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

(0) Obligation:

Clauses:

times(X, Y, Z) :- mult(X, Y, 0, Z).
mult(0, Y, 0, 0).
mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z).
mult(X, Y, s(W), s(Z)) :- mult(X, Y, W, Z).

Query: times(g,g,a)

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

Transformed Prolog program to (Pi-)TRS.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
2 [label="A: times(T1, T2, T3)\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
5 [label="5: times(T1, T2, T3), SCOPE: 1, CLAUSE: 0\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: mult(T7, T8, 0, T10)\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: mult(T7, T8, 0, T10), SCOPE: 2, CLAUSE: 1 | mult(T7, T8, 0, T10), SCOPE: 2, CLAUSE: 2 | mult(T7, T8, 0, T10), SCOPE: 2, CLAUSE: 3\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: mult(T7, T8, 0, T10), SCOPE: 2, CLAUSE: 1\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: mult(T7, T8, 0, T10), SCOPE: 2, CLAUSE: 2 | mult(T7, T8, 0, T10), SCOPE: 2, CLAUSE: 3\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: mult(T7, T8, 0, T10), SCOPE: 2, CLAUSE: 2\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: mult(T7, T8, 0, T10), SCOPE: 2, CLAUSE: 3\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="B: mult(T28, T29, T29, T31)\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: mult(T28, T29, T29, T31), SCOPE: 3, CLAUSE: 1 | mult(T28, T29, T29, T31), SCOPE: 3, CLAUSE: 2 | mult(T28, T29, T29, T31), SCOPE: 3, CLAUSE: 3\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: mult(T28, T29, T29, T31), SCOPE: 3, CLAUSE: 1\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: mult(T28, T29, T29, T31), SCOPE: 3, CLAUSE: 2 | mult(T28, T29, T29, T31), SCOPE: 3, CLAUSE: 3\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: mult(T28, T29, T29, T31), SCOPE: 3, CLAUSE: 2\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: mult(T28, T29, T29, T31), SCOPE: 3, CLAUSE: 3\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="C: mult(T51, 0, 0, T54)\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: mult(T51, 0, 0, T54), SCOPE: 4, CLAUSE: 1 | mult(T51, 0, 0, T54), SCOPE: 4, CLAUSE: 2 | mult(T51, 0, 0, T54), SCOPE: 4, CLAUSE: 3\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: mult(T51, 0, 0, T54), SCOPE: 4, CLAUSE: 1\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: mult(T51, 0, 0, T54), SCOPE: 4, CLAUSE: 2 | mult(T51, 0, 0, T54), SCOPE: 4, CLAUSE: 3\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: mult(T51, 0, 0, T54), SCOPE: 4, CLAUSE: 2\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: mult(T51, 0, 0, T54), SCOPE: 4, CLAUSE: 3\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: mult(T63, 0, 0, T65)\n\nT63 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: mult(T75, s(T77), T77, T79)\n\nT75 is ground\nT77 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: mult(T75, s(T77), T77, T79), SCOPE: 5, CLAUSE: 1 | mult(T75, s(T77), T77, T79), SCOPE: 5, CLAUSE: 2 | mult(T75, s(T77), T77, T79), SCOPE: 5, CLAUSE: 3\n\nT75 is ground\nT77 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: mult(T75, s(T77), T77, T79), SCOPE: 5, CLAUSE: 1\n\nT75 is ground\nT77 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: mult(T75, s(T77), T77, T79), SCOPE: 5, CLAUSE: 2 | mult(T75, s(T77), T77, T79), SCOPE: 5, CLAUSE: 3\n\nT75 is ground\nT77 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: mult(T75, s(T77), T77, T79), SCOPE: 5, CLAUSE: 2\n\nT75 is ground\nT77 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: mult(T75, s(T77), T77, T79), SCOPE: 5, CLAUSE: 3\n\nT75 is ground\nT77 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="D: mult(T99, s(0), s(0), T102)\n\nT99 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: mult(T99, s(0), s(0), T102), SCOPE: 6, CLAUSE: 1 | mult(T99, s(0), s(0), T102), SCOPE: 6, CLAUSE: 2 | mult(T99, s(0), s(0), T102), SCOPE: 6, CLAUSE: 3\n\nT99 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: mult(T99, s(0), s(0), T102), SCOPE: 6, CLAUSE: 2 | mult(T99, s(0), s(0), T102), SCOPE: 6, CLAUSE: 3\n\nT99 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: mult(T99, s(0), s(0), T102), SCOPE: 6, CLAUSE: 3\n\nT99 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: mult(T108, s(0), 0, T110)\n\nT108 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: mult(T108, s(0), 0, T110), SCOPE: 7, CLAUSE: 1 | mult(T108, s(0), 0, T110), SCOPE: 7, CLAUSE: 2 | mult(T108, s(0), 0, T110), SCOPE: 7, CLAUSE: 3\n\nT108 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: mult(T108, s(0), 0, T110), SCOPE: 7, CLAUSE: 1\n\nT108 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: mult(T108, s(0), 0, T110), SCOPE: 7, CLAUSE: 2 | mult(T108, s(0), 0, T110), SCOPE: 7, CLAUSE: 3\n\nT108 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: mult(T108, s(0), 0, T110), SCOPE: 7, CLAUSE: 2\n\nT108 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: mult(T108, s(0), 0, T110), SCOPE: 7, CLAUSE: 3\n\nT108 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: mult(T119, s(0), s(0), T121)\n\nT119 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: mult(T131, s(s(T133)), T133, T135)\n\nT131 is ground\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: mult(T131, s(s(T133)), T133, T135), SCOPE: 8, CLAUSE: 1 | mult(T131, s(s(T133)), T133, T135), SCOPE: 8, CLAUSE: 2 | mult(T131, s(s(T133)), T133, T135), SCOPE: 8, CLAUSE: 3\n\nT131 is ground\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: mult(T131, s(s(T133)), T133, T135), SCOPE: 8, CLAUSE: 1\n\nT131 is ground\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: mult(T131, s(s(T133)), T133, T135), SCOPE: 8, CLAUSE: 2 | mult(T131, s(s(T133)), T133, T135), SCOPE: 8, CLAUSE: 3\n\nT131 is ground\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: mult(T131, s(s(T133)), T133, T135), SCOPE: 8, CLAUSE: 2\n\nT131 is ground\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: mult(T131, s(s(T133)), T133, T135), SCOPE: 8, CLAUSE: 3\n\nT131 is ground\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="E: mult(T155, s(s(0)), s(s(0)), T158)\n\nT155 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: mult(T155, s(s(0)), s(s(0)), T158), SCOPE: 9, CLAUSE: 1 | mult(T155, s(s(0)), s(s(0)), T158), SCOPE: 9, CLAUSE: 2 | mult(T155, s(s(0)), s(s(0)), T158), SCOPE: 9, CLAUSE: 3\n\nT155 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: mult(T155, s(s(0)), s(s(0)), T158), SCOPE: 9, CLAUSE: 2 | mult(T155, s(s(0)), s(s(0)), T158), SCOPE: 9, CLAUSE: 3\n\nT155 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: mult(T155, s(s(0)), s(s(0)), T158), SCOPE: 9, CLAUSE: 3\n\nT155 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: mult(T164, s(s(0)), s(0), T166)\n\nT164 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: mult(T164, s(s(0)), s(0), T166), SCOPE: 10, CLAUSE: 1 | mult(T164, s(s(0)), s(0), T166), SCOPE: 10, CLAUSE: 2 | mult(T164, s(s(0)), s(0), T166), SCOPE: 10, CLAUSE: 3\n\nT164 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: mult(T164, s(s(0)), s(0), T166), SCOPE: 10, CLAUSE: 2 | mult(T164, s(s(0)), s(0), T166), SCOPE: 10, CLAUSE: 3\n\nT164 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: mult(T164, s(s(0)), s(0), T166), SCOPE: 10, CLAUSE: 3\n\nT164 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: mult(T172, s(s(0)), 0, T174)\n\nT172 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="227: mult(T172, s(s(0)), 0, T174), SCOPE: 11, CLAUSE: 1 | mult(T172, s(s(0)), 0, T174), SCOPE: 11, CLAUSE: 2 | mult(T172, s(s(0)), 0, T174), SCOPE: 11, CLAUSE: 3\n\nT172 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
229 [label="229: mult(T172, s(s(0)), 0, T174), SCOPE: 11, CLAUSE: 1\n\nT172 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: mult(T172, s(s(0)), 0, T174), SCOPE: 11, CLAUSE: 2 | mult(T172, s(s(0)), 0, T174), SCOPE: 11, CLAUSE: 3\n\nT172 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
234 [label="234: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
235 [label="235: mult(T172, s(s(0)), 0, T174), SCOPE: 11, CLAUSE: 2\n\nT172 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
236 [label="236: mult(T172, s(s(0)), 0, T174), SCOPE: 11, CLAUSE: 3\n\nT172 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
239 [label="239: mult(T183, s(s(0)), s(s(0)), T185)\n\nT183 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
241 [label="241: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
247 [label="247: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="250: mult(T195, s(s(s(T197))), T197, T199)\n\nT195 is ground\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
251 [label="251: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="258: mult(T195, s(s(s(T197))), T197, T199), SCOPE: 12, CLAUSE: 1 | mult(T195, s(s(s(T197))), T197, T199), SCOPE: 12, CLAUSE: 2 | mult(T195, s(s(s(T197))), T197, T199), SCOPE: 12, CLAUSE: 3\n\nT195 is ground\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: mult(T195, s(s(s(T197))), T197, T199), SCOPE: 12, CLAUSE: 1\n\nT195 is ground\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: mult(T195, s(s(s(T197))), T197, T199), SCOPE: 12, CLAUSE: 2 | mult(T195, s(s(s(T197))), T197, T199), SCOPE: 12, CLAUSE: 3\n\nT195 is ground\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
268 [label="268: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
269 [label="269: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="270: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
273 [label="273: mult(T195, s(s(s(T197))), T197, T199), SCOPE: 12, CLAUSE: 2\n\nT195 is ground\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
274 [label="274: mult(T195, s(s(s(T197))), T197, T199), SCOPE: 12, CLAUSE: 3\n\nT195 is ground\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
278 [label="F: mult(T219, s(s(s(0))), s(s(s(0))), T222)\n\nT219 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
279 [label="279: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
284 [label="284: mult(T219, s(s(s(0))), s(s(s(0))), T222), SCOPE: 13, CLAUSE: 1 | mult(T219, s(s(s(0))), s(s(s(0))), T222), SCOPE: 13, CLAUSE: 2 | mult(T219, s(s(s(0))), s(s(s(0))), T222), SCOPE: 13, CLAUSE: 3\n\nT219 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
286 [label="286: mult(T219, s(s(s(0))), s(s(s(0))), T222), SCOPE: 13, CLAUSE: 2 | mult(T219, s(s(s(0))), s(s(s(0))), T222), SCOPE: 13, CLAUSE: 3\n\nT219 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
289 [label="289: mult(T219, s(s(s(0))), s(s(s(0))), T222), SCOPE: 13, CLAUSE: 3\n\nT219 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
298 [label="298: mult(T228, s(s(s(0))), s(s(0)), T230)\n\nT228 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
299 [label="299: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
302 [label="302: mult(T228, s(s(s(0))), s(s(0)), T230), SCOPE: 14, CLAUSE: 1 | mult(T228, s(s(s(0))), s(s(0)), T230), SCOPE: 14, CLAUSE: 2 | mult(T228, s(s(s(0))), s(s(0)), T230), SCOPE: 14, CLAUSE: 3\n\nT228 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
303 [label="303: mult(T228, s(s(s(0))), s(s(0)), T230), SCOPE: 14, CLAUSE: 2 | mult(T228, s(s(s(0))), s(s(0)), T230), SCOPE: 14, CLAUSE: 3\n\nT228 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
305 [label="305: mult(T228, s(s(s(0))), s(s(0)), T230), SCOPE: 14, CLAUSE: 3\n\nT228 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
306 [label="306: mult(T236, s(s(s(0))), s(0), T238)\n\nT236 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
308 [label="308: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
313 [label="313: mult(T236, s(s(s(0))), s(0), T238), SCOPE: 15, CLAUSE: 1 | mult(T236, s(s(s(0))), s(0), T238), SCOPE: 15, CLAUSE: 2 | mult(T236, s(s(s(0))), s(0), T238), SCOPE: 15, CLAUSE: 3\n\nT236 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
314 [label="314: mult(T236, s(s(s(0))), s(0), T238), SCOPE: 15, CLAUSE: 2 | mult(T236, s(s(s(0))), s(0), T238), SCOPE: 15, CLAUSE: 3\n\nT236 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
317 [label="317: mult(T236, s(s(s(0))), s(0), T238), SCOPE: 15, CLAUSE: 3\n\nT236 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
324 [label="324: mult(T244, s(s(s(0))), 0, T246)\n\nT244 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
325 [label="325: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
328 [label="328: mult(T244, s(s(s(0))), 0, T246), SCOPE: 16, CLAUSE: 1 | mult(T244, s(s(s(0))), 0, T246), SCOPE: 16, CLAUSE: 2 | mult(T244, s(s(s(0))), 0, T246), SCOPE: 16, CLAUSE: 3\n\nT244 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
329 [label="329: mult(T244, s(s(s(0))), 0, T246), SCOPE: 16, CLAUSE: 1\n\nT244 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
330 [label="330: mult(T244, s(s(s(0))), 0, T246), SCOPE: 16, CLAUSE: 2 | mult(T244, s(s(s(0))), 0, T246), SCOPE: 16, CLAUSE: 3\n\nT244 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
333 [label="333: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
334 [label="334: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
335 [label="335: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
342 [label="342: mult(T244, s(s(s(0))), 0, T246), SCOPE: 16, CLAUSE: 2\n\nT244 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
343 [label="343: mult(T244, s(s(s(0))), 0, T246), SCOPE: 16, CLAUSE: 3\n\nT244 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
348 [label="348: mult(T255, s(s(s(0))), s(s(s(0))), T257)\n\nT255 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
349 [label="349: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
352 [label="352: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
355 [label="355: mult(T267, s(s(s(s(T269)))), T269, T271)\n\nT267 is ground\nT269 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
357 [label="357: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
362 [label="362: mult(T267, s(s(s(s(T269)))), T269, T271), SCOPE: 17, CLAUSE: 1 | mult(T267, s(s(s(s(T269)))), T269, T271), SCOPE: 17, CLAUSE: 2 | mult(T267, s(s(s(s(T269)))), T269, T271), SCOPE: 17, CLAUSE: 3\n\nT267 is ground\nT269 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
364 [label="364: mult(T267, s(s(s(s(T269)))), T269, T271), SCOPE: 17, CLAUSE: 1\n\nT267 is ground\nT269 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
365 [label="365: mult(T267, s(s(s(s(T269)))), T269, T271), SCOPE: 17, CLAUSE: 2 | mult(T267, s(s(s(s(T269)))), T269, T271), SCOPE: 17, CLAUSE: 3\n\nT267 is ground\nT269 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
366 [label="366: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
367 [label="367: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
368 [label="368: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
371 [label="371: mult(T267, s(s(s(s(T269)))), T269, T271), SCOPE: 17, CLAUSE: 2\n\nT267 is ground\nT269 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
372 [label="372: mult(T267, s(s(s(s(T269)))), T269, T271), SCOPE: 17, CLAUSE: 3\n\nT267 is ground\nT269 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
376 [label="G: mult(T291, s(s(s(s(0)))), s(s(s(s(0)))), T294)\n\nT291 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
378 [label="378: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
381 [label="381: mult(T291, s(s(s(s(0)))), s(s(s(s(0)))), T294), SCOPE: 18, CLAUSE: 1 | mult(T291, s(s(s(s(0)))), s(s(s(s(0)))), T294), SCOPE: 18, CLAUSE: 2 | mult(T291, s(s(s(s(0)))), s(s(s(s(0)))), T294), SCOPE: 18, CLAUSE: 3\n\nT291 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
382 [label="382: mult(T291, s(s(s(s(0)))), s(s(s(s(0)))), T294), SCOPE: 18, CLAUSE: 2 | mult(T291, s(s(s(s(0)))), s(s(s(s(0)))), T294), SCOPE: 18, CLAUSE: 3\n\nT291 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
383 [label="383: mult(T291, s(s(s(s(0)))), s(s(s(s(0)))), T294), SCOPE: 18, CLAUSE: 3\n\nT291 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
409 [label="409: mult(T300, s(s(s(s(0)))), s(s(s(0))), T302)\n\nT300 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
411 [label="411: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
414 [label="414: mult(T300, s(s(s(s(0)))), s(s(s(0))), T302), SCOPE: 19, CLAUSE: 1 | mult(T300, s(s(s(s(0)))), s(s(s(0))), T302), SCOPE: 19, CLAUSE: 2 | mult(T300, s(s(s(s(0)))), s(s(s(0))), T302), SCOPE: 19, CLAUSE: 3\n\nT300 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
415 [label="415: mult(T300, s(s(s(s(0)))), s(s(s(0))), T302), SCOPE: 19, CLAUSE: 2 | mult(T300, s(s(s(s(0)))), s(s(s(0))), T302), SCOPE: 19, CLAUSE: 3\n\nT300 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
418 [label="418: mult(T300, s(s(s(s(0)))), s(s(s(0))), T302), SCOPE: 19, CLAUSE: 3\n\nT300 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
422 [label="422: mult(T308, s(s(s(s(0)))), s(s(0)), T310)\n\nT308 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
423 [label="423: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
425 [label="425: mult(T308, s(s(s(s(0)))), s(s(0)), T310), SCOPE: 20, CLAUSE: 1 | mult(T308, s(s(s(s(0)))), s(s(0)), T310), SCOPE: 20, CLAUSE: 2 | mult(T308, s(s(s(s(0)))), s(s(0)), T310), SCOPE: 20, CLAUSE: 3\n\nT308 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
426 [label="426: mult(T308, s(s(s(s(0)))), s(s(0)), T310), SCOPE: 20, CLAUSE: 2 | mult(T308, s(s(s(s(0)))), s(s(0)), T310), SCOPE: 20, CLAUSE: 3\n\nT308 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
429 [label="429: mult(T308, s(s(s(s(0)))), s(s(0)), T310), SCOPE: 20, CLAUSE: 3\n\nT308 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
430 [label="430: mult(T316, s(s(s(s(0)))), s(0), T318)\n\nT316 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
432 [label="432: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
459 [label="459: mult(T316, s(s(s(s(0)))), s(0), T318), SCOPE: 21, CLAUSE: 1 | mult(T316, s(s(s(s(0)))), s(0), T318), SCOPE: 21, CLAUSE: 2 | mult(T316, s(s(s(s(0)))), s(0), T318), SCOPE: 21, CLAUSE: 3\n\nT316 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
461 [label="461: mult(T316, s(s(s(s(0)))), s(0), T318), SCOPE: 21, CLAUSE: 2 | mult(T316, s(s(s(s(0)))), s(0), T318), SCOPE: 21, CLAUSE: 3\n\nT316 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
463 [label="463: mult(T316, s(s(s(s(0)))), s(0), T318), SCOPE: 21, CLAUSE: 3\n\nT316 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
469 [label="469: mult(T324, s(s(s(s(0)))), 0, T326)\n\nT324 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
470 [label="470: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
485 [label="485: mult(T324, s(s(s(s(0)))), 0, T326), SCOPE: 22, CLAUSE: 1 | mult(T324, s(s(s(s(0)))), 0, T326), SCOPE: 22, CLAUSE: 2 | mult(T324, s(s(s(s(0)))), 0, T326), SCOPE: 22, CLAUSE: 3\n\nT324 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
488 [label="488: mult(T324, s(s(s(s(0)))), 0, T326), SCOPE: 22, CLAUSE: 1\n\nT324 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
489 [label="489: mult(T324, s(s(s(s(0)))), 0, T326), SCOPE: 22, CLAUSE: 2 | mult(T324, s(s(s(s(0)))), 0, T326), SCOPE: 22, CLAUSE: 3\n\nT324 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
492 [label="492: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
493 [label="493: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
494 [label="494: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
495 [label="495: mult(T324, s(s(s(s(0)))), 0, T326), SCOPE: 22, CLAUSE: 2\n\nT324 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
496 [label="496: mult(T324, s(s(s(s(0)))), 0, T326), SCOPE: 22, CLAUSE: 3\n\nT324 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
498 [label="498: mult(T335, s(s(s(s(0)))), s(s(s(s(0)))), T337)\n\nT335 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
501 [label="501: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
509 [label="509: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
512 [label="512: mult(T347, s(s(s(s(s(T349))))), T349, T351)\n\nT347 is ground\nT349 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
513 [label="513: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
515 [label="515: mult(T347, s(s(s(s(s(T349))))), T349, T351), SCOPE: 23, CLAUSE: 1 | mult(T347, s(s(s(s(s(T349))))), T349, T351), SCOPE: 23, CLAUSE: 2 | mult(T347, s(s(s(s(s(T349))))), T349, T351), SCOPE: 23, CLAUSE: 3\n\nT347 is ground\nT349 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
520 [label="520: mult(T347, s(s(s(s(s(T349))))), T349, T351), SCOPE: 23, CLAUSE: 1\n\nT347 is ground\nT349 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
521 [label="521: mult(T347, s(s(s(s(s(T349))))), T349, T351), SCOPE: 23, CLAUSE: 2 | mult(T347, s(s(s(s(s(T349))))), T349, T351), SCOPE: 23, CLAUSE: 3\n\nT347 is ground\nT349 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
523 [label="523: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
524 [label="524: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
525 [label="525: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
528 [label="528: mult(T347, s(s(s(s(s(T349))))), T349, T351), SCOPE: 23, CLAUSE: 2\n\nT347 is ground\nT349 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
529 [label="529: mult(T347, s(s(s(s(s(T349))))), T349, T351), SCOPE: 23, CLAUSE: 3\n\nT347 is ground\nT349 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
530 [label="H: mult(T371, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T374)\n\nT371 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
531 [label="531: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
541 [label="541: mult(T371, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T374), SCOPE: 24, CLAUSE: 1 | mult(T371, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T374), SCOPE: 24, CLAUSE: 2 | mult(T371, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T374), SCOPE: 24, CLAUSE: 3\n\nT371 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
544 [label="544: mult(T371, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T374), SCOPE: 24, CLAUSE: 2 | mult(T371, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T374), SCOPE: 24, CLAUSE: 3\n\nT371 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
545 [label="545: mult(T371, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T374), SCOPE: 24, CLAUSE: 3\n\nT371 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
553 [label="553: mult(T380, s(s(s(s(s(0))))), s(s(s(s(0)))), T382)\n\nT380 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
554 [label="554: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
558 [label="558: mult(T380, s(s(s(s(s(0))))), s(s(s(s(0)))), T382), SCOPE: 25, CLAUSE: 1 | mult(T380, s(s(s(s(s(0))))), s(s(s(s(0)))), T382), SCOPE: 25, CLAUSE: 2 | mult(T380, s(s(s(s(s(0))))), s(s(s(s(0)))), T382), SCOPE: 25, CLAUSE: 3\n\nT380 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
559 [label="559: mult(T380, s(s(s(s(s(0))))), s(s(s(s(0)))), T382), SCOPE: 25, CLAUSE: 2 | mult(T380, s(s(s(s(s(0))))), s(s(s(s(0)))), T382), SCOPE: 25, CLAUSE: 3\n\nT380 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
560 [label="560: mult(T380, s(s(s(s(s(0))))), s(s(s(s(0)))), T382), SCOPE: 25, CLAUSE: 3\n\nT380 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
561 [label="561: mult(T388, s(s(s(s(s(0))))), s(s(s(0))), T390)\n\nT388 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
562 [label="562: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
573 [label="573: mult(T388, s(s(s(s(s(0))))), s(s(s(0))), T390), SCOPE: 26, CLAUSE: 1 | mult(T388, s(s(s(s(s(0))))), s(s(s(0))), T390), SCOPE: 26, CLAUSE: 2 | mult(T388, s(s(s(s(s(0))))), s(s(s(0))), T390), SCOPE: 26, CLAUSE: 3\n\nT388 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
574 [label="574: mult(T388, s(s(s(s(s(0))))), s(s(s(0))), T390), SCOPE: 26, CLAUSE: 2 | mult(T388, s(s(s(s(s(0))))), s(s(s(0))), T390), SCOPE: 26, CLAUSE: 3\n\nT388 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
575 [label="575: mult(T388, s(s(s(s(s(0))))), s(s(s(0))), T390), SCOPE: 26, CLAUSE: 3\n\nT388 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
581 [label="581: mult(T396, s(s(s(s(s(0))))), s(s(0)), T398)\n\nT396 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
582 [label="582: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
586 [label="586: mult(T396, s(s(s(s(s(0))))), s(s(0)), T398), SCOPE: 27, CLAUSE: 1 | mult(T396, s(s(s(s(s(0))))), s(s(0)), T398), SCOPE: 27, CLAUSE: 2 | mult(T396, s(s(s(s(s(0))))), s(s(0)), T398), SCOPE: 27, CLAUSE: 3\n\nT396 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
587 [label="587: mult(T396, s(s(s(s(s(0))))), s(s(0)), T398), SCOPE: 27, CLAUSE: 2 | mult(T396, s(s(s(s(s(0))))), s(s(0)), T398), SCOPE: 27, CLAUSE: 3\n\nT396 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
589 [label="589: mult(T396, s(s(s(s(s(0))))), s(s(0)), T398), SCOPE: 27, CLAUSE: 3\n\nT396 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
591 [label="591: mult(T404, s(s(s(s(s(0))))), s(0), T406)\n\nT404 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
592 [label="592: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
598 [label="598: mult(T404, s(s(s(s(s(0))))), s(0), T406), SCOPE: 28, CLAUSE: 1 | mult(T404, s(s(s(s(s(0))))), s(0), T406), SCOPE: 28, CLAUSE: 2 | mult(T404, s(s(s(s(s(0))))), s(0), T406), SCOPE: 28, CLAUSE: 3\n\nT404 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
601 [label="601: mult(T404, s(s(s(s(s(0))))), s(0), T406), SCOPE: 28, CLAUSE: 2 | mult(T404, s(s(s(s(s(0))))), s(0), T406), SCOPE: 28, CLAUSE: 3\n\nT404 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
602 [label="602: mult(T404, s(s(s(s(s(0))))), s(0), T406), SCOPE: 28, CLAUSE: 3\n\nT404 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
604 [label="604: mult(T412, s(s(s(s(s(0))))), 0, T414)\n\nT412 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
605 [label="605: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
609 [label="609: mult(T412, s(s(s(s(s(0))))), 0, T414), SCOPE: 29, CLAUSE: 1 | mult(T412, s(s(s(s(s(0))))), 0, T414), SCOPE: 29, CLAUSE: 2 | mult(T412, s(s(s(s(s(0))))), 0, T414), SCOPE: 29, CLAUSE: 3\n\nT412 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
612 [label="612: mult(T412, s(s(s(s(s(0))))), 0, T414), SCOPE: 29, CLAUSE: 1\n\nT412 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
613 [label="613: mult(T412, s(s(s(s(s(0))))), 0, T414), SCOPE: 29, CLAUSE: 2 | mult(T412, s(s(s(s(s(0))))), 0, T414), SCOPE: 29, CLAUSE: 3\n\nT412 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
614 [label="614: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
615 [label="615: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
616 [label="616: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
617 [label="617: mult(T412, s(s(s(s(s(0))))), 0, T414), SCOPE: 29, CLAUSE: 2\n\nT412 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
618 [label="618: mult(T412, s(s(s(s(s(0))))), 0, T414), SCOPE: 29, CLAUSE: 3\n\nT412 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
623 [label="623: mult(T423, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T425)\n\nT423 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
624 [label="624: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
630 [label="630: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
631 [label="631: mult(T435, s(s(s(s(s(s(T437)))))), T437, T439)\n\nT435 is ground\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
632 [label="632: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
638 [label="638: mult(T435, s(s(s(s(s(s(T437)))))), T437, T439), SCOPE: 30, CLAUSE: 1 | mult(T435, s(s(s(s(s(s(T437)))))), T437, T439), SCOPE: 30, CLAUSE: 2 | mult(T435, s(s(s(s(s(s(T437)))))), T437, T439), SCOPE: 30, CLAUSE: 3\n\nT435 is ground\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
639 [label="639: mult(T435, s(s(s(s(s(s(T437)))))), T437, T439), SCOPE: 30, CLAUSE: 1\n\nT435 is ground\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
640 [label="640: mult(T435, s(s(s(s(s(s(T437)))))), T437, T439), SCOPE: 30, CLAUSE: 2 | mult(T435, s(s(s(s(s(s(T437)))))), T437, T439), SCOPE: 30, CLAUSE: 3\n\nT435 is ground\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
643 [label="643: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
644 [label="644: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
645 [label="645: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
648 [label="648: mult(T435, s(s(s(s(s(s(T437)))))), T437, T439), SCOPE: 30, CLAUSE: 2\n\nT435 is ground\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
649 [label="649: mult(T435, s(s(s(s(s(s(T437)))))), T437, T439), SCOPE: 30, CLAUSE: 3\n\nT435 is ground\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
659 [label="I: mult(T459, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T462)\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
660 [label="660: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
663 [label="663: mult(T459, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T462), SCOPE: 31, CLAUSE: 1 | mult(T459, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T462), SCOPE: 31, CLAUSE: 2 | mult(T459, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T462), SCOPE: 31, CLAUSE: 3\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
664 [label="664: mult(T459, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T462), SCOPE: 31, CLAUSE: 2 | mult(T459, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T462), SCOPE: 31, CLAUSE: 3\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
666 [label="666: mult(T459, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T462), SCOPE: 31, CLAUSE: 3\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
668 [label="668: mult(T468, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T470)\n\nT468 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
669 [label="669: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
676 [label="676: mult(T468, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T470), SCOPE: 32, CLAUSE: 1 | mult(T468, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T470), SCOPE: 32, CLAUSE: 2 | mult(T468, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T470), SCOPE: 32, CLAUSE: 3\n\nT468 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
692 [label="692: mult(T468, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T470), SCOPE: 32, CLAUSE: 2 | mult(T468, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T470), SCOPE: 32, CLAUSE: 3\n\nT468 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
694 [label="694: mult(T468, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T470), SCOPE: 32, CLAUSE: 3\n\nT468 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
705 [label="705: mult(T476, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T478)\n\nT476 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
706 [label="706: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
711 [label="711: mult(T476, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T478), SCOPE: 33, CLAUSE: 1 | mult(T476, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T478), SCOPE: 33, CLAUSE: 2 | mult(T476, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T478), SCOPE: 33, CLAUSE: 3\n\nT476 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
720 [label="720: mult(T476, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T478), SCOPE: 33, CLAUSE: 2 | mult(T476, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T478), SCOPE: 33, CLAUSE: 3\n\nT476 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
721 [label="721: mult(T476, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T478), SCOPE: 33, CLAUSE: 3\n\nT476 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
731 [label="731: mult(T484, s(s(s(s(s(s(0)))))), s(s(s(0))), T486)\n\nT484 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
732 [label="732: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
745 [label="745: mult(T484, s(s(s(s(s(s(0)))))), s(s(s(0))), T486), SCOPE: 34, CLAUSE: 1 | mult(T484, s(s(s(s(s(s(0)))))), s(s(s(0))), T486), SCOPE: 34, CLAUSE: 2 | mult(T484, s(s(s(s(s(s(0)))))), s(s(s(0))), T486), SCOPE: 34, CLAUSE: 3\n\nT484 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
746 [label="746: mult(T484, s(s(s(s(s(s(0)))))), s(s(s(0))), T486), SCOPE: 34, CLAUSE: 2 | mult(T484, s(s(s(s(s(s(0)))))), s(s(s(0))), T486), SCOPE: 34, CLAUSE: 3\n\nT484 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
749 [label="749: mult(T484, s(s(s(s(s(s(0)))))), s(s(s(0))), T486), SCOPE: 34, CLAUSE: 3\n\nT484 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
753 [label="753: mult(T492, s(s(s(s(s(s(0)))))), s(s(0)), T494)\n\nT492 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
754 [label="754: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
770 [label="770: mult(T492, s(s(s(s(s(s(0)))))), s(s(0)), T494), SCOPE: 35, CLAUSE: 1 | mult(T492, s(s(s(s(s(s(0)))))), s(s(0)), T494), SCOPE: 35, CLAUSE: 2 | mult(T492, s(s(s(s(s(s(0)))))), s(s(0)), T494), SCOPE: 35, CLAUSE: 3\n\nT492 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
771 [label="771: mult(T492, s(s(s(s(s(s(0)))))), s(s(0)), T494), SCOPE: 35, CLAUSE: 2 | mult(T492, s(s(s(s(s(s(0)))))), s(s(0)), T494), SCOPE: 35, CLAUSE: 3\n\nT492 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
772 [label="772: mult(T492, s(s(s(s(s(s(0)))))), s(s(0)), T494), SCOPE: 35, CLAUSE: 3\n\nT492 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
777 [label="777: mult(T500, s(s(s(s(s(s(0)))))), s(0), T502)\n\nT500 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
778 [label="778: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
796 [label="796: mult(T500, s(s(s(s(s(s(0)))))), s(0), T502), SCOPE: 36, CLAUSE: 1 | mult(T500, s(s(s(s(s(s(0)))))), s(0), T502), SCOPE: 36, CLAUSE: 2 | mult(T500, s(s(s(s(s(s(0)))))), s(0), T502), SCOPE: 36, CLAUSE: 3\n\nT500 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
798 [label="798: mult(T500, s(s(s(s(s(s(0)))))), s(0), T502), SCOPE: 36, CLAUSE: 2 | mult(T500, s(s(s(s(s(s(0)))))), s(0), T502), SCOPE: 36, CLAUSE: 3\n\nT500 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
800 [label="800: mult(T500, s(s(s(s(s(s(0)))))), s(0), T502), SCOPE: 36, CLAUSE: 3\n\nT500 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
811 [label="811: mult(T508, s(s(s(s(s(s(0)))))), 0, T510)\n\nT508 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
812 [label="812: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
820 [label="820: mult(T508, s(s(s(s(s(s(0)))))), 0, T510), SCOPE: 37, CLAUSE: 1 | mult(T508, s(s(s(s(s(s(0)))))), 0, T510), SCOPE: 37, CLAUSE: 2 | mult(T508, s(s(s(s(s(s(0)))))), 0, T510), SCOPE: 37, CLAUSE: 3\n\nT508 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
821 [label="821: mult(T508, s(s(s(s(s(s(0)))))), 0, T510), SCOPE: 37, CLAUSE: 1\n\nT508 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
822 [label="822: mult(T508, s(s(s(s(s(s(0)))))), 0, T510), SCOPE: 37, CLAUSE: 2 | mult(T508, s(s(s(s(s(s(0)))))), 0, T510), SCOPE: 37, CLAUSE: 3\n\nT508 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
823 [label="823: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
824 [label="824: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
826 [label="826: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
831 [label="831: mult(T508, s(s(s(s(s(s(0)))))), 0, T510), SCOPE: 37, CLAUSE: 2\n\nT508 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
832 [label="832: mult(T508, s(s(s(s(s(s(0)))))), 0, T510), SCOPE: 37, CLAUSE: 3\n\nT508 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
838 [label="838: mult(T519, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T521)\n\nT519 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
839 [label="839: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
843 [label="843: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
846 [label="846: mult(T531, s(s(s(s(s(s(s(T533))))))), T533, T535)\n\nT531 is ground\nT533 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
847 [label="847: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
849 [label="849: mult(T531, s(s(s(s(s(s(s(T533))))))), T533, T535), SCOPE: 38, CLAUSE: 1 | mult(T531, s(s(s(s(s(s(s(T533))))))), T533, T535), SCOPE: 38, CLAUSE: 2 | mult(T531, s(s(s(s(s(s(s(T533))))))), T533, T535), SCOPE: 38, CLAUSE: 3\n\nT531 is ground\nT533 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
854 [label="854: mult(T531, s(s(s(s(s(s(s(T533))))))), T533, T535), SCOPE: 38, CLAUSE: 1\n\nT531 is ground\nT533 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
855 [label="855: mult(T531, s(s(s(s(s(s(s(T533))))))), T533, T535), SCOPE: 38, CLAUSE: 2 | mult(T531, s(s(s(s(s(s(s(T533))))))), T533, T535), SCOPE: 38, CLAUSE: 3\n\nT531 is ground\nT533 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
856 [label="856: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
857 [label="857: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
858 [label="858: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
860 [label="860: mult(T531, s(s(s(s(s(s(s(T533))))))), T533, T535), SCOPE: 38, CLAUSE: 2\n\nT531 is ground\nT533 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
861 [label="861: mult(T531, s(s(s(s(s(s(s(T533))))))), T533, T535), SCOPE: 38, CLAUSE: 3\n\nT531 is ground\nT533 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
870 [label="J: mult(T555, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T558)\n\nT555 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
871 [label="871: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
878 [label="878: mult(T555, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T558), SCOPE: 39, CLAUSE: 1 | mult(T555, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T558), SCOPE: 39, CLAUSE: 2 | mult(T555, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T558), SCOPE: 39, CLAUSE: 3\n\nT555 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
879 [label="879: mult(T555, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T558), SCOPE: 39, CLAUSE: 2 | mult(T555, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T558), SCOPE: 39, CLAUSE: 3\n\nT555 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
883 [label="883: mult(T555, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T558), SCOPE: 39, CLAUSE: 3\n\nT555 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
884 [label="884: mult(T564, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(0)))))), T566)\n\nT564 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
885 [label="885: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
891 [label="891: mult(T564, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(0)))))), T566), SCOPE: 40, CLAUSE: 1 | mult(T564, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(0)))))), T566), SCOPE: 40, CLAUSE: 2 | mult(T564, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(0)))))), T566), SCOPE: 40, CLAUSE: 3\n\nT564 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
892 [label="892: mult(T564, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(0)))))), T566), SCOPE: 40, CLAUSE: 2 | mult(T564, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(0)))))), T566), SCOPE: 40, CLAUSE: 3\n\nT564 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
893 [label="893: mult(T564, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(0)))))), T566), SCOPE: 40, CLAUSE: 3\n\nT564 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
897 [label="897: mult(T572, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(0))))), T574)\n\nT572 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
898 [label="898: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
902 [label="902: mult(T572, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(0))))), T574), SCOPE: 41, CLAUSE: 1 | mult(T572, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(0))))), T574), SCOPE: 41, CLAUSE: 2 | mult(T572, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(0))))), T574), SCOPE: 41, CLAUSE: 3\n\nT572 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
904 [label="904: mult(T572, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(0))))), T574), SCOPE: 41, CLAUSE: 2 | mult(T572, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(0))))), T574), SCOPE: 41, CLAUSE: 3\n\nT572 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
905 [label="905: mult(T572, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(0))))), T574), SCOPE: 41, CLAUSE: 3\n\nT572 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
911 [label="911: mult(T580, s(s(s(s(s(s(s(0))))))), s(s(s(s(0)))), T582)\n\nT580 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
912 [label="912: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
914 [label="914: mult(T580, s(s(s(s(s(s(s(0))))))), s(s(s(s(0)))), T582), SCOPE: 42, CLAUSE: 1 | mult(T580, s(s(s(s(s(s(s(0))))))), s(s(s(s(0)))), T582), SCOPE: 42, CLAUSE: 2 | mult(T580, s(s(s(s(s(s(s(0))))))), s(s(s(s(0)))), T582), SCOPE: 42, CLAUSE: 3\n\nT580 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
916 [label="916: mult(T580, s(s(s(s(s(s(s(0))))))), s(s(s(s(0)))), T582), SCOPE: 42, CLAUSE: 2 | mult(T580, s(s(s(s(s(s(s(0))))))), s(s(s(s(0)))), T582), SCOPE: 42, CLAUSE: 3\n\nT580 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
918 [label="918: mult(T580, s(s(s(s(s(s(s(0))))))), s(s(s(s(0)))), T582), SCOPE: 42, CLAUSE: 3\n\nT580 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
923 [label="923: mult(T588, s(s(s(s(s(s(s(0))))))), s(s(s(0))), T590)\n\nT588 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
924 [label="924: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
926 [label="926: mult(T588, s(s(s(s(s(s(s(0))))))), s(s(s(0))), T590), SCOPE: 43, CLAUSE: 1 | mult(T588, s(s(s(s(s(s(s(0))))))), s(s(s(0))), T590), SCOPE: 43, CLAUSE: 2 | mult(T588, s(s(s(s(s(s(s(0))))))), s(s(s(0))), T590), SCOPE: 43, CLAUSE: 3\n\nT588 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
928 [label="928: mult(T588, s(s(s(s(s(s(s(0))))))), s(s(s(0))), T590), SCOPE: 43, CLAUSE: 2 | mult(T588, s(s(s(s(s(s(s(0))))))), s(s(s(0))), T590), SCOPE: 43, CLAUSE: 3\n\nT588 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
930 [label="930: mult(T588, s(s(s(s(s(s(s(0))))))), s(s(s(0))), T590), SCOPE: 43, CLAUSE: 3\n\nT588 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
934 [label="934: mult(T596, s(s(s(s(s(s(s(0))))))), s(s(0)), T598)\n\nT596 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
935 [label="935: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
939 [label="939: mult(T596, s(s(s(s(s(s(s(0))))))), s(s(0)), T598), SCOPE: 44, CLAUSE: 1 | mult(T596, s(s(s(s(s(s(s(0))))))), s(s(0)), T598), SCOPE: 44, CLAUSE: 2 | mult(T596, s(s(s(s(s(s(s(0))))))), s(s(0)), T598), SCOPE: 44, CLAUSE: 3\n\nT596 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
940 [label="940: mult(T596, s(s(s(s(s(s(s(0))))))), s(s(0)), T598), SCOPE: 44, CLAUSE: 2 | mult(T596, s(s(s(s(s(s(s(0))))))), s(s(0)), T598), SCOPE: 44, CLAUSE: 3\n\nT596 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
943 [label="943: mult(T596, s(s(s(s(s(s(s(0))))))), s(s(0)), T598), SCOPE: 44, CLAUSE: 3\n\nT596 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
945 [label="945: mult(T604, s(s(s(s(s(s(s(0))))))), s(0), T606)\n\nT604 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
946 [label="946: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
954 [label="954: mult(T604, s(s(s(s(s(s(s(0))))))), s(0), T606), SCOPE: 45, CLAUSE: 1 | mult(T604, s(s(s(s(s(s(s(0))))))), s(0), T606), SCOPE: 45, CLAUSE: 2 | mult(T604, s(s(s(s(s(s(s(0))))))), s(0), T606), SCOPE: 45, CLAUSE: 3\n\nT604 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
955 [label="955: mult(T604, s(s(s(s(s(s(s(0))))))), s(0), T606), SCOPE: 45, CLAUSE: 2 | mult(T604, s(s(s(s(s(s(s(0))))))), s(0), T606), SCOPE: 45, CLAUSE: 3\n\nT604 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
958 [label="958: mult(T604, s(s(s(s(s(s(s(0))))))), s(0), T606), SCOPE: 45, CLAUSE: 3\n\nT604 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
961 [label="961: mult(T612, s(s(s(s(s(s(s(0))))))), 0, T614)\n\nT612 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
962 [label="962: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
967 [label="967: mult(T612, s(s(s(s(s(s(s(0))))))), 0, T614), SCOPE: 46, CLAUSE: 1 | mult(T612, s(s(s(s(s(s(s(0))))))), 0, T614), SCOPE: 46, CLAUSE: 2 | mult(T612, s(s(s(s(s(s(s(0))))))), 0, T614), SCOPE: 46, CLAUSE: 3\n\nT612 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
968 [label="968: mult(T612, s(s(s(s(s(s(s(0))))))), 0, T614), SCOPE: 46, CLAUSE: 1\n\nT612 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
969 [label="969: mult(T612, s(s(s(s(s(s(s(0))))))), 0, T614), SCOPE: 46, CLAUSE: 2 | mult(T612, s(s(s(s(s(s(s(0))))))), 0, T614), SCOPE: 46, CLAUSE: 3\n\nT612 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
970 [label="970: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
971 [label="971: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
972 [label="972: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
975 [label="975: mult(T612, s(s(s(s(s(s(s(0))))))), 0, T614), SCOPE: 46, CLAUSE: 2\n\nT612 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
976 [label="976: mult(T612, s(s(s(s(s(s(s(0))))))), 0, T614), SCOPE: 46, CLAUSE: 3\n\nT612 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
979 [label="979: mult(T623, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T625)\n\nT623 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
980 [label="980: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
981 [label="981: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
983 [label="983: mult(T635, s(s(s(s(s(s(s(s(T637)))))))), T637, T639)\n\nT635 is ground\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
984 [label="984: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
987 [label="K: mult(T635, s(T642), T637, T639)\n\nT635 is ground\nT637 is ground\nT642 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
989 [label="989: mult(T635, s(T642), T637, T639), SCOPE: 47, CLAUSE: 1 | mult(T635, s(T642), T637, T639), SCOPE: 47, CLAUSE: 2 | mult(T635, s(T642), T637, T639), SCOPE: 47, CLAUSE: 3\n\nT635 is ground\nT637 is ground\nT642 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
992 [label="992: mult(T635, s(T642), T637, T639), SCOPE: 47, CLAUSE: 1\n\nT635 is ground\nT637 is ground\nT642 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
993 [label="993: mult(T635, s(T642), T637, T639), SCOPE: 47, CLAUSE: 2 | mult(T635, s(T642), T637, T639), SCOPE: 47, CLAUSE: 3\n\nT635 is ground\nT637 is ground\nT642 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
994 [label="994: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
995 [label="995: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
996 [label="996: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
998 [label="998: mult(T635, s(T642), T637, T639), SCOPE: 47, CLAUSE: 2\n\nT635 is ground\nT637 is ground\nT642 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
999 [label="999: mult(T635, s(T642), T637, T639), SCOPE: 47, CLAUSE: 3\n\nT635 is ground\nT637 is ground\nT642 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1005 [label="1005: mult(T662, s(T663), s(T663), T665)\n\nT662 is ground\nT663 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1006 [label="1006: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1012 [label="1012: mult(T676, s(T677), T678, T680)\n\nT676 is ground\nT677 is ground\nT678 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1013 [label="1013: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1014 [label="1014: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1015 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2 -> 1015 [arrowhead = none ];
1015 -> 5;

1016 [label="ONLY EVAL with clause\ntimes(X4, X5, X6) :- mult(X4, X5, 0, X6).\nand substitutionT1 -> T7,\nX4 -> T7,\nT2 -> T8,\nX5 -> T8,\nT3 -> T10,\nX6 -> T10,\nT9 -> T10", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 1016 [arrowhead = none ];
1016 -> 8;

1017 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
8 -> 1017 [arrowhead = none ];
1017 -> 9;

1018 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
9 -> 1018 [arrowhead = none ];
1018 -> 12;

1019 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
9 -> 1019 [arrowhead = none ];
1019 -> 15;

1020 [label="EVAL with clause\nmult(0, X11, 0, 0).\nand substitutionT7 -> 0,\nT8 -> T15,\nX11 -> T15,\nT10 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 1020 [arrowhead = none ];
1020 -> 16;

1021 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 1021 [arrowhead = none ];
1021 -> 19;

1022 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
15 -> 1022 [arrowhead = none ];
1022 -> 27;

1023 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
15 -> 1023 [arrowhead = none ];
1023 -> 28;

1024 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 1024 [arrowhead = none ];
1024 -> 20;

1025 [label="EVAL with clause\nmult(s(X24), X25, 0, X26) :- mult(X24, X25, X25, X26).\nand substitutionX24 -> T28,\nT7 -> s(T28),\nT8 -> T29,\nX25 -> T29,\nT10 -> T31,\nX26 -> T31,\nT30 -> T31", fontsize=14, style = filled, fillcolor = lightblue];
27 -> 1025 [arrowhead = none ];
1025 -> 36;

1026 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
27 -> 1026 [arrowhead = none ];
1026 -> 37;

1027 [label="BACKTRACK\nfor clause: mult(X, Y, s(W), s(Z)) :- mult(X, Y, W, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
28 -> 1027 [arrowhead = none ];
1027 -> 1014;

1028 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
36 -> 1028 [arrowhead = none ];
1028 -> 39;

1029 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
39 -> 1029 [arrowhead = none ];
1029 -> 42;

1030 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
39 -> 1030 [arrowhead = none ];
1030 -> 43;

1031 [label="EVAL with clause\nmult(0, X33, 0, 0).\nand substitutionT28 -> 0,\nT29 -> 0,\nX33 -> 0,\nT38 -> 0,\nT31 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
42 -> 1031 [arrowhead = none ];
1031 -> 48;

1032 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
42 -> 1032 [arrowhead = none ];
1032 -> 50;

1033 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
43 -> 1033 [arrowhead = none ];
1033 -> 55;

1034 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
43 -> 1034 [arrowhead = none ];
1034 -> 56;

1035 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
48 -> 1035 [arrowhead = none ];
1035 -> 51;

1036 [label="EVAL with clause\nmult(s(X46), X47, 0, X48) :- mult(X46, X47, X47, X48).\nand substitutionX46 -> T51,\nT28 -> s(T51),\nT29 -> 0,\nX47 -> 0,\nT52 -> 0,\nT31 -> T54,\nX48 -> T54,\nT53 -> T54", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 1036 [arrowhead = none ];
1036 -> 61;

1037 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
55 -> 1037 [arrowhead = none ];
1037 -> 62;

1038 [label="EVAL with clause\nmult(X85, X86, s(X87), s(X88)) :- mult(X85, X86, X87, X88).\nand substitutionT28 -> T75,\nX85 -> T75,\nT29 -> s(T77),\nX86 -> s(T77),\nX87 -> T77,\nT76 -> s(T77),\nX88 -> T79,\nT31 -> s(T79),\nT78 -> T79", fontsize=14, style = filled, fillcolor = lightblue];
56 -> 1038 [arrowhead = none ];
1038 -> 93;

1039 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
56 -> 1039 [arrowhead = none ];
1039 -> 96;

1040 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
61 -> 1040 [arrowhead = none ];
1040 -> 66;

1041 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
66 -> 1041 [arrowhead = none ];
1041 -> 67;

1042 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
66 -> 1042 [arrowhead = none ];
1042 -> 68;

1043 [label="EVAL with clause\nmult(0, X55, 0, 0).\nand substitutionT51 -> 0,\nX55 -> 0,\nT54 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 1043 [arrowhead = none ];
1043 -> 73;

1044 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
67 -> 1044 [arrowhead = none ];
1044 -> 75;

1045 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
68 -> 1045 [arrowhead = none ];
1045 -> 80;

1046 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
68 -> 1046 [arrowhead = none ];
1046 -> 81;

1047 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
73 -> 1047 [arrowhead = none ];
1047 -> 77;

1048 [label="EVAL with clause\nmult(s(X68), X69, 0, X70) :- mult(X68, X69, X69, X70).\nand substitutionX68 -> T63,\nT51 -> s(T63),\nX69 -> 0,\nT54 -> T65,\nX70 -> T65,\nT64 -> T65", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 1048 [arrowhead = none ];
1048 -> 84;

1049 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
80 -> 1049 [arrowhead = none ];
1049 -> 85;

1050 [label="BACKTRACK\nfor clause: mult(X, Y, s(W), s(Z)) :- mult(X, Y, W, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
81 -> 1050 [arrowhead = none ];
1050 -> 87;

1051 [label="INSTANCE with matching:\nT51 -> T63\nT54 -> T65", fontsize=14, style = filled, fillcolor = lightgrey];
84 -> 1051 [arrowhead = none , style=dashed];
1051 -> 61[style=dashed];

1052 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
93 -> 1052 [arrowhead = none ];
1052 -> 101;

1053 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
101 -> 1053 [arrowhead = none ];
1053 -> 105;

1054 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
101 -> 1054 [arrowhead = none ];
1054 -> 106;

1055 [label="EVAL with clause\nmult(0, X95, 0, 0).\nand substitutionT75 -> 0,\nT77 -> 0,\nX95 -> s(0),\nT86 -> 0,\nT79 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 1055 [arrowhead = none ];
1055 -> 108;

1056 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
105 -> 1056 [arrowhead = none ];
1056 -> 109;

1057 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
106 -> 1057 [arrowhead = none ];
1057 -> 114;

1058 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
106 -> 1058 [arrowhead = none ];
1058 -> 115;

1059 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
108 -> 1059 [arrowhead = none ];
1059 -> 110;

1060 [label="EVAL with clause\nmult(s(X108), X109, 0, X110) :- mult(X108, X109, X109, X110).\nand substitutionX108 -> T99,\nT75 -> s(T99),\nT77 -> 0,\nX109 -> s(0),\nT100 -> 0,\nT79 -> T102,\nX110 -> T102,\nT101 -> T102", fontsize=14, style = filled, fillcolor = lightblue];
114 -> 1060 [arrowhead = none ];
1060 -> 121;

1061 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
114 -> 1061 [arrowhead = none ];
1061 -> 123;

1062 [label="EVAL with clause\nmult(X165, X166, s(X167), s(X168)) :- mult(X165, X166, X167, X168).\nand substitutionT75 -> T131,\nX165 -> T131,\nT77 -> s(T133),\nX166 -> s(s(T133)),\nX167 -> T133,\nT132 -> s(T133),\nX168 -> T135,\nT79 -> s(T135),\nT134 -> T135", fontsize=14, style = filled, fillcolor = lightblue];
115 -> 1062 [arrowhead = none ];
1062 -> 164;

1063 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
115 -> 1063 [arrowhead = none ];
1063 -> 165;

1064 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
121 -> 1064 [arrowhead = none ];
1064 -> 127;

1065 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
127 -> 1065 [arrowhead = none ];
1065 -> 128;

1066 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
128 -> 1066 [arrowhead = none ];
1066 -> 129;

1067 [label="EVAL with clause\nmult(X125, X126, s(X127), s(X128)) :- mult(X125, X126, X127, X128).\nand substitutionT99 -> T108,\nX125 -> T108,\nX126 -> s(0),\nX127 -> 0,\nX128 -> T110,\nT102 -> s(T110),\nT109 -> T110", fontsize=14, style = filled, fillcolor = lightblue];
129 -> 1067 [arrowhead = none ];
1067 -> 133;

1068 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 1068 [arrowhead = none ];
1068 -> 134;

1069 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
133 -> 1069 [arrowhead = none ];
1069 -> 137;

1070 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
137 -> 1070 [arrowhead = none ];
1070 -> 138;

1071 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
137 -> 1071 [arrowhead = none ];
1071 -> 139;

1072 [label="EVAL with clause\nmult(0, X135, 0, 0).\nand substitutionT108 -> 0,\nX135 -> s(0),\nT110 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
138 -> 1072 [arrowhead = none ];
1072 -> 144;

1073 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
138 -> 1073 [arrowhead = none ];
1073 -> 146;

1074 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
139 -> 1074 [arrowhead = none ];
1074 -> 151;

1075 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
139 -> 1075 [arrowhead = none ];
1075 -> 152;

1076 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
144 -> 1076 [arrowhead = none ];
1076 -> 147;

1077 [label="EVAL with clause\nmult(s(X148), X149, 0, X150) :- mult(X148, X149, X149, X150).\nand substitutionX148 -> T119,\nT108 -> s(T119),\nX149 -> s(0),\nT110 -> T121,\nX150 -> T121,\nT120 -> T121", fontsize=14, style = filled, fillcolor = lightblue];
151 -> 1077 [arrowhead = none ];
1077 -> 156;

1078 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
151 -> 1078 [arrowhead = none ];
1078 -> 157;

1079 [label="BACKTRACK\nfor clause: mult(X, Y, s(W), s(Z)) :- mult(X, Y, W, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
152 -> 1079 [arrowhead = none ];
1079 -> 160;

1080 [label="INSTANCE with matching:\nT99 -> T119\nT102 -> T121", fontsize=14, style = filled, fillcolor = lightgrey];
156 -> 1080 [arrowhead = none , style=dashed];
1080 -> 121[style=dashed];

1081 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
164 -> 1081 [arrowhead = none ];
1081 -> 172;

1082 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
172 -> 1082 [arrowhead = none ];
1082 -> 175;

1083 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
172 -> 1083 [arrowhead = none ];
1083 -> 176;

1084 [label="EVAL with clause\nmult(0, X175, 0, 0).\nand substitutionT131 -> 0,\nT133 -> 0,\nX175 -> s(s(0)),\nT142 -> 0,\nT135 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
175 -> 1084 [arrowhead = none ];
1084 -> 179;

1085 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
175 -> 1085 [arrowhead = none ];
1085 -> 180;

1086 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 1086 [arrowhead = none ];
1086 -> 185;

1087 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 1087 [arrowhead = none ];
1087 -> 187;

1088 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
179 -> 1088 [arrowhead = none ];
1088 -> 181;

1089 [label="EVAL with clause\nmult(s(X188), X189, 0, X190) :- mult(X188, X189, X189, X190).\nand substitutionX188 -> T155,\nT131 -> s(T155),\nT133 -> 0,\nX189 -> s(s(0)),\nT156 -> 0,\nT135 -> T158,\nX190 -> T158,\nT157 -> T158", fontsize=14, style = filled, fillcolor = lightblue];
185 -> 1089 [arrowhead = none ];
1089 -> 192;

1090 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
185 -> 1090 [arrowhead = none ];
1090 -> 194;

1091 [label="EVAL with clause\nmult(X263, X264, s(X265), s(X266)) :- mult(X263, X264, X265, X266).\nand substitutionT131 -> T195,\nX263 -> T195,\nT133 -> s(T197),\nX264 -> s(s(s(T197))),\nX265 -> T197,\nT196 -> s(T197),\nX266 -> T199,\nT135 -> s(T199),\nT198 -> T199", fontsize=14, style = filled, fillcolor = lightblue];
187 -> 1091 [arrowhead = none ];
1091 -> 250;

1092 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
187 -> 1092 [arrowhead = none ];
1092 -> 251;

1093 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
192 -> 1093 [arrowhead = none ];
1093 -> 196;

1094 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
196 -> 1094 [arrowhead = none ];
1094 -> 198;

1095 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
198 -> 1095 [arrowhead = none ];
1095 -> 200;

1096 [label="EVAL with clause\nmult(X205, X206, s(X207), s(X208)) :- mult(X205, X206, X207, X208).\nand substitutionT155 -> T164,\nX205 -> T164,\nX206 -> s(s(0)),\nX207 -> s(0),\nX208 -> T166,\nT158 -> s(T166),\nT165 -> T166", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 1096 [arrowhead = none ];
1096 -> 204;

1097 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
200 -> 1097 [arrowhead = none ];
1097 -> 205;

1098 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
204 -> 1098 [arrowhead = none ];
1098 -> 208;

1099 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
208 -> 1099 [arrowhead = none ];
1099 -> 210;

1100 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
210 -> 1100 [arrowhead = none ];
1100 -> 215;

1101 [label="EVAL with clause\nmult(X223, X224, s(X225), s(X226)) :- mult(X223, X224, X225, X226).\nand substitutionT164 -> T172,\nX223 -> T172,\nX224 -> s(s(0)),\nX225 -> 0,\nX226 -> T174,\nT166 -> s(T174),\nT173 -> T174", fontsize=14, style = filled, fillcolor = lightblue];
215 -> 1101 [arrowhead = none ];
1101 -> 222;

1102 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
215 -> 1102 [arrowhead = none ];
1102 -> 223;

1103 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
222 -> 1103 [arrowhead = none ];
1103 -> 227;

1104 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
227 -> 1104 [arrowhead = none ];
1104 -> 229;

1105 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
227 -> 1105 [arrowhead = none ];
1105 -> 230;

1106 [label="EVAL with clause\nmult(0, X233, 0, 0).\nand substitutionT172 -> 0,\nX233 -> s(s(0)),\nT174 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
229 -> 1106 [arrowhead = none ];
1106 -> 232;

1107 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
229 -> 1107 [arrowhead = none ];
1107 -> 233;

1108 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
230 -> 1108 [arrowhead = none ];
1108 -> 235;

1109 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
230 -> 1109 [arrowhead = none ];
1109 -> 236;

1110 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
232 -> 1110 [arrowhead = none ];
1110 -> 234;

1111 [label="EVAL with clause\nmult(s(X246), X247, 0, X248) :- mult(X246, X247, X247, X248).\nand substitutionX246 -> T183,\nT172 -> s(T183),\nX247 -> s(s(0)),\nT174 -> T185,\nX248 -> T185,\nT184 -> T185", fontsize=14, style = filled, fillcolor = lightblue];
235 -> 1111 [arrowhead = none ];
1111 -> 239;

1112 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
235 -> 1112 [arrowhead = none ];
1112 -> 241;

1113 [label="BACKTRACK\nfor clause: mult(X, Y, s(W), s(Z)) :- mult(X, Y, W, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
236 -> 1113 [arrowhead = none ];
1113 -> 247;

1114 [label="INSTANCE with matching:\nT155 -> T183\nT158 -> T185", fontsize=14, style = filled, fillcolor = lightgrey];
239 -> 1114 [arrowhead = none , style=dashed];
1114 -> 192[style=dashed];

1115 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
250 -> 1115 [arrowhead = none ];
1115 -> 258;

1116 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
258 -> 1116 [arrowhead = none ];
1116 -> 263;

1117 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
258 -> 1117 [arrowhead = none ];
1117 -> 264;

1118 [label="EVAL with clause\nmult(0, X273, 0, 0).\nand substitutionT195 -> 0,\nT197 -> 0,\nX273 -> s(s(s(0))),\nT206 -> 0,\nT199 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
263 -> 1118 [arrowhead = none ];
1118 -> 268;

1119 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
263 -> 1119 [arrowhead = none ];
1119 -> 269;

1120 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
264 -> 1120 [arrowhead = none ];
1120 -> 273;

1121 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
264 -> 1121 [arrowhead = none ];
1121 -> 274;

1122 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
268 -> 1122 [arrowhead = none ];
1122 -> 270;

1123 [label="EVAL with clause\nmult(s(X286), X287, 0, X288) :- mult(X286, X287, X287, X288).\nand substitutionX286 -> T219,\nT195 -> s(T219),\nT197 -> 0,\nX287 -> s(s(s(0))),\nT220 -> 0,\nT199 -> T222,\nX288 -> T222,\nT221 -> T222", fontsize=14, style = filled, fillcolor = lightblue];
273 -> 1123 [arrowhead = none ];
1123 -> 278;

1124 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
273 -> 1124 [arrowhead = none ];
1124 -> 279;

1125 [label="EVAL with clause\nmult(X379, X380, s(X381), s(X382)) :- mult(X379, X380, X381, X382).\nand substitutionT195 -> T267,\nX379 -> T267,\nT197 -> s(T269),\nX380 -> s(s(s(s(T269)))),\nX381 -> T269,\nT268 -> s(T269),\nX382 -> T271,\nT199 -> s(T271),\nT270 -> T271", fontsize=14, style = filled, fillcolor = lightblue];
274 -> 1125 [arrowhead = none ];
1125 -> 355;

1126 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
274 -> 1126 [arrowhead = none ];
1126 -> 357;

1127 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
278 -> 1127 [arrowhead = none ];
1127 -> 284;

1128 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
284 -> 1128 [arrowhead = none ];
1128 -> 286;

1129 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
286 -> 1129 [arrowhead = none ];
1129 -> 289;

1130 [label="EVAL with clause\nmult(X303, X304, s(X305), s(X306)) :- mult(X303, X304, X305, X306).\nand substitutionT219 -> T228,\nX303 -> T228,\nX304 -> s(s(s(0))),\nX305 -> s(s(0)),\nX306 -> T230,\nT222 -> s(T230),\nT229 -> T230", fontsize=14, style = filled, fillcolor = lightblue];
289 -> 1130 [arrowhead = none ];
1130 -> 298;

1131 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
289 -> 1131 [arrowhead = none ];
1131 -> 299;

1132 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
298 -> 1132 [arrowhead = none ];
1132 -> 302;

1133 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
302 -> 1133 [arrowhead = none ];
1133 -> 303;

1134 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
303 -> 1134 [arrowhead = none ];
1134 -> 305;

1135 [label="EVAL with clause\nmult(X321, X322, s(X323), s(X324)) :- mult(X321, X322, X323, X324).\nand substitutionT228 -> T236,\nX321 -> T236,\nX322 -> s(s(s(0))),\nX323 -> s(0),\nX324 -> T238,\nT230 -> s(T238),\nT237 -> T238", fontsize=14, style = filled, fillcolor = lightblue];
305 -> 1135 [arrowhead = none ];
1135 -> 306;

1136 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
305 -> 1136 [arrowhead = none ];
1136 -> 308;

1137 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
306 -> 1137 [arrowhead = none ];
1137 -> 313;

1138 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
313 -> 1138 [arrowhead = none ];
1138 -> 314;

1139 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
314 -> 1139 [arrowhead = none ];
1139 -> 317;

1140 [label="EVAL with clause\nmult(X339, X340, s(X341), s(X342)) :- mult(X339, X340, X341, X342).\nand substitutionT236 -> T244,\nX339 -> T244,\nX340 -> s(s(s(0))),\nX341 -> 0,\nX342 -> T246,\nT238 -> s(T246),\nT245 -> T246", fontsize=14, style = filled, fillcolor = lightblue];
317 -> 1140 [arrowhead = none ];
1140 -> 324;

1141 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
317 -> 1141 [arrowhead = none ];
1141 -> 325;

1142 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
324 -> 1142 [arrowhead = none ];
1142 -> 328;

1143 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
328 -> 1143 [arrowhead = none ];
1143 -> 329;

1144 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
328 -> 1144 [arrowhead = none ];
1144 -> 330;

1145 [label="EVAL with clause\nmult(0, X349, 0, 0).\nand substitutionT244 -> 0,\nX349 -> s(s(s(0))),\nT246 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
329 -> 1145 [arrowhead = none ];
1145 -> 333;

1146 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
329 -> 1146 [arrowhead = none ];
1146 -> 334;

1147 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
330 -> 1147 [arrowhead = none ];
1147 -> 342;

1148 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
330 -> 1148 [arrowhead = none ];
1148 -> 343;

1149 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
333 -> 1149 [arrowhead = none ];
1149 -> 335;

1150 [label="EVAL with clause\nmult(s(X362), X363, 0, X364) :- mult(X362, X363, X363, X364).\nand substitutionX362 -> T255,\nT244 -> s(T255),\nX363 -> s(s(s(0))),\nT246 -> T257,\nX364 -> T257,\nT256 -> T257", fontsize=14, style = filled, fillcolor = lightblue];
342 -> 1150 [arrowhead = none ];
1150 -> 348;

1151 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
342 -> 1151 [arrowhead = none ];
1151 -> 349;

1152 [label="BACKTRACK\nfor clause: mult(X, Y, s(W), s(Z)) :- mult(X, Y, W, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
343 -> 1152 [arrowhead = none ];
1152 -> 352;

1153 [label="INSTANCE with matching:\nT219 -> T255\nT222 -> T257", fontsize=14, style = filled, fillcolor = lightgrey];
348 -> 1153 [arrowhead = none , style=dashed];
1153 -> 278[style=dashed];

1154 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
355 -> 1154 [arrowhead = none ];
1154 -> 362;

1155 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
362 -> 1155 [arrowhead = none ];
1155 -> 364;

1156 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
362 -> 1156 [arrowhead = none ];
1156 -> 365;

1157 [label="EVAL with clause\nmult(0, X389, 0, 0).\nand substitutionT267 -> 0,\nT269 -> 0,\nX389 -> s(s(s(s(0)))),\nT278 -> 0,\nT271 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
364 -> 1157 [arrowhead = none ];
1157 -> 366;

1158 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
364 -> 1158 [arrowhead = none ];
1158 -> 367;

1159 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
365 -> 1159 [arrowhead = none ];
1159 -> 371;

1160 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
365 -> 1160 [arrowhead = none ];
1160 -> 372;

1161 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
366 -> 1161 [arrowhead = none ];
1161 -> 368;

1162 [label="EVAL with clause\nmult(s(X402), X403, 0, X404) :- mult(X402, X403, X403, X404).\nand substitutionX402 -> T291,\nT267 -> s(T291),\nT269 -> 0,\nX403 -> s(s(s(s(0)))),\nT292 -> 0,\nT271 -> T294,\nX404 -> T294,\nT293 -> T294", fontsize=14, style = filled, fillcolor = lightblue];
371 -> 1162 [arrowhead = none ];
1162 -> 376;

1163 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
371 -> 1163 [arrowhead = none ];
1163 -> 378;

1164 [label="EVAL with clause\nmult(X513, X514, s(X515), s(X516)) :- mult(X513, X514, X515, X516).\nand substitutionT267 -> T347,\nX513 -> T347,\nT269 -> s(T349),\nX514 -> s(s(s(s(s(T349))))),\nX515 -> T349,\nT348 -> s(T349),\nX516 -> T351,\nT271 -> s(T351),\nT350 -> T351", fontsize=14, style = filled, fillcolor = lightblue];
372 -> 1164 [arrowhead = none ];
1164 -> 512;

1165 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
372 -> 1165 [arrowhead = none ];
1165 -> 513;

1166 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
376 -> 1166 [arrowhead = none ];
1166 -> 381;

1167 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
381 -> 1167 [arrowhead = none ];
1167 -> 382;

1168 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
382 -> 1168 [arrowhead = none ];
1168 -> 383;

1169 [label="EVAL with clause\nmult(X419, X420, s(X421), s(X422)) :- mult(X419, X420, X421, X422).\nand substitutionT291 -> T300,\nX419 -> T300,\nX420 -> s(s(s(s(0)))),\nX421 -> s(s(s(0))),\nX422 -> T302,\nT294 -> s(T302),\nT301 -> T302", fontsize=14, style = filled, fillcolor = lightblue];
383 -> 1169 [arrowhead = none ];
1169 -> 409;

1170 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
383 -> 1170 [arrowhead = none ];
1170 -> 411;

1171 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
409 -> 1171 [arrowhead = none ];
1171 -> 414;

1172 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
414 -> 1172 [arrowhead = none ];
1172 -> 415;

1173 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
415 -> 1173 [arrowhead = none ];
1173 -> 418;

1174 [label="EVAL with clause\nmult(X437, X438, s(X439), s(X440)) :- mult(X437, X438, X439, X440).\nand substitutionT300 -> T308,\nX437 -> T308,\nX438 -> s(s(s(s(0)))),\nX439 -> s(s(0)),\nX440 -> T310,\nT302 -> s(T310),\nT309 -> T310", fontsize=14, style = filled, fillcolor = lightblue];
418 -> 1174 [arrowhead = none ];
1174 -> 422;

1175 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
418 -> 1175 [arrowhead = none ];
1175 -> 423;

1176 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
422 -> 1176 [arrowhead = none ];
1176 -> 425;

1177 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
425 -> 1177 [arrowhead = none ];
1177 -> 426;

1178 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
426 -> 1178 [arrowhead = none ];
1178 -> 429;

1179 [label="EVAL with clause\nmult(X455, X456, s(X457), s(X458)) :- mult(X455, X456, X457, X458).\nand substitutionT308 -> T316,\nX455 -> T316,\nX456 -> s(s(s(s(0)))),\nX457 -> s(0),\nX458 -> T318,\nT310 -> s(T318),\nT317 -> T318", fontsize=14, style = filled, fillcolor = lightblue];
429 -> 1179 [arrowhead = none ];
1179 -> 430;

1180 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
429 -> 1180 [arrowhead = none ];
1180 -> 432;

1181 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
430 -> 1181 [arrowhead = none ];
1181 -> 459;

1182 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
459 -> 1182 [arrowhead = none ];
1182 -> 461;

1183 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
461 -> 1183 [arrowhead = none ];
1183 -> 463;

1184 [label="EVAL with clause\nmult(X473, X474, s(X475), s(X476)) :- mult(X473, X474, X475, X476).\nand substitutionT316 -> T324,\nX473 -> T324,\nX474 -> s(s(s(s(0)))),\nX475 -> 0,\nX476 -> T326,\nT318 -> s(T326),\nT325 -> T326", fontsize=14, style = filled, fillcolor = lightblue];
463 -> 1184 [arrowhead = none ];
1184 -> 469;

1185 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
463 -> 1185 [arrowhead = none ];
1185 -> 470;

1186 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
469 -> 1186 [arrowhead = none ];
1186 -> 485;

1187 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
485 -> 1187 [arrowhead = none ];
1187 -> 488;

1188 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
485 -> 1188 [arrowhead = none ];
1188 -> 489;

1189 [label="EVAL with clause\nmult(0, X483, 0, 0).\nand substitutionT324 -> 0,\nX483 -> s(s(s(s(0)))),\nT326 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
488 -> 1189 [arrowhead = none ];
1189 -> 492;

1190 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
488 -> 1190 [arrowhead = none ];
1190 -> 493;

1191 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
489 -> 1191 [arrowhead = none ];
1191 -> 495;

1192 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
489 -> 1192 [arrowhead = none ];
1192 -> 496;

1193 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
492 -> 1193 [arrowhead = none ];
1193 -> 494;

1194 [label="EVAL with clause\nmult(s(X496), X497, 0, X498) :- mult(X496, X497, X497, X498).\nand substitutionX496 -> T335,\nT324 -> s(T335),\nX497 -> s(s(s(s(0)))),\nT326 -> T337,\nX498 -> T337,\nT336 -> T337", fontsize=14, style = filled, fillcolor = lightblue];
495 -> 1194 [arrowhead = none ];
1194 -> 498;

1195 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
495 -> 1195 [arrowhead = none ];
1195 -> 501;

1196 [label="BACKTRACK\nfor clause: mult(X, Y, s(W), s(Z)) :- mult(X, Y, W, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
496 -> 1196 [arrowhead = none ];
1196 -> 509;

1197 [label="INSTANCE with matching:\nT291 -> T335\nT294 -> T337", fontsize=14, style = filled, fillcolor = lightgrey];
498 -> 1197 [arrowhead = none , style=dashed];
1197 -> 376[style=dashed];

1198 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
512 -> 1198 [arrowhead = none ];
1198 -> 515;

1199 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
515 -> 1199 [arrowhead = none ];
1199 -> 520;

1200 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
515 -> 1200 [arrowhead = none ];
1200 -> 521;

1201 [label="EVAL with clause\nmult(0, X523, 0, 0).\nand substitutionT347 -> 0,\nT349 -> 0,\nX523 -> s(s(s(s(s(0))))),\nT358 -> 0,\nT351 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
520 -> 1201 [arrowhead = none ];
1201 -> 523;

1202 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
520 -> 1202 [arrowhead = none ];
1202 -> 524;

1203 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
521 -> 1203 [arrowhead = none ];
1203 -> 528;

1204 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
521 -> 1204 [arrowhead = none ];
1204 -> 529;

1205 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
523 -> 1205 [arrowhead = none ];
1205 -> 525;

1206 [label="EVAL with clause\nmult(s(X536), X537, 0, X538) :- mult(X536, X537, X537, X538).\nand substitutionX536 -> T371,\nT347 -> s(T371),\nT349 -> 0,\nX537 -> s(s(s(s(s(0))))),\nT372 -> 0,\nT351 -> T374,\nX538 -> T374,\nT373 -> T374", fontsize=14, style = filled, fillcolor = lightblue];
528 -> 1206 [arrowhead = none ];
1206 -> 530;

1207 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
528 -> 1207 [arrowhead = none ];
1207 -> 531;

1208 [label="EVAL with clause\nmult(X665, X666, s(X667), s(X668)) :- mult(X665, X666, X667, X668).\nand substitutionT347 -> T435,\nX665 -> T435,\nT349 -> s(T437),\nX666 -> s(s(s(s(s(s(T437)))))),\nX667 -> T437,\nT436 -> s(T437),\nX668 -> T439,\nT351 -> s(T439),\nT438 -> T439", fontsize=14, style = filled, fillcolor = lightblue];
529 -> 1208 [arrowhead = none ];
1208 -> 631;

1209 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
529 -> 1209 [arrowhead = none ];
1209 -> 632;

1210 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
530 -> 1210 [arrowhead = none ];
1210 -> 541;

1211 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
541 -> 1211 [arrowhead = none ];
1211 -> 544;

1212 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
544 -> 1212 [arrowhead = none ];
1212 -> 545;

1213 [label="EVAL with clause\nmult(X553, X554, s(X555), s(X556)) :- mult(X553, X554, X555, X556).\nand substitutionT371 -> T380,\nX553 -> T380,\nX554 -> s(s(s(s(s(0))))),\nX555 -> s(s(s(s(0)))),\nX556 -> T382,\nT374 -> s(T382),\nT381 -> T382", fontsize=14, style = filled, fillcolor = lightblue];
545 -> 1213 [arrowhead = none ];
1213 -> 553;

1214 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
545 -> 1214 [arrowhead = none ];
1214 -> 554;

1215 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
553 -> 1215 [arrowhead = none ];
1215 -> 558;

1216 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
558 -> 1216 [arrowhead = none ];
1216 -> 559;

1217 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
559 -> 1217 [arrowhead = none ];
1217 -> 560;

1218 [label="EVAL with clause\nmult(X571, X572, s(X573), s(X574)) :- mult(X571, X572, X573, X574).\nand substitutionT380 -> T388,\nX571 -> T388,\nX572 -> s(s(s(s(s(0))))),\nX573 -> s(s(s(0))),\nX574 -> T390,\nT382 -> s(T390),\nT389 -> T390", fontsize=14, style = filled, fillcolor = lightblue];
560 -> 1218 [arrowhead = none ];
1218 -> 561;

1219 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
560 -> 1219 [arrowhead = none ];
1219 -> 562;

1220 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
561 -> 1220 [arrowhead = none ];
1220 -> 573;

1221 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
573 -> 1221 [arrowhead = none ];
1221 -> 574;

1222 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
574 -> 1222 [arrowhead = none ];
1222 -> 575;

1223 [label="EVAL with clause\nmult(X589, X590, s(X591), s(X592)) :- mult(X589, X590, X591, X592).\nand substitutionT388 -> T396,\nX589 -> T396,\nX590 -> s(s(s(s(s(0))))),\nX591 -> s(s(0)),\nX592 -> T398,\nT390 -> s(T398),\nT397 -> T398", fontsize=14, style = filled, fillcolor = lightblue];
575 -> 1223 [arrowhead = none ];
1223 -> 581;

1224 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
575 -> 1224 [arrowhead = none ];
1224 -> 582;

1225 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
581 -> 1225 [arrowhead = none ];
1225 -> 586;

1226 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
586 -> 1226 [arrowhead = none ];
1226 -> 587;

1227 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
587 -> 1227 [arrowhead = none ];
1227 -> 589;

1228 [label="EVAL with clause\nmult(X607, X608, s(X609), s(X610)) :- mult(X607, X608, X609, X610).\nand substitutionT396 -> T404,\nX607 -> T404,\nX608 -> s(s(s(s(s(0))))),\nX609 -> s(0),\nX610 -> T406,\nT398 -> s(T406),\nT405 -> T406", fontsize=14, style = filled, fillcolor = lightblue];
589 -> 1228 [arrowhead = none ];
1228 -> 591;

1229 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
589 -> 1229 [arrowhead = none ];
1229 -> 592;

1230 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
591 -> 1230 [arrowhead = none ];
1230 -> 598;

1231 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
598 -> 1231 [arrowhead = none ];
1231 -> 601;

1232 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
601 -> 1232 [arrowhead = none ];
1232 -> 602;

1233 [label="EVAL with clause\nmult(X625, X626, s(X627), s(X628)) :- mult(X625, X626, X627, X628).\nand substitutionT404 -> T412,\nX625 -> T412,\nX626 -> s(s(s(s(s(0))))),\nX627 -> 0,\nX628 -> T414,\nT406 -> s(T414),\nT413 -> T414", fontsize=14, style = filled, fillcolor = lightblue];
602 -> 1233 [arrowhead = none ];
1233 -> 604;

1234 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
602 -> 1234 [arrowhead = none ];
1234 -> 605;

1235 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
604 -> 1235 [arrowhead = none ];
1235 -> 609;

1236 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
609 -> 1236 [arrowhead = none ];
1236 -> 612;

1237 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
609 -> 1237 [arrowhead = none ];
1237 -> 613;

1238 [label="EVAL with clause\nmult(0, X635, 0, 0).\nand substitutionT412 -> 0,\nX635 -> s(s(s(s(s(0))))),\nT414 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
612 -> 1238 [arrowhead = none ];
1238 -> 614;

1239 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
612 -> 1239 [arrowhead = none ];
1239 -> 615;

1240 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
613 -> 1240 [arrowhead = none ];
1240 -> 617;

1241 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
613 -> 1241 [arrowhead = none ];
1241 -> 618;

1242 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
614 -> 1242 [arrowhead = none ];
1242 -> 616;

1243 [label="EVAL with clause\nmult(s(X648), X649, 0, X650) :- mult(X648, X649, X649, X650).\nand substitutionX648 -> T423,\nT412 -> s(T423),\nX649 -> s(s(s(s(s(0))))),\nT414 -> T425,\nX650 -> T425,\nT424 -> T425", fontsize=14, style = filled, fillcolor = lightblue];
617 -> 1243 [arrowhead = none ];
1243 -> 623;

1244 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
617 -> 1244 [arrowhead = none ];
1244 -> 624;

1245 [label="BACKTRACK\nfor clause: mult(X, Y, s(W), s(Z)) :- mult(X, Y, W, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
618 -> 1245 [arrowhead = none ];
1245 -> 630;

1246 [label="INSTANCE with matching:\nT371 -> T423\nT374 -> T425", fontsize=14, style = filled, fillcolor = lightgrey];
623 -> 1246 [arrowhead = none , style=dashed];
1246 -> 530[style=dashed];

1247 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
631 -> 1247 [arrowhead = none ];
1247 -> 638;

1248 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
638 -> 1248 [arrowhead = none ];
1248 -> 639;

1249 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
638 -> 1249 [arrowhead = none ];
1249 -> 640;

1250 [label="EVAL with clause\nmult(0, X675, 0, 0).\nand substitutionT435 -> 0,\nT437 -> 0,\nX675 -> s(s(s(s(s(s(0)))))),\nT446 -> 0,\nT439 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
639 -> 1250 [arrowhead = none ];
1250 -> 643;

1251 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
639 -> 1251 [arrowhead = none ];
1251 -> 644;

1252 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
640 -> 1252 [arrowhead = none ];
1252 -> 648;

1253 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
640 -> 1253 [arrowhead = none ];
1253 -> 649;

1254 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
643 -> 1254 [arrowhead = none ];
1254 -> 645;

1255 [label="EVAL with clause\nmult(s(X688), X689, 0, X690) :- mult(X688, X689, X689, X690).\nand substitutionX688 -> T459,\nT435 -> s(T459),\nT437 -> 0,\nX689 -> s(s(s(s(s(s(0)))))),\nT460 -> 0,\nT439 -> T462,\nX690 -> T462,\nT461 -> T462", fontsize=14, style = filled, fillcolor = lightblue];
648 -> 1255 [arrowhead = none ];
1255 -> 659;

1256 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
648 -> 1256 [arrowhead = none ];
1256 -> 660;

1257 [label="EVAL with clause\nmult(X835, X836, s(X837), s(X838)) :- mult(X835, X836, X837, X838).\nand substitutionT435 -> T531,\nX835 -> T531,\nT437 -> s(T533),\nX836 -> s(s(s(s(s(s(s(T533))))))),\nX837 -> T533,\nT532 -> s(T533),\nX838 -> T535,\nT439 -> s(T535),\nT534 -> T535", fontsize=14, style = filled, fillcolor = lightblue];
649 -> 1257 [arrowhead = none ];
1257 -> 846;

1258 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
649 -> 1258 [arrowhead = none ];
1258 -> 847;

1259 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
659 -> 1259 [arrowhead = none ];
1259 -> 663;

1260 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
663 -> 1260 [arrowhead = none ];
1260 -> 664;

1261 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
664 -> 1261 [arrowhead = none ];
1261 -> 666;

1262 [label="EVAL with clause\nmult(X705, X706, s(X707), s(X708)) :- mult(X705, X706, X707, X708).\nand substitutionT459 -> T468,\nX705 -> T468,\nX706 -> s(s(s(s(s(s(0)))))),\nX707 -> s(s(s(s(s(0))))),\nX708 -> T470,\nT462 -> s(T470),\nT469 -> T470", fontsize=14, style = filled, fillcolor = lightblue];
666 -> 1262 [arrowhead = none ];
1262 -> 668;

1263 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
666 -> 1263 [arrowhead = none ];
1263 -> 669;

1264 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
668 -> 1264 [arrowhead = none ];
1264 -> 676;

1265 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
676 -> 1265 [arrowhead = none ];
1265 -> 692;

1266 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
692 -> 1266 [arrowhead = none ];
1266 -> 694;

1267 [label="EVAL with clause\nmult(X723, X724, s(X725), s(X726)) :- mult(X723, X724, X725, X726).\nand substitutionT468 -> T476,\nX723 -> T476,\nX724 -> s(s(s(s(s(s(0)))))),\nX725 -> s(s(s(s(0)))),\nX726 -> T478,\nT470 -> s(T478),\nT477 -> T478", fontsize=14, style = filled, fillcolor = lightblue];
694 -> 1267 [arrowhead = none ];
1267 -> 705;

1268 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
694 -> 1268 [arrowhead = none ];
1268 -> 706;

1269 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
705 -> 1269 [arrowhead = none ];
1269 -> 711;

1270 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
711 -> 1270 [arrowhead = none ];
1270 -> 720;

1271 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
720 -> 1271 [arrowhead = none ];
1271 -> 721;

1272 [label="EVAL with clause\nmult(X741, X742, s(X743), s(X744)) :- mult(X741, X742, X743, X744).\nand substitutionT476 -> T484,\nX741 -> T484,\nX742 -> s(s(s(s(s(s(0)))))),\nX743 -> s(s(s(0))),\nX744 -> T486,\nT478 -> s(T486),\nT485 -> T486", fontsize=14, style = filled, fillcolor = lightblue];
721 -> 1272 [arrowhead = none ];
1272 -> 731;

1273 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
721 -> 1273 [arrowhead = none ];
1273 -> 732;

1274 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
731 -> 1274 [arrowhead = none ];
1274 -> 745;

1275 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
745 -> 1275 [arrowhead = none ];
1275 -> 746;

1276 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
746 -> 1276 [arrowhead = none ];
1276 -> 749;

1277 [label="EVAL with clause\nmult(X759, X760, s(X761), s(X762)) :- mult(X759, X760, X761, X762).\nand substitutionT484 -> T492,\nX759 -> T492,\nX760 -> s(s(s(s(s(s(0)))))),\nX761 -> s(s(0)),\nX762 -> T494,\nT486 -> s(T494),\nT493 -> T494", fontsize=14, style = filled, fillcolor = lightblue];
749 -> 1277 [arrowhead = none ];
1277 -> 753;

1278 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
749 -> 1278 [arrowhead = none ];
1278 -> 754;

1279 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
753 -> 1279 [arrowhead = none ];
1279 -> 770;

1280 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
770 -> 1280 [arrowhead = none ];
1280 -> 771;

1281 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
771 -> 1281 [arrowhead = none ];
1281 -> 772;

1282 [label="EVAL with clause\nmult(X777, X778, s(X779), s(X780)) :- mult(X777, X778, X779, X780).\nand substitutionT492 -> T500,\nX777 -> T500,\nX778 -> s(s(s(s(s(s(0)))))),\nX779 -> s(0),\nX780 -> T502,\nT494 -> s(T502),\nT501 -> T502", fontsize=14, style = filled, fillcolor = lightblue];
772 -> 1282 [arrowhead = none ];
1282 -> 777;

1283 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
772 -> 1283 [arrowhead = none ];
1283 -> 778;

1284 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
777 -> 1284 [arrowhead = none ];
1284 -> 796;

1285 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
796 -> 1285 [arrowhead = none ];
1285 -> 798;

1286 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
798 -> 1286 [arrowhead = none ];
1286 -> 800;

1287 [label="EVAL with clause\nmult(X795, X796, s(X797), s(X798)) :- mult(X795, X796, X797, X798).\nand substitutionT500 -> T508,\nX795 -> T508,\nX796 -> s(s(s(s(s(s(0)))))),\nX797 -> 0,\nX798 -> T510,\nT502 -> s(T510),\nT509 -> T510", fontsize=14, style = filled, fillcolor = lightblue];
800 -> 1287 [arrowhead = none ];
1287 -> 811;

1288 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
800 -> 1288 [arrowhead = none ];
1288 -> 812;

1289 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
811 -> 1289 [arrowhead = none ];
1289 -> 820;

1290 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
820 -> 1290 [arrowhead = none ];
1290 -> 821;

1291 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
820 -> 1291 [arrowhead = none ];
1291 -> 822;

1292 [label="EVAL with clause\nmult(0, X805, 0, 0).\nand substitutionT508 -> 0,\nX805 -> s(s(s(s(s(s(0)))))),\nT510 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
821 -> 1292 [arrowhead = none ];
1292 -> 823;

1293 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
821 -> 1293 [arrowhead = none ];
1293 -> 824;

1294 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
822 -> 1294 [arrowhead = none ];
1294 -> 831;

1295 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
822 -> 1295 [arrowhead = none ];
1295 -> 832;

1296 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
823 -> 1296 [arrowhead = none ];
1296 -> 826;

1297 [label="EVAL with clause\nmult(s(X818), X819, 0, X820) :- mult(X818, X819, X819, X820).\nand substitutionX818 -> T519,\nT508 -> s(T519),\nX819 -> s(s(s(s(s(s(0)))))),\nT510 -> T521,\nX820 -> T521,\nT520 -> T521", fontsize=14, style = filled, fillcolor = lightblue];
831 -> 1297 [arrowhead = none ];
1297 -> 838;

1298 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
831 -> 1298 [arrowhead = none ];
1298 -> 839;

1299 [label="BACKTRACK\nfor clause: mult(X, Y, s(W), s(Z)) :- mult(X, Y, W, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
832 -> 1299 [arrowhead = none ];
1299 -> 843;

1300 [label="INSTANCE with matching:\nT459 -> T519\nT462 -> T521", fontsize=14, style = filled, fillcolor = lightgrey];
838 -> 1300 [arrowhead = none , style=dashed];
1300 -> 659[style=dashed];

1301 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
846 -> 1301 [arrowhead = none ];
1301 -> 849;

1302 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
849 -> 1302 [arrowhead = none ];
1302 -> 854;

1303 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
849 -> 1303 [arrowhead = none ];
1303 -> 855;

1304 [label="EVAL with clause\nmult(0, X845, 0, 0).\nand substitutionT531 -> 0,\nT533 -> 0,\nX845 -> s(s(s(s(s(s(s(0))))))),\nT542 -> 0,\nT535 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
854 -> 1304 [arrowhead = none ];
1304 -> 856;

1305 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
854 -> 1305 [arrowhead = none ];
1305 -> 857;

1306 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
855 -> 1306 [arrowhead = none ];
1306 -> 860;

1307 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
855 -> 1307 [arrowhead = none ];
1307 -> 861;

1308 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
856 -> 1308 [arrowhead = none ];
1308 -> 858;

1309 [label="EVAL with clause\nmult(s(X858), X859, 0, X860) :- mult(X858, X859, X859, X860).\nand substitutionX858 -> T555,\nT531 -> s(T555),\nT533 -> 0,\nX859 -> s(s(s(s(s(s(s(0))))))),\nT556 -> 0,\nT535 -> T558,\nX860 -> T558,\nT557 -> T558", fontsize=14, style = filled, fillcolor = lightblue];
860 -> 1309 [arrowhead = none ];
1309 -> 870;

1310 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
860 -> 1310 [arrowhead = none ];
1310 -> 871;

1311 [label="EVAL with clause\nmult(X1023, X1024, s(X1025), s(X1026)) :- mult(X1023, X1024, X1025, X1026).\nand substitutionT531 -> T635,\nX1023 -> T635,\nT533 -> s(T637),\nX1024 -> s(s(s(s(s(s(s(s(T637)))))))),\nX1025 -> T637,\nT636 -> s(T637),\nX1026 -> T639,\nT535 -> s(T639),\nT638 -> T639", fontsize=14, style = filled, fillcolor = lightblue];
861 -> 1311 [arrowhead = none ];
1311 -> 983;

1312 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
861 -> 1312 [arrowhead = none ];
1312 -> 984;

1313 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
870 -> 1313 [arrowhead = none ];
1313 -> 878;

1314 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
878 -> 1314 [arrowhead = none ];
1314 -> 879;

1315 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
879 -> 1315 [arrowhead = none ];
1315 -> 883;

1316 [label="EVAL with clause\nmult(X875, X876, s(X877), s(X878)) :- mult(X875, X876, X877, X878).\nand substitutionT555 -> T564,\nX875 -> T564,\nX876 -> s(s(s(s(s(s(s(0))))))),\nX877 -> s(s(s(s(s(s(0)))))),\nX878 -> T566,\nT558 -> s(T566),\nT565 -> T566", fontsize=14, style = filled, fillcolor = lightblue];
883 -> 1316 [arrowhead = none ];
1316 -> 884;

1317 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
883 -> 1317 [arrowhead = none ];
1317 -> 885;

1318 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
884 -> 1318 [arrowhead = none ];
1318 -> 891;

1319 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
891 -> 1319 [arrowhead = none ];
1319 -> 892;

1320 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
892 -> 1320 [arrowhead = none ];
1320 -> 893;

1321 [label="EVAL with clause\nmult(X893, X894, s(X895), s(X896)) :- mult(X893, X894, X895, X896).\nand substitutionT564 -> T572,\nX893 -> T572,\nX894 -> s(s(s(s(s(s(s(0))))))),\nX895 -> s(s(s(s(s(0))))),\nX896 -> T574,\nT566 -> s(T574),\nT573 -> T574", fontsize=14, style = filled, fillcolor = lightblue];
893 -> 1321 [arrowhead = none ];
1321 -> 897;

1322 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
893 -> 1322 [arrowhead = none ];
1322 -> 898;

1323 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
897 -> 1323 [arrowhead = none ];
1323 -> 902;

1324 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
902 -> 1324 [arrowhead = none ];
1324 -> 904;

1325 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
904 -> 1325 [arrowhead = none ];
1325 -> 905;

1326 [label="EVAL with clause\nmult(X911, X912, s(X913), s(X914)) :- mult(X911, X912, X913, X914).\nand substitutionT572 -> T580,\nX911 -> T580,\nX912 -> s(s(s(s(s(s(s(0))))))),\nX913 -> s(s(s(s(0)))),\nX914 -> T582,\nT574 -> s(T582),\nT581 -> T582", fontsize=14, style = filled, fillcolor = lightblue];
905 -> 1326 [arrowhead = none ];
1326 -> 911;

1327 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
905 -> 1327 [arrowhead = none ];
1327 -> 912;

1328 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
911 -> 1328 [arrowhead = none ];
1328 -> 914;

1329 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
914 -> 1329 [arrowhead = none ];
1329 -> 916;

1330 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
916 -> 1330 [arrowhead = none ];
1330 -> 918;

1331 [label="EVAL with clause\nmult(X929, X930, s(X931), s(X932)) :- mult(X929, X930, X931, X932).\nand substitutionT580 -> T588,\nX929 -> T588,\nX930 -> s(s(s(s(s(s(s(0))))))),\nX931 -> s(s(s(0))),\nX932 -> T590,\nT582 -> s(T590),\nT589 -> T590", fontsize=14, style = filled, fillcolor = lightblue];
918 -> 1331 [arrowhead = none ];
1331 -> 923;

1332 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
918 -> 1332 [arrowhead = none ];
1332 -> 924;

1333 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
923 -> 1333 [arrowhead = none ];
1333 -> 926;

1334 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
926 -> 1334 [arrowhead = none ];
1334 -> 928;

1335 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
928 -> 1335 [arrowhead = none ];
1335 -> 930;

1336 [label="EVAL with clause\nmult(X947, X948, s(X949), s(X950)) :- mult(X947, X948, X949, X950).\nand substitutionT588 -> T596,\nX947 -> T596,\nX948 -> s(s(s(s(s(s(s(0))))))),\nX949 -> s(s(0)),\nX950 -> T598,\nT590 -> s(T598),\nT597 -> T598", fontsize=14, style = filled, fillcolor = lightblue];
930 -> 1336 [arrowhead = none ];
1336 -> 934;

1337 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
930 -> 1337 [arrowhead = none ];
1337 -> 935;

1338 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
934 -> 1338 [arrowhead = none ];
1338 -> 939;

1339 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
939 -> 1339 [arrowhead = none ];
1339 -> 940;

1340 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
940 -> 1340 [arrowhead = none ];
1340 -> 943;

1341 [label="EVAL with clause\nmult(X965, X966, s(X967), s(X968)) :- mult(X965, X966, X967, X968).\nand substitutionT596 -> T604,\nX965 -> T604,\nX966 -> s(s(s(s(s(s(s(0))))))),\nX967 -> s(0),\nX968 -> T606,\nT598 -> s(T606),\nT605 -> T606", fontsize=14, style = filled, fillcolor = lightblue];
943 -> 1341 [arrowhead = none ];
1341 -> 945;

1342 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
943 -> 1342 [arrowhead = none ];
1342 -> 946;

1343 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
945 -> 1343 [arrowhead = none ];
1343 -> 954;

1344 [label="BACKTRACK\nfor clause: mult(0, Y, 0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
954 -> 1344 [arrowhead = none ];
1344 -> 955;

1345 [label="BACKTRACK\nfor clause: mult(s(U), Y, 0, Z) :- mult(U, Y, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
955 -> 1345 [arrowhead = none ];
1345 -> 958;

1346 [label="EVAL with clause\nmult(X983, X984, s(X985), s(X986)) :- mult(X983, X984, X985, X986).\nand substitutionT604 -> T612,\nX983 -> T612,\nX984 -> s(s(s(s(s(s(s(0))))))),\nX985 -> 0,\nX986 -> T614,\nT606 -> s(T614),\nT613 -> T614", fontsize=14, style = filled, fillcolor = lightblue];
958 -> 1346 [arrowhead = none ];
1346 -> 961;

1347 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
958 -> 1347 [arrowhead = none ];
1347 -> 962;

1348 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
961 -> 1348 [arrowhead = none ];
1348 -> 967;

1349 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
967 -> 1349 [arrowhead = none ];
1349 -> 968;

1350 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
967 -> 1350 [arrowhead = none ];
1350 -> 969;

1351 [label="EVAL with clause\nmult(0, X993, 0, 0).\nand substitutionT612 -> 0,\nX993 -> s(s(s(s(s(s(s(0))))))),\nT614 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
968 -> 1351 [arrowhead = none ];
1351 -> 970;

1352 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
968 -> 1352 [arrowhead = none ];
1352 -> 971;

1353 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
969 -> 1353 [arrowhead = none ];
1353 -> 975;

1354 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
969 -> 1354 [arrowhead = none ];
1354 -> 976;

1355 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
970 -> 1355 [arrowhead = none ];
1355 -> 972;

1356 [label="EVAL with clause\nmult(s(X1006), X1007, 0, X1008) :- mult(X1006, X1007, X1007, X1008).\nand substitutionX1006 -> T623,\nT612 -> s(T623),\nX1007 -> s(s(s(s(s(s(s(0))))))),\nT614 -> T625,\nX1008 -> T625,\nT624 -> T625", fontsize=14, style = filled, fillcolor = lightblue];
975 -> 1356 [arrowhead = none ];
1356 -> 979;

1357 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
975 -> 1357 [arrowhead = none ];
1357 -> 980;

1358 [label="BACKTRACK\nfor clause: mult(X, Y, s(W), s(Z)) :- mult(X, Y, W, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
976 -> 1358 [arrowhead = none ];
1358 -> 981;

1359 [label="INSTANCE with matching:\nT555 -> T623\nT558 -> T625", fontsize=14, style = filled, fillcolor = lightgrey];
979 -> 1359 [arrowhead = none , style=dashed];
1359 -> 870[style=dashed];

1360 [label="GENERALIZATION\nT642 <-- s(s(s(s(s(s(s(T637)))))))\n\nNew Knowledge:\nT642 is ground", fontsize=14, style = filled, fillcolor = violet];
983 -> 1360 [arrowhead = none ];
1360 -> 987;

1361 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
987 -> 1361 [arrowhead = none ];
1361 -> 989;

1362 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
989 -> 1362 [arrowhead = none ];
1362 -> 992;

1363 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
989 -> 1363 [arrowhead = none ];
1363 -> 993;

1364 [label="EVAL with clause\nmult(0, X1035, 0, 0).\nand substitutionT635 -> 0,\nT642 -> T649,\nX1035 -> s(T649),\nT637 -> 0,\nT639 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
992 -> 1364 [arrowhead = none ];
1364 -> 994;

1365 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
992 -> 1365 [arrowhead = none ];
1365 -> 995;

1366 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
993 -> 1366 [arrowhead = none ];
1366 -> 998;

1367 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
993 -> 1367 [arrowhead = none ];
1367 -> 999;

1368 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
994 -> 1368 [arrowhead = none ];
1368 -> 996;

1369 [label="EVAL with clause\nmult(s(X1048), X1049, 0, X1050) :- mult(X1048, X1049, X1049, X1050).\nand substitutionX1048 -> T662,\nT635 -> s(T662),\nT642 -> T663,\nX1049 -> s(T663),\nT637 -> 0,\nT639 -> T665,\nX1050 -> T665,\nT664 -> T665", fontsize=14, style = filled, fillcolor = lightblue];
998 -> 1369 [arrowhead = none ];
1369 -> 1005;

1370 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
998 -> 1370 [arrowhead = none ];
1370 -> 1006;

1371 [label="EVAL with clause\nmult(X1061, X1062, s(X1063), s(X1064)) :- mult(X1061, X1062, X1063, X1064).\nand substitutionT635 -> T676,\nX1061 -> T676,\nT642 -> T677,\nX1062 -> s(T677),\nX1063 -> T678,\nT637 -> s(T678),\nX1064 -> T680,\nT639 -> s(T680),\nT679 -> T680", fontsize=14, style = filled, fillcolor = lightblue];
999 -> 1371 [arrowhead = none ];
1371 -> 1012;

1372 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
999 -> 1372 [arrowhead = none ];
1372 -> 1013;

1373 [label="INSTANCE with matching:\nT28 -> T662\nT29 -> s(T663)\nT31 -> T665", fontsize=14, style = filled, fillcolor = lightgrey];
1005 -> 1373 [arrowhead = none , style=dashed];
1373 -> 36[style=dashed];

1374 [label="INSTANCE with matching:\nT635 -> T676\nT642 -> T677\nT637 -> T678\nT639 -> T680", fontsize=14, style = filled, fillcolor = lightgrey];
1012 -> 1374 [arrowhead = none , style=dashed];
1374 -> 987[style=dashed];

}

(2) Obligation:

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

timesA_in_gga(0, T15, 0) → timesA_out_gga(0, T15, 0)
timesA_in_gga(s(T28), T29, T31) → U1_gga(T28, T29, T31, multB_in_gga(T28, T29, T31))
multB_in_gga(0, 0, 0) → multB_out_gga(0, 0, 0)
multB_in_gga(s(T51), 0, T54) → U12_gga(T51, T54, multC_in_ga(T51, T54))
multC_in_ga(0, 0) → multC_out_ga(0, 0)
multC_in_ga(s(T63), T65) → U2_ga(T63, T65, multC_in_ga(T63, T65))
U2_ga(T63, T65, multC_out_ga(T63, T65)) → multC_out_ga(s(T63), T65)
U12_gga(T51, T54, multC_out_ga(T51, T54)) → multB_out_gga(s(T51), 0, T54)
multB_in_gga(0, s(0), s(0)) → multB_out_gga(0, s(0), s(0))
multB_in_gga(s(T99), s(0), s(T102)) → U13_gga(T99, T102, multD_in_ga(T99, T102))
multD_in_ga(0, s(0)) → multD_out_ga(0, s(0))
multD_in_ga(s(T119), s(T121)) → U3_ga(T119, T121, multD_in_ga(T119, T121))
U3_ga(T119, T121, multD_out_ga(T119, T121)) → multD_out_ga(s(T119), s(T121))
U13_gga(T99, T102, multD_out_ga(T99, T102)) → multB_out_gga(s(T99), s(0), s(T102))
multB_in_gga(0, s(s(0)), s(s(0))) → multB_out_gga(0, s(s(0)), s(s(0)))
multB_in_gga(s(T155), s(s(0)), s(s(T158))) → U14_gga(T155, T158, multE_in_ga(T155, T158))
multE_in_ga(0, s(s(0))) → multE_out_ga(0, s(s(0)))
multE_in_ga(s(T183), s(s(T185))) → U4_ga(T183, T185, multE_in_ga(T183, T185))
U4_ga(T183, T185, multE_out_ga(T183, T185)) → multE_out_ga(s(T183), s(s(T185)))
U14_gga(T155, T158, multE_out_ga(T155, T158)) → multB_out_gga(s(T155), s(s(0)), s(s(T158)))
multB_in_gga(0, s(s(s(0))), s(s(s(0)))) → multB_out_gga(0, s(s(s(0))), s(s(s(0))))
multB_in_gga(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_gga(T219, T222, multF_in_ga(T219, T222))
multF_in_ga(0, s(s(s(0)))) → multF_out_ga(0, s(s(s(0))))
multF_in_ga(s(T255), s(s(s(T257)))) → U5_ga(T255, T257, multF_in_ga(T255, T257))
U5_ga(T255, T257, multF_out_ga(T255, T257)) → multF_out_ga(s(T255), s(s(s(T257))))
U15_gga(T219, T222, multF_out_ga(T219, T222)) → multB_out_gga(s(T219), s(s(s(0))), s(s(s(T222))))
multB_in_gga(0, s(s(s(s(0)))), s(s(s(s(0))))) → multB_out_gga(0, s(s(s(s(0)))), s(s(s(s(0)))))
multB_in_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_gga(T291, T294, multG_in_ga(T291, T294))
multG_in_ga(0, s(s(s(s(0))))) → multG_out_ga(0, s(s(s(s(0)))))
multG_in_ga(s(T335), s(s(s(s(T337))))) → U6_ga(T335, T337, multG_in_ga(T335, T337))
U6_ga(T335, T337, multG_out_ga(T335, T337)) → multG_out_ga(s(T335), s(s(s(s(T337)))))
U16_gga(T291, T294, multG_out_ga(T291, T294)) → multB_out_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294)))))
multB_in_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → multB_out_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
multB_in_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_gga(T371, T374, multH_in_ga(T371, T374))
multH_in_ga(0, s(s(s(s(s(0)))))) → multH_out_ga(0, s(s(s(s(s(0))))))
multH_in_ga(s(T423), s(s(s(s(s(T425)))))) → U7_ga(T423, T425, multH_in_ga(T423, T425))
U7_ga(T423, T425, multH_out_ga(T423, T425)) → multH_out_ga(s(T423), s(s(s(s(s(T425))))))
U17_gga(T371, T374, multH_out_ga(T371, T374)) → multB_out_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374))))))
multB_in_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → multB_out_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
multB_in_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_gga(T459, T462, multI_in_ga(T459, T462))
multI_in_ga(0, s(s(s(s(s(s(0))))))) → multI_out_ga(0, s(s(s(s(s(s(0)))))))
multI_in_ga(s(T519), s(s(s(s(s(s(T521))))))) → U8_ga(T519, T521, multI_in_ga(T519, T521))
U8_ga(T519, T521, multI_out_ga(T519, T521)) → multI_out_ga(s(T519), s(s(s(s(s(s(T521)))))))
U18_gga(T459, T462, multI_out_ga(T459, T462)) → multB_out_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462)))))))
multB_in_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → multB_out_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
multB_in_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_gga(T555, T558, multJ_in_ga(T555, T558))
multJ_in_ga(0, s(s(s(s(s(s(s(0)))))))) → multJ_out_ga(0, s(s(s(s(s(s(s(0))))))))
multJ_in_ga(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_ga(T623, T625, multJ_in_ga(T623, T625))
U9_ga(T623, T625, multJ_out_ga(T623, T625)) → multJ_out_ga(s(T623), s(s(s(s(s(s(s(T625))))))))
U19_gga(T555, T558, multJ_out_ga(T555, T558)) → multB_out_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558))))))))
multB_in_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_gga(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
multK_in_ggga(0, T649, 0, 0) → multK_out_ggga(0, T649, 0, 0)
multK_in_ggga(s(T662), T663, 0, T665) → U10_ggga(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
U10_ggga(T662, T663, T665, multB_out_gga(T662, s(T663), T665)) → multK_out_ggga(s(T662), T663, 0, T665)
multK_in_ggga(T676, T677, s(T678), s(T680)) → U11_ggga(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
U11_ggga(T676, T677, T678, T680, multK_out_ggga(T676, T677, T678, T680)) → multK_out_ggga(T676, T677, s(T678), s(T680))
U20_gga(T635, T637, T639, multK_out_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)) → multB_out_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639)))))))))
U1_gga(T28, T29, T31, multB_out_gga(T28, T29, T31)) → timesA_out_gga(s(T28), T29, T31)

The argument filtering Pi contains the following mapping:
timesA_in_gga(x1, x2, x3)  =  timesA_in_gga(x1, x2)
0  =  0
timesA_out_gga(x1, x2, x3)  =  timesA_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
multB_in_gga(x1, x2, x3)  =  multB_in_gga(x1, x2)
multB_out_gga(x1, x2, x3)  =  multB_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3)  =  U12_gga(x1, x3)
multC_in_ga(x1, x2)  =  multC_in_ga(x1)
multC_out_ga(x1, x2)  =  multC_out_ga(x1, x2)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U13_gga(x1, x2, x3)  =  U13_gga(x1, x3)
multD_in_ga(x1, x2)  =  multD_in_ga(x1)
multD_out_ga(x1, x2)  =  multD_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U14_gga(x1, x2, x3)  =  U14_gga(x1, x3)
multE_in_ga(x1, x2)  =  multE_in_ga(x1)
multE_out_ga(x1, x2)  =  multE_out_ga(x1, x2)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
multF_in_ga(x1, x2)  =  multF_in_ga(x1)
multF_out_ga(x1, x2)  =  multF_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
multG_in_ga(x1, x2)  =  multG_in_ga(x1)
multG_out_ga(x1, x2)  =  multG_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U17_gga(x1, x2, x3)  =  U17_gga(x1, x3)
multH_in_ga(x1, x2)  =  multH_in_ga(x1)
multH_out_ga(x1, x2)  =  multH_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
multI_in_ga(x1, x2)  =  multI_in_ga(x1)
multI_out_ga(x1, x2)  =  multI_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
multJ_in_ga(x1, x2)  =  multJ_in_ga(x1)
multJ_out_ga(x1, x2)  =  multJ_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
multK_in_ggga(x1, x2, x3, x4)  =  multK_in_ggga(x1, x2, x3)
multK_out_ggga(x1, x2, x3, x4)  =  multK_out_ggga(x1, x2, x3, x4)
U10_ggga(x1, x2, x3, x4)  =  U10_ggga(x1, x2, x4)
U11_ggga(x1, x2, x3, x4, x5)  =  U11_ggga(x1, x2, x3, x5)

(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:

TIMESA_IN_GGA(s(T28), T29, T31) → U1_GGA(T28, T29, T31, multB_in_gga(T28, T29, T31))
TIMESA_IN_GGA(s(T28), T29, T31) → MULTB_IN_GGA(T28, T29, T31)
MULTB_IN_GGA(s(T51), 0, T54) → U12_GGA(T51, T54, multC_in_ga(T51, T54))
MULTB_IN_GGA(s(T51), 0, T54) → MULTC_IN_GA(T51, T54)
MULTC_IN_GA(s(T63), T65) → U2_GA(T63, T65, multC_in_ga(T63, T65))
MULTC_IN_GA(s(T63), T65) → MULTC_IN_GA(T63, T65)
MULTB_IN_GGA(s(T99), s(0), s(T102)) → U13_GGA(T99, T102, multD_in_ga(T99, T102))
MULTB_IN_GGA(s(T99), s(0), s(T102)) → MULTD_IN_GA(T99, T102)
MULTD_IN_GA(s(T119), s(T121)) → U3_GA(T119, T121, multD_in_ga(T119, T121))
MULTD_IN_GA(s(T119), s(T121)) → MULTD_IN_GA(T119, T121)
MULTB_IN_GGA(s(T155), s(s(0)), s(s(T158))) → U14_GGA(T155, T158, multE_in_ga(T155, T158))
MULTB_IN_GGA(s(T155), s(s(0)), s(s(T158))) → MULTE_IN_GA(T155, T158)
MULTE_IN_GA(s(T183), s(s(T185))) → U4_GA(T183, T185, multE_in_ga(T183, T185))
MULTE_IN_GA(s(T183), s(s(T185))) → MULTE_IN_GA(T183, T185)
MULTB_IN_GGA(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_GGA(T219, T222, multF_in_ga(T219, T222))
MULTB_IN_GGA(s(T219), s(s(s(0))), s(s(s(T222)))) → MULTF_IN_GA(T219, T222)
MULTF_IN_GA(s(T255), s(s(s(T257)))) → U5_GA(T255, T257, multF_in_ga(T255, T257))
MULTF_IN_GA(s(T255), s(s(s(T257)))) → MULTF_IN_GA(T255, T257)
MULTB_IN_GGA(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_GGA(T291, T294, multG_in_ga(T291, T294))
MULTB_IN_GGA(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → MULTG_IN_GA(T291, T294)
MULTG_IN_GA(s(T335), s(s(s(s(T337))))) → U6_GA(T335, T337, multG_in_ga(T335, T337))
MULTG_IN_GA(s(T335), s(s(s(s(T337))))) → MULTG_IN_GA(T335, T337)
MULTB_IN_GGA(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_GGA(T371, T374, multH_in_ga(T371, T374))
MULTB_IN_GGA(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → MULTH_IN_GA(T371, T374)
MULTH_IN_GA(s(T423), s(s(s(s(s(T425)))))) → U7_GA(T423, T425, multH_in_ga(T423, T425))
MULTH_IN_GA(s(T423), s(s(s(s(s(T425)))))) → MULTH_IN_GA(T423, T425)
MULTB_IN_GGA(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_GGA(T459, T462, multI_in_ga(T459, T462))
MULTB_IN_GGA(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → MULTI_IN_GA(T459, T462)
MULTI_IN_GA(s(T519), s(s(s(s(s(s(T521))))))) → U8_GA(T519, T521, multI_in_ga(T519, T521))
MULTI_IN_GA(s(T519), s(s(s(s(s(s(T521))))))) → MULTI_IN_GA(T519, T521)
MULTB_IN_GGA(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_GGA(T555, T558, multJ_in_ga(T555, T558))
MULTB_IN_GGA(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → MULTJ_IN_GA(T555, T558)
MULTJ_IN_GA(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_GA(T623, T625, multJ_in_ga(T623, T625))
MULTJ_IN_GA(s(T623), s(s(s(s(s(s(s(T625)))))))) → MULTJ_IN_GA(T623, T625)
MULTB_IN_GGA(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_GGA(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
MULTB_IN_GGA(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → MULTK_IN_GGGA(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)
MULTK_IN_GGGA(s(T662), T663, 0, T665) → U10_GGGA(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
MULTK_IN_GGGA(s(T662), T663, 0, T665) → MULTB_IN_GGA(T662, s(T663), T665)
MULTK_IN_GGGA(T676, T677, s(T678), s(T680)) → U11_GGGA(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
MULTK_IN_GGGA(T676, T677, s(T678), s(T680)) → MULTK_IN_GGGA(T676, T677, T678, T680)

The TRS R consists of the following rules:

timesA_in_gga(0, T15, 0) → timesA_out_gga(0, T15, 0)
timesA_in_gga(s(T28), T29, T31) → U1_gga(T28, T29, T31, multB_in_gga(T28, T29, T31))
multB_in_gga(0, 0, 0) → multB_out_gga(0, 0, 0)
multB_in_gga(s(T51), 0, T54) → U12_gga(T51, T54, multC_in_ga(T51, T54))
multC_in_ga(0, 0) → multC_out_ga(0, 0)
multC_in_ga(s(T63), T65) → U2_ga(T63, T65, multC_in_ga(T63, T65))
U2_ga(T63, T65, multC_out_ga(T63, T65)) → multC_out_ga(s(T63), T65)
U12_gga(T51, T54, multC_out_ga(T51, T54)) → multB_out_gga(s(T51), 0, T54)
multB_in_gga(0, s(0), s(0)) → multB_out_gga(0, s(0), s(0))
multB_in_gga(s(T99), s(0), s(T102)) → U13_gga(T99, T102, multD_in_ga(T99, T102))
multD_in_ga(0, s(0)) → multD_out_ga(0, s(0))
multD_in_ga(s(T119), s(T121)) → U3_ga(T119, T121, multD_in_ga(T119, T121))
U3_ga(T119, T121, multD_out_ga(T119, T121)) → multD_out_ga(s(T119), s(T121))
U13_gga(T99, T102, multD_out_ga(T99, T102)) → multB_out_gga(s(T99), s(0), s(T102))
multB_in_gga(0, s(s(0)), s(s(0))) → multB_out_gga(0, s(s(0)), s(s(0)))
multB_in_gga(s(T155), s(s(0)), s(s(T158))) → U14_gga(T155, T158, multE_in_ga(T155, T158))
multE_in_ga(0, s(s(0))) → multE_out_ga(0, s(s(0)))
multE_in_ga(s(T183), s(s(T185))) → U4_ga(T183, T185, multE_in_ga(T183, T185))
U4_ga(T183, T185, multE_out_ga(T183, T185)) → multE_out_ga(s(T183), s(s(T185)))
U14_gga(T155, T158, multE_out_ga(T155, T158)) → multB_out_gga(s(T155), s(s(0)), s(s(T158)))
multB_in_gga(0, s(s(s(0))), s(s(s(0)))) → multB_out_gga(0, s(s(s(0))), s(s(s(0))))
multB_in_gga(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_gga(T219, T222, multF_in_ga(T219, T222))
multF_in_ga(0, s(s(s(0)))) → multF_out_ga(0, s(s(s(0))))
multF_in_ga(s(T255), s(s(s(T257)))) → U5_ga(T255, T257, multF_in_ga(T255, T257))
U5_ga(T255, T257, multF_out_ga(T255, T257)) → multF_out_ga(s(T255), s(s(s(T257))))
U15_gga(T219, T222, multF_out_ga(T219, T222)) → multB_out_gga(s(T219), s(s(s(0))), s(s(s(T222))))
multB_in_gga(0, s(s(s(s(0)))), s(s(s(s(0))))) → multB_out_gga(0, s(s(s(s(0)))), s(s(s(s(0)))))
multB_in_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_gga(T291, T294, multG_in_ga(T291, T294))
multG_in_ga(0, s(s(s(s(0))))) → multG_out_ga(0, s(s(s(s(0)))))
multG_in_ga(s(T335), s(s(s(s(T337))))) → U6_ga(T335, T337, multG_in_ga(T335, T337))
U6_ga(T335, T337, multG_out_ga(T335, T337)) → multG_out_ga(s(T335), s(s(s(s(T337)))))
U16_gga(T291, T294, multG_out_ga(T291, T294)) → multB_out_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294)))))
multB_in_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → multB_out_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
multB_in_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_gga(T371, T374, multH_in_ga(T371, T374))
multH_in_ga(0, s(s(s(s(s(0)))))) → multH_out_ga(0, s(s(s(s(s(0))))))
multH_in_ga(s(T423), s(s(s(s(s(T425)))))) → U7_ga(T423, T425, multH_in_ga(T423, T425))
U7_ga(T423, T425, multH_out_ga(T423, T425)) → multH_out_ga(s(T423), s(s(s(s(s(T425))))))
U17_gga(T371, T374, multH_out_ga(T371, T374)) → multB_out_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374))))))
multB_in_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → multB_out_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
multB_in_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_gga(T459, T462, multI_in_ga(T459, T462))
multI_in_ga(0, s(s(s(s(s(s(0))))))) → multI_out_ga(0, s(s(s(s(s(s(0)))))))
multI_in_ga(s(T519), s(s(s(s(s(s(T521))))))) → U8_ga(T519, T521, multI_in_ga(T519, T521))
U8_ga(T519, T521, multI_out_ga(T519, T521)) → multI_out_ga(s(T519), s(s(s(s(s(s(T521)))))))
U18_gga(T459, T462, multI_out_ga(T459, T462)) → multB_out_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462)))))))
multB_in_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → multB_out_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
multB_in_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_gga(T555, T558, multJ_in_ga(T555, T558))
multJ_in_ga(0, s(s(s(s(s(s(s(0)))))))) → multJ_out_ga(0, s(s(s(s(s(s(s(0))))))))
multJ_in_ga(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_ga(T623, T625, multJ_in_ga(T623, T625))
U9_ga(T623, T625, multJ_out_ga(T623, T625)) → multJ_out_ga(s(T623), s(s(s(s(s(s(s(T625))))))))
U19_gga(T555, T558, multJ_out_ga(T555, T558)) → multB_out_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558))))))))
multB_in_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_gga(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
multK_in_ggga(0, T649, 0, 0) → multK_out_ggga(0, T649, 0, 0)
multK_in_ggga(s(T662), T663, 0, T665) → U10_ggga(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
U10_ggga(T662, T663, T665, multB_out_gga(T662, s(T663), T665)) → multK_out_ggga(s(T662), T663, 0, T665)
multK_in_ggga(T676, T677, s(T678), s(T680)) → U11_ggga(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
U11_ggga(T676, T677, T678, T680, multK_out_ggga(T676, T677, T678, T680)) → multK_out_ggga(T676, T677, s(T678), s(T680))
U20_gga(T635, T637, T639, multK_out_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)) → multB_out_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639)))))))))
U1_gga(T28, T29, T31, multB_out_gga(T28, T29, T31)) → timesA_out_gga(s(T28), T29, T31)

The argument filtering Pi contains the following mapping:
timesA_in_gga(x1, x2, x3)  =  timesA_in_gga(x1, x2)
0  =  0
timesA_out_gga(x1, x2, x3)  =  timesA_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
multB_in_gga(x1, x2, x3)  =  multB_in_gga(x1, x2)
multB_out_gga(x1, x2, x3)  =  multB_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3)  =  U12_gga(x1, x3)
multC_in_ga(x1, x2)  =  multC_in_ga(x1)
multC_out_ga(x1, x2)  =  multC_out_ga(x1, x2)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U13_gga(x1, x2, x3)  =  U13_gga(x1, x3)
multD_in_ga(x1, x2)  =  multD_in_ga(x1)
multD_out_ga(x1, x2)  =  multD_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U14_gga(x1, x2, x3)  =  U14_gga(x1, x3)
multE_in_ga(x1, x2)  =  multE_in_ga(x1)
multE_out_ga(x1, x2)  =  multE_out_ga(x1, x2)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
multF_in_ga(x1, x2)  =  multF_in_ga(x1)
multF_out_ga(x1, x2)  =  multF_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
multG_in_ga(x1, x2)  =  multG_in_ga(x1)
multG_out_ga(x1, x2)  =  multG_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U17_gga(x1, x2, x3)  =  U17_gga(x1, x3)
multH_in_ga(x1, x2)  =  multH_in_ga(x1)
multH_out_ga(x1, x2)  =  multH_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
multI_in_ga(x1, x2)  =  multI_in_ga(x1)
multI_out_ga(x1, x2)  =  multI_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
multJ_in_ga(x1, x2)  =  multJ_in_ga(x1)
multJ_out_ga(x1, x2)  =  multJ_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
multK_in_ggga(x1, x2, x3, x4)  =  multK_in_ggga(x1, x2, x3)
multK_out_ggga(x1, x2, x3, x4)  =  multK_out_ggga(x1, x2, x3, x4)
U10_ggga(x1, x2, x3, x4)  =  U10_ggga(x1, x2, x4)
U11_ggga(x1, x2, x3, x4, x5)  =  U11_ggga(x1, x2, x3, x5)
TIMESA_IN_GGA(x1, x2, x3)  =  TIMESA_IN_GGA(x1, x2)
U1_GGA(x1, x2, x3, x4)  =  U1_GGA(x1, x2, x4)
MULTB_IN_GGA(x1, x2, x3)  =  MULTB_IN_GGA(x1, x2)
U12_GGA(x1, x2, x3)  =  U12_GGA(x1, x3)
MULTC_IN_GA(x1, x2)  =  MULTC_IN_GA(x1)
U2_GA(x1, x2, x3)  =  U2_GA(x1, x3)
U13_GGA(x1, x2, x3)  =  U13_GGA(x1, x3)
MULTD_IN_GA(x1, x2)  =  MULTD_IN_GA(x1)
U3_GA(x1, x2, x3)  =  U3_GA(x1, x3)
U14_GGA(x1, x2, x3)  =  U14_GGA(x1, x3)
MULTE_IN_GA(x1, x2)  =  MULTE_IN_GA(x1)
U4_GA(x1, x2, x3)  =  U4_GA(x1, x3)
U15_GGA(x1, x2, x3)  =  U15_GGA(x1, x3)
MULTF_IN_GA(x1, x2)  =  MULTF_IN_GA(x1)
U5_GA(x1, x2, x3)  =  U5_GA(x1, x3)
U16_GGA(x1, x2, x3)  =  U16_GGA(x1, x3)
MULTG_IN_GA(x1, x2)  =  MULTG_IN_GA(x1)
U6_GA(x1, x2, x3)  =  U6_GA(x1, x3)
U17_GGA(x1, x2, x3)  =  U17_GGA(x1, x3)
MULTH_IN_GA(x1, x2)  =  MULTH_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x1, x3)
U18_GGA(x1, x2, x3)  =  U18_GGA(x1, x3)
MULTI_IN_GA(x1, x2)  =  MULTI_IN_GA(x1)
U8_GA(x1, x2, x3)  =  U8_GA(x1, x3)
U19_GGA(x1, x2, x3)  =  U19_GGA(x1, x3)
MULTJ_IN_GA(x1, x2)  =  MULTJ_IN_GA(x1)
U9_GA(x1, x2, x3)  =  U9_GA(x1, x3)
U20_GGA(x1, x2, x3, x4)  =  U20_GGA(x1, x2, x4)
MULTK_IN_GGGA(x1, x2, x3, x4)  =  MULTK_IN_GGGA(x1, x2, x3)
U10_GGGA(x1, x2, x3, x4)  =  U10_GGGA(x1, x2, x4)
U11_GGGA(x1, x2, x3, x4, x5)  =  U11_GGGA(x1, x2, x3, x5)

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

(4) Obligation:

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

TIMESA_IN_GGA(s(T28), T29, T31) → U1_GGA(T28, T29, T31, multB_in_gga(T28, T29, T31))
TIMESA_IN_GGA(s(T28), T29, T31) → MULTB_IN_GGA(T28, T29, T31)
MULTB_IN_GGA(s(T51), 0, T54) → U12_GGA(T51, T54, multC_in_ga(T51, T54))
MULTB_IN_GGA(s(T51), 0, T54) → MULTC_IN_GA(T51, T54)
MULTC_IN_GA(s(T63), T65) → U2_GA(T63, T65, multC_in_ga(T63, T65))
MULTC_IN_GA(s(T63), T65) → MULTC_IN_GA(T63, T65)
MULTB_IN_GGA(s(T99), s(0), s(T102)) → U13_GGA(T99, T102, multD_in_ga(T99, T102))
MULTB_IN_GGA(s(T99), s(0), s(T102)) → MULTD_IN_GA(T99, T102)
MULTD_IN_GA(s(T119), s(T121)) → U3_GA(T119, T121, multD_in_ga(T119, T121))
MULTD_IN_GA(s(T119), s(T121)) → MULTD_IN_GA(T119, T121)
MULTB_IN_GGA(s(T155), s(s(0)), s(s(T158))) → U14_GGA(T155, T158, multE_in_ga(T155, T158))
MULTB_IN_GGA(s(T155), s(s(0)), s(s(T158))) → MULTE_IN_GA(T155, T158)
MULTE_IN_GA(s(T183), s(s(T185))) → U4_GA(T183, T185, multE_in_ga(T183, T185))
MULTE_IN_GA(s(T183), s(s(T185))) → MULTE_IN_GA(T183, T185)
MULTB_IN_GGA(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_GGA(T219, T222, multF_in_ga(T219, T222))
MULTB_IN_GGA(s(T219), s(s(s(0))), s(s(s(T222)))) → MULTF_IN_GA(T219, T222)
MULTF_IN_GA(s(T255), s(s(s(T257)))) → U5_GA(T255, T257, multF_in_ga(T255, T257))
MULTF_IN_GA(s(T255), s(s(s(T257)))) → MULTF_IN_GA(T255, T257)
MULTB_IN_GGA(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_GGA(T291, T294, multG_in_ga(T291, T294))
MULTB_IN_GGA(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → MULTG_IN_GA(T291, T294)
MULTG_IN_GA(s(T335), s(s(s(s(T337))))) → U6_GA(T335, T337, multG_in_ga(T335, T337))
MULTG_IN_GA(s(T335), s(s(s(s(T337))))) → MULTG_IN_GA(T335, T337)
MULTB_IN_GGA(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_GGA(T371, T374, multH_in_ga(T371, T374))
MULTB_IN_GGA(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → MULTH_IN_GA(T371, T374)
MULTH_IN_GA(s(T423), s(s(s(s(s(T425)))))) → U7_GA(T423, T425, multH_in_ga(T423, T425))
MULTH_IN_GA(s(T423), s(s(s(s(s(T425)))))) → MULTH_IN_GA(T423, T425)
MULTB_IN_GGA(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_GGA(T459, T462, multI_in_ga(T459, T462))
MULTB_IN_GGA(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → MULTI_IN_GA(T459, T462)
MULTI_IN_GA(s(T519), s(s(s(s(s(s(T521))))))) → U8_GA(T519, T521, multI_in_ga(T519, T521))
MULTI_IN_GA(s(T519), s(s(s(s(s(s(T521))))))) → MULTI_IN_GA(T519, T521)
MULTB_IN_GGA(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_GGA(T555, T558, multJ_in_ga(T555, T558))
MULTB_IN_GGA(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → MULTJ_IN_GA(T555, T558)
MULTJ_IN_GA(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_GA(T623, T625, multJ_in_ga(T623, T625))
MULTJ_IN_GA(s(T623), s(s(s(s(s(s(s(T625)))))))) → MULTJ_IN_GA(T623, T625)
MULTB_IN_GGA(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_GGA(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
MULTB_IN_GGA(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → MULTK_IN_GGGA(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)
MULTK_IN_GGGA(s(T662), T663, 0, T665) → U10_GGGA(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
MULTK_IN_GGGA(s(T662), T663, 0, T665) → MULTB_IN_GGA(T662, s(T663), T665)
MULTK_IN_GGGA(T676, T677, s(T678), s(T680)) → U11_GGGA(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
MULTK_IN_GGGA(T676, T677, s(T678), s(T680)) → MULTK_IN_GGGA(T676, T677, T678, T680)

The TRS R consists of the following rules:

timesA_in_gga(0, T15, 0) → timesA_out_gga(0, T15, 0)
timesA_in_gga(s(T28), T29, T31) → U1_gga(T28, T29, T31, multB_in_gga(T28, T29, T31))
multB_in_gga(0, 0, 0) → multB_out_gga(0, 0, 0)
multB_in_gga(s(T51), 0, T54) → U12_gga(T51, T54, multC_in_ga(T51, T54))
multC_in_ga(0, 0) → multC_out_ga(0, 0)
multC_in_ga(s(T63), T65) → U2_ga(T63, T65, multC_in_ga(T63, T65))
U2_ga(T63, T65, multC_out_ga(T63, T65)) → multC_out_ga(s(T63), T65)
U12_gga(T51, T54, multC_out_ga(T51, T54)) → multB_out_gga(s(T51), 0, T54)
multB_in_gga(0, s(0), s(0)) → multB_out_gga(0, s(0), s(0))
multB_in_gga(s(T99), s(0), s(T102)) → U13_gga(T99, T102, multD_in_ga(T99, T102))
multD_in_ga(0, s(0)) → multD_out_ga(0, s(0))
multD_in_ga(s(T119), s(T121)) → U3_ga(T119, T121, multD_in_ga(T119, T121))
U3_ga(T119, T121, multD_out_ga(T119, T121)) → multD_out_ga(s(T119), s(T121))
U13_gga(T99, T102, multD_out_ga(T99, T102)) → multB_out_gga(s(T99), s(0), s(T102))
multB_in_gga(0, s(s(0)), s(s(0))) → multB_out_gga(0, s(s(0)), s(s(0)))
multB_in_gga(s(T155), s(s(0)), s(s(T158))) → U14_gga(T155, T158, multE_in_ga(T155, T158))
multE_in_ga(0, s(s(0))) → multE_out_ga(0, s(s(0)))
multE_in_ga(s(T183), s(s(T185))) → U4_ga(T183, T185, multE_in_ga(T183, T185))
U4_ga(T183, T185, multE_out_ga(T183, T185)) → multE_out_ga(s(T183), s(s(T185)))
U14_gga(T155, T158, multE_out_ga(T155, T158)) → multB_out_gga(s(T155), s(s(0)), s(s(T158)))
multB_in_gga(0, s(s(s(0))), s(s(s(0)))) → multB_out_gga(0, s(s(s(0))), s(s(s(0))))
multB_in_gga(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_gga(T219, T222, multF_in_ga(T219, T222))
multF_in_ga(0, s(s(s(0)))) → multF_out_ga(0, s(s(s(0))))
multF_in_ga(s(T255), s(s(s(T257)))) → U5_ga(T255, T257, multF_in_ga(T255, T257))
U5_ga(T255, T257, multF_out_ga(T255, T257)) → multF_out_ga(s(T255), s(s(s(T257))))
U15_gga(T219, T222, multF_out_ga(T219, T222)) → multB_out_gga(s(T219), s(s(s(0))), s(s(s(T222))))
multB_in_gga(0, s(s(s(s(0)))), s(s(s(s(0))))) → multB_out_gga(0, s(s(s(s(0)))), s(s(s(s(0)))))
multB_in_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_gga(T291, T294, multG_in_ga(T291, T294))
multG_in_ga(0, s(s(s(s(0))))) → multG_out_ga(0, s(s(s(s(0)))))
multG_in_ga(s(T335), s(s(s(s(T337))))) → U6_ga(T335, T337, multG_in_ga(T335, T337))
U6_ga(T335, T337, multG_out_ga(T335, T337)) → multG_out_ga(s(T335), s(s(s(s(T337)))))
U16_gga(T291, T294, multG_out_ga(T291, T294)) → multB_out_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294)))))
multB_in_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → multB_out_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
multB_in_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_gga(T371, T374, multH_in_ga(T371, T374))
multH_in_ga(0, s(s(s(s(s(0)))))) → multH_out_ga(0, s(s(s(s(s(0))))))
multH_in_ga(s(T423), s(s(s(s(s(T425)))))) → U7_ga(T423, T425, multH_in_ga(T423, T425))
U7_ga(T423, T425, multH_out_ga(T423, T425)) → multH_out_ga(s(T423), s(s(s(s(s(T425))))))
U17_gga(T371, T374, multH_out_ga(T371, T374)) → multB_out_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374))))))
multB_in_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → multB_out_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
multB_in_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_gga(T459, T462, multI_in_ga(T459, T462))
multI_in_ga(0, s(s(s(s(s(s(0))))))) → multI_out_ga(0, s(s(s(s(s(s(0)))))))
multI_in_ga(s(T519), s(s(s(s(s(s(T521))))))) → U8_ga(T519, T521, multI_in_ga(T519, T521))
U8_ga(T519, T521, multI_out_ga(T519, T521)) → multI_out_ga(s(T519), s(s(s(s(s(s(T521)))))))
U18_gga(T459, T462, multI_out_ga(T459, T462)) → multB_out_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462)))))))
multB_in_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → multB_out_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
multB_in_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_gga(T555, T558, multJ_in_ga(T555, T558))
multJ_in_ga(0, s(s(s(s(s(s(s(0)))))))) → multJ_out_ga(0, s(s(s(s(s(s(s(0))))))))
multJ_in_ga(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_ga(T623, T625, multJ_in_ga(T623, T625))
U9_ga(T623, T625, multJ_out_ga(T623, T625)) → multJ_out_ga(s(T623), s(s(s(s(s(s(s(T625))))))))
U19_gga(T555, T558, multJ_out_ga(T555, T558)) → multB_out_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558))))))))
multB_in_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_gga(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
multK_in_ggga(0, T649, 0, 0) → multK_out_ggga(0, T649, 0, 0)
multK_in_ggga(s(T662), T663, 0, T665) → U10_ggga(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
U10_ggga(T662, T663, T665, multB_out_gga(T662, s(T663), T665)) → multK_out_ggga(s(T662), T663, 0, T665)
multK_in_ggga(T676, T677, s(T678), s(T680)) → U11_ggga(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
U11_ggga(T676, T677, T678, T680, multK_out_ggga(T676, T677, T678, T680)) → multK_out_ggga(T676, T677, s(T678), s(T680))
U20_gga(T635, T637, T639, multK_out_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)) → multB_out_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639)))))))))
U1_gga(T28, T29, T31, multB_out_gga(T28, T29, T31)) → timesA_out_gga(s(T28), T29, T31)

The argument filtering Pi contains the following mapping:
timesA_in_gga(x1, x2, x3)  =  timesA_in_gga(x1, x2)
0  =  0
timesA_out_gga(x1, x2, x3)  =  timesA_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
multB_in_gga(x1, x2, x3)  =  multB_in_gga(x1, x2)
multB_out_gga(x1, x2, x3)  =  multB_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3)  =  U12_gga(x1, x3)
multC_in_ga(x1, x2)  =  multC_in_ga(x1)
multC_out_ga(x1, x2)  =  multC_out_ga(x1, x2)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U13_gga(x1, x2, x3)  =  U13_gga(x1, x3)
multD_in_ga(x1, x2)  =  multD_in_ga(x1)
multD_out_ga(x1, x2)  =  multD_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U14_gga(x1, x2, x3)  =  U14_gga(x1, x3)
multE_in_ga(x1, x2)  =  multE_in_ga(x1)
multE_out_ga(x1, x2)  =  multE_out_ga(x1, x2)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
multF_in_ga(x1, x2)  =  multF_in_ga(x1)
multF_out_ga(x1, x2)  =  multF_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
multG_in_ga(x1, x2)  =  multG_in_ga(x1)
multG_out_ga(x1, x2)  =  multG_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U17_gga(x1, x2, x3)  =  U17_gga(x1, x3)
multH_in_ga(x1, x2)  =  multH_in_ga(x1)
multH_out_ga(x1, x2)  =  multH_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
multI_in_ga(x1, x2)  =  multI_in_ga(x1)
multI_out_ga(x1, x2)  =  multI_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
multJ_in_ga(x1, x2)  =  multJ_in_ga(x1)
multJ_out_ga(x1, x2)  =  multJ_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
multK_in_ggga(x1, x2, x3, x4)  =  multK_in_ggga(x1, x2, x3)
multK_out_ggga(x1, x2, x3, x4)  =  multK_out_ggga(x1, x2, x3, x4)
U10_ggga(x1, x2, x3, x4)  =  U10_ggga(x1, x2, x4)
U11_ggga(x1, x2, x3, x4, x5)  =  U11_ggga(x1, x2, x3, x5)
TIMESA_IN_GGA(x1, x2, x3)  =  TIMESA_IN_GGA(x1, x2)
U1_GGA(x1, x2, x3, x4)  =  U1_GGA(x1, x2, x4)
MULTB_IN_GGA(x1, x2, x3)  =  MULTB_IN_GGA(x1, x2)
U12_GGA(x1, x2, x3)  =  U12_GGA(x1, x3)
MULTC_IN_GA(x1, x2)  =  MULTC_IN_GA(x1)
U2_GA(x1, x2, x3)  =  U2_GA(x1, x3)
U13_GGA(x1, x2, x3)  =  U13_GGA(x1, x3)
MULTD_IN_GA(x1, x2)  =  MULTD_IN_GA(x1)
U3_GA(x1, x2, x3)  =  U3_GA(x1, x3)
U14_GGA(x1, x2, x3)  =  U14_GGA(x1, x3)
MULTE_IN_GA(x1, x2)  =  MULTE_IN_GA(x1)
U4_GA(x1, x2, x3)  =  U4_GA(x1, x3)
U15_GGA(x1, x2, x3)  =  U15_GGA(x1, x3)
MULTF_IN_GA(x1, x2)  =  MULTF_IN_GA(x1)
U5_GA(x1, x2, x3)  =  U5_GA(x1, x3)
U16_GGA(x1, x2, x3)  =  U16_GGA(x1, x3)
MULTG_IN_GA(x1, x2)  =  MULTG_IN_GA(x1)
U6_GA(x1, x2, x3)  =  U6_GA(x1, x3)
U17_GGA(x1, x2, x3)  =  U17_GGA(x1, x3)
MULTH_IN_GA(x1, x2)  =  MULTH_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x1, x3)
U18_GGA(x1, x2, x3)  =  U18_GGA(x1, x3)
MULTI_IN_GA(x1, x2)  =  MULTI_IN_GA(x1)
U8_GA(x1, x2, x3)  =  U8_GA(x1, x3)
U19_GGA(x1, x2, x3)  =  U19_GGA(x1, x3)
MULTJ_IN_GA(x1, x2)  =  MULTJ_IN_GA(x1)
U9_GA(x1, x2, x3)  =  U9_GA(x1, x3)
U20_GGA(x1, x2, x3, x4)  =  U20_GGA(x1, x2, x4)
MULTK_IN_GGGA(x1, x2, x3, x4)  =  MULTK_IN_GGGA(x1, x2, x3)
U10_GGGA(x1, x2, x3, x4)  =  U10_GGGA(x1, x2, x4)
U11_GGGA(x1, x2, x3, x4, x5)  =  U11_GGGA(x1, x2, x3, x5)

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

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 9 SCCs with 29 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

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

MULTJ_IN_GA(s(T623), s(s(s(s(s(s(s(T625)))))))) → MULTJ_IN_GA(T623, T625)

The TRS R consists of the following rules:

timesA_in_gga(0, T15, 0) → timesA_out_gga(0, T15, 0)
timesA_in_gga(s(T28), T29, T31) → U1_gga(T28, T29, T31, multB_in_gga(T28, T29, T31))
multB_in_gga(0, 0, 0) → multB_out_gga(0, 0, 0)
multB_in_gga(s(T51), 0, T54) → U12_gga(T51, T54, multC_in_ga(T51, T54))
multC_in_ga(0, 0) → multC_out_ga(0, 0)
multC_in_ga(s(T63), T65) → U2_ga(T63, T65, multC_in_ga(T63, T65))
U2_ga(T63, T65, multC_out_ga(T63, T65)) → multC_out_ga(s(T63), T65)
U12_gga(T51, T54, multC_out_ga(T51, T54)) → multB_out_gga(s(T51), 0, T54)
multB_in_gga(0, s(0), s(0)) → multB_out_gga(0, s(0), s(0))
multB_in_gga(s(T99), s(0), s(T102)) → U13_gga(T99, T102, multD_in_ga(T99, T102))
multD_in_ga(0, s(0)) → multD_out_ga(0, s(0))
multD_in_ga(s(T119), s(T121)) → U3_ga(T119, T121, multD_in_ga(T119, T121))
U3_ga(T119, T121, multD_out_ga(T119, T121)) → multD_out_ga(s(T119), s(T121))
U13_gga(T99, T102, multD_out_ga(T99, T102)) → multB_out_gga(s(T99), s(0), s(T102))
multB_in_gga(0, s(s(0)), s(s(0))) → multB_out_gga(0, s(s(0)), s(s(0)))
multB_in_gga(s(T155), s(s(0)), s(s(T158))) → U14_gga(T155, T158, multE_in_ga(T155, T158))
multE_in_ga(0, s(s(0))) → multE_out_ga(0, s(s(0)))
multE_in_ga(s(T183), s(s(T185))) → U4_ga(T183, T185, multE_in_ga(T183, T185))
U4_ga(T183, T185, multE_out_ga(T183, T185)) → multE_out_ga(s(T183), s(s(T185)))
U14_gga(T155, T158, multE_out_ga(T155, T158)) → multB_out_gga(s(T155), s(s(0)), s(s(T158)))
multB_in_gga(0, s(s(s(0))), s(s(s(0)))) → multB_out_gga(0, s(s(s(0))), s(s(s(0))))
multB_in_gga(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_gga(T219, T222, multF_in_ga(T219, T222))
multF_in_ga(0, s(s(s(0)))) → multF_out_ga(0, s(s(s(0))))
multF_in_ga(s(T255), s(s(s(T257)))) → U5_ga(T255, T257, multF_in_ga(T255, T257))
U5_ga(T255, T257, multF_out_ga(T255, T257)) → multF_out_ga(s(T255), s(s(s(T257))))
U15_gga(T219, T222, multF_out_ga(T219, T222)) → multB_out_gga(s(T219), s(s(s(0))), s(s(s(T222))))
multB_in_gga(0, s(s(s(s(0)))), s(s(s(s(0))))) → multB_out_gga(0, s(s(s(s(0)))), s(s(s(s(0)))))
multB_in_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_gga(T291, T294, multG_in_ga(T291, T294))
multG_in_ga(0, s(s(s(s(0))))) → multG_out_ga(0, s(s(s(s(0)))))
multG_in_ga(s(T335), s(s(s(s(T337))))) → U6_ga(T335, T337, multG_in_ga(T335, T337))
U6_ga(T335, T337, multG_out_ga(T335, T337)) → multG_out_ga(s(T335), s(s(s(s(T337)))))
U16_gga(T291, T294, multG_out_ga(T291, T294)) → multB_out_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294)))))
multB_in_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → multB_out_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
multB_in_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_gga(T371, T374, multH_in_ga(T371, T374))
multH_in_ga(0, s(s(s(s(s(0)))))) → multH_out_ga(0, s(s(s(s(s(0))))))
multH_in_ga(s(T423), s(s(s(s(s(T425)))))) → U7_ga(T423, T425, multH_in_ga(T423, T425))
U7_ga(T423, T425, multH_out_ga(T423, T425)) → multH_out_ga(s(T423), s(s(s(s(s(T425))))))
U17_gga(T371, T374, multH_out_ga(T371, T374)) → multB_out_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374))))))
multB_in_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → multB_out_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
multB_in_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_gga(T459, T462, multI_in_ga(T459, T462))
multI_in_ga(0, s(s(s(s(s(s(0))))))) → multI_out_ga(0, s(s(s(s(s(s(0)))))))
multI_in_ga(s(T519), s(s(s(s(s(s(T521))))))) → U8_ga(T519, T521, multI_in_ga(T519, T521))
U8_ga(T519, T521, multI_out_ga(T519, T521)) → multI_out_ga(s(T519), s(s(s(s(s(s(T521)))))))
U18_gga(T459, T462, multI_out_ga(T459, T462)) → multB_out_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462)))))))
multB_in_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → multB_out_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
multB_in_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_gga(T555, T558, multJ_in_ga(T555, T558))
multJ_in_ga(0, s(s(s(s(s(s(s(0)))))))) → multJ_out_ga(0, s(s(s(s(s(s(s(0))))))))
multJ_in_ga(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_ga(T623, T625, multJ_in_ga(T623, T625))
U9_ga(T623, T625, multJ_out_ga(T623, T625)) → multJ_out_ga(s(T623), s(s(s(s(s(s(s(T625))))))))
U19_gga(T555, T558, multJ_out_ga(T555, T558)) → multB_out_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558))))))))
multB_in_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_gga(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
multK_in_ggga(0, T649, 0, 0) → multK_out_ggga(0, T649, 0, 0)
multK_in_ggga(s(T662), T663, 0, T665) → U10_ggga(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
U10_ggga(T662, T663, T665, multB_out_gga(T662, s(T663), T665)) → multK_out_ggga(s(T662), T663, 0, T665)
multK_in_ggga(T676, T677, s(T678), s(T680)) → U11_ggga(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
U11_ggga(T676, T677, T678, T680, multK_out_ggga(T676, T677, T678, T680)) → multK_out_ggga(T676, T677, s(T678), s(T680))
U20_gga(T635, T637, T639, multK_out_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)) → multB_out_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639)))))))))
U1_gga(T28, T29, T31, multB_out_gga(T28, T29, T31)) → timesA_out_gga(s(T28), T29, T31)

The argument filtering Pi contains the following mapping:
timesA_in_gga(x1, x2, x3)  =  timesA_in_gga(x1, x2)
0  =  0
timesA_out_gga(x1, x2, x3)  =  timesA_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
multB_in_gga(x1, x2, x3)  =  multB_in_gga(x1, x2)
multB_out_gga(x1, x2, x3)  =  multB_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3)  =  U12_gga(x1, x3)
multC_in_ga(x1, x2)  =  multC_in_ga(x1)
multC_out_ga(x1, x2)  =  multC_out_ga(x1, x2)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U13_gga(x1, x2, x3)  =  U13_gga(x1, x3)
multD_in_ga(x1, x2)  =  multD_in_ga(x1)
multD_out_ga(x1, x2)  =  multD_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U14_gga(x1, x2, x3)  =  U14_gga(x1, x3)
multE_in_ga(x1, x2)  =  multE_in_ga(x1)
multE_out_ga(x1, x2)  =  multE_out_ga(x1, x2)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
multF_in_ga(x1, x2)  =  multF_in_ga(x1)
multF_out_ga(x1, x2)  =  multF_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
multG_in_ga(x1, x2)  =  multG_in_ga(x1)
multG_out_ga(x1, x2)  =  multG_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U17_gga(x1, x2, x3)  =  U17_gga(x1, x3)
multH_in_ga(x1, x2)  =  multH_in_ga(x1)
multH_out_ga(x1, x2)  =  multH_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
multI_in_ga(x1, x2)  =  multI_in_ga(x1)
multI_out_ga(x1, x2)  =  multI_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
multJ_in_ga(x1, x2)  =  multJ_in_ga(x1)
multJ_out_ga(x1, x2)  =  multJ_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
multK_in_ggga(x1, x2, x3, x4)  =  multK_in_ggga(x1, x2, x3)
multK_out_ggga(x1, x2, x3, x4)  =  multK_out_ggga(x1, x2, x3, x4)
U10_ggga(x1, x2, x3, x4)  =  U10_ggga(x1, x2, x4)
U11_ggga(x1, x2, x3, x4, x5)  =  U11_ggga(x1, x2, x3, x5)
MULTJ_IN_GA(x1, x2)  =  MULTJ_IN_GA(x1)

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:

MULTJ_IN_GA(s(T623), s(s(s(s(s(s(s(T625)))))))) → MULTJ_IN_GA(T623, T625)

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

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

(10) PiDPToQDPProof (SOUND transformation)

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

(11) Obligation:

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

MULTJ_IN_GA(s(T623)) → MULTJ_IN_GA(T623)

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:

• MULTJ_IN_GA(s(T623)) → MULTJ_IN_GA(T623)
  The graph contains the following edges 1 > 1

(13) YES

(14) Obligation:

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

MULTI_IN_GA(s(T519), s(s(s(s(s(s(T521))))))) → MULTI_IN_GA(T519, T521)

The TRS R consists of the following rules:

timesA_in_gga(0, T15, 0) → timesA_out_gga(0, T15, 0)
timesA_in_gga(s(T28), T29, T31) → U1_gga(T28, T29, T31, multB_in_gga(T28, T29, T31))
multB_in_gga(0, 0, 0) → multB_out_gga(0, 0, 0)
multB_in_gga(s(T51), 0, T54) → U12_gga(T51, T54, multC_in_ga(T51, T54))
multC_in_ga(0, 0) → multC_out_ga(0, 0)
multC_in_ga(s(T63), T65) → U2_ga(T63, T65, multC_in_ga(T63, T65))
U2_ga(T63, T65, multC_out_ga(T63, T65)) → multC_out_ga(s(T63), T65)
U12_gga(T51, T54, multC_out_ga(T51, T54)) → multB_out_gga(s(T51), 0, T54)
multB_in_gga(0, s(0), s(0)) → multB_out_gga(0, s(0), s(0))
multB_in_gga(s(T99), s(0), s(T102)) → U13_gga(T99, T102, multD_in_ga(T99, T102))
multD_in_ga(0, s(0)) → multD_out_ga(0, s(0))
multD_in_ga(s(T119), s(T121)) → U3_ga(T119, T121, multD_in_ga(T119, T121))
U3_ga(T119, T121, multD_out_ga(T119, T121)) → multD_out_ga(s(T119), s(T121))
U13_gga(T99, T102, multD_out_ga(T99, T102)) → multB_out_gga(s(T99), s(0), s(T102))
multB_in_gga(0, s(s(0)), s(s(0))) → multB_out_gga(0, s(s(0)), s(s(0)))
multB_in_gga(s(T155), s(s(0)), s(s(T158))) → U14_gga(T155, T158, multE_in_ga(T155, T158))
multE_in_ga(0, s(s(0))) → multE_out_ga(0, s(s(0)))
multE_in_ga(s(T183), s(s(T185))) → U4_ga(T183, T185, multE_in_ga(T183, T185))
U4_ga(T183, T185, multE_out_ga(T183, T185)) → multE_out_ga(s(T183), s(s(T185)))
U14_gga(T155, T158, multE_out_ga(T155, T158)) → multB_out_gga(s(T155), s(s(0)), s(s(T158)))
multB_in_gga(0, s(s(s(0))), s(s(s(0)))) → multB_out_gga(0, s(s(s(0))), s(s(s(0))))
multB_in_gga(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_gga(T219, T222, multF_in_ga(T219, T222))
multF_in_ga(0, s(s(s(0)))) → multF_out_ga(0, s(s(s(0))))
multF_in_ga(s(T255), s(s(s(T257)))) → U5_ga(T255, T257, multF_in_ga(T255, T257))
U5_ga(T255, T257, multF_out_ga(T255, T257)) → multF_out_ga(s(T255), s(s(s(T257))))
U15_gga(T219, T222, multF_out_ga(T219, T222)) → multB_out_gga(s(T219), s(s(s(0))), s(s(s(T222))))
multB_in_gga(0, s(s(s(s(0)))), s(s(s(s(0))))) → multB_out_gga(0, s(s(s(s(0)))), s(s(s(s(0)))))
multB_in_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_gga(T291, T294, multG_in_ga(T291, T294))
multG_in_ga(0, s(s(s(s(0))))) → multG_out_ga(0, s(s(s(s(0)))))
multG_in_ga(s(T335), s(s(s(s(T337))))) → U6_ga(T335, T337, multG_in_ga(T335, T337))
U6_ga(T335, T337, multG_out_ga(T335, T337)) → multG_out_ga(s(T335), s(s(s(s(T337)))))
U16_gga(T291, T294, multG_out_ga(T291, T294)) → multB_out_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294)))))
multB_in_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → multB_out_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
multB_in_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_gga(T371, T374, multH_in_ga(T371, T374))
multH_in_ga(0, s(s(s(s(s(0)))))) → multH_out_ga(0, s(s(s(s(s(0))))))
multH_in_ga(s(T423), s(s(s(s(s(T425)))))) → U7_ga(T423, T425, multH_in_ga(T423, T425))
U7_ga(T423, T425, multH_out_ga(T423, T425)) → multH_out_ga(s(T423), s(s(s(s(s(T425))))))
U17_gga(T371, T374, multH_out_ga(T371, T374)) → multB_out_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374))))))
multB_in_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → multB_out_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
multB_in_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_gga(T459, T462, multI_in_ga(T459, T462))
multI_in_ga(0, s(s(s(s(s(s(0))))))) → multI_out_ga(0, s(s(s(s(s(s(0)))))))
multI_in_ga(s(T519), s(s(s(s(s(s(T521))))))) → U8_ga(T519, T521, multI_in_ga(T519, T521))
U8_ga(T519, T521, multI_out_ga(T519, T521)) → multI_out_ga(s(T519), s(s(s(s(s(s(T521)))))))
U18_gga(T459, T462, multI_out_ga(T459, T462)) → multB_out_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462)))))))
multB_in_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → multB_out_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
multB_in_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_gga(T555, T558, multJ_in_ga(T555, T558))
multJ_in_ga(0, s(s(s(s(s(s(s(0)))))))) → multJ_out_ga(0, s(s(s(s(s(s(s(0))))))))
multJ_in_ga(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_ga(T623, T625, multJ_in_ga(T623, T625))
U9_ga(T623, T625, multJ_out_ga(T623, T625)) → multJ_out_ga(s(T623), s(s(s(s(s(s(s(T625))))))))
U19_gga(T555, T558, multJ_out_ga(T555, T558)) → multB_out_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558))))))))
multB_in_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_gga(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
multK_in_ggga(0, T649, 0, 0) → multK_out_ggga(0, T649, 0, 0)
multK_in_ggga(s(T662), T663, 0, T665) → U10_ggga(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
U10_ggga(T662, T663, T665, multB_out_gga(T662, s(T663), T665)) → multK_out_ggga(s(T662), T663, 0, T665)
multK_in_ggga(T676, T677, s(T678), s(T680)) → U11_ggga(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
U11_ggga(T676, T677, T678, T680, multK_out_ggga(T676, T677, T678, T680)) → multK_out_ggga(T676, T677, s(T678), s(T680))
U20_gga(T635, T637, T639, multK_out_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)) → multB_out_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639)))))))))
U1_gga(T28, T29, T31, multB_out_gga(T28, T29, T31)) → timesA_out_gga(s(T28), T29, T31)

The argument filtering Pi contains the following mapping:
timesA_in_gga(x1, x2, x3)  =  timesA_in_gga(x1, x2)
0  =  0
timesA_out_gga(x1, x2, x3)  =  timesA_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
multB_in_gga(x1, x2, x3)  =  multB_in_gga(x1, x2)
multB_out_gga(x1, x2, x3)  =  multB_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3)  =  U12_gga(x1, x3)
multC_in_ga(x1, x2)  =  multC_in_ga(x1)
multC_out_ga(x1, x2)  =  multC_out_ga(x1, x2)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U13_gga(x1, x2, x3)  =  U13_gga(x1, x3)
multD_in_ga(x1, x2)  =  multD_in_ga(x1)
multD_out_ga(x1, x2)  =  multD_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U14_gga(x1, x2, x3)  =  U14_gga(x1, x3)
multE_in_ga(x1, x2)  =  multE_in_ga(x1)
multE_out_ga(x1, x2)  =  multE_out_ga(x1, x2)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
multF_in_ga(x1, x2)  =  multF_in_ga(x1)
multF_out_ga(x1, x2)  =  multF_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
multG_in_ga(x1, x2)  =  multG_in_ga(x1)
multG_out_ga(x1, x2)  =  multG_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U17_gga(x1, x2, x3)  =  U17_gga(x1, x3)
multH_in_ga(x1, x2)  =  multH_in_ga(x1)
multH_out_ga(x1, x2)  =  multH_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
multI_in_ga(x1, x2)  =  multI_in_ga(x1)
multI_out_ga(x1, x2)  =  multI_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
multJ_in_ga(x1, x2)  =  multJ_in_ga(x1)
multJ_out_ga(x1, x2)  =  multJ_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
multK_in_ggga(x1, x2, x3, x4)  =  multK_in_ggga(x1, x2, x3)
multK_out_ggga(x1, x2, x3, x4)  =  multK_out_ggga(x1, x2, x3, x4)
U10_ggga(x1, x2, x3, x4)  =  U10_ggga(x1, x2, x4)
U11_ggga(x1, x2, x3, x4, x5)  =  U11_ggga(x1, x2, x3, x5)
MULTI_IN_GA(x1, x2)  =  MULTI_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:

MULTI_IN_GA(s(T519), s(s(s(s(s(s(T521))))))) → MULTI_IN_GA(T519, T521)

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

MULTI_IN_GA(s(T519)) → MULTI_IN_GA(T519)

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:

• MULTI_IN_GA(s(T519)) → MULTI_IN_GA(T519)
  The graph contains the following edges 1 > 1

(20) YES

(21) Obligation:

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

MULTH_IN_GA(s(T423), s(s(s(s(s(T425)))))) → MULTH_IN_GA(T423, T425)

The TRS R consists of the following rules:

timesA_in_gga(0, T15, 0) → timesA_out_gga(0, T15, 0)
timesA_in_gga(s(T28), T29, T31) → U1_gga(T28, T29, T31, multB_in_gga(T28, T29, T31))
multB_in_gga(0, 0, 0) → multB_out_gga(0, 0, 0)
multB_in_gga(s(T51), 0, T54) → U12_gga(T51, T54, multC_in_ga(T51, T54))
multC_in_ga(0, 0) → multC_out_ga(0, 0)
multC_in_ga(s(T63), T65) → U2_ga(T63, T65, multC_in_ga(T63, T65))
U2_ga(T63, T65, multC_out_ga(T63, T65)) → multC_out_ga(s(T63), T65)
U12_gga(T51, T54, multC_out_ga(T51, T54)) → multB_out_gga(s(T51), 0, T54)
multB_in_gga(0, s(0), s(0)) → multB_out_gga(0, s(0), s(0))
multB_in_gga(s(T99), s(0), s(T102)) → U13_gga(T99, T102, multD_in_ga(T99, T102))
multD_in_ga(0, s(0)) → multD_out_ga(0, s(0))
multD_in_ga(s(T119), s(T121)) → U3_ga(T119, T121, multD_in_ga(T119, T121))
U3_ga(T119, T121, multD_out_ga(T119, T121)) → multD_out_ga(s(T119), s(T121))
U13_gga(T99, T102, multD_out_ga(T99, T102)) → multB_out_gga(s(T99), s(0), s(T102))
multB_in_gga(0, s(s(0)), s(s(0))) → multB_out_gga(0, s(s(0)), s(s(0)))
multB_in_gga(s(T155), s(s(0)), s(s(T158))) → U14_gga(T155, T158, multE_in_ga(T155, T158))
multE_in_ga(0, s(s(0))) → multE_out_ga(0, s(s(0)))
multE_in_ga(s(T183), s(s(T185))) → U4_ga(T183, T185, multE_in_ga(T183, T185))
U4_ga(T183, T185, multE_out_ga(T183, T185)) → multE_out_ga(s(T183), s(s(T185)))
U14_gga(T155, T158, multE_out_ga(T155, T158)) → multB_out_gga(s(T155), s(s(0)), s(s(T158)))
multB_in_gga(0, s(s(s(0))), s(s(s(0)))) → multB_out_gga(0, s(s(s(0))), s(s(s(0))))
multB_in_gga(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_gga(T219, T222, multF_in_ga(T219, T222))
multF_in_ga(0, s(s(s(0)))) → multF_out_ga(0, s(s(s(0))))
multF_in_ga(s(T255), s(s(s(T257)))) → U5_ga(T255, T257, multF_in_ga(T255, T257))
U5_ga(T255, T257, multF_out_ga(T255, T257)) → multF_out_ga(s(T255), s(s(s(T257))))
U15_gga(T219, T222, multF_out_ga(T219, T222)) → multB_out_gga(s(T219), s(s(s(0))), s(s(s(T222))))
multB_in_gga(0, s(s(s(s(0)))), s(s(s(s(0))))) → multB_out_gga(0, s(s(s(s(0)))), s(s(s(s(0)))))
multB_in_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_gga(T291, T294, multG_in_ga(T291, T294))
multG_in_ga(0, s(s(s(s(0))))) → multG_out_ga(0, s(s(s(s(0)))))
multG_in_ga(s(T335), s(s(s(s(T337))))) → U6_ga(T335, T337, multG_in_ga(T335, T337))
U6_ga(T335, T337, multG_out_ga(T335, T337)) → multG_out_ga(s(T335), s(s(s(s(T337)))))
U16_gga(T291, T294, multG_out_ga(T291, T294)) → multB_out_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294)))))
multB_in_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → multB_out_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
multB_in_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_gga(T371, T374, multH_in_ga(T371, T374))
multH_in_ga(0, s(s(s(s(s(0)))))) → multH_out_ga(0, s(s(s(s(s(0))))))
multH_in_ga(s(T423), s(s(s(s(s(T425)))))) → U7_ga(T423, T425, multH_in_ga(T423, T425))
U7_ga(T423, T425, multH_out_ga(T423, T425)) → multH_out_ga(s(T423), s(s(s(s(s(T425))))))
U17_gga(T371, T374, multH_out_ga(T371, T374)) → multB_out_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374))))))
multB_in_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → multB_out_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
multB_in_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_gga(T459, T462, multI_in_ga(T459, T462))
multI_in_ga(0, s(s(s(s(s(s(0))))))) → multI_out_ga(0, s(s(s(s(s(s(0)))))))
multI_in_ga(s(T519), s(s(s(s(s(s(T521))))))) → U8_ga(T519, T521, multI_in_ga(T519, T521))
U8_ga(T519, T521, multI_out_ga(T519, T521)) → multI_out_ga(s(T519), s(s(s(s(s(s(T521)))))))
U18_gga(T459, T462, multI_out_ga(T459, T462)) → multB_out_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462)))))))
multB_in_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → multB_out_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
multB_in_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_gga(T555, T558, multJ_in_ga(T555, T558))
multJ_in_ga(0, s(s(s(s(s(s(s(0)))))))) → multJ_out_ga(0, s(s(s(s(s(s(s(0))))))))
multJ_in_ga(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_ga(T623, T625, multJ_in_ga(T623, T625))
U9_ga(T623, T625, multJ_out_ga(T623, T625)) → multJ_out_ga(s(T623), s(s(s(s(s(s(s(T625))))))))
U19_gga(T555, T558, multJ_out_ga(T555, T558)) → multB_out_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558))))))))
multB_in_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_gga(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
multK_in_ggga(0, T649, 0, 0) → multK_out_ggga(0, T649, 0, 0)
multK_in_ggga(s(T662), T663, 0, T665) → U10_ggga(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
U10_ggga(T662, T663, T665, multB_out_gga(T662, s(T663), T665)) → multK_out_ggga(s(T662), T663, 0, T665)
multK_in_ggga(T676, T677, s(T678), s(T680)) → U11_ggga(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
U11_ggga(T676, T677, T678, T680, multK_out_ggga(T676, T677, T678, T680)) → multK_out_ggga(T676, T677, s(T678), s(T680))
U20_gga(T635, T637, T639, multK_out_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)) → multB_out_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639)))))))))
U1_gga(T28, T29, T31, multB_out_gga(T28, T29, T31)) → timesA_out_gga(s(T28), T29, T31)

The argument filtering Pi contains the following mapping:
timesA_in_gga(x1, x2, x3)  =  timesA_in_gga(x1, x2)
0  =  0
timesA_out_gga(x1, x2, x3)  =  timesA_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
multB_in_gga(x1, x2, x3)  =  multB_in_gga(x1, x2)
multB_out_gga(x1, x2, x3)  =  multB_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3)  =  U12_gga(x1, x3)
multC_in_ga(x1, x2)  =  multC_in_ga(x1)
multC_out_ga(x1, x2)  =  multC_out_ga(x1, x2)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U13_gga(x1, x2, x3)  =  U13_gga(x1, x3)
multD_in_ga(x1, x2)  =  multD_in_ga(x1)
multD_out_ga(x1, x2)  =  multD_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U14_gga(x1, x2, x3)  =  U14_gga(x1, x3)
multE_in_ga(x1, x2)  =  multE_in_ga(x1)
multE_out_ga(x1, x2)  =  multE_out_ga(x1, x2)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
multF_in_ga(x1, x2)  =  multF_in_ga(x1)
multF_out_ga(x1, x2)  =  multF_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
multG_in_ga(x1, x2)  =  multG_in_ga(x1)
multG_out_ga(x1, x2)  =  multG_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U17_gga(x1, x2, x3)  =  U17_gga(x1, x3)
multH_in_ga(x1, x2)  =  multH_in_ga(x1)
multH_out_ga(x1, x2)  =  multH_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
multI_in_ga(x1, x2)  =  multI_in_ga(x1)
multI_out_ga(x1, x2)  =  multI_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
multJ_in_ga(x1, x2)  =  multJ_in_ga(x1)
multJ_out_ga(x1, x2)  =  multJ_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
multK_in_ggga(x1, x2, x3, x4)  =  multK_in_ggga(x1, x2, x3)
multK_out_ggga(x1, x2, x3, x4)  =  multK_out_ggga(x1, x2, x3, x4)
U10_ggga(x1, x2, x3, x4)  =  U10_ggga(x1, x2, x4)
U11_ggga(x1, x2, x3, x4, x5)  =  U11_ggga(x1, x2, x3, x5)
MULTH_IN_GA(x1, x2)  =  MULTH_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:

MULTH_IN_GA(s(T423), s(s(s(s(s(T425)))))) → MULTH_IN_GA(T423, T425)

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

MULTH_IN_GA(s(T423)) → MULTH_IN_GA(T423)

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:

• MULTH_IN_GA(s(T423)) → MULTH_IN_GA(T423)
  The graph contains the following edges 1 > 1

(27) YES

(28) Obligation:

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

MULTG_IN_GA(s(T335), s(s(s(s(T337))))) → MULTG_IN_GA(T335, T337)

The TRS R consists of the following rules:

timesA_in_gga(0, T15, 0) → timesA_out_gga(0, T15, 0)
timesA_in_gga(s(T28), T29, T31) → U1_gga(T28, T29, T31, multB_in_gga(T28, T29, T31))
multB_in_gga(0, 0, 0) → multB_out_gga(0, 0, 0)
multB_in_gga(s(T51), 0, T54) → U12_gga(T51, T54, multC_in_ga(T51, T54))
multC_in_ga(0, 0) → multC_out_ga(0, 0)
multC_in_ga(s(T63), T65) → U2_ga(T63, T65, multC_in_ga(T63, T65))
U2_ga(T63, T65, multC_out_ga(T63, T65)) → multC_out_ga(s(T63), T65)
U12_gga(T51, T54, multC_out_ga(T51, T54)) → multB_out_gga(s(T51), 0, T54)
multB_in_gga(0, s(0), s(0)) → multB_out_gga(0, s(0), s(0))
multB_in_gga(s(T99), s(0), s(T102)) → U13_gga(T99, T102, multD_in_ga(T99, T102))
multD_in_ga(0, s(0)) → multD_out_ga(0, s(0))
multD_in_ga(s(T119), s(T121)) → U3_ga(T119, T121, multD_in_ga(T119, T121))
U3_ga(T119, T121, multD_out_ga(T119, T121)) → multD_out_ga(s(T119), s(T121))
U13_gga(T99, T102, multD_out_ga(T99, T102)) → multB_out_gga(s(T99), s(0), s(T102))
multB_in_gga(0, s(s(0)), s(s(0))) → multB_out_gga(0, s(s(0)), s(s(0)))
multB_in_gga(s(T155), s(s(0)), s(s(T158))) → U14_gga(T155, T158, multE_in_ga(T155, T158))
multE_in_ga(0, s(s(0))) → multE_out_ga(0, s(s(0)))
multE_in_ga(s(T183), s(s(T185))) → U4_ga(T183, T185, multE_in_ga(T183, T185))
U4_ga(T183, T185, multE_out_ga(T183, T185)) → multE_out_ga(s(T183), s(s(T185)))
U14_gga(T155, T158, multE_out_ga(T155, T158)) → multB_out_gga(s(T155), s(s(0)), s(s(T158)))
multB_in_gga(0, s(s(s(0))), s(s(s(0)))) → multB_out_gga(0, s(s(s(0))), s(s(s(0))))
multB_in_gga(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_gga(T219, T222, multF_in_ga(T219, T222))
multF_in_ga(0, s(s(s(0)))) → multF_out_ga(0, s(s(s(0))))
multF_in_ga(s(T255), s(s(s(T257)))) → U5_ga(T255, T257, multF_in_ga(T255, T257))
U5_ga(T255, T257, multF_out_ga(T255, T257)) → multF_out_ga(s(T255), s(s(s(T257))))
U15_gga(T219, T222, multF_out_ga(T219, T222)) → multB_out_gga(s(T219), s(s(s(0))), s(s(s(T222))))
multB_in_gga(0, s(s(s(s(0)))), s(s(s(s(0))))) → multB_out_gga(0, s(s(s(s(0)))), s(s(s(s(0)))))
multB_in_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_gga(T291, T294, multG_in_ga(T291, T294))
multG_in_ga(0, s(s(s(s(0))))) → multG_out_ga(0, s(s(s(s(0)))))
multG_in_ga(s(T335), s(s(s(s(T337))))) → U6_ga(T335, T337, multG_in_ga(T335, T337))
U6_ga(T335, T337, multG_out_ga(T335, T337)) → multG_out_ga(s(T335), s(s(s(s(T337)))))
U16_gga(T291, T294, multG_out_ga(T291, T294)) → multB_out_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294)))))
multB_in_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → multB_out_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
multB_in_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_gga(T371, T374, multH_in_ga(T371, T374))
multH_in_ga(0, s(s(s(s(s(0)))))) → multH_out_ga(0, s(s(s(s(s(0))))))
multH_in_ga(s(T423), s(s(s(s(s(T425)))))) → U7_ga(T423, T425, multH_in_ga(T423, T425))
U7_ga(T423, T425, multH_out_ga(T423, T425)) → multH_out_ga(s(T423), s(s(s(s(s(T425))))))
U17_gga(T371, T374, multH_out_ga(T371, T374)) → multB_out_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374))))))
multB_in_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → multB_out_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
multB_in_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_gga(T459, T462, multI_in_ga(T459, T462))
multI_in_ga(0, s(s(s(s(s(s(0))))))) → multI_out_ga(0, s(s(s(s(s(s(0)))))))
multI_in_ga(s(T519), s(s(s(s(s(s(T521))))))) → U8_ga(T519, T521, multI_in_ga(T519, T521))
U8_ga(T519, T521, multI_out_ga(T519, T521)) → multI_out_ga(s(T519), s(s(s(s(s(s(T521)))))))
U18_gga(T459, T462, multI_out_ga(T459, T462)) → multB_out_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462)))))))
multB_in_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → multB_out_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
multB_in_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_gga(T555, T558, multJ_in_ga(T555, T558))
multJ_in_ga(0, s(s(s(s(s(s(s(0)))))))) → multJ_out_ga(0, s(s(s(s(s(s(s(0))))))))
multJ_in_ga(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_ga(T623, T625, multJ_in_ga(T623, T625))
U9_ga(T623, T625, multJ_out_ga(T623, T625)) → multJ_out_ga(s(T623), s(s(s(s(s(s(s(T625))))))))
U19_gga(T555, T558, multJ_out_ga(T555, T558)) → multB_out_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558))))))))
multB_in_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_gga(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
multK_in_ggga(0, T649, 0, 0) → multK_out_ggga(0, T649, 0, 0)
multK_in_ggga(s(T662), T663, 0, T665) → U10_ggga(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
U10_ggga(T662, T663, T665, multB_out_gga(T662, s(T663), T665)) → multK_out_ggga(s(T662), T663, 0, T665)
multK_in_ggga(T676, T677, s(T678), s(T680)) → U11_ggga(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
U11_ggga(T676, T677, T678, T680, multK_out_ggga(T676, T677, T678, T680)) → multK_out_ggga(T676, T677, s(T678), s(T680))
U20_gga(T635, T637, T639, multK_out_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)) → multB_out_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639)))))))))
U1_gga(T28, T29, T31, multB_out_gga(T28, T29, T31)) → timesA_out_gga(s(T28), T29, T31)

The argument filtering Pi contains the following mapping:
timesA_in_gga(x1, x2, x3)  =  timesA_in_gga(x1, x2)
0  =  0
timesA_out_gga(x1, x2, x3)  =  timesA_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
multB_in_gga(x1, x2, x3)  =  multB_in_gga(x1, x2)
multB_out_gga(x1, x2, x3)  =  multB_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3)  =  U12_gga(x1, x3)
multC_in_ga(x1, x2)  =  multC_in_ga(x1)
multC_out_ga(x1, x2)  =  multC_out_ga(x1, x2)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U13_gga(x1, x2, x3)  =  U13_gga(x1, x3)
multD_in_ga(x1, x2)  =  multD_in_ga(x1)
multD_out_ga(x1, x2)  =  multD_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U14_gga(x1, x2, x3)  =  U14_gga(x1, x3)
multE_in_ga(x1, x2)  =  multE_in_ga(x1)
multE_out_ga(x1, x2)  =  multE_out_ga(x1, x2)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
multF_in_ga(x1, x2)  =  multF_in_ga(x1)
multF_out_ga(x1, x2)  =  multF_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
multG_in_ga(x1, x2)  =  multG_in_ga(x1)
multG_out_ga(x1, x2)  =  multG_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U17_gga(x1, x2, x3)  =  U17_gga(x1, x3)
multH_in_ga(x1, x2)  =  multH_in_ga(x1)
multH_out_ga(x1, x2)  =  multH_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
multI_in_ga(x1, x2)  =  multI_in_ga(x1)
multI_out_ga(x1, x2)  =  multI_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
multJ_in_ga(x1, x2)  =  multJ_in_ga(x1)
multJ_out_ga(x1, x2)  =  multJ_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
multK_in_ggga(x1, x2, x3, x4)  =  multK_in_ggga(x1, x2, x3)
multK_out_ggga(x1, x2, x3, x4)  =  multK_out_ggga(x1, x2, x3, x4)
U10_ggga(x1, x2, x3, x4)  =  U10_ggga(x1, x2, x4)
U11_ggga(x1, x2, x3, x4, x5)  =  U11_ggga(x1, x2, x3, x5)
MULTG_IN_GA(x1, x2)  =  MULTG_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:

MULTG_IN_GA(s(T335), s(s(s(s(T337))))) → MULTG_IN_GA(T335, T337)

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

MULTG_IN_GA(s(T335)) → MULTG_IN_GA(T335)

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:

• MULTG_IN_GA(s(T335)) → MULTG_IN_GA(T335)
  The graph contains the following edges 1 > 1

(34) YES

(35) Obligation:

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

MULTF_IN_GA(s(T255), s(s(s(T257)))) → MULTF_IN_GA(T255, T257)

The TRS R consists of the following rules:

timesA_in_gga(0, T15, 0) → timesA_out_gga(0, T15, 0)
timesA_in_gga(s(T28), T29, T31) → U1_gga(T28, T29, T31, multB_in_gga(T28, T29, T31))
multB_in_gga(0, 0, 0) → multB_out_gga(0, 0, 0)
multB_in_gga(s(T51), 0, T54) → U12_gga(T51, T54, multC_in_ga(T51, T54))
multC_in_ga(0, 0) → multC_out_ga(0, 0)
multC_in_ga(s(T63), T65) → U2_ga(T63, T65, multC_in_ga(T63, T65))
U2_ga(T63, T65, multC_out_ga(T63, T65)) → multC_out_ga(s(T63), T65)
U12_gga(T51, T54, multC_out_ga(T51, T54)) → multB_out_gga(s(T51), 0, T54)
multB_in_gga(0, s(0), s(0)) → multB_out_gga(0, s(0), s(0))
multB_in_gga(s(T99), s(0), s(T102)) → U13_gga(T99, T102, multD_in_ga(T99, T102))
multD_in_ga(0, s(0)) → multD_out_ga(0, s(0))
multD_in_ga(s(T119), s(T121)) → U3_ga(T119, T121, multD_in_ga(T119, T121))
U3_ga(T119, T121, multD_out_ga(T119, T121)) → multD_out_ga(s(T119), s(T121))
U13_gga(T99, T102, multD_out_ga(T99, T102)) → multB_out_gga(s(T99), s(0), s(T102))
multB_in_gga(0, s(s(0)), s(s(0))) → multB_out_gga(0, s(s(0)), s(s(0)))
multB_in_gga(s(T155), s(s(0)), s(s(T158))) → U14_gga(T155, T158, multE_in_ga(T155, T158))
multE_in_ga(0, s(s(0))) → multE_out_ga(0, s(s(0)))
multE_in_ga(s(T183), s(s(T185))) → U4_ga(T183, T185, multE_in_ga(T183, T185))
U4_ga(T183, T185, multE_out_ga(T183, T185)) → multE_out_ga(s(T183), s(s(T185)))
U14_gga(T155, T158, multE_out_ga(T155, T158)) → multB_out_gga(s(T155), s(s(0)), s(s(T158)))
multB_in_gga(0, s(s(s(0))), s(s(s(0)))) → multB_out_gga(0, s(s(s(0))), s(s(s(0))))
multB_in_gga(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_gga(T219, T222, multF_in_ga(T219, T222))
multF_in_ga(0, s(s(s(0)))) → multF_out_ga(0, s(s(s(0))))
multF_in_ga(s(T255), s(s(s(T257)))) → U5_ga(T255, T257, multF_in_ga(T255, T257))
U5_ga(T255, T257, multF_out_ga(T255, T257)) → multF_out_ga(s(T255), s(s(s(T257))))
U15_gga(T219, T222, multF_out_ga(T219, T222)) → multB_out_gga(s(T219), s(s(s(0))), s(s(s(T222))))
multB_in_gga(0, s(s(s(s(0)))), s(s(s(s(0))))) → multB_out_gga(0, s(s(s(s(0)))), s(s(s(s(0)))))
multB_in_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_gga(T291, T294, multG_in_ga(T291, T294))
multG_in_ga(0, s(s(s(s(0))))) → multG_out_ga(0, s(s(s(s(0)))))
multG_in_ga(s(T335), s(s(s(s(T337))))) → U6_ga(T335, T337, multG_in_ga(T335, T337))
U6_ga(T335, T337, multG_out_ga(T335, T337)) → multG_out_ga(s(T335), s(s(s(s(T337)))))
U16_gga(T291, T294, multG_out_ga(T291, T294)) → multB_out_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294)))))
multB_in_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → multB_out_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
multB_in_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_gga(T371, T374, multH_in_ga(T371, T374))
multH_in_ga(0, s(s(s(s(s(0)))))) → multH_out_ga(0, s(s(s(s(s(0))))))
multH_in_ga(s(T423), s(s(s(s(s(T425)))))) → U7_ga(T423, T425, multH_in_ga(T423, T425))
U7_ga(T423, T425, multH_out_ga(T423, T425)) → multH_out_ga(s(T423), s(s(s(s(s(T425))))))
U17_gga(T371, T374, multH_out_ga(T371, T374)) → multB_out_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374))))))
multB_in_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → multB_out_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
multB_in_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_gga(T459, T462, multI_in_ga(T459, T462))
multI_in_ga(0, s(s(s(s(s(s(0))))))) → multI_out_ga(0, s(s(s(s(s(s(0)))))))
multI_in_ga(s(T519), s(s(s(s(s(s(T521))))))) → U8_ga(T519, T521, multI_in_ga(T519, T521))
U8_ga(T519, T521, multI_out_ga(T519, T521)) → multI_out_ga(s(T519), s(s(s(s(s(s(T521)))))))
U18_gga(T459, T462, multI_out_ga(T459, T462)) → multB_out_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462)))))))
multB_in_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → multB_out_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
multB_in_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_gga(T555, T558, multJ_in_ga(T555, T558))
multJ_in_ga(0, s(s(s(s(s(s(s(0)))))))) → multJ_out_ga(0, s(s(s(s(s(s(s(0))))))))
multJ_in_ga(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_ga(T623, T625, multJ_in_ga(T623, T625))
U9_ga(T623, T625, multJ_out_ga(T623, T625)) → multJ_out_ga(s(T623), s(s(s(s(s(s(s(T625))))))))
U19_gga(T555, T558, multJ_out_ga(T555, T558)) → multB_out_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558))))))))
multB_in_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_gga(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
multK_in_ggga(0, T649, 0, 0) → multK_out_ggga(0, T649, 0, 0)
multK_in_ggga(s(T662), T663, 0, T665) → U10_ggga(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
U10_ggga(T662, T663, T665, multB_out_gga(T662, s(T663), T665)) → multK_out_ggga(s(T662), T663, 0, T665)
multK_in_ggga(T676, T677, s(T678), s(T680)) → U11_ggga(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
U11_ggga(T676, T677, T678, T680, multK_out_ggga(T676, T677, T678, T680)) → multK_out_ggga(T676, T677, s(T678), s(T680))
U20_gga(T635, T637, T639, multK_out_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)) → multB_out_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639)))))))))
U1_gga(T28, T29, T31, multB_out_gga(T28, T29, T31)) → timesA_out_gga(s(T28), T29, T31)

The argument filtering Pi contains the following mapping:
timesA_in_gga(x1, x2, x3)  =  timesA_in_gga(x1, x2)
0  =  0
timesA_out_gga(x1, x2, x3)  =  timesA_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
multB_in_gga(x1, x2, x3)  =  multB_in_gga(x1, x2)
multB_out_gga(x1, x2, x3)  =  multB_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3)  =  U12_gga(x1, x3)
multC_in_ga(x1, x2)  =  multC_in_ga(x1)
multC_out_ga(x1, x2)  =  multC_out_ga(x1, x2)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U13_gga(x1, x2, x3)  =  U13_gga(x1, x3)
multD_in_ga(x1, x2)  =  multD_in_ga(x1)
multD_out_ga(x1, x2)  =  multD_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U14_gga(x1, x2, x3)  =  U14_gga(x1, x3)
multE_in_ga(x1, x2)  =  multE_in_ga(x1)
multE_out_ga(x1, x2)  =  multE_out_ga(x1, x2)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
multF_in_ga(x1, x2)  =  multF_in_ga(x1)
multF_out_ga(x1, x2)  =  multF_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
multG_in_ga(x1, x2)  =  multG_in_ga(x1)
multG_out_ga(x1, x2)  =  multG_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U17_gga(x1, x2, x3)  =  U17_gga(x1, x3)
multH_in_ga(x1, x2)  =  multH_in_ga(x1)
multH_out_ga(x1, x2)  =  multH_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
multI_in_ga(x1, x2)  =  multI_in_ga(x1)
multI_out_ga(x1, x2)  =  multI_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
multJ_in_ga(x1, x2)  =  multJ_in_ga(x1)
multJ_out_ga(x1, x2)  =  multJ_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
multK_in_ggga(x1, x2, x3, x4)  =  multK_in_ggga(x1, x2, x3)
multK_out_ggga(x1, x2, x3, x4)  =  multK_out_ggga(x1, x2, x3, x4)
U10_ggga(x1, x2, x3, x4)  =  U10_ggga(x1, x2, x4)
U11_ggga(x1, x2, x3, x4, x5)  =  U11_ggga(x1, x2, x3, x5)
MULTF_IN_GA(x1, x2)  =  MULTF_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:

MULTF_IN_GA(s(T255), s(s(s(T257)))) → MULTF_IN_GA(T255, T257)

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

MULTF_IN_GA(s(T255)) → MULTF_IN_GA(T255)

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:

• MULTF_IN_GA(s(T255)) → MULTF_IN_GA(T255)
  The graph contains the following edges 1 > 1

(41) YES

(42) Obligation:

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

MULTE_IN_GA(s(T183), s(s(T185))) → MULTE_IN_GA(T183, T185)

The TRS R consists of the following rules:

timesA_in_gga(0, T15, 0) → timesA_out_gga(0, T15, 0)
timesA_in_gga(s(T28), T29, T31) → U1_gga(T28, T29, T31, multB_in_gga(T28, T29, T31))
multB_in_gga(0, 0, 0) → multB_out_gga(0, 0, 0)
multB_in_gga(s(T51), 0, T54) → U12_gga(T51, T54, multC_in_ga(T51, T54))
multC_in_ga(0, 0) → multC_out_ga(0, 0)
multC_in_ga(s(T63), T65) → U2_ga(T63, T65, multC_in_ga(T63, T65))
U2_ga(T63, T65, multC_out_ga(T63, T65)) → multC_out_ga(s(T63), T65)
U12_gga(T51, T54, multC_out_ga(T51, T54)) → multB_out_gga(s(T51), 0, T54)
multB_in_gga(0, s(0), s(0)) → multB_out_gga(0, s(0), s(0))
multB_in_gga(s(T99), s(0), s(T102)) → U13_gga(T99, T102, multD_in_ga(T99, T102))
multD_in_ga(0, s(0)) → multD_out_ga(0, s(0))
multD_in_ga(s(T119), s(T121)) → U3_ga(T119, T121, multD_in_ga(T119, T121))
U3_ga(T119, T121, multD_out_ga(T119, T121)) → multD_out_ga(s(T119), s(T121))
U13_gga(T99, T102, multD_out_ga(T99, T102)) → multB_out_gga(s(T99), s(0), s(T102))
multB_in_gga(0, s(s(0)), s(s(0))) → multB_out_gga(0, s(s(0)), s(s(0)))
multB_in_gga(s(T155), s(s(0)), s(s(T158))) → U14_gga(T155, T158, multE_in_ga(T155, T158))
multE_in_ga(0, s(s(0))) → multE_out_ga(0, s(s(0)))
multE_in_ga(s(T183), s(s(T185))) → U4_ga(T183, T185, multE_in_ga(T183, T185))
U4_ga(T183, T185, multE_out_ga(T183, T185)) → multE_out_ga(s(T183), s(s(T185)))
U14_gga(T155, T158, multE_out_ga(T155, T158)) → multB_out_gga(s(T155), s(s(0)), s(s(T158)))
multB_in_gga(0, s(s(s(0))), s(s(s(0)))) → multB_out_gga(0, s(s(s(0))), s(s(s(0))))
multB_in_gga(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_gga(T219, T222, multF_in_ga(T219, T222))
multF_in_ga(0, s(s(s(0)))) → multF_out_ga(0, s(s(s(0))))
multF_in_ga(s(T255), s(s(s(T257)))) → U5_ga(T255, T257, multF_in_ga(T255, T257))
U5_ga(T255, T257, multF_out_ga(T255, T257)) → multF_out_ga(s(T255), s(s(s(T257))))
U15_gga(T219, T222, multF_out_ga(T219, T222)) → multB_out_gga(s(T219), s(s(s(0))), s(s(s(T222))))
multB_in_gga(0, s(s(s(s(0)))), s(s(s(s(0))))) → multB_out_gga(0, s(s(s(s(0)))), s(s(s(s(0)))))
multB_in_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_gga(T291, T294, multG_in_ga(T291, T294))
multG_in_ga(0, s(s(s(s(0))))) → multG_out_ga(0, s(s(s(s(0)))))
multG_in_ga(s(T335), s(s(s(s(T337))))) → U6_ga(T335, T337, multG_in_ga(T335, T337))
U6_ga(T335, T337, multG_out_ga(T335, T337)) → multG_out_ga(s(T335), s(s(s(s(T337)))))
U16_gga(T291, T294, multG_out_ga(T291, T294)) → multB_out_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294)))))
multB_in_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → multB_out_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
multB_in_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_gga(T371, T374, multH_in_ga(T371, T374))
multH_in_ga(0, s(s(s(s(s(0)))))) → multH_out_ga(0, s(s(s(s(s(0))))))
multH_in_ga(s(T423), s(s(s(s(s(T425)))))) → U7_ga(T423, T425, multH_in_ga(T423, T425))
U7_ga(T423, T425, multH_out_ga(T423, T425)) → multH_out_ga(s(T423), s(s(s(s(s(T425))))))
U17_gga(T371, T374, multH_out_ga(T371, T374)) → multB_out_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374))))))
multB_in_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → multB_out_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
multB_in_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_gga(T459, T462, multI_in_ga(T459, T462))
multI_in_ga(0, s(s(s(s(s(s(0))))))) → multI_out_ga(0, s(s(s(s(s(s(0)))))))
multI_in_ga(s(T519), s(s(s(s(s(s(T521))))))) → U8_ga(T519, T521, multI_in_ga(T519, T521))
U8_ga(T519, T521, multI_out_ga(T519, T521)) → multI_out_ga(s(T519), s(s(s(s(s(s(T521)))))))
U18_gga(T459, T462, multI_out_ga(T459, T462)) → multB_out_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462)))))))
multB_in_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → multB_out_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
multB_in_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_gga(T555, T558, multJ_in_ga(T555, T558))
multJ_in_ga(0, s(s(s(s(s(s(s(0)))))))) → multJ_out_ga(0, s(s(s(s(s(s(s(0))))))))
multJ_in_ga(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_ga(T623, T625, multJ_in_ga(T623, T625))
U9_ga(T623, T625, multJ_out_ga(T623, T625)) → multJ_out_ga(s(T623), s(s(s(s(s(s(s(T625))))))))
U19_gga(T555, T558, multJ_out_ga(T555, T558)) → multB_out_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558))))))))
multB_in_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_gga(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
multK_in_ggga(0, T649, 0, 0) → multK_out_ggga(0, T649, 0, 0)
multK_in_ggga(s(T662), T663, 0, T665) → U10_ggga(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
U10_ggga(T662, T663, T665, multB_out_gga(T662, s(T663), T665)) → multK_out_ggga(s(T662), T663, 0, T665)
multK_in_ggga(T676, T677, s(T678), s(T680)) → U11_ggga(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
U11_ggga(T676, T677, T678, T680, multK_out_ggga(T676, T677, T678, T680)) → multK_out_ggga(T676, T677, s(T678), s(T680))
U20_gga(T635, T637, T639, multK_out_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)) → multB_out_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639)))))))))
U1_gga(T28, T29, T31, multB_out_gga(T28, T29, T31)) → timesA_out_gga(s(T28), T29, T31)

The argument filtering Pi contains the following mapping:
timesA_in_gga(x1, x2, x3)  =  timesA_in_gga(x1, x2)
0  =  0
timesA_out_gga(x1, x2, x3)  =  timesA_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
multB_in_gga(x1, x2, x3)  =  multB_in_gga(x1, x2)
multB_out_gga(x1, x2, x3)  =  multB_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3)  =  U12_gga(x1, x3)
multC_in_ga(x1, x2)  =  multC_in_ga(x1)
multC_out_ga(x1, x2)  =  multC_out_ga(x1, x2)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U13_gga(x1, x2, x3)  =  U13_gga(x1, x3)
multD_in_ga(x1, x2)  =  multD_in_ga(x1)
multD_out_ga(x1, x2)  =  multD_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U14_gga(x1, x2, x3)  =  U14_gga(x1, x3)
multE_in_ga(x1, x2)  =  multE_in_ga(x1)
multE_out_ga(x1, x2)  =  multE_out_ga(x1, x2)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
multF_in_ga(x1, x2)  =  multF_in_ga(x1)
multF_out_ga(x1, x2)  =  multF_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
multG_in_ga(x1, x2)  =  multG_in_ga(x1)
multG_out_ga(x1, x2)  =  multG_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U17_gga(x1, x2, x3)  =  U17_gga(x1, x3)
multH_in_ga(x1, x2)  =  multH_in_ga(x1)
multH_out_ga(x1, x2)  =  multH_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
multI_in_ga(x1, x2)  =  multI_in_ga(x1)
multI_out_ga(x1, x2)  =  multI_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
multJ_in_ga(x1, x2)  =  multJ_in_ga(x1)
multJ_out_ga(x1, x2)  =  multJ_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
multK_in_ggga(x1, x2, x3, x4)  =  multK_in_ggga(x1, x2, x3)
multK_out_ggga(x1, x2, x3, x4)  =  multK_out_ggga(x1, x2, x3, x4)
U10_ggga(x1, x2, x3, x4)  =  U10_ggga(x1, x2, x4)
U11_ggga(x1, x2, x3, x4, x5)  =  U11_ggga(x1, x2, x3, x5)
MULTE_IN_GA(x1, x2)  =  MULTE_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:

MULTE_IN_GA(s(T183), s(s(T185))) → MULTE_IN_GA(T183, T185)

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

MULTE_IN_GA(s(T183)) → MULTE_IN_GA(T183)

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:

• MULTE_IN_GA(s(T183)) → MULTE_IN_GA(T183)
  The graph contains the following edges 1 > 1

(48) YES

(49) Obligation:

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

MULTD_IN_GA(s(T119), s(T121)) → MULTD_IN_GA(T119, T121)

The TRS R consists of the following rules:

timesA_in_gga(0, T15, 0) → timesA_out_gga(0, T15, 0)
timesA_in_gga(s(T28), T29, T31) → U1_gga(T28, T29, T31, multB_in_gga(T28, T29, T31))
multB_in_gga(0, 0, 0) → multB_out_gga(0, 0, 0)
multB_in_gga(s(T51), 0, T54) → U12_gga(T51, T54, multC_in_ga(T51, T54))
multC_in_ga(0, 0) → multC_out_ga(0, 0)
multC_in_ga(s(T63), T65) → U2_ga(T63, T65, multC_in_ga(T63, T65))
U2_ga(T63, T65, multC_out_ga(T63, T65)) → multC_out_ga(s(T63), T65)
U12_gga(T51, T54, multC_out_ga(T51, T54)) → multB_out_gga(s(T51), 0, T54)
multB_in_gga(0, s(0), s(0)) → multB_out_gga(0, s(0), s(0))
multB_in_gga(s(T99), s(0), s(T102)) → U13_gga(T99, T102, multD_in_ga(T99, T102))
multD_in_ga(0, s(0)) → multD_out_ga(0, s(0))
multD_in_ga(s(T119), s(T121)) → U3_ga(T119, T121, multD_in_ga(T119, T121))
U3_ga(T119, T121, multD_out_ga(T119, T121)) → multD_out_ga(s(T119), s(T121))
U13_gga(T99, T102, multD_out_ga(T99, T102)) → multB_out_gga(s(T99), s(0), s(T102))
multB_in_gga(0, s(s(0)), s(s(0))) → multB_out_gga(0, s(s(0)), s(s(0)))
multB_in_gga(s(T155), s(s(0)), s(s(T158))) → U14_gga(T155, T158, multE_in_ga(T155, T158))
multE_in_ga(0, s(s(0))) → multE_out_ga(0, s(s(0)))
multE_in_ga(s(T183), s(s(T185))) → U4_ga(T183, T185, multE_in_ga(T183, T185))
U4_ga(T183, T185, multE_out_ga(T183, T185)) → multE_out_ga(s(T183), s(s(T185)))
U14_gga(T155, T158, multE_out_ga(T155, T158)) → multB_out_gga(s(T155), s(s(0)), s(s(T158)))
multB_in_gga(0, s(s(s(0))), s(s(s(0)))) → multB_out_gga(0, s(s(s(0))), s(s(s(0))))
multB_in_gga(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_gga(T219, T222, multF_in_ga(T219, T222))
multF_in_ga(0, s(s(s(0)))) → multF_out_ga(0, s(s(s(0))))
multF_in_ga(s(T255), s(s(s(T257)))) → U5_ga(T255, T257, multF_in_ga(T255, T257))
U5_ga(T255, T257, multF_out_ga(T255, T257)) → multF_out_ga(s(T255), s(s(s(T257))))
U15_gga(T219, T222, multF_out_ga(T219, T222)) → multB_out_gga(s(T219), s(s(s(0))), s(s(s(T222))))
multB_in_gga(0, s(s(s(s(0)))), s(s(s(s(0))))) → multB_out_gga(0, s(s(s(s(0)))), s(s(s(s(0)))))
multB_in_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_gga(T291, T294, multG_in_ga(T291, T294))
multG_in_ga(0, s(s(s(s(0))))) → multG_out_ga(0, s(s(s(s(0)))))
multG_in_ga(s(T335), s(s(s(s(T337))))) → U6_ga(T335, T337, multG_in_ga(T335, T337))
U6_ga(T335, T337, multG_out_ga(T335, T337)) → multG_out_ga(s(T335), s(s(s(s(T337)))))
U16_gga(T291, T294, multG_out_ga(T291, T294)) → multB_out_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294)))))
multB_in_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → multB_out_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
multB_in_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_gga(T371, T374, multH_in_ga(T371, T374))
multH_in_ga(0, s(s(s(s(s(0)))))) → multH_out_ga(0, s(s(s(s(s(0))))))
multH_in_ga(s(T423), s(s(s(s(s(T425)))))) → U7_ga(T423, T425, multH_in_ga(T423, T425))
U7_ga(T423, T425, multH_out_ga(T423, T425)) → multH_out_ga(s(T423), s(s(s(s(s(T425))))))
U17_gga(T371, T374, multH_out_ga(T371, T374)) → multB_out_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374))))))
multB_in_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → multB_out_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
multB_in_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_gga(T459, T462, multI_in_ga(T459, T462))
multI_in_ga(0, s(s(s(s(s(s(0))))))) → multI_out_ga(0, s(s(s(s(s(s(0)))))))
multI_in_ga(s(T519), s(s(s(s(s(s(T521))))))) → U8_ga(T519, T521, multI_in_ga(T519, T521))
U8_ga(T519, T521, multI_out_ga(T519, T521)) → multI_out_ga(s(T519), s(s(s(s(s(s(T521)))))))
U18_gga(T459, T462, multI_out_ga(T459, T462)) → multB_out_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462)))))))
multB_in_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → multB_out_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
multB_in_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_gga(T555, T558, multJ_in_ga(T555, T558))
multJ_in_ga(0, s(s(s(s(s(s(s(0)))))))) → multJ_out_ga(0, s(s(s(s(s(s(s(0))))))))
multJ_in_ga(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_ga(T623, T625, multJ_in_ga(T623, T625))
U9_ga(T623, T625, multJ_out_ga(T623, T625)) → multJ_out_ga(s(T623), s(s(s(s(s(s(s(T625))))))))
U19_gga(T555, T558, multJ_out_ga(T555, T558)) → multB_out_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558))))))))
multB_in_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_gga(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
multK_in_ggga(0, T649, 0, 0) → multK_out_ggga(0, T649, 0, 0)
multK_in_ggga(s(T662), T663, 0, T665) → U10_ggga(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
U10_ggga(T662, T663, T665, multB_out_gga(T662, s(T663), T665)) → multK_out_ggga(s(T662), T663, 0, T665)
multK_in_ggga(T676, T677, s(T678), s(T680)) → U11_ggga(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
U11_ggga(T676, T677, T678, T680, multK_out_ggga(T676, T677, T678, T680)) → multK_out_ggga(T676, T677, s(T678), s(T680))
U20_gga(T635, T637, T639, multK_out_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)) → multB_out_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639)))))))))
U1_gga(T28, T29, T31, multB_out_gga(T28, T29, T31)) → timesA_out_gga(s(T28), T29, T31)

The argument filtering Pi contains the following mapping:
timesA_in_gga(x1, x2, x3)  =  timesA_in_gga(x1, x2)
0  =  0
timesA_out_gga(x1, x2, x3)  =  timesA_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
multB_in_gga(x1, x2, x3)  =  multB_in_gga(x1, x2)
multB_out_gga(x1, x2, x3)  =  multB_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3)  =  U12_gga(x1, x3)
multC_in_ga(x1, x2)  =  multC_in_ga(x1)
multC_out_ga(x1, x2)  =  multC_out_ga(x1, x2)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U13_gga(x1, x2, x3)  =  U13_gga(x1, x3)
multD_in_ga(x1, x2)  =  multD_in_ga(x1)
multD_out_ga(x1, x2)  =  multD_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U14_gga(x1, x2, x3)  =  U14_gga(x1, x3)
multE_in_ga(x1, x2)  =  multE_in_ga(x1)
multE_out_ga(x1, x2)  =  multE_out_ga(x1, x2)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
multF_in_ga(x1, x2)  =  multF_in_ga(x1)
multF_out_ga(x1, x2)  =  multF_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
multG_in_ga(x1, x2)  =  multG_in_ga(x1)
multG_out_ga(x1, x2)  =  multG_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U17_gga(x1, x2, x3)  =  U17_gga(x1, x3)
multH_in_ga(x1, x2)  =  multH_in_ga(x1)
multH_out_ga(x1, x2)  =  multH_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
multI_in_ga(x1, x2)  =  multI_in_ga(x1)
multI_out_ga(x1, x2)  =  multI_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
multJ_in_ga(x1, x2)  =  multJ_in_ga(x1)
multJ_out_ga(x1, x2)  =  multJ_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
multK_in_ggga(x1, x2, x3, x4)  =  multK_in_ggga(x1, x2, x3)
multK_out_ggga(x1, x2, x3, x4)  =  multK_out_ggga(x1, x2, x3, x4)
U10_ggga(x1, x2, x3, x4)  =  U10_ggga(x1, x2, x4)
U11_ggga(x1, x2, x3, x4, x5)  =  U11_ggga(x1, x2, x3, x5)
MULTD_IN_GA(x1, x2)  =  MULTD_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:

MULTD_IN_GA(s(T119), s(T121)) → MULTD_IN_GA(T119, T121)

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

MULTD_IN_GA(s(T119)) → MULTD_IN_GA(T119)

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:

• MULTD_IN_GA(s(T119)) → MULTD_IN_GA(T119)
  The graph contains the following edges 1 > 1

(55) YES

(56) Obligation:

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

MULTB_IN_GGA(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → MULTK_IN_GGGA(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)
MULTK_IN_GGGA(s(T662), T663, 0, T665) → MULTB_IN_GGA(T662, s(T663), T665)
MULTK_IN_GGGA(T676, T677, s(T678), s(T680)) → MULTK_IN_GGGA(T676, T677, T678, T680)

The TRS R consists of the following rules:

timesA_in_gga(0, T15, 0) → timesA_out_gga(0, T15, 0)
timesA_in_gga(s(T28), T29, T31) → U1_gga(T28, T29, T31, multB_in_gga(T28, T29, T31))
multB_in_gga(0, 0, 0) → multB_out_gga(0, 0, 0)
multB_in_gga(s(T51), 0, T54) → U12_gga(T51, T54, multC_in_ga(T51, T54))
multC_in_ga(0, 0) → multC_out_ga(0, 0)
multC_in_ga(s(T63), T65) → U2_ga(T63, T65, multC_in_ga(T63, T65))
U2_ga(T63, T65, multC_out_ga(T63, T65)) → multC_out_ga(s(T63), T65)
U12_gga(T51, T54, multC_out_ga(T51, T54)) → multB_out_gga(s(T51), 0, T54)
multB_in_gga(0, s(0), s(0)) → multB_out_gga(0, s(0), s(0))
multB_in_gga(s(T99), s(0), s(T102)) → U13_gga(T99, T102, multD_in_ga(T99, T102))
multD_in_ga(0, s(0)) → multD_out_ga(0, s(0))
multD_in_ga(s(T119), s(T121)) → U3_ga(T119, T121, multD_in_ga(T119, T121))
U3_ga(T119, T121, multD_out_ga(T119, T121)) → multD_out_ga(s(T119), s(T121))
U13_gga(T99, T102, multD_out_ga(T99, T102)) → multB_out_gga(s(T99), s(0), s(T102))
multB_in_gga(0, s(s(0)), s(s(0))) → multB_out_gga(0, s(s(0)), s(s(0)))
multB_in_gga(s(T155), s(s(0)), s(s(T158))) → U14_gga(T155, T158, multE_in_ga(T155, T158))
multE_in_ga(0, s(s(0))) → multE_out_ga(0, s(s(0)))
multE_in_ga(s(T183), s(s(T185))) → U4_ga(T183, T185, multE_in_ga(T183, T185))
U4_ga(T183, T185, multE_out_ga(T183, T185)) → multE_out_ga(s(T183), s(s(T185)))
U14_gga(T155, T158, multE_out_ga(T155, T158)) → multB_out_gga(s(T155), s(s(0)), s(s(T158)))
multB_in_gga(0, s(s(s(0))), s(s(s(0)))) → multB_out_gga(0, s(s(s(0))), s(s(s(0))))
multB_in_gga(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_gga(T219, T222, multF_in_ga(T219, T222))
multF_in_ga(0, s(s(s(0)))) → multF_out_ga(0, s(s(s(0))))
multF_in_ga(s(T255), s(s(s(T257)))) → U5_ga(T255, T257, multF_in_ga(T255, T257))
U5_ga(T255, T257, multF_out_ga(T255, T257)) → multF_out_ga(s(T255), s(s(s(T257))))
U15_gga(T219, T222, multF_out_ga(T219, T222)) → multB_out_gga(s(T219), s(s(s(0))), s(s(s(T222))))
multB_in_gga(0, s(s(s(s(0)))), s(s(s(s(0))))) → multB_out_gga(0, s(s(s(s(0)))), s(s(s(s(0)))))
multB_in_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_gga(T291, T294, multG_in_ga(T291, T294))
multG_in_ga(0, s(s(s(s(0))))) → multG_out_ga(0, s(s(s(s(0)))))
multG_in_ga(s(T335), s(s(s(s(T337))))) → U6_ga(T335, T337, multG_in_ga(T335, T337))
U6_ga(T335, T337, multG_out_ga(T335, T337)) → multG_out_ga(s(T335), s(s(s(s(T337)))))
U16_gga(T291, T294, multG_out_ga(T291, T294)) → multB_out_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294)))))
multB_in_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → multB_out_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
multB_in_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_gga(T371, T374, multH_in_ga(T371, T374))
multH_in_ga(0, s(s(s(s(s(0)))))) → multH_out_ga(0, s(s(s(s(s(0))))))
multH_in_ga(s(T423), s(s(s(s(s(T425)))))) → U7_ga(T423, T425, multH_in_ga(T423, T425))
U7_ga(T423, T425, multH_out_ga(T423, T425)) → multH_out_ga(s(T423), s(s(s(s(s(T425))))))
U17_gga(T371, T374, multH_out_ga(T371, T374)) → multB_out_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374))))))
multB_in_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → multB_out_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
multB_in_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_gga(T459, T462, multI_in_ga(T459, T462))
multI_in_ga(0, s(s(s(s(s(s(0))))))) → multI_out_ga(0, s(s(s(s(s(s(0)))))))
multI_in_ga(s(T519), s(s(s(s(s(s(T521))))))) → U8_ga(T519, T521, multI_in_ga(T519, T521))
U8_ga(T519, T521, multI_out_ga(T519, T521)) → multI_out_ga(s(T519), s(s(s(s(s(s(T521)))))))
U18_gga(T459, T462, multI_out_ga(T459, T462)) → multB_out_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462)))))))
multB_in_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → multB_out_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
multB_in_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_gga(T555, T558, multJ_in_ga(T555, T558))
multJ_in_ga(0, s(s(s(s(s(s(s(0)))))))) → multJ_out_ga(0, s(s(s(s(s(s(s(0))))))))
multJ_in_ga(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_ga(T623, T625, multJ_in_ga(T623, T625))
U9_ga(T623, T625, multJ_out_ga(T623, T625)) → multJ_out_ga(s(T623), s(s(s(s(s(s(s(T625))))))))
U19_gga(T555, T558, multJ_out_ga(T555, T558)) → multB_out_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558))))))))
multB_in_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_gga(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
multK_in_ggga(0, T649, 0, 0) → multK_out_ggga(0, T649, 0, 0)
multK_in_ggga(s(T662), T663, 0, T665) → U10_ggga(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
U10_ggga(T662, T663, T665, multB_out_gga(T662, s(T663), T665)) → multK_out_ggga(s(T662), T663, 0, T665)
multK_in_ggga(T676, T677, s(T678), s(T680)) → U11_ggga(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
U11_ggga(T676, T677, T678, T680, multK_out_ggga(T676, T677, T678, T680)) → multK_out_ggga(T676, T677, s(T678), s(T680))
U20_gga(T635, T637, T639, multK_out_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)) → multB_out_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639)))))))))
U1_gga(T28, T29, T31, multB_out_gga(T28, T29, T31)) → timesA_out_gga(s(T28), T29, T31)

The argument filtering Pi contains the following mapping:
timesA_in_gga(x1, x2, x3)  =  timesA_in_gga(x1, x2)
0  =  0
timesA_out_gga(x1, x2, x3)  =  timesA_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
multB_in_gga(x1, x2, x3)  =  multB_in_gga(x1, x2)
multB_out_gga(x1, x2, x3)  =  multB_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3)  =  U12_gga(x1, x3)
multC_in_ga(x1, x2)  =  multC_in_ga(x1)
multC_out_ga(x1, x2)  =  multC_out_ga(x1, x2)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U13_gga(x1, x2, x3)  =  U13_gga(x1, x3)
multD_in_ga(x1, x2)  =  multD_in_ga(x1)
multD_out_ga(x1, x2)  =  multD_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U14_gga(x1, x2, x3)  =  U14_gga(x1, x3)
multE_in_ga(x1, x2)  =  multE_in_ga(x1)
multE_out_ga(x1, x2)  =  multE_out_ga(x1, x2)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
multF_in_ga(x1, x2)  =  multF_in_ga(x1)
multF_out_ga(x1, x2)  =  multF_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
multG_in_ga(x1, x2)  =  multG_in_ga(x1)
multG_out_ga(x1, x2)  =  multG_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U17_gga(x1, x2, x3)  =  U17_gga(x1, x3)
multH_in_ga(x1, x2)  =  multH_in_ga(x1)
multH_out_ga(x1, x2)  =  multH_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
multI_in_ga(x1, x2)  =  multI_in_ga(x1)
multI_out_ga(x1, x2)  =  multI_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
multJ_in_ga(x1, x2)  =  multJ_in_ga(x1)
multJ_out_ga(x1, x2)  =  multJ_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
multK_in_ggga(x1, x2, x3, x4)  =  multK_in_ggga(x1, x2, x3)
multK_out_ggga(x1, x2, x3, x4)  =  multK_out_ggga(x1, x2, x3, x4)
U10_ggga(x1, x2, x3, x4)  =  U10_ggga(x1, x2, x4)
U11_ggga(x1, x2, x3, x4, x5)  =  U11_ggga(x1, x2, x3, x5)
MULTB_IN_GGA(x1, x2, x3)  =  MULTB_IN_GGA(x1, x2)
MULTK_IN_GGGA(x1, x2, x3, x4)  =  MULTK_IN_GGGA(x1, x2, x3)

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:

MULTB_IN_GGA(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → MULTK_IN_GGGA(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)
MULTK_IN_GGGA(s(T662), T663, 0, T665) → MULTB_IN_GGA(T662, s(T663), T665)
MULTK_IN_GGGA(T676, T677, s(T678), s(T680)) → MULTK_IN_GGGA(T676, T677, T678, T680)

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

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

(59) PiDPToQDPProof (SOUND transformation)

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

(60) Obligation:

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

MULTB_IN_GGA(T635, s(s(s(s(s(s(s(s(T637))))))))) → MULTK_IN_GGGA(T635, s(s(s(s(s(s(s(T637))))))), T637)
MULTK_IN_GGGA(s(T662), T663, 0) → MULTB_IN_GGA(T662, s(T663))
MULTK_IN_GGGA(T676, T677, s(T678)) → MULTK_IN_GGGA(T676, T677, T678)

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:

• MULTK_IN_GGGA(s(T662), T663, 0) → MULTB_IN_GGA(T662, s(T663))
  The graph contains the following edges 1 > 1

• MULTK_IN_GGGA(T676, T677, s(T678)) → MULTK_IN_GGGA(T676, T677, T678)
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3

• MULTB_IN_GGA(T635, s(s(s(s(s(s(s(s(T637))))))))) → MULTK_IN_GGGA(T635, s(s(s(s(s(s(s(T637))))))), T637)
  The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3

(62) YES

(63) Obligation:

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

MULTC_IN_GA(s(T63), T65) → MULTC_IN_GA(T63, T65)

The TRS R consists of the following rules:

timesA_in_gga(0, T15, 0) → timesA_out_gga(0, T15, 0)
timesA_in_gga(s(T28), T29, T31) → U1_gga(T28, T29, T31, multB_in_gga(T28, T29, T31))
multB_in_gga(0, 0, 0) → multB_out_gga(0, 0, 0)
multB_in_gga(s(T51), 0, T54) → U12_gga(T51, T54, multC_in_ga(T51, T54))
multC_in_ga(0, 0) → multC_out_ga(0, 0)
multC_in_ga(s(T63), T65) → U2_ga(T63, T65, multC_in_ga(T63, T65))
U2_ga(T63, T65, multC_out_ga(T63, T65)) → multC_out_ga(s(T63), T65)
U12_gga(T51, T54, multC_out_ga(T51, T54)) → multB_out_gga(s(T51), 0, T54)
multB_in_gga(0, s(0), s(0)) → multB_out_gga(0, s(0), s(0))
multB_in_gga(s(T99), s(0), s(T102)) → U13_gga(T99, T102, multD_in_ga(T99, T102))
multD_in_ga(0, s(0)) → multD_out_ga(0, s(0))
multD_in_ga(s(T119), s(T121)) → U3_ga(T119, T121, multD_in_ga(T119, T121))
U3_ga(T119, T121, multD_out_ga(T119, T121)) → multD_out_ga(s(T119), s(T121))
U13_gga(T99, T102, multD_out_ga(T99, T102)) → multB_out_gga(s(T99), s(0), s(T102))
multB_in_gga(0, s(s(0)), s(s(0))) → multB_out_gga(0, s(s(0)), s(s(0)))
multB_in_gga(s(T155), s(s(0)), s(s(T158))) → U14_gga(T155, T158, multE_in_ga(T155, T158))
multE_in_ga(0, s(s(0))) → multE_out_ga(0, s(s(0)))
multE_in_ga(s(T183), s(s(T185))) → U4_ga(T183, T185, multE_in_ga(T183, T185))
U4_ga(T183, T185, multE_out_ga(T183, T185)) → multE_out_ga(s(T183), s(s(T185)))
U14_gga(T155, T158, multE_out_ga(T155, T158)) → multB_out_gga(s(T155), s(s(0)), s(s(T158)))
multB_in_gga(0, s(s(s(0))), s(s(s(0)))) → multB_out_gga(0, s(s(s(0))), s(s(s(0))))
multB_in_gga(s(T219), s(s(s(0))), s(s(s(T222)))) → U15_gga(T219, T222, multF_in_ga(T219, T222))
multF_in_ga(0, s(s(s(0)))) → multF_out_ga(0, s(s(s(0))))
multF_in_ga(s(T255), s(s(s(T257)))) → U5_ga(T255, T257, multF_in_ga(T255, T257))
U5_ga(T255, T257, multF_out_ga(T255, T257)) → multF_out_ga(s(T255), s(s(s(T257))))
U15_gga(T219, T222, multF_out_ga(T219, T222)) → multB_out_gga(s(T219), s(s(s(0))), s(s(s(T222))))
multB_in_gga(0, s(s(s(s(0)))), s(s(s(s(0))))) → multB_out_gga(0, s(s(s(s(0)))), s(s(s(s(0)))))
multB_in_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294))))) → U16_gga(T291, T294, multG_in_ga(T291, T294))
multG_in_ga(0, s(s(s(s(0))))) → multG_out_ga(0, s(s(s(s(0)))))
multG_in_ga(s(T335), s(s(s(s(T337))))) → U6_ga(T335, T337, multG_in_ga(T335, T337))
U6_ga(T335, T337, multG_out_ga(T335, T337)) → multG_out_ga(s(T335), s(s(s(s(T337)))))
U16_gga(T291, T294, multG_out_ga(T291, T294)) → multB_out_gga(s(T291), s(s(s(s(0)))), s(s(s(s(T294)))))
multB_in_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → multB_out_gga(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
multB_in_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374)))))) → U17_gga(T371, T374, multH_in_ga(T371, T374))
multH_in_ga(0, s(s(s(s(s(0)))))) → multH_out_ga(0, s(s(s(s(s(0))))))
multH_in_ga(s(T423), s(s(s(s(s(T425)))))) → U7_ga(T423, T425, multH_in_ga(T423, T425))
U7_ga(T423, T425, multH_out_ga(T423, T425)) → multH_out_ga(s(T423), s(s(s(s(s(T425))))))
U17_gga(T371, T374, multH_out_ga(T371, T374)) → multB_out_gga(s(T371), s(s(s(s(s(0))))), s(s(s(s(s(T374))))))
multB_in_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → multB_out_gga(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
multB_in_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462))))))) → U18_gga(T459, T462, multI_in_ga(T459, T462))
multI_in_ga(0, s(s(s(s(s(s(0))))))) → multI_out_ga(0, s(s(s(s(s(s(0)))))))
multI_in_ga(s(T519), s(s(s(s(s(s(T521))))))) → U8_ga(T519, T521, multI_in_ga(T519, T521))
U8_ga(T519, T521, multI_out_ga(T519, T521)) → multI_out_ga(s(T519), s(s(s(s(s(s(T521)))))))
U18_gga(T459, T462, multI_out_ga(T459, T462)) → multB_out_gga(s(T459), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(T462)))))))
multB_in_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → multB_out_gga(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
multB_in_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558)))))))) → U19_gga(T555, T558, multJ_in_ga(T555, T558))
multJ_in_ga(0, s(s(s(s(s(s(s(0)))))))) → multJ_out_ga(0, s(s(s(s(s(s(s(0))))))))
multJ_in_ga(s(T623), s(s(s(s(s(s(s(T625)))))))) → U9_ga(T623, T625, multJ_in_ga(T623, T625))
U9_ga(T623, T625, multJ_out_ga(T623, T625)) → multJ_out_ga(s(T623), s(s(s(s(s(s(s(T625))))))))
U19_gga(T555, T558, multJ_out_ga(T555, T558)) → multB_out_gga(s(T555), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T558))))))))
multB_in_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639))))))))) → U20_gga(T635, T637, T639, multK_in_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639))
multK_in_ggga(0, T649, 0, 0) → multK_out_ggga(0, T649, 0, 0)
multK_in_ggga(s(T662), T663, 0, T665) → U10_ggga(T662, T663, T665, multB_in_gga(T662, s(T663), T665))
U10_ggga(T662, T663, T665, multB_out_gga(T662, s(T663), T665)) → multK_out_ggga(s(T662), T663, 0, T665)
multK_in_ggga(T676, T677, s(T678), s(T680)) → U11_ggga(T676, T677, T678, T680, multK_in_ggga(T676, T677, T678, T680))
U11_ggga(T676, T677, T678, T680, multK_out_ggga(T676, T677, T678, T680)) → multK_out_ggga(T676, T677, s(T678), s(T680))
U20_gga(T635, T637, T639, multK_out_ggga(T635, s(s(s(s(s(s(s(T637))))))), T637, T639)) → multB_out_gga(T635, s(s(s(s(s(s(s(s(T637)))))))), s(s(s(s(s(s(s(s(T639)))))))))
U1_gga(T28, T29, T31, multB_out_gga(T28, T29, T31)) → timesA_out_gga(s(T28), T29, T31)

The argument filtering Pi contains the following mapping:
timesA_in_gga(x1, x2, x3)  =  timesA_in_gga(x1, x2)
0  =  0
timesA_out_gga(x1, x2, x3)  =  timesA_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
multB_in_gga(x1, x2, x3)  =  multB_in_gga(x1, x2)
multB_out_gga(x1, x2, x3)  =  multB_out_gga(x1, x2, x3)
U12_gga(x1, x2, x3)  =  U12_gga(x1, x3)
multC_in_ga(x1, x2)  =  multC_in_ga(x1)
multC_out_ga(x1, x2)  =  multC_out_ga(x1, x2)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U13_gga(x1, x2, x3)  =  U13_gga(x1, x3)
multD_in_ga(x1, x2)  =  multD_in_ga(x1)
multD_out_ga(x1, x2)  =  multD_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U14_gga(x1, x2, x3)  =  U14_gga(x1, x3)
multE_in_ga(x1, x2)  =  multE_in_ga(x1)
multE_out_ga(x1, x2)  =  multE_out_ga(x1, x2)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
multF_in_ga(x1, x2)  =  multF_in_ga(x1)
multF_out_ga(x1, x2)  =  multF_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
multG_in_ga(x1, x2)  =  multG_in_ga(x1)
multG_out_ga(x1, x2)  =  multG_out_ga(x1, x2)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U17_gga(x1, x2, x3)  =  U17_gga(x1, x3)
multH_in_ga(x1, x2)  =  multH_in_ga(x1)
multH_out_ga(x1, x2)  =  multH_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
multI_in_ga(x1, x2)  =  multI_in_ga(x1)
multI_out_ga(x1, x2)  =  multI_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
multJ_in_ga(x1, x2)  =  multJ_in_ga(x1)
multJ_out_ga(x1, x2)  =  multJ_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
multK_in_ggga(x1, x2, x3, x4)  =  multK_in_ggga(x1, x2, x3)
multK_out_ggga(x1, x2, x3, x4)  =  multK_out_ggga(x1, x2, x3, x4)
U10_ggga(x1, x2, x3, x4)  =  U10_ggga(x1, x2, x4)
U11_ggga(x1, x2, x3, x4, x5)  =  U11_ggga(x1, x2, x3, x5)
MULTC_IN_GA(x1, x2)  =  MULTC_IN_GA(x1)

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:

MULTC_IN_GA(s(T63), T65) → MULTC_IN_GA(T63, T65)

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

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

(66) PiDPToQDPProof (SOUND transformation)

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

(67) Obligation:

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

MULTC_IN_GA(s(T63)) → MULTC_IN_GA(T63)

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:

• MULTC_IN_GA(s(T63)) → MULTC_IN_GA(T63)
  The graph contains the following edges 1 > 1

(69) YES