Left Termination proof of /tmp/tmpLIoI4J/evaluate.pl

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

0 Prolog

↳1 PrologToPiTRSViaGraphTransformerProof (⇒, 256 ms)

↳2 PiTRS

↳3 DependencyPairsProof (⇔, 685 ms)

↳4 PiDP

↳5 DependencyGraphProof (⇔, 50 ms)

↳6 AND

    ↳7 PiDP

        ↳8 UsableRulesProof (⇔, 0 ms)

        ↳9 PiDP

        ↳10 PiDPToQDPProof (⇒, 3 ms)

        ↳11 QDP

        ↳12 QDPSizeChangeProof (⇔, 0 ms)

        ↳13 YES

    ↳14 PiDP

        ↳15 UsableRulesProof (⇔, 0 ms)

        ↳16 PiDP

        ↳17 PiDPToQDPProof (⇒, 0 ms)

        ↳18 QDP

        ↳19 QDPSizeChangeProof (⇔, 0 ms)

        ↳20 YES

    ↳21 PiDP

        ↳22 UsableRulesProof (⇔, 0 ms)

        ↳23 PiDP

        ↳24 PiDPToQDPProof (⇒, 0 ms)

        ↳25 QDP

        ↳26 QDPSizeChangeProof (⇔, 0 ms)

        ↳27 YES

    ↳28 PiDP

        ↳29 UsableRulesProof (⇔, 0 ms)

        ↳30 PiDP

        ↳31 PiDPToQDPProof (⇒, 0 ms)

        ↳32 QDP

        ↳33 QDPSizeChangeProof (⇔, 0 ms)

        ↳34 YES

    ↳35 PiDP

        ↳36 UsableRulesProof (⇔, 0 ms)

        ↳37 PiDP

        ↳38 PiDPToQDPProof (⇔, 0 ms)

        ↳39 QDP

        ↳40 QDPSizeChangeProof (⇔, 0 ms)

        ↳41 YES

    ↳42 PiDP

        ↳43 UsableRulesProof (⇔, 0 ms)

        ↳44 PiDP

        ↳45 PiDPToQDPProof (⇒, 64 ms)

        ↳46 QDP

        ↳47 QDPSizeChangeProof (⇔, 0 ms)

        ↳48 YES

(0) Obligation:

Clauses:

myis(Z, X) :- evaluate(X, Z).
evaluate(+(X, Y), Z) :- ','(evaluate(X, X1), ','(evaluate(Y, Y1), add(X1, Y1, Z))).
evaluate(-(X, Y), Z) :- ','(evaluate(X, X1), ','(evaluate(Y, Y1), sub(X1, Y1, Z))).
evaluate(*(X, Y), Z) :- ','(evaluate(X, X1), ','(evaluate(Y, Y1), mult(X1, Y1, Z))).
evaluate(X, X) :- myinteger(X).
myinteger(s(X)) :- myinteger(X).
myinteger(0).
add(s(X), Y, s(Z)) :- add(X, Y, Z).
add(0, X, X).
sub(s(X), s(Y), Z) :- sub(X, Y, Z).
sub(X, 0, X).
mult(s(X), Y, R) :- ','(mult(X, Y, Z), add(Y, Z, R)).
mult(0, Y, 0).
notEq(s(X), s(Y)) :- notEq(X, Y).
notEq(s(X), 0).
notEq(0, s(X)).
lt(s(X), s(Y)) :- lt(X, Y).
lt(0, s(Y)).
gt(s(X), s(Y)) :- gt(X, Y).
gt(s(X), 0).
le(s(X), s(Y)) :- le(X, Y).
le(0, s(Y)).
le(0, 0).

Query: myis(a,g)

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

Transformed Prolog program to (Pi-)TRS.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
3 [label="A: myis(T1, T2)\n\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
4 [label="4: myis(T1, T2), SCOPE: 1, CLAUSE: 0\n\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="B: evaluate(T6, T7)\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: evaluate(T6, T7), SCOPE: 2, CLAUSE: 1 | evaluate(T6, T7), SCOPE: 2, CLAUSE: 2 | evaluate(T6, T7), SCOPE: 2, CLAUSE: 3 | evaluate(T6, T7), SCOPE: 2, CLAUSE: 4\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: evaluate(T6, T7), SCOPE: 2, CLAUSE: 1\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: evaluate(T6, T7), SCOPE: 2, CLAUSE: 2 | evaluate(T6, T7), SCOPE: 2, CLAUSE: 3 | evaluate(T6, T7), SCOPE: 2, CLAUSE: 4\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="C: ','(evaluate(T20, X25), ','(evaluate(T21, X26), add(X25, X26, T23)))\n\nT20 is ground\nT21 is ground\nX25 is free\nX26 is free", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: evaluate(T20, X25)\n\nT20 is ground\nX25 is free", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="N: ','(evaluate(T21, X26), add(T26, X26, T23))\n\nT21 is ground\nT26 is ground\nX26 is free", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: evaluate(T21, X26)\n\nT21 is ground\nX26 is free", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="G: add(T26, T31, T23)\n\nT26 is ground\nT31 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: add(T26, T31, T23), SCOPE: 3, CLAUSE: 7 | add(T26, T31, T23), SCOPE: 3, CLAUSE: 8\n\nT26 is ground\nT31 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: add(T26, T31, T23), SCOPE: 3, CLAUSE: 7\n\nT26 is ground\nT31 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: add(T26, T31, T23), SCOPE: 3, CLAUSE: 8\n\nT26 is ground\nT31 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: add(T49, T50, T52)\n\nT49 is ground\nT50 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: evaluate(T6, T7), SCOPE: 2, CLAUSE: 2\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: evaluate(T6, T7), SCOPE: 2, CLAUSE: 3 | evaluate(T6, T7), SCOPE: 2, CLAUSE: 4\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="D: ','(evaluate(T71, X94), ','(evaluate(T72, X95), sub(X94, X95, T74)))\n\nT71 is ground\nT72 is ground\nX94 is free\nX95 is free", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: evaluate(T71, X94)\n\nT71 is ground\nX94 is free", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="O: ','(evaluate(T72, X95), sub(T77, X95, T74))\n\nT72 is ground\nT77 is ground\nX95 is free", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: evaluate(T72, X95)\n\nT72 is ground\nX95 is free", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="H: sub(T77, T82, T74)\n\nT77 is ground\nT82 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: sub(T77, T82, T74), SCOPE: 4, CLAUSE: 9 | sub(T77, T82, T74), SCOPE: 4, CLAUSE: 10\n\nT77 is ground\nT82 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: sub(T77, T82, T74), SCOPE: 4, CLAUSE: 9\n\nT77 is ground\nT82 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: sub(T77, T82, T74), SCOPE: 4, CLAUSE: 10\n\nT77 is ground\nT82 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: sub(T100, T101, T103)\n\nT100 is ground\nT101 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: evaluate(T6, T7), SCOPE: 2, CLAUSE: 3\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: evaluate(T6, T7), SCOPE: 2, CLAUSE: 4\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="E: ','(evaluate(T122, X163), ','(evaluate(T123, X164), mult(X163, X164, T125)))\n\nT122 is ground\nT123 is ground\nX163 is free\nX164 is free", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: evaluate(T122, X163)\n\nT122 is ground\nX163 is free", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="P: ','(evaluate(T123, X164), mult(T128, X164, T125))\n\nT123 is ground\nT128 is ground\nX164 is free", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: evaluate(T123, X164)\n\nT123 is ground\nX164 is free", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="L: mult(T128, T133, T125)\n\nT128 is ground\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: mult(T128, T133, T125), SCOPE: 5, CLAUSE: 11 | mult(T128, T133, T125), SCOPE: 5, CLAUSE: 12\n\nT128 is ground\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: mult(T128, T133, T125), SCOPE: 5, CLAUSE: 11\n\nT128 is ground\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: mult(T128, T133, T125), SCOPE: 5, CLAUSE: 12\n\nT128 is ground\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="M: ','(mult(T151, T152, X210), add(T152, X210, T154))\n\nT151 is ground\nT152 is ground\nX210 is free", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="I: mult(T151, T152, X210)\n\nT151 is ground\nT152 is ground\nX210 is free", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: add(T152, T157, T154)\n\nT152 is ground\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: mult(T151, T152, X210), SCOPE: 6, CLAUSE: 11 | mult(T151, T152, X210), SCOPE: 6, CLAUSE: 12\n\nT151 is ground\nT152 is ground\nX210 is free", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: mult(T151, T152, X210), SCOPE: 6, CLAUSE: 11\n\nT151 is ground\nT152 is ground\nX210 is free", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: mult(T151, T152, X210), SCOPE: 6, CLAUSE: 12\n\nT151 is ground\nT152 is ground\nX210 is free", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="J: ','(mult(T168, T169, X242), add(T169, X242, X243))\n\nT168 is ground\nT169 is ground\nX243 is free\nX242 is free", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: mult(T168, T169, X242)\n\nT168 is ground\nT169 is ground\nX242 is free", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="K: add(T169, T172, X243)\n\nT169 is ground\nT172 is ground\nX243 is free", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: add(T169, T172, X243), SCOPE: 7, CLAUSE: 7 | add(T169, T172, X243), SCOPE: 7, CLAUSE: 8\n\nT169 is ground\nT172 is ground\nX243 is free", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: add(T169, T172, X243), SCOPE: 7, CLAUSE: 7\n\nT169 is ground\nT172 is ground\nX243 is free", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: add(T169, T172, X243), SCOPE: 7, CLAUSE: 8\n\nT169 is ground\nT172 is ground\nX243 is free", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: add(T185, T186, X277)\n\nT185 is ground\nT186 is ground\nX277 is free", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="F: myinteger(T203)\n\nT203 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: myinteger(T203), SCOPE: 8, CLAUSE: 5 | myinteger(T203), SCOPE: 8, CLAUSE: 6\n\nT203 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: myinteger(T203), SCOPE: 8, CLAUSE: 5\n\nT203 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: myinteger(T203), SCOPE: 8, CLAUSE: 6\n\nT203 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: myinteger(T209)\n\nT209 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 197 [arrowhead = none ];
197 -> 4;

198 [label="ONLY EVAL with clause\nmyis(X4, X5) :- evaluate(X5, X4).\nand substitutionT1 -> T7,\nX4 -> T7,\nT2 -> T6,\nX5 -> T6,\nT5 -> T7", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 198 [arrowhead = none ];
198 -> 11;

199 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
11 -> 199 [arrowhead = none ];
199 -> 12;

200 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
12 -> 200 [arrowhead = none ];
200 -> 14;

201 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
12 -> 201 [arrowhead = none ];
201 -> 15;

202 [label="EVAL with clause\nevaluate(+(X22, X23), X24) :- ','(evaluate(X22, X25), ','(evaluate(X23, X26), add(X25, X26, X24))).\nand substitutionX22 -> T20,\nX23 -> T21,\nT6 -> +(T20, T21),\nT7 -> T23,\nX24 -> T23,\nT22 -> T23", fontsize=14, style = filled, fillcolor = lightblue];
14 -> 202 [arrowhead = none ];
202 -> 18;

203 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
14 -> 203 [arrowhead = none ];
203 -> 19;

204 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
15 -> 204 [arrowhead = none ];
204 -> 54;

205 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
15 -> 205 [arrowhead = none ];
205 -> 55;

206 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
18 -> 206 [arrowhead = none ];
206 -> 23;

207 [label="SPLIT 2\nnew knowledge:\nT20 is ground\nT26 is ground\nreplacements:X25 -> T26", fontsize=14, style = filled, fillcolor = violet];
18 -> 207 [arrowhead = none ];
207 -> 24;

208 [label="INSTANCE with matching:\nT6 -> T20\nT7 -> X25", fontsize=14, style = filled, fillcolor = lightgrey];
23 -> 208 [arrowhead = none , style=dashed];
208 -> 11[style=dashed];

209 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
24 -> 209 [arrowhead = none ];
209 -> 29;

210 [label="SPLIT 2\nnew knowledge:\nT21 is ground\nT31 is ground\nreplacements:X26 -> T31", fontsize=14, style = filled, fillcolor = violet];
24 -> 210 [arrowhead = none ];
210 -> 30;

211 [label="INSTANCE with matching:\nT6 -> T21\nT7 -> X26", fontsize=14, style = filled, fillcolor = lightgrey];
29 -> 211 [arrowhead = none , style=dashed];
211 -> 11[style=dashed];

212 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
30 -> 212 [arrowhead = none ];
212 -> 35;

213 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
35 -> 213 [arrowhead = none ];
213 -> 36;

214 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
35 -> 214 [arrowhead = none ];
214 -> 37;

215 [label="EVAL with clause\nadd(s(X66), X67, s(X68)) :- add(X66, X67, X68).\nand substitutionX66 -> T49,\nT26 -> s(T49),\nT31 -> T50,\nX67 -> T50,\nX68 -> T52,\nT23 -> s(T52),\nT51 -> T52", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 215 [arrowhead = none ];
215 -> 41;

216 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
36 -> 216 [arrowhead = none ];
216 -> 42;

217 [label="EVAL with clause\nadd(0, X74, X74).\nand substitutionT26 -> 0,\nT31 -> T58,\nX74 -> T58,\nT23 -> T58", fontsize=14, style = filled, fillcolor = lightblue];
37 -> 217 [arrowhead = none ];
217 -> 46;

218 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
37 -> 218 [arrowhead = none ];
218 -> 48;

219 [label="INSTANCE with matching:\nT26 -> T49\nT31 -> T50\nT23 -> T52", fontsize=14, style = filled, fillcolor = lightgrey];
41 -> 219 [arrowhead = none , style=dashed];
219 -> 30[style=dashed];

220 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
46 -> 220 [arrowhead = none ];
220 -> 49;

221 [label="EVAL with clause\nevaluate(-(X91, X92), X93) :- ','(evaluate(X91, X94), ','(evaluate(X92, X95), sub(X94, X95, X93))).\nand substitutionX91 -> T71,\nX92 -> T72,\nT6 -> -(T71, T72),\nT7 -> T74,\nX93 -> T74,\nT73 -> T74", fontsize=14, style = filled, fillcolor = lightblue];
54 -> 221 [arrowhead = none ];
221 -> 58;

222 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
54 -> 222 [arrowhead = none ];
222 -> 59;

223 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
55 -> 223 [arrowhead = none ];
223 -> 97;

224 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
55 -> 224 [arrowhead = none ];
224 -> 98;

225 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
58 -> 225 [arrowhead = none ];
225 -> 62;

226 [label="SPLIT 2\nnew knowledge:\nT71 is ground\nT77 is ground\nreplacements:X94 -> T77", fontsize=14, style = filled, fillcolor = violet];
58 -> 226 [arrowhead = none ];
226 -> 63;

227 [label="INSTANCE with matching:\nT6 -> T71\nT7 -> X94", fontsize=14, style = filled, fillcolor = lightgrey];
62 -> 227 [arrowhead = none , style=dashed];
227 -> 11[style=dashed];

228 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
63 -> 228 [arrowhead = none ];
228 -> 70;

229 [label="SPLIT 2\nnew knowledge:\nT72 is ground\nT82 is ground\nreplacements:X95 -> T82", fontsize=14, style = filled, fillcolor = violet];
63 -> 229 [arrowhead = none ];
229 -> 71;

230 [label="INSTANCE with matching:\nT6 -> T72\nT7 -> X95", fontsize=14, style = filled, fillcolor = lightgrey];
70 -> 230 [arrowhead = none , style=dashed];
230 -> 11[style=dashed];

231 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
71 -> 231 [arrowhead = none ];
231 -> 77;

232 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 232 [arrowhead = none ];
232 -> 81;

233 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 233 [arrowhead = none ];
233 -> 83;

234 [label="EVAL with clause\nsub(s(X135), s(X136), X137) :- sub(X135, X136, X137).\nand substitutionX135 -> T100,\nT77 -> s(T100),\nX136 -> T101,\nT82 -> s(T101),\nT74 -> T103,\nX137 -> T103,\nT102 -> T103", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 234 [arrowhead = none ];
234 -> 86;

235 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
81 -> 235 [arrowhead = none ];
235 -> 88;

236 [label="EVAL with clause\nsub(X143, 0, X143).\nand substitutionT77 -> T109,\nX143 -> T109,\nT82 -> 0,\nT74 -> T109", fontsize=14, style = filled, fillcolor = lightblue];
83 -> 236 [arrowhead = none ];
236 -> 90;

237 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 237 [arrowhead = none ];
237 -> 93;

238 [label="INSTANCE with matching:\nT77 -> T100\nT82 -> T101\nT74 -> T103", fontsize=14, style = filled, fillcolor = lightgrey];
86 -> 238 [arrowhead = none , style=dashed];
238 -> 71[style=dashed];

239 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
90 -> 239 [arrowhead = none ];
239 -> 94;

240 [label="EVAL with clause\nevaluate(*(X160, X161), X162) :- ','(evaluate(X160, X163), ','(evaluate(X161, X164), mult(X163, X164, X162))).\nand substitutionX160 -> T122,\nX161 -> T123,\nT6 -> *(T122, T123),\nT7 -> T125,\nX162 -> T125,\nT124 -> T125", fontsize=14, style = filled, fillcolor = lightblue];
97 -> 240 [arrowhead = none ];
240 -> 103;

241 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
97 -> 241 [arrowhead = none ];
241 -> 104;

242 [label="EVAL with clause\nevaluate(X296, X296) :- myinteger(X296).\nand substitutionT6 -> T203,\nX296 -> T203,\nT7 -> T203", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 242 [arrowhead = none ];
242 -> 184;

243 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
98 -> 243 [arrowhead = none ];
243 -> 185;

244 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
103 -> 244 [arrowhead = none ];
244 -> 109;

245 [label="SPLIT 2\nnew knowledge:\nT122 is ground\nT128 is ground\nreplacements:X163 -> T128", fontsize=14, style = filled, fillcolor = violet];
103 -> 245 [arrowhead = none ];
245 -> 110;

246 [label="INSTANCE with matching:\nT6 -> T122\nT7 -> X163", fontsize=14, style = filled, fillcolor = lightgrey];
109 -> 246 [arrowhead = none , style=dashed];
246 -> 11[style=dashed];

247 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
110 -> 247 [arrowhead = none ];
247 -> 113;

248 [label="SPLIT 2\nnew knowledge:\nT123 is ground\nT133 is ground\nreplacements:X164 -> T133", fontsize=14, style = filled, fillcolor = violet];
110 -> 248 [arrowhead = none ];
248 -> 114;

249 [label="INSTANCE with matching:\nT6 -> T123\nT7 -> X164", fontsize=14, style = filled, fillcolor = lightgrey];
113 -> 249 [arrowhead = none , style=dashed];
249 -> 11[style=dashed];

250 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
114 -> 250 [arrowhead = none ];
250 -> 116;

251 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
116 -> 251 [arrowhead = none ];
251 -> 121;

252 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
116 -> 252 [arrowhead = none ];
252 -> 122;

253 [label="EVAL with clause\nmult(s(X207), X208, X209) :- ','(mult(X207, X208, X210), add(X208, X210, X209)).\nand substitutionX207 -> T151,\nT128 -> s(T151),\nT133 -> T152,\nX208 -> T152,\nT125 -> T154,\nX209 -> T154,\nT153 -> T154", fontsize=14, style = filled, fillcolor = lightblue];
121 -> 253 [arrowhead = none ];
253 -> 126;

254 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
121 -> 254 [arrowhead = none ];
254 -> 129;

255 [label="EVAL with clause\nmult(0, X293, 0).\nand substitutionT128 -> 0,\nT133 -> T200,\nX293 -> T200,\nT125 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 255 [arrowhead = none ];
255 -> 181;

256 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
122 -> 256 [arrowhead = none ];
256 -> 182;

257 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
126 -> 257 [arrowhead = none ];
257 -> 132;

258 [label="SPLIT 2\nnew knowledge:\nT151 is ground\nT152 is ground\nT157 is ground\nreplacements:X210 -> T157", fontsize=14, style = filled, fillcolor = violet];
126 -> 258 [arrowhead = none ];
258 -> 133;

259 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
132 -> 259 [arrowhead = none ];
259 -> 134;

260 [label="INSTANCE with matching:\nT26 -> T152\nT31 -> T157\nT23 -> T154", fontsize=14, style = filled, fillcolor = lightgrey];
133 -> 260 [arrowhead = none , style=dashed];
260 -> 30[style=dashed];

261 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
134 -> 261 [arrowhead = none ];
261 -> 137;

262 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
134 -> 262 [arrowhead = none ];
262 -> 138;

263 [label="EVAL with clause\nmult(s(X239), X240, X241) :- ','(mult(X239, X240, X242), add(X240, X242, X241)).\nand substitutionX239 -> T168,\nT151 -> s(T168),\nT152 -> T169,\nX240 -> T169,\nX210 -> X243,\nX241 -> X243", fontsize=14, style = filled, fillcolor = lightblue];
137 -> 263 [arrowhead = none ];
263 -> 141;

264 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
137 -> 264 [arrowhead = none ];
264 -> 142;

265 [label="EVAL with clause\nmult(0, X287, 0).\nand substitutionT151 -> 0,\nT152 -> T194,\nX287 -> T194,\nX210 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
138 -> 265 [arrowhead = none ];
265 -> 172;

266 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
138 -> 266 [arrowhead = none ];
266 -> 173;

267 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
141 -> 267 [arrowhead = none ];
267 -> 145;

268 [label="SPLIT 2\nnew knowledge:\nT168 is ground\nT169 is ground\nT172 is ground\nreplacements:X242 -> T172", fontsize=14, style = filled, fillcolor = violet];
141 -> 268 [arrowhead = none ];
268 -> 146;

269 [label="INSTANCE with matching:\nT151 -> T168\nT152 -> T169\nX210 -> X242", fontsize=14, style = filled, fillcolor = lightgrey];
145 -> 269 [arrowhead = none , style=dashed];
269 -> 132[style=dashed];

270 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
146 -> 270 [arrowhead = none ];
270 -> 153;

271 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
153 -> 271 [arrowhead = none ];
271 -> 156;

272 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
153 -> 272 [arrowhead = none ];
272 -> 157;

273 [label="EVAL with clause\nadd(s(X274), X275, s(X276)) :- add(X274, X275, X276).\nand substitutionX274 -> T185,\nT169 -> s(T185),\nT172 -> T186,\nX275 -> T186,\nX276 -> X277,\nX243 -> s(X277)", fontsize=14, style = filled, fillcolor = lightblue];
156 -> 273 [arrowhead = none ];
273 -> 161;

274 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
156 -> 274 [arrowhead = none ];
274 -> 164;

275 [label="EVAL with clause\nadd(0, X284, X284).\nand substitutionT169 -> 0,\nT172 -> T191,\nX284 -> T191,\nX243 -> T191", fontsize=14, style = filled, fillcolor = lightblue];
157 -> 275 [arrowhead = none ];
275 -> 169;

276 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
157 -> 276 [arrowhead = none ];
276 -> 170;

277 [label="INSTANCE with matching:\nT169 -> T185\nT172 -> T186\nX243 -> X277", fontsize=14, style = filled, fillcolor = lightgrey];
161 -> 277 [arrowhead = none , style=dashed];
277 -> 146[style=dashed];

278 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
169 -> 278 [arrowhead = none ];
278 -> 171;

279 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
172 -> 279 [arrowhead = none ];
279 -> 174;

280 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
181 -> 280 [arrowhead = none ];
280 -> 183;

281 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
184 -> 281 [arrowhead = none ];
281 -> 186;

282 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
186 -> 282 [arrowhead = none ];
282 -> 187;

283 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
186 -> 283 [arrowhead = none ];
283 -> 189;

284 [label="EVAL with clause\nmyinteger(s(X302)) :- myinteger(X302).\nand substitutionX302 -> T209,\nT203 -> s(T209)", fontsize=14, style = filled, fillcolor = lightblue];
187 -> 284 [arrowhead = none ];
284 -> 191;

285 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
187 -> 285 [arrowhead = none ];
285 -> 192;

286 [label="EVAL with clause\nmyinteger(0).\nand substitutionT203 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
189 -> 286 [arrowhead = none ];
286 -> 193;

287 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
189 -> 287 [arrowhead = none ];
287 -> 194;

288 [label="INSTANCE with matching:\nT203 -> T209", fontsize=14, style = filled, fillcolor = lightgrey];
191 -> 288 [arrowhead = none , style=dashed];
288 -> 184[style=dashed];

289 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
193 -> 289 [arrowhead = none ];
289 -> 196;

}

(2) Obligation:

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

myisA_in_ag(T7, T6) → U1_ag(T7, T6, evaluateB_in_ga(T6, T7))
evaluateB_in_ga(+(T20, T21), T23) → U2_ga(T20, T21, T23, pC_in_gagaa(T20, X25, T21, X26, T23))
pC_in_gagaa(T20, T26, T21, X26, T23) → U12_gagaa(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
evaluateB_in_ga(-(T71, T72), T74) → U3_ga(T71, T72, T74, pD_in_gagaa(T71, X94, T72, X95, T74))
pD_in_gagaa(T71, T77, T72, X95, T74) → U16_gagaa(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
evaluateB_in_ga(*(T122, T123), T125) → U4_ga(T122, T123, T125, pE_in_gagaa(T122, X163, T123, X164, T125))
pE_in_gagaa(T122, T128, T123, X164, T125) → U20_gagaa(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
evaluateB_in_ga(T203, T203) → U5_ga(T203, myintegerF_in_g(T203))
myintegerF_in_g(s(T209)) → U10_g(T209, myintegerF_in_g(T209))
myintegerF_in_g(0) → myintegerF_out_g(0)
U10_g(T209, myintegerF_out_g(T209)) → myintegerF_out_g(s(T209))
U5_ga(T203, myintegerF_out_g(T203)) → evaluateB_out_ga(T203, T203)
U20_gagaa(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → U21_gagaa(T122, T128, T123, X164, T125, pP_in_gaga(T123, X164, T128, T125))
pP_in_gaga(T123, T133, T128, T125) → U22_gaga(T123, T133, T128, T125, evaluateB_in_ga(T123, T133))
U22_gaga(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → U23_gaga(T123, T133, T128, T125, multL_in_gga(T128, T133, T125))
multL_in_gga(s(T151), T152, T154) → U11_gga(T151, T152, T154, pM_in_ggaa(T151, T152, X210, T154))
pM_in_ggaa(T151, T152, T157, T154) → U24_ggaa(T151, T152, T157, T154, multI_in_gga(T151, T152, T157))
multI_in_gga(s(T168), T169, X243) → U8_gga(T168, T169, X243, pJ_in_ggaa(T168, T169, X242, X243))
pJ_in_ggaa(T168, T169, T172, X243) → U26_ggaa(T168, T169, T172, X243, multI_in_gga(T168, T169, T172))
multI_in_gga(0, T194, 0) → multI_out_gga(0, T194, 0)
U26_ggaa(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → U27_ggaa(T168, T169, T172, X243, addK_in_gga(T169, T172, X243))
addK_in_gga(s(T185), T186, s(X277)) → U9_gga(T185, T186, X277, addK_in_gga(T185, T186, X277))
addK_in_gga(0, T191, T191) → addK_out_gga(0, T191, T191)
U9_gga(T185, T186, X277, addK_out_gga(T185, T186, X277)) → addK_out_gga(s(T185), T186, s(X277))
U27_ggaa(T168, T169, T172, X243, addK_out_gga(T169, T172, X243)) → pJ_out_ggaa(T168, T169, T172, X243)
U8_gga(T168, T169, X243, pJ_out_ggaa(T168, T169, X242, X243)) → multI_out_gga(s(T168), T169, X243)
U24_ggaa(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → U25_ggaa(T151, T152, T157, T154, addG_in_gga(T152, T157, T154))
addG_in_gga(s(T49), T50, s(T52)) → U6_gga(T49, T50, T52, addG_in_gga(T49, T50, T52))
addG_in_gga(0, T58, T58) → addG_out_gga(0, T58, T58)
U6_gga(T49, T50, T52, addG_out_gga(T49, T50, T52)) → addG_out_gga(s(T49), T50, s(T52))
U25_ggaa(T151, T152, T157, T154, addG_out_gga(T152, T157, T154)) → pM_out_ggaa(T151, T152, T157, T154)
U11_gga(T151, T152, T154, pM_out_ggaa(T151, T152, X210, T154)) → multL_out_gga(s(T151), T152, T154)
multL_in_gga(0, T200, 0) → multL_out_gga(0, T200, 0)
U23_gaga(T123, T133, T128, T125, multL_out_gga(T128, T133, T125)) → pP_out_gaga(T123, T133, T128, T125)
U21_gagaa(T122, T128, T123, X164, T125, pP_out_gaga(T123, X164, T128, T125)) → pE_out_gagaa(T122, T128, T123, X164, T125)
U4_ga(T122, T123, T125, pE_out_gagaa(T122, X163, T123, X164, T125)) → evaluateB_out_ga(*(T122, T123), T125)
U16_gagaa(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → U17_gagaa(T71, T77, T72, X95, T74, pO_in_gaga(T72, X95, T77, T74))
pO_in_gaga(T72, T82, T77, T74) → U18_gaga(T72, T82, T77, T74, evaluateB_in_ga(T72, T82))
U18_gaga(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → U19_gaga(T72, T82, T77, T74, subH_in_gga(T77, T82, T74))
subH_in_gga(s(T100), s(T101), T103) → U7_gga(T100, T101, T103, subH_in_gga(T100, T101, T103))
subH_in_gga(T109, 0, T109) → subH_out_gga(T109, 0, T109)
U7_gga(T100, T101, T103, subH_out_gga(T100, T101, T103)) → subH_out_gga(s(T100), s(T101), T103)
U19_gaga(T72, T82, T77, T74, subH_out_gga(T77, T82, T74)) → pO_out_gaga(T72, T82, T77, T74)
U17_gagaa(T71, T77, T72, X95, T74, pO_out_gaga(T72, X95, T77, T74)) → pD_out_gagaa(T71, T77, T72, X95, T74)
U3_ga(T71, T72, T74, pD_out_gagaa(T71, X94, T72, X95, T74)) → evaluateB_out_ga(-(T71, T72), T74)
U12_gagaa(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → U13_gagaa(T20, T26, T21, X26, T23, pN_in_gaga(T21, X26, T26, T23))
pN_in_gaga(T21, T31, T26, T23) → U14_gaga(T21, T31, T26, T23, evaluateB_in_ga(T21, T31))
U14_gaga(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → U15_gaga(T21, T31, T26, T23, addG_in_gga(T26, T31, T23))
U15_gaga(T21, T31, T26, T23, addG_out_gga(T26, T31, T23)) → pN_out_gaga(T21, T31, T26, T23)
U13_gagaa(T20, T26, T21, X26, T23, pN_out_gaga(T21, X26, T26, T23)) → pC_out_gagaa(T20, T26, T21, X26, T23)
U2_ga(T20, T21, T23, pC_out_gagaa(T20, X25, T21, X26, T23)) → evaluateB_out_ga(+(T20, T21), T23)
U1_ag(T7, T6, evaluateB_out_ga(T6, T7)) → myisA_out_ag(T7, T6)

(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:

MYISA_IN_AG(T7, T6) → U1_AG(T7, T6, evaluateB_in_ga(T6, T7))
MYISA_IN_AG(T7, T6) → EVALUATEB_IN_GA(T6, T7)
EVALUATEB_IN_GA(+(T20, T21), T23) → U2_GA(T20, T21, T23, pC_in_gagaa(T20, X25, T21, X26, T23))
EVALUATEB_IN_GA(+(T20, T21), T23) → PC_IN_GAGAA(T20, X25, T21, X26, T23)
PC_IN_GAGAA(T20, T26, T21, X26, T23) → U12_GAGAA(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
PC_IN_GAGAA(T20, T26, T21, X26, T23) → EVALUATEB_IN_GA(T20, T26)
EVALUATEB_IN_GA(-(T71, T72), T74) → U3_GA(T71, T72, T74, pD_in_gagaa(T71, X94, T72, X95, T74))
EVALUATEB_IN_GA(-(T71, T72), T74) → PD_IN_GAGAA(T71, X94, T72, X95, T74)
PD_IN_GAGAA(T71, T77, T72, X95, T74) → U16_GAGAA(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
PD_IN_GAGAA(T71, T77, T72, X95, T74) → EVALUATEB_IN_GA(T71, T77)
EVALUATEB_IN_GA(*(T122, T123), T125) → U4_GA(T122, T123, T125, pE_in_gagaa(T122, X163, T123, X164, T125))
EVALUATEB_IN_GA(*(T122, T123), T125) → PE_IN_GAGAA(T122, X163, T123, X164, T125)
PE_IN_GAGAA(T122, T128, T123, X164, T125) → U20_GAGAA(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
PE_IN_GAGAA(T122, T128, T123, X164, T125) → EVALUATEB_IN_GA(T122, T128)
EVALUATEB_IN_GA(T203, T203) → U5_GA(T203, myintegerF_in_g(T203))
EVALUATEB_IN_GA(T203, T203) → MYINTEGERF_IN_G(T203)
MYINTEGERF_IN_G(s(T209)) → U10_G(T209, myintegerF_in_g(T209))
MYINTEGERF_IN_G(s(T209)) → MYINTEGERF_IN_G(T209)
U20_GAGAA(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → U21_GAGAA(T122, T128, T123, X164, T125, pP_in_gaga(T123, X164, T128, T125))
U20_GAGAA(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → PP_IN_GAGA(T123, X164, T128, T125)
PP_IN_GAGA(T123, T133, T128, T125) → U22_GAGA(T123, T133, T128, T125, evaluateB_in_ga(T123, T133))
PP_IN_GAGA(T123, T133, T128, T125) → EVALUATEB_IN_GA(T123, T133)
U22_GAGA(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → U23_GAGA(T123, T133, T128, T125, multL_in_gga(T128, T133, T125))
U22_GAGA(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → MULTL_IN_GGA(T128, T133, T125)
MULTL_IN_GGA(s(T151), T152, T154) → U11_GGA(T151, T152, T154, pM_in_ggaa(T151, T152, X210, T154))
MULTL_IN_GGA(s(T151), T152, T154) → PM_IN_GGAA(T151, T152, X210, T154)
PM_IN_GGAA(T151, T152, T157, T154) → U24_GGAA(T151, T152, T157, T154, multI_in_gga(T151, T152, T157))
PM_IN_GGAA(T151, T152, T157, T154) → MULTI_IN_GGA(T151, T152, T157)
MULTI_IN_GGA(s(T168), T169, X243) → U8_GGA(T168, T169, X243, pJ_in_ggaa(T168, T169, X242, X243))
MULTI_IN_GGA(s(T168), T169, X243) → PJ_IN_GGAA(T168, T169, X242, X243)
PJ_IN_GGAA(T168, T169, T172, X243) → U26_GGAA(T168, T169, T172, X243, multI_in_gga(T168, T169, T172))
PJ_IN_GGAA(T168, T169, T172, X243) → MULTI_IN_GGA(T168, T169, T172)
U26_GGAA(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → U27_GGAA(T168, T169, T172, X243, addK_in_gga(T169, T172, X243))
U26_GGAA(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → ADDK_IN_GGA(T169, T172, X243)
ADDK_IN_GGA(s(T185), T186, s(X277)) → U9_GGA(T185, T186, X277, addK_in_gga(T185, T186, X277))
ADDK_IN_GGA(s(T185), T186, s(X277)) → ADDK_IN_GGA(T185, T186, X277)
U24_GGAA(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → U25_GGAA(T151, T152, T157, T154, addG_in_gga(T152, T157, T154))
U24_GGAA(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → ADDG_IN_GGA(T152, T157, T154)
ADDG_IN_GGA(s(T49), T50, s(T52)) → U6_GGA(T49, T50, T52, addG_in_gga(T49, T50, T52))
ADDG_IN_GGA(s(T49), T50, s(T52)) → ADDG_IN_GGA(T49, T50, T52)
U16_GAGAA(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → U17_GAGAA(T71, T77, T72, X95, T74, pO_in_gaga(T72, X95, T77, T74))
U16_GAGAA(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → PO_IN_GAGA(T72, X95, T77, T74)
PO_IN_GAGA(T72, T82, T77, T74) → U18_GAGA(T72, T82, T77, T74, evaluateB_in_ga(T72, T82))
PO_IN_GAGA(T72, T82, T77, T74) → EVALUATEB_IN_GA(T72, T82)
U18_GAGA(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → U19_GAGA(T72, T82, T77, T74, subH_in_gga(T77, T82, T74))
U18_GAGA(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → SUBH_IN_GGA(T77, T82, T74)
SUBH_IN_GGA(s(T100), s(T101), T103) → U7_GGA(T100, T101, T103, subH_in_gga(T100, T101, T103))
SUBH_IN_GGA(s(T100), s(T101), T103) → SUBH_IN_GGA(T100, T101, T103)
U12_GAGAA(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → U13_GAGAA(T20, T26, T21, X26, T23, pN_in_gaga(T21, X26, T26, T23))
U12_GAGAA(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → PN_IN_GAGA(T21, X26, T26, T23)
PN_IN_GAGA(T21, T31, T26, T23) → U14_GAGA(T21, T31, T26, T23, evaluateB_in_ga(T21, T31))
PN_IN_GAGA(T21, T31, T26, T23) → EVALUATEB_IN_GA(T21, T31)
U14_GAGA(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → U15_GAGA(T21, T31, T26, T23, addG_in_gga(T26, T31, T23))
U14_GAGA(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → ADDG_IN_GGA(T26, T31, T23)

The TRS R consists of the following rules:

myisA_in_ag(T7, T6) → U1_ag(T7, T6, evaluateB_in_ga(T6, T7))
evaluateB_in_ga(+(T20, T21), T23) → U2_ga(T20, T21, T23, pC_in_gagaa(T20, X25, T21, X26, T23))
pC_in_gagaa(T20, T26, T21, X26, T23) → U12_gagaa(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
evaluateB_in_ga(-(T71, T72), T74) → U3_ga(T71, T72, T74, pD_in_gagaa(T71, X94, T72, X95, T74))
pD_in_gagaa(T71, T77, T72, X95, T74) → U16_gagaa(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
evaluateB_in_ga(*(T122, T123), T125) → U4_ga(T122, T123, T125, pE_in_gagaa(T122, X163, T123, X164, T125))
pE_in_gagaa(T122, T128, T123, X164, T125) → U20_gagaa(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
evaluateB_in_ga(T203, T203) → U5_ga(T203, myintegerF_in_g(T203))
myintegerF_in_g(s(T209)) → U10_g(T209, myintegerF_in_g(T209))
myintegerF_in_g(0) → myintegerF_out_g(0)
U10_g(T209, myintegerF_out_g(T209)) → myintegerF_out_g(s(T209))
U5_ga(T203, myintegerF_out_g(T203)) → evaluateB_out_ga(T203, T203)
U20_gagaa(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → U21_gagaa(T122, T128, T123, X164, T125, pP_in_gaga(T123, X164, T128, T125))
pP_in_gaga(T123, T133, T128, T125) → U22_gaga(T123, T133, T128, T125, evaluateB_in_ga(T123, T133))
U22_gaga(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → U23_gaga(T123, T133, T128, T125, multL_in_gga(T128, T133, T125))
multL_in_gga(s(T151), T152, T154) → U11_gga(T151, T152, T154, pM_in_ggaa(T151, T152, X210, T154))
pM_in_ggaa(T151, T152, T157, T154) → U24_ggaa(T151, T152, T157, T154, multI_in_gga(T151, T152, T157))
multI_in_gga(s(T168), T169, X243) → U8_gga(T168, T169, X243, pJ_in_ggaa(T168, T169, X242, X243))
pJ_in_ggaa(T168, T169, T172, X243) → U26_ggaa(T168, T169, T172, X243, multI_in_gga(T168, T169, T172))
multI_in_gga(0, T194, 0) → multI_out_gga(0, T194, 0)
U26_ggaa(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → U27_ggaa(T168, T169, T172, X243, addK_in_gga(T169, T172, X243))
addK_in_gga(s(T185), T186, s(X277)) → U9_gga(T185, T186, X277, addK_in_gga(T185, T186, X277))
addK_in_gga(0, T191, T191) → addK_out_gga(0, T191, T191)
U9_gga(T185, T186, X277, addK_out_gga(T185, T186, X277)) → addK_out_gga(s(T185), T186, s(X277))
U27_ggaa(T168, T169, T172, X243, addK_out_gga(T169, T172, X243)) → pJ_out_ggaa(T168, T169, T172, X243)
U8_gga(T168, T169, X243, pJ_out_ggaa(T168, T169, X242, X243)) → multI_out_gga(s(T168), T169, X243)
U24_ggaa(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → U25_ggaa(T151, T152, T157, T154, addG_in_gga(T152, T157, T154))
addG_in_gga(s(T49), T50, s(T52)) → U6_gga(T49, T50, T52, addG_in_gga(T49, T50, T52))
addG_in_gga(0, T58, T58) → addG_out_gga(0, T58, T58)
U6_gga(T49, T50, T52, addG_out_gga(T49, T50, T52)) → addG_out_gga(s(T49), T50, s(T52))
U25_ggaa(T151, T152, T157, T154, addG_out_gga(T152, T157, T154)) → pM_out_ggaa(T151, T152, T157, T154)
U11_gga(T151, T152, T154, pM_out_ggaa(T151, T152, X210, T154)) → multL_out_gga(s(T151), T152, T154)
multL_in_gga(0, T200, 0) → multL_out_gga(0, T200, 0)
U23_gaga(T123, T133, T128, T125, multL_out_gga(T128, T133, T125)) → pP_out_gaga(T123, T133, T128, T125)
U21_gagaa(T122, T128, T123, X164, T125, pP_out_gaga(T123, X164, T128, T125)) → pE_out_gagaa(T122, T128, T123, X164, T125)
U4_ga(T122, T123, T125, pE_out_gagaa(T122, X163, T123, X164, T125)) → evaluateB_out_ga(*(T122, T123), T125)
U16_gagaa(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → U17_gagaa(T71, T77, T72, X95, T74, pO_in_gaga(T72, X95, T77, T74))
pO_in_gaga(T72, T82, T77, T74) → U18_gaga(T72, T82, T77, T74, evaluateB_in_ga(T72, T82))
U18_gaga(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → U19_gaga(T72, T82, T77, T74, subH_in_gga(T77, T82, T74))
subH_in_gga(s(T100), s(T101), T103) → U7_gga(T100, T101, T103, subH_in_gga(T100, T101, T103))
subH_in_gga(T109, 0, T109) → subH_out_gga(T109, 0, T109)
U7_gga(T100, T101, T103, subH_out_gga(T100, T101, T103)) → subH_out_gga(s(T100), s(T101), T103)
U19_gaga(T72, T82, T77, T74, subH_out_gga(T77, T82, T74)) → pO_out_gaga(T72, T82, T77, T74)
U17_gagaa(T71, T77, T72, X95, T74, pO_out_gaga(T72, X95, T77, T74)) → pD_out_gagaa(T71, T77, T72, X95, T74)
U3_ga(T71, T72, T74, pD_out_gagaa(T71, X94, T72, X95, T74)) → evaluateB_out_ga(-(T71, T72), T74)
U12_gagaa(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → U13_gagaa(T20, T26, T21, X26, T23, pN_in_gaga(T21, X26, T26, T23))
pN_in_gaga(T21, T31, T26, T23) → U14_gaga(T21, T31, T26, T23, evaluateB_in_ga(T21, T31))
U14_gaga(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → U15_gaga(T21, T31, T26, T23, addG_in_gga(T26, T31, T23))
U15_gaga(T21, T31, T26, T23, addG_out_gga(T26, T31, T23)) → pN_out_gaga(T21, T31, T26, T23)
U13_gagaa(T20, T26, T21, X26, T23, pN_out_gaga(T21, X26, T26, T23)) → pC_out_gagaa(T20, T26, T21, X26, T23)
U2_ga(T20, T21, T23, pC_out_gagaa(T20, X25, T21, X26, T23)) → evaluateB_out_ga(+(T20, T21), T23)
U1_ag(T7, T6, evaluateB_out_ga(T6, T7)) → myisA_out_ag(T7, T6)

The argument filtering Pi contains the following mapping:
myisA_in_ag(x1, x2) = myisA_in_ag(x2)
U1_ag(x1, x2, x3) = U1_ag(x2, x3)
evaluateB_in_ga(x1, x2) = evaluateB_in_ga(x1)
+(x1, x2) = +(x1, x2)
U2_ga(x1, x2, x3, x4) = U2_ga(x1, x2, x4)
pC_in_gagaa(x1, x2, x3, x4, x5) = pC_in_gagaa(x1, x3)
U12_gagaa(x1, x2, x3, x4, x5, x6) = U12_gagaa(x1, x3, x6)
-(x1, x2) = -(x1, x2)
U3_ga(x1, x2, x3, x4) = U3_ga(x1, x2, x4)
pD_in_gagaa(x1, x2, x3, x4, x5) = pD_in_gagaa(x1, x3)
U16_gagaa(x1, x2, x3, x4, x5, x6) = U16_gagaa(x1, x3, x6)
*(x1, x2) = *(x1, x2)
U4_ga(x1, x2, x3, x4) = U4_ga(x1, x2, x4)
pE_in_gagaa(x1, x2, x3, x4, x5) = pE_in_gagaa(x1, x3)
U20_gagaa(x1, x2, x3, x4, x5, x6) = U20_gagaa(x1, x3, x6)
U5_ga(x1, x2) = U5_ga(x1, x2)
myintegerF_in_g(x1) = myintegerF_in_g(x1)
s(x1) = s(x1)
U10_g(x1, x2) = U10_g(x1, x2)
0 = 0
myintegerF_out_g(x1) = myintegerF_out_g(x1)
evaluateB_out_ga(x1, x2) = evaluateB_out_ga(x1, x2)
U21_gagaa(x1, x2, x3, x4, x5, x6) = U21_gagaa(x1, x2, x3, x6)
pP_in_gaga(x1, x2, x3, x4) = pP_in_gaga(x1, x3)
U22_gaga(x1, x2, x3, x4, x5) = U22_gaga(x1, x3, x5)
U23_gaga(x1, x2, x3, x4, x5) = U23_gaga(x1, x2, x3, x5)
multL_in_gga(x1, x2, x3) = multL_in_gga(x1, x2)
U11_gga(x1, x2, x3, x4) = U11_gga(x1, x2, x4)
pM_in_ggaa(x1, x2, x3, x4) = pM_in_ggaa(x1, x2)
U24_ggaa(x1, x2, x3, x4, x5) = U24_ggaa(x1, x2, x5)
multI_in_gga(x1, x2, x3) = multI_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4) = U8_gga(x1, x2, x4)
pJ_in_ggaa(x1, x2, x3, x4) = pJ_in_ggaa(x1, x2)
U26_ggaa(x1, x2, x3, x4, x5) = U26_ggaa(x1, x2, x5)
multI_out_gga(x1, x2, x3) = multI_out_gga(x1, x2, x3)
U27_ggaa(x1, x2, x3, x4, x5) = U27_ggaa(x1, x2, x3, x5)
addK_in_gga(x1, x2, x3) = addK_in_gga(x1, x2)
U9_gga(x1, x2, x3, x4) = U9_gga(x1, x2, x4)
addK_out_gga(x1, x2, x3) = addK_out_gga(x1, x2, x3)
pJ_out_ggaa(x1, x2, x3, x4) = pJ_out_ggaa(x1, x2, x3, x4)
U25_ggaa(x1, x2, x3, x4, x5) = U25_ggaa(x1, x2, x3, x5)
addG_in_gga(x1, x2, x3) = addG_in_gga(x1, x2)
U6_gga(x1, x2, x3, x4) = U6_gga(x1, x2, x4)
addG_out_gga(x1, x2, x3) = addG_out_gga(x1, x2, x3)
pM_out_ggaa(x1, x2, x3, x4) = pM_out_ggaa(x1, x2, x3, x4)
multL_out_gga(x1, x2, x3) = multL_out_gga(x1, x2, x3)
pP_out_gaga(x1, x2, x3, x4) = pP_out_gaga(x1, x2, x3, x4)
pE_out_gagaa(x1, x2, x3, x4, x5) = pE_out_gagaa(x1, x2, x3, x4, x5)
U17_gagaa(x1, x2, x3, x4, x5, x6) = U17_gagaa(x1, x2, x3, x6)
pO_in_gaga(x1, x2, x3, x4) = pO_in_gaga(x1, x3)
U18_gaga(x1, x2, x3, x4, x5) = U18_gaga(x1, x3, x5)
U19_gaga(x1, x2, x3, x4, x5) = U19_gaga(x1, x2, x3, x5)
subH_in_gga(x1, x2, x3) = subH_in_gga(x1, x2)
U7_gga(x1, x2, x3, x4) = U7_gga(x1, x2, x4)
subH_out_gga(x1, x2, x3) = subH_out_gga(x1, x2, x3)
pO_out_gaga(x1, x2, x3, x4) = pO_out_gaga(x1, x2, x3, x4)
pD_out_gagaa(x1, x2, x3, x4, x5) = pD_out_gagaa(x1, x2, x3, x4, x5)
U13_gagaa(x1, x2, x3, x4, x5, x6) = U13_gagaa(x1, x2, x3, x6)
pN_in_gaga(x1, x2, x3, x4) = pN_in_gaga(x1, x3)
U14_gaga(x1, x2, x3, x4, x5) = U14_gaga(x1, x3, x5)
U15_gaga(x1, x2, x3, x4, x5) = U15_gaga(x1, x2, x3, x5)
pN_out_gaga(x1, x2, x3, x4) = pN_out_gaga(x1, x2, x3, x4)
pC_out_gagaa(x1, x2, x3, x4, x5) = pC_out_gagaa(x1, x2, x3, x4, x5)
myisA_out_ag(x1, x2) = myisA_out_ag(x1, x2)
MYISA_IN_AG(x1, x2) = MYISA_IN_AG(x2)
U1_AG(x1, x2, x3) = U1_AG(x2, x3)
EVALUATEB_IN_GA(x1, x2) = EVALUATEB_IN_GA(x1)
U2_GA(x1, x2, x3, x4) = U2_GA(x1, x2, x4)
PC_IN_GAGAA(x1, x2, x3, x4, x5) = PC_IN_GAGAA(x1, x3)
U12_GAGAA(x1, x2, x3, x4, x5, x6) = U12_GAGAA(x1, x3, x6)
U3_GA(x1, x2, x3, x4) = U3_GA(x1, x2, x4)
PD_IN_GAGAA(x1, x2, x3, x4, x5) = PD_IN_GAGAA(x1, x3)
U16_GAGAA(x1, x2, x3, x4, x5, x6) = U16_GAGAA(x1, x3, x6)
U4_GA(x1, x2, x3, x4) = U4_GA(x1, x2, x4)
PE_IN_GAGAA(x1, x2, x3, x4, x5) = PE_IN_GAGAA(x1, x3)
U20_GAGAA(x1, x2, x3, x4, x5, x6) = U20_GAGAA(x1, x3, x6)
U5_GA(x1, x2) = U5_GA(x1, x2)
MYINTEGERF_IN_G(x1) = MYINTEGERF_IN_G(x1)
U10_G(x1, x2) = U10_G(x1, x2)
U21_GAGAA(x1, x2, x3, x4, x5, x6) = U21_GAGAA(x1, x2, x3, x6)
PP_IN_GAGA(x1, x2, x3, x4) = PP_IN_GAGA(x1, x3)
U22_GAGA(x1, x2, x3, x4, x5) = U22_GAGA(x1, x3, x5)
U23_GAGA(x1, x2, x3, x4, x5) = U23_GAGA(x1, x2, x3, x5)
MULTL_IN_GGA(x1, x2, x3) = MULTL_IN_GGA(x1, x2)
U11_GGA(x1, x2, x3, x4) = U11_GGA(x1, x2, x4)
PM_IN_GGAA(x1, x2, x3, x4) = PM_IN_GGAA(x1, x2)
U24_GGAA(x1, x2, x3, x4, x5) = U24_GGAA(x1, x2, x5)
MULTI_IN_GGA(x1, x2, x3) = MULTI_IN_GGA(x1, x2)
U8_GGA(x1, x2, x3, x4) = U8_GGA(x1, x2, x4)
PJ_IN_GGAA(x1, x2, x3, x4) = PJ_IN_GGAA(x1, x2)
U26_GGAA(x1, x2, x3, x4, x5) = U26_GGAA(x1, x2, x5)
U27_GGAA(x1, x2, x3, x4, x5) = U27_GGAA(x1, x2, x3, x5)
ADDK_IN_GGA(x1, x2, x3) = ADDK_IN_GGA(x1, x2)
U9_GGA(x1, x2, x3, x4) = U9_GGA(x1, x2, x4)
U25_GGAA(x1, x2, x3, x4, x5) = U25_GGAA(x1, x2, x3, x5)
ADDG_IN_GGA(x1, x2, x3) = ADDG_IN_GGA(x1, x2)
U6_GGA(x1, x2, x3, x4) = U6_GGA(x1, x2, x4)
U17_GAGAA(x1, x2, x3, x4, x5, x6) = U17_GAGAA(x1, x2, x3, x6)
PO_IN_GAGA(x1, x2, x3, x4) = PO_IN_GAGA(x1, x3)
U18_GAGA(x1, x2, x3, x4, x5) = U18_GAGA(x1, x3, x5)
U19_GAGA(x1, x2, x3, x4, x5) = U19_GAGA(x1, x2, x3, x5)
SUBH_IN_GGA(x1, x2, x3) = SUBH_IN_GGA(x1, x2)
U7_GGA(x1, x2, x3, x4) = U7_GGA(x1, x2, x4)
U13_GAGAA(x1, x2, x3, x4, x5, x6) = U13_GAGAA(x1, x2, x3, x6)
PN_IN_GAGA(x1, x2, x3, x4) = PN_IN_GAGA(x1, x3)
U14_GAGA(x1, x2, x3, x4, x5) = U14_GAGA(x1, x3, x5)
U15_GAGA(x1, x2, x3, x4, x5) = U15_GAGA(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:

MYISA_IN_AG(T7, T6) → U1_AG(T7, T6, evaluateB_in_ga(T6, T7))
MYISA_IN_AG(T7, T6) → EVALUATEB_IN_GA(T6, T7)
EVALUATEB_IN_GA(+(T20, T21), T23) → U2_GA(T20, T21, T23, pC_in_gagaa(T20, X25, T21, X26, T23))
EVALUATEB_IN_GA(+(T20, T21), T23) → PC_IN_GAGAA(T20, X25, T21, X26, T23)
PC_IN_GAGAA(T20, T26, T21, X26, T23) → U12_GAGAA(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
PC_IN_GAGAA(T20, T26, T21, X26, T23) → EVALUATEB_IN_GA(T20, T26)
EVALUATEB_IN_GA(-(T71, T72), T74) → U3_GA(T71, T72, T74, pD_in_gagaa(T71, X94, T72, X95, T74))
EVALUATEB_IN_GA(-(T71, T72), T74) → PD_IN_GAGAA(T71, X94, T72, X95, T74)
PD_IN_GAGAA(T71, T77, T72, X95, T74) → U16_GAGAA(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
PD_IN_GAGAA(T71, T77, T72, X95, T74) → EVALUATEB_IN_GA(T71, T77)
EVALUATEB_IN_GA(*(T122, T123), T125) → U4_GA(T122, T123, T125, pE_in_gagaa(T122, X163, T123, X164, T125))
EVALUATEB_IN_GA(*(T122, T123), T125) → PE_IN_GAGAA(T122, X163, T123, X164, T125)
PE_IN_GAGAA(T122, T128, T123, X164, T125) → U20_GAGAA(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
PE_IN_GAGAA(T122, T128, T123, X164, T125) → EVALUATEB_IN_GA(T122, T128)
EVALUATEB_IN_GA(T203, T203) → U5_GA(T203, myintegerF_in_g(T203))
EVALUATEB_IN_GA(T203, T203) → MYINTEGERF_IN_G(T203)
MYINTEGERF_IN_G(s(T209)) → U10_G(T209, myintegerF_in_g(T209))
MYINTEGERF_IN_G(s(T209)) → MYINTEGERF_IN_G(T209)
U20_GAGAA(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → U21_GAGAA(T122, T128, T123, X164, T125, pP_in_gaga(T123, X164, T128, T125))
U20_GAGAA(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → PP_IN_GAGA(T123, X164, T128, T125)
PP_IN_GAGA(T123, T133, T128, T125) → U22_GAGA(T123, T133, T128, T125, evaluateB_in_ga(T123, T133))
PP_IN_GAGA(T123, T133, T128, T125) → EVALUATEB_IN_GA(T123, T133)
U22_GAGA(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → U23_GAGA(T123, T133, T128, T125, multL_in_gga(T128, T133, T125))
U22_GAGA(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → MULTL_IN_GGA(T128, T133, T125)
MULTL_IN_GGA(s(T151), T152, T154) → U11_GGA(T151, T152, T154, pM_in_ggaa(T151, T152, X210, T154))
MULTL_IN_GGA(s(T151), T152, T154) → PM_IN_GGAA(T151, T152, X210, T154)
PM_IN_GGAA(T151, T152, T157, T154) → U24_GGAA(T151, T152, T157, T154, multI_in_gga(T151, T152, T157))
PM_IN_GGAA(T151, T152, T157, T154) → MULTI_IN_GGA(T151, T152, T157)
MULTI_IN_GGA(s(T168), T169, X243) → U8_GGA(T168, T169, X243, pJ_in_ggaa(T168, T169, X242, X243))
MULTI_IN_GGA(s(T168), T169, X243) → PJ_IN_GGAA(T168, T169, X242, X243)
PJ_IN_GGAA(T168, T169, T172, X243) → U26_GGAA(T168, T169, T172, X243, multI_in_gga(T168, T169, T172))
PJ_IN_GGAA(T168, T169, T172, X243) → MULTI_IN_GGA(T168, T169, T172)
U26_GGAA(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → U27_GGAA(T168, T169, T172, X243, addK_in_gga(T169, T172, X243))
U26_GGAA(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → ADDK_IN_GGA(T169, T172, X243)
ADDK_IN_GGA(s(T185), T186, s(X277)) → U9_GGA(T185, T186, X277, addK_in_gga(T185, T186, X277))
ADDK_IN_GGA(s(T185), T186, s(X277)) → ADDK_IN_GGA(T185, T186, X277)
U24_GGAA(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → U25_GGAA(T151, T152, T157, T154, addG_in_gga(T152, T157, T154))
U24_GGAA(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → ADDG_IN_GGA(T152, T157, T154)
ADDG_IN_GGA(s(T49), T50, s(T52)) → U6_GGA(T49, T50, T52, addG_in_gga(T49, T50, T52))
ADDG_IN_GGA(s(T49), T50, s(T52)) → ADDG_IN_GGA(T49, T50, T52)
U16_GAGAA(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → U17_GAGAA(T71, T77, T72, X95, T74, pO_in_gaga(T72, X95, T77, T74))
U16_GAGAA(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → PO_IN_GAGA(T72, X95, T77, T74)
PO_IN_GAGA(T72, T82, T77, T74) → U18_GAGA(T72, T82, T77, T74, evaluateB_in_ga(T72, T82))
PO_IN_GAGA(T72, T82, T77, T74) → EVALUATEB_IN_GA(T72, T82)
U18_GAGA(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → U19_GAGA(T72, T82, T77, T74, subH_in_gga(T77, T82, T74))
U18_GAGA(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → SUBH_IN_GGA(T77, T82, T74)
SUBH_IN_GGA(s(T100), s(T101), T103) → U7_GGA(T100, T101, T103, subH_in_gga(T100, T101, T103))
SUBH_IN_GGA(s(T100), s(T101), T103) → SUBH_IN_GGA(T100, T101, T103)
U12_GAGAA(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → U13_GAGAA(T20, T26, T21, X26, T23, pN_in_gaga(T21, X26, T26, T23))
U12_GAGAA(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → PN_IN_GAGA(T21, X26, T26, T23)
PN_IN_GAGA(T21, T31, T26, T23) → U14_GAGA(T21, T31, T26, T23, evaluateB_in_ga(T21, T31))
PN_IN_GAGA(T21, T31, T26, T23) → EVALUATEB_IN_GA(T21, T31)
U14_GAGA(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → U15_GAGA(T21, T31, T26, T23, addG_in_gga(T26, T31, T23))
U14_GAGA(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → ADDG_IN_GGA(T26, T31, T23)

The TRS R consists of the following rules:

myisA_in_ag(T7, T6) → U1_ag(T7, T6, evaluateB_in_ga(T6, T7))
evaluateB_in_ga(+(T20, T21), T23) → U2_ga(T20, T21, T23, pC_in_gagaa(T20, X25, T21, X26, T23))
pC_in_gagaa(T20, T26, T21, X26, T23) → U12_gagaa(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
evaluateB_in_ga(-(T71, T72), T74) → U3_ga(T71, T72, T74, pD_in_gagaa(T71, X94, T72, X95, T74))
pD_in_gagaa(T71, T77, T72, X95, T74) → U16_gagaa(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
evaluateB_in_ga(*(T122, T123), T125) → U4_ga(T122, T123, T125, pE_in_gagaa(T122, X163, T123, X164, T125))
pE_in_gagaa(T122, T128, T123, X164, T125) → U20_gagaa(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
evaluateB_in_ga(T203, T203) → U5_ga(T203, myintegerF_in_g(T203))
myintegerF_in_g(s(T209)) → U10_g(T209, myintegerF_in_g(T209))
myintegerF_in_g(0) → myintegerF_out_g(0)
U10_g(T209, myintegerF_out_g(T209)) → myintegerF_out_g(s(T209))
U5_ga(T203, myintegerF_out_g(T203)) → evaluateB_out_ga(T203, T203)
U20_gagaa(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → U21_gagaa(T122, T128, T123, X164, T125, pP_in_gaga(T123, X164, T128, T125))
pP_in_gaga(T123, T133, T128, T125) → U22_gaga(T123, T133, T128, T125, evaluateB_in_ga(T123, T133))
U22_gaga(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → U23_gaga(T123, T133, T128, T125, multL_in_gga(T128, T133, T125))
multL_in_gga(s(T151), T152, T154) → U11_gga(T151, T152, T154, pM_in_ggaa(T151, T152, X210, T154))
pM_in_ggaa(T151, T152, T157, T154) → U24_ggaa(T151, T152, T157, T154, multI_in_gga(T151, T152, T157))
multI_in_gga(s(T168), T169, X243) → U8_gga(T168, T169, X243, pJ_in_ggaa(T168, T169, X242, X243))
pJ_in_ggaa(T168, T169, T172, X243) → U26_ggaa(T168, T169, T172, X243, multI_in_gga(T168, T169, T172))
multI_in_gga(0, T194, 0) → multI_out_gga(0, T194, 0)
U26_ggaa(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → U27_ggaa(T168, T169, T172, X243, addK_in_gga(T169, T172, X243))
addK_in_gga(s(T185), T186, s(X277)) → U9_gga(T185, T186, X277, addK_in_gga(T185, T186, X277))
addK_in_gga(0, T191, T191) → addK_out_gga(0, T191, T191)
U9_gga(T185, T186, X277, addK_out_gga(T185, T186, X277)) → addK_out_gga(s(T185), T186, s(X277))
U27_ggaa(T168, T169, T172, X243, addK_out_gga(T169, T172, X243)) → pJ_out_ggaa(T168, T169, T172, X243)
U8_gga(T168, T169, X243, pJ_out_ggaa(T168, T169, X242, X243)) → multI_out_gga(s(T168), T169, X243)
U24_ggaa(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → U25_ggaa(T151, T152, T157, T154, addG_in_gga(T152, T157, T154))
addG_in_gga(s(T49), T50, s(T52)) → U6_gga(T49, T50, T52, addG_in_gga(T49, T50, T52))
addG_in_gga(0, T58, T58) → addG_out_gga(0, T58, T58)
U6_gga(T49, T50, T52, addG_out_gga(T49, T50, T52)) → addG_out_gga(s(T49), T50, s(T52))
U25_ggaa(T151, T152, T157, T154, addG_out_gga(T152, T157, T154)) → pM_out_ggaa(T151, T152, T157, T154)
U11_gga(T151, T152, T154, pM_out_ggaa(T151, T152, X210, T154)) → multL_out_gga(s(T151), T152, T154)
multL_in_gga(0, T200, 0) → multL_out_gga(0, T200, 0)
U23_gaga(T123, T133, T128, T125, multL_out_gga(T128, T133, T125)) → pP_out_gaga(T123, T133, T128, T125)
U21_gagaa(T122, T128, T123, X164, T125, pP_out_gaga(T123, X164, T128, T125)) → pE_out_gagaa(T122, T128, T123, X164, T125)
U4_ga(T122, T123, T125, pE_out_gagaa(T122, X163, T123, X164, T125)) → evaluateB_out_ga(*(T122, T123), T125)
U16_gagaa(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → U17_gagaa(T71, T77, T72, X95, T74, pO_in_gaga(T72, X95, T77, T74))
pO_in_gaga(T72, T82, T77, T74) → U18_gaga(T72, T82, T77, T74, evaluateB_in_ga(T72, T82))
U18_gaga(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → U19_gaga(T72, T82, T77, T74, subH_in_gga(T77, T82, T74))
subH_in_gga(s(T100), s(T101), T103) → U7_gga(T100, T101, T103, subH_in_gga(T100, T101, T103))
subH_in_gga(T109, 0, T109) → subH_out_gga(T109, 0, T109)
U7_gga(T100, T101, T103, subH_out_gga(T100, T101, T103)) → subH_out_gga(s(T100), s(T101), T103)
U19_gaga(T72, T82, T77, T74, subH_out_gga(T77, T82, T74)) → pO_out_gaga(T72, T82, T77, T74)
U17_gagaa(T71, T77, T72, X95, T74, pO_out_gaga(T72, X95, T77, T74)) → pD_out_gagaa(T71, T77, T72, X95, T74)
U3_ga(T71, T72, T74, pD_out_gagaa(T71, X94, T72, X95, T74)) → evaluateB_out_ga(-(T71, T72), T74)
U12_gagaa(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → U13_gagaa(T20, T26, T21, X26, T23, pN_in_gaga(T21, X26, T26, T23))
pN_in_gaga(T21, T31, T26, T23) → U14_gaga(T21, T31, T26, T23, evaluateB_in_ga(T21, T31))
U14_gaga(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → U15_gaga(T21, T31, T26, T23, addG_in_gga(T26, T31, T23))
U15_gaga(T21, T31, T26, T23, addG_out_gga(T26, T31, T23)) → pN_out_gaga(T21, T31, T26, T23)
U13_gagaa(T20, T26, T21, X26, T23, pN_out_gaga(T21, X26, T26, T23)) → pC_out_gagaa(T20, T26, T21, X26, T23)
U2_ga(T20, T21, T23, pC_out_gagaa(T20, X25, T21, X26, T23)) → evaluateB_out_ga(+(T20, T21), T23)
U1_ag(T7, T6, evaluateB_out_ga(T6, T7)) → myisA_out_ag(T7, T6)

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 6 SCCs with 33 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

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

SUBH_IN_GGA(s(T100), s(T101), T103) → SUBH_IN_GGA(T100, T101, T103)

The TRS R consists of the following rules:

myisA_in_ag(T7, T6) → U1_ag(T7, T6, evaluateB_in_ga(T6, T7))
evaluateB_in_ga(+(T20, T21), T23) → U2_ga(T20, T21, T23, pC_in_gagaa(T20, X25, T21, X26, T23))
pC_in_gagaa(T20, T26, T21, X26, T23) → U12_gagaa(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
evaluateB_in_ga(-(T71, T72), T74) → U3_ga(T71, T72, T74, pD_in_gagaa(T71, X94, T72, X95, T74))
pD_in_gagaa(T71, T77, T72, X95, T74) → U16_gagaa(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
evaluateB_in_ga(*(T122, T123), T125) → U4_ga(T122, T123, T125, pE_in_gagaa(T122, X163, T123, X164, T125))
pE_in_gagaa(T122, T128, T123, X164, T125) → U20_gagaa(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
evaluateB_in_ga(T203, T203) → U5_ga(T203, myintegerF_in_g(T203))
myintegerF_in_g(s(T209)) → U10_g(T209, myintegerF_in_g(T209))
myintegerF_in_g(0) → myintegerF_out_g(0)
U10_g(T209, myintegerF_out_g(T209)) → myintegerF_out_g(s(T209))
U5_ga(T203, myintegerF_out_g(T203)) → evaluateB_out_ga(T203, T203)
U20_gagaa(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → U21_gagaa(T122, T128, T123, X164, T125, pP_in_gaga(T123, X164, T128, T125))
pP_in_gaga(T123, T133, T128, T125) → U22_gaga(T123, T133, T128, T125, evaluateB_in_ga(T123, T133))
U22_gaga(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → U23_gaga(T123, T133, T128, T125, multL_in_gga(T128, T133, T125))
multL_in_gga(s(T151), T152, T154) → U11_gga(T151, T152, T154, pM_in_ggaa(T151, T152, X210, T154))
pM_in_ggaa(T151, T152, T157, T154) → U24_ggaa(T151, T152, T157, T154, multI_in_gga(T151, T152, T157))
multI_in_gga(s(T168), T169, X243) → U8_gga(T168, T169, X243, pJ_in_ggaa(T168, T169, X242, X243))
pJ_in_ggaa(T168, T169, T172, X243) → U26_ggaa(T168, T169, T172, X243, multI_in_gga(T168, T169, T172))
multI_in_gga(0, T194, 0) → multI_out_gga(0, T194, 0)
U26_ggaa(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → U27_ggaa(T168, T169, T172, X243, addK_in_gga(T169, T172, X243))
addK_in_gga(s(T185), T186, s(X277)) → U9_gga(T185, T186, X277, addK_in_gga(T185, T186, X277))
addK_in_gga(0, T191, T191) → addK_out_gga(0, T191, T191)
U9_gga(T185, T186, X277, addK_out_gga(T185, T186, X277)) → addK_out_gga(s(T185), T186, s(X277))
U27_ggaa(T168, T169, T172, X243, addK_out_gga(T169, T172, X243)) → pJ_out_ggaa(T168, T169, T172, X243)
U8_gga(T168, T169, X243, pJ_out_ggaa(T168, T169, X242, X243)) → multI_out_gga(s(T168), T169, X243)
U24_ggaa(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → U25_ggaa(T151, T152, T157, T154, addG_in_gga(T152, T157, T154))
addG_in_gga(s(T49), T50, s(T52)) → U6_gga(T49, T50, T52, addG_in_gga(T49, T50, T52))
addG_in_gga(0, T58, T58) → addG_out_gga(0, T58, T58)
U6_gga(T49, T50, T52, addG_out_gga(T49, T50, T52)) → addG_out_gga(s(T49), T50, s(T52))
U25_ggaa(T151, T152, T157, T154, addG_out_gga(T152, T157, T154)) → pM_out_ggaa(T151, T152, T157, T154)
U11_gga(T151, T152, T154, pM_out_ggaa(T151, T152, X210, T154)) → multL_out_gga(s(T151), T152, T154)
multL_in_gga(0, T200, 0) → multL_out_gga(0, T200, 0)
U23_gaga(T123, T133, T128, T125, multL_out_gga(T128, T133, T125)) → pP_out_gaga(T123, T133, T128, T125)
U21_gagaa(T122, T128, T123, X164, T125, pP_out_gaga(T123, X164, T128, T125)) → pE_out_gagaa(T122, T128, T123, X164, T125)
U4_ga(T122, T123, T125, pE_out_gagaa(T122, X163, T123, X164, T125)) → evaluateB_out_ga(*(T122, T123), T125)
U16_gagaa(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → U17_gagaa(T71, T77, T72, X95, T74, pO_in_gaga(T72, X95, T77, T74))
pO_in_gaga(T72, T82, T77, T74) → U18_gaga(T72, T82, T77, T74, evaluateB_in_ga(T72, T82))
U18_gaga(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → U19_gaga(T72, T82, T77, T74, subH_in_gga(T77, T82, T74))
subH_in_gga(s(T100), s(T101), T103) → U7_gga(T100, T101, T103, subH_in_gga(T100, T101, T103))
subH_in_gga(T109, 0, T109) → subH_out_gga(T109, 0, T109)
U7_gga(T100, T101, T103, subH_out_gga(T100, T101, T103)) → subH_out_gga(s(T100), s(T101), T103)
U19_gaga(T72, T82, T77, T74, subH_out_gga(T77, T82, T74)) → pO_out_gaga(T72, T82, T77, T74)
U17_gagaa(T71, T77, T72, X95, T74, pO_out_gaga(T72, X95, T77, T74)) → pD_out_gagaa(T71, T77, T72, X95, T74)
U3_ga(T71, T72, T74, pD_out_gagaa(T71, X94, T72, X95, T74)) → evaluateB_out_ga(-(T71, T72), T74)
U12_gagaa(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → U13_gagaa(T20, T26, T21, X26, T23, pN_in_gaga(T21, X26, T26, T23))
pN_in_gaga(T21, T31, T26, T23) → U14_gaga(T21, T31, T26, T23, evaluateB_in_ga(T21, T31))
U14_gaga(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → U15_gaga(T21, T31, T26, T23, addG_in_gga(T26, T31, T23))
U15_gaga(T21, T31, T26, T23, addG_out_gga(T26, T31, T23)) → pN_out_gaga(T21, T31, T26, T23)
U13_gagaa(T20, T26, T21, X26, T23, pN_out_gaga(T21, X26, T26, T23)) → pC_out_gagaa(T20, T26, T21, X26, T23)
U2_ga(T20, T21, T23, pC_out_gagaa(T20, X25, T21, X26, T23)) → evaluateB_out_ga(+(T20, T21), T23)
U1_ag(T7, T6, evaluateB_out_ga(T6, T7)) → myisA_out_ag(T7, T6)

(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:

SUBH_IN_GGA(s(T100), s(T101), T103) → SUBH_IN_GGA(T100, T101, T103)

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

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

(10) PiDPToQDPProof (SOUND transformation)

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

(11) Obligation:

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

SUBH_IN_GGA(s(T100), s(T101)) → SUBH_IN_GGA(T100, T101)

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:

SUBH_IN_GGA(s(T100), s(T101)) → SUBH_IN_GGA(T100, T101)
The graph contains the following edges 1 > 1, 2 > 2

(13) YES

(14) Obligation:

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

ADDG_IN_GGA(s(T49), T50, s(T52)) → ADDG_IN_GGA(T49, T50, T52)

The TRS R consists of the following rules:

myisA_in_ag(T7, T6) → U1_ag(T7, T6, evaluateB_in_ga(T6, T7))
evaluateB_in_ga(+(T20, T21), T23) → U2_ga(T20, T21, T23, pC_in_gagaa(T20, X25, T21, X26, T23))
pC_in_gagaa(T20, T26, T21, X26, T23) → U12_gagaa(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
evaluateB_in_ga(-(T71, T72), T74) → U3_ga(T71, T72, T74, pD_in_gagaa(T71, X94, T72, X95, T74))
pD_in_gagaa(T71, T77, T72, X95, T74) → U16_gagaa(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
evaluateB_in_ga(*(T122, T123), T125) → U4_ga(T122, T123, T125, pE_in_gagaa(T122, X163, T123, X164, T125))
pE_in_gagaa(T122, T128, T123, X164, T125) → U20_gagaa(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
evaluateB_in_ga(T203, T203) → U5_ga(T203, myintegerF_in_g(T203))
myintegerF_in_g(s(T209)) → U10_g(T209, myintegerF_in_g(T209))
myintegerF_in_g(0) → myintegerF_out_g(0)
U10_g(T209, myintegerF_out_g(T209)) → myintegerF_out_g(s(T209))
U5_ga(T203, myintegerF_out_g(T203)) → evaluateB_out_ga(T203, T203)
U20_gagaa(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → U21_gagaa(T122, T128, T123, X164, T125, pP_in_gaga(T123, X164, T128, T125))
pP_in_gaga(T123, T133, T128, T125) → U22_gaga(T123, T133, T128, T125, evaluateB_in_ga(T123, T133))
U22_gaga(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → U23_gaga(T123, T133, T128, T125, multL_in_gga(T128, T133, T125))
multL_in_gga(s(T151), T152, T154) → U11_gga(T151, T152, T154, pM_in_ggaa(T151, T152, X210, T154))
pM_in_ggaa(T151, T152, T157, T154) → U24_ggaa(T151, T152, T157, T154, multI_in_gga(T151, T152, T157))
multI_in_gga(s(T168), T169, X243) → U8_gga(T168, T169, X243, pJ_in_ggaa(T168, T169, X242, X243))
pJ_in_ggaa(T168, T169, T172, X243) → U26_ggaa(T168, T169, T172, X243, multI_in_gga(T168, T169, T172))
multI_in_gga(0, T194, 0) → multI_out_gga(0, T194, 0)
U26_ggaa(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → U27_ggaa(T168, T169, T172, X243, addK_in_gga(T169, T172, X243))
addK_in_gga(s(T185), T186, s(X277)) → U9_gga(T185, T186, X277, addK_in_gga(T185, T186, X277))
addK_in_gga(0, T191, T191) → addK_out_gga(0, T191, T191)
U9_gga(T185, T186, X277, addK_out_gga(T185, T186, X277)) → addK_out_gga(s(T185), T186, s(X277))
U27_ggaa(T168, T169, T172, X243, addK_out_gga(T169, T172, X243)) → pJ_out_ggaa(T168, T169, T172, X243)
U8_gga(T168, T169, X243, pJ_out_ggaa(T168, T169, X242, X243)) → multI_out_gga(s(T168), T169, X243)
U24_ggaa(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → U25_ggaa(T151, T152, T157, T154, addG_in_gga(T152, T157, T154))
addG_in_gga(s(T49), T50, s(T52)) → U6_gga(T49, T50, T52, addG_in_gga(T49, T50, T52))
addG_in_gga(0, T58, T58) → addG_out_gga(0, T58, T58)
U6_gga(T49, T50, T52, addG_out_gga(T49, T50, T52)) → addG_out_gga(s(T49), T50, s(T52))
U25_ggaa(T151, T152, T157, T154, addG_out_gga(T152, T157, T154)) → pM_out_ggaa(T151, T152, T157, T154)
U11_gga(T151, T152, T154, pM_out_ggaa(T151, T152, X210, T154)) → multL_out_gga(s(T151), T152, T154)
multL_in_gga(0, T200, 0) → multL_out_gga(0, T200, 0)
U23_gaga(T123, T133, T128, T125, multL_out_gga(T128, T133, T125)) → pP_out_gaga(T123, T133, T128, T125)
U21_gagaa(T122, T128, T123, X164, T125, pP_out_gaga(T123, X164, T128, T125)) → pE_out_gagaa(T122, T128, T123, X164, T125)
U4_ga(T122, T123, T125, pE_out_gagaa(T122, X163, T123, X164, T125)) → evaluateB_out_ga(*(T122, T123), T125)
U16_gagaa(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → U17_gagaa(T71, T77, T72, X95, T74, pO_in_gaga(T72, X95, T77, T74))
pO_in_gaga(T72, T82, T77, T74) → U18_gaga(T72, T82, T77, T74, evaluateB_in_ga(T72, T82))
U18_gaga(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → U19_gaga(T72, T82, T77, T74, subH_in_gga(T77, T82, T74))
subH_in_gga(s(T100), s(T101), T103) → U7_gga(T100, T101, T103, subH_in_gga(T100, T101, T103))
subH_in_gga(T109, 0, T109) → subH_out_gga(T109, 0, T109)
U7_gga(T100, T101, T103, subH_out_gga(T100, T101, T103)) → subH_out_gga(s(T100), s(T101), T103)
U19_gaga(T72, T82, T77, T74, subH_out_gga(T77, T82, T74)) → pO_out_gaga(T72, T82, T77, T74)
U17_gagaa(T71, T77, T72, X95, T74, pO_out_gaga(T72, X95, T77, T74)) → pD_out_gagaa(T71, T77, T72, X95, T74)
U3_ga(T71, T72, T74, pD_out_gagaa(T71, X94, T72, X95, T74)) → evaluateB_out_ga(-(T71, T72), T74)
U12_gagaa(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → U13_gagaa(T20, T26, T21, X26, T23, pN_in_gaga(T21, X26, T26, T23))
pN_in_gaga(T21, T31, T26, T23) → U14_gaga(T21, T31, T26, T23, evaluateB_in_ga(T21, T31))
U14_gaga(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → U15_gaga(T21, T31, T26, T23, addG_in_gga(T26, T31, T23))
U15_gaga(T21, T31, T26, T23, addG_out_gga(T26, T31, T23)) → pN_out_gaga(T21, T31, T26, T23)
U13_gagaa(T20, T26, T21, X26, T23, pN_out_gaga(T21, X26, T26, T23)) → pC_out_gagaa(T20, T26, T21, X26, T23)
U2_ga(T20, T21, T23, pC_out_gagaa(T20, X25, T21, X26, T23)) → evaluateB_out_ga(+(T20, T21), T23)
U1_ag(T7, T6, evaluateB_out_ga(T6, T7)) → myisA_out_ag(T7, T6)

(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:

ADDG_IN_GGA(s(T49), T50, s(T52)) → ADDG_IN_GGA(T49, T50, T52)

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

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

(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:

ADDG_IN_GGA(s(T49), T50) → ADDG_IN_GGA(T49, T50)

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:

ADDG_IN_GGA(s(T49), T50) → ADDG_IN_GGA(T49, T50)
The graph contains the following edges 1 > 1, 2 >= 2

(20) YES

(21) Obligation:

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

ADDK_IN_GGA(s(T185), T186, s(X277)) → ADDK_IN_GGA(T185, T186, X277)

The TRS R consists of the following rules:

myisA_in_ag(T7, T6) → U1_ag(T7, T6, evaluateB_in_ga(T6, T7))
evaluateB_in_ga(+(T20, T21), T23) → U2_ga(T20, T21, T23, pC_in_gagaa(T20, X25, T21, X26, T23))
pC_in_gagaa(T20, T26, T21, X26, T23) → U12_gagaa(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
evaluateB_in_ga(-(T71, T72), T74) → U3_ga(T71, T72, T74, pD_in_gagaa(T71, X94, T72, X95, T74))
pD_in_gagaa(T71, T77, T72, X95, T74) → U16_gagaa(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
evaluateB_in_ga(*(T122, T123), T125) → U4_ga(T122, T123, T125, pE_in_gagaa(T122, X163, T123, X164, T125))
pE_in_gagaa(T122, T128, T123, X164, T125) → U20_gagaa(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
evaluateB_in_ga(T203, T203) → U5_ga(T203, myintegerF_in_g(T203))
myintegerF_in_g(s(T209)) → U10_g(T209, myintegerF_in_g(T209))
myintegerF_in_g(0) → myintegerF_out_g(0)
U10_g(T209, myintegerF_out_g(T209)) → myintegerF_out_g(s(T209))
U5_ga(T203, myintegerF_out_g(T203)) → evaluateB_out_ga(T203, T203)
U20_gagaa(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → U21_gagaa(T122, T128, T123, X164, T125, pP_in_gaga(T123, X164, T128, T125))
pP_in_gaga(T123, T133, T128, T125) → U22_gaga(T123, T133, T128, T125, evaluateB_in_ga(T123, T133))
U22_gaga(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → U23_gaga(T123, T133, T128, T125, multL_in_gga(T128, T133, T125))
multL_in_gga(s(T151), T152, T154) → U11_gga(T151, T152, T154, pM_in_ggaa(T151, T152, X210, T154))
pM_in_ggaa(T151, T152, T157, T154) → U24_ggaa(T151, T152, T157, T154, multI_in_gga(T151, T152, T157))
multI_in_gga(s(T168), T169, X243) → U8_gga(T168, T169, X243, pJ_in_ggaa(T168, T169, X242, X243))
pJ_in_ggaa(T168, T169, T172, X243) → U26_ggaa(T168, T169, T172, X243, multI_in_gga(T168, T169, T172))
multI_in_gga(0, T194, 0) → multI_out_gga(0, T194, 0)
U26_ggaa(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → U27_ggaa(T168, T169, T172, X243, addK_in_gga(T169, T172, X243))
addK_in_gga(s(T185), T186, s(X277)) → U9_gga(T185, T186, X277, addK_in_gga(T185, T186, X277))
addK_in_gga(0, T191, T191) → addK_out_gga(0, T191, T191)
U9_gga(T185, T186, X277, addK_out_gga(T185, T186, X277)) → addK_out_gga(s(T185), T186, s(X277))
U27_ggaa(T168, T169, T172, X243, addK_out_gga(T169, T172, X243)) → pJ_out_ggaa(T168, T169, T172, X243)
U8_gga(T168, T169, X243, pJ_out_ggaa(T168, T169, X242, X243)) → multI_out_gga(s(T168), T169, X243)
U24_ggaa(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → U25_ggaa(T151, T152, T157, T154, addG_in_gga(T152, T157, T154))
addG_in_gga(s(T49), T50, s(T52)) → U6_gga(T49, T50, T52, addG_in_gga(T49, T50, T52))
addG_in_gga(0, T58, T58) → addG_out_gga(0, T58, T58)
U6_gga(T49, T50, T52, addG_out_gga(T49, T50, T52)) → addG_out_gga(s(T49), T50, s(T52))
U25_ggaa(T151, T152, T157, T154, addG_out_gga(T152, T157, T154)) → pM_out_ggaa(T151, T152, T157, T154)
U11_gga(T151, T152, T154, pM_out_ggaa(T151, T152, X210, T154)) → multL_out_gga(s(T151), T152, T154)
multL_in_gga(0, T200, 0) → multL_out_gga(0, T200, 0)
U23_gaga(T123, T133, T128, T125, multL_out_gga(T128, T133, T125)) → pP_out_gaga(T123, T133, T128, T125)
U21_gagaa(T122, T128, T123, X164, T125, pP_out_gaga(T123, X164, T128, T125)) → pE_out_gagaa(T122, T128, T123, X164, T125)
U4_ga(T122, T123, T125, pE_out_gagaa(T122, X163, T123, X164, T125)) → evaluateB_out_ga(*(T122, T123), T125)
U16_gagaa(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → U17_gagaa(T71, T77, T72, X95, T74, pO_in_gaga(T72, X95, T77, T74))
pO_in_gaga(T72, T82, T77, T74) → U18_gaga(T72, T82, T77, T74, evaluateB_in_ga(T72, T82))
U18_gaga(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → U19_gaga(T72, T82, T77, T74, subH_in_gga(T77, T82, T74))
subH_in_gga(s(T100), s(T101), T103) → U7_gga(T100, T101, T103, subH_in_gga(T100, T101, T103))
subH_in_gga(T109, 0, T109) → subH_out_gga(T109, 0, T109)
U7_gga(T100, T101, T103, subH_out_gga(T100, T101, T103)) → subH_out_gga(s(T100), s(T101), T103)
U19_gaga(T72, T82, T77, T74, subH_out_gga(T77, T82, T74)) → pO_out_gaga(T72, T82, T77, T74)
U17_gagaa(T71, T77, T72, X95, T74, pO_out_gaga(T72, X95, T77, T74)) → pD_out_gagaa(T71, T77, T72, X95, T74)
U3_ga(T71, T72, T74, pD_out_gagaa(T71, X94, T72, X95, T74)) → evaluateB_out_ga(-(T71, T72), T74)
U12_gagaa(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → U13_gagaa(T20, T26, T21, X26, T23, pN_in_gaga(T21, X26, T26, T23))
pN_in_gaga(T21, T31, T26, T23) → U14_gaga(T21, T31, T26, T23, evaluateB_in_ga(T21, T31))
U14_gaga(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → U15_gaga(T21, T31, T26, T23, addG_in_gga(T26, T31, T23))
U15_gaga(T21, T31, T26, T23, addG_out_gga(T26, T31, T23)) → pN_out_gaga(T21, T31, T26, T23)
U13_gagaa(T20, T26, T21, X26, T23, pN_out_gaga(T21, X26, T26, T23)) → pC_out_gagaa(T20, T26, T21, X26, T23)
U2_ga(T20, T21, T23, pC_out_gagaa(T20, X25, T21, X26, T23)) → evaluateB_out_ga(+(T20, T21), T23)
U1_ag(T7, T6, evaluateB_out_ga(T6, T7)) → myisA_out_ag(T7, T6)

(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:

ADDK_IN_GGA(s(T185), T186, s(X277)) → ADDK_IN_GGA(T185, T186, X277)

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

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:

ADDK_IN_GGA(s(T185), T186) → ADDK_IN_GGA(T185, T186)

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:

ADDK_IN_GGA(s(T185), T186) → ADDK_IN_GGA(T185, T186)
The graph contains the following edges 1 > 1, 2 >= 2

(27) YES

(28) Obligation:

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

MULTI_IN_GGA(s(T168), T169, X243) → PJ_IN_GGAA(T168, T169, X242, X243)
PJ_IN_GGAA(T168, T169, T172, X243) → MULTI_IN_GGA(T168, T169, T172)

The TRS R consists of the following rules:

myisA_in_ag(T7, T6) → U1_ag(T7, T6, evaluateB_in_ga(T6, T7))
evaluateB_in_ga(+(T20, T21), T23) → U2_ga(T20, T21, T23, pC_in_gagaa(T20, X25, T21, X26, T23))
pC_in_gagaa(T20, T26, T21, X26, T23) → U12_gagaa(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
evaluateB_in_ga(-(T71, T72), T74) → U3_ga(T71, T72, T74, pD_in_gagaa(T71, X94, T72, X95, T74))
pD_in_gagaa(T71, T77, T72, X95, T74) → U16_gagaa(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
evaluateB_in_ga(*(T122, T123), T125) → U4_ga(T122, T123, T125, pE_in_gagaa(T122, X163, T123, X164, T125))
pE_in_gagaa(T122, T128, T123, X164, T125) → U20_gagaa(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
evaluateB_in_ga(T203, T203) → U5_ga(T203, myintegerF_in_g(T203))
myintegerF_in_g(s(T209)) → U10_g(T209, myintegerF_in_g(T209))
myintegerF_in_g(0) → myintegerF_out_g(0)
U10_g(T209, myintegerF_out_g(T209)) → myintegerF_out_g(s(T209))
U5_ga(T203, myintegerF_out_g(T203)) → evaluateB_out_ga(T203, T203)
U20_gagaa(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → U21_gagaa(T122, T128, T123, X164, T125, pP_in_gaga(T123, X164, T128, T125))
pP_in_gaga(T123, T133, T128, T125) → U22_gaga(T123, T133, T128, T125, evaluateB_in_ga(T123, T133))
U22_gaga(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → U23_gaga(T123, T133, T128, T125, multL_in_gga(T128, T133, T125))
multL_in_gga(s(T151), T152, T154) → U11_gga(T151, T152, T154, pM_in_ggaa(T151, T152, X210, T154))
pM_in_ggaa(T151, T152, T157, T154) → U24_ggaa(T151, T152, T157, T154, multI_in_gga(T151, T152, T157))
multI_in_gga(s(T168), T169, X243) → U8_gga(T168, T169, X243, pJ_in_ggaa(T168, T169, X242, X243))
pJ_in_ggaa(T168, T169, T172, X243) → U26_ggaa(T168, T169, T172, X243, multI_in_gga(T168, T169, T172))
multI_in_gga(0, T194, 0) → multI_out_gga(0, T194, 0)
U26_ggaa(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → U27_ggaa(T168, T169, T172, X243, addK_in_gga(T169, T172, X243))
addK_in_gga(s(T185), T186, s(X277)) → U9_gga(T185, T186, X277, addK_in_gga(T185, T186, X277))
addK_in_gga(0, T191, T191) → addK_out_gga(0, T191, T191)
U9_gga(T185, T186, X277, addK_out_gga(T185, T186, X277)) → addK_out_gga(s(T185), T186, s(X277))
U27_ggaa(T168, T169, T172, X243, addK_out_gga(T169, T172, X243)) → pJ_out_ggaa(T168, T169, T172, X243)
U8_gga(T168, T169, X243, pJ_out_ggaa(T168, T169, X242, X243)) → multI_out_gga(s(T168), T169, X243)
U24_ggaa(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → U25_ggaa(T151, T152, T157, T154, addG_in_gga(T152, T157, T154))
addG_in_gga(s(T49), T50, s(T52)) → U6_gga(T49, T50, T52, addG_in_gga(T49, T50, T52))
addG_in_gga(0, T58, T58) → addG_out_gga(0, T58, T58)
U6_gga(T49, T50, T52, addG_out_gga(T49, T50, T52)) → addG_out_gga(s(T49), T50, s(T52))
U25_ggaa(T151, T152, T157, T154, addG_out_gga(T152, T157, T154)) → pM_out_ggaa(T151, T152, T157, T154)
U11_gga(T151, T152, T154, pM_out_ggaa(T151, T152, X210, T154)) → multL_out_gga(s(T151), T152, T154)
multL_in_gga(0, T200, 0) → multL_out_gga(0, T200, 0)
U23_gaga(T123, T133, T128, T125, multL_out_gga(T128, T133, T125)) → pP_out_gaga(T123, T133, T128, T125)
U21_gagaa(T122, T128, T123, X164, T125, pP_out_gaga(T123, X164, T128, T125)) → pE_out_gagaa(T122, T128, T123, X164, T125)
U4_ga(T122, T123, T125, pE_out_gagaa(T122, X163, T123, X164, T125)) → evaluateB_out_ga(*(T122, T123), T125)
U16_gagaa(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → U17_gagaa(T71, T77, T72, X95, T74, pO_in_gaga(T72, X95, T77, T74))
pO_in_gaga(T72, T82, T77, T74) → U18_gaga(T72, T82, T77, T74, evaluateB_in_ga(T72, T82))
U18_gaga(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → U19_gaga(T72, T82, T77, T74, subH_in_gga(T77, T82, T74))
subH_in_gga(s(T100), s(T101), T103) → U7_gga(T100, T101, T103, subH_in_gga(T100, T101, T103))
subH_in_gga(T109, 0, T109) → subH_out_gga(T109, 0, T109)
U7_gga(T100, T101, T103, subH_out_gga(T100, T101, T103)) → subH_out_gga(s(T100), s(T101), T103)
U19_gaga(T72, T82, T77, T74, subH_out_gga(T77, T82, T74)) → pO_out_gaga(T72, T82, T77, T74)
U17_gagaa(T71, T77, T72, X95, T74, pO_out_gaga(T72, X95, T77, T74)) → pD_out_gagaa(T71, T77, T72, X95, T74)
U3_ga(T71, T72, T74, pD_out_gagaa(T71, X94, T72, X95, T74)) → evaluateB_out_ga(-(T71, T72), T74)
U12_gagaa(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → U13_gagaa(T20, T26, T21, X26, T23, pN_in_gaga(T21, X26, T26, T23))
pN_in_gaga(T21, T31, T26, T23) → U14_gaga(T21, T31, T26, T23, evaluateB_in_ga(T21, T31))
U14_gaga(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → U15_gaga(T21, T31, T26, T23, addG_in_gga(T26, T31, T23))
U15_gaga(T21, T31, T26, T23, addG_out_gga(T26, T31, T23)) → pN_out_gaga(T21, T31, T26, T23)
U13_gagaa(T20, T26, T21, X26, T23, pN_out_gaga(T21, X26, T26, T23)) → pC_out_gagaa(T20, T26, T21, X26, T23)
U2_ga(T20, T21, T23, pC_out_gagaa(T20, X25, T21, X26, T23)) → evaluateB_out_ga(+(T20, T21), T23)
U1_ag(T7, T6, evaluateB_out_ga(T6, T7)) → myisA_out_ag(T7, T6)

(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:

MULTI_IN_GGA(s(T168), T169, X243) → PJ_IN_GGAA(T168, T169, X242, X243)
PJ_IN_GGAA(T168, T169, T172, X243) → MULTI_IN_GGA(T168, T169, T172)

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

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:

MULTI_IN_GGA(s(T168), T169) → PJ_IN_GGAA(T168, T169)
PJ_IN_GGAA(T168, T169) → MULTI_IN_GGA(T168, T169)

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:

PJ_IN_GGAA(T168, T169) → MULTI_IN_GGA(T168, T169)
The graph contains the following edges 1 >= 1, 2 >= 2
MULTI_IN_GGA(s(T168), T169) → PJ_IN_GGAA(T168, T169)
The graph contains the following edges 1 > 1, 2 >= 2

(34) YES

(35) Obligation:

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

MYINTEGERF_IN_G(s(T209)) → MYINTEGERF_IN_G(T209)

The TRS R consists of the following rules:

myisA_in_ag(T7, T6) → U1_ag(T7, T6, evaluateB_in_ga(T6, T7))
evaluateB_in_ga(+(T20, T21), T23) → U2_ga(T20, T21, T23, pC_in_gagaa(T20, X25, T21, X26, T23))
pC_in_gagaa(T20, T26, T21, X26, T23) → U12_gagaa(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
evaluateB_in_ga(-(T71, T72), T74) → U3_ga(T71, T72, T74, pD_in_gagaa(T71, X94, T72, X95, T74))
pD_in_gagaa(T71, T77, T72, X95, T74) → U16_gagaa(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
evaluateB_in_ga(*(T122, T123), T125) → U4_ga(T122, T123, T125, pE_in_gagaa(T122, X163, T123, X164, T125))
pE_in_gagaa(T122, T128, T123, X164, T125) → U20_gagaa(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
evaluateB_in_ga(T203, T203) → U5_ga(T203, myintegerF_in_g(T203))
myintegerF_in_g(s(T209)) → U10_g(T209, myintegerF_in_g(T209))
myintegerF_in_g(0) → myintegerF_out_g(0)
U10_g(T209, myintegerF_out_g(T209)) → myintegerF_out_g(s(T209))
U5_ga(T203, myintegerF_out_g(T203)) → evaluateB_out_ga(T203, T203)
U20_gagaa(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → U21_gagaa(T122, T128, T123, X164, T125, pP_in_gaga(T123, X164, T128, T125))
pP_in_gaga(T123, T133, T128, T125) → U22_gaga(T123, T133, T128, T125, evaluateB_in_ga(T123, T133))
U22_gaga(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → U23_gaga(T123, T133, T128, T125, multL_in_gga(T128, T133, T125))
multL_in_gga(s(T151), T152, T154) → U11_gga(T151, T152, T154, pM_in_ggaa(T151, T152, X210, T154))
pM_in_ggaa(T151, T152, T157, T154) → U24_ggaa(T151, T152, T157, T154, multI_in_gga(T151, T152, T157))
multI_in_gga(s(T168), T169, X243) → U8_gga(T168, T169, X243, pJ_in_ggaa(T168, T169, X242, X243))
pJ_in_ggaa(T168, T169, T172, X243) → U26_ggaa(T168, T169, T172, X243, multI_in_gga(T168, T169, T172))
multI_in_gga(0, T194, 0) → multI_out_gga(0, T194, 0)
U26_ggaa(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → U27_ggaa(T168, T169, T172, X243, addK_in_gga(T169, T172, X243))
addK_in_gga(s(T185), T186, s(X277)) → U9_gga(T185, T186, X277, addK_in_gga(T185, T186, X277))
addK_in_gga(0, T191, T191) → addK_out_gga(0, T191, T191)
U9_gga(T185, T186, X277, addK_out_gga(T185, T186, X277)) → addK_out_gga(s(T185), T186, s(X277))
U27_ggaa(T168, T169, T172, X243, addK_out_gga(T169, T172, X243)) → pJ_out_ggaa(T168, T169, T172, X243)
U8_gga(T168, T169, X243, pJ_out_ggaa(T168, T169, X242, X243)) → multI_out_gga(s(T168), T169, X243)
U24_ggaa(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → U25_ggaa(T151, T152, T157, T154, addG_in_gga(T152, T157, T154))
addG_in_gga(s(T49), T50, s(T52)) → U6_gga(T49, T50, T52, addG_in_gga(T49, T50, T52))
addG_in_gga(0, T58, T58) → addG_out_gga(0, T58, T58)
U6_gga(T49, T50, T52, addG_out_gga(T49, T50, T52)) → addG_out_gga(s(T49), T50, s(T52))
U25_ggaa(T151, T152, T157, T154, addG_out_gga(T152, T157, T154)) → pM_out_ggaa(T151, T152, T157, T154)
U11_gga(T151, T152, T154, pM_out_ggaa(T151, T152, X210, T154)) → multL_out_gga(s(T151), T152, T154)
multL_in_gga(0, T200, 0) → multL_out_gga(0, T200, 0)
U23_gaga(T123, T133, T128, T125, multL_out_gga(T128, T133, T125)) → pP_out_gaga(T123, T133, T128, T125)
U21_gagaa(T122, T128, T123, X164, T125, pP_out_gaga(T123, X164, T128, T125)) → pE_out_gagaa(T122, T128, T123, X164, T125)
U4_ga(T122, T123, T125, pE_out_gagaa(T122, X163, T123, X164, T125)) → evaluateB_out_ga(*(T122, T123), T125)
U16_gagaa(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → U17_gagaa(T71, T77, T72, X95, T74, pO_in_gaga(T72, X95, T77, T74))
pO_in_gaga(T72, T82, T77, T74) → U18_gaga(T72, T82, T77, T74, evaluateB_in_ga(T72, T82))
U18_gaga(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → U19_gaga(T72, T82, T77, T74, subH_in_gga(T77, T82, T74))
subH_in_gga(s(T100), s(T101), T103) → U7_gga(T100, T101, T103, subH_in_gga(T100, T101, T103))
subH_in_gga(T109, 0, T109) → subH_out_gga(T109, 0, T109)
U7_gga(T100, T101, T103, subH_out_gga(T100, T101, T103)) → subH_out_gga(s(T100), s(T101), T103)
U19_gaga(T72, T82, T77, T74, subH_out_gga(T77, T82, T74)) → pO_out_gaga(T72, T82, T77, T74)
U17_gagaa(T71, T77, T72, X95, T74, pO_out_gaga(T72, X95, T77, T74)) → pD_out_gagaa(T71, T77, T72, X95, T74)
U3_ga(T71, T72, T74, pD_out_gagaa(T71, X94, T72, X95, T74)) → evaluateB_out_ga(-(T71, T72), T74)
U12_gagaa(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → U13_gagaa(T20, T26, T21, X26, T23, pN_in_gaga(T21, X26, T26, T23))
pN_in_gaga(T21, T31, T26, T23) → U14_gaga(T21, T31, T26, T23, evaluateB_in_ga(T21, T31))
U14_gaga(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → U15_gaga(T21, T31, T26, T23, addG_in_gga(T26, T31, T23))
U15_gaga(T21, T31, T26, T23, addG_out_gga(T26, T31, T23)) → pN_out_gaga(T21, T31, T26, T23)
U13_gagaa(T20, T26, T21, X26, T23, pN_out_gaga(T21, X26, T26, T23)) → pC_out_gagaa(T20, T26, T21, X26, T23)
U2_ga(T20, T21, T23, pC_out_gagaa(T20, X25, T21, X26, T23)) → evaluateB_out_ga(+(T20, T21), T23)
U1_ag(T7, T6, evaluateB_out_ga(T6, T7)) → myisA_out_ag(T7, T6)

(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:

MYINTEGERF_IN_G(s(T209)) → MYINTEGERF_IN_G(T209)

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

(38) PiDPToQDPProof (EQUIVALENT 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:

MYINTEGERF_IN_G(s(T209)) → MYINTEGERF_IN_G(T209)

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:

MYINTEGERF_IN_G(s(T209)) → MYINTEGERF_IN_G(T209)
The graph contains the following edges 1 > 1

(41) YES

(42) Obligation:

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

EVALUATEB_IN_GA(+(T20, T21), T23) → PC_IN_GAGAA(T20, X25, T21, X26, T23)
PC_IN_GAGAA(T20, T26, T21, X26, T23) → U12_GAGAA(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
U12_GAGAA(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → PN_IN_GAGA(T21, X26, T26, T23)
PN_IN_GAGA(T21, T31, T26, T23) → EVALUATEB_IN_GA(T21, T31)
EVALUATEB_IN_GA(-(T71, T72), T74) → PD_IN_GAGAA(T71, X94, T72, X95, T74)
PD_IN_GAGAA(T71, T77, T72, X95, T74) → U16_GAGAA(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
U16_GAGAA(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → PO_IN_GAGA(T72, X95, T77, T74)
PO_IN_GAGA(T72, T82, T77, T74) → EVALUATEB_IN_GA(T72, T82)
EVALUATEB_IN_GA(*(T122, T123), T125) → PE_IN_GAGAA(T122, X163, T123, X164, T125)
PE_IN_GAGAA(T122, T128, T123, X164, T125) → U20_GAGAA(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
U20_GAGAA(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → PP_IN_GAGA(T123, X164, T128, T125)
PP_IN_GAGA(T123, T133, T128, T125) → EVALUATEB_IN_GA(T123, T133)
PE_IN_GAGAA(T122, T128, T123, X164, T125) → EVALUATEB_IN_GA(T122, T128)
PD_IN_GAGAA(T71, T77, T72, X95, T74) → EVALUATEB_IN_GA(T71, T77)
PC_IN_GAGAA(T20, T26, T21, X26, T23) → EVALUATEB_IN_GA(T20, T26)

The TRS R consists of the following rules:

myisA_in_ag(T7, T6) → U1_ag(T7, T6, evaluateB_in_ga(T6, T7))
evaluateB_in_ga(+(T20, T21), T23) → U2_ga(T20, T21, T23, pC_in_gagaa(T20, X25, T21, X26, T23))
pC_in_gagaa(T20, T26, T21, X26, T23) → U12_gagaa(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
evaluateB_in_ga(-(T71, T72), T74) → U3_ga(T71, T72, T74, pD_in_gagaa(T71, X94, T72, X95, T74))
pD_in_gagaa(T71, T77, T72, X95, T74) → U16_gagaa(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
evaluateB_in_ga(*(T122, T123), T125) → U4_ga(T122, T123, T125, pE_in_gagaa(T122, X163, T123, X164, T125))
pE_in_gagaa(T122, T128, T123, X164, T125) → U20_gagaa(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
evaluateB_in_ga(T203, T203) → U5_ga(T203, myintegerF_in_g(T203))
myintegerF_in_g(s(T209)) → U10_g(T209, myintegerF_in_g(T209))
myintegerF_in_g(0) → myintegerF_out_g(0)
U10_g(T209, myintegerF_out_g(T209)) → myintegerF_out_g(s(T209))
U5_ga(T203, myintegerF_out_g(T203)) → evaluateB_out_ga(T203, T203)
U20_gagaa(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → U21_gagaa(T122, T128, T123, X164, T125, pP_in_gaga(T123, X164, T128, T125))
pP_in_gaga(T123, T133, T128, T125) → U22_gaga(T123, T133, T128, T125, evaluateB_in_ga(T123, T133))
U22_gaga(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → U23_gaga(T123, T133, T128, T125, multL_in_gga(T128, T133, T125))
multL_in_gga(s(T151), T152, T154) → U11_gga(T151, T152, T154, pM_in_ggaa(T151, T152, X210, T154))
pM_in_ggaa(T151, T152, T157, T154) → U24_ggaa(T151, T152, T157, T154, multI_in_gga(T151, T152, T157))
multI_in_gga(s(T168), T169, X243) → U8_gga(T168, T169, X243, pJ_in_ggaa(T168, T169, X242, X243))
pJ_in_ggaa(T168, T169, T172, X243) → U26_ggaa(T168, T169, T172, X243, multI_in_gga(T168, T169, T172))
multI_in_gga(0, T194, 0) → multI_out_gga(0, T194, 0)
U26_ggaa(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → U27_ggaa(T168, T169, T172, X243, addK_in_gga(T169, T172, X243))
addK_in_gga(s(T185), T186, s(X277)) → U9_gga(T185, T186, X277, addK_in_gga(T185, T186, X277))
addK_in_gga(0, T191, T191) → addK_out_gga(0, T191, T191)
U9_gga(T185, T186, X277, addK_out_gga(T185, T186, X277)) → addK_out_gga(s(T185), T186, s(X277))
U27_ggaa(T168, T169, T172, X243, addK_out_gga(T169, T172, X243)) → pJ_out_ggaa(T168, T169, T172, X243)
U8_gga(T168, T169, X243, pJ_out_ggaa(T168, T169, X242, X243)) → multI_out_gga(s(T168), T169, X243)
U24_ggaa(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → U25_ggaa(T151, T152, T157, T154, addG_in_gga(T152, T157, T154))
addG_in_gga(s(T49), T50, s(T52)) → U6_gga(T49, T50, T52, addG_in_gga(T49, T50, T52))
addG_in_gga(0, T58, T58) → addG_out_gga(0, T58, T58)
U6_gga(T49, T50, T52, addG_out_gga(T49, T50, T52)) → addG_out_gga(s(T49), T50, s(T52))
U25_ggaa(T151, T152, T157, T154, addG_out_gga(T152, T157, T154)) → pM_out_ggaa(T151, T152, T157, T154)
U11_gga(T151, T152, T154, pM_out_ggaa(T151, T152, X210, T154)) → multL_out_gga(s(T151), T152, T154)
multL_in_gga(0, T200, 0) → multL_out_gga(0, T200, 0)
U23_gaga(T123, T133, T128, T125, multL_out_gga(T128, T133, T125)) → pP_out_gaga(T123, T133, T128, T125)
U21_gagaa(T122, T128, T123, X164, T125, pP_out_gaga(T123, X164, T128, T125)) → pE_out_gagaa(T122, T128, T123, X164, T125)
U4_ga(T122, T123, T125, pE_out_gagaa(T122, X163, T123, X164, T125)) → evaluateB_out_ga(*(T122, T123), T125)
U16_gagaa(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → U17_gagaa(T71, T77, T72, X95, T74, pO_in_gaga(T72, X95, T77, T74))
pO_in_gaga(T72, T82, T77, T74) → U18_gaga(T72, T82, T77, T74, evaluateB_in_ga(T72, T82))
U18_gaga(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → U19_gaga(T72, T82, T77, T74, subH_in_gga(T77, T82, T74))
subH_in_gga(s(T100), s(T101), T103) → U7_gga(T100, T101, T103, subH_in_gga(T100, T101, T103))
subH_in_gga(T109, 0, T109) → subH_out_gga(T109, 0, T109)
U7_gga(T100, T101, T103, subH_out_gga(T100, T101, T103)) → subH_out_gga(s(T100), s(T101), T103)
U19_gaga(T72, T82, T77, T74, subH_out_gga(T77, T82, T74)) → pO_out_gaga(T72, T82, T77, T74)
U17_gagaa(T71, T77, T72, X95, T74, pO_out_gaga(T72, X95, T77, T74)) → pD_out_gagaa(T71, T77, T72, X95, T74)
U3_ga(T71, T72, T74, pD_out_gagaa(T71, X94, T72, X95, T74)) → evaluateB_out_ga(-(T71, T72), T74)
U12_gagaa(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → U13_gagaa(T20, T26, T21, X26, T23, pN_in_gaga(T21, X26, T26, T23))
pN_in_gaga(T21, T31, T26, T23) → U14_gaga(T21, T31, T26, T23, evaluateB_in_ga(T21, T31))
U14_gaga(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → U15_gaga(T21, T31, T26, T23, addG_in_gga(T26, T31, T23))
U15_gaga(T21, T31, T26, T23, addG_out_gga(T26, T31, T23)) → pN_out_gaga(T21, T31, T26, T23)
U13_gagaa(T20, T26, T21, X26, T23, pN_out_gaga(T21, X26, T26, T23)) → pC_out_gagaa(T20, T26, T21, X26, T23)
U2_ga(T20, T21, T23, pC_out_gagaa(T20, X25, T21, X26, T23)) → evaluateB_out_ga(+(T20, T21), T23)
U1_ag(T7, T6, evaluateB_out_ga(T6, T7)) → myisA_out_ag(T7, T6)

The argument filtering Pi contains the following mapping:
myisA_in_ag(x1, x2) = myisA_in_ag(x2)
U1_ag(x1, x2, x3) = U1_ag(x2, x3)
evaluateB_in_ga(x1, x2) = evaluateB_in_ga(x1)
+(x1, x2) = +(x1, x2)
U2_ga(x1, x2, x3, x4) = U2_ga(x1, x2, x4)
pC_in_gagaa(x1, x2, x3, x4, x5) = pC_in_gagaa(x1, x3)
U12_gagaa(x1, x2, x3, x4, x5, x6) = U12_gagaa(x1, x3, x6)
-(x1, x2) = -(x1, x2)
U3_ga(x1, x2, x3, x4) = U3_ga(x1, x2, x4)
pD_in_gagaa(x1, x2, x3, x4, x5) = pD_in_gagaa(x1, x3)
U16_gagaa(x1, x2, x3, x4, x5, x6) = U16_gagaa(x1, x3, x6)
*(x1, x2) = *(x1, x2)
U4_ga(x1, x2, x3, x4) = U4_ga(x1, x2, x4)
pE_in_gagaa(x1, x2, x3, x4, x5) = pE_in_gagaa(x1, x3)
U20_gagaa(x1, x2, x3, x4, x5, x6) = U20_gagaa(x1, x3, x6)
U5_ga(x1, x2) = U5_ga(x1, x2)
myintegerF_in_g(x1) = myintegerF_in_g(x1)
s(x1) = s(x1)
U10_g(x1, x2) = U10_g(x1, x2)
0 = 0
myintegerF_out_g(x1) = myintegerF_out_g(x1)
evaluateB_out_ga(x1, x2) = evaluateB_out_ga(x1, x2)
U21_gagaa(x1, x2, x3, x4, x5, x6) = U21_gagaa(x1, x2, x3, x6)
pP_in_gaga(x1, x2, x3, x4) = pP_in_gaga(x1, x3)
U22_gaga(x1, x2, x3, x4, x5) = U22_gaga(x1, x3, x5)
U23_gaga(x1, x2, x3, x4, x5) = U23_gaga(x1, x2, x3, x5)
multL_in_gga(x1, x2, x3) = multL_in_gga(x1, x2)
U11_gga(x1, x2, x3, x4) = U11_gga(x1, x2, x4)
pM_in_ggaa(x1, x2, x3, x4) = pM_in_ggaa(x1, x2)
U24_ggaa(x1, x2, x3, x4, x5) = U24_ggaa(x1, x2, x5)
multI_in_gga(x1, x2, x3) = multI_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4) = U8_gga(x1, x2, x4)
pJ_in_ggaa(x1, x2, x3, x4) = pJ_in_ggaa(x1, x2)
U26_ggaa(x1, x2, x3, x4, x5) = U26_ggaa(x1, x2, x5)
multI_out_gga(x1, x2, x3) = multI_out_gga(x1, x2, x3)
U27_ggaa(x1, x2, x3, x4, x5) = U27_ggaa(x1, x2, x3, x5)
addK_in_gga(x1, x2, x3) = addK_in_gga(x1, x2)
U9_gga(x1, x2, x3, x4) = U9_gga(x1, x2, x4)
addK_out_gga(x1, x2, x3) = addK_out_gga(x1, x2, x3)
pJ_out_ggaa(x1, x2, x3, x4) = pJ_out_ggaa(x1, x2, x3, x4)
U25_ggaa(x1, x2, x3, x4, x5) = U25_ggaa(x1, x2, x3, x5)
addG_in_gga(x1, x2, x3) = addG_in_gga(x1, x2)
U6_gga(x1, x2, x3, x4) = U6_gga(x1, x2, x4)
addG_out_gga(x1, x2, x3) = addG_out_gga(x1, x2, x3)
pM_out_ggaa(x1, x2, x3, x4) = pM_out_ggaa(x1, x2, x3, x4)
multL_out_gga(x1, x2, x3) = multL_out_gga(x1, x2, x3)
pP_out_gaga(x1, x2, x3, x4) = pP_out_gaga(x1, x2, x3, x4)
pE_out_gagaa(x1, x2, x3, x4, x5) = pE_out_gagaa(x1, x2, x3, x4, x5)
U17_gagaa(x1, x2, x3, x4, x5, x6) = U17_gagaa(x1, x2, x3, x6)
pO_in_gaga(x1, x2, x3, x4) = pO_in_gaga(x1, x3)
U18_gaga(x1, x2, x3, x4, x5) = U18_gaga(x1, x3, x5)
U19_gaga(x1, x2, x3, x4, x5) = U19_gaga(x1, x2, x3, x5)
subH_in_gga(x1, x2, x3) = subH_in_gga(x1, x2)
U7_gga(x1, x2, x3, x4) = U7_gga(x1, x2, x4)
subH_out_gga(x1, x2, x3) = subH_out_gga(x1, x2, x3)
pO_out_gaga(x1, x2, x3, x4) = pO_out_gaga(x1, x2, x3, x4)
pD_out_gagaa(x1, x2, x3, x4, x5) = pD_out_gagaa(x1, x2, x3, x4, x5)
U13_gagaa(x1, x2, x3, x4, x5, x6) = U13_gagaa(x1, x2, x3, x6)
pN_in_gaga(x1, x2, x3, x4) = pN_in_gaga(x1, x3)
U14_gaga(x1, x2, x3, x4, x5) = U14_gaga(x1, x3, x5)
U15_gaga(x1, x2, x3, x4, x5) = U15_gaga(x1, x2, x3, x5)
pN_out_gaga(x1, x2, x3, x4) = pN_out_gaga(x1, x2, x3, x4)
pC_out_gagaa(x1, x2, x3, x4, x5) = pC_out_gagaa(x1, x2, x3, x4, x5)
myisA_out_ag(x1, x2) = myisA_out_ag(x1, x2)
EVALUATEB_IN_GA(x1, x2) = EVALUATEB_IN_GA(x1)
PC_IN_GAGAA(x1, x2, x3, x4, x5) = PC_IN_GAGAA(x1, x3)
U12_GAGAA(x1, x2, x3, x4, x5, x6) = U12_GAGAA(x1, x3, x6)
PD_IN_GAGAA(x1, x2, x3, x4, x5) = PD_IN_GAGAA(x1, x3)
U16_GAGAA(x1, x2, x3, x4, x5, x6) = U16_GAGAA(x1, x3, x6)
PE_IN_GAGAA(x1, x2, x3, x4, x5) = PE_IN_GAGAA(x1, x3)
U20_GAGAA(x1, x2, x3, x4, x5, x6) = U20_GAGAA(x1, x3, x6)
PP_IN_GAGA(x1, x2, x3, x4) = PP_IN_GAGA(x1, x3)
PO_IN_GAGA(x1, x2, x3, x4) = PO_IN_GAGA(x1, x3)
PN_IN_GAGA(x1, x2, x3, x4) = PN_IN_GAGA(x1, x3)

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:

EVALUATEB_IN_GA(+(T20, T21), T23) → PC_IN_GAGAA(T20, X25, T21, X26, T23)
PC_IN_GAGAA(T20, T26, T21, X26, T23) → U12_GAGAA(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
U12_GAGAA(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → PN_IN_GAGA(T21, X26, T26, T23)
PN_IN_GAGA(T21, T31, T26, T23) → EVALUATEB_IN_GA(T21, T31)
EVALUATEB_IN_GA(-(T71, T72), T74) → PD_IN_GAGAA(T71, X94, T72, X95, T74)
PD_IN_GAGAA(T71, T77, T72, X95, T74) → U16_GAGAA(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
U16_GAGAA(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → PO_IN_GAGA(T72, X95, T77, T74)
PO_IN_GAGA(T72, T82, T77, T74) → EVALUATEB_IN_GA(T72, T82)
EVALUATEB_IN_GA(*(T122, T123), T125) → PE_IN_GAGAA(T122, X163, T123, X164, T125)
PE_IN_GAGAA(T122, T128, T123, X164, T125) → U20_GAGAA(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
U20_GAGAA(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → PP_IN_GAGA(T123, X164, T128, T125)
PP_IN_GAGA(T123, T133, T128, T125) → EVALUATEB_IN_GA(T123, T133)
PE_IN_GAGAA(T122, T128, T123, X164, T125) → EVALUATEB_IN_GA(T122, T128)
PD_IN_GAGAA(T71, T77, T72, X95, T74) → EVALUATEB_IN_GA(T71, T77)
PC_IN_GAGAA(T20, T26, T21, X26, T23) → EVALUATEB_IN_GA(T20, T26)

The TRS R consists of the following rules:

evaluateB_in_ga(+(T20, T21), T23) → U2_ga(T20, T21, T23, pC_in_gagaa(T20, X25, T21, X26, T23))
evaluateB_in_ga(-(T71, T72), T74) → U3_ga(T71, T72, T74, pD_in_gagaa(T71, X94, T72, X95, T74))
evaluateB_in_ga(*(T122, T123), T125) → U4_ga(T122, T123, T125, pE_in_gagaa(T122, X163, T123, X164, T125))
evaluateB_in_ga(T203, T203) → U5_ga(T203, myintegerF_in_g(T203))
U2_ga(T20, T21, T23, pC_out_gagaa(T20, X25, T21, X26, T23)) → evaluateB_out_ga(+(T20, T21), T23)
U3_ga(T71, T72, T74, pD_out_gagaa(T71, X94, T72, X95, T74)) → evaluateB_out_ga(-(T71, T72), T74)
U4_ga(T122, T123, T125, pE_out_gagaa(T122, X163, T123, X164, T125)) → evaluateB_out_ga(*(T122, T123), T125)
U5_ga(T203, myintegerF_out_g(T203)) → evaluateB_out_ga(T203, T203)
pC_in_gagaa(T20, T26, T21, X26, T23) → U12_gagaa(T20, T26, T21, X26, T23, evaluateB_in_ga(T20, T26))
pD_in_gagaa(T71, T77, T72, X95, T74) → U16_gagaa(T71, T77, T72, X95, T74, evaluateB_in_ga(T71, T77))
pE_in_gagaa(T122, T128, T123, X164, T125) → U20_gagaa(T122, T128, T123, X164, T125, evaluateB_in_ga(T122, T128))
myintegerF_in_g(s(T209)) → U10_g(T209, myintegerF_in_g(T209))
myintegerF_in_g(0) → myintegerF_out_g(0)
U12_gagaa(T20, T26, T21, X26, T23, evaluateB_out_ga(T20, T26)) → U13_gagaa(T20, T26, T21, X26, T23, pN_in_gaga(T21, X26, T26, T23))
U16_gagaa(T71, T77, T72, X95, T74, evaluateB_out_ga(T71, T77)) → U17_gagaa(T71, T77, T72, X95, T74, pO_in_gaga(T72, X95, T77, T74))
U20_gagaa(T122, T128, T123, X164, T125, evaluateB_out_ga(T122, T128)) → U21_gagaa(T122, T128, T123, X164, T125, pP_in_gaga(T123, X164, T128, T125))
U10_g(T209, myintegerF_out_g(T209)) → myintegerF_out_g(s(T209))
U13_gagaa(T20, T26, T21, X26, T23, pN_out_gaga(T21, X26, T26, T23)) → pC_out_gagaa(T20, T26, T21, X26, T23)
U17_gagaa(T71, T77, T72, X95, T74, pO_out_gaga(T72, X95, T77, T74)) → pD_out_gagaa(T71, T77, T72, X95, T74)
U21_gagaa(T122, T128, T123, X164, T125, pP_out_gaga(T123, X164, T128, T125)) → pE_out_gagaa(T122, T128, T123, X164, T125)
pN_in_gaga(T21, T31, T26, T23) → U14_gaga(T21, T31, T26, T23, evaluateB_in_ga(T21, T31))
pO_in_gaga(T72, T82, T77, T74) → U18_gaga(T72, T82, T77, T74, evaluateB_in_ga(T72, T82))
pP_in_gaga(T123, T133, T128, T125) → U22_gaga(T123, T133, T128, T125, evaluateB_in_ga(T123, T133))
U14_gaga(T21, T31, T26, T23, evaluateB_out_ga(T21, T31)) → U15_gaga(T21, T31, T26, T23, addG_in_gga(T26, T31, T23))
U18_gaga(T72, T82, T77, T74, evaluateB_out_ga(T72, T82)) → U19_gaga(T72, T82, T77, T74, subH_in_gga(T77, T82, T74))
U22_gaga(T123, T133, T128, T125, evaluateB_out_ga(T123, T133)) → U23_gaga(T123, T133, T128, T125, multL_in_gga(T128, T133, T125))
U15_gaga(T21, T31, T26, T23, addG_out_gga(T26, T31, T23)) → pN_out_gaga(T21, T31, T26, T23)
U19_gaga(T72, T82, T77, T74, subH_out_gga(T77, T82, T74)) → pO_out_gaga(T72, T82, T77, T74)
U23_gaga(T123, T133, T128, T125, multL_out_gga(T128, T133, T125)) → pP_out_gaga(T123, T133, T128, T125)
addG_in_gga(s(T49), T50, s(T52)) → U6_gga(T49, T50, T52, addG_in_gga(T49, T50, T52))
addG_in_gga(0, T58, T58) → addG_out_gga(0, T58, T58)
subH_in_gga(s(T100), s(T101), T103) → U7_gga(T100, T101, T103, subH_in_gga(T100, T101, T103))
subH_in_gga(T109, 0, T109) → subH_out_gga(T109, 0, T109)
multL_in_gga(s(T151), T152, T154) → U11_gga(T151, T152, T154, pM_in_ggaa(T151, T152, X210, T154))
multL_in_gga(0, T200, 0) → multL_out_gga(0, T200, 0)
U6_gga(T49, T50, T52, addG_out_gga(T49, T50, T52)) → addG_out_gga(s(T49), T50, s(T52))
U7_gga(T100, T101, T103, subH_out_gga(T100, T101, T103)) → subH_out_gga(s(T100), s(T101), T103)
U11_gga(T151, T152, T154, pM_out_ggaa(T151, T152, X210, T154)) → multL_out_gga(s(T151), T152, T154)
pM_in_ggaa(T151, T152, T157, T154) → U24_ggaa(T151, T152, T157, T154, multI_in_gga(T151, T152, T157))
U24_ggaa(T151, T152, T157, T154, multI_out_gga(T151, T152, T157)) → U25_ggaa(T151, T152, T157, T154, addG_in_gga(T152, T157, T154))
multI_in_gga(s(T168), T169, X243) → U8_gga(T168, T169, X243, pJ_in_ggaa(T168, T169, X242, X243))
multI_in_gga(0, T194, 0) → multI_out_gga(0, T194, 0)
U25_ggaa(T151, T152, T157, T154, addG_out_gga(T152, T157, T154)) → pM_out_ggaa(T151, T152, T157, T154)
U8_gga(T168, T169, X243, pJ_out_ggaa(T168, T169, X242, X243)) → multI_out_gga(s(T168), T169, X243)
pJ_in_ggaa(T168, T169, T172, X243) → U26_ggaa(T168, T169, T172, X243, multI_in_gga(T168, T169, T172))
U26_ggaa(T168, T169, T172, X243, multI_out_gga(T168, T169, T172)) → U27_ggaa(T168, T169, T172, X243, addK_in_gga(T169, T172, X243))
U27_ggaa(T168, T169, T172, X243, addK_out_gga(T169, T172, X243)) → pJ_out_ggaa(T168, T169, T172, X243)
addK_in_gga(s(T185), T186, s(X277)) → U9_gga(T185, T186, X277, addK_in_gga(T185, T186, X277))
addK_in_gga(0, T191, T191) → addK_out_gga(0, T191, T191)
U9_gga(T185, T186, X277, addK_out_gga(T185, T186, X277)) → addK_out_gga(s(T185), T186, s(X277))

The argument filtering Pi contains the following mapping:
evaluateB_in_ga(x1, x2) = evaluateB_in_ga(x1)
+(x1, x2) = +(x1, x2)
U2_ga(x1, x2, x3, x4) = U2_ga(x1, x2, x4)
pC_in_gagaa(x1, x2, x3, x4, x5) = pC_in_gagaa(x1, x3)
U12_gagaa(x1, x2, x3, x4, x5, x6) = U12_gagaa(x1, x3, x6)
-(x1, x2) = -(x1, x2)
U3_ga(x1, x2, x3, x4) = U3_ga(x1, x2, x4)
pD_in_gagaa(x1, x2, x3, x4, x5) = pD_in_gagaa(x1, x3)
U16_gagaa(x1, x2, x3, x4, x5, x6) = U16_gagaa(x1, x3, x6)
*(x1, x2) = *(x1, x2)
U4_ga(x1, x2, x3, x4) = U4_ga(x1, x2, x4)
pE_in_gagaa(x1, x2, x3, x4, x5) = pE_in_gagaa(x1, x3)
U20_gagaa(x1, x2, x3, x4, x5, x6) = U20_gagaa(x1, x3, x6)
U5_ga(x1, x2) = U5_ga(x1, x2)
myintegerF_in_g(x1) = myintegerF_in_g(x1)
s(x1) = s(x1)
U10_g(x1, x2) = U10_g(x1, x2)
0 = 0
myintegerF_out_g(x1) = myintegerF_out_g(x1)
evaluateB_out_ga(x1, x2) = evaluateB_out_ga(x1, x2)
U21_gagaa(x1, x2, x3, x4, x5, x6) = U21_gagaa(x1, x2, x3, x6)
pP_in_gaga(x1, x2, x3, x4) = pP_in_gaga(x1, x3)
U22_gaga(x1, x2, x3, x4, x5) = U22_gaga(x1, x3, x5)
U23_gaga(x1, x2, x3, x4, x5) = U23_gaga(x1, x2, x3, x5)
multL_in_gga(x1, x2, x3) = multL_in_gga(x1, x2)
U11_gga(x1, x2, x3, x4) = U11_gga(x1, x2, x4)
pM_in_ggaa(x1, x2, x3, x4) = pM_in_ggaa(x1, x2)
U24_ggaa(x1, x2, x3, x4, x5) = U24_ggaa(x1, x2, x5)
multI_in_gga(x1, x2, x3) = multI_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4) = U8_gga(x1, x2, x4)
pJ_in_ggaa(x1, x2, x3, x4) = pJ_in_ggaa(x1, x2)
U26_ggaa(x1, x2, x3, x4, x5) = U26_ggaa(x1, x2, x5)
multI_out_gga(x1, x2, x3) = multI_out_gga(x1, x2, x3)
U27_ggaa(x1, x2, x3, x4, x5) = U27_ggaa(x1, x2, x3, x5)
addK_in_gga(x1, x2, x3) = addK_in_gga(x1, x2)
U9_gga(x1, x2, x3, x4) = U9_gga(x1, x2, x4)
addK_out_gga(x1, x2, x3) = addK_out_gga(x1, x2, x3)
pJ_out_ggaa(x1, x2, x3, x4) = pJ_out_ggaa(x1, x2, x3, x4)
U25_ggaa(x1, x2, x3, x4, x5) = U25_ggaa(x1, x2, x3, x5)
addG_in_gga(x1, x2, x3) = addG_in_gga(x1, x2)
U6_gga(x1, x2, x3, x4) = U6_gga(x1, x2, x4)
addG_out_gga(x1, x2, x3) = addG_out_gga(x1, x2, x3)
pM_out_ggaa(x1, x2, x3, x4) = pM_out_ggaa(x1, x2, x3, x4)
multL_out_gga(x1, x2, x3) = multL_out_gga(x1, x2, x3)
pP_out_gaga(x1, x2, x3, x4) = pP_out_gaga(x1, x2, x3, x4)
pE_out_gagaa(x1, x2, x3, x4, x5) = pE_out_gagaa(x1, x2, x3, x4, x5)
U17_gagaa(x1, x2, x3, x4, x5, x6) = U17_gagaa(x1, x2, x3, x6)
pO_in_gaga(x1, x2, x3, x4) = pO_in_gaga(x1, x3)
U18_gaga(x1, x2, x3, x4, x5) = U18_gaga(x1, x3, x5)
U19_gaga(x1, x2, x3, x4, x5) = U19_gaga(x1, x2, x3, x5)
subH_in_gga(x1, x2, x3) = subH_in_gga(x1, x2)
U7_gga(x1, x2, x3, x4) = U7_gga(x1, x2, x4)
subH_out_gga(x1, x2, x3) = subH_out_gga(x1, x2, x3)
pO_out_gaga(x1, x2, x3, x4) = pO_out_gaga(x1, x2, x3, x4)
pD_out_gagaa(x1, x2, x3, x4, x5) = pD_out_gagaa(x1, x2, x3, x4, x5)
U13_gagaa(x1, x2, x3, x4, x5, x6) = U13_gagaa(x1, x2, x3, x6)
pN_in_gaga(x1, x2, x3, x4) = pN_in_gaga(x1, x3)
U14_gaga(x1, x2, x3, x4, x5) = U14_gaga(x1, x3, x5)
U15_gaga(x1, x2, x3, x4, x5) = U15_gaga(x1, x2, x3, x5)
pN_out_gaga(x1, x2, x3, x4) = pN_out_gaga(x1, x2, x3, x4)
pC_out_gagaa(x1, x2, x3, x4, x5) = pC_out_gagaa(x1, x2, x3, x4, x5)
EVALUATEB_IN_GA(x1, x2) = EVALUATEB_IN_GA(x1)
PC_IN_GAGAA(x1, x2, x3, x4, x5) = PC_IN_GAGAA(x1, x3)
U12_GAGAA(x1, x2, x3, x4, x5, x6) = U12_GAGAA(x1, x3, x6)
PD_IN_GAGAA(x1, x2, x3, x4, x5) = PD_IN_GAGAA(x1, x3)
U16_GAGAA(x1, x2, x3, x4, x5, x6) = U16_GAGAA(x1, x3, x6)
PE_IN_GAGAA(x1, x2, x3, x4, x5) = PE_IN_GAGAA(x1, x3)
U20_GAGAA(x1, x2, x3, x4, x5, x6) = U20_GAGAA(x1, x3, x6)
PP_IN_GAGA(x1, x2, x3, x4) = PP_IN_GAGA(x1, x3)
PO_IN_GAGA(x1, x2, x3, x4) = PO_IN_GAGA(x1, x3)
PN_IN_GAGA(x1, x2, x3, x4) = PN_IN_GAGA(x1, x3)

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:

EVALUATEB_IN_GA(+(T20, T21)) → PC_IN_GAGAA(T20, T21)
PC_IN_GAGAA(T20, T21) → U12_GAGAA(T20, T21, evaluateB_in_ga(T20))
U12_GAGAA(T20, T21, evaluateB_out_ga(T20, T26)) → PN_IN_GAGA(T21, T26)
PN_IN_GAGA(T21, T26) → EVALUATEB_IN_GA(T21)
EVALUATEB_IN_GA(-(T71, T72)) → PD_IN_GAGAA(T71, T72)
PD_IN_GAGAA(T71, T72) → U16_GAGAA(T71, T72, evaluateB_in_ga(T71))
U16_GAGAA(T71, T72, evaluateB_out_ga(T71, T77)) → PO_IN_GAGA(T72, T77)
PO_IN_GAGA(T72, T77) → EVALUATEB_IN_GA(T72)
EVALUATEB_IN_GA(*(T122, T123)) → PE_IN_GAGAA(T122, T123)
PE_IN_GAGAA(T122, T123) → U20_GAGAA(T122, T123, evaluateB_in_ga(T122))
U20_GAGAA(T122, T123, evaluateB_out_ga(T122, T128)) → PP_IN_GAGA(T123, T128)
PP_IN_GAGA(T123, T128) → EVALUATEB_IN_GA(T123)
PE_IN_GAGAA(T122, T123) → EVALUATEB_IN_GA(T122)
PD_IN_GAGAA(T71, T72) → EVALUATEB_IN_GA(T71)
PC_IN_GAGAA(T20, T21) → EVALUATEB_IN_GA(T20)

The TRS R consists of the following rules:

evaluateB_in_ga(+(T20, T21)) → U2_ga(T20, T21, pC_in_gagaa(T20, T21))
evaluateB_in_ga(-(T71, T72)) → U3_ga(T71, T72, pD_in_gagaa(T71, T72))
evaluateB_in_ga(*(T122, T123)) → U4_ga(T122, T123, pE_in_gagaa(T122, T123))
evaluateB_in_ga(T203) → U5_ga(T203, myintegerF_in_g(T203))
U2_ga(T20, T21, pC_out_gagaa(T20, X25, T21, X26, T23)) → evaluateB_out_ga(+(T20, T21), T23)
U3_ga(T71, T72, pD_out_gagaa(T71, X94, T72, X95, T74)) → evaluateB_out_ga(-(T71, T72), T74)
U4_ga(T122, T123, pE_out_gagaa(T122, X163, T123, X164, T125)) → evaluateB_out_ga(*(T122, T123), T125)
U5_ga(T203, myintegerF_out_g(T203)) → evaluateB_out_ga(T203, T203)
pC_in_gagaa(T20, T21) → U12_gagaa(T20, T21, evaluateB_in_ga(T20))
pD_in_gagaa(T71, T72) → U16_gagaa(T71, T72, evaluateB_in_ga(T71))
pE_in_gagaa(T122, T123) → U20_gagaa(T122, T123, evaluateB_in_ga(T122))
myintegerF_in_g(s(T209)) → U10_g(T209, myintegerF_in_g(T209))
myintegerF_in_g(0) → myintegerF_out_g(0)
U12_gagaa(T20, T21, evaluateB_out_ga(T20, T26)) → U13_gagaa(T20, T26, T21, pN_in_gaga(T21, T26))
U16_gagaa(T71, T72, evaluateB_out_ga(T71, T77)) → U17_gagaa(T71, T77, T72, pO_in_gaga(T72, T77))
U20_gagaa(T122, T123, evaluateB_out_ga(T122, T128)) → U21_gagaa(T122, T128, T123, pP_in_gaga(T123, T128))
U10_g(T209, myintegerF_out_g(T209)) → myintegerF_out_g(s(T209))
U13_gagaa(T20, T26, T21, pN_out_gaga(T21, X26, T26, T23)) → pC_out_gagaa(T20, T26, T21, X26, T23)
U17_gagaa(T71, T77, T72, pO_out_gaga(T72, X95, T77, T74)) → pD_out_gagaa(T71, T77, T72, X95, T74)
U21_gagaa(T122, T128, T123, pP_out_gaga(T123, X164, T128, T125)) → pE_out_gagaa(T122, T128, T123, X164, T125)
pN_in_gaga(T21, T26) → U14_gaga(T21, T26, evaluateB_in_ga(T21))
pO_in_gaga(T72, T77) → U18_gaga(T72, T77, evaluateB_in_ga(T72))
pP_in_gaga(T123, T128) → U22_gaga(T123, T128, evaluateB_in_ga(T123))
U14_gaga(T21, T26, evaluateB_out_ga(T21, T31)) → U15_gaga(T21, T31, T26, addG_in_gga(T26, T31))
U18_gaga(T72, T77, evaluateB_out_ga(T72, T82)) → U19_gaga(T72, T82, T77, subH_in_gga(T77, T82))
U22_gaga(T123, T128, evaluateB_out_ga(T123, T133)) → U23_gaga(T123, T133, T128, multL_in_gga(T128, T133))
U15_gaga(T21, T31, T26, addG_out_gga(T26, T31, T23)) → pN_out_gaga(T21, T31, T26, T23)
U19_gaga(T72, T82, T77, subH_out_gga(T77, T82, T74)) → pO_out_gaga(T72, T82, T77, T74)
U23_gaga(T123, T133, T128, multL_out_gga(T128, T133, T125)) → pP_out_gaga(T123, T133, T128, T125)
addG_in_gga(s(T49), T50) → U6_gga(T49, T50, addG_in_gga(T49, T50))
addG_in_gga(0, T58) → addG_out_gga(0, T58, T58)
subH_in_gga(s(T100), s(T101)) → U7_gga(T100, T101, subH_in_gga(T100, T101))
subH_in_gga(T109, 0) → subH_out_gga(T109, 0, T109)
multL_in_gga(s(T151), T152) → U11_gga(T151, T152, pM_in_ggaa(T151, T152))
multL_in_gga(0, T200) → multL_out_gga(0, T200, 0)
U6_gga(T49, T50, addG_out_gga(T49, T50, T52)) → addG_out_gga(s(T49), T50, s(T52))
U7_gga(T100, T101, subH_out_gga(T100, T101, T103)) → subH_out_gga(s(T100), s(T101), T103)
U11_gga(T151, T152, pM_out_ggaa(T151, T152, X210, T154)) → multL_out_gga(s(T151), T152, T154)
pM_in_ggaa(T151, T152) → U24_ggaa(T151, T152, multI_in_gga(T151, T152))
U24_ggaa(T151, T152, multI_out_gga(T151, T152, T157)) → U25_ggaa(T151, T152, T157, addG_in_gga(T152, T157))
multI_in_gga(s(T168), T169) → U8_gga(T168, T169, pJ_in_ggaa(T168, T169))
multI_in_gga(0, T194) → multI_out_gga(0, T194, 0)
U25_ggaa(T151, T152, T157, addG_out_gga(T152, T157, T154)) → pM_out_ggaa(T151, T152, T157, T154)
U8_gga(T168, T169, pJ_out_ggaa(T168, T169, X242, X243)) → multI_out_gga(s(T168), T169, X243)
pJ_in_ggaa(T168, T169) → U26_ggaa(T168, T169, multI_in_gga(T168, T169))
U26_ggaa(T168, T169, multI_out_gga(T168, T169, T172)) → U27_ggaa(T168, T169, T172, addK_in_gga(T169, T172))
U27_ggaa(T168, T169, T172, addK_out_gga(T169, T172, X243)) → pJ_out_ggaa(T168, T169, T172, X243)
addK_in_gga(s(T185), T186) → U9_gga(T185, T186, addK_in_gga(T185, T186))
addK_in_gga(0, T191) → addK_out_gga(0, T191, T191)
U9_gga(T185, T186, addK_out_gga(T185, T186, X277)) → addK_out_gga(s(T185), T186, s(X277))

The set Q consists of the following terms:

evaluateB_in_ga(x0)
U2_ga(x0, x1, x2)
U3_ga(x0, x1, x2)
U4_ga(x0, x1, x2)
U5_ga(x0, x1)
pC_in_gagaa(x0, x1)
pD_in_gagaa(x0, x1)
pE_in_gagaa(x0, x1)
myintegerF_in_g(x0)
U12_gagaa(x0, x1, x2)
U16_gagaa(x0, x1, x2)
U20_gagaa(x0, x1, x2)
U10_g(x0, x1)
U13_gagaa(x0, x1, x2, x3)
U17_gagaa(x0, x1, x2, x3)
U21_gagaa(x0, x1, x2, x3)
pN_in_gaga(x0, x1)
pO_in_gaga(x0, x1)
pP_in_gaga(x0, x1)
U14_gaga(x0, x1, x2)
U18_gaga(x0, x1, x2)
U22_gaga(x0, x1, x2)
U15_gaga(x0, x1, x2, x3)
U19_gaga(x0, x1, x2, x3)
U23_gaga(x0, x1, x2, x3)
addG_in_gga(x0, x1)
subH_in_gga(x0, x1)
multL_in_gga(x0, x1)
U6_gga(x0, x1, x2)
U7_gga(x0, x1, x2)
U11_gga(x0, x1, x2)
pM_in_ggaa(x0, x1)
U24_ggaa(x0, x1, x2)
multI_in_gga(x0, x1)
U25_ggaa(x0, x1, x2, x3)
U8_gga(x0, x1, x2)
pJ_in_ggaa(x0, x1)
U26_ggaa(x0, x1, x2)
U27_ggaa(x0, x1, x2, x3)
addK_in_gga(x0, x1)
U9_gga(x0, x1, x2)

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:

PC_IN_GAGAA(T20, T21) → EVALUATEB_IN_GA(T20)
The graph contains the following edges 1 >= 1
PC_IN_GAGAA(T20, T21) → U12_GAGAA(T20, T21, evaluateB_in_ga(T20))
The graph contains the following edges 1 >= 1, 2 >= 2
U12_GAGAA(T20, T21, evaluateB_out_ga(T20, T26)) → PN_IN_GAGA(T21, T26)
The graph contains the following edges 2 >= 1, 3 > 2
EVALUATEB_IN_GA(+(T20, T21)) → PC_IN_GAGAA(T20, T21)
The graph contains the following edges 1 > 1, 1 > 2
PN_IN_GAGA(T21, T26) → EVALUATEB_IN_GA(T21)
The graph contains the following edges 1 >= 1
PD_IN_GAGAA(T71, T72) → EVALUATEB_IN_GA(T71)
The graph contains the following edges 1 >= 1
PD_IN_GAGAA(T71, T72) → U16_GAGAA(T71, T72, evaluateB_in_ga(T71))
The graph contains the following edges 1 >= 1, 2 >= 2
EVALUATEB_IN_GA(-(T71, T72)) → PD_IN_GAGAA(T71, T72)
The graph contains the following edges 1 > 1, 1 > 2
EVALUATEB_IN_GA(*(T122, T123)) → PE_IN_GAGAA(T122, T123)
The graph contains the following edges 1 > 1, 1 > 2
U16_GAGAA(T71, T72, evaluateB_out_ga(T71, T77)) → PO_IN_GAGA(T72, T77)
The graph contains the following edges 2 >= 1, 3 > 2
PO_IN_GAGA(T72, T77) → EVALUATEB_IN_GA(T72)
The graph contains the following edges 1 >= 1
PE_IN_GAGAA(T122, T123) → EVALUATEB_IN_GA(T122)
The graph contains the following edges 1 >= 1
PP_IN_GAGA(T123, T128) → EVALUATEB_IN_GA(T123)
The graph contains the following edges 1 >= 1
PE_IN_GAGAA(T122, T123) → U20_GAGAA(T122, T123, evaluateB_in_ga(T122))
The graph contains the following edges 1 >= 1, 2 >= 2
U20_GAGAA(T122, T123, evaluateB_out_ga(T122, T128)) → PP_IN_GAGA(T123, T128)
The graph contains the following edges 2 >= 1, 3 > 2

(0) Obligation:

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

(2) Obligation:

(3) DependencyPairsProof (EQUIVALENT transformation)

(4) Obligation:

(5) DependencyGraphProof (EQUIVALENT transformation)

(6) Complex Obligation (AND)

(7) Obligation:

(8) UsableRulesProof (EQUIVALENT transformation)

(9) Obligation:

(10) PiDPToQDPProof (SOUND transformation)

(11) Obligation:

(12) QDPSizeChangeProof (EQUIVALENT transformation)

(13) YES

(14) Obligation:

(15) UsableRulesProof (EQUIVALENT transformation)

(16) Obligation:

(17) PiDPToQDPProof (SOUND transformation)

(18) Obligation:

(19) QDPSizeChangeProof (EQUIVALENT transformation)

(20) YES

(21) Obligation:

(22) UsableRulesProof (EQUIVALENT transformation)

(23) Obligation:

(24) PiDPToQDPProof (SOUND transformation)

(25) Obligation:

(26) QDPSizeChangeProof (EQUIVALENT transformation)

(27) YES

(28) Obligation:

(29) UsableRulesProof (EQUIVALENT transformation)

(30) Obligation:

(31) PiDPToQDPProof (SOUND transformation)

(32) Obligation:

(33) QDPSizeChangeProof (EQUIVALENT transformation)

(34) YES

(35) Obligation:

(36) UsableRulesProof (EQUIVALENT transformation)

(37) Obligation:

(38) PiDPToQDPProof (EQUIVALENT transformation)

(39) Obligation:

(40) QDPSizeChangeProof (EQUIVALENT transformation)

(41) YES

(42) Obligation:

(43) UsableRulesProof (EQUIVALENT transformation)

(44) Obligation:

(45) PiDPToQDPProof (SOUND transformation)

(46) Obligation:

(47) QDPSizeChangeProof (EQUIVALENT transformation)

(48) YES