1, x3)
quotJ_in_ga(x1, x2) = quotJ_in_ga(x1)
quotJ_out_ga(x1, x2) = quotJ_out_ga(x1, x2)
U18_ga(x1, x2, x3) = U18_ga(x1, x3)
divA_out_gga(x1, x2, x3) = divA_out_gga(x1, x2, x3)
DIVA_IN_GGA(x1, x2, x3) = DIVA_IN_GGA(x1, x2)
U1_GGA(x1, x2, x3, x4) = U1_GGA(x1, x2, x4)
QUOTB_IN_GGA(x1, x2, x3) = QUOTB_IN_GGA(x1, x2)
U4_GGA(x1, x2, x3, x4) = U4_GGA(x1, x2, x4)
QUOTC_IN_GGGA(x1, x2, x3, x4) = QUOTC_IN_GGGA(x1, x2, x3)
U2_GGGA(x1, x2, x3, x4, x5) = U2_GGGA(x1, x2, x3, x5)
U3_GGGA(x1, x2, x3, x4) = U3_GGGA(x1, x2, x4)
U5_GGA(x1, x2, x3) = U5_GGA(x1, x3)
QUOTD_IN_GA(x1, x2) = QUOTD_IN_GA(x1)
U12_GA(x1, x2, x3) = U12_GA(x1, x3)
U6_GGA(x1, x2, x3) = U6_GGA(x1, x3)
QUOTE_IN_GA(x1, x2) = QUOTE_IN_GA(x1)
U13_GA(x1, x2, x3) = U13_GA(x1, x3)
U7_GGA(x1, x2, x3) = U7_GGA(x1, x3)
QUOTF_IN_GA(x1, x2) = QUOTF_IN_GA(x1)
U14_GA(x1, x2, x3) = U14_GA(x1, x3)
U8_GGA(x1, x2, x3) = U8_GGA(x1, x3)
QUOTG_IN_GA(x1, x2) = QUOTG_IN_GA(x1)
U15_GA(x1, x2, x3) = U15_GA(x1, x3)
U9_GGA(x1, x2, x3) = U9_GGA(x1, x3)
QUOTH_IN_GA(x1, x2) = QUOTH_IN_GA(x1)
U16_GA(x1, x2, x3) = U16_GA(x1, x3)
U10_GGA(x1, x2, x3) = U10_GGA(x1, x3)
QUOTI_IN_GA(x1, x2) = QUOTI_IN_GA(x1)
U17_GA(x1, x2, x3) = U17_GA(x1, x3)
U11_GGA(x1, x2, x3) = U11_GGA(x1, x3)
QUOTJ_IN_GA(x1, x2) = QUOTJ_IN_GA(x1)
U18_GA(x1, x2, x3) = U18_GA(x1, x3)

We have to consider all (P,R,Pi)-chains

(4) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

DIVA_IN_GGA(T7, T8, T10) → U1_GGA(T7, T8, T10, quotB_in_gga(T7, T8, T10))
DIVA_IN_GGA(T7, T8, T10) → QUOTB_IN_GGA(T7, T8, T10)
QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U4_GGA(T189, T190, T192, quotC_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → QUOTC_IN_GGGA(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)
QUOTC_IN_GGGA(s(T226), s(T227), T228, T230) → U2_GGGA(T226, T227, T228, T230, quotC_in_ggga(T226, T227, T228, T230))
QUOTC_IN_GGGA(s(T226), s(T227), T228, T230) → QUOTC_IN_GGGA(T226, T227, T228, T230)
QUOTC_IN_GGGA(T241, 0, T242, s(T244)) → U3_GGGA(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
QUOTC_IN_GGGA(T241, 0, T242, s(T244)) → QUOTB_IN_GGA(T241, s(T242), T244)
QUOTB_IN_GGA(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U5_GGA(T251, T253, quotD_in_ga(T251, T253))
QUOTB_IN_GGA(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → QUOTD_IN_GA(T251, T253)
QUOTD_IN_GA(s(s(s(s(s(s(s(T336))))))), s(T338)) → U12_GA(T336, T338, quotD_in_ga(T336, T338))
QUOTD_IN_GA(s(s(s(s(s(s(s(T336))))))), s(T338)) → QUOTD_IN_GA(T336, T338)
QUOTB_IN_GGA(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U6_GGA(T350, T352, quotE_in_ga(T350, T352))
QUOTB_IN_GGA(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → QUOTE_IN_GA(T350, T352)
QUOTE_IN_GA(s(s(s(s(s(s(T424)))))), s(T426)) → U13_GA(T424, T426, quotE_in_ga(T424, T426))
QUOTE_IN_GA(s(s(s(s(s(s(T424)))))), s(T426)) → QUOTE_IN_GA(T424, T426)
QUOTB_IN_GGA(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U7_GGA(T437, T439, quotF_in_ga(T437, T439))
QUOTB_IN_GGA(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → QUOTF_IN_GA(T437, T439)
QUOTF_IN_GA(s(s(s(s(s(T500))))), s(T502)) → U14_GA(T500, T502, quotF_in_ga(T500, T502))
QUOTF_IN_GA(s(s(s(s(s(T500))))), s(T502)) → QUOTF_IN_GA(T500, T502)
QUOTB_IN_GGA(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U8_GGA(T512, T514, quotG_in_ga(T512, T514))
QUOTB_IN_GGA(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → QUOTG_IN_GA(T512, T514)
QUOTG_IN_GA(s(s(s(s(T564)))), s(T566)) → U15_GA(T564, T566, quotG_in_ga(T564, T566))
QUOTG_IN_GA(s(s(s(s(T564)))), s(T566)) → QUOTG_IN_GA(T564, T566)
QUOTB_IN_GGA(s(s(s(T575))), s(s(s(0))), s(T577)) → U9_GGA(T575, T577, quotH_in_ga(T575, T577))
QUOTB_IN_GGA(s(s(s(T575))), s(s(s(0))), s(T577)) → QUOTH_IN_GA(T575, T577)
QUOTH_IN_GA(s(s(s(T616))), s(T618)) → U16_GA(T616, T618, quotH_in_ga(T616, T618))
QUOTH_IN_GA(s(s(s(T616))), s(T618)) → QUOTH_IN_GA(T616, T618)
QUOTB_IN_GGA(s(s(T626)), s(s(0)), s(T628)) → U10_GGA(T626, T628, quotI_in_ga(T626, T628))
QUOTB_IN_GGA(s(s(T626)), s(s(0)), s(T628)) → QUOTI_IN_GA(T626, T628)
QUOTI_IN_GA(s(s(T656)), s(T658)) → U17_GA(T656, T658, quotI_in_ga(T656, T658))
QUOTI_IN_GA(s(s(T656)), s(T658)) → QUOTI_IN_GA(T656, T658)
QUOTB_IN_GGA(s(T665), s(0), s(T667)) → U11_GGA(T665, T667, quotJ_in_ga(T665, T667))
QUOTB_IN_GGA(s(T665), s(0), s(T667)) → QUOTJ_IN_GA(T665, T667)
QUOTJ_IN_GA(s(T684), s(T686)) → U18_GA(T684, T686, quotJ_in_ga(T684, T686))
QUOTJ_IN_GA(s(T684), s(T686)) → QUOTJ_IN_GA(T684, T686)

The TRS R consists of the following rules:

divA_in_gga(T7, T8, T10) → U1_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U4_gga(T189, T190, T192, quotC_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotC_in_ggga(0, s(T208), T209, 0) → quotC_out_ggga(0, s(T208), T209, 0)
quotC_in_ggga(s(T226), s(T227), T228, T230) → U2_ggga(T226, T227, T228, T230, quotC_in_ggga(T226, T227, T228, T230))
quotC_in_ggga(T241, 0, T242, s(T244)) → U3_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U5_gga(T251, T253, quotD_in_ga(T251, T253))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(0)))))), 0) → quotD_out_ga(s(s(s(s(s(s(0)))))), 0)
quotD_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U12_ga(T336, T338, quotD_in_ga(T336, T338))
U12_ga(T336, T338, quotD_out_ga(T336, T338)) → quotD_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U5_gga(T251, T253, quotD_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U6_gga(T350, T352, quotE_in_ga(T350, T352))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(0))))), 0) → quotE_out_ga(s(s(s(s(s(0))))), 0)
quotE_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U13_ga(T424, T426, quotE_in_ga(T424, T426))
U13_ga(T424, T426, quotE_out_ga(T424, T426)) → quotE_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U6_gga(T350, T352, quotE_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U7_gga(T437, T439, quotF_in_ga(T437, T439))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(0)))), 0) → quotF_out_ga(s(s(s(s(0)))), 0)
quotF_in_ga(s(s(s(s(s(T500))))), s(T502)) → U14_ga(T500, T502, quotF_in_ga(T500, T502))
U14_ga(T500, T502, quotF_out_ga(T500, T502)) → quotF_out_ga(s(s(s(s(s(T500))))), s(T502))
U7_gga(T437, T439, quotF_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U8_gga(T512, T514, quotG_in_ga(T512, T514))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(0))), 0) → quotG_out_ga(s(s(s(0))), 0)
quotG_in_ga(s(s(s(s(T564)))), s(T566)) → U15_ga(T564, T566, quotG_in_ga(T564, T566))
U15_ga(T564, T566, quotG_out_ga(T564, T566)) → quotG_out_ga(s(s(s(s(T564)))), s(T566))
U8_gga(T512, T514, quotG_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U9_gga(T575, T577, quotH_in_ga(T575, T577))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(0)), 0) → quotH_out_ga(s(s(0)), 0)
quotH_in_ga(s(s(s(T616))), s(T618)) → U16_ga(T616, T618, quotH_in_ga(T616, T618))
U16_ga(T616, T618, quotH_out_ga(T616, T618)) → quotH_out_ga(s(s(s(T616))), s(T618))
U9_gga(T575, T577, quotH_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U10_gga(T626, T628, quotI_in_ga(T626, T628))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(0), 0) → quotI_out_ga(s(0), 0)
quotI_in_ga(s(s(T656)), s(T658)) → U17_ga(T656, T658, quotI_in_ga(T656, T658))
U17_ga(T656, T658, quotI_out_ga(T656, T658)) → quotI_out_ga(s(s(T656)), s(T658))
U10_gga(T626, T628, quotI_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U11_gga(T665, T667, quotJ_in_ga(T665, T667))
quotJ_in_ga(0, 0) → quotJ_out_ga(0, 0)
quotJ_in_ga(s(T684), s(T686)) → U18_ga(T684, T686, quotJ_in_ga(T684, T686))
U18_ga(T684, T686, quotJ_out_ga(T684, T686)) → quotJ_out_ga(s(T684), s(T686))
U11_gga(T665, T667, quotJ_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U3_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotC_out_ggga(T241, 0, T242, s(T244))
U2_ggga(T226, T227, T228, T230, quotC_out_ggga(T226, T227, T228, T230)) → quotC_out_ggga(s(T226), s(T227), T228, T230)
U4_gga(T189, T190, T192, quotC_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U1_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divA_out_gga(T7, T8, T10)

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 8 SCCs with 26 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTJ_IN_GA(s(T684), s(T686)) → QUOTJ_IN_GA(T684, T686)

The TRS R consists of the following rules:

divA_in_gga(T7, T8, T10) → U1_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U4_gga(T189, T190, T192, quotC_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotC_in_ggga(0, s(T208), T209, 0) → quotC_out_ggga(0, s(T208), T209, 0)
quotC_in_ggga(s(T226), s(T227), T228, T230) → U2_ggga(T226, T227, T228, T230, quotC_in_ggga(T226, T227, T228, T230))
quotC_in_ggga(T241, 0, T242, s(T244)) → U3_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U5_gga(T251, T253, quotD_in_ga(T251, T253))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(0)))))), 0) → quotD_out_ga(s(s(s(s(s(s(0)))))), 0)
quotD_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U12_ga(T336, T338, quotD_in_ga(T336, T338))
U12_ga(T336, T338, quotD_out_ga(T336, T338)) → quotD_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U5_gga(T251, T253, quotD_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U6_gga(T350, T352, quotE_in_ga(T350, T352))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(0))))), 0) → quotE_out_ga(s(s(s(s(s(0))))), 0)
quotE_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U13_ga(T424, T426, quotE_in_ga(T424, T426))
U13_ga(T424, T426, quotE_out_ga(T424, T426)) → quotE_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U6_gga(T350, T352, quotE_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U7_gga(T437, T439, quotF_in_ga(T437, T439))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(0)))), 0) → quotF_out_ga(s(s(s(s(0)))), 0)
quotF_in_ga(s(s(s(s(s(T500))))), s(T502)) → U14_ga(T500, T502, quotF_in_ga(T500, T502))
U14_ga(T500, T502, quotF_out_ga(T500, T502)) → quotF_out_ga(s(s(s(s(s(T500))))), s(T502))
U7_gga(T437, T439, quotF_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U8_gga(T512, T514, quotG_in_ga(T512, T514))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(0))), 0) → quotG_out_ga(s(s(s(0))), 0)
quotG_in_ga(s(s(s(s(T564)))), s(T566)) → U15_ga(T564, T566, quotG_in_ga(T564, T566))
U15_ga(T564, T566, quotG_out_ga(T564, T566)) → quotG_out_ga(s(s(s(s(T564)))), s(T566))
U8_gga(T512, T514, quotG_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U9_gga(T575, T577, quotH_in_ga(T575, T577))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(0)), 0) → quotH_out_ga(s(s(0)), 0)
quotH_in_ga(s(s(s(T616))), s(T618)) → U16_ga(T616, T618, quotH_in_ga(T616, T618))
U16_ga(T616, T618, quotH_out_ga(T616, T618)) → quotH_out_ga(s(s(s(T616))), s(T618))
U9_gga(T575, T577, quotH_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U10_gga(T626, T628, quotI_in_ga(T626, T628))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(0), 0) → quotI_out_ga(s(0), 0)
quotI_in_ga(s(s(T656)), s(T658)) → U17_ga(T656, T658, quotI_in_ga(T656, T658))
U17_ga(T656, T658, quotI_out_ga(T656, T658)) → quotI_out_ga(s(s(T656)), s(T658))
U10_gga(T626, T628, quotI_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U11_gga(T665, T667, quotJ_in_ga(T665, T667))
quotJ_in_ga(0, 0) → quotJ_out_ga(0, 0)
quotJ_in_ga(s(T684), s(T686)) → U18_ga(T684, T686, quotJ_in_ga(T684, T686))
U18_ga(T684, T686, quotJ_out_ga(T684, T686)) → quotJ_out_ga(s(T684), s(T686))
U11_gga(T665, T667, quotJ_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U3_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotC_out_ggga(T241, 0, T242, s(T244))
U2_ggga(T226, T227, T228, T230, quotC_out_ggga(T226, T227, T228, T230)) → quotC_out_ggga(s(T226), s(T227), T228, T230)
U4_gga(T189, T190, T192, quotC_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U1_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divA_out_gga(T7, T8, T10)

(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:

QUOTJ_IN_GA(s(T684), s(T686)) → QUOTJ_IN_GA(T684, T686)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTJ_IN_GA(x1, x2) = QUOTJ_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:

QUOTJ_IN_GA(s(T684)) → QUOTJ_IN_GA(T684)

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:

QUOTJ_IN_GA(s(T684)) → QUOTJ_IN_GA(T684)
The graph contains the following edges 1 > 1

(13) YES

(14) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTI_IN_GA(s(s(T656)), s(T658)) → QUOTI_IN_GA(T656, T658)

The TRS R consists of the following rules:

divA_in_gga(T7, T8, T10) → U1_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U4_gga(T189, T190, T192, quotC_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotC_in_ggga(0, s(T208), T209, 0) → quotC_out_ggga(0, s(T208), T209, 0)
quotC_in_ggga(s(T226), s(T227), T228, T230) → U2_ggga(T226, T227, T228, T230, quotC_in_ggga(T226, T227, T228, T230))
quotC_in_ggga(T241, 0, T242, s(T244)) → U3_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U5_gga(T251, T253, quotD_in_ga(T251, T253))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(0)))))), 0) → quotD_out_ga(s(s(s(s(s(s(0)))))), 0)
quotD_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U12_ga(T336, T338, quotD_in_ga(T336, T338))
U12_ga(T336, T338, quotD_out_ga(T336, T338)) → quotD_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U5_gga(T251, T253, quotD_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U6_gga(T350, T352, quotE_in_ga(T350, T352))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(0))))), 0) → quotE_out_ga(s(s(s(s(s(0))))), 0)
quotE_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U13_ga(T424, T426, quotE_in_ga(T424, T426))
U13_ga(T424, T426, quotE_out_ga(T424, T426)) → quotE_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U6_gga(T350, T352, quotE_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U7_gga(T437, T439, quotF_in_ga(T437, T439))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(0)))), 0) → quotF_out_ga(s(s(s(s(0)))), 0)
quotF_in_ga(s(s(s(s(s(T500))))), s(T502)) → U14_ga(T500, T502, quotF_in_ga(T500, T502))
U14_ga(T500, T502, quotF_out_ga(T500, T502)) → quotF_out_ga(s(s(s(s(s(T500))))), s(T502))
U7_gga(T437, T439, quotF_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U8_gga(T512, T514, quotG_in_ga(T512, T514))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(0))), 0) → quotG_out_ga(s(s(s(0))), 0)
quotG_in_ga(s(s(s(s(T564)))), s(T566)) → U15_ga(T564, T566, quotG_in_ga(T564, T566))
U15_ga(T564, T566, quotG_out_ga(T564, T566)) → quotG_out_ga(s(s(s(s(T564)))), s(T566))
U8_gga(T512, T514, quotG_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U9_gga(T575, T577, quotH_in_ga(T575, T577))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(0)), 0) → quotH_out_ga(s(s(0)), 0)
quotH_in_ga(s(s(s(T616))), s(T618)) → U16_ga(T616, T618, quotH_in_ga(T616, T618))
U16_ga(T616, T618, quotH_out_ga(T616, T618)) → quotH_out_ga(s(s(s(T616))), s(T618))
U9_gga(T575, T577, quotH_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U10_gga(T626, T628, quotI_in_ga(T626, T628))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(0), 0) → quotI_out_ga(s(0), 0)
quotI_in_ga(s(s(T656)), s(T658)) → U17_ga(T656, T658, quotI_in_ga(T656, T658))
U17_ga(T656, T658, quotI_out_ga(T656, T658)) → quotI_out_ga(s(s(T656)), s(T658))
U10_gga(T626, T628, quotI_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U11_gga(T665, T667, quotJ_in_ga(T665, T667))
quotJ_in_ga(0, 0) → quotJ_out_ga(0, 0)
quotJ_in_ga(s(T684), s(T686)) → U18_ga(T684, T686, quotJ_in_ga(T684, T686))
U18_ga(T684, T686, quotJ_out_ga(T684, T686)) → quotJ_out_ga(s(T684), s(T686))
U11_gga(T665, T667, quotJ_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U3_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotC_out_ggga(T241, 0, T242, s(T244))
U2_ggga(T226, T227, T228, T230, quotC_out_ggga(T226, T227, T228, T230)) → quotC_out_ggga(s(T226), s(T227), T228, T230)
U4_gga(T189, T190, T192, quotC_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U1_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divA_out_gga(T7, T8, T10)

(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:

QUOTI_IN_GA(s(s(T656)), s(T658)) → QUOTI_IN_GA(T656, T658)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTI_IN_GA(x1, x2) = QUOTI_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:

QUOTI_IN_GA(s(s(T656))) → QUOTI_IN_GA(T656)

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:

QUOTI_IN_GA(s(s(T656))) → QUOTI_IN_GA(T656)
The graph contains the following edges 1 > 1

(20) YES

(21) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTH_IN_GA(s(s(s(T616))), s(T618)) → QUOTH_IN_GA(T616, T618)

The TRS R consists of the following rules:

divA_in_gga(T7, T8, T10) → U1_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U4_gga(T189, T190, T192, quotC_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotC_in_ggga(0, s(T208), T209, 0) → quotC_out_ggga(0, s(T208), T209, 0)
quotC_in_ggga(s(T226), s(T227), T228, T230) → U2_ggga(T226, T227, T228, T230, quotC_in_ggga(T226, T227, T228, T230))
quotC_in_ggga(T241, 0, T242, s(T244)) → U3_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U5_gga(T251, T253, quotD_in_ga(T251, T253))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(0)))))), 0) → quotD_out_ga(s(s(s(s(s(s(0)))))), 0)
quotD_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U12_ga(T336, T338, quotD_in_ga(T336, T338))
U12_ga(T336, T338, quotD_out_ga(T336, T338)) → quotD_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U5_gga(T251, T253, quotD_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U6_gga(T350, T352, quotE_in_ga(T350, T352))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(0))))), 0) → quotE_out_ga(s(s(s(s(s(0))))), 0)
quotE_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U13_ga(T424, T426, quotE_in_ga(T424, T426))
U13_ga(T424, T426, quotE_out_ga(T424, T426)) → quotE_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U6_gga(T350, T352, quotE_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U7_gga(T437, T439, quotF_in_ga(T437, T439))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(0)))), 0) → quotF_out_ga(s(s(s(s(0)))), 0)
quotF_in_ga(s(s(s(s(s(T500))))), s(T502)) → U14_ga(T500, T502, quotF_in_ga(T500, T502))
U14_ga(T500, T502, quotF_out_ga(T500, T502)) → quotF_out_ga(s(s(s(s(s(T500))))), s(T502))
U7_gga(T437, T439, quotF_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U8_gga(T512, T514, quotG_in_ga(T512, T514))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(0))), 0) → quotG_out_ga(s(s(s(0))), 0)
quotG_in_ga(s(s(s(s(T564)))), s(T566)) → U15_ga(T564, T566, quotG_in_ga(T564, T566))
U15_ga(T564, T566, quotG_out_ga(T564, T566)) → quotG_out_ga(s(s(s(s(T564)))), s(T566))
U8_gga(T512, T514, quotG_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U9_gga(T575, T577, quotH_in_ga(T575, T577))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(0)), 0) → quotH_out_ga(s(s(0)), 0)
quotH_in_ga(s(s(s(T616))), s(T618)) → U16_ga(T616, T618, quotH_in_ga(T616, T618))
U16_ga(T616, T618, quotH_out_ga(T616, T618)) → quotH_out_ga(s(s(s(T616))), s(T618))
U9_gga(T575, T577, quotH_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U10_gga(T626, T628, quotI_in_ga(T626, T628))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(0), 0) → quotI_out_ga(s(0), 0)
quotI_in_ga(s(s(T656)), s(T658)) → U17_ga(T656, T658, quotI_in_ga(T656, T658))
U17_ga(T656, T658, quotI_out_ga(T656, T658)) → quotI_out_ga(s(s(T656)), s(T658))
U10_gga(T626, T628, quotI_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U11_gga(T665, T667, quotJ_in_ga(T665, T667))
quotJ_in_ga(0, 0) → quotJ_out_ga(0, 0)
quotJ_in_ga(s(T684), s(T686)) → U18_ga(T684, T686, quotJ_in_ga(T684, T686))
U18_ga(T684, T686, quotJ_out_ga(T684, T686)) → quotJ_out_ga(s(T684), s(T686))
U11_gga(T665, T667, quotJ_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U3_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotC_out_ggga(T241, 0, T242, s(T244))
U2_ggga(T226, T227, T228, T230, quotC_out_ggga(T226, T227, T228, T230)) → quotC_out_ggga(s(T226), s(T227), T228, T230)
U4_gga(T189, T190, T192, quotC_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U1_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divA_out_gga(T7, T8, T10)

(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:

QUOTH_IN_GA(s(s(s(T616))), s(T618)) → QUOTH_IN_GA(T616, T618)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTH_IN_GA(x1, x2) = QUOTH_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:

QUOTH_IN_GA(s(s(s(T616)))) → QUOTH_IN_GA(T616)

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:

QUOTH_IN_GA(s(s(s(T616)))) → QUOTH_IN_GA(T616)
The graph contains the following edges 1 > 1

(27) YES

(28) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTG_IN_GA(s(s(s(s(T564)))), s(T566)) → QUOTG_IN_GA(T564, T566)

The TRS R consists of the following rules:

divA_in_gga(T7, T8, T10) → U1_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U4_gga(T189, T190, T192, quotC_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotC_in_ggga(0, s(T208), T209, 0) → quotC_out_ggga(0, s(T208), T209, 0)
quotC_in_ggga(s(T226), s(T227), T228, T230) → U2_ggga(T226, T227, T228, T230, quotC_in_ggga(T226, T227, T228, T230))
quotC_in_ggga(T241, 0, T242, s(T244)) → U3_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U5_gga(T251, T253, quotD_in_ga(T251, T253))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(0)))))), 0) → quotD_out_ga(s(s(s(s(s(s(0)))))), 0)
quotD_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U12_ga(T336, T338, quotD_in_ga(T336, T338))
U12_ga(T336, T338, quotD_out_ga(T336, T338)) → quotD_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U5_gga(T251, T253, quotD_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U6_gga(T350, T352, quotE_in_ga(T350, T352))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(0))))), 0) → quotE_out_ga(s(s(s(s(s(0))))), 0)
quotE_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U13_ga(T424, T426, quotE_in_ga(T424, T426))
U13_ga(T424, T426, quotE_out_ga(T424, T426)) → quotE_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U6_gga(T350, T352, quotE_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U7_gga(T437, T439, quotF_in_ga(T437, T439))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(0)))), 0) → quotF_out_ga(s(s(s(s(0)))), 0)
quotF_in_ga(s(s(s(s(s(T500))))), s(T502)) → U14_ga(T500, T502, quotF_in_ga(T500, T502))
U14_ga(T500, T502, quotF_out_ga(T500, T502)) → quotF_out_ga(s(s(s(s(s(T500))))), s(T502))
U7_gga(T437, T439, quotF_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U8_gga(T512, T514, quotG_in_ga(T512, T514))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(0))), 0) → quotG_out_ga(s(s(s(0))), 0)
quotG_in_ga(s(s(s(s(T564)))), s(T566)) → U15_ga(T564, T566, quotG_in_ga(T564, T566))
U15_ga(T564, T566, quotG_out_ga(T564, T566)) → quotG_out_ga(s(s(s(s(T564)))), s(T566))
U8_gga(T512, T514, quotG_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U9_gga(T575, T577, quotH_in_ga(T575, T577))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(0)), 0) → quotH_out_ga(s(s(0)), 0)
quotH_in_ga(s(s(s(T616))), s(T618)) → U16_ga(T616, T618, quotH_in_ga(T616, T618))
U16_ga(T616, T618, quotH_out_ga(T616, T618)) → quotH_out_ga(s(s(s(T616))), s(T618))
U9_gga(T575, T577, quotH_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U10_gga(T626, T628, quotI_in_ga(T626, T628))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(0), 0) → quotI_out_ga(s(0), 0)
quotI_in_ga(s(s(T656)), s(T658)) → U17_ga(T656, T658, quotI_in_ga(T656, T658))
U17_ga(T656, T658, quotI_out_ga(T656, T658)) → quotI_out_ga(s(s(T656)), s(T658))
U10_gga(T626, T628, quotI_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U11_gga(T665, T667, quotJ_in_ga(T665, T667))
quotJ_in_ga(0, 0) → quotJ_out_ga(0, 0)
quotJ_in_ga(s(T684), s(T686)) → U18_ga(T684, T686, quotJ_in_ga(T684, T686))
U18_ga(T684, T686, quotJ_out_ga(T684, T686)) → quotJ_out_ga(s(T684), s(T686))
U11_gga(T665, T667, quotJ_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U3_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotC_out_ggga(T241, 0, T242, s(T244))
U2_ggga(T226, T227, T228, T230, quotC_out_ggga(T226, T227, T228, T230)) → quotC_out_ggga(s(T226), s(T227), T228, T230)
U4_gga(T189, T190, T192, quotC_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U1_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divA_out_gga(T7, T8, T10)

(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:

QUOTG_IN_GA(s(s(s(s(T564)))), s(T566)) → QUOTG_IN_GA(T564, T566)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTG_IN_GA(x1, x2) = QUOTG_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:

QUOTG_IN_GA(s(s(s(s(T564))))) → QUOTG_IN_GA(T564)

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:

QUOTG_IN_GA(s(s(s(s(T564))))) → QUOTG_IN_GA(T564)
The graph contains the following edges 1 > 1

(34) YES

(35) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTF_IN_GA(s(s(s(s(s(T500))))), s(T502)) → QUOTF_IN_GA(T500, T502)

The TRS R consists of the following rules:

divA_in_gga(T7, T8, T10) → U1_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U4_gga(T189, T190, T192, quotC_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotC_in_ggga(0, s(T208), T209, 0) → quotC_out_ggga(0, s(T208), T209, 0)
quotC_in_ggga(s(T226), s(T227), T228, T230) → U2_ggga(T226, T227, T228, T230, quotC_in_ggga(T226, T227, T228, T230))
quotC_in_ggga(T241, 0, T242, s(T244)) → U3_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U5_gga(T251, T253, quotD_in_ga(T251, T253))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(0)))))), 0) → quotD_out_ga(s(s(s(s(s(s(0)))))), 0)
quotD_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U12_ga(T336, T338, quotD_in_ga(T336, T338))
U12_ga(T336, T338, quotD_out_ga(T336, T338)) → quotD_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U5_gga(T251, T253, quotD_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U6_gga(T350, T352, quotE_in_ga(T350, T352))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(0))))), 0) → quotE_out_ga(s(s(s(s(s(0))))), 0)
quotE_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U13_ga(T424, T426, quotE_in_ga(T424, T426))
U13_ga(T424, T426, quotE_out_ga(T424, T426)) → quotE_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U6_gga(T350, T352, quotE_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U7_gga(T437, T439, quotF_in_ga(T437, T439))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(0)))), 0) → quotF_out_ga(s(s(s(s(0)))), 0)
quotF_in_ga(s(s(s(s(s(T500))))), s(T502)) → U14_ga(T500, T502, quotF_in_ga(T500, T502))
U14_ga(T500, T502, quotF_out_ga(T500, T502)) → quotF_out_ga(s(s(s(s(s(T500))))), s(T502))
U7_gga(T437, T439, quotF_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U8_gga(T512, T514, quotG_in_ga(T512, T514))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(0))), 0) → quotG_out_ga(s(s(s(0))), 0)
quotG_in_ga(s(s(s(s(T564)))), s(T566)) → U15_ga(T564, T566, quotG_in_ga(T564, T566))
U15_ga(T564, T566, quotG_out_ga(T564, T566)) → quotG_out_ga(s(s(s(s(T564)))), s(T566))
U8_gga(T512, T514, quotG_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U9_gga(T575, T577, quotH_in_ga(T575, T577))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(0)), 0) → quotH_out_ga(s(s(0)), 0)
quotH_in_ga(s(s(s(T616))), s(T618)) → U16_ga(T616, T618, quotH_in_ga(T616, T618))
U16_ga(T616, T618, quotH_out_ga(T616, T618)) → quotH_out_ga(s(s(s(T616))), s(T618))
U9_gga(T575, T577, quotH_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U10_gga(T626, T628, quotI_in_ga(T626, T628))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(0), 0) → quotI_out_ga(s(0), 0)
quotI_in_ga(s(s(T656)), s(T658)) → U17_ga(T656, T658, quotI_in_ga(T656, T658))
U17_ga(T656, T658, quotI_out_ga(T656, T658)) → quotI_out_ga(s(s(T656)), s(T658))
U10_gga(T626, T628, quotI_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U11_gga(T665, T667, quotJ_in_ga(T665, T667))
quotJ_in_ga(0, 0) → quotJ_out_ga(0, 0)
quotJ_in_ga(s(T684), s(T686)) → U18_ga(T684, T686, quotJ_in_ga(T684, T686))
U18_ga(T684, T686, quotJ_out_ga(T684, T686)) → quotJ_out_ga(s(T684), s(T686))
U11_gga(T665, T667, quotJ_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U3_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotC_out_ggga(T241, 0, T242, s(T244))
U2_ggga(T226, T227, T228, T230, quotC_out_ggga(T226, T227, T228, T230)) → quotC_out_ggga(s(T226), s(T227), T228, T230)
U4_gga(T189, T190, T192, quotC_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U1_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divA_out_gga(T7, T8, T10)

(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:

QUOTF_IN_GA(s(s(s(s(s(T500))))), s(T502)) → QUOTF_IN_GA(T500, T502)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTF_IN_GA(x1, x2) = QUOTF_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:

QUOTF_IN_GA(s(s(s(s(s(T500)))))) → QUOTF_IN_GA(T500)

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:

QUOTF_IN_GA(s(s(s(s(s(T500)))))) → QUOTF_IN_GA(T500)
The graph contains the following edges 1 > 1

(41) YES

(42) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTE_IN_GA(s(s(s(s(s(s(T424)))))), s(T426)) → QUOTE_IN_GA(T424, T426)

The TRS R consists of the following rules:

divA_in_gga(T7, T8, T10) → U1_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U4_gga(T189, T190, T192, quotC_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotC_in_ggga(0, s(T208), T209, 0) → quotC_out_ggga(0, s(T208), T209, 0)
quotC_in_ggga(s(T226), s(T227), T228, T230) → U2_ggga(T226, T227, T228, T230, quotC_in_ggga(T226, T227, T228, T230))
quotC_in_ggga(T241, 0, T242, s(T244)) → U3_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U5_gga(T251, T253, quotD_in_ga(T251, T253))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(0)))))), 0) → quotD_out_ga(s(s(s(s(s(s(0)))))), 0)
quotD_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U12_ga(T336, T338, quotD_in_ga(T336, T338))
U12_ga(T336, T338, quotD_out_ga(T336, T338)) → quotD_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U5_gga(T251, T253, quotD_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U6_gga(T350, T352, quotE_in_ga(T350, T352))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(0))))), 0) → quotE_out_ga(s(s(s(s(s(0))))), 0)
quotE_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U13_ga(T424, T426, quotE_in_ga(T424, T426))
U13_ga(T424, T426, quotE_out_ga(T424, T426)) → quotE_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U6_gga(T350, T352, quotE_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U7_gga(T437, T439, quotF_in_ga(T437, T439))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(0)))), 0) → quotF_out_ga(s(s(s(s(0)))), 0)
quotF_in_ga(s(s(s(s(s(T500))))), s(T502)) → U14_ga(T500, T502, quotF_in_ga(T500, T502))
U14_ga(T500, T502, quotF_out_ga(T500, T502)) → quotF_out_ga(s(s(s(s(s(T500))))), s(T502))
U7_gga(T437, T439, quotF_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U8_gga(T512, T514, quotG_in_ga(T512, T514))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(0))), 0) → quotG_out_ga(s(s(s(0))), 0)
quotG_in_ga(s(s(s(s(T564)))), s(T566)) → U15_ga(T564, T566, quotG_in_ga(T564, T566))
U15_ga(T564, T566, quotG_out_ga(T564, T566)) → quotG_out_ga(s(s(s(s(T564)))), s(T566))
U8_gga(T512, T514, quotG_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U9_gga(T575, T577, quotH_in_ga(T575, T577))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(0)), 0) → quotH_out_ga(s(s(0)), 0)
quotH_in_ga(s(s(s(T616))), s(T618)) → U16_ga(T616, T618, quotH_in_ga(T616, T618))
U16_ga(T616, T618, quotH_out_ga(T616, T618)) → quotH_out_ga(s(s(s(T616))), s(T618))
U9_gga(T575, T577, quotH_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U10_gga(T626, T628, quotI_in_ga(T626, T628))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(0), 0) → quotI_out_ga(s(0), 0)
quotI_in_ga(s(s(T656)), s(T658)) → U17_ga(T656, T658, quotI_in_ga(T656, T658))
U17_ga(T656, T658, quotI_out_ga(T656, T658)) → quotI_out_ga(s(s(T656)), s(T658))
U10_gga(T626, T628, quotI_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U11_gga(T665, T667, quotJ_in_ga(T665, T667))
quotJ_in_ga(0, 0) → quotJ_out_ga(0, 0)
quotJ_in_ga(s(T684), s(T686)) → U18_ga(T684, T686, quotJ_in_ga(T684, T686))
U18_ga(T684, T686, quotJ_out_ga(T684, T686)) → quotJ_out_ga(s(T684), s(T686))
U11_gga(T665, T667, quotJ_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U3_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotC_out_ggga(T241, 0, T242, s(T244))
U2_ggga(T226, T227, T228, T230, quotC_out_ggga(T226, T227, T228, T230)) → quotC_out_ggga(s(T226), s(T227), T228, T230)
U4_gga(T189, T190, T192, quotC_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U1_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divA_out_gga(T7, T8, T10)

(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:

QUOTE_IN_GA(s(s(s(s(s(s(T424)))))), s(T426)) → QUOTE_IN_GA(T424, T426)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTE_IN_GA(x1, x2) = QUOTE_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:

QUOTE_IN_GA(s(s(s(s(s(s(T424))))))) → QUOTE_IN_GA(T424)

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:

QUOTE_IN_GA(s(s(s(s(s(s(T424))))))) → QUOTE_IN_GA(T424)
The graph contains the following edges 1 > 1

(48) YES

(49) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTD_IN_GA(s(s(s(s(s(s(s(T336))))))), s(T338)) → QUOTD_IN_GA(T336, T338)

The TRS R consists of the following rules:

divA_in_gga(T7, T8, T10) → U1_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U4_gga(T189, T190, T192, quotC_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotC_in_ggga(0, s(T208), T209, 0) → quotC_out_ggga(0, s(T208), T209, 0)
quotC_in_ggga(s(T226), s(T227), T228, T230) → U2_ggga(T226, T227, T228, T230, quotC_in_ggga(T226, T227, T228, T230))
quotC_in_ggga(T241, 0, T242, s(T244)) → U3_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U5_gga(T251, T253, quotD_in_ga(T251, T253))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(0)))))), 0) → quotD_out_ga(s(s(s(s(s(s(0)))))), 0)
quotD_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U12_ga(T336, T338, quotD_in_ga(T336, T338))
U12_ga(T336, T338, quotD_out_ga(T336, T338)) → quotD_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U5_gga(T251, T253, quotD_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U6_gga(T350, T352, quotE_in_ga(T350, T352))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(0))))), 0) → quotE_out_ga(s(s(s(s(s(0))))), 0)
quotE_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U13_ga(T424, T426, quotE_in_ga(T424, T426))
U13_ga(T424, T426, quotE_out_ga(T424, T426)) → quotE_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U6_gga(T350, T352, quotE_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U7_gga(T437, T439, quotF_in_ga(T437, T439))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(0)))), 0) → quotF_out_ga(s(s(s(s(0)))), 0)
quotF_in_ga(s(s(s(s(s(T500))))), s(T502)) → U14_ga(T500, T502, quotF_in_ga(T500, T502))
U14_ga(T500, T502, quotF_out_ga(T500, T502)) → quotF_out_ga(s(s(s(s(s(T500))))), s(T502))
U7_gga(T437, T439, quotF_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U8_gga(T512, T514, quotG_in_ga(T512, T514))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(0))), 0) → quotG_out_ga(s(s(s(0))), 0)
quotG_in_ga(s(s(s(s(T564)))), s(T566)) → U15_ga(T564, T566, quotG_in_ga(T564, T566))
U15_ga(T564, T566, quotG_out_ga(T564, T566)) → quotG_out_ga(s(s(s(s(T564)))), s(T566))
U8_gga(T512, T514, quotG_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U9_gga(T575, T577, quotH_in_ga(T575, T577))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(0)), 0) → quotH_out_ga(s(s(0)), 0)
quotH_in_ga(s(s(s(T616))), s(T618)) → U16_ga(T616, T618, quotH_in_ga(T616, T618))
U16_ga(T616, T618, quotH_out_ga(T616, T618)) → quotH_out_ga(s(s(s(T616))), s(T618))
U9_gga(T575, T577, quotH_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U10_gga(T626, T628, quotI_in_ga(T626, T628))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(0), 0) → quotI_out_ga(s(0), 0)
quotI_in_ga(s(s(T656)), s(T658)) → U17_ga(T656, T658, quotI_in_ga(T656, T658))
U17_ga(T656, T658, quotI_out_ga(T656, T658)) → quotI_out_ga(s(s(T656)), s(T658))
U10_gga(T626, T628, quotI_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U11_gga(T665, T667, quotJ_in_ga(T665, T667))
quotJ_in_ga(0, 0) → quotJ_out_ga(0, 0)
quotJ_in_ga(s(T684), s(T686)) → U18_ga(T684, T686, quotJ_in_ga(T684, T686))
U18_ga(T684, T686, quotJ_out_ga(T684, T686)) → quotJ_out_ga(s(T684), s(T686))
U11_gga(T665, T667, quotJ_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U3_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotC_out_ggga(T241, 0, T242, s(T244))
U2_ggga(T226, T227, T228, T230, quotC_out_ggga(T226, T227, T228, T230)) → quotC_out_ggga(s(T226), s(T227), T228, T230)
U4_gga(T189, T190, T192, quotC_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U1_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divA_out_gga(T7, T8, T10)

(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:

QUOTD_IN_GA(s(s(s(s(s(s(s(T336))))))), s(T338)) → QUOTD_IN_GA(T336, T338)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTD_IN_GA(x1, x2) = QUOTD_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:

QUOTD_IN_GA(s(s(s(s(s(s(s(T336)))))))) → QUOTD_IN_GA(T336)

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:

QUOTD_IN_GA(s(s(s(s(s(s(s(T336)))))))) → QUOTD_IN_GA(T336)
The graph contains the following edges 1 > 1

(55) YES

(56) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → QUOTC_IN_GGGA(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)
QUOTC_IN_GGGA(s(T226), s(T227), T228, T230) → QUOTC_IN_GGGA(T226, T227, T228, T230)
QUOTC_IN_GGGA(T241, 0, T242, s(T244)) → QUOTB_IN_GGA(T241, s(T242), T244)

The TRS R consists of the following rules:

divA_in_gga(T7, T8, T10) → U1_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U4_gga(T189, T190, T192, quotC_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotC_in_ggga(0, s(T208), T209, 0) → quotC_out_ggga(0, s(T208), T209, 0)
quotC_in_ggga(s(T226), s(T227), T228, T230) → U2_ggga(T226, T227, T228, T230, quotC_in_ggga(T226, T227, T228, T230))
quotC_in_ggga(T241, 0, T242, s(T244)) → U3_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U5_gga(T251, T253, quotD_in_ga(T251, T253))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(0)))))), 0) → quotD_out_ga(s(s(s(s(s(s(0)))))), 0)
quotD_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U12_ga(T336, T338, quotD_in_ga(T336, T338))
U12_ga(T336, T338, quotD_out_ga(T336, T338)) → quotD_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U5_gga(T251, T253, quotD_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U6_gga(T350, T352, quotE_in_ga(T350, T352))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(0))))), 0) → quotE_out_ga(s(s(s(s(s(0))))), 0)
quotE_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U13_ga(T424, T426, quotE_in_ga(T424, T426))
U13_ga(T424, T426, quotE_out_ga(T424, T426)) → quotE_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U6_gga(T350, T352, quotE_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U7_gga(T437, T439, quotF_in_ga(T437, T439))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(0)))), 0) → quotF_out_ga(s(s(s(s(0)))), 0)
quotF_in_ga(s(s(s(s(s(T500))))), s(T502)) → U14_ga(T500, T502, quotF_in_ga(T500, T502))
U14_ga(T500, T502, quotF_out_ga(T500, T502)) → quotF_out_ga(s(s(s(s(s(T500))))), s(T502))
U7_gga(T437, T439, quotF_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U8_gga(T512, T514, quotG_in_ga(T512, T514))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(0))), 0) → quotG_out_ga(s(s(s(0))), 0)
quotG_in_ga(s(s(s(s(T564)))), s(T566)) → U15_ga(T564, T566, quotG_in_ga(T564, T566))
U15_ga(T564, T566, quotG_out_ga(T564, T566)) → quotG_out_ga(s(s(s(s(T564)))), s(T566))
U8_gga(T512, T514, quotG_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U9_gga(T575, T577, quotH_in_ga(T575, T577))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(0)), 0) → quotH_out_ga(s(s(0)), 0)
quotH_in_ga(s(s(s(T616))), s(T618)) → U16_ga(T616, T618, quotH_in_ga(T616, T618))
U16_ga(T616, T618, quotH_out_ga(T616, T618)) → quotH_out_ga(s(s(s(T616))), s(T618))
U9_gga(T575, T577, quotH_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U10_gga(T626, T628, quotI_in_ga(T626, T628))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(0), 0) → quotI_out_ga(s(0), 0)
quotI_in_ga(s(s(T656)), s(T658)) → U17_ga(T656, T658, quotI_in_ga(T656, T658))
U17_ga(T656, T658, quotI_out_ga(T656, T658)) → quotI_out_ga(s(s(T656)), s(T658))
U10_gga(T626, T628, quotI_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U11_gga(T665, T667, quotJ_in_ga(T665, T667))
quotJ_in_ga(0, 0) → quotJ_out_ga(0, 0)
quotJ_in_ga(s(T684), s(T686)) → U18_ga(T684, T686, quotJ_in_ga(T684, T686))
U18_ga(T684, T686, quotJ_out_ga(T684, T686)) → quotJ_out_ga(s(T684), s(T686))
U11_gga(T665, T667, quotJ_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U3_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotC_out_ggga(T241, 0, T242, s(T244))
U2_ggga(T226, T227, T228, T230, quotC_out_ggga(T226, T227, T228, T230)) → quotC_out_ggga(s(T226), s(T227), T228, T230)
U4_gga(T189, T190, T192, quotC_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U1_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divA_out_gga(T7, T8, T10)

(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:

QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → QUOTC_IN_GGGA(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)
QUOTC_IN_GGGA(s(T226), s(T227), T228, T230) → QUOTC_IN_GGGA(T226, T227, T228, T230)
QUOTC_IN_GGGA(T241, 0, T242, s(T244)) → QUOTB_IN_GGA(T241, s(T242), T244)

R is empty.
The argument filtering Pi contains the following mapping:
0 = 0
s(x1) = s(x1)
QUOTB_IN_GGA(x1, x2, x3) = QUOTB_IN_GGA(x1, x2)
QUOTC_IN_GGGA(x1, x2, x3, x4) = QUOTC_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:

QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190))))))))) → QUOTC_IN_GGGA(T189, T190, s(s(s(s(s(s(s(T190))))))))
QUOTC_IN_GGGA(s(T226), s(T227), T228) → QUOTC_IN_GGGA(T226, T227, T228)
QUOTC_IN_GGGA(T241, 0, T242) → QUOTB_IN_GGA(T241, s(T242))

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:

QUOTC_IN_GGGA(T241, 0, T242) → QUOTB_IN_GGA(T241, s(T242))
The graph contains the following edges 1 >= 1
QUOTC_IN_GGGA(s(T226), s(T227), T228) → QUOTC_IN_GGGA(T226, T227, T228)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190))))))))) → QUOTC_IN_GGGA(T189, T190, s(s(s(s(s(s(s(T190))))))))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3

(0) Obligation:

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

(2) Obligation:

(3) DependencyPairsProof (EQUIVALENT transformation)

(4) Obligation:

(5) DependencyGraphProof (EQUIVALENT transformation)

(6) Complex Obligation (AND)

(7) Obligation:

(8) UsableRulesProof (EQUIVALENT transformation)

(9) Obligation:

(10) PiDPToQDPProof (SOUND transformation)

(11) Obligation:

(12) QDPSizeChangeProof (EQUIVALENT transformation)

(13) YES

(14) Obligation:

(15) UsableRulesProof (EQUIVALENT transformation)

(16) Obligation:

(17) PiDPToQDPProof (SOUND transformation)

(18) Obligation:

(19) QDPSizeChangeProof (EQUIVALENT transformation)

(20) YES

(21) Obligation:

(22) UsableRulesProof (EQUIVALENT transformation)

(23) Obligation:

(24) PiDPToQDPProof (SOUND transformation)

(25) Obligation:

(26) QDPSizeChangeProof (EQUIVALENT transformation)

(27) YES

(28) Obligation:

(29) UsableRulesProof (EQUIVALENT transformation)

(30) Obligation:

(31) PiDPToQDPProof (SOUND transformation)

(32) Obligation:

(33) QDPSizeChangeProof (EQUIVALENT transformation)

(34) YES

(35) Obligation:

(36) UsableRulesProof (EQUIVALENT transformation)

(37) Obligation:

(38) PiDPToQDPProof (SOUND transformation)

(39) Obligation:

(40) QDPSizeChangeProof (EQUIVALENT transformation)

(41) YES

(42) Obligation:

(43) UsableRulesProof (EQUIVALENT transformation)

(44) Obligation:

(45) PiDPToQDPProof (SOUND transformation)

(46) Obligation:

(47) QDPSizeChangeProof (EQUIVALENT transformation)

(48) YES

(49) Obligation:

(50) UsableRulesProof (EQUIVALENT transformation)

(51) Obligation:

(52) PiDPToQDPProof (SOUND transformation)

(53) Obligation:

(54) QDPSizeChangeProof (EQUIVALENT transformation)

(55) YES

(56) Obligation:

(57) UsableRulesProof (EQUIVALENT transformation)

(58) Obligation:

(59) PiDPToQDPProof (SOUND transformation)

(60) Obligation:

(61) QDPSizeChangeProof (EQUIVALENT transformation)

(62) YES