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

(0) Obligation:

Clauses:

queens(Y) :- ','(perm(.(s(0), .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), [])))))))), Y), safe(Y)).
perm([], []).
perm(.(X, Y), .(V, Res)) :- ','(delete(V, .(X, Y), Rest), perm(Rest, Res)).
delete(X, .(X, Y), Y).
delete(X, .(F, T), .(F, R)) :- delete(X, T, R).
safe([]).
safe(.(X, Y)) :- ','(noattack(X, Y, s(0)), safe(Y)).
noattack(X, [], N).
noattack(X, .(F, T), N) :- ','(notEq(X, F), ','(add(F, N, FplusN), ','(notEq(X, FplusN), ','(add(X, N, XplusN), ','(notEq(F, XplusN), noattack(X, T, s(N))))))).
add(0, X, X).
add(s(X), Y, s(Z)) :- add(X, Y, Z).
notEq(0, s(X)).
notEq(s(X), 0).
notEq(s(X), s(Y)) :- notEq(X, Y).

Query: queens(a)

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

Transformed Prolog program to (Pi-)TRS.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
2 [label="A: queens(T1)\n\n", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
5 [label="5: queens(T1), SCOPE: 1, CLAUSE: 0\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: ','(perm(.(s(0), .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), [])))))))), T4), safe(T4))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: ','(perm(.(s(0), .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), [])))))))), T4), safe(T4)), SCOPE: 2, CLAUSE: 1 | ','(perm(.(s(0), .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), [])))))))), T4), safe(T4)), SCOPE: 2, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: ','(perm(.(s(0), .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), [])))))))), T4), safe(T4)), SCOPE: 2, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: ','(','(delete(T11, .(s(0), .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), [])))))))), X16), perm(X16, T12)), safe(.(T11, T12)))\n\nX16 is free", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="B: ','(','(delete(T11, .(s(0), T15), X16), perm(X16, T12)), safe(.(T11, T12)))\n\nT15 is ground\nX16 is free", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="O: delete(T11, .(s(0), T15), X16)\n\nT15 is ground\nX16 is free", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="N9: ','(perm(T20, T21), safe(.(T22, T21)))\n\nT22 is ground\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: delete(T11, .(s(0), T15), X16), SCOPE: 3, CLAUSE: 3 | delete(T11, .(s(0), T15), X16), SCOPE: 3, CLAUSE: 4\n\nT15 is ground\nX16 is free", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: delete(T11, .(s(0), T15), X16), SCOPE: 3, CLAUSE: 3\n\nT15 is ground\nX16 is free", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: delete(T11, .(s(0), T15), X16), SCOPE: 3, CLAUSE: 4\n\nT15 is ground\nX16 is free", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="C: delete(T48, T47, X57)\n\nT47 is ground\nX57 is free", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: delete(T48, T47, X57), SCOPE: 4, CLAUSE: 3 | delete(T48, T47, X57), SCOPE: 4, CLAUSE: 4\n\nT47 is ground\nX57 is free", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: delete(T48, T47, X57), SCOPE: 4, CLAUSE: 3\n\nT47 is ground\nX57 is free", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: delete(T48, T47, X57), SCOPE: 4, CLAUSE: 4\n\nT47 is ground\nX57 is free", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: delete(T72, T71, X86)\n\nT71 is ground\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="D: perm(T20, T21)\n\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="P: safe(.(T22, T77))\n\nT22 is ground\nT77 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: perm(T20, T21), SCOPE: 5, CLAUSE: 1 | perm(T20, T21), SCOPE: 5, CLAUSE: 2\n\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: perm(T20, T21), SCOPE: 5, CLAUSE: 1\n\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: perm(T20, T21), SCOPE: 5, CLAUSE: 2\n\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="E: ','(delete(T90, .(T86, T87), X104), perm(X104, T91))\n\nT86 is ground\nT87 is ground\nX104 is free", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: delete(T90, .(T86, T87), X104)\n\nT86 is ground\nT87 is ground\nX104 is free", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: perm(T96, T97)\n\nT96 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: safe(.(T22, T77)), SCOPE: 6, CLAUSE: 5 | safe(.(T22, T77)), SCOPE: 6, CLAUSE: 6\n\nT22 is ground\nT77 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: safe(.(T22, T77)), SCOPE: 6, CLAUSE: 6\n\nT22 is ground\nT77 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="Q: ','(noattack(T108, T109, s(0)), safe(T109))\n\nT108 is ground\nT109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="R: noattack(T108, T109, s(0))\n\nT108 is ground\nT109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="T: safe(T109)\n\nT109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: noattack(T108, T109, s(0)), SCOPE: 7, CLAUSE: 7 | noattack(T108, T109, s(0)), SCOPE: 7, CLAUSE: 8\n\nT108 is ground\nT109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: noattack(T108, T109, s(0)), SCOPE: 7, CLAUSE: 7\n\nT108 is ground\nT109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: noattack(T108, T109, s(0)), SCOPE: 7, CLAUSE: 8\n\nT108 is ground\nT109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="S: ','(notEq(T125, T126), ','(add(T126, s(0), X155), ','(notEq(T125, X155), ','(add(T125, s(0), X156), ','(notEq(T126, X156), noattack(T125, T127, s(s(0))))))))\n\nT125 is ground\nT126 is ground\nT127 is ground\nX155 is free\nX156 is free", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="F: notEq(T125, T126)\n\nT125 is ground\nT126 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="N10: ','(add(T126, s(0), X155), ','(notEq(T125, X155), ','(add(T125, s(0), X156), ','(notEq(T126, X156), noattack(T125, T127, s(s(0)))))))\n\nT125 is ground\nT126 is ground\nT127 is ground\nX155 is free\nX156 is free", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: notEq(T125, T126), SCOPE: 8, CLAUSE: 11 | notEq(T125, T126), SCOPE: 8, CLAUSE: 12 | notEq(T125, T126), SCOPE: 8, CLAUSE: 13\n\nT125 is ground\nT126 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: notEq(T125, T126), SCOPE: 8, CLAUSE: 11\n\nT125 is ground\nT126 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: notEq(T125, T126), SCOPE: 8, CLAUSE: 12 | notEq(T125, T126), SCOPE: 8, CLAUSE: 13\n\nT125 is ground\nT126 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: notEq(T125, T126), SCOPE: 8, CLAUSE: 12\n\nT125 is ground\nT126 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: notEq(T125, T126), SCOPE: 8, CLAUSE: 13\n\nT125 is ground\nT126 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: notEq(T146, T147)\n\nT146 is ground\nT147 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="G: add(T126, s(0), X155)\n\nT126 is ground\nX155 is free", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="N11: ','(notEq(T125, T150), ','(add(T125, s(0), X156), ','(notEq(T126, X156), noattack(T125, T127, s(s(0))))))\n\nT125 is ground\nT126 is ground\nT127 is ground\nT150 is ground\nX156 is free", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: add(T126, s(0), X155), SCOPE: 9, CLAUSE: 9 | add(T126, s(0), X155), SCOPE: 9, CLAUSE: 10\n\nT126 is ground\nX155 is free", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: add(T126, s(0), X155), SCOPE: 9, CLAUSE: 9\n\nT126 is ground\nX155 is free", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: add(T126, s(0), X155), SCOPE: 9, CLAUSE: 10\n\nT126 is ground\nX155 is free", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: add(T153, s(0), X199)\n\nT153 is ground\nX199 is free", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: notEq(T125, T150)\n\nT125 is ground\nT150 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="N12: ','(add(T125, s(0), X156), ','(notEq(T126, X156), noattack(T125, T127, s(s(0)))))\n\nT125 is ground\nT126 is ground\nT127 is ground\nX156 is free", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: add(T125, s(0), X156)\n\nT125 is ground\nX156 is free", fontsize=16, style=filled, fillcolor=lightyellow];
238 [label="N13: ','(notEq(T126, T158), noattack(T125, T127, s(s(0))))\n\nT125 is ground\nT126 is ground\nT127 is ground\nT158 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
241 [label="241: notEq(T126, T158)\n\nT126 is ground\nT158 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
242 [label="U: noattack(T125, T127, s(s(0)))\n\nT125 is ground\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
244 [label="244: noattack(T125, T127, s(s(0))), SCOPE: 10, CLAUSE: 7 | noattack(T125, T127, s(s(0))), SCOPE: 10, CLAUSE: 8\n\nT125 is ground\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
247 [label="247: noattack(T125, T127, s(s(0))), SCOPE: 10, CLAUSE: 7\n\nT125 is ground\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="248: noattack(T125, T127, s(s(0))), SCOPE: 10, CLAUSE: 8\n\nT125 is ground\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
252 [label="252: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="253: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
255 [label="255: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="V: ','(notEq(T176, T177), ','(add(T177, s(s(0)), X242), ','(notEq(T176, X242), ','(add(T176, s(s(0)), X243), ','(notEq(T177, X243), noattack(T176, T178, s(s(s(0)))))))))\n\nT176 is ground\nT177 is ground\nT178 is ground\nX242 is free\nX243 is free", fontsize=16, style=filled, fillcolor=lightyellow];
260 [label="260: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: notEq(T176, T177)\n\nT176 is ground\nT177 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="N14: ','(add(T177, s(s(0)), X242), ','(notEq(T176, X242), ','(add(T176, s(s(0)), X243), ','(notEq(T177, X243), noattack(T176, T178, s(s(s(0))))))))\n\nT176 is ground\nT177 is ground\nT178 is ground\nX242 is free\nX243 is free", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="H: add(T177, s(s(0)), X242)\n\nT177 is ground\nX242 is free", fontsize=16, style=filled, fillcolor=lightyellow];
268 [label="N15: ','(notEq(T176, T183), ','(add(T176, s(s(0)), X243), ','(notEq(T177, X243), noattack(T176, T178, s(s(s(0)))))))\n\nT176 is ground\nT177 is ground\nT178 is ground\nT183 is ground\nX243 is free", fontsize=16, style=filled, fillcolor=lightyellow];
272 [label="272: add(T177, s(s(0)), X242), SCOPE: 11, CLAUSE: 9 | add(T177, s(s(0)), X242), SCOPE: 11, CLAUSE: 10\n\nT177 is ground\nX242 is free", fontsize=16, style=filled, fillcolor=lightyellow];
275 [label="275: add(T177, s(s(0)), X242), SCOPE: 11, CLAUSE: 9\n\nT177 is ground\nX242 is free", fontsize=16, style=filled, fillcolor=lightyellow];
276 [label="276: add(T177, s(s(0)), X242), SCOPE: 11, CLAUSE: 10\n\nT177 is ground\nX242 is free", fontsize=16, style=filled, fillcolor=lightyellow];
280 [label="280: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
281 [label="281: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
282 [label="282: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
287 [label="287: add(T186, s(s(0)), X268)\n\nT186 is ground\nX268 is free", fontsize=16, style=filled, fillcolor=lightyellow];
288 [label="288: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
295 [label="295: notEq(T176, T183)\n\nT176 is ground\nT183 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
296 [label="N16: ','(add(T176, s(s(0)), X243), ','(notEq(T177, X243), noattack(T176, T178, s(s(s(0))))))\n\nT176 is ground\nT177 is ground\nT178 is ground\nX243 is free", fontsize=16, style=filled, fillcolor=lightyellow];
299 [label="299: add(T176, s(s(0)), X243)\n\nT176 is ground\nX243 is free", fontsize=16, style=filled, fillcolor=lightyellow];
300 [label="N17: ','(notEq(T177, T191), noattack(T176, T178, s(s(s(0)))))\n\nT176 is ground\nT177 is ground\nT178 is ground\nT191 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
303 [label="303: notEq(T177, T191)\n\nT177 is ground\nT191 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
304 [label="W: noattack(T176, T178, s(s(s(0))))\n\nT176 is ground\nT178 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
314 [label="314: noattack(T176, T178, s(s(s(0)))), SCOPE: 12, CLAUSE: 7 | noattack(T176, T178, s(s(s(0)))), SCOPE: 12, CLAUSE: 8\n\nT176 is ground\nT178 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
316 [label="316: noattack(T176, T178, s(s(s(0)))), SCOPE: 12, CLAUSE: 7\n\nT176 is ground\nT178 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
317 [label="317: noattack(T176, T178, s(s(s(0)))), SCOPE: 12, CLAUSE: 8\n\nT176 is ground\nT178 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
320 [label="320: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
321 [label="321: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
322 [label="322: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
323 [label="X: ','(notEq(T209, T210), ','(add(T210, s(s(s(0))), X311), ','(notEq(T209, X311), ','(add(T209, s(s(s(0))), X312), ','(notEq(T210, X312), noattack(T209, T211, s(s(s(s(0))))))))))\n\nT209 is ground\nT210 is ground\nT211 is ground\nX311 is free\nX312 is free", fontsize=16, style=filled, fillcolor=lightyellow];
324 [label="324: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
329 [label="329: notEq(T209, T210)\n\nT209 is ground\nT210 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
330 [label="N18: ','(add(T210, s(s(s(0))), X311), ','(notEq(T209, X311), ','(add(T209, s(s(s(0))), X312), ','(notEq(T210, X312), noattack(T209, T211, s(s(s(s(0)))))))))\n\nT209 is ground\nT210 is ground\nT211 is ground\nX311 is free\nX312 is free", fontsize=16, style=filled, fillcolor=lightyellow];
335 [label="I: add(T210, s(s(s(0))), X311)\n\nT210 is ground\nX311 is free", fontsize=16, style=filled, fillcolor=lightyellow];
336 [label="N19: ','(notEq(T209, T216), ','(add(T209, s(s(s(0))), X312), ','(notEq(T210, X312), noattack(T209, T211, s(s(s(s(0))))))))\n\nT209 is ground\nT210 is ground\nT211 is ground\nT216 is ground\nX312 is free", fontsize=16, style=filled, fillcolor=lightyellow];
339 [label="339: add(T210, s(s(s(0))), X311), SCOPE: 13, CLAUSE: 9 | add(T210, s(s(s(0))), X311), SCOPE: 13, CLAUSE: 10\n\nT210 is ground\nX311 is free", fontsize=16, style=filled, fillcolor=lightyellow];
340 [label="340: add(T210, s(s(s(0))), X311), SCOPE: 13, CLAUSE: 9\n\nT210 is ground\nX311 is free", fontsize=16, style=filled, fillcolor=lightyellow];
341 [label="341: add(T210, s(s(s(0))), X311), SCOPE: 13, CLAUSE: 10\n\nT210 is ground\nX311 is free", fontsize=16, style=filled, fillcolor=lightyellow];
342 [label="342: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
343 [label="343: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
344 [label="344: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
349 [label="349: add(T219, s(s(s(0))), X337)\n\nT219 is ground\nX337 is free", fontsize=16, style=filled, fillcolor=lightyellow];
350 [label="350: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
358 [label="358: notEq(T209, T216)\n\nT209 is ground\nT216 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
359 [label="N20: ','(add(T209, s(s(s(0))), X312), ','(notEq(T210, X312), noattack(T209, T211, s(s(s(s(0)))))))\n\nT209 is ground\nT210 is ground\nT211 is ground\nX312 is free", fontsize=16, style=filled, fillcolor=lightyellow];
365 [label="365: add(T209, s(s(s(0))), X312)\n\nT209 is ground\nX312 is free", fontsize=16, style=filled, fillcolor=lightyellow];
366 [label="N21: ','(notEq(T210, T224), noattack(T209, T211, s(s(s(s(0))))))\n\nT209 is ground\nT210 is ground\nT211 is ground\nT224 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
372 [label="372: notEq(T210, T224)\n\nT210 is ground\nT224 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
373 [label="Y: noattack(T209, T211, s(s(s(s(0)))))\n\nT209 is ground\nT211 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
381 [label="381: noattack(T209, T211, s(s(s(s(0))))), SCOPE: 14, CLAUSE: 7 | noattack(T209, T211, s(s(s(s(0))))), SCOPE: 14, CLAUSE: 8\n\nT209 is ground\nT211 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
384 [label="384: noattack(T209, T211, s(s(s(s(0))))), SCOPE: 14, CLAUSE: 7\n\nT209 is ground\nT211 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
385 [label="385: noattack(T209, T211, s(s(s(s(0))))), SCOPE: 14, CLAUSE: 8\n\nT209 is ground\nT211 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
386 [label="386: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
387 [label="387: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
388 [label="388: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
389 [label="Z: ','(notEq(T242, T243), ','(add(T243, s(s(s(s(0)))), X380), ','(notEq(T242, X380), ','(add(T242, s(s(s(s(0)))), X381), ','(notEq(T243, X381), noattack(T242, T244, s(s(s(s(s(0)))))))))))\n\nT242 is ground\nT243 is ground\nT244 is ground\nX380 is free\nX381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
390 [label="390: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
395 [label="395: notEq(T242, T243)\n\nT242 is ground\nT243 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
396 [label="N22: ','(add(T243, s(s(s(s(0)))), X380), ','(notEq(T242, X380), ','(add(T242, s(s(s(s(0)))), X381), ','(notEq(T243, X381), noattack(T242, T244, s(s(s(s(s(0))))))))))\n\nT242 is ground\nT243 is ground\nT244 is ground\nX380 is free\nX381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
399 [label="J: add(T243, s(s(s(s(0)))), X380)\n\nT243 is ground\nX380 is free", fontsize=16, style=filled, fillcolor=lightyellow];
400 [label="N23: ','(notEq(T242, T249), ','(add(T242, s(s(s(s(0)))), X381), ','(notEq(T243, X381), noattack(T242, T244, s(s(s(s(s(0)))))))))\n\nT242 is ground\nT243 is ground\nT244 is ground\nT249 is ground\nX381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
409 [label="409: add(T243, s(s(s(s(0)))), X380), SCOPE: 15, CLAUSE: 9 | add(T243, s(s(s(s(0)))), X380), SCOPE: 15, CLAUSE: 10\n\nT243 is ground\nX380 is free", fontsize=16, style=filled, fillcolor=lightyellow];
410 [label="410: add(T243, s(s(s(s(0)))), X380), SCOPE: 15, CLAUSE: 9\n\nT243 is ground\nX380 is free", fontsize=16, style=filled, fillcolor=lightyellow];
411 [label="411: add(T243, s(s(s(s(0)))), X380), SCOPE: 15, CLAUSE: 10\n\nT243 is ground\nX380 is free", fontsize=16, style=filled, fillcolor=lightyellow];
413 [label="413: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
415 [label="415: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
416 [label="416: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
417 [label="417: add(T252, s(s(s(s(0)))), X406)\n\nT252 is ground\nX406 is free", fontsize=16, style=filled, fillcolor=lightyellow];
418 [label="418: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
427 [label="427: notEq(T242, T249)\n\nT242 is ground\nT249 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
428 [label="N24: ','(add(T242, s(s(s(s(0)))), X381), ','(notEq(T243, X381), noattack(T242, T244, s(s(s(s(s(0))))))))\n\nT242 is ground\nT243 is ground\nT244 is ground\nX381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
431 [label="431: add(T242, s(s(s(s(0)))), X381)\n\nT242 is ground\nX381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
432 [label="N25: ','(notEq(T243, T257), noattack(T242, T244, s(s(s(s(s(0)))))))\n\nT242 is ground\nT243 is ground\nT244 is ground\nT257 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
435 [label="435: notEq(T243, T257)\n\nT243 is ground\nT257 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
436 [label="N1: noattack(T242, T244, s(s(s(s(s(0))))))\n\nT242 is ground\nT244 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
445 [label="445: noattack(T242, T244, s(s(s(s(s(0)))))), SCOPE: 16, CLAUSE: 7 | noattack(T242, T244, s(s(s(s(s(0)))))), SCOPE: 16, CLAUSE: 8\n\nT242 is ground\nT244 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
448 [label="448: noattack(T242, T244, s(s(s(s(s(0)))))), SCOPE: 16, CLAUSE: 7\n\nT242 is ground\nT244 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
449 [label="449: noattack(T242, T244, s(s(s(s(s(0)))))), SCOPE: 16, CLAUSE: 8\n\nT242 is ground\nT244 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
452 [label="452: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
453 [label="453: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
454 [label="454: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
457 [label="N2: ','(notEq(T275, T276), ','(add(T276, s(s(s(s(s(0))))), X449), ','(notEq(T275, X449), ','(add(T275, s(s(s(s(s(0))))), X450), ','(notEq(T276, X450), noattack(T275, T277, s(s(s(s(s(s(0))))))))))))\n\nT275 is ground\nT276 is ground\nT277 is ground\nX449 is free\nX450 is free", fontsize=16, style=filled, fillcolor=lightyellow];
458 [label="458: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
459 [label="459: notEq(T275, T276)\n\nT275 is ground\nT276 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
461 [label="N26: ','(add(T276, s(s(s(s(s(0))))), X449), ','(notEq(T275, X449), ','(add(T275, s(s(s(s(s(0))))), X450), ','(notEq(T276, X450), noattack(T275, T277, s(s(s(s(s(s(0)))))))))))\n\nT275 is ground\nT276 is ground\nT277 is ground\nX449 is free\nX450 is free", fontsize=16, style=filled, fillcolor=lightyellow];
466 [label="K: add(T276, s(s(s(s(s(0))))), X449)\n\nT276 is ground\nX449 is free", fontsize=16, style=filled, fillcolor=lightyellow];
467 [label="N27: ','(notEq(T275, T282), ','(add(T275, s(s(s(s(s(0))))), X450), ','(notEq(T276, X450), noattack(T275, T277, s(s(s(s(s(s(0))))))))))\n\nT275 is ground\nT276 is ground\nT277 is ground\nT282 is ground\nX450 is free", fontsize=16, style=filled, fillcolor=lightyellow];
471 [label="471: add(T276, s(s(s(s(s(0))))), X449), SCOPE: 17, CLAUSE: 9 | add(T276, s(s(s(s(s(0))))), X449), SCOPE: 17, CLAUSE: 10\n\nT276 is ground\nX449 is free", fontsize=16, style=filled, fillcolor=lightyellow];
474 [label="474: add(T276, s(s(s(s(s(0))))), X449), SCOPE: 17, CLAUSE: 9\n\nT276 is ground\nX449 is free", fontsize=16, style=filled, fillcolor=lightyellow];
475 [label="475: add(T276, s(s(s(s(s(0))))), X449), SCOPE: 17, CLAUSE: 10\n\nT276 is ground\nX449 is free", fontsize=16, style=filled, fillcolor=lightyellow];
477 [label="477: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
479 [label="479: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
480 [label="480: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
481 [label="481: add(T285, s(s(s(s(s(0))))), X475)\n\nT285 is ground\nX475 is free", fontsize=16, style=filled, fillcolor=lightyellow];
482 [label="482: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
489 [label="489: notEq(T275, T282)\n\nT275 is ground\nT282 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
490 [label="N28: ','(add(T275, s(s(s(s(s(0))))), X450), ','(notEq(T276, X450), noattack(T275, T277, s(s(s(s(s(s(0)))))))))\n\nT275 is ground\nT276 is ground\nT277 is ground\nX450 is free", fontsize=16, style=filled, fillcolor=lightyellow];
497 [label="497: add(T275, s(s(s(s(s(0))))), X450)\n\nT275 is ground\nX450 is free", fontsize=16, style=filled, fillcolor=lightyellow];
498 [label="N29: ','(notEq(T276, T290), noattack(T275, T277, s(s(s(s(s(s(0))))))))\n\nT275 is ground\nT276 is ground\nT277 is ground\nT290 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
501 [label="501: notEq(T276, T290)\n\nT276 is ground\nT290 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
502 [label="N3: noattack(T275, T277, s(s(s(s(s(s(0)))))))\n\nT275 is ground\nT277 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
505 [label="505: noattack(T275, T277, s(s(s(s(s(s(0))))))), SCOPE: 18, CLAUSE: 7 | noattack(T275, T277, s(s(s(s(s(s(0))))))), SCOPE: 18, CLAUSE: 8\n\nT275 is ground\nT277 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
509 [label="509: noattack(T275, T277, s(s(s(s(s(s(0))))))), SCOPE: 18, CLAUSE: 7\n\nT275 is ground\nT277 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
510 [label="510: noattack(T275, T277, s(s(s(s(s(s(0))))))), SCOPE: 18, CLAUSE: 8\n\nT275 is ground\nT277 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
514 [label="514: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
515 [label="515: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
516 [label="516: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
527 [label="N4: ','(notEq(T308, T309), ','(add(T309, s(s(s(s(s(s(0)))))), X518), ','(notEq(T308, X518), ','(add(T308, s(s(s(s(s(s(0)))))), X519), ','(notEq(T309, X519), noattack(T308, T310, s(s(s(s(s(s(s(0)))))))))))))\n\nT308 is ground\nT309 is ground\nT310 is ground\nX518 is free\nX519 is free", fontsize=16, style=filled, fillcolor=lightyellow];
528 [label="528: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
533 [label="533: notEq(T308, T309)\n\nT308 is ground\nT309 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
534 [label="N30: ','(add(T309, s(s(s(s(s(s(0)))))), X518), ','(notEq(T308, X518), ','(add(T308, s(s(s(s(s(s(0)))))), X519), ','(notEq(T309, X519), noattack(T308, T310, s(s(s(s(s(s(s(0))))))))))))\n\nT308 is ground\nT309 is ground\nT310 is ground\nX518 is free\nX519 is free", fontsize=16, style=filled, fillcolor=lightyellow];
537 [label="L: add(T309, s(s(s(s(s(s(0)))))), X518)\n\nT309 is ground\nX518 is free", fontsize=16, style=filled, fillcolor=lightyellow];
538 [label="N31: ','(notEq(T308, T315), ','(add(T308, s(s(s(s(s(s(0)))))), X519), ','(notEq(T309, X519), noattack(T308, T310, s(s(s(s(s(s(s(0)))))))))))\n\nT308 is ground\nT309 is ground\nT310 is ground\nT315 is ground\nX519 is free", fontsize=16, style=filled, fillcolor=lightyellow];
541 [label="541: add(T309, s(s(s(s(s(s(0)))))), X518), SCOPE: 19, CLAUSE: 9 | add(T309, s(s(s(s(s(s(0)))))), X518), SCOPE: 19, CLAUSE: 10\n\nT309 is ground\nX518 is free", fontsize=16, style=filled, fillcolor=lightyellow];
542 [label="542: add(T309, s(s(s(s(s(s(0)))))), X518), SCOPE: 19, CLAUSE: 9\n\nT309 is ground\nX518 is free", fontsize=16, style=filled, fillcolor=lightyellow];
543 [label="543: add(T309, s(s(s(s(s(s(0)))))), X518), SCOPE: 19, CLAUSE: 10\n\nT309 is ground\nX518 is free", fontsize=16, style=filled, fillcolor=lightyellow];
544 [label="544: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
545 [label="545: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
546 [label="546: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
552 [label="552: add(T318, s(s(s(s(s(s(0)))))), X544)\n\nT318 is ground\nX544 is free", fontsize=16, style=filled, fillcolor=lightyellow];
553 [label="553: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
561 [label="561: notEq(T308, T315)\n\nT308 is ground\nT315 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
562 [label="N32: ','(add(T308, s(s(s(s(s(s(0)))))), X519), ','(notEq(T309, X519), noattack(T308, T310, s(s(s(s(s(s(s(0))))))))))\n\nT308 is ground\nT309 is ground\nT310 is ground\nX519 is free", fontsize=16, style=filled, fillcolor=lightyellow];
565 [label="565: add(T308, s(s(s(s(s(s(0)))))), X519)\n\nT308 is ground\nX519 is free", fontsize=16, style=filled, fillcolor=lightyellow];
566 [label="N33: ','(notEq(T309, T323), noattack(T308, T310, s(s(s(s(s(s(s(0)))))))))\n\nT308 is ground\nT309 is ground\nT310 is ground\nT323 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
569 [label="569: notEq(T309, T323)\n\nT309 is ground\nT323 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
570 [label="N5: noattack(T308, T310, s(s(s(s(s(s(s(0))))))))\n\nT308 is ground\nT310 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
579 [label="579: noattack(T308, T310, s(s(s(s(s(s(s(0)))))))), SCOPE: 20, CLAUSE: 7 | noattack(T308, T310, s(s(s(s(s(s(s(0)))))))), SCOPE: 20, CLAUSE: 8\n\nT308 is ground\nT310 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
581 [label="581: noattack(T308, T310, s(s(s(s(s(s(s(0)))))))), SCOPE: 20, CLAUSE: 7\n\nT308 is ground\nT310 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
582 [label="582: noattack(T308, T310, s(s(s(s(s(s(s(0)))))))), SCOPE: 20, CLAUSE: 8\n\nT308 is ground\nT310 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
585 [label="585: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
586 [label="586: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
587 [label="587: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
593 [label="593: ','(notEq(T341, T342), ','(add(T342, s(s(s(s(s(s(s(0))))))), X587), ','(notEq(T341, X587), ','(add(T341, s(s(s(s(s(s(s(0))))))), X588), ','(notEq(T342, X588), noattack(T341, T343, s(s(s(s(s(s(s(s(0))))))))))))))\n\nT341 is ground\nT342 is ground\nT343 is ground\nX587 is free\nX588 is free", fontsize=16, style=filled, fillcolor=lightyellow];
594 [label="594: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
599 [label="N6: ','(notEq(T341, T342), ','(add(T342, s(s(s(s(s(s(s(0))))))), X587), ','(notEq(T341, X587), ','(add(T341, s(s(s(s(s(s(s(0))))))), X588), ','(notEq(T342, X588), noattack(T341, T343, s(T346)))))))\n\nT341 is ground\nT342 is ground\nT343 is ground\nT346 is ground\nX587 is free\nX588 is free", fontsize=16, style=filled, fillcolor=lightyellow];
604 [label="604: notEq(T341, T342)\n\nT341 is ground\nT342 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
605 [label="N34: ','(add(T342, s(s(s(s(s(s(s(0))))))), X587), ','(notEq(T341, X587), ','(add(T341, s(s(s(s(s(s(s(0))))))), X588), ','(notEq(T342, X588), noattack(T341, T343, s(T346))))))\n\nT341 is ground\nT342 is ground\nT343 is ground\nT346 is ground\nX587 is free\nX588 is free", fontsize=16, style=filled, fillcolor=lightyellow];
611 [label="M: add(T342, s(s(s(s(s(s(s(0))))))), X587)\n\nT342 is ground\nX587 is free", fontsize=16, style=filled, fillcolor=lightyellow];
612 [label="N35: ','(notEq(T341, T351), ','(add(T341, s(s(s(s(s(s(s(0))))))), X588), ','(notEq(T342, X588), noattack(T341, T343, s(T346)))))\n\nT341 is ground\nT342 is ground\nT343 is ground\nT346 is ground\nT351 is ground\nX588 is free", fontsize=16, style=filled, fillcolor=lightyellow];
615 [label="615: add(T342, s(s(s(s(s(s(s(0))))))), X587), SCOPE: 21, CLAUSE: 9 | add(T342, s(s(s(s(s(s(s(0))))))), X587), SCOPE: 21, CLAUSE: 10\n\nT342 is ground\nX587 is free", fontsize=16, style=filled, fillcolor=lightyellow];
619 [label="619: add(T342, s(s(s(s(s(s(s(0))))))), X587), SCOPE: 21, CLAUSE: 9\n\nT342 is ground\nX587 is free", fontsize=16, style=filled, fillcolor=lightyellow];
620 [label="620: add(T342, s(s(s(s(s(s(s(0))))))), X587), SCOPE: 21, CLAUSE: 10\n\nT342 is ground\nX587 is free", fontsize=16, style=filled, fillcolor=lightyellow];
621 [label="621: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
622 [label="622: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
623 [label="623: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
627 [label="627: add(T354, s(s(s(s(s(s(s(0))))))), X615)\n\nT354 is ground\nX615 is free", fontsize=16, style=filled, fillcolor=lightyellow];
628 [label="628: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
637 [label="637: notEq(T341, T351)\n\nT341 is ground\nT351 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
638 [label="N36: ','(add(T341, s(s(s(s(s(s(s(0))))))), X588), ','(notEq(T342, X588), noattack(T341, T343, s(T346))))\n\nT341 is ground\nT342 is ground\nT343 is ground\nT346 is ground\nX588 is free", fontsize=16, style=filled, fillcolor=lightyellow];
641 [label="641: add(T341, s(s(s(s(s(s(s(0))))))), X588)\n\nT341 is ground\nX588 is free", fontsize=16, style=filled, fillcolor=lightyellow];
642 [label="N37: ','(notEq(T342, T359), noattack(T341, T343, s(T346)))\n\nT341 is ground\nT342 is ground\nT343 is ground\nT346 is ground\nT359 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
647 [label="647: notEq(T342, T359)\n\nT342 is ground\nT359 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
648 [label="N7: noattack(T341, T343, s(T346))\n\nT341 is ground\nT343 is ground\nT346 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
659 [label="659: noattack(T341, T343, s(T346)), SCOPE: 22, CLAUSE: 7 | noattack(T341, T343, s(T346)), SCOPE: 22, CLAUSE: 8\n\nT341 is ground\nT343 is ground\nT346 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
660 [label="660: noattack(T341, T343, s(T346)), SCOPE: 22, CLAUSE: 7\n\nT341 is ground\nT343 is ground\nT346 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
661 [label="661: noattack(T341, T343, s(T346)), SCOPE: 22, CLAUSE: 8\n\nT341 is ground\nT343 is ground\nT346 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
662 [label="662: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
663 [label="663: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
664 [label="664: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
667 [label="N8: ','(notEq(T386, T387), ','(add(T387, s(T389), X658), ','(notEq(T386, X658), ','(add(T386, s(T389), X659), ','(notEq(T387, X659), noattack(T386, T388, s(s(T389))))))))\n\nT386 is ground\nT387 is ground\nT388 is ground\nT389 is ground\nX658 is free\nX659 is free", fontsize=16, style=filled, fillcolor=lightyellow];
668 [label="668: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
671 [label="671: notEq(T386, T387)\n\nT386 is ground\nT387 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
672 [label="N38: ','(add(T387, s(T389), X658), ','(notEq(T386, X658), ','(add(T386, s(T389), X659), ','(notEq(T387, X659), noattack(T386, T388, s(s(T389)))))))\n\nT386 is ground\nT387 is ground\nT388 is ground\nT389 is ground\nX658 is free\nX659 is free", fontsize=16, style=filled, fillcolor=lightyellow];
676 [label="N: add(T387, s(T389), X658)\n\nT387 is ground\nT389 is ground\nX658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
677 [label="N39: ','(notEq(T386, T396), ','(add(T386, s(T389), X659), ','(notEq(T387, X659), noattack(T386, T388, s(s(T389))))))\n\nT386 is ground\nT387 is ground\nT388 is ground\nT389 is ground\nT396 is ground\nX659 is free", fontsize=16, style=filled, fillcolor=lightyellow];
685 [label="685: add(T387, s(T389), X658), SCOPE: 23, CLAUSE: 9 | add(T387, s(T389), X658), SCOPE: 23, CLAUSE: 10\n\nT387 is ground\nT389 is ground\nX658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
686 [label="686: add(T387, s(T389), X658), SCOPE: 23, CLAUSE: 9\n\nT387 is ground\nT389 is ground\nX658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
687 [label="687: add(T387, s(T389), X658), SCOPE: 23, CLAUSE: 10\n\nT387 is ground\nT389 is ground\nX658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
688 [label="688: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
689 [label="689: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
690 [label="690: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
694 [label="694: add(T408, s(T409), X684)\n\nT408 is ground\nT409 is ground\nX684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
695 [label="695: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
703 [label="703: notEq(T386, T396)\n\nT386 is ground\nT396 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
704 [label="N40: ','(add(T386, s(T389), X659), ','(notEq(T387, X659), noattack(T386, T388, s(s(T389)))))\n\nT386 is ground\nT387 is ground\nT388 is ground\nT389 is ground\nX659 is free", fontsize=16, style=filled, fillcolor=lightyellow];
708 [label="708: add(T386, s(T389), X659)\n\nT386 is ground\nT389 is ground\nX659 is free", fontsize=16, style=filled, fillcolor=lightyellow];
709 [label="709: ','(notEq(T387, T418), noattack(T386, T388, s(s(T389))))\n\nT386 is ground\nT387 is ground\nT388 is ground\nT389 is ground\nT418 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
719 [label="719: safe(T109), SCOPE: 24, CLAUSE: 5 | safe(T109), SCOPE: 24, CLAUSE: 6\n\nT109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
720 [label="720: safe(T109), SCOPE: 24, CLAUSE: 5\n\nT109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
721 [label="721: safe(T109), SCOPE: 24, CLAUSE: 6\n\nT109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
722 [label="722: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
723 [label="723: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
724 [label="724: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
725 [label="725: ','(noattack(T427, T428, s(0)), safe(T428))\n\nT427 is ground\nT428 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
726 [label="726: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
727 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2 -> 727 [arrowhead = none ];
727 -> 5;

728 [label="ONLY EVAL with clause\nqueens(X2) :- ','(perm(.(s(0), .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), [])))))))), X2), safe(X2)).\nand substitutionT1 -> T4,\nX2 -> T4,\nT3 -> T4", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 728 [arrowhead = none ];
728 -> 7;

729 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
7 -> 729 [arrowhead = none ];
729 -> 9;

730 [label="BACKTRACK\nfor clause: perm([], [])because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 730 [arrowhead = none ];
730 -> 11;

731 [label="EVAL with clause\nperm(.(X12, X13), .(X14, X15)) :- ','(delete(X14, .(X12, X13), X16), perm(X16, X15)).\nand substitutionX12 -> s(0),\nX13 -> .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))),\nX14 -> T11,\nX15 -> T12,\nT4 -> .(T11, T12),\nT9 -> T11,\nT10 -> T12", fontsize=14, style = filled, fillcolor = lightblue];
11 -> 731 [arrowhead = none ];
731 -> 23;

732 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 732 [arrowhead = none ];
732 -> 25;

733 [label="GENERALIZATION\nT15 <-- .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), [])))))))\n\nNew Knowledge:\nT15 is ground", fontsize=14, style = filled, fillcolor = violet];
23 -> 733 [arrowhead = none ];
733 -> 33;

734 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
33 -> 734 [arrowhead = none ];
734 -> 35;

735 [label="SPLIT 2\nnew knowledge:\nT22 is ground\nT15 is ground\nT20 is ground\nreplacements:X16 -> T20,\nT12 -> T21,\nT11 -> T22", fontsize=14, style = filled, fillcolor = violet];
33 -> 735 [arrowhead = none ];
735 -> 36;

736 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
35 -> 736 [arrowhead = none ];
736 -> 39;

737 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
36 -> 737 [arrowhead = none ];
737 -> 79;

738 [label="SPLIT 2\nnew knowledge:\nT20 is ground\nT77 is ground\nreplacements:T21 -> T77", fontsize=14, style = filled, fillcolor = violet];
36 -> 738 [arrowhead = none ];
738 -> 82;

739 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
39 -> 739 [arrowhead = none ];
739 -> 41;

740 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
39 -> 740 [arrowhead = none ];
740 -> 42;

741 [label="EVAL with clause\ndelete(X37, .(X37, X38), X38).\nand substitutionT11 -> s(0),\nX37 -> s(0),\nT35 -> s(0),\nT15 -> T36,\nX38 -> T36,\nX16 -> T36", fontsize=14, style = filled, fillcolor = lightblue];
41 -> 741 [arrowhead = none ];
741 -> 46;

742 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 742 [arrowhead = none ];
742 -> 47;

743 [label="ONLY EVAL with clause\ndelete(X53, .(X54, X55), .(X54, X56)) :- delete(X53, X55, X56).\nand substitutionT11 -> T48,\nX53 -> T48,\nX54 -> s(0),\nT15 -> T47,\nX55 -> T47,\nX56 -> X57,\nX16 -> .(s(0), X57),\nT46 -> T48", fontsize=14, style = filled, fillcolor = lightblue];
42 -> 743 [arrowhead = none ];
743 -> 55;

744 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
46 -> 744 [arrowhead = none ];
744 -> 48;

745 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
55 -> 745 [arrowhead = none ];
745 -> 59;

746 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
59 -> 746 [arrowhead = none ];
746 -> 60;

747 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
59 -> 747 [arrowhead = none ];
747 -> 61;

748 [label="EVAL with clause\ndelete(X70, .(X70, X71), X71).\nand substitutionT48 -> T61,\nX70 -> T61,\nX71 -> T62,\nT47 -> .(T61, T62),\nX57 -> T62", fontsize=14, style = filled, fillcolor = lightblue];
60 -> 748 [arrowhead = none ];
748 -> 63;

749 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
60 -> 749 [arrowhead = none ];
749 -> 64;

750 [label="EVAL with clause\ndelete(X82, .(X83, X84), .(X83, X85)) :- delete(X82, X84, X85).\nand substitutionT48 -> T72,\nX82 -> T72,\nX83 -> T70,\nX84 -> T71,\nT47 -> .(T70, T71),\nX85 -> X86,\nX57 -> .(T70, X86),\nT69 -> T72", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 750 [arrowhead = none ];
750 -> 69;

751 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
61 -> 751 [arrowhead = none ];
751 -> 70;

752 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
63 -> 752 [arrowhead = none ];
752 -> 65;

753 [label="INSTANCE with matching:\nT48 -> T72\nT47 -> T71\nX57 -> X86", fontsize=14, style = filled, fillcolor = lightgrey];
69 -> 753 [arrowhead = none , style=dashed];
753 -> 55[style=dashed];

754 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
79 -> 754 [arrowhead = none ];
754 -> 86;

755 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
82 -> 755 [arrowhead = none ];
755 -> 120;

756 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
86 -> 756 [arrowhead = none ];
756 -> 87;

757 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
86 -> 757 [arrowhead = none ];
757 -> 88;

758 [label="EVAL with clause\nperm([], []).\nand substitutionT20 -> [],\nT21 -> []", fontsize=14, style = filled, fillcolor = lightblue];
87 -> 758 [arrowhead = none ];
758 -> 89;

759 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
87 -> 759 [arrowhead = none ];
759 -> 90;

760 [label="EVAL with clause\nperm(.(X100, X101), .(X102, X103)) :- ','(delete(X102, .(X100, X101), X104), perm(X104, X103)).\nand substitutionX100 -> T86,\nX101 -> T87,\nT20 -> .(T86, T87),\nX102 -> T90,\nX103 -> T91,\nT21 -> .(T90, T91),\nT88 -> T90,\nT89 -> T91", fontsize=14, style = filled, fillcolor = lightblue];
88 -> 760 [arrowhead = none ];
760 -> 101;

761 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
88 -> 761 [arrowhead = none ];
761 -> 102;

762 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
89 -> 762 [arrowhead = none ];
762 -> 91;

763 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
101 -> 763 [arrowhead = none ];
763 -> 108;

764 [label="SPLIT 2\nnew knowledge:\nT90 is ground\nT86 is ground\nT87 is ground\nT96 is ground\nreplacements:X104 -> T96,\nT91 -> T97", fontsize=14, style = filled, fillcolor = violet];
101 -> 764 [arrowhead = none ];
764 -> 109;

765 [label="INSTANCE with matching:\nT48 -> T90\nT47 -> .(T86, T87)\nX57 -> X104", fontsize=14, style = filled, fillcolor = lightgrey];
108 -> 765 [arrowhead = none , style=dashed];
765 -> 55[style=dashed];

766 [label="INSTANCE with matching:\nT20 -> T96\nT21 -> T97", fontsize=14, style = filled, fillcolor = lightgrey];
109 -> 766 [arrowhead = none , style=dashed];
766 -> 79[style=dashed];

767 [label="BACKTRACK\nfor clause: safe([])because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
120 -> 767 [arrowhead = none ];
767 -> 121;

768 [label="ONLY EVAL with clause\nsafe(.(X121, X122)) :- ','(noattack(X121, X122, s(0)), safe(X122)).\nand substitutionT22 -> T108,\nX121 -> T108,\nT77 -> T109,\nX122 -> T109", fontsize=14, style = filled, fillcolor = lightblue];
121 -> 768 [arrowhead = none ];
768 -> 128;

769 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
128 -> 769 [arrowhead = none ];
769 -> 134;

770 [label="SPLIT 2\nnew knowledge:\nT108 is ground\nT109 is ground", fontsize=14, style = filled, fillcolor = violet];
128 -> 770 [arrowhead = none ];
770 -> 135;

771 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
134 -> 771 [arrowhead = none ];
771 -> 138;

772 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
135 -> 772 [arrowhead = none ];
772 -> 719;

773 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
138 -> 773 [arrowhead = none ];
773 -> 140;

774 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
138 -> 774 [arrowhead = none ];
774 -> 141;

775 [label="EVAL with clause\nnoattack(X139, [], X140).\nand substitutionT108 -> T118,\nX139 -> T118,\nT109 -> [],\nX140 -> s(0)", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 775 [arrowhead = none ];
775 -> 144;

776 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
140 -> 776 [arrowhead = none ];
776 -> 145;

777 [label="EVAL with clause\nnoattack(X151, .(X152, X153), X154) :- ','(notEq(X151, X152), ','(add(X152, X154, X155), ','(notEq(X151, X155), ','(add(X151, X154, X156), ','(notEq(X152, X156), noattack(X151, X153, s(X154))))))).\nand substitutionT108 -> T125,\nX151 -> T125,\nX152 -> T126,\nX153 -> T127,\nT109 -> .(T126, T127),\nX154 -> s(0)", fontsize=14, style = filled, fillcolor = lightblue];
141 -> 777 [arrowhead = none ];
777 -> 152;

778 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
141 -> 778 [arrowhead = none ];
778 -> 153;

779 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
144 -> 779 [arrowhead = none ];
779 -> 146;

780 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
152 -> 780 [arrowhead = none ];
780 -> 161;

781 [label="SPLIT 2\nnew knowledge:\nT125 is ground\nT126 is ground", fontsize=14, style = filled, fillcolor = violet];
152 -> 781 [arrowhead = none ];
781 -> 162;

782 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
161 -> 782 [arrowhead = none ];
782 -> 168;

783 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
162 -> 783 [arrowhead = none ];
783 -> 201;

784 [label="SPLIT 2\nnew knowledge:\nT126 is ground\nT150 is ground\nreplacements:X155 -> T150", fontsize=14, style = filled, fillcolor = violet];
162 -> 784 [arrowhead = none ];
784 -> 202;

785 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
168 -> 785 [arrowhead = none ];
785 -> 171;

786 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
168 -> 786 [arrowhead = none ];
786 -> 173;

787 [label="EVAL with clause\nnotEq(0, s(X165)).\nand substitutionT125 -> 0,\nX165 -> T136,\nT126 -> s(T136)", fontsize=14, style = filled, fillcolor = lightblue];
171 -> 787 [arrowhead = none ];
787 -> 177;

788 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
171 -> 788 [arrowhead = none ];
788 -> 178;

789 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
173 -> 789 [arrowhead = none ];
789 -> 181;

790 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
173 -> 790 [arrowhead = none ];
790 -> 183;

791 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
177 -> 791 [arrowhead = none ];
791 -> 179;

792 [label="EVAL with clause\nnotEq(s(X170), 0).\nand substitutionX170 -> T141,\nT125 -> s(T141),\nT126 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
181 -> 792 [arrowhead = none ];
792 -> 187;

793 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
181 -> 793 [arrowhead = none ];
793 -> 188;

794 [label="EVAL with clause\nnotEq(s(X175), s(X176)) :- notEq(X175, X176).\nand substitutionX175 -> T146,\nT125 -> s(T146),\nX176 -> T147,\nT126 -> s(T147)", fontsize=14, style = filled, fillcolor = lightblue];
183 -> 794 [arrowhead = none ];
794 -> 192;

795 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
183 -> 795 [arrowhead = none ];
795 -> 193;

796 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
187 -> 796 [arrowhead = none ];
796 -> 189;

797 [label="INSTANCE with matching:\nT125 -> T146\nT126 -> T147", fontsize=14, style = filled, fillcolor = lightgrey];
192 -> 797 [arrowhead = none , style=dashed];
797 -> 161[style=dashed];

798 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
201 -> 798 [arrowhead = none ];
798 -> 205;

799 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
202 -> 799 [arrowhead = none ];
799 -> 224;

800 [label="SPLIT 2\nnew knowledge:\nT125 is ground\nT150 is ground", fontsize=14, style = filled, fillcolor = violet];
202 -> 800 [arrowhead = none ];
800 -> 226;

801 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
205 -> 801 [arrowhead = none ];
801 -> 207;

802 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
205 -> 802 [arrowhead = none ];
802 -> 208;

803 [label="EVAL with clause\nadd(0, X187, X187).\nand substitutionT126 -> 0,\nX187 -> s(0),\nX155 -> s(0)", fontsize=14, style = filled, fillcolor = lightblue];
207 -> 803 [arrowhead = none ];
803 -> 211;

804 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
207 -> 804 [arrowhead = none ];
804 -> 212;

805 [label="EVAL with clause\nadd(s(X196), X197, s(X198)) :- add(X196, X197, X198).\nand substitutionX196 -> T153,\nT126 -> s(T153),\nX197 -> s(0),\nX198 -> X199,\nX155 -> s(X199)", fontsize=14, style = filled, fillcolor = lightblue];
208 -> 805 [arrowhead = none ];
805 -> 217;

806 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
208 -> 806 [arrowhead = none ];
806 -> 218;

807 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
211 -> 807 [arrowhead = none ];
807 -> 213;

808 [label="INSTANCE with matching:\nT126 -> T153\nX155 -> X199", fontsize=14, style = filled, fillcolor = lightgrey];
217 -> 808 [arrowhead = none , style=dashed];
808 -> 201[style=dashed];

809 [label="INSTANCE with matching:\nT126 -> T150", fontsize=14, style = filled, fillcolor = lightgrey];
224 -> 809 [arrowhead = none , style=dashed];
809 -> 161[style=dashed];

810 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
226 -> 810 [arrowhead = none ];
810 -> 237;

811 [label="SPLIT 2\nnew knowledge:\nT125 is ground\nT158 is ground\nreplacements:X156 -> T158", fontsize=14, style = filled, fillcolor = violet];
226 -> 811 [arrowhead = none ];
811 -> 238;

812 [label="INSTANCE with matching:\nT126 -> T125\nX155 -> X156", fontsize=14, style = filled, fillcolor = lightgrey];
237 -> 812 [arrowhead = none , style=dashed];
812 -> 201[style=dashed];

813 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
238 -> 813 [arrowhead = none ];
813 -> 241;

814 [label="SPLIT 2\nnew knowledge:\nT126 is ground\nT158 is ground", fontsize=14, style = filled, fillcolor = violet];
238 -> 814 [arrowhead = none ];
814 -> 242;

815 [label="INSTANCE with matching:\nT125 -> T126\nT126 -> T158", fontsize=14, style = filled, fillcolor = lightgrey];
241 -> 815 [arrowhead = none , style=dashed];
815 -> 161[style=dashed];

816 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
242 -> 816 [arrowhead = none ];
816 -> 244;

817 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
244 -> 817 [arrowhead = none ];
817 -> 247;

818 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
244 -> 818 [arrowhead = none ];
818 -> 248;

819 [label="EVAL with clause\nnoattack(X226, [], X227).\nand substitutionT125 -> T169,\nX226 -> T169,\nT127 -> [],\nX227 -> s(s(0))", fontsize=14, style = filled, fillcolor = lightblue];
247 -> 819 [arrowhead = none ];
819 -> 252;

820 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
247 -> 820 [arrowhead = none ];
820 -> 253;

821 [label="EVAL with clause\nnoattack(X238, .(X239, X240), X241) :- ','(notEq(X238, X239), ','(add(X239, X241, X242), ','(notEq(X238, X242), ','(add(X238, X241, X243), ','(notEq(X239, X243), noattack(X238, X240, s(X241))))))).\nand substitutionT125 -> T176,\nX238 -> T176,\nX239 -> T177,\nX240 -> T178,\nT127 -> .(T177, T178),\nX241 -> s(s(0))", fontsize=14, style = filled, fillcolor = lightblue];
248 -> 821 [arrowhead = none ];
821 -> 259;

822 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
248 -> 822 [arrowhead = none ];
822 -> 260;

823 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
252 -> 823 [arrowhead = none ];
823 -> 255;

824 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
259 -> 824 [arrowhead = none ];
824 -> 263;

825 [label="SPLIT 2\nnew knowledge:\nT176 is ground\nT177 is ground", fontsize=14, style = filled, fillcolor = violet];
259 -> 825 [arrowhead = none ];
825 -> 264;

826 [label="INSTANCE with matching:\nT125 -> T176\nT126 -> T177", fontsize=14, style = filled, fillcolor = lightgrey];
263 -> 826 [arrowhead = none , style=dashed];
826 -> 161[style=dashed];

827 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
264 -> 827 [arrowhead = none ];
827 -> 267;

828 [label="SPLIT 2\nnew knowledge:\nT177 is ground\nT183 is ground\nreplacements:X242 -> T183", fontsize=14, style = filled, fillcolor = violet];
264 -> 828 [arrowhead = none ];
828 -> 268;

829 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
267 -> 829 [arrowhead = none ];
829 -> 272;

830 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
268 -> 830 [arrowhead = none ];
830 -> 295;

831 [label="SPLIT 2\nnew knowledge:\nT176 is ground\nT183 is ground", fontsize=14, style = filled, fillcolor = violet];
268 -> 831 [arrowhead = none ];
831 -> 296;

832 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
272 -> 832 [arrowhead = none ];
832 -> 275;

833 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
272 -> 833 [arrowhead = none ];
833 -> 276;

834 [label="EVAL with clause\nadd(0, X256, X256).\nand substitutionT177 -> 0,\nX256 -> s(s(0)),\nX242 -> s(s(0))", fontsize=14, style = filled, fillcolor = lightblue];
275 -> 834 [arrowhead = none ];
834 -> 280;

835 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
275 -> 835 [arrowhead = none ];
835 -> 281;

836 [label="EVAL with clause\nadd(s(X265), X266, s(X267)) :- add(X265, X266, X267).\nand substitutionX265 -> T186,\nT177 -> s(T186),\nX266 -> s(s(0)),\nX267 -> X268,\nX242 -> s(X268)", fontsize=14, style = filled, fillcolor = lightblue];
276 -> 836 [arrowhead = none ];
836 -> 287;

837 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
276 -> 837 [arrowhead = none ];
837 -> 288;

838 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
280 -> 838 [arrowhead = none ];
838 -> 282;

839 [label="INSTANCE with matching:\nT177 -> T186\nX242 -> X268", fontsize=14, style = filled, fillcolor = lightgrey];
287 -> 839 [arrowhead = none , style=dashed];
839 -> 267[style=dashed];

840 [label="INSTANCE with matching:\nT125 -> T176\nT126 -> T183", fontsize=14, style = filled, fillcolor = lightgrey];
295 -> 840 [arrowhead = none , style=dashed];
840 -> 161[style=dashed];

841 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
296 -> 841 [arrowhead = none ];
841 -> 299;

842 [label="SPLIT 2\nnew knowledge:\nT176 is ground\nT191 is ground\nreplacements:X243 -> T191", fontsize=14, style = filled, fillcolor = violet];
296 -> 842 [arrowhead = none ];
842 -> 300;

843 [label="INSTANCE with matching:\nT177 -> T176\nX242 -> X243", fontsize=14, style = filled, fillcolor = lightgrey];
299 -> 843 [arrowhead = none , style=dashed];
843 -> 267[style=dashed];

844 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
300 -> 844 [arrowhead = none ];
844 -> 303;

845 [label="SPLIT 2\nnew knowledge:\nT177 is ground\nT191 is ground", fontsize=14, style = filled, fillcolor = violet];
300 -> 845 [arrowhead = none ];
845 -> 304;

846 [label="INSTANCE with matching:\nT125 -> T177\nT126 -> T191", fontsize=14, style = filled, fillcolor = lightgrey];
303 -> 846 [arrowhead = none , style=dashed];
846 -> 161[style=dashed];

847 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
304 -> 847 [arrowhead = none ];
847 -> 314;

848 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
314 -> 848 [arrowhead = none ];
848 -> 316;

849 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
314 -> 849 [arrowhead = none ];
849 -> 317;

850 [label="EVAL with clause\nnoattack(X295, [], X296).\nand substitutionT176 -> T202,\nX295 -> T202,\nT178 -> [],\nX296 -> s(s(s(0)))", fontsize=14, style = filled, fillcolor = lightblue];
316 -> 850 [arrowhead = none ];
850 -> 320;

851 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
316 -> 851 [arrowhead = none ];
851 -> 321;

852 [label="EVAL with clause\nnoattack(X307, .(X308, X309), X310) :- ','(notEq(X307, X308), ','(add(X308, X310, X311), ','(notEq(X307, X311), ','(add(X307, X310, X312), ','(notEq(X308, X312), noattack(X307, X309, s(X310))))))).\nand substitutionT176 -> T209,\nX307 -> T209,\nX308 -> T210,\nX309 -> T211,\nT178 -> .(T210, T211),\nX310 -> s(s(s(0)))", fontsize=14, style = filled, fillcolor = lightblue];
317 -> 852 [arrowhead = none ];
852 -> 323;

853 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
317 -> 853 [arrowhead = none ];
853 -> 324;

854 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
320 -> 854 [arrowhead = none ];
854 -> 322;

855 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
323 -> 855 [arrowhead = none ];
855 -> 329;

856 [label="SPLIT 2\nnew knowledge:\nT209 is ground\nT210 is ground", fontsize=14, style = filled, fillcolor = violet];
323 -> 856 [arrowhead = none ];
856 -> 330;

857 [label="INSTANCE with matching:\nT125 -> T209\nT126 -> T210", fontsize=14, style = filled, fillcolor = lightgrey];
329 -> 857 [arrowhead = none , style=dashed];
857 -> 161[style=dashed];

858 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
330 -> 858 [arrowhead = none ];
858 -> 335;

859 [label="SPLIT 2\nnew knowledge:\nT210 is ground\nT216 is ground\nreplacements:X311 -> T216", fontsize=14, style = filled, fillcolor = violet];
330 -> 859 [arrowhead = none ];
859 -> 336;

860 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
335 -> 860 [arrowhead = none ];
860 -> 339;

861 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
336 -> 861 [arrowhead = none ];
861 -> 358;

862 [label="SPLIT 2\nnew knowledge:\nT209 is ground\nT216 is ground", fontsize=14, style = filled, fillcolor = violet];
336 -> 862 [arrowhead = none ];
862 -> 359;

863 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
339 -> 863 [arrowhead = none ];
863 -> 340;

864 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
339 -> 864 [arrowhead = none ];
864 -> 341;

865 [label="EVAL with clause\nadd(0, X325, X325).\nand substitutionT210 -> 0,\nX325 -> s(s(s(0))),\nX311 -> s(s(s(0)))", fontsize=14, style = filled, fillcolor = lightblue];
340 -> 865 [arrowhead = none ];
865 -> 342;

866 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
340 -> 866 [arrowhead = none ];
866 -> 343;

867 [label="EVAL with clause\nadd(s(X334), X335, s(X336)) :- add(X334, X335, X336).\nand substitutionX334 -> T219,\nT210 -> s(T219),\nX335 -> s(s(s(0))),\nX336 -> X337,\nX311 -> s(X337)", fontsize=14, style = filled, fillcolor = lightblue];
341 -> 867 [arrowhead = none ];
867 -> 349;

868 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
341 -> 868 [arrowhead = none ];
868 -> 350;

869 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
342 -> 869 [arrowhead = none ];
869 -> 344;

870 [label="INSTANCE with matching:\nT210 -> T219\nX311 -> X337", fontsize=14, style = filled, fillcolor = lightgrey];
349 -> 870 [arrowhead = none , style=dashed];
870 -> 335[style=dashed];

871 [label="INSTANCE with matching:\nT125 -> T209\nT126 -> T216", fontsize=14, style = filled, fillcolor = lightgrey];
358 -> 871 [arrowhead = none , style=dashed];
871 -> 161[style=dashed];

872 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
359 -> 872 [arrowhead = none ];
872 -> 365;

873 [label="SPLIT 2\nnew knowledge:\nT209 is ground\nT224 is ground\nreplacements:X312 -> T224", fontsize=14, style = filled, fillcolor = violet];
359 -> 873 [arrowhead = none ];
873 -> 366;

874 [label="INSTANCE with matching:\nT210 -> T209\nX311 -> X312", fontsize=14, style = filled, fillcolor = lightgrey];
365 -> 874 [arrowhead = none , style=dashed];
874 -> 335[style=dashed];

875 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
366 -> 875 [arrowhead = none ];
875 -> 372;

876 [label="SPLIT 2\nnew knowledge:\nT210 is ground\nT224 is ground", fontsize=14, style = filled, fillcolor = violet];
366 -> 876 [arrowhead = none ];
876 -> 373;

877 [label="INSTANCE with matching:\nT125 -> T210\nT126 -> T224", fontsize=14, style = filled, fillcolor = lightgrey];
372 -> 877 [arrowhead = none , style=dashed];
877 -> 161[style=dashed];

878 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
373 -> 878 [arrowhead = none ];
878 -> 381;

879 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
381 -> 879 [arrowhead = none ];
879 -> 384;

880 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
381 -> 880 [arrowhead = none ];
880 -> 385;

881 [label="EVAL with clause\nnoattack(X364, [], X365).\nand substitutionT209 -> T235,\nX364 -> T235,\nT211 -> [],\nX365 -> s(s(s(s(0))))", fontsize=14, style = filled, fillcolor = lightblue];
384 -> 881 [arrowhead = none ];
881 -> 386;

882 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
384 -> 882 [arrowhead = none ];
882 -> 387;

883 [label="EVAL with clause\nnoattack(X376, .(X377, X378), X379) :- ','(notEq(X376, X377), ','(add(X377, X379, X380), ','(notEq(X376, X380), ','(add(X376, X379, X381), ','(notEq(X377, X381), noattack(X376, X378, s(X379))))))).\nand substitutionT209 -> T242,\nX376 -> T242,\nX377 -> T243,\nX378 -> T244,\nT211 -> .(T243, T244),\nX379 -> s(s(s(s(0))))", fontsize=14, style = filled, fillcolor = lightblue];
385 -> 883 [arrowhead = none ];
883 -> 389;

884 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
385 -> 884 [arrowhead = none ];
884 -> 390;

885 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
386 -> 885 [arrowhead = none ];
885 -> 388;

886 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
389 -> 886 [arrowhead = none ];
886 -> 395;

887 [label="SPLIT 2\nnew knowledge:\nT242 is ground\nT243 is ground", fontsize=14, style = filled, fillcolor = violet];
389 -> 887 [arrowhead = none ];
887 -> 396;

888 [label="INSTANCE with matching:\nT125 -> T242\nT126 -> T243", fontsize=14, style = filled, fillcolor = lightgrey];
395 -> 888 [arrowhead = none , style=dashed];
888 -> 161[style=dashed];

889 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
396 -> 889 [arrowhead = none ];
889 -> 399;

890 [label="SPLIT 2\nnew knowledge:\nT243 is ground\nT249 is ground\nreplacements:X380 -> T249", fontsize=14, style = filled, fillcolor = violet];
396 -> 890 [arrowhead = none ];
890 -> 400;

891 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
399 -> 891 [arrowhead = none ];
891 -> 409;

892 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
400 -> 892 [arrowhead = none ];
892 -> 427;

893 [label="SPLIT 2\nnew knowledge:\nT242 is ground\nT249 is ground", fontsize=14, style = filled, fillcolor = violet];
400 -> 893 [arrowhead = none ];
893 -> 428;

894 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
409 -> 894 [arrowhead = none ];
894 -> 410;

895 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
409 -> 895 [arrowhead = none ];
895 -> 411;

896 [label="EVAL with clause\nadd(0, X394, X394).\nand substitutionT243 -> 0,\nX394 -> s(s(s(s(0)))),\nX380 -> s(s(s(s(0))))", fontsize=14, style = filled, fillcolor = lightblue];
410 -> 896 [arrowhead = none ];
896 -> 413;

897 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
410 -> 897 [arrowhead = none ];
897 -> 415;

898 [label="EVAL with clause\nadd(s(X403), X404, s(X405)) :- add(X403, X404, X405).\nand substitutionX403 -> T252,\nT243 -> s(T252),\nX404 -> s(s(s(s(0)))),\nX405 -> X406,\nX380 -> s(X406)", fontsize=14, style = filled, fillcolor = lightblue];
411 -> 898 [arrowhead = none ];
898 -> 417;

899 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
411 -> 899 [arrowhead = none ];
899 -> 418;

900 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
413 -> 900 [arrowhead = none ];
900 -> 416;

901 [label="INSTANCE with matching:\nT243 -> T252\nX380 -> X406", fontsize=14, style = filled, fillcolor = lightgrey];
417 -> 901 [arrowhead = none , style=dashed];
901 -> 399[style=dashed];

902 [label="INSTANCE with matching:\nT125 -> T242\nT126 -> T249", fontsize=14, style = filled, fillcolor = lightgrey];
427 -> 902 [arrowhead = none , style=dashed];
902 -> 161[style=dashed];

903 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
428 -> 903 [arrowhead = none ];
903 -> 431;

904 [label="SPLIT 2\nnew knowledge:\nT242 is ground\nT257 is ground\nreplacements:X381 -> T257", fontsize=14, style = filled, fillcolor = violet];
428 -> 904 [arrowhead = none ];
904 -> 432;

905 [label="INSTANCE with matching:\nT243 -> T242\nX380 -> X381", fontsize=14, style = filled, fillcolor = lightgrey];
431 -> 905 [arrowhead = none , style=dashed];
905 -> 399[style=dashed];

906 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
432 -> 906 [arrowhead = none ];
906 -> 435;

907 [label="SPLIT 2\nnew knowledge:\nT243 is ground\nT257 is ground", fontsize=14, style = filled, fillcolor = violet];
432 -> 907 [arrowhead = none ];
907 -> 436;

908 [label="INSTANCE with matching:\nT125 -> T243\nT126 -> T257", fontsize=14, style = filled, fillcolor = lightgrey];
435 -> 908 [arrowhead = none , style=dashed];
908 -> 161[style=dashed];

909 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
436 -> 909 [arrowhead = none ];
909 -> 445;

910 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
445 -> 910 [arrowhead = none ];
910 -> 448;

911 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
445 -> 911 [arrowhead = none ];
911 -> 449;

912 [label="EVAL with clause\nnoattack(X433, [], X434).\nand substitutionT242 -> T268,\nX433 -> T268,\nT244 -> [],\nX434 -> s(s(s(s(s(0)))))", fontsize=14, style = filled, fillcolor = lightblue];
448 -> 912 [arrowhead = none ];
912 -> 452;

913 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
448 -> 913 [arrowhead = none ];
913 -> 453;

914 [label="EVAL with clause\nnoattack(X445, .(X446, X447), X448) :- ','(notEq(X445, X446), ','(add(X446, X448, X449), ','(notEq(X445, X449), ','(add(X445, X448, X450), ','(notEq(X446, X450), noattack(X445, X447, s(X448))))))).\nand substitutionT242 -> T275,\nX445 -> T275,\nX446 -> T276,\nX447 -> T277,\nT244 -> .(T276, T277),\nX448 -> s(s(s(s(s(0)))))", fontsize=14, style = filled, fillcolor = lightblue];
449 -> 914 [arrowhead = none ];
914 -> 457;

915 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
449 -> 915 [arrowhead = none ];
915 -> 458;

916 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
452 -> 916 [arrowhead = none ];
916 -> 454;

917 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
457 -> 917 [arrowhead = none ];
917 -> 459;

918 [label="SPLIT 2\nnew knowledge:\nT275 is ground\nT276 is ground", fontsize=14, style = filled, fillcolor = violet];
457 -> 918 [arrowhead = none ];
918 -> 461;

919 [label="INSTANCE with matching:\nT125 -> T275\nT126 -> T276", fontsize=14, style = filled, fillcolor = lightgrey];
459 -> 919 [arrowhead = none , style=dashed];
919 -> 161[style=dashed];

920 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
461 -> 920 [arrowhead = none ];
920 -> 466;

921 [label="SPLIT 2\nnew knowledge:\nT276 is ground\nT282 is ground\nreplacements:X449 -> T282", fontsize=14, style = filled, fillcolor = violet];
461 -> 921 [arrowhead = none ];
921 -> 467;

922 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
466 -> 922 [arrowhead = none ];
922 -> 471;

923 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
467 -> 923 [arrowhead = none ];
923 -> 489;

924 [label="SPLIT 2\nnew knowledge:\nT275 is ground\nT282 is ground", fontsize=14, style = filled, fillcolor = violet];
467 -> 924 [arrowhead = none ];
924 -> 490;

925 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
471 -> 925 [arrowhead = none ];
925 -> 474;

926 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
471 -> 926 [arrowhead = none ];
926 -> 475;

927 [label="EVAL with clause\nadd(0, X463, X463).\nand substitutionT276 -> 0,\nX463 -> s(s(s(s(s(0))))),\nX449 -> s(s(s(s(s(0)))))", fontsize=14, style = filled, fillcolor = lightblue];
474 -> 927 [arrowhead = none ];
927 -> 477;

928 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
474 -> 928 [arrowhead = none ];
928 -> 479;

929 [label="EVAL with clause\nadd(s(X472), X473, s(X474)) :- add(X472, X473, X474).\nand substitutionX472 -> T285,\nT276 -> s(T285),\nX473 -> s(s(s(s(s(0))))),\nX474 -> X475,\nX449 -> s(X475)", fontsize=14, style = filled, fillcolor = lightblue];
475 -> 929 [arrowhead = none ];
929 -> 481;

930 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
475 -> 930 [arrowhead = none ];
930 -> 482;

931 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
477 -> 931 [arrowhead = none ];
931 -> 480;

932 [label="INSTANCE with matching:\nT276 -> T285\nX449 -> X475", fontsize=14, style = filled, fillcolor = lightgrey];
481 -> 932 [arrowhead = none , style=dashed];
932 -> 466[style=dashed];

933 [label="INSTANCE with matching:\nT125 -> T275\nT126 -> T282", fontsize=14, style = filled, fillcolor = lightgrey];
489 -> 933 [arrowhead = none , style=dashed];
933 -> 161[style=dashed];

934 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
490 -> 934 [arrowhead = none ];
934 -> 497;

935 [label="SPLIT 2\nnew knowledge:\nT275 is ground\nT290 is ground\nreplacements:X450 -> T290", fontsize=14, style = filled, fillcolor = violet];
490 -> 935 [arrowhead = none ];
935 -> 498;

936 [label="INSTANCE with matching:\nT276 -> T275\nX449 -> X450", fontsize=14, style = filled, fillcolor = lightgrey];
497 -> 936 [arrowhead = none , style=dashed];
936 -> 466[style=dashed];

937 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
498 -> 937 [arrowhead = none ];
937 -> 501;

938 [label="SPLIT 2\nnew knowledge:\nT276 is ground\nT290 is ground", fontsize=14, style = filled, fillcolor = violet];
498 -> 938 [arrowhead = none ];
938 -> 502;

939 [label="INSTANCE with matching:\nT125 -> T276\nT126 -> T290", fontsize=14, style = filled, fillcolor = lightgrey];
501 -> 939 [arrowhead = none , style=dashed];
939 -> 161[style=dashed];

940 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
502 -> 940 [arrowhead = none ];
940 -> 505;

941 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
505 -> 941 [arrowhead = none ];
941 -> 509;

942 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
505 -> 942 [arrowhead = none ];
942 -> 510;

943 [label="EVAL with clause\nnoattack(X502, [], X503).\nand substitutionT275 -> T301,\nX502 -> T301,\nT277 -> [],\nX503 -> s(s(s(s(s(s(0))))))", fontsize=14, style = filled, fillcolor = lightblue];
509 -> 943 [arrowhead = none ];
943 -> 514;

944 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
509 -> 944 [arrowhead = none ];
944 -> 515;

945 [label="EVAL with clause\nnoattack(X514, .(X515, X516), X517) :- ','(notEq(X514, X515), ','(add(X515, X517, X518), ','(notEq(X514, X518), ','(add(X514, X517, X519), ','(notEq(X515, X519), noattack(X514, X516, s(X517))))))).\nand substitutionT275 -> T308,\nX514 -> T308,\nX515 -> T309,\nX516 -> T310,\nT277 -> .(T309, T310),\nX517 -> s(s(s(s(s(s(0))))))", fontsize=14, style = filled, fillcolor = lightblue];
510 -> 945 [arrowhead = none ];
945 -> 527;

946 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
510 -> 946 [arrowhead = none ];
946 -> 528;

947 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
514 -> 947 [arrowhead = none ];
947 -> 516;

948 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
527 -> 948 [arrowhead = none ];
948 -> 533;

949 [label="SPLIT 2\nnew knowledge:\nT308 is ground\nT309 is ground", fontsize=14, style = filled, fillcolor = violet];
527 -> 949 [arrowhead = none ];
949 -> 534;

950 [label="INSTANCE with matching:\nT125 -> T308\nT126 -> T309", fontsize=14, style = filled, fillcolor = lightgrey];
533 -> 950 [arrowhead = none , style=dashed];
950 -> 161[style=dashed];

951 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
534 -> 951 [arrowhead = none ];
951 -> 537;

952 [label="SPLIT 2\nnew knowledge:\nT309 is ground\nT315 is ground\nreplacements:X518 -> T315", fontsize=14, style = filled, fillcolor = violet];
534 -> 952 [arrowhead = none ];
952 -> 538;

953 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
537 -> 953 [arrowhead = none ];
953 -> 541;

954 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
538 -> 954 [arrowhead = none ];
954 -> 561;

955 [label="SPLIT 2\nnew knowledge:\nT308 is ground\nT315 is ground", fontsize=14, style = filled, fillcolor = violet];
538 -> 955 [arrowhead = none ];
955 -> 562;

956 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
541 -> 956 [arrowhead = none ];
956 -> 542;

957 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
541 -> 957 [arrowhead = none ];
957 -> 543;

958 [label="EVAL with clause\nadd(0, X532, X532).\nand substitutionT309 -> 0,\nX532 -> s(s(s(s(s(s(0)))))),\nX518 -> s(s(s(s(s(s(0))))))", fontsize=14, style = filled, fillcolor = lightblue];
542 -> 958 [arrowhead = none ];
958 -> 544;

959 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
542 -> 959 [arrowhead = none ];
959 -> 545;

960 [label="EVAL with clause\nadd(s(X541), X542, s(X543)) :- add(X541, X542, X543).\nand substitutionX541 -> T318,\nT309 -> s(T318),\nX542 -> s(s(s(s(s(s(0)))))),\nX543 -> X544,\nX518 -> s(X544)", fontsize=14, style = filled, fillcolor = lightblue];
543 -> 960 [arrowhead = none ];
960 -> 552;

961 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
543 -> 961 [arrowhead = none ];
961 -> 553;

962 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
544 -> 962 [arrowhead = none ];
962 -> 546;

963 [label="INSTANCE with matching:\nT309 -> T318\nX518 -> X544", fontsize=14, style = filled, fillcolor = lightgrey];
552 -> 963 [arrowhead = none , style=dashed];
963 -> 537[style=dashed];

964 [label="INSTANCE with matching:\nT125 -> T308\nT126 -> T315", fontsize=14, style = filled, fillcolor = lightgrey];
561 -> 964 [arrowhead = none , style=dashed];
964 -> 161[style=dashed];

965 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
562 -> 965 [arrowhead = none ];
965 -> 565;

966 [label="SPLIT 2\nnew knowledge:\nT308 is ground\nT323 is ground\nreplacements:X519 -> T323", fontsize=14, style = filled, fillcolor = violet];
562 -> 966 [arrowhead = none ];
966 -> 566;

967 [label="INSTANCE with matching:\nT309 -> T308\nX518 -> X519", fontsize=14, style = filled, fillcolor = lightgrey];
565 -> 967 [arrowhead = none , style=dashed];
967 -> 537[style=dashed];

968 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
566 -> 968 [arrowhead = none ];
968 -> 569;

969 [label="SPLIT 2\nnew knowledge:\nT309 is ground\nT323 is ground", fontsize=14, style = filled, fillcolor = violet];
566 -> 969 [arrowhead = none ];
969 -> 570;

970 [label="INSTANCE with matching:\nT125 -> T309\nT126 -> T323", fontsize=14, style = filled, fillcolor = lightgrey];
569 -> 970 [arrowhead = none , style=dashed];
970 -> 161[style=dashed];

971 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
570 -> 971 [arrowhead = none ];
971 -> 579;

972 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
579 -> 972 [arrowhead = none ];
972 -> 581;

973 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
579 -> 973 [arrowhead = none ];
973 -> 582;

974 [label="EVAL with clause\nnoattack(X571, [], X572).\nand substitutionT308 -> T334,\nX571 -> T334,\nT310 -> [],\nX572 -> s(s(s(s(s(s(s(0)))))))", fontsize=14, style = filled, fillcolor = lightblue];
581 -> 974 [arrowhead = none ];
974 -> 585;

975 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
581 -> 975 [arrowhead = none ];
975 -> 586;

976 [label="EVAL with clause\nnoattack(X583, .(X584, X585), X586) :- ','(notEq(X583, X584), ','(add(X584, X586, X587), ','(notEq(X583, X587), ','(add(X583, X586, X588), ','(notEq(X584, X588), noattack(X583, X585, s(X586))))))).\nand substitutionT308 -> T341,\nX583 -> T341,\nX584 -> T342,\nX585 -> T343,\nT310 -> .(T342, T343),\nX586 -> s(s(s(s(s(s(s(0)))))))", fontsize=14, style = filled, fillcolor = lightblue];
582 -> 976 [arrowhead = none ];
976 -> 593;

977 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
582 -> 977 [arrowhead = none ];
977 -> 594;

978 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
585 -> 978 [arrowhead = none ];
978 -> 587;

979 [label="GENERALIZATION\nT346 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT346 is ground", fontsize=14, style = filled, fillcolor = violet];
593 -> 979 [arrowhead = none ];
979 -> 599;

980 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
599 -> 980 [arrowhead = none ];
980 -> 604;

981 [label="SPLIT 2\nnew knowledge:\nT341 is ground\nT342 is ground", fontsize=14, style = filled, fillcolor = violet];
599 -> 981 [arrowhead = none ];
981 -> 605;

982 [label="INSTANCE with matching:\nT125 -> T341\nT126 -> T342", fontsize=14, style = filled, fillcolor = lightgrey];
604 -> 982 [arrowhead = none , style=dashed];
982 -> 161[style=dashed];

983 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
605 -> 983 [arrowhead = none ];
983 -> 611;

984 [label="SPLIT 2\nnew knowledge:\nT342 is ground\nT351 is ground\nreplacements:X587 -> T351", fontsize=14, style = filled, fillcolor = violet];
605 -> 984 [arrowhead = none ];
984 -> 612;

985 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
611 -> 985 [arrowhead = none ];
985 -> 615;

986 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
612 -> 986 [arrowhead = none ];
986 -> 637;

987 [label="SPLIT 2\nnew knowledge:\nT341 is ground\nT351 is ground", fontsize=14, style = filled, fillcolor = violet];
612 -> 987 [arrowhead = none ];
987 -> 638;

988 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
615 -> 988 [arrowhead = none ];
988 -> 619;

989 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
615 -> 989 [arrowhead = none ];
989 -> 620;

990 [label="EVAL with clause\nadd(0, X603, X603).\nand substitutionT342 -> 0,\nX603 -> s(s(s(s(s(s(s(0))))))),\nX587 -> s(s(s(s(s(s(s(0)))))))", fontsize=14, style = filled, fillcolor = lightblue];
619 -> 990 [arrowhead = none ];
990 -> 621;

991 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
619 -> 991 [arrowhead = none ];
991 -> 622;

992 [label="EVAL with clause\nadd(s(X612), X613, s(X614)) :- add(X612, X613, X614).\nand substitutionX612 -> T354,\nT342 -> s(T354),\nX613 -> s(s(s(s(s(s(s(0))))))),\nX614 -> X615,\nX587 -> s(X615)", fontsize=14, style = filled, fillcolor = lightblue];
620 -> 992 [arrowhead = none ];
992 -> 627;

993 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
620 -> 993 [arrowhead = none ];
993 -> 628;

994 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
621 -> 994 [arrowhead = none ];
994 -> 623;

995 [label="INSTANCE with matching:\nT342 -> T354\nX587 -> X615", fontsize=14, style = filled, fillcolor = lightgrey];
627 -> 995 [arrowhead = none , style=dashed];
995 -> 611[style=dashed];

996 [label="INSTANCE with matching:\nT125 -> T341\nT126 -> T351", fontsize=14, style = filled, fillcolor = lightgrey];
637 -> 996 [arrowhead = none , style=dashed];
996 -> 161[style=dashed];

997 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
638 -> 997 [arrowhead = none ];
997 -> 641;

998 [label="SPLIT 2\nnew knowledge:\nT341 is ground\nT359 is ground\nreplacements:X588 -> T359", fontsize=14, style = filled, fillcolor = violet];
638 -> 998 [arrowhead = none ];
998 -> 642;

999 [label="INSTANCE with matching:\nT342 -> T341\nX587 -> X588", fontsize=14, style = filled, fillcolor = lightgrey];
641 -> 999 [arrowhead = none , style=dashed];
999 -> 611[style=dashed];

1000 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
642 -> 1000 [arrowhead = none ];
1000 -> 647;

1001 [label="SPLIT 2\nnew knowledge:\nT342 is ground\nT359 is ground", fontsize=14, style = filled, fillcolor = violet];
642 -> 1001 [arrowhead = none ];
1001 -> 648;

1002 [label="INSTANCE with matching:\nT125 -> T342\nT126 -> T359", fontsize=14, style = filled, fillcolor = lightgrey];
647 -> 1002 [arrowhead = none , style=dashed];
1002 -> 161[style=dashed];

1003 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
648 -> 1003 [arrowhead = none ];
1003 -> 659;

1004 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
659 -> 1004 [arrowhead = none ];
1004 -> 660;

1005 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
659 -> 1005 [arrowhead = none ];
1005 -> 661;

1006 [label="EVAL with clause\nnoattack(X642, [], X643).\nand substitutionT341 -> T376,\nX642 -> T376,\nT343 -> [],\nT346 -> T377,\nX643 -> s(T377)", fontsize=14, style = filled, fillcolor = lightblue];
660 -> 1006 [arrowhead = none ];
1006 -> 662;

1007 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
660 -> 1007 [arrowhead = none ];
1007 -> 663;

1008 [label="EVAL with clause\nnoattack(X654, .(X655, X656), X657) :- ','(notEq(X654, X655), ','(add(X655, X657, X658), ','(notEq(X654, X658), ','(add(X654, X657, X659), ','(notEq(X655, X659), noattack(X654, X656, s(X657))))))).\nand substitutionT341 -> T386,\nX654 -> T386,\nX655 -> T387,\nX656 -> T388,\nT343 -> .(T387, T388),\nT346 -> T389,\nX657 -> s(T389)", fontsize=14, style = filled, fillcolor = lightblue];
661 -> 1008 [arrowhead = none ];
1008 -> 667;

1009 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
661 -> 1009 [arrowhead = none ];
1009 -> 668;

1010 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
662 -> 1010 [arrowhead = none ];
1010 -> 664;

1011 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
667 -> 1011 [arrowhead = none ];
1011 -> 671;

1012 [label="SPLIT 2\nnew knowledge:\nT386 is ground\nT387 is ground", fontsize=14, style = filled, fillcolor = violet];
667 -> 1012 [arrowhead = none ];
1012 -> 672;

1013 [label="INSTANCE with matching:\nT125 -> T386\nT126 -> T387", fontsize=14, style = filled, fillcolor = lightgrey];
671 -> 1013 [arrowhead = none , style=dashed];
1013 -> 161[style=dashed];

1014 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
672 -> 1014 [arrowhead = none ];
1014 -> 676;

1015 [label="SPLIT 2\nnew knowledge:\nT387 is ground\nT389 is ground\nT396 is ground\nreplacements:X658 -> T396", fontsize=14, style = filled, fillcolor = violet];
672 -> 1015 [arrowhead = none ];
1015 -> 677;

1016 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
676 -> 1016 [arrowhead = none ];
1016 -> 685;

1017 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
677 -> 1017 [arrowhead = none ];
1017 -> 703;

1018 [label="SPLIT 2\nnew knowledge:\nT386 is ground\nT396 is ground", fontsize=14, style = filled, fillcolor = violet];
677 -> 1018 [arrowhead = none ];
1018 -> 704;

1019 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
685 -> 1019 [arrowhead = none ];
1019 -> 686;

1020 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
685 -> 1020 [arrowhead = none ];
1020 -> 687;

1021 [label="EVAL with clause\nadd(0, X672, X672).\nand substitutionT387 -> 0,\nT389 -> T403,\nX672 -> s(T403),\nX658 -> s(T403)", fontsize=14, style = filled, fillcolor = lightblue];
686 -> 1021 [arrowhead = none ];
1021 -> 688;

1022 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
686 -> 1022 [arrowhead = none ];
1022 -> 689;

1023 [label="EVAL with clause\nadd(s(X681), X682, s(X683)) :- add(X681, X682, X683).\nand substitutionX681 -> T408,\nT387 -> s(T408),\nT389 -> T409,\nX682 -> s(T409),\nX683 -> X684,\nX658 -> s(X684)", fontsize=14, style = filled, fillcolor = lightblue];
687 -> 1023 [arrowhead = none ];
1023 -> 694;

1024 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
687 -> 1024 [arrowhead = none ];
1024 -> 695;

1025 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
688 -> 1025 [arrowhead = none ];
1025 -> 690;

1026 [label="INSTANCE with matching:\nT387 -> T408\nT389 -> T409\nX658 -> X684", fontsize=14, style = filled, fillcolor = lightgrey];
694 -> 1026 [arrowhead = none , style=dashed];
1026 -> 676[style=dashed];

1027 [label="INSTANCE with matching:\nT125 -> T386\nT126 -> T396", fontsize=14, style = filled, fillcolor = lightgrey];
703 -> 1027 [arrowhead = none , style=dashed];
1027 -> 161[style=dashed];

1028 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
704 -> 1028 [arrowhead = none ];
1028 -> 708;

1029 [label="SPLIT 2\nnew knowledge:\nT386 is ground\nT389 is ground\nT418 is ground\nreplacements:X659 -> T418", fontsize=14, style = filled, fillcolor = violet];
704 -> 1029 [arrowhead = none ];
1029 -> 709;

1030 [label="INSTANCE with matching:\nT387 -> T386\nX658 -> X659", fontsize=14, style = filled, fillcolor = lightgrey];
708 -> 1030 [arrowhead = none , style=dashed];
1030 -> 676[style=dashed];

1031 [label="INSTANCE with matching:\nT342 -> T387\nT359 -> T418\nT341 -> T386\nT343 -> T388\nT346 -> s(T389)", fontsize=14, style = filled, fillcolor = lightgrey];
709 -> 1031 [arrowhead = none , style=dashed];
1031 -> 642[style=dashed];

1032 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
719 -> 1032 [arrowhead = none ];
1032 -> 720;

1033 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
719 -> 1033 [arrowhead = none ];
1033 -> 721;

1034 [label="EVAL with clause\nsafe([]).\nand substitutionT109 -> []", fontsize=14, style = filled, fillcolor = lightblue];
720 -> 1034 [arrowhead = none ];
1034 -> 722;

1035 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
720 -> 1035 [arrowhead = none ];
1035 -> 723;

1036 [label="EVAL with clause\nsafe(.(X701, X702)) :- ','(noattack(X701, X702, s(0)), safe(X702)).\nand substitutionX701 -> T427,\nX702 -> T428,\nT109 -> .(T427, T428)", fontsize=14, style = filled, fillcolor = lightblue];
721 -> 1036 [arrowhead = none ];
1036 -> 725;

1037 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
721 -> 1037 [arrowhead = none ];
1037 -> 726;

1038 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
722 -> 1038 [arrowhead = none ];
1038 -> 724;

1039 [label="INSTANCE with matching:\nT108 -> T427\nT109 -> T428", fontsize=14, style = filled, fillcolor = lightgrey];
725 -> 1039 [arrowhead = none , style=dashed];
1039 -> 128[style=dashed];

}

(2) Obligation:

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

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)

(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:

QUEENSA_IN_A(.(T11, T12)) → U1_A(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
QUEENSA_IN_A(.(T11, T12)) → PB_IN_AGAA(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)
PB_IN_AGAA(T22, T15, T20, T21) → U24_AGAA(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
PB_IN_AGAA(T22, T15, T20, T21) → DELETEO_IN_AGA(T22, T15, T20)
DELETEO_IN_AGA(T48, T47, .(s(0), X57)) → U13_AGA(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
DELETEO_IN_AGA(T48, T47, .(s(0), X57)) → DELETEC_IN_AGA(T48, T47, X57)
DELETEC_IN_AGA(T72, .(T70, T71), .(T70, X86)) → U2_AGA(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
DELETEC_IN_AGA(T72, .(T70, T71), .(T70, X86)) → DELETEC_IN_AGA(T72, T71, X86)
U24_AGAA(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_AGAA(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
U24_AGAA(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → PN9_IN_GAG(T20, T21, T22)
PN9_IN_GAG(T20, T77, T22) → U26_GAG(T20, T77, T22, permD_in_ga(T20, T77))
PN9_IN_GAG(T20, T77, T22) → PERMD_IN_GA(T20, T77)
PERMD_IN_GA(.(T86, T87), .(T90, T91)) → U3_GA(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
PERMD_IN_GA(.(T86, T87), .(T90, T91)) → PE_IN_AGGAA(T90, T86, T87, X104, T91)
PE_IN_AGGAA(T90, T86, T87, T96, T97) → U28_AGGAA(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
PE_IN_AGGAA(T90, T86, T87, T96, T97) → DELETEC_IN_AGA(T90, .(T86, T87), T96)
U28_AGGAA(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_AGGAA(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U28_AGGAA(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → PERMD_IN_GA(T96, T97)
U26_GAG(T20, T77, T22, permD_out_ga(T20, T77)) → U27_GAG(T20, T77, T22, safeP_in_gg(T22, T77))
U26_GAG(T20, T77, T22, permD_out_ga(T20, T77)) → SAFEP_IN_GG(T22, T77)
SAFEP_IN_GG(T108, T109) → U14_GG(T108, T109, pQ_in_gg(T108, T109))
SAFEP_IN_GG(T108, T109) → PQ_IN_GG(T108, T109)
PQ_IN_GG(T108, T109) → U30_GG(T108, T109, noattackR_in_gg(T108, T109))
PQ_IN_GG(T108, T109) → NOATTACKR_IN_GG(T108, T109)
NOATTACKR_IN_GG(T125, .(T126, T127)) → U15_GG(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
NOATTACKR_IN_GG(T125, .(T126, T127)) → PS_IN_GGAAG(T125, T126, X155, X156, T127)
PS_IN_GGAAG(T125, T126, X155, X156, T127) → U32_GGAAG(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
PS_IN_GGAAG(T125, T126, X155, X156, T127) → NOTEQF_IN_GG(T125, T126)
NOTEQF_IN_GG(s(T146), s(T147)) → U4_GG(T146, T147, notEqF_in_gg(T146, T147))
NOTEQF_IN_GG(s(T146), s(T147)) → NOTEQF_IN_GG(T146, T147)
U32_GGAAG(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_GGAAG(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
U32_GGAAG(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → PN10_IN_GAGAG(T126, X155, T125, X156, T127)
PN10_IN_GAGAG(T126, T150, T125, X156, T127) → U34_GAGAG(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
PN10_IN_GAGAG(T126, T150, T125, X156, T127) → ADDG_IN_GA(T126, T150)
ADDG_IN_GA(s(T153), s(X199)) → U5_GA(T153, X199, addG_in_ga(T153, X199))
ADDG_IN_GA(s(T153), s(X199)) → ADDG_IN_GA(T153, X199)
U34_GAGAG(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_GAGAG(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
U34_GAGAG(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → PN11_IN_GGAGG(T125, T150, X156, T126, T127)
PN11_IN_GGAGG(T125, T150, X156, T126, T127) → U36_GGAGG(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
PN11_IN_GGAGG(T125, T150, X156, T126, T127) → NOTEQF_IN_GG(T125, T150)
U36_GGAGG(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_GGAGG(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
U36_GGAGG(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → PN12_IN_GAGG(T125, X156, T126, T127)
PN12_IN_GAGG(T125, T158, T126, T127) → U38_GAGG(T125, T158, T126, T127, addG_in_ga(T125, T158))
PN12_IN_GAGG(T125, T158, T126, T127) → ADDG_IN_GA(T125, T158)
U38_GAGG(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_GAGG(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
U38_GAGG(T125, T158, T126, T127, addG_out_ga(T125, T158)) → PN13_IN_GGGG(T126, T158, T125, T127)
PN13_IN_GGGG(T126, T158, T125, T127) → U40_GGGG(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
PN13_IN_GGGG(T126, T158, T125, T127) → NOTEQF_IN_GG(T126, T158)
U40_GGGG(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_GGGG(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
U40_GGGG(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → NOATTACKU_IN_GG(T125, T127)
NOATTACKU_IN_GG(T176, .(T177, T178)) → U17_GG(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
NOATTACKU_IN_GG(T176, .(T177, T178)) → PV_IN_GGAAG(T176, T177, X242, X243, T178)
PV_IN_GGAAG(T176, T177, X242, X243, T178) → U42_GGAAG(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
PV_IN_GGAAG(T176, T177, X242, X243, T178) → NOTEQF_IN_GG(T176, T177)
U42_GGAAG(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_GGAAG(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
U42_GGAAG(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → PN14_IN_GAGAG(T177, X242, T176, X243, T178)
PN14_IN_GAGAG(T177, T183, T176, X243, T178) → U44_GAGAG(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
PN14_IN_GAGAG(T177, T183, T176, X243, T178) → ADDH_IN_GA(T177, T183)
ADDH_IN_GA(s(T186), s(X268)) → U6_GA(T186, X268, addH_in_ga(T186, X268))
ADDH_IN_GA(s(T186), s(X268)) → ADDH_IN_GA(T186, X268)
U44_GAGAG(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_GAGAG(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
U44_GAGAG(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → PN15_IN_GGAGG(T176, T183, X243, T177, T178)
PN15_IN_GGAGG(T176, T183, X243, T177, T178) → U46_GGAGG(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
PN15_IN_GGAGG(T176, T183, X243, T177, T178) → NOTEQF_IN_GG(T176, T183)
U46_GGAGG(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_GGAGG(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
U46_GGAGG(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → PN16_IN_GAGG(T176, X243, T177, T178)
PN16_IN_GAGG(T176, T191, T177, T178) → U48_GAGG(T176, T191, T177, T178, addH_in_ga(T176, T191))
PN16_IN_GAGG(T176, T191, T177, T178) → ADDH_IN_GA(T176, T191)
U48_GAGG(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_GAGG(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
U48_GAGG(T176, T191, T177, T178, addH_out_ga(T176, T191)) → PN17_IN_GGGG(T177, T191, T176, T178)
PN17_IN_GGGG(T177, T191, T176, T178) → U50_GGGG(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
PN17_IN_GGGG(T177, T191, T176, T178) → NOTEQF_IN_GG(T177, T191)
U50_GGGG(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_GGGG(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
U50_GGGG(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → NOATTACKW_IN_GG(T176, T178)
NOATTACKW_IN_GG(T209, .(T210, T211)) → U18_GG(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
NOATTACKW_IN_GG(T209, .(T210, T211)) → PX_IN_GGAAG(T209, T210, X311, X312, T211)
PX_IN_GGAAG(T209, T210, X311, X312, T211) → U52_GGAAG(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
PX_IN_GGAAG(T209, T210, X311, X312, T211) → NOTEQF_IN_GG(T209, T210)
U52_GGAAG(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_GGAAG(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
U52_GGAAG(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → PN18_IN_GAGAG(T210, X311, T209, X312, T211)
PN18_IN_GAGAG(T210, T216, T209, X312, T211) → U54_GAGAG(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
PN18_IN_GAGAG(T210, T216, T209, X312, T211) → ADDI_IN_GA(T210, T216)
ADDI_IN_GA(s(T219), s(X337)) → U7_GA(T219, X337, addI_in_ga(T219, X337))
ADDI_IN_GA(s(T219), s(X337)) → ADDI_IN_GA(T219, X337)
U54_GAGAG(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_GAGAG(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
U54_GAGAG(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → PN19_IN_GGAGG(T209, T216, X312, T210, T211)
PN19_IN_GGAGG(T209, T216, X312, T210, T211) → U56_GGAGG(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
PN19_IN_GGAGG(T209, T216, X312, T210, T211) → NOTEQF_IN_GG(T209, T216)
U56_GGAGG(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_GGAGG(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
U56_GGAGG(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → PN20_IN_GAGG(T209, X312, T210, T211)
PN20_IN_GAGG(T209, T224, T210, T211) → U58_GAGG(T209, T224, T210, T211, addI_in_ga(T209, T224))
PN20_IN_GAGG(T209, T224, T210, T211) → ADDI_IN_GA(T209, T224)
U58_GAGG(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_GAGG(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
U58_GAGG(T209, T224, T210, T211, addI_out_ga(T209, T224)) → PN21_IN_GGGG(T210, T224, T209, T211)
PN21_IN_GGGG(T210, T224, T209, T211) → U60_GGGG(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
PN21_IN_GGGG(T210, T224, T209, T211) → NOTEQF_IN_GG(T210, T224)
U60_GGGG(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_GGGG(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
U60_GGGG(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → NOATTACKY_IN_GG(T209, T211)
NOATTACKY_IN_GG(T242, .(T243, T244)) → U19_GG(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
NOATTACKY_IN_GG(T242, .(T243, T244)) → PZ_IN_GGAAG(T242, T243, X380, X381, T244)
PZ_IN_GGAAG(T242, T243, X380, X381, T244) → U62_GGAAG(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
PZ_IN_GGAAG(T242, T243, X380, X381, T244) → NOTEQF_IN_GG(T242, T243)
U62_GGAAG(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_GGAAG(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
U62_GGAAG(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → PN22_IN_GAGAG(T243, X380, T242, X381, T244)
PN22_IN_GAGAG(T243, T249, T242, X381, T244) → U64_GAGAG(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
PN22_IN_GAGAG(T243, T249, T242, X381, T244) → ADDJ_IN_GA(T243, T249)
ADDJ_IN_GA(s(T252), s(X406)) → U8_GA(T252, X406, addJ_in_ga(T252, X406))
ADDJ_IN_GA(s(T252), s(X406)) → ADDJ_IN_GA(T252, X406)
U64_GAGAG(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_GAGAG(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
U64_GAGAG(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → PN23_IN_GGAGG(T242, T249, X381, T243, T244)
PN23_IN_GGAGG(T242, T249, X381, T243, T244) → U66_GGAGG(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
PN23_IN_GGAGG(T242, T249, X381, T243, T244) → NOTEQF_IN_GG(T242, T249)
U66_GGAGG(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_GGAGG(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
U66_GGAGG(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → PN24_IN_GAGG(T242, X381, T243, T244)
PN24_IN_GAGG(T242, T257, T243, T244) → U68_GAGG(T242, T257, T243, T244, addJ_in_ga(T242, T257))
PN24_IN_GAGG(T242, T257, T243, T244) → ADDJ_IN_GA(T242, T257)
U68_GAGG(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_GAGG(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
U68_GAGG(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → PN25_IN_GGGG(T243, T257, T242, T244)
PN25_IN_GGGG(T243, T257, T242, T244) → U70_GGGG(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
PN25_IN_GGGG(T243, T257, T242, T244) → NOTEQF_IN_GG(T243, T257)
U70_GGGG(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_GGGG(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
U70_GGGG(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → NOATTACKN1_IN_GG(T242, T244)
NOATTACKN1_IN_GG(T275, .(T276, T277)) → U20_GG(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
NOATTACKN1_IN_GG(T275, .(T276, T277)) → PN2_IN_GGAAG(T275, T276, X449, X450, T277)
PN2_IN_GGAAG(T275, T276, X449, X450, T277) → U72_GGAAG(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
PN2_IN_GGAAG(T275, T276, X449, X450, T277) → NOTEQF_IN_GG(T275, T276)
U72_GGAAG(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_GGAAG(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
U72_GGAAG(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → PN26_IN_GAGAG(T276, X449, T275, X450, T277)
PN26_IN_GAGAG(T276, T282, T275, X450, T277) → U74_GAGAG(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
PN26_IN_GAGAG(T276, T282, T275, X450, T277) → ADDK_IN_GA(T276, T282)
ADDK_IN_GA(s(T285), s(X475)) → U9_GA(T285, X475, addK_in_ga(T285, X475))
ADDK_IN_GA(s(T285), s(X475)) → ADDK_IN_GA(T285, X475)
U74_GAGAG(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_GAGAG(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
U74_GAGAG(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → PN27_IN_GGAGG(T275, T282, X450, T276, T277)
PN27_IN_GGAGG(T275, T282, X450, T276, T277) → U76_GGAGG(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
PN27_IN_GGAGG(T275, T282, X450, T276, T277) → NOTEQF_IN_GG(T275, T282)
U76_GGAGG(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_GGAGG(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
U76_GGAGG(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → PN28_IN_GAGG(T275, X450, T276, T277)
PN28_IN_GAGG(T275, T290, T276, T277) → U78_GAGG(T275, T290, T276, T277, addK_in_ga(T275, T290))
PN28_IN_GAGG(T275, T290, T276, T277) → ADDK_IN_GA(T275, T290)
U78_GAGG(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_GAGG(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
U78_GAGG(T275, T290, T276, T277, addK_out_ga(T275, T290)) → PN29_IN_GGGG(T276, T290, T275, T277)
PN29_IN_GGGG(T276, T290, T275, T277) → U80_GGGG(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
PN29_IN_GGGG(T276, T290, T275, T277) → NOTEQF_IN_GG(T276, T290)
U80_GGGG(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_GGGG(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
U80_GGGG(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → NOATTACKN3_IN_GG(T275, T277)
NOATTACKN3_IN_GG(T308, .(T309, T310)) → U21_GG(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
NOATTACKN3_IN_GG(T308, .(T309, T310)) → PN4_IN_GGAAG(T308, T309, X518, X519, T310)
PN4_IN_GGAAG(T308, T309, X518, X519, T310) → U82_GGAAG(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
PN4_IN_GGAAG(T308, T309, X518, X519, T310) → NOTEQF_IN_GG(T308, T309)
U82_GGAAG(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_GGAAG(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
U82_GGAAG(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → PN30_IN_GAGAG(T309, X518, T308, X519, T310)
PN30_IN_GAGAG(T309, T315, T308, X519, T310) → U84_GAGAG(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
PN30_IN_GAGAG(T309, T315, T308, X519, T310) → ADDL_IN_GA(T309, T315)
ADDL_IN_GA(s(T318), s(X544)) → U10_GA(T318, X544, addL_in_ga(T318, X544))
ADDL_IN_GA(s(T318), s(X544)) → ADDL_IN_GA(T318, X544)
U84_GAGAG(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_GAGAG(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
U84_GAGAG(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → PN31_IN_GGAGG(T308, T315, X519, T309, T310)
PN31_IN_GGAGG(T308, T315, X519, T309, T310) → U86_GGAGG(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
PN31_IN_GGAGG(T308, T315, X519, T309, T310) → NOTEQF_IN_GG(T308, T315)
U86_GGAGG(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_GGAGG(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
U86_GGAGG(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → PN32_IN_GAGG(T308, X519, T309, T310)
PN32_IN_GAGG(T308, T323, T309, T310) → U88_GAGG(T308, T323, T309, T310, addL_in_ga(T308, T323))
PN32_IN_GAGG(T308, T323, T309, T310) → ADDL_IN_GA(T308, T323)
U88_GAGG(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_GAGG(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
U88_GAGG(T308, T323, T309, T310, addL_out_ga(T308, T323)) → PN33_IN_GGGG(T309, T323, T308, T310)
PN33_IN_GGGG(T309, T323, T308, T310) → U90_GGGG(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
PN33_IN_GGGG(T309, T323, T308, T310) → NOTEQF_IN_GG(T309, T323)
U90_GGGG(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_GGGG(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
U90_GGGG(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → NOATTACKN5_IN_GG(T308, T310)
NOATTACKN5_IN_GG(T341, .(T342, T343)) → U22_GG(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
NOATTACKN5_IN_GG(T341, .(T342, T343)) → PN6_IN_GGAAGG(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))
PN6_IN_GGAAGG(T341, T342, X587, X588, T343, T346) → U92_GGAAGG(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
PN6_IN_GGAAGG(T341, T342, X587, X588, T343, T346) → NOTEQF_IN_GG(T341, T342)
U92_GGAAGG(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_GGAAGG(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
U92_GGAAGG(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → PN34_IN_GAGAGG(T342, X587, T341, X588, T343, T346)
PN34_IN_GAGAGG(T342, T351, T341, X588, T343, T346) → U94_GAGAGG(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
PN34_IN_GAGAGG(T342, T351, T341, X588, T343, T346) → ADDM_IN_GA(T342, T351)
ADDM_IN_GA(s(T354), s(X615)) → U11_GA(T354, X615, addM_in_ga(T354, X615))
ADDM_IN_GA(s(T354), s(X615)) → ADDM_IN_GA(T354, X615)
U94_GAGAGG(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_GAGAGG(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
U94_GAGAGG(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → PN35_IN_GGAGGG(T341, T351, X588, T342, T343, T346)
PN35_IN_GGAGGG(T341, T351, X588, T342, T343, T346) → U96_GGAGGG(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
PN35_IN_GGAGGG(T341, T351, X588, T342, T343, T346) → NOTEQF_IN_GG(T341, T351)
U96_GGAGGG(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_GGAGGG(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
U96_GGAGGG(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → PN36_IN_GAGGG(T341, X588, T342, T343, T346)
PN36_IN_GAGGG(T341, T359, T342, T343, T346) → U98_GAGGG(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
PN36_IN_GAGGG(T341, T359, T342, T343, T346) → ADDM_IN_GA(T341, T359)
U98_GAGGG(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_GAGGG(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
U98_GAGGG(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → PN37_IN_GGGGG(T342, T359, T341, T343, T346)
PN37_IN_GGGGG(T342, T359, T341, T343, T346) → U100_GGGGG(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
PN37_IN_GGGGG(T342, T359, T341, T343, T346) → NOTEQF_IN_GG(T342, T359)
U100_GGGGG(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_GGGGG(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
U100_GGGGG(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → NOATTACKN7_IN_GGG(T341, T343, T346)
NOATTACKN7_IN_GGG(T386, .(T387, T388), T389) → U23_GGG(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
NOATTACKN7_IN_GGG(T386, .(T387, T388), T389) → PN8_IN_GGGAAG(T386, T387, T389, X658, X659, T388)
PN8_IN_GGGAAG(T386, T387, T389, X658, X659, T388) → U102_GGGAAG(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
PN8_IN_GGGAAG(T386, T387, T389, X658, X659, T388) → NOTEQF_IN_GG(T386, T387)
U102_GGGAAG(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_GGGAAG(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
U102_GGGAAG(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → PN38_IN_GGAGAG(T387, T389, X658, T386, X659, T388)
PN38_IN_GGAGAG(T387, T389, T396, T386, X659, T388) → U104_GGAGAG(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
PN38_IN_GGAGAG(T387, T389, T396, T386, X659, T388) → ADDN_IN_GGA(T387, T389, T396)
ADDN_IN_GGA(s(T408), T409, s(X684)) → U12_GGA(T408, T409, X684, addN_in_gga(T408, T409, X684))
ADDN_IN_GGA(s(T408), T409, s(X684)) → ADDN_IN_GGA(T408, T409, X684)
U104_GGAGAG(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_GGAGAG(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
U104_GGAGAG(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → PN39_IN_GGGAGG(T386, T396, T389, X659, T387, T388)
PN39_IN_GGGAGG(T386, T396, T389, X659, T387, T388) → U106_GGGAGG(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
PN39_IN_GGGAGG(T386, T396, T389, X659, T387, T388) → NOTEQF_IN_GG(T386, T396)
U106_GGGAGG(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_GGGAGG(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
U106_GGGAGG(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → PN40_IN_GGAGG(T386, T389, X659, T387, T388)
PN40_IN_GGAGG(T386, T389, T418, T387, T388) → U108_GGAGG(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
PN40_IN_GGAGG(T386, T389, T418, T387, T388) → ADDN_IN_GGA(T386, T389, T418)
U108_GGAGG(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_GGAGG(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U108_GGAGG(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → PN37_IN_GGGGG(T387, T418, T386, T388, s(T389))
U30_GG(T108, T109, noattackR_out_gg(T108, T109)) → U31_GG(T108, T109, safeT_in_g(T109))
U30_GG(T108, T109, noattackR_out_gg(T108, T109)) → SAFET_IN_G(T109)
SAFET_IN_G(.(T427, T428)) → U16_G(T427, T428, pQ_in_gg(T427, T428))
SAFET_IN_G(.(T427, T428)) → PQ_IN_GG(T427, T428)

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
QUEENSA_IN_A(x1)  =  QUEENSA_IN_A
U1_A(x1, x2, x3)  =  U1_A(x3)
PB_IN_AGAA(x1, x2, x3, x4)  =  PB_IN_AGAA(x2)
U24_AGAA(x1, x2, x3, x4, x5)  =  U24_AGAA(x2, x5)
DELETEO_IN_AGA(x1, x2, x3)  =  DELETEO_IN_AGA(x2)
U13_AGA(x1, x2, x3, x4)  =  U13_AGA(x2, x4)
DELETEC_IN_AGA(x1, x2, x3)  =  DELETEC_IN_AGA(x2)
U2_AGA(x1, x2, x3, x4, x5)  =  U2_AGA(x2, x3, x5)
U25_AGAA(x1, x2, x3, x4, x5)  =  U25_AGAA(x1, x2, x3, x5)
PN9_IN_GAG(x1, x2, x3)  =  PN9_IN_GAG(x1, x3)
U26_GAG(x1, x2, x3, x4)  =  U26_GAG(x1, x3, x4)
PERMD_IN_GA(x1, x2)  =  PERMD_IN_GA(x1)
U3_GA(x1, x2, x3, x4, x5)  =  U3_GA(x1, x2, x5)
PE_IN_AGGAA(x1, x2, x3, x4, x5)  =  PE_IN_AGGAA(x2, x3)
U28_AGGAA(x1, x2, x3, x4, x5, x6)  =  U28_AGGAA(x2, x3, x6)
U29_AGGAA(x1, x2, x3, x4, x5, x6)  =  U29_AGGAA(x1, x2, x3, x4, x6)
U27_GAG(x1, x2, x3, x4)  =  U27_GAG(x1, x2, x3, x4)
SAFEP_IN_GG(x1, x2)  =  SAFEP_IN_GG(x1, x2)
U14_GG(x1, x2, x3)  =  U14_GG(x1, x2, x3)
PQ_IN_GG(x1, x2)  =  PQ_IN_GG(x1, x2)
U30_GG(x1, x2, x3)  =  U30_GG(x1, x2, x3)
NOATTACKR_IN_GG(x1, x2)  =  NOATTACKR_IN_GG(x1, x2)
U15_GG(x1, x2, x3, x4)  =  U15_GG(x1, x2, x3, x4)
PS_IN_GGAAG(x1, x2, x3, x4, x5)  =  PS_IN_GGAAG(x1, x2, x5)
U32_GGAAG(x1, x2, x3, x4, x5, x6)  =  U32_GGAAG(x1, x2, x5, x6)
NOTEQF_IN_GG(x1, x2)  =  NOTEQF_IN_GG(x1, x2)
U4_GG(x1, x2, x3)  =  U4_GG(x1, x2, x3)
U33_GGAAG(x1, x2, x3, x4, x5, x6)  =  U33_GGAAG(x1, x2, x5, x6)
PN10_IN_GAGAG(x1, x2, x3, x4, x5)  =  PN10_IN_GAGAG(x1, x3, x5)
U34_GAGAG(x1, x2, x3, x4, x5, x6)  =  U34_GAGAG(x1, x3, x5, x6)
ADDG_IN_GA(x1, x2)  =  ADDG_IN_GA(x1)
U5_GA(x1, x2, x3)  =  U5_GA(x1, x3)
U35_GAGAG(x1, x2, x3, x4, x5, x6)  =  U35_GAGAG(x1, x2, x3, x5, x6)
PN11_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN11_IN_GGAGG(x1, x2, x4, x5)
U36_GGAGG(x1, x2, x3, x4, x5, x6)  =  U36_GGAGG(x1, x2, x4, x5, x6)
U37_GGAGG(x1, x2, x3, x4, x5, x6)  =  U37_GGAGG(x1, x2, x4, x5, x6)
PN12_IN_GAGG(x1, x2, x3, x4)  =  PN12_IN_GAGG(x1, x3, x4)
U38_GAGG(x1, x2, x3, x4, x5)  =  U38_GAGG(x1, x3, x4, x5)
U39_GAGG(x1, x2, x3, x4, x5)  =  U39_GAGG(x1, x2, x3, x4, x5)
PN13_IN_GGGG(x1, x2, x3, x4)  =  PN13_IN_GGGG(x1, x2, x3, x4)
U40_GGGG(x1, x2, x3, x4, x5)  =  U40_GGGG(x1, x2, x3, x4, x5)
U41_GGGG(x1, x2, x3, x4, x5)  =  U41_GGGG(x1, x2, x3, x4, x5)
NOATTACKU_IN_GG(x1, x2)  =  NOATTACKU_IN_GG(x1, x2)
U17_GG(x1, x2, x3, x4)  =  U17_GG(x1, x2, x3, x4)
PV_IN_GGAAG(x1, x2, x3, x4, x5)  =  PV_IN_GGAAG(x1, x2, x5)
U42_GGAAG(x1, x2, x3, x4, x5, x6)  =  U42_GGAAG(x1, x2, x5, x6)
U43_GGAAG(x1, x2, x3, x4, x5, x6)  =  U43_GGAAG(x1, x2, x5, x6)
PN14_IN_GAGAG(x1, x2, x3, x4, x5)  =  PN14_IN_GAGAG(x1, x3, x5)
U44_GAGAG(x1, x2, x3, x4, x5, x6)  =  U44_GAGAG(x1, x3, x5, x6)
ADDH_IN_GA(x1, x2)  =  ADDH_IN_GA(x1)
U6_GA(x1, x2, x3)  =  U6_GA(x1, x3)
U45_GAGAG(x1, x2, x3, x4, x5, x6)  =  U45_GAGAG(x1, x2, x3, x5, x6)
PN15_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN15_IN_GGAGG(x1, x2, x4, x5)
U46_GGAGG(x1, x2, x3, x4, x5, x6)  =  U46_GGAGG(x1, x2, x4, x5, x6)
U47_GGAGG(x1, x2, x3, x4, x5, x6)  =  U47_GGAGG(x1, x2, x4, x5, x6)
PN16_IN_GAGG(x1, x2, x3, x4)  =  PN16_IN_GAGG(x1, x3, x4)
U48_GAGG(x1, x2, x3, x4, x5)  =  U48_GAGG(x1, x3, x4, x5)
U49_GAGG(x1, x2, x3, x4, x5)  =  U49_GAGG(x1, x2, x3, x4, x5)
PN17_IN_GGGG(x1, x2, x3, x4)  =  PN17_IN_GGGG(x1, x2, x3, x4)
U50_GGGG(x1, x2, x3, x4, x5)  =  U50_GGGG(x1, x2, x3, x4, x5)
U51_GGGG(x1, x2, x3, x4, x5)  =  U51_GGGG(x1, x2, x3, x4, x5)
NOATTACKW_IN_GG(x1, x2)  =  NOATTACKW_IN_GG(x1, x2)
U18_GG(x1, x2, x3, x4)  =  U18_GG(x1, x2, x3, x4)
PX_IN_GGAAG(x1, x2, x3, x4, x5)  =  PX_IN_GGAAG(x1, x2, x5)
U52_GGAAG(x1, x2, x3, x4, x5, x6)  =  U52_GGAAG(x1, x2, x5, x6)
U53_GGAAG(x1, x2, x3, x4, x5, x6)  =  U53_GGAAG(x1, x2, x5, x6)
PN18_IN_GAGAG(x1, x2, x3, x4, x5)  =  PN18_IN_GAGAG(x1, x3, x5)
U54_GAGAG(x1, x2, x3, x4, x5, x6)  =  U54_GAGAG(x1, x3, x5, x6)
ADDI_IN_GA(x1, x2)  =  ADDI_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x1, x3)
U55_GAGAG(x1, x2, x3, x4, x5, x6)  =  U55_GAGAG(x1, x2, x3, x5, x6)
PN19_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN19_IN_GGAGG(x1, x2, x4, x5)
U56_GGAGG(x1, x2, x3, x4, x5, x6)  =  U56_GGAGG(x1, x2, x4, x5, x6)
U57_GGAGG(x1, x2, x3, x4, x5, x6)  =  U57_GGAGG(x1, x2, x4, x5, x6)
PN20_IN_GAGG(x1, x2, x3, x4)  =  PN20_IN_GAGG(x1, x3, x4)
U58_GAGG(x1, x2, x3, x4, x5)  =  U58_GAGG(x1, x3, x4, x5)
U59_GAGG(x1, x2, x3, x4, x5)  =  U59_GAGG(x1, x2, x3, x4, x5)
PN21_IN_GGGG(x1, x2, x3, x4)  =  PN21_IN_GGGG(x1, x2, x3, x4)
U60_GGGG(x1, x2, x3, x4, x5)  =  U60_GGGG(x1, x2, x3, x4, x5)
U61_GGGG(x1, x2, x3, x4, x5)  =  U61_GGGG(x1, x2, x3, x4, x5)
NOATTACKY_IN_GG(x1, x2)  =  NOATTACKY_IN_GG(x1, x2)
U19_GG(x1, x2, x3, x4)  =  U19_GG(x1, x2, x3, x4)
PZ_IN_GGAAG(x1, x2, x3, x4, x5)  =  PZ_IN_GGAAG(x1, x2, x5)
U62_GGAAG(x1, x2, x3, x4, x5, x6)  =  U62_GGAAG(x1, x2, x5, x6)
U63_GGAAG(x1, x2, x3, x4, x5, x6)  =  U63_GGAAG(x1, x2, x5, x6)
PN22_IN_GAGAG(x1, x2, x3, x4, x5)  =  PN22_IN_GAGAG(x1, x3, x5)
U64_GAGAG(x1, x2, x3, x4, x5, x6)  =  U64_GAGAG(x1, x3, x5, x6)
ADDJ_IN_GA(x1, x2)  =  ADDJ_IN_GA(x1)
U8_GA(x1, x2, x3)  =  U8_GA(x1, x3)
U65_GAGAG(x1, x2, x3, x4, x5, x6)  =  U65_GAGAG(x1, x2, x3, x5, x6)
PN23_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN23_IN_GGAGG(x1, x2, x4, x5)
U66_GGAGG(x1, x2, x3, x4, x5, x6)  =  U66_GGAGG(x1, x2, x4, x5, x6)
U67_GGAGG(x1, x2, x3, x4, x5, x6)  =  U67_GGAGG(x1, x2, x4, x5, x6)
PN24_IN_GAGG(x1, x2, x3, x4)  =  PN24_IN_GAGG(x1, x3, x4)
U68_GAGG(x1, x2, x3, x4, x5)  =  U68_GAGG(x1, x3, x4, x5)
U69_GAGG(x1, x2, x3, x4, x5)  =  U69_GAGG(x1, x2, x3, x4, x5)
PN25_IN_GGGG(x1, x2, x3, x4)  =  PN25_IN_GGGG(x1, x2, x3, x4)
U70_GGGG(x1, x2, x3, x4, x5)  =  U70_GGGG(x1, x2, x3, x4, x5)
U71_GGGG(x1, x2, x3, x4, x5)  =  U71_GGGG(x1, x2, x3, x4, x5)
NOATTACKN1_IN_GG(x1, x2)  =  NOATTACKN1_IN_GG(x1, x2)
U20_GG(x1, x2, x3, x4)  =  U20_GG(x1, x2, x3, x4)
PN2_IN_GGAAG(x1, x2, x3, x4, x5)  =  PN2_IN_GGAAG(x1, x2, x5)
U72_GGAAG(x1, x2, x3, x4, x5, x6)  =  U72_GGAAG(x1, x2, x5, x6)
U73_GGAAG(x1, x2, x3, x4, x5, x6)  =  U73_GGAAG(x1, x2, x5, x6)
PN26_IN_GAGAG(x1, x2, x3, x4, x5)  =  PN26_IN_GAGAG(x1, x3, x5)
U74_GAGAG(x1, x2, x3, x4, x5, x6)  =  U74_GAGAG(x1, x3, x5, x6)
ADDK_IN_GA(x1, x2)  =  ADDK_IN_GA(x1)
U9_GA(x1, x2, x3)  =  U9_GA(x1, x3)
U75_GAGAG(x1, x2, x3, x4, x5, x6)  =  U75_GAGAG(x1, x2, x3, x5, x6)
PN27_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN27_IN_GGAGG(x1, x2, x4, x5)
U76_GGAGG(x1, x2, x3, x4, x5, x6)  =  U76_GGAGG(x1, x2, x4, x5, x6)
U77_GGAGG(x1, x2, x3, x4, x5, x6)  =  U77_GGAGG(x1, x2, x4, x5, x6)
PN28_IN_GAGG(x1, x2, x3, x4)  =  PN28_IN_GAGG(x1, x3, x4)
U78_GAGG(x1, x2, x3, x4, x5)  =  U78_GAGG(x1, x3, x4, x5)
U79_GAGG(x1, x2, x3, x4, x5)  =  U79_GAGG(x1, x2, x3, x4, x5)
PN29_IN_GGGG(x1, x2, x3, x4)  =  PN29_IN_GGGG(x1, x2, x3, x4)
U80_GGGG(x1, x2, x3, x4, x5)  =  U80_GGGG(x1, x2, x3, x4, x5)
U81_GGGG(x1, x2, x3, x4, x5)  =  U81_GGGG(x1, x2, x3, x4, x5)
NOATTACKN3_IN_GG(x1, x2)  =  NOATTACKN3_IN_GG(x1, x2)
U21_GG(x1, x2, x3, x4)  =  U21_GG(x1, x2, x3, x4)
PN4_IN_GGAAG(x1, x2, x3, x4, x5)  =  PN4_IN_GGAAG(x1, x2, x5)
U82_GGAAG(x1, x2, x3, x4, x5, x6)  =  U82_GGAAG(x1, x2, x5, x6)
U83_GGAAG(x1, x2, x3, x4, x5, x6)  =  U83_GGAAG(x1, x2, x5, x6)
PN30_IN_GAGAG(x1, x2, x3, x4, x5)  =  PN30_IN_GAGAG(x1, x3, x5)
U84_GAGAG(x1, x2, x3, x4, x5, x6)  =  U84_GAGAG(x1, x3, x5, x6)
ADDL_IN_GA(x1, x2)  =  ADDL_IN_GA(x1)
U10_GA(x1, x2, x3)  =  U10_GA(x1, x3)
U85_GAGAG(x1, x2, x3, x4, x5, x6)  =  U85_GAGAG(x1, x2, x3, x5, x6)
PN31_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN31_IN_GGAGG(x1, x2, x4, x5)
U86_GGAGG(x1, x2, x3, x4, x5, x6)  =  U86_GGAGG(x1, x2, x4, x5, x6)
U87_GGAGG(x1, x2, x3, x4, x5, x6)  =  U87_GGAGG(x1, x2, x4, x5, x6)
PN32_IN_GAGG(x1, x2, x3, x4)  =  PN32_IN_GAGG(x1, x3, x4)
U88_GAGG(x1, x2, x3, x4, x5)  =  U88_GAGG(x1, x3, x4, x5)
U89_GAGG(x1, x2, x3, x4, x5)  =  U89_GAGG(x1, x2, x3, x4, x5)
PN33_IN_GGGG(x1, x2, x3, x4)  =  PN33_IN_GGGG(x1, x2, x3, x4)
U90_GGGG(x1, x2, x3, x4, x5)  =  U90_GGGG(x1, x2, x3, x4, x5)
U91_GGGG(x1, x2, x3, x4, x5)  =  U91_GGGG(x1, x2, x3, x4, x5)
NOATTACKN5_IN_GG(x1, x2)  =  NOATTACKN5_IN_GG(x1, x2)
U22_GG(x1, x2, x3, x4)  =  U22_GG(x1, x2, x3, x4)
PN6_IN_GGAAGG(x1, x2, x3, x4, x5, x6)  =  PN6_IN_GGAAGG(x1, x2, x5, x6)
U92_GGAAGG(x1, x2, x3, x4, x5, x6, x7)  =  U92_GGAAGG(x1, x2, x5, x6, x7)
U93_GGAAGG(x1, x2, x3, x4, x5, x6, x7)  =  U93_GGAAGG(x1, x2, x5, x6, x7)
PN34_IN_GAGAGG(x1, x2, x3, x4, x5, x6)  =  PN34_IN_GAGAGG(x1, x3, x5, x6)
U94_GAGAGG(x1, x2, x3, x4, x5, x6, x7)  =  U94_GAGAGG(x1, x3, x5, x6, x7)
ADDM_IN_GA(x1, x2)  =  ADDM_IN_GA(x1)
U11_GA(x1, x2, x3)  =  U11_GA(x1, x3)
U95_GAGAGG(x1, x2, x3, x4, x5, x6, x7)  =  U95_GAGAGG(x1, x2, x3, x5, x6, x7)
PN35_IN_GGAGGG(x1, x2, x3, x4, x5, x6)  =  PN35_IN_GGAGGG(x1, x2, x4, x5, x6)
U96_GGAGGG(x1, x2, x3, x4, x5, x6, x7)  =  U96_GGAGGG(x1, x2, x4, x5, x6, x7)
U97_GGAGGG(x1, x2, x3, x4, x5, x6, x7)  =  U97_GGAGGG(x1, x2, x4, x5, x6, x7)
PN36_IN_GAGGG(x1, x2, x3, x4, x5)  =  PN36_IN_GAGGG(x1, x3, x4, x5)
U98_GAGGG(x1, x2, x3, x4, x5, x6)  =  U98_GAGGG(x1, x3, x4, x5, x6)
U99_GAGGG(x1, x2, x3, x4, x5, x6)  =  U99_GAGGG(x1, x2, x3, x4, x5, x6)
PN37_IN_GGGGG(x1, x2, x3, x4, x5)  =  PN37_IN_GGGGG(x1, x2, x3, x4, x5)
U100_GGGGG(x1, x2, x3, x4, x5, x6)  =  U100_GGGGG(x1, x2, x3, x4, x5, x6)
U101_GGGGG(x1, x2, x3, x4, x5, x6)  =  U101_GGGGG(x1, x2, x3, x4, x5, x6)
NOATTACKN7_IN_GGG(x1, x2, x3)  =  NOATTACKN7_IN_GGG(x1, x2, x3)
U23_GGG(x1, x2, x3, x4, x5)  =  U23_GGG(x1, x2, x3, x4, x5)
PN8_IN_GGGAAG(x1, x2, x3, x4, x5, x6)  =  PN8_IN_GGGAAG(x1, x2, x3, x6)
U102_GGGAAG(x1, x2, x3, x4, x5, x6, x7)  =  U102_GGGAAG(x1, x2, x3, x6, x7)
U103_GGGAAG(x1, x2, x3, x4, x5, x6, x7)  =  U103_GGGAAG(x1, x2, x3, x6, x7)
PN38_IN_GGAGAG(x1, x2, x3, x4, x5, x6)  =  PN38_IN_GGAGAG(x1, x2, x4, x6)
U104_GGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U104_GGAGAG(x1, x2, x4, x6, x7)
ADDN_IN_GGA(x1, x2, x3)  =  ADDN_IN_GGA(x1, x2)
U12_GGA(x1, x2, x3, x4)  =  U12_GGA(x1, x2, x4)
U105_GGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U105_GGAGAG(x1, x2, x3, x4, x6, x7)
PN39_IN_GGGAGG(x1, x2, x3, x4, x5, x6)  =  PN39_IN_GGGAGG(x1, x2, x3, x5, x6)
U106_GGGAGG(x1, x2, x3, x4, x5, x6, x7)  =  U106_GGGAGG(x1, x2, x3, x5, x6, x7)
U107_GGGAGG(x1, x2, x3, x4, x5, x6, x7)  =  U107_GGGAGG(x1, x2, x3, x5, x6, x7)
PN40_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN40_IN_GGAGG(x1, x2, x4, x5)
U108_GGAGG(x1, x2, x3, x4, x5, x6)  =  U108_GGAGG(x1, x2, x4, x5, x6)
U109_GGAGG(x1, x2, x3, x4, x5, x6)  =  U109_GGAGG(x1, x2, x3, x4, x5, x6)
U31_GG(x1, x2, x3)  =  U31_GG(x1, x2, x3)
SAFET_IN_G(x1)  =  SAFET_IN_G(x1)
U16_G(x1, x2, x3)  =  U16_G(x1, x2, x3)

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

(4) Obligation:

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

QUEENSA_IN_A(.(T11, T12)) → U1_A(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
QUEENSA_IN_A(.(T11, T12)) → PB_IN_AGAA(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)
PB_IN_AGAA(T22, T15, T20, T21) → U24_AGAA(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
PB_IN_AGAA(T22, T15, T20, T21) → DELETEO_IN_AGA(T22, T15, T20)
DELETEO_IN_AGA(T48, T47, .(s(0), X57)) → U13_AGA(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
DELETEO_IN_AGA(T48, T47, .(s(0), X57)) → DELETEC_IN_AGA(T48, T47, X57)
DELETEC_IN_AGA(T72, .(T70, T71), .(T70, X86)) → U2_AGA(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
DELETEC_IN_AGA(T72, .(T70, T71), .(T70, X86)) → DELETEC_IN_AGA(T72, T71, X86)
U24_AGAA(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_AGAA(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
U24_AGAA(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → PN9_IN_GAG(T20, T21, T22)
PN9_IN_GAG(T20, T77, T22) → U26_GAG(T20, T77, T22, permD_in_ga(T20, T77))
PN9_IN_GAG(T20, T77, T22) → PERMD_IN_GA(T20, T77)
PERMD_IN_GA(.(T86, T87), .(T90, T91)) → U3_GA(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
PERMD_IN_GA(.(T86, T87), .(T90, T91)) → PE_IN_AGGAA(T90, T86, T87, X104, T91)
PE_IN_AGGAA(T90, T86, T87, T96, T97) → U28_AGGAA(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
PE_IN_AGGAA(T90, T86, T87, T96, T97) → DELETEC_IN_AGA(T90, .(T86, T87), T96)
U28_AGGAA(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_AGGAA(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U28_AGGAA(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → PERMD_IN_GA(T96, T97)
U26_GAG(T20, T77, T22, permD_out_ga(T20, T77)) → U27_GAG(T20, T77, T22, safeP_in_gg(T22, T77))
U26_GAG(T20, T77, T22, permD_out_ga(T20, T77)) → SAFEP_IN_GG(T22, T77)
SAFEP_IN_GG(T108, T109) → U14_GG(T108, T109, pQ_in_gg(T108, T109))
SAFEP_IN_GG(T108, T109) → PQ_IN_GG(T108, T109)
PQ_IN_GG(T108, T109) → U30_GG(T108, T109, noattackR_in_gg(T108, T109))
PQ_IN_GG(T108, T109) → NOATTACKR_IN_GG(T108, T109)
NOATTACKR_IN_GG(T125, .(T126, T127)) → U15_GG(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
NOATTACKR_IN_GG(T125, .(T126, T127)) → PS_IN_GGAAG(T125, T126, X155, X156, T127)
PS_IN_GGAAG(T125, T126, X155, X156, T127) → U32_GGAAG(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
PS_IN_GGAAG(T125, T126, X155, X156, T127) → NOTEQF_IN_GG(T125, T126)
NOTEQF_IN_GG(s(T146), s(T147)) → U4_GG(T146, T147, notEqF_in_gg(T146, T147))
NOTEQF_IN_GG(s(T146), s(T147)) → NOTEQF_IN_GG(T146, T147)
U32_GGAAG(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_GGAAG(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
U32_GGAAG(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → PN10_IN_GAGAG(T126, X155, T125, X156, T127)
PN10_IN_GAGAG(T126, T150, T125, X156, T127) → U34_GAGAG(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
PN10_IN_GAGAG(T126, T150, T125, X156, T127) → ADDG_IN_GA(T126, T150)
ADDG_IN_GA(s(T153), s(X199)) → U5_GA(T153, X199, addG_in_ga(T153, X199))
ADDG_IN_GA(s(T153), s(X199)) → ADDG_IN_GA(T153, X199)
U34_GAGAG(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_GAGAG(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
U34_GAGAG(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → PN11_IN_GGAGG(T125, T150, X156, T126, T127)
PN11_IN_GGAGG(T125, T150, X156, T126, T127) → U36_GGAGG(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
PN11_IN_GGAGG(T125, T150, X156, T126, T127) → NOTEQF_IN_GG(T125, T150)
U36_GGAGG(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_GGAGG(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
U36_GGAGG(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → PN12_IN_GAGG(T125, X156, T126, T127)
PN12_IN_GAGG(T125, T158, T126, T127) → U38_GAGG(T125, T158, T126, T127, addG_in_ga(T125, T158))
PN12_IN_GAGG(T125, T158, T126, T127) → ADDG_IN_GA(T125, T158)
U38_GAGG(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_GAGG(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
U38_GAGG(T125, T158, T126, T127, addG_out_ga(T125, T158)) → PN13_IN_GGGG(T126, T158, T125, T127)
PN13_IN_GGGG(T126, T158, T125, T127) → U40_GGGG(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
PN13_IN_GGGG(T126, T158, T125, T127) → NOTEQF_IN_GG(T126, T158)
U40_GGGG(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_GGGG(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
U40_GGGG(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → NOATTACKU_IN_GG(T125, T127)
NOATTACKU_IN_GG(T176, .(T177, T178)) → U17_GG(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
NOATTACKU_IN_GG(T176, .(T177, T178)) → PV_IN_GGAAG(T176, T177, X242, X243, T178)
PV_IN_GGAAG(T176, T177, X242, X243, T178) → U42_GGAAG(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
PV_IN_GGAAG(T176, T177, X242, X243, T178) → NOTEQF_IN_GG(T176, T177)
U42_GGAAG(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_GGAAG(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
U42_GGAAG(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → PN14_IN_GAGAG(T177, X242, T176, X243, T178)
PN14_IN_GAGAG(T177, T183, T176, X243, T178) → U44_GAGAG(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
PN14_IN_GAGAG(T177, T183, T176, X243, T178) → ADDH_IN_GA(T177, T183)
ADDH_IN_GA(s(T186), s(X268)) → U6_GA(T186, X268, addH_in_ga(T186, X268))
ADDH_IN_GA(s(T186), s(X268)) → ADDH_IN_GA(T186, X268)
U44_GAGAG(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_GAGAG(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
U44_GAGAG(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → PN15_IN_GGAGG(T176, T183, X243, T177, T178)
PN15_IN_GGAGG(T176, T183, X243, T177, T178) → U46_GGAGG(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
PN15_IN_GGAGG(T176, T183, X243, T177, T178) → NOTEQF_IN_GG(T176, T183)
U46_GGAGG(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_GGAGG(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
U46_GGAGG(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → PN16_IN_GAGG(T176, X243, T177, T178)
PN16_IN_GAGG(T176, T191, T177, T178) → U48_GAGG(T176, T191, T177, T178, addH_in_ga(T176, T191))
PN16_IN_GAGG(T176, T191, T177, T178) → ADDH_IN_GA(T176, T191)
U48_GAGG(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_GAGG(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
U48_GAGG(T176, T191, T177, T178, addH_out_ga(T176, T191)) → PN17_IN_GGGG(T177, T191, T176, T178)
PN17_IN_GGGG(T177, T191, T176, T178) → U50_GGGG(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
PN17_IN_GGGG(T177, T191, T176, T178) → NOTEQF_IN_GG(T177, T191)
U50_GGGG(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_GGGG(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
U50_GGGG(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → NOATTACKW_IN_GG(T176, T178)
NOATTACKW_IN_GG(T209, .(T210, T211)) → U18_GG(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
NOATTACKW_IN_GG(T209, .(T210, T211)) → PX_IN_GGAAG(T209, T210, X311, X312, T211)
PX_IN_GGAAG(T209, T210, X311, X312, T211) → U52_GGAAG(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
PX_IN_GGAAG(T209, T210, X311, X312, T211) → NOTEQF_IN_GG(T209, T210)
U52_GGAAG(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_GGAAG(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
U52_GGAAG(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → PN18_IN_GAGAG(T210, X311, T209, X312, T211)
PN18_IN_GAGAG(T210, T216, T209, X312, T211) → U54_GAGAG(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
PN18_IN_GAGAG(T210, T216, T209, X312, T211) → ADDI_IN_GA(T210, T216)
ADDI_IN_GA(s(T219), s(X337)) → U7_GA(T219, X337, addI_in_ga(T219, X337))
ADDI_IN_GA(s(T219), s(X337)) → ADDI_IN_GA(T219, X337)
U54_GAGAG(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_GAGAG(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
U54_GAGAG(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → PN19_IN_GGAGG(T209, T216, X312, T210, T211)
PN19_IN_GGAGG(T209, T216, X312, T210, T211) → U56_GGAGG(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
PN19_IN_GGAGG(T209, T216, X312, T210, T211) → NOTEQF_IN_GG(T209, T216)
U56_GGAGG(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_GGAGG(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
U56_GGAGG(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → PN20_IN_GAGG(T209, X312, T210, T211)
PN20_IN_GAGG(T209, T224, T210, T211) → U58_GAGG(T209, T224, T210, T211, addI_in_ga(T209, T224))
PN20_IN_GAGG(T209, T224, T210, T211) → ADDI_IN_GA(T209, T224)
U58_GAGG(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_GAGG(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
U58_GAGG(T209, T224, T210, T211, addI_out_ga(T209, T224)) → PN21_IN_GGGG(T210, T224, T209, T211)
PN21_IN_GGGG(T210, T224, T209, T211) → U60_GGGG(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
PN21_IN_GGGG(T210, T224, T209, T211) → NOTEQF_IN_GG(T210, T224)
U60_GGGG(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_GGGG(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
U60_GGGG(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → NOATTACKY_IN_GG(T209, T211)
NOATTACKY_IN_GG(T242, .(T243, T244)) → U19_GG(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
NOATTACKY_IN_GG(T242, .(T243, T244)) → PZ_IN_GGAAG(T242, T243, X380, X381, T244)
PZ_IN_GGAAG(T242, T243, X380, X381, T244) → U62_GGAAG(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
PZ_IN_GGAAG(T242, T243, X380, X381, T244) → NOTEQF_IN_GG(T242, T243)
U62_GGAAG(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_GGAAG(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
U62_GGAAG(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → PN22_IN_GAGAG(T243, X380, T242, X381, T244)
PN22_IN_GAGAG(T243, T249, T242, X381, T244) → U64_GAGAG(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
PN22_IN_GAGAG(T243, T249, T242, X381, T244) → ADDJ_IN_GA(T243, T249)
ADDJ_IN_GA(s(T252), s(X406)) → U8_GA(T252, X406, addJ_in_ga(T252, X406))
ADDJ_IN_GA(s(T252), s(X406)) → ADDJ_IN_GA(T252, X406)
U64_GAGAG(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_GAGAG(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
U64_GAGAG(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → PN23_IN_GGAGG(T242, T249, X381, T243, T244)
PN23_IN_GGAGG(T242, T249, X381, T243, T244) → U66_GGAGG(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
PN23_IN_GGAGG(T242, T249, X381, T243, T244) → NOTEQF_IN_GG(T242, T249)
U66_GGAGG(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_GGAGG(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
U66_GGAGG(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → PN24_IN_GAGG(T242, X381, T243, T244)
PN24_IN_GAGG(T242, T257, T243, T244) → U68_GAGG(T242, T257, T243, T244, addJ_in_ga(T242, T257))
PN24_IN_GAGG(T242, T257, T243, T244) → ADDJ_IN_GA(T242, T257)
U68_GAGG(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_GAGG(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
U68_GAGG(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → PN25_IN_GGGG(T243, T257, T242, T244)
PN25_IN_GGGG(T243, T257, T242, T244) → U70_GGGG(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
PN25_IN_GGGG(T243, T257, T242, T244) → NOTEQF_IN_GG(T243, T257)
U70_GGGG(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_GGGG(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
U70_GGGG(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → NOATTACKN1_IN_GG(T242, T244)
NOATTACKN1_IN_GG(T275, .(T276, T277)) → U20_GG(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
NOATTACKN1_IN_GG(T275, .(T276, T277)) → PN2_IN_GGAAG(T275, T276, X449, X450, T277)
PN2_IN_GGAAG(T275, T276, X449, X450, T277) → U72_GGAAG(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
PN2_IN_GGAAG(T275, T276, X449, X450, T277) → NOTEQF_IN_GG(T275, T276)
U72_GGAAG(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_GGAAG(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
U72_GGAAG(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → PN26_IN_GAGAG(T276, X449, T275, X450, T277)
PN26_IN_GAGAG(T276, T282, T275, X450, T277) → U74_GAGAG(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
PN26_IN_GAGAG(T276, T282, T275, X450, T277) → ADDK_IN_GA(T276, T282)
ADDK_IN_GA(s(T285), s(X475)) → U9_GA(T285, X475, addK_in_ga(T285, X475))
ADDK_IN_GA(s(T285), s(X475)) → ADDK_IN_GA(T285, X475)
U74_GAGAG(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_GAGAG(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
U74_GAGAG(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → PN27_IN_GGAGG(T275, T282, X450, T276, T277)
PN27_IN_GGAGG(T275, T282, X450, T276, T277) → U76_GGAGG(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
PN27_IN_GGAGG(T275, T282, X450, T276, T277) → NOTEQF_IN_GG(T275, T282)
U76_GGAGG(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_GGAGG(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
U76_GGAGG(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → PN28_IN_GAGG(T275, X450, T276, T277)
PN28_IN_GAGG(T275, T290, T276, T277) → U78_GAGG(T275, T290, T276, T277, addK_in_ga(T275, T290))
PN28_IN_GAGG(T275, T290, T276, T277) → ADDK_IN_GA(T275, T290)
U78_GAGG(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_GAGG(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
U78_GAGG(T275, T290, T276, T277, addK_out_ga(T275, T290)) → PN29_IN_GGGG(T276, T290, T275, T277)
PN29_IN_GGGG(T276, T290, T275, T277) → U80_GGGG(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
PN29_IN_GGGG(T276, T290, T275, T277) → NOTEQF_IN_GG(T276, T290)
U80_GGGG(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_GGGG(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
U80_GGGG(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → NOATTACKN3_IN_GG(T275, T277)
NOATTACKN3_IN_GG(T308, .(T309, T310)) → U21_GG(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
NOATTACKN3_IN_GG(T308, .(T309, T310)) → PN4_IN_GGAAG(T308, T309, X518, X519, T310)
PN4_IN_GGAAG(T308, T309, X518, X519, T310) → U82_GGAAG(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
PN4_IN_GGAAG(T308, T309, X518, X519, T310) → NOTEQF_IN_GG(T308, T309)
U82_GGAAG(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_GGAAG(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
U82_GGAAG(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → PN30_IN_GAGAG(T309, X518, T308, X519, T310)
PN30_IN_GAGAG(T309, T315, T308, X519, T310) → U84_GAGAG(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
PN30_IN_GAGAG(T309, T315, T308, X519, T310) → ADDL_IN_GA(T309, T315)
ADDL_IN_GA(s(T318), s(X544)) → U10_GA(T318, X544, addL_in_ga(T318, X544))
ADDL_IN_GA(s(T318), s(X544)) → ADDL_IN_GA(T318, X544)
U84_GAGAG(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_GAGAG(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
U84_GAGAG(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → PN31_IN_GGAGG(T308, T315, X519, T309, T310)
PN31_IN_GGAGG(T308, T315, X519, T309, T310) → U86_GGAGG(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
PN31_IN_GGAGG(T308, T315, X519, T309, T310) → NOTEQF_IN_GG(T308, T315)
U86_GGAGG(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_GGAGG(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
U86_GGAGG(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → PN32_IN_GAGG(T308, X519, T309, T310)
PN32_IN_GAGG(T308, T323, T309, T310) → U88_GAGG(T308, T323, T309, T310, addL_in_ga(T308, T323))
PN32_IN_GAGG(T308, T323, T309, T310) → ADDL_IN_GA(T308, T323)
U88_GAGG(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_GAGG(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
U88_GAGG(T308, T323, T309, T310, addL_out_ga(T308, T323)) → PN33_IN_GGGG(T309, T323, T308, T310)
PN33_IN_GGGG(T309, T323, T308, T310) → U90_GGGG(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
PN33_IN_GGGG(T309, T323, T308, T310) → NOTEQF_IN_GG(T309, T323)
U90_GGGG(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_GGGG(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
U90_GGGG(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → NOATTACKN5_IN_GG(T308, T310)
NOATTACKN5_IN_GG(T341, .(T342, T343)) → U22_GG(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
NOATTACKN5_IN_GG(T341, .(T342, T343)) → PN6_IN_GGAAGG(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))
PN6_IN_GGAAGG(T341, T342, X587, X588, T343, T346) → U92_GGAAGG(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
PN6_IN_GGAAGG(T341, T342, X587, X588, T343, T346) → NOTEQF_IN_GG(T341, T342)
U92_GGAAGG(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_GGAAGG(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
U92_GGAAGG(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → PN34_IN_GAGAGG(T342, X587, T341, X588, T343, T346)
PN34_IN_GAGAGG(T342, T351, T341, X588, T343, T346) → U94_GAGAGG(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
PN34_IN_GAGAGG(T342, T351, T341, X588, T343, T346) → ADDM_IN_GA(T342, T351)
ADDM_IN_GA(s(T354), s(X615)) → U11_GA(T354, X615, addM_in_ga(T354, X615))
ADDM_IN_GA(s(T354), s(X615)) → ADDM_IN_GA(T354, X615)
U94_GAGAGG(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_GAGAGG(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
U94_GAGAGG(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → PN35_IN_GGAGGG(T341, T351, X588, T342, T343, T346)
PN35_IN_GGAGGG(T341, T351, X588, T342, T343, T346) → U96_GGAGGG(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
PN35_IN_GGAGGG(T341, T351, X588, T342, T343, T346) → NOTEQF_IN_GG(T341, T351)
U96_GGAGGG(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_GGAGGG(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
U96_GGAGGG(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → PN36_IN_GAGGG(T341, X588, T342, T343, T346)
PN36_IN_GAGGG(T341, T359, T342, T343, T346) → U98_GAGGG(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
PN36_IN_GAGGG(T341, T359, T342, T343, T346) → ADDM_IN_GA(T341, T359)
U98_GAGGG(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_GAGGG(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
U98_GAGGG(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → PN37_IN_GGGGG(T342, T359, T341, T343, T346)
PN37_IN_GGGGG(T342, T359, T341, T343, T346) → U100_GGGGG(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
PN37_IN_GGGGG(T342, T359, T341, T343, T346) → NOTEQF_IN_GG(T342, T359)
U100_GGGGG(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_GGGGG(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
U100_GGGGG(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → NOATTACKN7_IN_GGG(T341, T343, T346)
NOATTACKN7_IN_GGG(T386, .(T387, T388), T389) → U23_GGG(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
NOATTACKN7_IN_GGG(T386, .(T387, T388), T389) → PN8_IN_GGGAAG(T386, T387, T389, X658, X659, T388)
PN8_IN_GGGAAG(T386, T387, T389, X658, X659, T388) → U102_GGGAAG(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
PN8_IN_GGGAAG(T386, T387, T389, X658, X659, T388) → NOTEQF_IN_GG(T386, T387)
U102_GGGAAG(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_GGGAAG(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
U102_GGGAAG(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → PN38_IN_GGAGAG(T387, T389, X658, T386, X659, T388)
PN38_IN_GGAGAG(T387, T389, T396, T386, X659, T388) → U104_GGAGAG(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
PN38_IN_GGAGAG(T387, T389, T396, T386, X659, T388) → ADDN_IN_GGA(T387, T389, T396)
ADDN_IN_GGA(s(T408), T409, s(X684)) → U12_GGA(T408, T409, X684, addN_in_gga(T408, T409, X684))
ADDN_IN_GGA(s(T408), T409, s(X684)) → ADDN_IN_GGA(T408, T409, X684)
U104_GGAGAG(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_GGAGAG(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
U104_GGAGAG(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → PN39_IN_GGGAGG(T386, T396, T389, X659, T387, T388)
PN39_IN_GGGAGG(T386, T396, T389, X659, T387, T388) → U106_GGGAGG(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
PN39_IN_GGGAGG(T386, T396, T389, X659, T387, T388) → NOTEQF_IN_GG(T386, T396)
U106_GGGAGG(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_GGGAGG(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
U106_GGGAGG(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → PN40_IN_GGAGG(T386, T389, X659, T387, T388)
PN40_IN_GGAGG(T386, T389, T418, T387, T388) → U108_GGAGG(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
PN40_IN_GGAGG(T386, T389, T418, T387, T388) → ADDN_IN_GGA(T386, T389, T418)
U108_GGAGG(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_GGAGG(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U108_GGAGG(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → PN37_IN_GGGGG(T387, T418, T386, T388, s(T389))
U30_GG(T108, T109, noattackR_out_gg(T108, T109)) → U31_GG(T108, T109, safeT_in_g(T109))
U30_GG(T108, T109, noattackR_out_gg(T108, T109)) → SAFET_IN_G(T109)
SAFET_IN_G(.(T427, T428)) → U16_G(T427, T428, pQ_in_gg(T427, T428))
SAFET_IN_G(.(T427, T428)) → PQ_IN_GG(T427, T428)

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
QUEENSA_IN_A(x1)  =  QUEENSA_IN_A
U1_A(x1, x2, x3)  =  U1_A(x3)
PB_IN_AGAA(x1, x2, x3, x4)  =  PB_IN_AGAA(x2)
U24_AGAA(x1, x2, x3, x4, x5)  =  U24_AGAA(x2, x5)
DELETEO_IN_AGA(x1, x2, x3)  =  DELETEO_IN_AGA(x2)
U13_AGA(x1, x2, x3, x4)  =  U13_AGA(x2, x4)
DELETEC_IN_AGA(x1, x2, x3)  =  DELETEC_IN_AGA(x2)
U2_AGA(x1, x2, x3, x4, x5)  =  U2_AGA(x2, x3, x5)
U25_AGAA(x1, x2, x3, x4, x5)  =  U25_AGAA(x1, x2, x3, x5)
PN9_IN_GAG(x1, x2, x3)  =  PN9_IN_GAG(x1, x3)
U26_GAG(x1, x2, x3, x4)  =  U26_GAG(x1, x3, x4)
PERMD_IN_GA(x1, x2)  =  PERMD_IN_GA(x1)
U3_GA(x1, x2, x3, x4, x5)  =  U3_GA(x1, x2, x5)
PE_IN_AGGAA(x1, x2, x3, x4, x5)  =  PE_IN_AGGAA(x2, x3)
U28_AGGAA(x1, x2, x3, x4, x5, x6)  =  U28_AGGAA(x2, x3, x6)
U29_AGGAA(x1, x2, x3, x4, x5, x6)  =  U29_AGGAA(x1, x2, x3, x4, x6)
U27_GAG(x1, x2, x3, x4)  =  U27_GAG(x1, x2, x3, x4)
SAFEP_IN_GG(x1, x2)  =  SAFEP_IN_GG(x1, x2)
U14_GG(x1, x2, x3)  =  U14_GG(x1, x2, x3)
PQ_IN_GG(x1, x2)  =  PQ_IN_GG(x1, x2)
U30_GG(x1, x2, x3)  =  U30_GG(x1, x2, x3)
NOATTACKR_IN_GG(x1, x2)  =  NOATTACKR_IN_GG(x1, x2)
U15_GG(x1, x2, x3, x4)  =  U15_GG(x1, x2, x3, x4)
PS_IN_GGAAG(x1, x2, x3, x4, x5)  =  PS_IN_GGAAG(x1, x2, x5)
U32_GGAAG(x1, x2, x3, x4, x5, x6)  =  U32_GGAAG(x1, x2, x5, x6)
NOTEQF_IN_GG(x1, x2)  =  NOTEQF_IN_GG(x1, x2)
U4_GG(x1, x2, x3)  =  U4_GG(x1, x2, x3)
U33_GGAAG(x1, x2, x3, x4, x5, x6)  =  U33_GGAAG(x1, x2, x5, x6)
PN10_IN_GAGAG(x1, x2, x3, x4, x5)  =  PN10_IN_GAGAG(x1, x3, x5)
U34_GAGAG(x1, x2, x3, x4, x5, x6)  =  U34_GAGAG(x1, x3, x5, x6)
ADDG_IN_GA(x1, x2)  =  ADDG_IN_GA(x1)
U5_GA(x1, x2, x3)  =  U5_GA(x1, x3)
U35_GAGAG(x1, x2, x3, x4, x5, x6)  =  U35_GAGAG(x1, x2, x3, x5, x6)
PN11_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN11_IN_GGAGG(x1, x2, x4, x5)
U36_GGAGG(x1, x2, x3, x4, x5, x6)  =  U36_GGAGG(x1, x2, x4, x5, x6)
U37_GGAGG(x1, x2, x3, x4, x5, x6)  =  U37_GGAGG(x1, x2, x4, x5, x6)
PN12_IN_GAGG(x1, x2, x3, x4)  =  PN12_IN_GAGG(x1, x3, x4)
U38_GAGG(x1, x2, x3, x4, x5)  =  U38_GAGG(x1, x3, x4, x5)
U39_GAGG(x1, x2, x3, x4, x5)  =  U39_GAGG(x1, x2, x3, x4, x5)
PN13_IN_GGGG(x1, x2, x3, x4)  =  PN13_IN_GGGG(x1, x2, x3, x4)
U40_GGGG(x1, x2, x3, x4, x5)  =  U40_GGGG(x1, x2, x3, x4, x5)
U41_GGGG(x1, x2, x3, x4, x5)  =  U41_GGGG(x1, x2, x3, x4, x5)
NOATTACKU_IN_GG(x1, x2)  =  NOATTACKU_IN_GG(x1, x2)
U17_GG(x1, x2, x3, x4)  =  U17_GG(x1, x2, x3, x4)
PV_IN_GGAAG(x1, x2, x3, x4, x5)  =  PV_IN_GGAAG(x1, x2, x5)
U42_GGAAG(x1, x2, x3, x4, x5, x6)  =  U42_GGAAG(x1, x2, x5, x6)
U43_GGAAG(x1, x2, x3, x4, x5, x6)  =  U43_GGAAG(x1, x2, x5, x6)
PN14_IN_GAGAG(x1, x2, x3, x4, x5)  =  PN14_IN_GAGAG(x1, x3, x5)
U44_GAGAG(x1, x2, x3, x4, x5, x6)  =  U44_GAGAG(x1, x3, x5, x6)
ADDH_IN_GA(x1, x2)  =  ADDH_IN_GA(x1)
U6_GA(x1, x2, x3)  =  U6_GA(x1, x3)
U45_GAGAG(x1, x2, x3, x4, x5, x6)  =  U45_GAGAG(x1, x2, x3, x5, x6)
PN15_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN15_IN_GGAGG(x1, x2, x4, x5)
U46_GGAGG(x1, x2, x3, x4, x5, x6)  =  U46_GGAGG(x1, x2, x4, x5, x6)
U47_GGAGG(x1, x2, x3, x4, x5, x6)  =  U47_GGAGG(x1, x2, x4, x5, x6)
PN16_IN_GAGG(x1, x2, x3, x4)  =  PN16_IN_GAGG(x1, x3, x4)
U48_GAGG(x1, x2, x3, x4, x5)  =  U48_GAGG(x1, x3, x4, x5)
U49_GAGG(x1, x2, x3, x4, x5)  =  U49_GAGG(x1, x2, x3, x4, x5)
PN17_IN_GGGG(x1, x2, x3, x4)  =  PN17_IN_GGGG(x1, x2, x3, x4)
U50_GGGG(x1, x2, x3, x4, x5)  =  U50_GGGG(x1, x2, x3, x4, x5)
U51_GGGG(x1, x2, x3, x4, x5)  =  U51_GGGG(x1, x2, x3, x4, x5)
NOATTACKW_IN_GG(x1, x2)  =  NOATTACKW_IN_GG(x1, x2)
U18_GG(x1, x2, x3, x4)  =  U18_GG(x1, x2, x3, x4)
PX_IN_GGAAG(x1, x2, x3, x4, x5)  =  PX_IN_GGAAG(x1, x2, x5)
U52_GGAAG(x1, x2, x3, x4, x5, x6)  =  U52_GGAAG(x1, x2, x5, x6)
U53_GGAAG(x1, x2, x3, x4, x5, x6)  =  U53_GGAAG(x1, x2, x5, x6)
PN18_IN_GAGAG(x1, x2, x3, x4, x5)  =  PN18_IN_GAGAG(x1, x3, x5)
U54_GAGAG(x1, x2, x3, x4, x5, x6)  =  U54_GAGAG(x1, x3, x5, x6)
ADDI_IN_GA(x1, x2)  =  ADDI_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x1, x3)
U55_GAGAG(x1, x2, x3, x4, x5, x6)  =  U55_GAGAG(x1, x2, x3, x5, x6)
PN19_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN19_IN_GGAGG(x1, x2, x4, x5)
U56_GGAGG(x1, x2, x3, x4, x5, x6)  =  U56_GGAGG(x1, x2, x4, x5, x6)
U57_GGAGG(x1, x2, x3, x4, x5, x6)  =  U57_GGAGG(x1, x2, x4, x5, x6)
PN20_IN_GAGG(x1, x2, x3, x4)  =  PN20_IN_GAGG(x1, x3, x4)
U58_GAGG(x1, x2, x3, x4, x5)  =  U58_GAGG(x1, x3, x4, x5)
U59_GAGG(x1, x2, x3, x4, x5)  =  U59_GAGG(x1, x2, x3, x4, x5)
PN21_IN_GGGG(x1, x2, x3, x4)  =  PN21_IN_GGGG(x1, x2, x3, x4)
U60_GGGG(x1, x2, x3, x4, x5)  =  U60_GGGG(x1, x2, x3, x4, x5)
U61_GGGG(x1, x2, x3, x4, x5)  =  U61_GGGG(x1, x2, x3, x4, x5)
NOATTACKY_IN_GG(x1, x2)  =  NOATTACKY_IN_GG(x1, x2)
U19_GG(x1, x2, x3, x4)  =  U19_GG(x1, x2, x3, x4)
PZ_IN_GGAAG(x1, x2, x3, x4, x5)  =  PZ_IN_GGAAG(x1, x2, x5)
U62_GGAAG(x1, x2, x3, x4, x5, x6)  =  U62_GGAAG(x1, x2, x5, x6)
U63_GGAAG(x1, x2, x3, x4, x5, x6)  =  U63_GGAAG(x1, x2, x5, x6)
PN22_IN_GAGAG(x1, x2, x3, x4, x5)  =  PN22_IN_GAGAG(x1, x3, x5)
U64_GAGAG(x1, x2, x3, x4, x5, x6)  =  U64_GAGAG(x1, x3, x5, x6)
ADDJ_IN_GA(x1, x2)  =  ADDJ_IN_GA(x1)
U8_GA(x1, x2, x3)  =  U8_GA(x1, x3)
U65_GAGAG(x1, x2, x3, x4, x5, x6)  =  U65_GAGAG(x1, x2, x3, x5, x6)
PN23_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN23_IN_GGAGG(x1, x2, x4, x5)
U66_GGAGG(x1, x2, x3, x4, x5, x6)  =  U66_GGAGG(x1, x2, x4, x5, x6)
U67_GGAGG(x1, x2, x3, x4, x5, x6)  =  U67_GGAGG(x1, x2, x4, x5, x6)
PN24_IN_GAGG(x1, x2, x3, x4)  =  PN24_IN_GAGG(x1, x3, x4)
U68_GAGG(x1, x2, x3, x4, x5)  =  U68_GAGG(x1, x3, x4, x5)
U69_GAGG(x1, x2, x3, x4, x5)  =  U69_GAGG(x1, x2, x3, x4, x5)
PN25_IN_GGGG(x1, x2, x3, x4)  =  PN25_IN_GGGG(x1, x2, x3, x4)
U70_GGGG(x1, x2, x3, x4, x5)  =  U70_GGGG(x1, x2, x3, x4, x5)
U71_GGGG(x1, x2, x3, x4, x5)  =  U71_GGGG(x1, x2, x3, x4, x5)
NOATTACKN1_IN_GG(x1, x2)  =  NOATTACKN1_IN_GG(x1, x2)
U20_GG(x1, x2, x3, x4)  =  U20_GG(x1, x2, x3, x4)
PN2_IN_GGAAG(x1, x2, x3, x4, x5)  =  PN2_IN_GGAAG(x1, x2, x5)
U72_GGAAG(x1, x2, x3, x4, x5, x6)  =  U72_GGAAG(x1, x2, x5, x6)
U73_GGAAG(x1, x2, x3, x4, x5, x6)  =  U73_GGAAG(x1, x2, x5, x6)
PN26_IN_GAGAG(x1, x2, x3, x4, x5)  =  PN26_IN_GAGAG(x1, x3, x5)
U74_GAGAG(x1, x2, x3, x4, x5, x6)  =  U74_GAGAG(x1, x3, x5, x6)
ADDK_IN_GA(x1, x2)  =  ADDK_IN_GA(x1)
U9_GA(x1, x2, x3)  =  U9_GA(x1, x3)
U75_GAGAG(x1, x2, x3, x4, x5, x6)  =  U75_GAGAG(x1, x2, x3, x5, x6)
PN27_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN27_IN_GGAGG(x1, x2, x4, x5)
U76_GGAGG(x1, x2, x3, x4, x5, x6)  =  U76_GGAGG(x1, x2, x4, x5, x6)
U77_GGAGG(x1, x2, x3, x4, x5, x6)  =  U77_GGAGG(x1, x2, x4, x5, x6)
PN28_IN_GAGG(x1, x2, x3, x4)  =  PN28_IN_GAGG(x1, x3, x4)
U78_GAGG(x1, x2, x3, x4, x5)  =  U78_GAGG(x1, x3, x4, x5)
U79_GAGG(x1, x2, x3, x4, x5)  =  U79_GAGG(x1, x2, x3, x4, x5)
PN29_IN_GGGG(x1, x2, x3, x4)  =  PN29_IN_GGGG(x1, x2, x3, x4)
U80_GGGG(x1, x2, x3, x4, x5)  =  U80_GGGG(x1, x2, x3, x4, x5)
U81_GGGG(x1, x2, x3, x4, x5)  =  U81_GGGG(x1, x2, x3, x4, x5)
NOATTACKN3_IN_GG(x1, x2)  =  NOATTACKN3_IN_GG(x1, x2)
U21_GG(x1, x2, x3, x4)  =  U21_GG(x1, x2, x3, x4)
PN4_IN_GGAAG(x1, x2, x3, x4, x5)  =  PN4_IN_GGAAG(x1, x2, x5)
U82_GGAAG(x1, x2, x3, x4, x5, x6)  =  U82_GGAAG(x1, x2, x5, x6)
U83_GGAAG(x1, x2, x3, x4, x5, x6)  =  U83_GGAAG(x1, x2, x5, x6)
PN30_IN_GAGAG(x1, x2, x3, x4, x5)  =  PN30_IN_GAGAG(x1, x3, x5)
U84_GAGAG(x1, x2, x3, x4, x5, x6)  =  U84_GAGAG(x1, x3, x5, x6)
ADDL_IN_GA(x1, x2)  =  ADDL_IN_GA(x1)
U10_GA(x1, x2, x3)  =  U10_GA(x1, x3)
U85_GAGAG(x1, x2, x3, x4, x5, x6)  =  U85_GAGAG(x1, x2, x3, x5, x6)
PN31_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN31_IN_GGAGG(x1, x2, x4, x5)
U86_GGAGG(x1, x2, x3, x4, x5, x6)  =  U86_GGAGG(x1, x2, x4, x5, x6)
U87_GGAGG(x1, x2, x3, x4, x5, x6)  =  U87_GGAGG(x1, x2, x4, x5, x6)
PN32_IN_GAGG(x1, x2, x3, x4)  =  PN32_IN_GAGG(x1, x3, x4)
U88_GAGG(x1, x2, x3, x4, x5)  =  U88_GAGG(x1, x3, x4, x5)
U89_GAGG(x1, x2, x3, x4, x5)  =  U89_GAGG(x1, x2, x3, x4, x5)
PN33_IN_GGGG(x1, x2, x3, x4)  =  PN33_IN_GGGG(x1, x2, x3, x4)
U90_GGGG(x1, x2, x3, x4, x5)  =  U90_GGGG(x1, x2, x3, x4, x5)
U91_GGGG(x1, x2, x3, x4, x5)  =  U91_GGGG(x1, x2, x3, x4, x5)
NOATTACKN5_IN_GG(x1, x2)  =  NOATTACKN5_IN_GG(x1, x2)
U22_GG(x1, x2, x3, x4)  =  U22_GG(x1, x2, x3, x4)
PN6_IN_GGAAGG(x1, x2, x3, x4, x5, x6)  =  PN6_IN_GGAAGG(x1, x2, x5, x6)
U92_GGAAGG(x1, x2, x3, x4, x5, x6, x7)  =  U92_GGAAGG(x1, x2, x5, x6, x7)
U93_GGAAGG(x1, x2, x3, x4, x5, x6, x7)  =  U93_GGAAGG(x1, x2, x5, x6, x7)
PN34_IN_GAGAGG(x1, x2, x3, x4, x5, x6)  =  PN34_IN_GAGAGG(x1, x3, x5, x6)
U94_GAGAGG(x1, x2, x3, x4, x5, x6, x7)  =  U94_GAGAGG(x1, x3, x5, x6, x7)
ADDM_IN_GA(x1, x2)  =  ADDM_IN_GA(x1)
U11_GA(x1, x2, x3)  =  U11_GA(x1, x3)
U95_GAGAGG(x1, x2, x3, x4, x5, x6, x7)  =  U95_GAGAGG(x1, x2, x3, x5, x6, x7)
PN35_IN_GGAGGG(x1, x2, x3, x4, x5, x6)  =  PN35_IN_GGAGGG(x1, x2, x4, x5, x6)
U96_GGAGGG(x1, x2, x3, x4, x5, x6, x7)  =  U96_GGAGGG(x1, x2, x4, x5, x6, x7)
U97_GGAGGG(x1, x2, x3, x4, x5, x6, x7)  =  U97_GGAGGG(x1, x2, x4, x5, x6, x7)
PN36_IN_GAGGG(x1, x2, x3, x4, x5)  =  PN36_IN_GAGGG(x1, x3, x4, x5)
U98_GAGGG(x1, x2, x3, x4, x5, x6)  =  U98_GAGGG(x1, x3, x4, x5, x6)
U99_GAGGG(x1, x2, x3, x4, x5, x6)  =  U99_GAGGG(x1, x2, x3, x4, x5, x6)
PN37_IN_GGGGG(x1, x2, x3, x4, x5)  =  PN37_IN_GGGGG(x1, x2, x3, x4, x5)
U100_GGGGG(x1, x2, x3, x4, x5, x6)  =  U100_GGGGG(x1, x2, x3, x4, x5, x6)
U101_GGGGG(x1, x2, x3, x4, x5, x6)  =  U101_GGGGG(x1, x2, x3, x4, x5, x6)
NOATTACKN7_IN_GGG(x1, x2, x3)  =  NOATTACKN7_IN_GGG(x1, x2, x3)
U23_GGG(x1, x2, x3, x4, x5)  =  U23_GGG(x1, x2, x3, x4, x5)
PN8_IN_GGGAAG(x1, x2, x3, x4, x5, x6)  =  PN8_IN_GGGAAG(x1, x2, x3, x6)
U102_GGGAAG(x1, x2, x3, x4, x5, x6, x7)  =  U102_GGGAAG(x1, x2, x3, x6, x7)
U103_GGGAAG(x1, x2, x3, x4, x5, x6, x7)  =  U103_GGGAAG(x1, x2, x3, x6, x7)
PN38_IN_GGAGAG(x1, x2, x3, x4, x5, x6)  =  PN38_IN_GGAGAG(x1, x2, x4, x6)
U104_GGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U104_GGAGAG(x1, x2, x4, x6, x7)
ADDN_IN_GGA(x1, x2, x3)  =  ADDN_IN_GGA(x1, x2)
U12_GGA(x1, x2, x3, x4)  =  U12_GGA(x1, x2, x4)
U105_GGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U105_GGAGAG(x1, x2, x3, x4, x6, x7)
PN39_IN_GGGAGG(x1, x2, x3, x4, x5, x6)  =  PN39_IN_GGGAGG(x1, x2, x3, x5, x6)
U106_GGGAGG(x1, x2, x3, x4, x5, x6, x7)  =  U106_GGGAGG(x1, x2, x3, x5, x6, x7)
U107_GGGAGG(x1, x2, x3, x4, x5, x6, x7)  =  U107_GGGAGG(x1, x2, x3, x5, x6, x7)
PN40_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN40_IN_GGAGG(x1, x2, x4, x5)
U108_GGAGG(x1, x2, x3, x4, x5, x6)  =  U108_GGAGG(x1, x2, x4, x5, x6)
U109_GGAGG(x1, x2, x3, x4, x5, x6)  =  U109_GGAGG(x1, x2, x3, x4, x5, x6)
U31_GG(x1, x2, x3)  =  U31_GG(x1, x2, x3)
SAFET_IN_G(x1)  =  SAFET_IN_G(x1)
U16_G(x1, x2, x3)  =  U16_G(x1, x2, x3)

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

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 13 SCCs with 191 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

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

ADDN_IN_GGA(s(T408), T409, s(X684)) → ADDN_IN_GGA(T408, T409, X684)

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
ADDN_IN_GGA(x1, x2, x3)  =  ADDN_IN_GGA(x1, x2)

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

(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:

ADDN_IN_GGA(s(T408), T409, s(X684)) → ADDN_IN_GGA(T408, T409, X684)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
ADDN_IN_GGA(x1, x2, x3)  =  ADDN_IN_GGA(x1, x2)

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:

ADDN_IN_GGA(s(T408), T409) → ADDN_IN_GGA(T408, T409)

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:

• ADDN_IN_GGA(s(T408), T409) → ADDN_IN_GGA(T408, T409)
  The graph contains the following edges 1 > 1, 2 >= 2

(13) YES

(14) Obligation:

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

ADDM_IN_GA(s(T354), s(X615)) → ADDM_IN_GA(T354, X615)

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
ADDM_IN_GA(x1, x2)  =  ADDM_IN_GA(x1)

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

(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:

ADDM_IN_GA(s(T354), s(X615)) → ADDM_IN_GA(T354, X615)

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

ADDM_IN_GA(s(T354)) → ADDM_IN_GA(T354)

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:

• ADDM_IN_GA(s(T354)) → ADDM_IN_GA(T354)
  The graph contains the following edges 1 > 1

(20) YES

(21) Obligation:

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

ADDL_IN_GA(s(T318), s(X544)) → ADDL_IN_GA(T318, X544)

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
ADDL_IN_GA(x1, x2)  =  ADDL_IN_GA(x1)

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

(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:

ADDL_IN_GA(s(T318), s(X544)) → ADDL_IN_GA(T318, X544)

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

ADDL_IN_GA(s(T318)) → ADDL_IN_GA(T318)

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:

• ADDL_IN_GA(s(T318)) → ADDL_IN_GA(T318)
  The graph contains the following edges 1 > 1

(27) YES

(28) Obligation:

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

ADDK_IN_GA(s(T285), s(X475)) → ADDK_IN_GA(T285, X475)

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
ADDK_IN_GA(x1, x2)  =  ADDK_IN_GA(x1)

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

(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:

ADDK_IN_GA(s(T285), s(X475)) → ADDK_IN_GA(T285, X475)

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

ADDK_IN_GA(s(T285)) → ADDK_IN_GA(T285)

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:

• ADDK_IN_GA(s(T285)) → ADDK_IN_GA(T285)
  The graph contains the following edges 1 > 1

(34) YES

(35) Obligation:

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

ADDJ_IN_GA(s(T252), s(X406)) → ADDJ_IN_GA(T252, X406)

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
ADDJ_IN_GA(x1, x2)  =  ADDJ_IN_GA(x1)

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

(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:

ADDJ_IN_GA(s(T252), s(X406)) → ADDJ_IN_GA(T252, X406)

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

ADDJ_IN_GA(s(T252)) → ADDJ_IN_GA(T252)

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:

• ADDJ_IN_GA(s(T252)) → ADDJ_IN_GA(T252)
  The graph contains the following edges 1 > 1

(41) YES

(42) Obligation:

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

ADDI_IN_GA(s(T219), s(X337)) → ADDI_IN_GA(T219, X337)

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
ADDI_IN_GA(x1, x2)  =  ADDI_IN_GA(x1)

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

(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:

ADDI_IN_GA(s(T219), s(X337)) → ADDI_IN_GA(T219, X337)

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

ADDI_IN_GA(s(T219)) → ADDI_IN_GA(T219)

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:

• ADDI_IN_GA(s(T219)) → ADDI_IN_GA(T219)
  The graph contains the following edges 1 > 1

(48) YES

(49) Obligation:

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

ADDH_IN_GA(s(T186), s(X268)) → ADDH_IN_GA(T186, X268)

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
ADDH_IN_GA(x1, x2)  =  ADDH_IN_GA(x1)

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

(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:

ADDH_IN_GA(s(T186), s(X268)) → ADDH_IN_GA(T186, X268)

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

ADDH_IN_GA(s(T186)) → ADDH_IN_GA(T186)

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:

• ADDH_IN_GA(s(T186)) → ADDH_IN_GA(T186)
  The graph contains the following edges 1 > 1

(55) YES

(56) Obligation:

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

ADDG_IN_GA(s(T153), s(X199)) → ADDG_IN_GA(T153, X199)

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
ADDG_IN_GA(x1, x2)  =  ADDG_IN_GA(x1)

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

(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:

ADDG_IN_GA(s(T153), s(X199)) → ADDG_IN_GA(T153, X199)

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

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:

ADDG_IN_GA(s(T153)) → ADDG_IN_GA(T153)

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:

• ADDG_IN_GA(s(T153)) → ADDG_IN_GA(T153)
  The graph contains the following edges 1 > 1

(62) YES

(63) Obligation:

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

NOTEQF_IN_GG(s(T146), s(T147)) → NOTEQF_IN_GG(T146, T147)

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
NOTEQF_IN_GG(x1, x2)  =  NOTEQF_IN_GG(x1, x2)

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

(64) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(65) Obligation:

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

NOTEQF_IN_GG(s(T146), s(T147)) → NOTEQF_IN_GG(T146, T147)

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

(66) PiDPToQDPProof (EQUIVALENT transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(67) Obligation:

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

NOTEQF_IN_GG(s(T146), s(T147)) → NOTEQF_IN_GG(T146, T147)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(68) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

• NOTEQF_IN_GG(s(T146), s(T147)) → NOTEQF_IN_GG(T146, T147)
  The graph contains the following edges 1 > 1, 2 > 2

(69) YES

(70) Obligation:

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

PN37_IN_GGGGG(T342, T359, T341, T343, T346) → U100_GGGGG(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_GGGGG(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → NOATTACKN7_IN_GGG(T341, T343, T346)
NOATTACKN7_IN_GGG(T386, .(T387, T388), T389) → PN8_IN_GGGAAG(T386, T387, T389, X658, X659, T388)
PN8_IN_GGGAAG(T386, T387, T389, X658, X659, T388) → U102_GGGAAG(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_GGGAAG(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → PN38_IN_GGAGAG(T387, T389, X658, T386, X659, T388)
PN38_IN_GGAGAG(T387, T389, T396, T386, X659, T388) → U104_GGAGAG(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
U104_GGAGAG(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → PN39_IN_GGGAGG(T386, T396, T389, X659, T387, T388)
PN39_IN_GGGAGG(T386, T396, T389, X659, T387, T388) → U106_GGGAGG(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_GGGAGG(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → PN40_IN_GGAGG(T386, T389, X659, T387, T388)
PN40_IN_GGAGG(T386, T389, T418, T387, T388) → U108_GGAGG(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_GGAGG(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → PN37_IN_GGGGG(T387, T418, T386, T388, s(T389))

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
PN37_IN_GGGGG(x1, x2, x3, x4, x5)  =  PN37_IN_GGGGG(x1, x2, x3, x4, x5)
U100_GGGGG(x1, x2, x3, x4, x5, x6)  =  U100_GGGGG(x1, x2, x3, x4, x5, x6)
NOATTACKN7_IN_GGG(x1, x2, x3)  =  NOATTACKN7_IN_GGG(x1, x2, x3)
PN8_IN_GGGAAG(x1, x2, x3, x4, x5, x6)  =  PN8_IN_GGGAAG(x1, x2, x3, x6)
U102_GGGAAG(x1, x2, x3, x4, x5, x6, x7)  =  U102_GGGAAG(x1, x2, x3, x6, x7)
PN38_IN_GGAGAG(x1, x2, x3, x4, x5, x6)  =  PN38_IN_GGAGAG(x1, x2, x4, x6)
U104_GGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U104_GGAGAG(x1, x2, x4, x6, x7)
PN39_IN_GGGAGG(x1, x2, x3, x4, x5, x6)  =  PN39_IN_GGGAGG(x1, x2, x3, x5, x6)
U106_GGGAGG(x1, x2, x3, x4, x5, x6, x7)  =  U106_GGGAGG(x1, x2, x3, x5, x6, x7)
PN40_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN40_IN_GGAGG(x1, x2, x4, x5)
U108_GGAGG(x1, x2, x3, x4, x5, x6)  =  U108_GGAGG(x1, x2, x4, x5, x6)

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

(71) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(72) Obligation:

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

PN37_IN_GGGGG(T342, T359, T341, T343, T346) → U100_GGGGG(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_GGGGG(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → NOATTACKN7_IN_GGG(T341, T343, T346)
NOATTACKN7_IN_GGG(T386, .(T387, T388), T389) → PN8_IN_GGGAAG(T386, T387, T389, X658, X659, T388)
PN8_IN_GGGAAG(T386, T387, T389, X658, X659, T388) → U102_GGGAAG(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_GGGAAG(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → PN38_IN_GGAGAG(T387, T389, X658, T386, X659, T388)
PN38_IN_GGAGAG(T387, T389, T396, T386, X659, T388) → U104_GGAGAG(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
U104_GGAGAG(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → PN39_IN_GGGAGG(T386, T396, T389, X659, T387, T388)
PN39_IN_GGGAGG(T386, T396, T389, X659, T387, T388) → U106_GGGAGG(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_GGGAGG(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → PN40_IN_GGAGG(T386, T389, X659, T387, T388)
PN40_IN_GGAGG(T386, T389, T418, T387, T388) → U108_GGAGG(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_GGAGG(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → PN37_IN_GGGGG(T387, T418, T386, T388, s(T389))

The TRS R consists of the following rules:

notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
PN37_IN_GGGGG(x1, x2, x3, x4, x5)  =  PN37_IN_GGGGG(x1, x2, x3, x4, x5)
U100_GGGGG(x1, x2, x3, x4, x5, x6)  =  U100_GGGGG(x1, x2, x3, x4, x5, x6)
NOATTACKN7_IN_GGG(x1, x2, x3)  =  NOATTACKN7_IN_GGG(x1, x2, x3)
PN8_IN_GGGAAG(x1, x2, x3, x4, x5, x6)  =  PN8_IN_GGGAAG(x1, x2, x3, x6)
U102_GGGAAG(x1, x2, x3, x4, x5, x6, x7)  =  U102_GGGAAG(x1, x2, x3, x6, x7)
PN38_IN_GGAGAG(x1, x2, x3, x4, x5, x6)  =  PN38_IN_GGAGAG(x1, x2, x4, x6)
U104_GGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U104_GGAGAG(x1, x2, x4, x6, x7)
PN39_IN_GGGAGG(x1, x2, x3, x4, x5, x6)  =  PN39_IN_GGGAGG(x1, x2, x3, x5, x6)
U106_GGGAGG(x1, x2, x3, x4, x5, x6, x7)  =  U106_GGGAGG(x1, x2, x3, x5, x6, x7)
PN40_IN_GGAGG(x1, x2, x3, x4, x5)  =  PN40_IN_GGAGG(x1, x2, x4, x5)
U108_GGAGG(x1, x2, x3, x4, x5, x6)  =  U108_GGAGG(x1, x2, x4, x5, x6)

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

(73) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(74) Obligation:

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

PN37_IN_GGGGG(T342, T359, T341, T343, T346) → U100_GGGGG(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_GGGGG(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → NOATTACKN7_IN_GGG(T341, T343, T346)
NOATTACKN7_IN_GGG(T386, .(T387, T388), T389) → PN8_IN_GGGAAG(T386, T387, T389, T388)
PN8_IN_GGGAAG(T386, T387, T389, T388) → U102_GGGAAG(T386, T387, T389, T388, notEqF_in_gg(T386, T387))
U102_GGGAAG(T386, T387, T389, T388, notEqF_out_gg(T386, T387)) → PN38_IN_GGAGAG(T387, T389, T386, T388)
PN38_IN_GGAGAG(T387, T389, T386, T388) → U104_GGAGAG(T387, T389, T386, T388, addN_in_gga(T387, T389))
U104_GGAGAG(T387, T389, T386, T388, addN_out_gga(T387, T389, T396)) → PN39_IN_GGGAGG(T386, T396, T389, T387, T388)
PN39_IN_GGGAGG(T386, T396, T389, T387, T388) → U106_GGGAGG(T386, T396, T389, T387, T388, notEqF_in_gg(T386, T396))
U106_GGGAGG(T386, T396, T389, T387, T388, notEqF_out_gg(T386, T396)) → PN40_IN_GGAGG(T386, T389, T387, T388)
PN40_IN_GGAGG(T386, T389, T387, T388) → U108_GGAGG(T386, T389, T387, T388, addN_in_gga(T386, T389))
U108_GGAGG(T386, T389, T387, T388, addN_out_gga(T386, T389, T418)) → PN37_IN_GGGGG(T387, T418, T386, T388, s(T389))

The TRS R consists of the following rules:

notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
addN_in_gga(0, T403) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409) → U12_gga(T408, T409, addN_in_gga(T408, T409))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U12_gga(T408, T409, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))

The set Q consists of the following terms:

notEqF_in_gg(x0, x1)
addN_in_gga(x0, x1)
U4_gg(x0, x1, x2)
U12_gga(x0, x1, x2)

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

(75) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

• U100_GGGGG(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → NOATTACKN7_IN_GGG(T341, T343, T346)
  The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3

• U108_GGAGG(T386, T389, T387, T388, addN_out_gga(T386, T389, T418)) → PN37_IN_GGGGG(T387, T418, T386, T388, s(T389))
  The graph contains the following edges 3 >= 1, 5 > 2, 1 >= 3, 5 > 3, 4 >= 4

• NOATTACKN7_IN_GGG(T386, .(T387, T388), T389) → PN8_IN_GGGAAG(T386, T387, T389, T388)
  The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 2 > 4

• PN37_IN_GGGGG(T342, T359, T341, T343, T346) → U100_GGGGG(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5

• PN8_IN_GGGAAG(T386, T387, T389, T388) → U102_GGGAAG(T386, T387, T389, T388, notEqF_in_gg(T386, T387))
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4

• U102_GGGAAG(T386, T387, T389, T388, notEqF_out_gg(T386, T387)) → PN38_IN_GGAGAG(T387, T389, T386, T388)
  The graph contains the following edges 2 >= 1, 5 > 1, 3 >= 2, 1 >= 3, 5 > 3, 4 >= 4

• PN38_IN_GGAGAG(T387, T389, T386, T388) → U104_GGAGAG(T387, T389, T386, T388, addN_in_gga(T387, T389))
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4

• U104_GGAGAG(T387, T389, T386, T388, addN_out_gga(T387, T389, T396)) → PN39_IN_GGGAGG(T386, T396, T389, T387, T388)
  The graph contains the following edges 3 >= 1, 5 > 2, 2 >= 3, 5 > 3, 1 >= 4, 5 > 4, 4 >= 5

• PN39_IN_GGGAGG(T386, T396, T389, T387, T388) → U106_GGGAGG(T386, T396, T389, T387, T388, notEqF_in_gg(T386, T396))
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5

• U106_GGGAGG(T386, T396, T389, T387, T388, notEqF_out_gg(T386, T396)) → PN40_IN_GGAGG(T386, T389, T387, T388)
  The graph contains the following edges 1 >= 1, 6 > 1, 3 >= 2, 4 >= 3, 5 >= 4

• PN40_IN_GGAGG(T386, T389, T387, T388) → U108_GGAGG(T386, T389, T387, T388, addN_in_gga(T386, T389))
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4

(76) YES

(77) Obligation:

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

U30_GG(T108, T109, noattackR_out_gg(T108, T109)) → SAFET_IN_G(T109)
SAFET_IN_G(.(T427, T428)) → PQ_IN_GG(T427, T428)
PQ_IN_GG(T108, T109) → U30_GG(T108, T109, noattackR_in_gg(T108, T109))

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
PQ_IN_GG(x1, x2)  =  PQ_IN_GG(x1, x2)
U30_GG(x1, x2, x3)  =  U30_GG(x1, x2, x3)
SAFET_IN_G(x1)  =  SAFET_IN_G(x1)

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

(78) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(79) Obligation:

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

U30_GG(T108, T109, noattackR_out_gg(T108, T109)) → SAFET_IN_G(T109)
SAFET_IN_G(.(T427, T428)) → PQ_IN_GG(T427, T428)
PQ_IN_GG(T108, T109) → U30_GG(T108, T109, noattackR_in_gg(T108, T109))

The TRS R consists of the following rules:

noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
[]  =  []
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
PQ_IN_GG(x1, x2)  =  PQ_IN_GG(x1, x2)
U30_GG(x1, x2, x3)  =  U30_GG(x1, x2, x3)
SAFET_IN_G(x1)  =  SAFET_IN_G(x1)

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

(80) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(81) Obligation:

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

U30_GG(T108, T109, noattackR_out_gg(T108, T109)) → SAFET_IN_G(T109)
SAFET_IN_G(.(T427, T428)) → PQ_IN_GG(T427, T428)
PQ_IN_GG(T108, T109) → U30_GG(T108, T109, noattackR_in_gg(T108, T109))

The TRS R consists of the following rules:

noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, T127))
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
pS_in_ggaag(T125, T126, T127) → U32_ggaag(T125, T126, T127, notEqF_in_gg(T125, T126))
U32_ggaag(T125, T126, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, T127, pN10_in_gagag(T126, T125, T127))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U33_ggaag(T125, T126, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
pN10_in_gagag(T126, T125, T127) → U34_gagag(T126, T125, T127, addG_in_ga(T126))
U34_gagag(T126, T125, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, T127, pN11_in_ggagg(T125, T150, T126, T127))
addG_in_ga(0) → addG_out_ga(0, s(0))
addG_in_ga(s(T153)) → U5_ga(T153, addG_in_ga(T153))
U35_gagag(T126, T150, T125, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U5_ga(T153, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
pN11_in_ggagg(T125, T150, T126, T127) → U36_ggagg(T125, T150, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, T126, T127, pN12_in_gagg(T125, T126, T127))
U37_ggagg(T125, T150, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
pN12_in_gagg(T125, T126, T127) → U38_gagg(T125, T126, T127, addG_in_ga(T125))
U38_gagg(T125, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, T178))
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
pV_in_ggaag(T176, T177, T178) → U42_ggaag(T176, T177, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, T178, pN14_in_gagag(T177, T176, T178))
U43_ggaag(T176, T177, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
pN14_in_gagag(T177, T176, T178) → U44_gagag(T177, T176, T178, addH_in_ga(T177))
U44_gagag(T177, T176, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, T178, pN15_in_ggagg(T176, T183, T177, T178))
addH_in_ga(0) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186)) → U6_ga(T186, addH_in_ga(T186))
U45_gagag(T177, T183, T176, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U6_ga(T186, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
pN15_in_ggagg(T176, T183, T177, T178) → U46_ggagg(T176, T183, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, T177, T178, pN16_in_gagg(T176, T177, T178))
U47_ggagg(T176, T183, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
pN16_in_gagg(T176, T177, T178) → U48_gagg(T176, T177, T178, addH_in_ga(T176))
U48_gagg(T176, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, T211))
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
pX_in_ggaag(T209, T210, T211) → U52_ggaag(T209, T210, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, T211, pN18_in_gagag(T210, T209, T211))
U53_ggaag(T209, T210, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
pN18_in_gagag(T210, T209, T211) → U54_gagag(T210, T209, T211, addI_in_ga(T210))
U54_gagag(T210, T209, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, T211, pN19_in_ggagg(T209, T216, T210, T211))
addI_in_ga(0) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219)) → U7_ga(T219, addI_in_ga(T219))
U55_gagag(T210, T216, T209, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U7_ga(T219, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
pN19_in_ggagg(T209, T216, T210, T211) → U56_ggagg(T209, T216, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, T210, T211, pN20_in_gagg(T209, T210, T211))
U57_ggagg(T209, T216, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
pN20_in_gagg(T209, T210, T211) → U58_gagg(T209, T210, T211, addI_in_ga(T209))
U58_gagg(T209, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, T244))
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
pZ_in_ggaag(T242, T243, T244) → U62_ggaag(T242, T243, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, T244, pN22_in_gagag(T243, T242, T244))
U63_ggaag(T242, T243, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
pN22_in_gagag(T243, T242, T244) → U64_gagag(T243, T242, T244, addJ_in_ga(T243))
U64_gagag(T243, T242, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, T244, pN23_in_ggagg(T242, T249, T243, T244))
addJ_in_ga(0) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252)) → U8_ga(T252, addJ_in_ga(T252))
U65_gagag(T243, T249, T242, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U8_ga(T252, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
pN23_in_ggagg(T242, T249, T243, T244) → U66_ggagg(T242, T249, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, T243, T244, pN24_in_gagg(T242, T243, T244))
U67_ggagg(T242, T249, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
pN24_in_gagg(T242, T243, T244) → U68_gagg(T242, T243, T244, addJ_in_ga(T242))
U68_gagg(T242, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, T277))
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
pN2_in_ggaag(T275, T276, T277) → U72_ggaag(T275, T276, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, T277, pN26_in_gagag(T276, T275, T277))
U73_ggaag(T275, T276, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
pN26_in_gagag(T276, T275, T277) → U74_gagag(T276, T275, T277, addK_in_ga(T276))
U74_gagag(T276, T275, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, T277, pN27_in_ggagg(T275, T282, T276, T277))
addK_in_ga(0) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285)) → U9_ga(T285, addK_in_ga(T285))
U75_gagag(T276, T282, T275, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U9_ga(T285, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
pN27_in_ggagg(T275, T282, T276, T277) → U76_ggagg(T275, T282, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, T276, T277, pN28_in_gagg(T275, T276, T277))
U77_ggagg(T275, T282, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
pN28_in_gagg(T275, T276, T277) → U78_gagg(T275, T276, T277, addK_in_ga(T275))
U78_gagg(T275, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, T310))
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
pN4_in_ggaag(T308, T309, T310) → U82_ggaag(T308, T309, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, T310, pN30_in_gagag(T309, T308, T310))
U83_ggaag(T308, T309, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
pN30_in_gagag(T309, T308, T310) → U84_gagag(T309, T308, T310, addL_in_ga(T309))
U84_gagag(T309, T308, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, T310, pN31_in_ggagg(T308, T315, T309, T310))
addL_in_ga(0) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318)) → U10_ga(T318, addL_in_ga(T318))
U85_gagag(T309, T315, T308, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U10_ga(T318, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
pN31_in_ggagg(T308, T315, T309, T310) → U86_ggagg(T308, T315, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, T309, T310, pN32_in_gagg(T308, T309, T310))
U87_ggagg(T308, T315, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
pN32_in_gagg(T308, T309, T310) → U88_gagg(T308, T309, T310, addL_in_ga(T308))
U88_gagg(T308, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, T343, s(s(s(s(s(s(s(0)))))))))
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
pN6_in_ggaagg(T341, T342, T343, T346) → U92_ggaagg(T341, T342, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, T343, T346, pN34_in_gagagg(T342, T341, T343, T346))
U93_ggaagg(T341, T342, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
pN34_in_gagagg(T342, T341, T343, T346) → U94_gagagg(T342, T341, T343, T346, addM_in_ga(T342))
U94_gagagg(T342, T341, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, T343, T346, pN35_in_ggaggg(T341, T351, T342, T343, T346))
addM_in_ga(0) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354)) → U11_ga(T354, addM_in_ga(T354))
U95_gagagg(T342, T351, T341, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U11_ga(T354, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
pN35_in_ggaggg(T341, T351, T342, T343, T346) → U96_ggaggg(T341, T351, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, T342, T343, T346, pN36_in_gaggg(T341, T342, T343, T346))
U97_ggaggg(T341, T351, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
pN36_in_gaggg(T341, T342, T343, T346) → U98_gaggg(T341, T342, T343, T346, addM_in_ga(T341))
U98_gaggg(T341, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, T388))
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
pN8_in_gggaag(T386, T387, T389, T388) → U102_gggaag(T386, T387, T389, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, T388, pN38_in_ggagag(T387, T389, T386, T388))
U103_gggaag(T386, T387, T389, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
pN38_in_ggagag(T387, T389, T386, T388) → U104_ggagag(T387, T389, T386, T388, addN_in_gga(T387, T389))
U104_ggagag(T387, T389, T386, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, T388, pN39_in_gggagg(T386, T396, T389, T387, T388))
addN_in_gga(0, T403) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409) → U12_gga(T408, T409, addN_in_gga(T408, T409))
U105_ggagag(T387, T389, T396, T386, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U12_gga(T408, T409, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
pN39_in_gggagg(T386, T396, T389, T387, T388) → U106_gggagg(T386, T396, T389, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, T387, T388, pN40_in_ggagg(T386, T389, T387, T388))
U107_gggagg(T386, T396, T389, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
pN40_in_ggagg(T386, T389, T387, T388) → U108_ggagg(T386, T389, T387, T388, addN_in_gga(T386, T389))
U108_ggagg(T386, T389, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)

The set Q consists of the following terms:

noattackR_in_gg(x0, x1)
U15_gg(x0, x1, x2, x3)
pS_in_ggaag(x0, x1, x2)
U32_ggaag(x0, x1, x2, x3)
notEqF_in_gg(x0, x1)
U33_ggaag(x0, x1, x2, x3)
U4_gg(x0, x1, x2)
pN10_in_gagag(x0, x1, x2)
U34_gagag(x0, x1, x2, x3)
addG_in_ga(x0)
U35_gagag(x0, x1, x2, x3, x4)
U5_ga(x0, x1)
pN11_in_ggagg(x0, x1, x2, x3)
U36_ggagg(x0, x1, x2, x3, x4)
U37_ggagg(x0, x1, x2, x3, x4)
pN12_in_gagg(x0, x1, x2)
U38_gagg(x0, x1, x2, x3)
U39_gagg(x0, x1, x2, x3, x4)
pN13_in_gggg(x0, x1, x2, x3)
U40_gggg(x0, x1, x2, x3, x4)
U41_gggg(x0, x1, x2, x3, x4)
noattackU_in_gg(x0, x1)
U17_gg(x0, x1, x2, x3)
pV_in_ggaag(x0, x1, x2)
U42_ggaag(x0, x1, x2, x3)
U43_ggaag(x0, x1, x2, x3)
pN14_in_gagag(x0, x1, x2)
U44_gagag(x0, x1, x2, x3)
addH_in_ga(x0)
U45_gagag(x0, x1, x2, x3, x4)
U6_ga(x0, x1)
pN15_in_ggagg(x0, x1, x2, x3)
U46_ggagg(x0, x1, x2, x3, x4)
U47_ggagg(x0, x1, x2, x3, x4)
pN16_in_gagg(x0, x1, x2)
U48_gagg(x0, x1, x2, x3)
U49_gagg(x0, x1, x2, x3, x4)
pN17_in_gggg(x0, x1, x2, x3)
U50_gggg(x0, x1, x2, x3, x4)
U51_gggg(x0, x1, x2, x3, x4)
noattackW_in_gg(x0, x1)
U18_gg(x0, x1, x2, x3)
pX_in_ggaag(x0, x1, x2)
U52_ggaag(x0, x1, x2, x3)
U53_ggaag(x0, x1, x2, x3)
pN18_in_gagag(x0, x1, x2)
U54_gagag(x0, x1, x2, x3)
addI_in_ga(x0)
U55_gagag(x0, x1, x2, x3, x4)
U7_ga(x0, x1)
pN19_in_ggagg(x0, x1, x2, x3)
U56_ggagg(x0, x1, x2, x3, x4)
U57_ggagg(x0, x1, x2, x3, x4)
pN20_in_gagg(x0, x1, x2)
U58_gagg(x0, x1, x2, x3)
U59_gagg(x0, x1, x2, x3, x4)
pN21_in_gggg(x0, x1, x2, x3)
U60_gggg(x0, x1, x2, x3, x4)
U61_gggg(x0, x1, x2, x3, x4)
noattackY_in_gg(x0, x1)
U19_gg(x0, x1, x2, x3)
pZ_in_ggaag(x0, x1, x2)
U62_ggaag(x0, x1, x2, x3)
U63_ggaag(x0, x1, x2, x3)
pN22_in_gagag(x0, x1, x2)
U64_gagag(x0, x1, x2, x3)
addJ_in_ga(x0)
U65_gagag(x0, x1, x2, x3, x4)
U8_ga(x0, x1)
pN23_in_ggagg(x0, x1, x2, x3)
U66_ggagg(x0, x1, x2, x3, x4)
U67_ggagg(x0, x1, x2, x3, x4)
pN24_in_gagg(x0, x1, x2)
U68_gagg(x0, x1, x2, x3)
U69_gagg(x0, x1, x2, x3, x4)
pN25_in_gggg(x0, x1, x2, x3)
U70_gggg(x0, x1, x2, x3, x4)
U71_gggg(x0, x1, x2, x3, x4)
noattackN1_in_gg(x0, x1)
U20_gg(x0, x1, x2, x3)
pN2_in_ggaag(x0, x1, x2)
U72_ggaag(x0, x1, x2, x3)
U73_ggaag(x0, x1, x2, x3)
pN26_in_gagag(x0, x1, x2)
U74_gagag(x0, x1, x2, x3)
addK_in_ga(x0)
U75_gagag(x0, x1, x2, x3, x4)
U9_ga(x0, x1)
pN27_in_ggagg(x0, x1, x2, x3)
U76_ggagg(x0, x1, x2, x3, x4)
U77_ggagg(x0, x1, x2, x3, x4)
pN28_in_gagg(x0, x1, x2)
U78_gagg(x0, x1, x2, x3)
U79_gagg(x0, x1, x2, x3, x4)
pN29_in_gggg(x0, x1, x2, x3)
U80_gggg(x0, x1, x2, x3, x4)
U81_gggg(x0, x1, x2, x3, x4)
noattackN3_in_gg(x0, x1)
U21_gg(x0, x1, x2, x3)
pN4_in_ggaag(x0, x1, x2)
U82_ggaag(x0, x1, x2, x3)
U83_ggaag(x0, x1, x2, x3)
pN30_in_gagag(x0, x1, x2)
U84_gagag(x0, x1, x2, x3)
addL_in_ga(x0)
U85_gagag(x0, x1, x2, x3, x4)
U10_ga(x0, x1)
pN31_in_ggagg(x0, x1, x2, x3)
U86_ggagg(x0, x1, x2, x3, x4)
U87_ggagg(x0, x1, x2, x3, x4)
pN32_in_gagg(x0, x1, x2)
U88_gagg(x0, x1, x2, x3)
U89_gagg(x0, x1, x2, x3, x4)
pN33_in_gggg(x0, x1, x2, x3)
U90_gggg(x0, x1, x2, x3, x4)
U91_gggg(x0, x1, x2, x3, x4)
noattackN5_in_gg(x0, x1)
U22_gg(x0, x1, x2, x3)
pN6_in_ggaagg(x0, x1, x2, x3)
U92_ggaagg(x0, x1, x2, x3, x4)
U93_ggaagg(x0, x1, x2, x3, x4)
pN34_in_gagagg(x0, x1, x2, x3)
U94_gagagg(x0, x1, x2, x3, x4)
addM_in_ga(x0)
U95_gagagg(x0, x1, x2, x3, x4, x5)
U11_ga(x0, x1)
pN35_in_ggaggg(x0, x1, x2, x3, x4)
U96_ggaggg(x0, x1, x2, x3, x4, x5)
U97_ggaggg(x0, x1, x2, x3, x4, x5)
pN36_in_gaggg(x0, x1, x2, x3)
U98_gaggg(x0, x1, x2, x3, x4)
U99_gaggg(x0, x1, x2, x3, x4, x5)
pN37_in_ggggg(x0, x1, x2, x3, x4)
U100_ggggg(x0, x1, x2, x3, x4, x5)
U101_ggggg(x0, x1, x2, x3, x4, x5)
noattackN7_in_ggg(x0, x1, x2)
U23_ggg(x0, x1, x2, x3, x4)
pN8_in_gggaag(x0, x1, x2, x3)
U102_gggaag(x0, x1, x2, x3, x4)
U103_gggaag(x0, x1, x2, x3, x4)
pN38_in_ggagag(x0, x1, x2, x3)
U104_ggagag(x0, x1, x2, x3, x4)
addN_in_gga(x0, x1)
U105_ggagag(x0, x1, x2, x3, x4, x5)
U12_gga(x0, x1, x2)
pN39_in_gggagg(x0, x1, x2, x3, x4)
U106_gggagg(x0, x1, x2, x3, x4, x5)
U107_gggagg(x0, x1, x2, x3, x4, x5)
pN40_in_ggagg(x0, x1, x2, x3)
U108_ggagg(x0, x1, x2, x3, x4)
U109_ggagg(x0, x1, x2, x3, x4, x5)

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

(82) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

• SAFET_IN_G(.(T427, T428)) → PQ_IN_GG(T427, T428)
  The graph contains the following edges 1 > 1, 1 > 2

• PQ_IN_GG(T108, T109) → U30_GG(T108, T109, noattackR_in_gg(T108, T109))
  The graph contains the following edges 1 >= 1, 2 >= 2

• U30_GG(T108, T109, noattackR_out_gg(T108, T109)) → SAFET_IN_G(T109)
  The graph contains the following edges 2 >= 1, 3 > 1

(83) YES

(84) Obligation:

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

DELETEC_IN_AGA(T72, .(T70, T71), .(T70, X86)) → DELETEC_IN_AGA(T72, T71, X86)

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
DELETEC_IN_AGA(x1, x2, x3)  =  DELETEC_IN_AGA(x2)

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

(85) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(86) Obligation:

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

DELETEC_IN_AGA(T72, .(T70, T71), .(T70, X86)) → DELETEC_IN_AGA(T72, T71, X86)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
DELETEC_IN_AGA(x1, x2, x3)  =  DELETEC_IN_AGA(x2)

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

(87) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(88) Obligation:

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

DELETEC_IN_AGA(.(T70, T71)) → DELETEC_IN_AGA(T71)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(89) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

• DELETEC_IN_AGA(.(T70, T71)) → DELETEC_IN_AGA(T71)
  The graph contains the following edges 1 > 1

(90) YES

(91) Obligation:

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

PE_IN_AGGAA(T90, T86, T87, T96, T97) → U28_AGGAA(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_AGGAA(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → PERMD_IN_GA(T96, T97)
PERMD_IN_GA(.(T86, T87), .(T90, T91)) → PE_IN_AGGAA(T90, T86, T87, X104, T91)

The TRS R consists of the following rules:

queensA_in_a(.(T11, T12)) → U1_a(T11, T12, pB_in_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12))
pB_in_agaa(T22, T15, T20, T21) → U24_agaa(T22, T15, T20, T21, deleteO_in_aga(T22, T15, T20))
deleteO_in_aga(s(0), T36, T36) → deleteO_out_aga(s(0), T36, T36)
deleteO_in_aga(T48, T47, .(s(0), X57)) → U13_aga(T48, T47, X57, deleteC_in_aga(T48, T47, X57))
deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))
U13_aga(T48, T47, X57, deleteC_out_aga(T48, T47, X57)) → deleteO_out_aga(T48, T47, .(s(0), X57))
U24_agaa(T22, T15, T20, T21, deleteO_out_aga(T22, T15, T20)) → U25_agaa(T22, T15, T20, T21, pN9_in_gag(T20, T21, T22))
pN9_in_gag(T20, T77, T22) → U26_gag(T20, T77, T22, permD_in_ga(T20, T77))
permD_in_ga([], []) → permD_out_ga([], [])
permD_in_ga(.(T86, T87), .(T90, T91)) → U3_ga(T86, T87, T90, T91, pE_in_aggaa(T90, T86, T87, X104, T91))
pE_in_aggaa(T90, T86, T87, T96, T97) → U28_aggaa(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_aggaa(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → U29_aggaa(T90, T86, T87, T96, T97, permD_in_ga(T96, T97))
U29_aggaa(T90, T86, T87, T96, T97, permD_out_ga(T96, T97)) → pE_out_aggaa(T90, T86, T87, T96, T97)
U3_ga(T86, T87, T90, T91, pE_out_aggaa(T90, T86, T87, X104, T91)) → permD_out_ga(.(T86, T87), .(T90, T91))
U26_gag(T20, T77, T22, permD_out_ga(T20, T77)) → U27_gag(T20, T77, T22, safeP_in_gg(T22, T77))
safeP_in_gg(T108, T109) → U14_gg(T108, T109, pQ_in_gg(T108, T109))
pQ_in_gg(T108, T109) → U30_gg(T108, T109, noattackR_in_gg(T108, T109))
noattackR_in_gg(T118, []) → noattackR_out_gg(T118, [])
noattackR_in_gg(T125, .(T126, T127)) → U15_gg(T125, T126, T127, pS_in_ggaag(T125, T126, X155, X156, T127))
pS_in_ggaag(T125, T126, X155, X156, T127) → U32_ggaag(T125, T126, X155, X156, T127, notEqF_in_gg(T125, T126))
notEqF_in_gg(0, s(T136)) → notEqF_out_gg(0, s(T136))
notEqF_in_gg(s(T141), 0) → notEqF_out_gg(s(T141), 0)
notEqF_in_gg(s(T146), s(T147)) → U4_gg(T146, T147, notEqF_in_gg(T146, T147))
U4_gg(T146, T147, notEqF_out_gg(T146, T147)) → notEqF_out_gg(s(T146), s(T147))
U32_ggaag(T125, T126, X155, X156, T127, notEqF_out_gg(T125, T126)) → U33_ggaag(T125, T126, X155, X156, T127, pN10_in_gagag(T126, X155, T125, X156, T127))
pN10_in_gagag(T126, T150, T125, X156, T127) → U34_gagag(T126, T150, T125, X156, T127, addG_in_ga(T126, T150))
addG_in_ga(0, s(0)) → addG_out_ga(0, s(0))
addG_in_ga(s(T153), s(X199)) → U5_ga(T153, X199, addG_in_ga(T153, X199))
U5_ga(T153, X199, addG_out_ga(T153, X199)) → addG_out_ga(s(T153), s(X199))
U34_gagag(T126, T150, T125, X156, T127, addG_out_ga(T126, T150)) → U35_gagag(T126, T150, T125, X156, T127, pN11_in_ggagg(T125, T150, X156, T126, T127))
pN11_in_ggagg(T125, T150, X156, T126, T127) → U36_ggagg(T125, T150, X156, T126, T127, notEqF_in_gg(T125, T150))
U36_ggagg(T125, T150, X156, T126, T127, notEqF_out_gg(T125, T150)) → U37_ggagg(T125, T150, X156, T126, T127, pN12_in_gagg(T125, X156, T126, T127))
pN12_in_gagg(T125, T158, T126, T127) → U38_gagg(T125, T158, T126, T127, addG_in_ga(T125, T158))
U38_gagg(T125, T158, T126, T127, addG_out_ga(T125, T158)) → U39_gagg(T125, T158, T126, T127, pN13_in_gggg(T126, T158, T125, T127))
pN13_in_gggg(T126, T158, T125, T127) → U40_gggg(T126, T158, T125, T127, notEqF_in_gg(T126, T158))
U40_gggg(T126, T158, T125, T127, notEqF_out_gg(T126, T158)) → U41_gggg(T126, T158, T125, T127, noattackU_in_gg(T125, T127))
noattackU_in_gg(T169, []) → noattackU_out_gg(T169, [])
noattackU_in_gg(T176, .(T177, T178)) → U17_gg(T176, T177, T178, pV_in_ggaag(T176, T177, X242, X243, T178))
pV_in_ggaag(T176, T177, X242, X243, T178) → U42_ggaag(T176, T177, X242, X243, T178, notEqF_in_gg(T176, T177))
U42_ggaag(T176, T177, X242, X243, T178, notEqF_out_gg(T176, T177)) → U43_ggaag(T176, T177, X242, X243, T178, pN14_in_gagag(T177, X242, T176, X243, T178))
pN14_in_gagag(T177, T183, T176, X243, T178) → U44_gagag(T177, T183, T176, X243, T178, addH_in_ga(T177, T183))
addH_in_ga(0, s(s(0))) → addH_out_ga(0, s(s(0)))
addH_in_ga(s(T186), s(X268)) → U6_ga(T186, X268, addH_in_ga(T186, X268))
U6_ga(T186, X268, addH_out_ga(T186, X268)) → addH_out_ga(s(T186), s(X268))
U44_gagag(T177, T183, T176, X243, T178, addH_out_ga(T177, T183)) → U45_gagag(T177, T183, T176, X243, T178, pN15_in_ggagg(T176, T183, X243, T177, T178))
pN15_in_ggagg(T176, T183, X243, T177, T178) → U46_ggagg(T176, T183, X243, T177, T178, notEqF_in_gg(T176, T183))
U46_ggagg(T176, T183, X243, T177, T178, notEqF_out_gg(T176, T183)) → U47_ggagg(T176, T183, X243, T177, T178, pN16_in_gagg(T176, X243, T177, T178))
pN16_in_gagg(T176, T191, T177, T178) → U48_gagg(T176, T191, T177, T178, addH_in_ga(T176, T191))
U48_gagg(T176, T191, T177, T178, addH_out_ga(T176, T191)) → U49_gagg(T176, T191, T177, T178, pN17_in_gggg(T177, T191, T176, T178))
pN17_in_gggg(T177, T191, T176, T178) → U50_gggg(T177, T191, T176, T178, notEqF_in_gg(T177, T191))
U50_gggg(T177, T191, T176, T178, notEqF_out_gg(T177, T191)) → U51_gggg(T177, T191, T176, T178, noattackW_in_gg(T176, T178))
noattackW_in_gg(T202, []) → noattackW_out_gg(T202, [])
noattackW_in_gg(T209, .(T210, T211)) → U18_gg(T209, T210, T211, pX_in_ggaag(T209, T210, X311, X312, T211))
pX_in_ggaag(T209, T210, X311, X312, T211) → U52_ggaag(T209, T210, X311, X312, T211, notEqF_in_gg(T209, T210))
U52_ggaag(T209, T210, X311, X312, T211, notEqF_out_gg(T209, T210)) → U53_ggaag(T209, T210, X311, X312, T211, pN18_in_gagag(T210, X311, T209, X312, T211))
pN18_in_gagag(T210, T216, T209, X312, T211) → U54_gagag(T210, T216, T209, X312, T211, addI_in_ga(T210, T216))
addI_in_ga(0, s(s(s(0)))) → addI_out_ga(0, s(s(s(0))))
addI_in_ga(s(T219), s(X337)) → U7_ga(T219, X337, addI_in_ga(T219, X337))
U7_ga(T219, X337, addI_out_ga(T219, X337)) → addI_out_ga(s(T219), s(X337))
U54_gagag(T210, T216, T209, X312, T211, addI_out_ga(T210, T216)) → U55_gagag(T210, T216, T209, X312, T211, pN19_in_ggagg(T209, T216, X312, T210, T211))
pN19_in_ggagg(T209, T216, X312, T210, T211) → U56_ggagg(T209, T216, X312, T210, T211, notEqF_in_gg(T209, T216))
U56_ggagg(T209, T216, X312, T210, T211, notEqF_out_gg(T209, T216)) → U57_ggagg(T209, T216, X312, T210, T211, pN20_in_gagg(T209, X312, T210, T211))
pN20_in_gagg(T209, T224, T210, T211) → U58_gagg(T209, T224, T210, T211, addI_in_ga(T209, T224))
U58_gagg(T209, T224, T210, T211, addI_out_ga(T209, T224)) → U59_gagg(T209, T224, T210, T211, pN21_in_gggg(T210, T224, T209, T211))
pN21_in_gggg(T210, T224, T209, T211) → U60_gggg(T210, T224, T209, T211, notEqF_in_gg(T210, T224))
U60_gggg(T210, T224, T209, T211, notEqF_out_gg(T210, T224)) → U61_gggg(T210, T224, T209, T211, noattackY_in_gg(T209, T211))
noattackY_in_gg(T235, []) → noattackY_out_gg(T235, [])
noattackY_in_gg(T242, .(T243, T244)) → U19_gg(T242, T243, T244, pZ_in_ggaag(T242, T243, X380, X381, T244))
pZ_in_ggaag(T242, T243, X380, X381, T244) → U62_ggaag(T242, T243, X380, X381, T244, notEqF_in_gg(T242, T243))
U62_ggaag(T242, T243, X380, X381, T244, notEqF_out_gg(T242, T243)) → U63_ggaag(T242, T243, X380, X381, T244, pN22_in_gagag(T243, X380, T242, X381, T244))
pN22_in_gagag(T243, T249, T242, X381, T244) → U64_gagag(T243, T249, T242, X381, T244, addJ_in_ga(T243, T249))
addJ_in_ga(0, s(s(s(s(0))))) → addJ_out_ga(0, s(s(s(s(0)))))
addJ_in_ga(s(T252), s(X406)) → U8_ga(T252, X406, addJ_in_ga(T252, X406))
U8_ga(T252, X406, addJ_out_ga(T252, X406)) → addJ_out_ga(s(T252), s(X406))
U64_gagag(T243, T249, T242, X381, T244, addJ_out_ga(T243, T249)) → U65_gagag(T243, T249, T242, X381, T244, pN23_in_ggagg(T242, T249, X381, T243, T244))
pN23_in_ggagg(T242, T249, X381, T243, T244) → U66_ggagg(T242, T249, X381, T243, T244, notEqF_in_gg(T242, T249))
U66_ggagg(T242, T249, X381, T243, T244, notEqF_out_gg(T242, T249)) → U67_ggagg(T242, T249, X381, T243, T244, pN24_in_gagg(T242, X381, T243, T244))
pN24_in_gagg(T242, T257, T243, T244) → U68_gagg(T242, T257, T243, T244, addJ_in_ga(T242, T257))
U68_gagg(T242, T257, T243, T244, addJ_out_ga(T242, T257)) → U69_gagg(T242, T257, T243, T244, pN25_in_gggg(T243, T257, T242, T244))
pN25_in_gggg(T243, T257, T242, T244) → U70_gggg(T243, T257, T242, T244, notEqF_in_gg(T243, T257))
U70_gggg(T243, T257, T242, T244, notEqF_out_gg(T243, T257)) → U71_gggg(T243, T257, T242, T244, noattackN1_in_gg(T242, T244))
noattackN1_in_gg(T268, []) → noattackN1_out_gg(T268, [])
noattackN1_in_gg(T275, .(T276, T277)) → U20_gg(T275, T276, T277, pN2_in_ggaag(T275, T276, X449, X450, T277))
pN2_in_ggaag(T275, T276, X449, X450, T277) → U72_ggaag(T275, T276, X449, X450, T277, notEqF_in_gg(T275, T276))
U72_ggaag(T275, T276, X449, X450, T277, notEqF_out_gg(T275, T276)) → U73_ggaag(T275, T276, X449, X450, T277, pN26_in_gagag(T276, X449, T275, X450, T277))
pN26_in_gagag(T276, T282, T275, X450, T277) → U74_gagag(T276, T282, T275, X450, T277, addK_in_ga(T276, T282))
addK_in_ga(0, s(s(s(s(s(0)))))) → addK_out_ga(0, s(s(s(s(s(0))))))
addK_in_ga(s(T285), s(X475)) → U9_ga(T285, X475, addK_in_ga(T285, X475))
U9_ga(T285, X475, addK_out_ga(T285, X475)) → addK_out_ga(s(T285), s(X475))
U74_gagag(T276, T282, T275, X450, T277, addK_out_ga(T276, T282)) → U75_gagag(T276, T282, T275, X450, T277, pN27_in_ggagg(T275, T282, X450, T276, T277))
pN27_in_ggagg(T275, T282, X450, T276, T277) → U76_ggagg(T275, T282, X450, T276, T277, notEqF_in_gg(T275, T282))
U76_ggagg(T275, T282, X450, T276, T277, notEqF_out_gg(T275, T282)) → U77_ggagg(T275, T282, X450, T276, T277, pN28_in_gagg(T275, X450, T276, T277))
pN28_in_gagg(T275, T290, T276, T277) → U78_gagg(T275, T290, T276, T277, addK_in_ga(T275, T290))
U78_gagg(T275, T290, T276, T277, addK_out_ga(T275, T290)) → U79_gagg(T275, T290, T276, T277, pN29_in_gggg(T276, T290, T275, T277))
pN29_in_gggg(T276, T290, T275, T277) → U80_gggg(T276, T290, T275, T277, notEqF_in_gg(T276, T290))
U80_gggg(T276, T290, T275, T277, notEqF_out_gg(T276, T290)) → U81_gggg(T276, T290, T275, T277, noattackN3_in_gg(T275, T277))
noattackN3_in_gg(T301, []) → noattackN3_out_gg(T301, [])
noattackN3_in_gg(T308, .(T309, T310)) → U21_gg(T308, T309, T310, pN4_in_ggaag(T308, T309, X518, X519, T310))
pN4_in_ggaag(T308, T309, X518, X519, T310) → U82_ggaag(T308, T309, X518, X519, T310, notEqF_in_gg(T308, T309))
U82_ggaag(T308, T309, X518, X519, T310, notEqF_out_gg(T308, T309)) → U83_ggaag(T308, T309, X518, X519, T310, pN30_in_gagag(T309, X518, T308, X519, T310))
pN30_in_gagag(T309, T315, T308, X519, T310) → U84_gagag(T309, T315, T308, X519, T310, addL_in_ga(T309, T315))
addL_in_ga(0, s(s(s(s(s(s(0))))))) → addL_out_ga(0, s(s(s(s(s(s(0)))))))
addL_in_ga(s(T318), s(X544)) → U10_ga(T318, X544, addL_in_ga(T318, X544))
U10_ga(T318, X544, addL_out_ga(T318, X544)) → addL_out_ga(s(T318), s(X544))
U84_gagag(T309, T315, T308, X519, T310, addL_out_ga(T309, T315)) → U85_gagag(T309, T315, T308, X519, T310, pN31_in_ggagg(T308, T315, X519, T309, T310))
pN31_in_ggagg(T308, T315, X519, T309, T310) → U86_ggagg(T308, T315, X519, T309, T310, notEqF_in_gg(T308, T315))
U86_ggagg(T308, T315, X519, T309, T310, notEqF_out_gg(T308, T315)) → U87_ggagg(T308, T315, X519, T309, T310, pN32_in_gagg(T308, X519, T309, T310))
pN32_in_gagg(T308, T323, T309, T310) → U88_gagg(T308, T323, T309, T310, addL_in_ga(T308, T323))
U88_gagg(T308, T323, T309, T310, addL_out_ga(T308, T323)) → U89_gagg(T308, T323, T309, T310, pN33_in_gggg(T309, T323, T308, T310))
pN33_in_gggg(T309, T323, T308, T310) → U90_gggg(T309, T323, T308, T310, notEqF_in_gg(T309, T323))
U90_gggg(T309, T323, T308, T310, notEqF_out_gg(T309, T323)) → U91_gggg(T309, T323, T308, T310, noattackN5_in_gg(T308, T310))
noattackN5_in_gg(T334, []) → noattackN5_out_gg(T334, [])
noattackN5_in_gg(T341, .(T342, T343)) → U22_gg(T341, T342, T343, pN6_in_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0)))))))))
pN6_in_ggaagg(T341, T342, X587, X588, T343, T346) → U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_in_gg(T341, T342))
U92_ggaagg(T341, T342, X587, X588, T343, T346, notEqF_out_gg(T341, T342)) → U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_in_gagagg(T342, X587, T341, X588, T343, T346))
pN34_in_gagagg(T342, T351, T341, X588, T343, T346) → U94_gagagg(T342, T351, T341, X588, T343, T346, addM_in_ga(T342, T351))
addM_in_ga(0, s(s(s(s(s(s(s(0)))))))) → addM_out_ga(0, s(s(s(s(s(s(s(0))))))))
addM_in_ga(s(T354), s(X615)) → U11_ga(T354, X615, addM_in_ga(T354, X615))
U11_ga(T354, X615, addM_out_ga(T354, X615)) → addM_out_ga(s(T354), s(X615))
U94_gagagg(T342, T351, T341, X588, T343, T346, addM_out_ga(T342, T351)) → U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_in_ggaggg(T341, T351, X588, T342, T343, T346))
pN35_in_ggaggg(T341, T351, X588, T342, T343, T346) → U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_in_gg(T341, T351))
U96_ggaggg(T341, T351, X588, T342, T343, T346, notEqF_out_gg(T341, T351)) → U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_in_gaggg(T341, X588, T342, T343, T346))
pN36_in_gaggg(T341, T359, T342, T343, T346) → U98_gaggg(T341, T359, T342, T343, T346, addM_in_ga(T341, T359))
U98_gaggg(T341, T359, T342, T343, T346, addM_out_ga(T341, T359)) → U99_gaggg(T341, T359, T342, T343, T346, pN37_in_ggggg(T342, T359, T341, T343, T346))
pN37_in_ggggg(T342, T359, T341, T343, T346) → U100_ggggg(T342, T359, T341, T343, T346, notEqF_in_gg(T342, T359))
U100_ggggg(T342, T359, T341, T343, T346, notEqF_out_gg(T342, T359)) → U101_ggggg(T342, T359, T341, T343, T346, noattackN7_in_ggg(T341, T343, T346))
noattackN7_in_ggg(T376, [], T377) → noattackN7_out_ggg(T376, [], T377)
noattackN7_in_ggg(T386, .(T387, T388), T389) → U23_ggg(T386, T387, T388, T389, pN8_in_gggaag(T386, T387, T389, X658, X659, T388))
pN8_in_gggaag(T386, T387, T389, X658, X659, T388) → U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_in_gg(T386, T387))
U102_gggaag(T386, T387, T389, X658, X659, T388, notEqF_out_gg(T386, T387)) → U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_in_ggagag(T387, T389, X658, T386, X659, T388))
pN38_in_ggagag(T387, T389, T396, T386, X659, T388) → U104_ggagag(T387, T389, T396, T386, X659, T388, addN_in_gga(T387, T389, T396))
addN_in_gga(0, T403, s(T403)) → addN_out_gga(0, T403, s(T403))
addN_in_gga(s(T408), T409, s(X684)) → U12_gga(T408, T409, X684, addN_in_gga(T408, T409, X684))
U12_gga(T408, T409, X684, addN_out_gga(T408, T409, X684)) → addN_out_gga(s(T408), T409, s(X684))
U104_ggagag(T387, T389, T396, T386, X659, T388, addN_out_gga(T387, T389, T396)) → U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_in_gggagg(T386, T396, T389, X659, T387, T388))
pN39_in_gggagg(T386, T396, T389, X659, T387, T388) → U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_in_gg(T386, T396))
U106_gggagg(T386, T396, T389, X659, T387, T388, notEqF_out_gg(T386, T396)) → U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_in_ggagg(T386, T389, X659, T387, T388))
pN40_in_ggagg(T386, T389, T418, T387, T388) → U108_ggagg(T386, T389, T418, T387, T388, addN_in_gga(T386, T389, T418))
U108_ggagg(T386, T389, T418, T387, T388, addN_out_gga(T386, T389, T418)) → U109_ggagg(T386, T389, T418, T387, T388, pN37_in_ggggg(T387, T418, T386, T388, s(T389)))
U109_ggagg(T386, T389, T418, T387, T388, pN37_out_ggggg(T387, T418, T386, T388, s(T389))) → pN40_out_ggagg(T386, T389, T418, T387, T388)
U107_gggagg(T386, T396, T389, X659, T387, T388, pN40_out_ggagg(T386, T389, X659, T387, T388)) → pN39_out_gggagg(T386, T396, T389, X659, T387, T388)
U105_ggagag(T387, T389, T396, T386, X659, T388, pN39_out_gggagg(T386, T396, T389, X659, T387, T388)) → pN38_out_ggagag(T387, T389, T396, T386, X659, T388)
U103_gggaag(T386, T387, T389, X658, X659, T388, pN38_out_ggagag(T387, T389, X658, T386, X659, T388)) → pN8_out_gggaag(T386, T387, T389, X658, X659, T388)
U23_ggg(T386, T387, T388, T389, pN8_out_gggaag(T386, T387, T389, X658, X659, T388)) → noattackN7_out_ggg(T386, .(T387, T388), T389)
U101_ggggg(T342, T359, T341, T343, T346, noattackN7_out_ggg(T341, T343, T346)) → pN37_out_ggggg(T342, T359, T341, T343, T346)
U99_gaggg(T341, T359, T342, T343, T346, pN37_out_ggggg(T342, T359, T341, T343, T346)) → pN36_out_gaggg(T341, T359, T342, T343, T346)
U97_ggaggg(T341, T351, X588, T342, T343, T346, pN36_out_gaggg(T341, X588, T342, T343, T346)) → pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)
U95_gagagg(T342, T351, T341, X588, T343, T346, pN35_out_ggaggg(T341, T351, X588, T342, T343, T346)) → pN34_out_gagagg(T342, T351, T341, X588, T343, T346)
U93_ggaagg(T341, T342, X587, X588, T343, T346, pN34_out_gagagg(T342, X587, T341, X588, T343, T346)) → pN6_out_ggaagg(T341, T342, X587, X588, T343, T346)
U22_gg(T341, T342, T343, pN6_out_ggaagg(T341, T342, X587, X588, T343, s(s(s(s(s(s(s(0))))))))) → noattackN5_out_gg(T341, .(T342, T343))
U91_gggg(T309, T323, T308, T310, noattackN5_out_gg(T308, T310)) → pN33_out_gggg(T309, T323, T308, T310)
U89_gagg(T308, T323, T309, T310, pN33_out_gggg(T309, T323, T308, T310)) → pN32_out_gagg(T308, T323, T309, T310)
U87_ggagg(T308, T315, X519, T309, T310, pN32_out_gagg(T308, X519, T309, T310)) → pN31_out_ggagg(T308, T315, X519, T309, T310)
U85_gagag(T309, T315, T308, X519, T310, pN31_out_ggagg(T308, T315, X519, T309, T310)) → pN30_out_gagag(T309, T315, T308, X519, T310)
U83_ggaag(T308, T309, X518, X519, T310, pN30_out_gagag(T309, X518, T308, X519, T310)) → pN4_out_ggaag(T308, T309, X518, X519, T310)
U21_gg(T308, T309, T310, pN4_out_ggaag(T308, T309, X518, X519, T310)) → noattackN3_out_gg(T308, .(T309, T310))
U81_gggg(T276, T290, T275, T277, noattackN3_out_gg(T275, T277)) → pN29_out_gggg(T276, T290, T275, T277)
U79_gagg(T275, T290, T276, T277, pN29_out_gggg(T276, T290, T275, T277)) → pN28_out_gagg(T275, T290, T276, T277)
U77_ggagg(T275, T282, X450, T276, T277, pN28_out_gagg(T275, X450, T276, T277)) → pN27_out_ggagg(T275, T282, X450, T276, T277)
U75_gagag(T276, T282, T275, X450, T277, pN27_out_ggagg(T275, T282, X450, T276, T277)) → pN26_out_gagag(T276, T282, T275, X450, T277)
U73_ggaag(T275, T276, X449, X450, T277, pN26_out_gagag(T276, X449, T275, X450, T277)) → pN2_out_ggaag(T275, T276, X449, X450, T277)
U20_gg(T275, T276, T277, pN2_out_ggaag(T275, T276, X449, X450, T277)) → noattackN1_out_gg(T275, .(T276, T277))
U71_gggg(T243, T257, T242, T244, noattackN1_out_gg(T242, T244)) → pN25_out_gggg(T243, T257, T242, T244)
U69_gagg(T242, T257, T243, T244, pN25_out_gggg(T243, T257, T242, T244)) → pN24_out_gagg(T242, T257, T243, T244)
U67_ggagg(T242, T249, X381, T243, T244, pN24_out_gagg(T242, X381, T243, T244)) → pN23_out_ggagg(T242, T249, X381, T243, T244)
U65_gagag(T243, T249, T242, X381, T244, pN23_out_ggagg(T242, T249, X381, T243, T244)) → pN22_out_gagag(T243, T249, T242, X381, T244)
U63_ggaag(T242, T243, X380, X381, T244, pN22_out_gagag(T243, X380, T242, X381, T244)) → pZ_out_ggaag(T242, T243, X380, X381, T244)
U19_gg(T242, T243, T244, pZ_out_ggaag(T242, T243, X380, X381, T244)) → noattackY_out_gg(T242, .(T243, T244))
U61_gggg(T210, T224, T209, T211, noattackY_out_gg(T209, T211)) → pN21_out_gggg(T210, T224, T209, T211)
U59_gagg(T209, T224, T210, T211, pN21_out_gggg(T210, T224, T209, T211)) → pN20_out_gagg(T209, T224, T210, T211)
U57_ggagg(T209, T216, X312, T210, T211, pN20_out_gagg(T209, X312, T210, T211)) → pN19_out_ggagg(T209, T216, X312, T210, T211)
U55_gagag(T210, T216, T209, X312, T211, pN19_out_ggagg(T209, T216, X312, T210, T211)) → pN18_out_gagag(T210, T216, T209, X312, T211)
U53_ggaag(T209, T210, X311, X312, T211, pN18_out_gagag(T210, X311, T209, X312, T211)) → pX_out_ggaag(T209, T210, X311, X312, T211)
U18_gg(T209, T210, T211, pX_out_ggaag(T209, T210, X311, X312, T211)) → noattackW_out_gg(T209, .(T210, T211))
U51_gggg(T177, T191, T176, T178, noattackW_out_gg(T176, T178)) → pN17_out_gggg(T177, T191, T176, T178)
U49_gagg(T176, T191, T177, T178, pN17_out_gggg(T177, T191, T176, T178)) → pN16_out_gagg(T176, T191, T177, T178)
U47_ggagg(T176, T183, X243, T177, T178, pN16_out_gagg(T176, X243, T177, T178)) → pN15_out_ggagg(T176, T183, X243, T177, T178)
U45_gagag(T177, T183, T176, X243, T178, pN15_out_ggagg(T176, T183, X243, T177, T178)) → pN14_out_gagag(T177, T183, T176, X243, T178)
U43_ggaag(T176, T177, X242, X243, T178, pN14_out_gagag(T177, X242, T176, X243, T178)) → pV_out_ggaag(T176, T177, X242, X243, T178)
U17_gg(T176, T177, T178, pV_out_ggaag(T176, T177, X242, X243, T178)) → noattackU_out_gg(T176, .(T177, T178))
U41_gggg(T126, T158, T125, T127, noattackU_out_gg(T125, T127)) → pN13_out_gggg(T126, T158, T125, T127)
U39_gagg(T125, T158, T126, T127, pN13_out_gggg(T126, T158, T125, T127)) → pN12_out_gagg(T125, T158, T126, T127)
U37_ggagg(T125, T150, X156, T126, T127, pN12_out_gagg(T125, X156, T126, T127)) → pN11_out_ggagg(T125, T150, X156, T126, T127)
U35_gagag(T126, T150, T125, X156, T127, pN11_out_ggagg(T125, T150, X156, T126, T127)) → pN10_out_gagag(T126, T150, T125, X156, T127)
U33_ggaag(T125, T126, X155, X156, T127, pN10_out_gagag(T126, X155, T125, X156, T127)) → pS_out_ggaag(T125, T126, X155, X156, T127)
U15_gg(T125, T126, T127, pS_out_ggaag(T125, T126, X155, X156, T127)) → noattackR_out_gg(T125, .(T126, T127))
U30_gg(T108, T109, noattackR_out_gg(T108, T109)) → U31_gg(T108, T109, safeT_in_g(T109))
safeT_in_g([]) → safeT_out_g([])
safeT_in_g(.(T427, T428)) → U16_g(T427, T428, pQ_in_gg(T427, T428))
U16_g(T427, T428, pQ_out_gg(T427, T428)) → safeT_out_g(.(T427, T428))
U31_gg(T108, T109, safeT_out_g(T109)) → pQ_out_gg(T108, T109)
U14_gg(T108, T109, pQ_out_gg(T108, T109)) → safeP_out_gg(T108, T109)
U27_gag(T20, T77, T22, safeP_out_gg(T22, T77)) → pN9_out_gag(T20, T77, T22)
U25_agaa(T22, T15, T20, T21, pN9_out_gag(T20, T21, T22)) → pB_out_agaa(T22, T15, T20, T21)
U1_a(T11, T12, pB_out_agaa(T11, .(s(s(0)), .(s(s(s(0))), .(s(s(s(s(0)))), .(s(s(s(s(s(0))))), .(s(s(s(s(s(s(0)))))), .(s(s(s(s(s(s(s(0))))))), .(s(s(s(s(s(s(s(s(0)))))))), []))))))), X16, T12)) → queensA_out_a(.(T11, T12))

The argument filtering Pi contains the following mapping:
queensA_in_a(x1)  =  queensA_in_a
U1_a(x1, x2, x3)  =  U1_a(x3)
pB_in_agaa(x1, x2, x3, x4)  =  pB_in_agaa(x2)
U24_agaa(x1, x2, x3, x4, x5)  =  U24_agaa(x2, x5)
deleteO_in_aga(x1, x2, x3)  =  deleteO_in_aga(x2)
deleteO_out_aga(x1, x2, x3)  =  deleteO_out_aga(x1, x2, x3)
U13_aga(x1, x2, x3, x4)  =  U13_aga(x2, x4)
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
U25_agaa(x1, x2, x3, x4, x5)  =  U25_agaa(x1, x2, x3, x5)
pN9_in_gag(x1, x2, x3)  =  pN9_in_gag(x1, x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x1, x3, x4)
permD_in_ga(x1, x2)  =  permD_in_ga(x1)
[]  =  []
permD_out_ga(x1, x2)  =  permD_out_ga(x1, x2)
U3_ga(x1, x2, x3, x4, x5)  =  U3_ga(x1, x2, x5)
pE_in_aggaa(x1, x2, x3, x4, x5)  =  pE_in_aggaa(x2, x3)
U28_aggaa(x1, x2, x3, x4, x5, x6)  =  U28_aggaa(x2, x3, x6)
U29_aggaa(x1, x2, x3, x4, x5, x6)  =  U29_aggaa(x1, x2, x3, x4, x6)
pE_out_aggaa(x1, x2, x3, x4, x5)  =  pE_out_aggaa(x1, x2, x3, x4, x5)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x2, x3, x4)
safeP_in_gg(x1, x2)  =  safeP_in_gg(x1, x2)
U14_gg(x1, x2, x3)  =  U14_gg(x1, x2, x3)
pQ_in_gg(x1, x2)  =  pQ_in_gg(x1, x2)
U30_gg(x1, x2, x3)  =  U30_gg(x1, x2, x3)
noattackR_in_gg(x1, x2)  =  noattackR_in_gg(x1, x2)
noattackR_out_gg(x1, x2)  =  noattackR_out_gg(x1, x2)
U15_gg(x1, x2, x3, x4)  =  U15_gg(x1, x2, x3, x4)
pS_in_ggaag(x1, x2, x3, x4, x5)  =  pS_in_ggaag(x1, x2, x5)
U32_ggaag(x1, x2, x3, x4, x5, x6)  =  U32_ggaag(x1, x2, x5, x6)
notEqF_in_gg(x1, x2)  =  notEqF_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
notEqF_out_gg(x1, x2)  =  notEqF_out_gg(x1, x2)
U4_gg(x1, x2, x3)  =  U4_gg(x1, x2, x3)
U33_ggaag(x1, x2, x3, x4, x5, x6)  =  U33_ggaag(x1, x2, x5, x6)
pN10_in_gagag(x1, x2, x3, x4, x5)  =  pN10_in_gagag(x1, x3, x5)
U34_gagag(x1, x2, x3, x4, x5, x6)  =  U34_gagag(x1, x3, x5, x6)
addG_in_ga(x1, x2)  =  addG_in_ga(x1)
addG_out_ga(x1, x2)  =  addG_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U35_gagag(x1, x2, x3, x4, x5, x6)  =  U35_gagag(x1, x2, x3, x5, x6)
pN11_in_ggagg(x1, x2, x3, x4, x5)  =  pN11_in_ggagg(x1, x2, x4, x5)
U36_ggagg(x1, x2, x3, x4, x5, x6)  =  U36_ggagg(x1, x2, x4, x5, x6)
U37_ggagg(x1, x2, x3, x4, x5, x6)  =  U37_ggagg(x1, x2, x4, x5, x6)
pN12_in_gagg(x1, x2, x3, x4)  =  pN12_in_gagg(x1, x3, x4)
U38_gagg(x1, x2, x3, x4, x5)  =  U38_gagg(x1, x3, x4, x5)
U39_gagg(x1, x2, x3, x4, x5)  =  U39_gagg(x1, x2, x3, x4, x5)
pN13_in_gggg(x1, x2, x3, x4)  =  pN13_in_gggg(x1, x2, x3, x4)
U40_gggg(x1, x2, x3, x4, x5)  =  U40_gggg(x1, x2, x3, x4, x5)
U41_gggg(x1, x2, x3, x4, x5)  =  U41_gggg(x1, x2, x3, x4, x5)
noattackU_in_gg(x1, x2)  =  noattackU_in_gg(x1, x2)
noattackU_out_gg(x1, x2)  =  noattackU_out_gg(x1, x2)
U17_gg(x1, x2, x3, x4)  =  U17_gg(x1, x2, x3, x4)
pV_in_ggaag(x1, x2, x3, x4, x5)  =  pV_in_ggaag(x1, x2, x5)
U42_ggaag(x1, x2, x3, x4, x5, x6)  =  U42_ggaag(x1, x2, x5, x6)
U43_ggaag(x1, x2, x3, x4, x5, x6)  =  U43_ggaag(x1, x2, x5, x6)
pN14_in_gagag(x1, x2, x3, x4, x5)  =  pN14_in_gagag(x1, x3, x5)
U44_gagag(x1, x2, x3, x4, x5, x6)  =  U44_gagag(x1, x3, x5, x6)
addH_in_ga(x1, x2)  =  addH_in_ga(x1)
addH_out_ga(x1, x2)  =  addH_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U45_gagag(x1, x2, x3, x4, x5, x6)  =  U45_gagag(x1, x2, x3, x5, x6)
pN15_in_ggagg(x1, x2, x3, x4, x5)  =  pN15_in_ggagg(x1, x2, x4, x5)
U46_ggagg(x1, x2, x3, x4, x5, x6)  =  U46_ggagg(x1, x2, x4, x5, x6)
U47_ggagg(x1, x2, x3, x4, x5, x6)  =  U47_ggagg(x1, x2, x4, x5, x6)
pN16_in_gagg(x1, x2, x3, x4)  =  pN16_in_gagg(x1, x3, x4)
U48_gagg(x1, x2, x3, x4, x5)  =  U48_gagg(x1, x3, x4, x5)
U49_gagg(x1, x2, x3, x4, x5)  =  U49_gagg(x1, x2, x3, x4, x5)
pN17_in_gggg(x1, x2, x3, x4)  =  pN17_in_gggg(x1, x2, x3, x4)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
U51_gggg(x1, x2, x3, x4, x5)  =  U51_gggg(x1, x2, x3, x4, x5)
noattackW_in_gg(x1, x2)  =  noattackW_in_gg(x1, x2)
noattackW_out_gg(x1, x2)  =  noattackW_out_gg(x1, x2)
U18_gg(x1, x2, x3, x4)  =  U18_gg(x1, x2, x3, x4)
pX_in_ggaag(x1, x2, x3, x4, x5)  =  pX_in_ggaag(x1, x2, x5)
U52_ggaag(x1, x2, x3, x4, x5, x6)  =  U52_ggaag(x1, x2, x5, x6)
U53_ggaag(x1, x2, x3, x4, x5, x6)  =  U53_ggaag(x1, x2, x5, x6)
pN18_in_gagag(x1, x2, x3, x4, x5)  =  pN18_in_gagag(x1, x3, x5)
U54_gagag(x1, x2, x3, x4, x5, x6)  =  U54_gagag(x1, x3, x5, x6)
addI_in_ga(x1, x2)  =  addI_in_ga(x1)
addI_out_ga(x1, x2)  =  addI_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U55_gagag(x1, x2, x3, x4, x5, x6)  =  U55_gagag(x1, x2, x3, x5, x6)
pN19_in_ggagg(x1, x2, x3, x4, x5)  =  pN19_in_ggagg(x1, x2, x4, x5)
U56_ggagg(x1, x2, x3, x4, x5, x6)  =  U56_ggagg(x1, x2, x4, x5, x6)
U57_ggagg(x1, x2, x3, x4, x5, x6)  =  U57_ggagg(x1, x2, x4, x5, x6)
pN20_in_gagg(x1, x2, x3, x4)  =  pN20_in_gagg(x1, x3, x4)
U58_gagg(x1, x2, x3, x4, x5)  =  U58_gagg(x1, x3, x4, x5)
U59_gagg(x1, x2, x3, x4, x5)  =  U59_gagg(x1, x2, x3, x4, x5)
pN21_in_gggg(x1, x2, x3, x4)  =  pN21_in_gggg(x1, x2, x3, x4)
U60_gggg(x1, x2, x3, x4, x5)  =  U60_gggg(x1, x2, x3, x4, x5)
U61_gggg(x1, x2, x3, x4, x5)  =  U61_gggg(x1, x2, x3, x4, x5)
noattackY_in_gg(x1, x2)  =  noattackY_in_gg(x1, x2)
noattackY_out_gg(x1, x2)  =  noattackY_out_gg(x1, x2)
U19_gg(x1, x2, x3, x4)  =  U19_gg(x1, x2, x3, x4)
pZ_in_ggaag(x1, x2, x3, x4, x5)  =  pZ_in_ggaag(x1, x2, x5)
U62_ggaag(x1, x2, x3, x4, x5, x6)  =  U62_ggaag(x1, x2, x5, x6)
U63_ggaag(x1, x2, x3, x4, x5, x6)  =  U63_ggaag(x1, x2, x5, x6)
pN22_in_gagag(x1, x2, x3, x4, x5)  =  pN22_in_gagag(x1, x3, x5)
U64_gagag(x1, x2, x3, x4, x5, x6)  =  U64_gagag(x1, x3, x5, x6)
addJ_in_ga(x1, x2)  =  addJ_in_ga(x1)
addJ_out_ga(x1, x2)  =  addJ_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U65_gagag(x1, x2, x3, x4, x5, x6)  =  U65_gagag(x1, x2, x3, x5, x6)
pN23_in_ggagg(x1, x2, x3, x4, x5)  =  pN23_in_ggagg(x1, x2, x4, x5)
U66_ggagg(x1, x2, x3, x4, x5, x6)  =  U66_ggagg(x1, x2, x4, x5, x6)
U67_ggagg(x1, x2, x3, x4, x5, x6)  =  U67_ggagg(x1, x2, x4, x5, x6)
pN24_in_gagg(x1, x2, x3, x4)  =  pN24_in_gagg(x1, x3, x4)
U68_gagg(x1, x2, x3, x4, x5)  =  U68_gagg(x1, x3, x4, x5)
U69_gagg(x1, x2, x3, x4, x5)  =  U69_gagg(x1, x2, x3, x4, x5)
pN25_in_gggg(x1, x2, x3, x4)  =  pN25_in_gggg(x1, x2, x3, x4)
U70_gggg(x1, x2, x3, x4, x5)  =  U70_gggg(x1, x2, x3, x4, x5)
U71_gggg(x1, x2, x3, x4, x5)  =  U71_gggg(x1, x2, x3, x4, x5)
noattackN1_in_gg(x1, x2)  =  noattackN1_in_gg(x1, x2)
noattackN1_out_gg(x1, x2)  =  noattackN1_out_gg(x1, x2)
U20_gg(x1, x2, x3, x4)  =  U20_gg(x1, x2, x3, x4)
pN2_in_ggaag(x1, x2, x3, x4, x5)  =  pN2_in_ggaag(x1, x2, x5)
U72_ggaag(x1, x2, x3, x4, x5, x6)  =  U72_ggaag(x1, x2, x5, x6)
U73_ggaag(x1, x2, x3, x4, x5, x6)  =  U73_ggaag(x1, x2, x5, x6)
pN26_in_gagag(x1, x2, x3, x4, x5)  =  pN26_in_gagag(x1, x3, x5)
U74_gagag(x1, x2, x3, x4, x5, x6)  =  U74_gagag(x1, x3, x5, x6)
addK_in_ga(x1, x2)  =  addK_in_ga(x1)
addK_out_ga(x1, x2)  =  addK_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U75_gagag(x1, x2, x3, x4, x5, x6)  =  U75_gagag(x1, x2, x3, x5, x6)
pN27_in_ggagg(x1, x2, x3, x4, x5)  =  pN27_in_ggagg(x1, x2, x4, x5)
U76_ggagg(x1, x2, x3, x4, x5, x6)  =  U76_ggagg(x1, x2, x4, x5, x6)
U77_ggagg(x1, x2, x3, x4, x5, x6)  =  U77_ggagg(x1, x2, x4, x5, x6)
pN28_in_gagg(x1, x2, x3, x4)  =  pN28_in_gagg(x1, x3, x4)
U78_gagg(x1, x2, x3, x4, x5)  =  U78_gagg(x1, x3, x4, x5)
U79_gagg(x1, x2, x3, x4, x5)  =  U79_gagg(x1, x2, x3, x4, x5)
pN29_in_gggg(x1, x2, x3, x4)  =  pN29_in_gggg(x1, x2, x3, x4)
U80_gggg(x1, x2, x3, x4, x5)  =  U80_gggg(x1, x2, x3, x4, x5)
U81_gggg(x1, x2, x3, x4, x5)  =  U81_gggg(x1, x2, x3, x4, x5)
noattackN3_in_gg(x1, x2)  =  noattackN3_in_gg(x1, x2)
noattackN3_out_gg(x1, x2)  =  noattackN3_out_gg(x1, x2)
U21_gg(x1, x2, x3, x4)  =  U21_gg(x1, x2, x3, x4)
pN4_in_ggaag(x1, x2, x3, x4, x5)  =  pN4_in_ggaag(x1, x2, x5)
U82_ggaag(x1, x2, x3, x4, x5, x6)  =  U82_ggaag(x1, x2, x5, x6)
U83_ggaag(x1, x2, x3, x4, x5, x6)  =  U83_ggaag(x1, x2, x5, x6)
pN30_in_gagag(x1, x2, x3, x4, x5)  =  pN30_in_gagag(x1, x3, x5)
U84_gagag(x1, x2, x3, x4, x5, x6)  =  U84_gagag(x1, x3, x5, x6)
addL_in_ga(x1, x2)  =  addL_in_ga(x1)
addL_out_ga(x1, x2)  =  addL_out_ga(x1, x2)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U85_gagag(x1, x2, x3, x4, x5, x6)  =  U85_gagag(x1, x2, x3, x5, x6)
pN31_in_ggagg(x1, x2, x3, x4, x5)  =  pN31_in_ggagg(x1, x2, x4, x5)
U86_ggagg(x1, x2, x3, x4, x5, x6)  =  U86_ggagg(x1, x2, x4, x5, x6)
U87_ggagg(x1, x2, x3, x4, x5, x6)  =  U87_ggagg(x1, x2, x4, x5, x6)
pN32_in_gagg(x1, x2, x3, x4)  =  pN32_in_gagg(x1, x3, x4)
U88_gagg(x1, x2, x3, x4, x5)  =  U88_gagg(x1, x3, x4, x5)
U89_gagg(x1, x2, x3, x4, x5)  =  U89_gagg(x1, x2, x3, x4, x5)
pN33_in_gggg(x1, x2, x3, x4)  =  pN33_in_gggg(x1, x2, x3, x4)
U90_gggg(x1, x2, x3, x4, x5)  =  U90_gggg(x1, x2, x3, x4, x5)
U91_gggg(x1, x2, x3, x4, x5)  =  U91_gggg(x1, x2, x3, x4, x5)
noattackN5_in_gg(x1, x2)  =  noattackN5_in_gg(x1, x2)
noattackN5_out_gg(x1, x2)  =  noattackN5_out_gg(x1, x2)
U22_gg(x1, x2, x3, x4)  =  U22_gg(x1, x2, x3, x4)
pN6_in_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_in_ggaagg(x1, x2, x5, x6)
U92_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U92_ggaagg(x1, x2, x5, x6, x7)
U93_ggaagg(x1, x2, x3, x4, x5, x6, x7)  =  U93_ggaagg(x1, x2, x5, x6, x7)
pN34_in_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_in_gagagg(x1, x3, x5, x6)
U94_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U94_gagagg(x1, x3, x5, x6, x7)
addM_in_ga(x1, x2)  =  addM_in_ga(x1)
addM_out_ga(x1, x2)  =  addM_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U95_gagagg(x1, x2, x3, x4, x5, x6, x7)  =  U95_gagagg(x1, x2, x3, x5, x6, x7)
pN35_in_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_in_ggaggg(x1, x2, x4, x5, x6)
U96_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U96_ggaggg(x1, x2, x4, x5, x6, x7)
U97_ggaggg(x1, x2, x3, x4, x5, x6, x7)  =  U97_ggaggg(x1, x2, x4, x5, x6, x7)
pN36_in_gaggg(x1, x2, x3, x4, x5)  =  pN36_in_gaggg(x1, x3, x4, x5)
U98_gaggg(x1, x2, x3, x4, x5, x6)  =  U98_gaggg(x1, x3, x4, x5, x6)
U99_gaggg(x1, x2, x3, x4, x5, x6)  =  U99_gaggg(x1, x2, x3, x4, x5, x6)
pN37_in_ggggg(x1, x2, x3, x4, x5)  =  pN37_in_ggggg(x1, x2, x3, x4, x5)
U100_ggggg(x1, x2, x3, x4, x5, x6)  =  U100_ggggg(x1, x2, x3, x4, x5, x6)
U101_ggggg(x1, x2, x3, x4, x5, x6)  =  U101_ggggg(x1, x2, x3, x4, x5, x6)
noattackN7_in_ggg(x1, x2, x3)  =  noattackN7_in_ggg(x1, x2, x3)
noattackN7_out_ggg(x1, x2, x3)  =  noattackN7_out_ggg(x1, x2, x3)
U23_ggg(x1, x2, x3, x4, x5)  =  U23_ggg(x1, x2, x3, x4, x5)
pN8_in_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_in_gggaag(x1, x2, x3, x6)
U102_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U102_gggaag(x1, x2, x3, x6, x7)
U103_gggaag(x1, x2, x3, x4, x5, x6, x7)  =  U103_gggaag(x1, x2, x3, x6, x7)
pN38_in_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_in_ggagag(x1, x2, x4, x6)
U104_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U104_ggagag(x1, x2, x4, x6, x7)
addN_in_gga(x1, x2, x3)  =  addN_in_gga(x1, x2)
addN_out_gga(x1, x2, x3)  =  addN_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
U105_ggagag(x1, x2, x3, x4, x5, x6, x7)  =  U105_ggagag(x1, x2, x3, x4, x6, x7)
pN39_in_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_in_gggagg(x1, x2, x3, x5, x6)
U106_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U106_gggagg(x1, x2, x3, x5, x6, x7)
U107_gggagg(x1, x2, x3, x4, x5, x6, x7)  =  U107_gggagg(x1, x2, x3, x5, x6, x7)
pN40_in_ggagg(x1, x2, x3, x4, x5)  =  pN40_in_ggagg(x1, x2, x4, x5)
U108_ggagg(x1, x2, x3, x4, x5, x6)  =  U108_ggagg(x1, x2, x4, x5, x6)
U109_ggagg(x1, x2, x3, x4, x5, x6)  =  U109_ggagg(x1, x2, x3, x4, x5, x6)
pN37_out_ggggg(x1, x2, x3, x4, x5)  =  pN37_out_ggggg(x1, x2, x3, x4, x5)
pN40_out_ggagg(x1, x2, x3, x4, x5)  =  pN40_out_ggagg(x1, x2, x3, x4, x5)
pN39_out_gggagg(x1, x2, x3, x4, x5, x6)  =  pN39_out_gggagg(x1, x2, x3, x4, x5, x6)
pN38_out_ggagag(x1, x2, x3, x4, x5, x6)  =  pN38_out_ggagag(x1, x2, x3, x4, x5, x6)
pN8_out_gggaag(x1, x2, x3, x4, x5, x6)  =  pN8_out_gggaag(x1, x2, x3, x4, x5, x6)
pN36_out_gaggg(x1, x2, x3, x4, x5)  =  pN36_out_gaggg(x1, x2, x3, x4, x5)
pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)  =  pN35_out_ggaggg(x1, x2, x3, x4, x5, x6)
pN34_out_gagagg(x1, x2, x3, x4, x5, x6)  =  pN34_out_gagagg(x1, x2, x3, x4, x5, x6)
pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)  =  pN6_out_ggaagg(x1, x2, x3, x4, x5, x6)
pN33_out_gggg(x1, x2, x3, x4)  =  pN33_out_gggg(x1, x2, x3, x4)
pN32_out_gagg(x1, x2, x3, x4)  =  pN32_out_gagg(x1, x2, x3, x4)
pN31_out_ggagg(x1, x2, x3, x4, x5)  =  pN31_out_ggagg(x1, x2, x3, x4, x5)
pN30_out_gagag(x1, x2, x3, x4, x5)  =  pN30_out_gagag(x1, x2, x3, x4, x5)
pN4_out_ggaag(x1, x2, x3, x4, x5)  =  pN4_out_ggaag(x1, x2, x3, x4, x5)
pN29_out_gggg(x1, x2, x3, x4)  =  pN29_out_gggg(x1, x2, x3, x4)
pN28_out_gagg(x1, x2, x3, x4)  =  pN28_out_gagg(x1, x2, x3, x4)
pN27_out_ggagg(x1, x2, x3, x4, x5)  =  pN27_out_ggagg(x1, x2, x3, x4, x5)
pN26_out_gagag(x1, x2, x3, x4, x5)  =  pN26_out_gagag(x1, x2, x3, x4, x5)
pN2_out_ggaag(x1, x2, x3, x4, x5)  =  pN2_out_ggaag(x1, x2, x3, x4, x5)
pN25_out_gggg(x1, x2, x3, x4)  =  pN25_out_gggg(x1, x2, x3, x4)
pN24_out_gagg(x1, x2, x3, x4)  =  pN24_out_gagg(x1, x2, x3, x4)
pN23_out_ggagg(x1, x2, x3, x4, x5)  =  pN23_out_ggagg(x1, x2, x3, x4, x5)
pN22_out_gagag(x1, x2, x3, x4, x5)  =  pN22_out_gagag(x1, x2, x3, x4, x5)
pZ_out_ggaag(x1, x2, x3, x4, x5)  =  pZ_out_ggaag(x1, x2, x3, x4, x5)
pN21_out_gggg(x1, x2, x3, x4)  =  pN21_out_gggg(x1, x2, x3, x4)
pN20_out_gagg(x1, x2, x3, x4)  =  pN20_out_gagg(x1, x2, x3, x4)
pN19_out_ggagg(x1, x2, x3, x4, x5)  =  pN19_out_ggagg(x1, x2, x3, x4, x5)
pN18_out_gagag(x1, x2, x3, x4, x5)  =  pN18_out_gagag(x1, x2, x3, x4, x5)
pX_out_ggaag(x1, x2, x3, x4, x5)  =  pX_out_ggaag(x1, x2, x3, x4, x5)
pN17_out_gggg(x1, x2, x3, x4)  =  pN17_out_gggg(x1, x2, x3, x4)
pN16_out_gagg(x1, x2, x3, x4)  =  pN16_out_gagg(x1, x2, x3, x4)
pN15_out_ggagg(x1, x2, x3, x4, x5)  =  pN15_out_ggagg(x1, x2, x3, x4, x5)
pN14_out_gagag(x1, x2, x3, x4, x5)  =  pN14_out_gagag(x1, x2, x3, x4, x5)
pV_out_ggaag(x1, x2, x3, x4, x5)  =  pV_out_ggaag(x1, x2, x3, x4, x5)
pN13_out_gggg(x1, x2, x3, x4)  =  pN13_out_gggg(x1, x2, x3, x4)
pN12_out_gagg(x1, x2, x3, x4)  =  pN12_out_gagg(x1, x2, x3, x4)
pN11_out_ggagg(x1, x2, x3, x4, x5)  =  pN11_out_ggagg(x1, x2, x3, x4, x5)
pN10_out_gagag(x1, x2, x3, x4, x5)  =  pN10_out_gagag(x1, x2, x3, x4, x5)
pS_out_ggaag(x1, x2, x3, x4, x5)  =  pS_out_ggaag(x1, x2, x3, x4, x5)
U31_gg(x1, x2, x3)  =  U31_gg(x1, x2, x3)
safeT_in_g(x1)  =  safeT_in_g(x1)
safeT_out_g(x1)  =  safeT_out_g(x1)
U16_g(x1, x2, x3)  =  U16_g(x1, x2, x3)
pQ_out_gg(x1, x2)  =  pQ_out_gg(x1, x2)
safeP_out_gg(x1, x2)  =  safeP_out_gg(x1, x2)
pN9_out_gag(x1, x2, x3)  =  pN9_out_gag(x1, x2, x3)
pB_out_agaa(x1, x2, x3, x4)  =  pB_out_agaa(x1, x2, x3, x4)
queensA_out_a(x1)  =  queensA_out_a(x1)
PERMD_IN_GA(x1, x2)  =  PERMD_IN_GA(x1)
PE_IN_AGGAA(x1, x2, x3, x4, x5)  =  PE_IN_AGGAA(x2, x3)
U28_AGGAA(x1, x2, x3, x4, x5, x6)  =  U28_AGGAA(x2, x3, x6)

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

(92) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(93) Obligation:

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

PE_IN_AGGAA(T90, T86, T87, T96, T97) → U28_AGGAA(T90, T86, T87, T96, T97, deleteC_in_aga(T90, .(T86, T87), T96))
U28_AGGAA(T90, T86, T87, T96, T97, deleteC_out_aga(T90, .(T86, T87), T96)) → PERMD_IN_GA(T96, T97)
PERMD_IN_GA(.(T86, T87), .(T90, T91)) → PE_IN_AGGAA(T90, T86, T87, X104, T91)

The TRS R consists of the following rules:

deleteC_in_aga(T61, .(T61, T62), T62) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(T72, .(T70, T71), .(T70, X86)) → U2_aga(T72, T70, T71, X86, deleteC_in_aga(T72, T71, X86))
U2_aga(T72, T70, T71, X86, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))

The argument filtering Pi contains the following mapping:
deleteC_in_aga(x1, x2, x3)  =  deleteC_in_aga(x2)
.(x1, x2)  =  .(x1, x2)
deleteC_out_aga(x1, x2, x3)  =  deleteC_out_aga(x1, x2, x3)
U2_aga(x1, x2, x3, x4, x5)  =  U2_aga(x2, x3, x5)
PERMD_IN_GA(x1, x2)  =  PERMD_IN_GA(x1)
PE_IN_AGGAA(x1, x2, x3, x4, x5)  =  PE_IN_AGGAA(x2, x3)
U28_AGGAA(x1, x2, x3, x4, x5, x6)  =  U28_AGGAA(x2, x3, x6)

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

(94) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(95) Obligation:

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

PE_IN_AGGAA(T86, T87) → U28_AGGAA(T86, T87, deleteC_in_aga(.(T86, T87)))
U28_AGGAA(T86, T87, deleteC_out_aga(T90, .(T86, T87), T96)) → PERMD_IN_GA(T96)
PERMD_IN_GA(.(T86, T87)) → PE_IN_AGGAA(T86, T87)

The TRS R consists of the following rules:

deleteC_in_aga(.(T61, T62)) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(.(T70, T71)) → U2_aga(T70, T71, deleteC_in_aga(T71))
U2_aga(T70, T71, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))

The set Q consists of the following terms:

deleteC_in_aga(x0)
U2_aga(x0, x1, x2)

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

(96) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].

The following pairs can be oriented strictly and are deleted.

U28_AGGAA(T86, T87, deleteC_out_aga(T90, .(T86, T87), T96)) → PERMD_IN_GA(T96)

The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(.(x₁, x₂)) = 1 + x₂   
POL(PERMD_IN_GA(x₁)) = x₁   
POL(PE_IN_AGGAA(x₁, x₂)) = 1 + x₂   
POL(U28_AGGAA(x₁, x₂, x₃)) = x₃   
POL(U2_aga(x₁, x₂, x₃)) = 1 + x₃   
POL(deleteC_in_aga(x₁)) = x₁   
POL(deleteC_out_aga(x₁, x₂, x₃)) = 1 + x₃   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

deleteC_in_aga(.(T61, T62)) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(.(T70, T71)) → U2_aga(T70, T71, deleteC_in_aga(T71))
U2_aga(T70, T71, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))

(97) Obligation:

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

PE_IN_AGGAA(T86, T87) → U28_AGGAA(T86, T87, deleteC_in_aga(.(T86, T87)))
PERMD_IN_GA(.(T86, T87)) → PE_IN_AGGAA(T86, T87)

The TRS R consists of the following rules:

deleteC_in_aga(.(T61, T62)) → deleteC_out_aga(T61, .(T61, T62), T62)
deleteC_in_aga(.(T70, T71)) → U2_aga(T70, T71, deleteC_in_aga(T71))
U2_aga(T70, T71, deleteC_out_aga(T72, T71, X86)) → deleteC_out_aga(T72, .(T70, T71), .(T70, X86))

The set Q consists of the following terms:

deleteC_in_aga(x0)
U2_aga(x0, x1, x2)

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

(98) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.

(99) TRUE