Left Termination proof of /tmp/tmp4MXaj5/d.pl

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

0 Prolog

↳1 PrologToDTProblemTransformerProof (⇒, 588 ms)

↳2 TRIPLES

↳3 TriplesToPiDPProof (⇒, 2141 ms)

↳4 PiDP

↳5 DependencyGraphProof (⇔, 24 ms)

↳6 AND

    ↳7 PiDP

        ↳8 UsableRulesProof (⇔, 0 ms)

        ↳9 PiDP

        ↳10 PiDPToQDPProof (⇔, 4 ms)

        ↳11 QDP

        ↳12 QDPSizeChangeProof (⇔, 0 ms)

        ↳13 YES

    ↳14 PiDP

        ↳15 UsableRulesProof (⇔, 337 ms)

        ↳16 PiDP

        ↳17 PiDPToQDPProof (⇒, 360 ms)

        ↳18 QDP

        ↳19 QDPOrderProof (⇔, 4652 ms)

        ↳20 QDP

        ↳21 DependencyGraphProof (⇔, 0 ms)

        ↳22 QDP

        ↳23 UsableRulesProof (⇔, 0 ms)

        ↳24 QDP

        ↳25 QReductionProof (⇔, 0 ms)

        ↳26 QDP

        ↳27 QDPSizeChangeProof (⇔, 0 ms)

        ↳28 YES

(0) Obligation:

Clauses:

d(X, X, 1).
d(T, X1, 0) :- isnumber(T).
d(times(U, V), X, +(times(B, U), times(A, V))) :- ','(d(U, X, A), d(V, X, B)).
d(div(U, V), X, W) :- d(times(U, power(V, p(0))), X, W).
d(power(U, V), X, times(V, times(W, power(U, p(V))))) :- ','(isnumber(V), d(U, X, W)).
isnumber(0).
isnumber(s(X)) :- isnumber(X).
isnumber(p(X)) :- isnumber(X).

Query: d(g,g,a)

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph DT10.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="B: d(T1, T2, T3)\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: d(T1, T2, T3), SCOPE: 1, CLAUSE: 0 | d(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | d(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | d(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | d(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | d(T5, T5, T3), SCOPE: 1, CLAUSE: 1 | d(T5, T5, T3), SCOPE: 1, CLAUSE: 2 | d(T5, T5, T3), SCOPE: 1, CLAUSE: 3 | d(T5, T5, T3), SCOPE: 1, CLAUSE: 4\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: d(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | d(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | d(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | d(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT2 is ground\nX3 is free\nd(T1, T2, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: d(T5, T5, T3), SCOPE: 1, CLAUSE: 1 | d(T5, T5, T3), SCOPE: 1, CLAUSE: 2 | d(T5, T5, T3), SCOPE: 1, CLAUSE: 3 | d(T5, T5, T3), SCOPE: 1, CLAUSE: 4\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: isnumber(T7) | d(T7, T7, T3), SCOPE: 1, CLAUSE: 2 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 3 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 4\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: d(T5, T5, T3), SCOPE: 1, CLAUSE: 2 | d(T5, T5, T3), SCOPE: 1, CLAUSE: 3 | d(T5, T5, T3), SCOPE: 1, CLAUSE: 4\n\nT5 is ground\nX6 is free\nX7 is free\nd(T5, T5, T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: isnumber(T7), SCOPE: 2, CLAUSE: 5 | isnumber(T7), SCOPE: 2, CLAUSE: 6 | isnumber(T7), SCOPE: 2, CLAUSE: 7 | ?_2 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 2 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 3 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 4\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: isnumber(T7), SCOPE: 2, CLAUSE: 5\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: isnumber(T7), SCOPE: 2, CLAUSE: 6 | isnumber(T7), SCOPE: 2, CLAUSE: 7 | ?_2 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 2 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 3 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 4\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: isnumber(T7), SCOPE: 2, CLAUSE: 6\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: isnumber(T7), SCOPE: 2, CLAUSE: 7 | ?_2 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 2 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 3 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 4\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="A: isnumber(T12)\n\nT12 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: isnumber(T12), SCOPE: 3, CLAUSE: 5 | isnumber(T12), SCOPE: 3, CLAUSE: 6 | isnumber(T12), SCOPE: 3, CLAUSE: 7\n\nT12 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: isnumber(T12), SCOPE: 3, CLAUSE: 5\n\nT12 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: isnumber(T12), SCOPE: 3, CLAUSE: 6 | isnumber(T12), SCOPE: 3, CLAUSE: 7\n\nT12 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: isnumber(T12), SCOPE: 3, CLAUSE: 6\n\nT12 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: isnumber(T12), SCOPE: 3, CLAUSE: 7\n\nT12 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: isnumber(T17)\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: isnumber(T20)\n\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: isnumber(T7), SCOPE: 2, CLAUSE: 7\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ?_2 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 2 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 3 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 4\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: isnumber(T25)\n\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: d(T7, T7, T3), SCOPE: 1, CLAUSE: 2 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 3 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 4\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: d(T7, T7, T3), SCOPE: 1, CLAUSE: 2\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: d(T7, T7, T3), SCOPE: 1, CLAUSE: 3 | d(T7, T7, T3), SCOPE: 1, CLAUSE: 4\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(d(T42, times(T42, T43), T46), d(T43, times(T42, T43), T47))\n\nT42 is ground\nT43 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: d(T42, times(T42, T43), T46)\n\nT42 is ground\nT43 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: d(T43, times(T42, T43), T52)\n\nT42 is ground\nT43 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: d(T7, T7, T3), SCOPE: 1, CLAUSE: 3\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: d(T7, T7, T3), SCOPE: 1, CLAUSE: 4\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: d(times(T73, power(T74, p(0))), div(T73, T74), T76)\n\nT73 is ground\nT74 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(isnumber(T88), d(T87, power(T87, T88), T90))\n\nT87 is ground\nT88 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: isnumber(T88)\n\nT88 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: d(T87, power(T87, T88), T90)\n\nT87 is ground\nT88 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)) | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 3 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nT100 is ground\nX6 is free\nX7 is free\nd(times(T99, T100), times(T99, T100), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: d(T5, T5, T3), SCOPE: 1, CLAUSE: 3 | d(T5, T5, T3), SCOPE: 1, CLAUSE: 4\n\nT5 is ground\nX6 is free\nX7 is free\nX98 is free\nX99 is free\nX100 is free\nX101 is free\nX102 is free\nd(T5, T5, T3) !=? d(X6, X7, 0)\nd(T5, T5, T3) !=? d(times(X98, X99), X100, +(times(X101, X98), times(X102, X99)))", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 0 | ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 1 | ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 2 | ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 3 | ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 4 | ?_4 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 3 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nT100 is ground\nX6 is free\nX7 is free\nd(times(T99, T100), times(T99, T100), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 1 | ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 2 | ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 3 | ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 4 | ?_4 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 3 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nT100 is ground\nX6 is free\nX7 is free\nd(times(T99, T100), times(T99, T100), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 1\n\nT99 is ground\nT100 is ground\nX6 is free\nX7 is free\nd(times(T99, T100), times(T99, T100), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 2 | ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 3 | ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 4 | ?_4 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 3 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nT100 is ground\nX6 is free\nX7 is free\nd(times(T99, T100), times(T99, T100), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ','(isnumber(T115), d(T116, times(T115, T116), T117))\n\nT115 is ground\nT116 is ground\nX6 is free\nX7 is free\nd(times(T115, T116), times(T115, T116), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: isnumber(T115)\n\nT115 is ground\nT116 is ground\nX6 is free\nX7 is free\nd(times(T115, T116), times(T115, T116), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: d(T116, times(T115, T116), T117)\n\nT115 is ground\nT116 is ground\nX6 is free\nX7 is free\nd(times(T115, T116), times(T115, T116), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 2\n\nT99 is ground\nT100 is ground\nX6 is free\nX7 is free\nd(times(T99, T100), times(T99, T100), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 3 | ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 4 | ?_4 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 3 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nT100 is ground\nX6 is free\nX7 is free\nd(times(T99, T100), times(T99, T100), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(','(d(T142, times(times(T142, T143), T144), T147), d(T143, times(times(T142, T143), T144), T148)), d(T144, times(times(T142, T143), T144), T149))\n\nT142 is ground\nT143 is ground\nT144 is ground\nX6 is free\nX7 is free\nd(times(times(T142, T143), T144), times(times(T142, T143), T144), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: d(T142, times(times(T142, T143), T144), T147)\n\nT142 is ground\nT143 is ground\nT144 is ground\nX6 is free\nX7 is free\nd(times(times(T142, T143), T144), times(times(T142, T143), T144), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: ','(d(T143, times(times(T142, T143), T144), T156), d(T144, times(times(T142, T143), T144), T157))\n\nT142 is ground\nT143 is ground\nT144 is ground\nX6 is free\nX7 is free\nd(times(times(T142, T143), T144), times(times(T142, T143), T144), T158) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: d(T143, times(times(T142, T143), T144), T156)\n\nT142 is ground\nT143 is ground\nT144 is ground\nX6 is free\nX7 is free\nd(times(times(T142, T143), T144), times(times(T142, T143), T144), T158) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: d(T144, times(times(T142, T143), T144), T171)\n\nT142 is ground\nT143 is ground\nT144 is ground\nX6 is free\nX7 is free\nd(times(times(T142, T143), T144), times(times(T142, T143), T144), T172) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 3\n\nT99 is ground\nT100 is ground\nX6 is free\nX7 is free\nd(times(T99, T100), times(T99, T100), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 4 | ?_4 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 3 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nT100 is ground\nX6 is free\nX7 is free\nd(times(T99, T100), times(T99, T100), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: ','(d(times(T201, power(T202, p(0))), times(div(T201, T202), T203), T205), d(T203, times(div(T201, T202), T203), T206))\n\nT201 is ground\nT202 is ground\nT203 is ground\nX6 is free\nX7 is free\nd(times(div(T201, T202), T203), times(div(T201, T202), T203), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: d(times(T201, power(T202, p(0))), times(div(T201, T202), T203), T205)\n\nT201 is ground\nT202 is ground\nT203 is ground\nX6 is free\nX7 is free\nd(times(div(T201, T202), T203), times(div(T201, T202), T203), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: d(T203, times(div(T201, T202), T203), T211)\n\nT201 is ground\nT202 is ground\nT203 is ground\nX6 is free\nX7 is free\nd(times(div(T201, T202), T203), times(div(T201, T202), T203), T212) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: ','(d(T99, times(T99, T100), T103), d(T100, times(T99, T100), T104)), SCOPE: 4, CLAUSE: 4\n\nT99 is ground\nT100 is ground\nX6 is free\nX7 is free\nd(times(T99, T100), times(T99, T100), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: ?_4 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 3 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nT100 is ground\nX6 is free\nX7 is free\nd(times(T99, T100), times(T99, T100), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: ','(','(isnumber(T240), d(T239, times(power(T239, T240), T241), T243)), d(T241, times(power(T239, T240), T241), T244))\n\nT239 is ground\nT240 is ground\nT241 is ground\nX6 is free\nX7 is free\nd(times(power(T239, T240), T241), times(power(T239, T240), T241), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: isnumber(T240)\n\nT239 is ground\nT240 is ground\nT241 is ground\nX6 is free\nX7 is free\nd(times(power(T239, T240), T241), times(power(T239, T240), T241), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: ','(d(T239, times(power(T239, T240), T241), T243), d(T241, times(power(T239, T240), T241), T244))\n\nT239 is ground\nT240 is ground\nT241 is ground\nX6 is free\nX7 is free\nd(times(power(T239, T240), T241), times(power(T239, T240), T241), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: d(T239, times(power(T239, T240), T241), T243)\n\nT239 is ground\nT240 is ground\nT241 is ground\nX6 is free\nX7 is free\nd(times(power(T239, T240), T241), times(power(T239, T240), T241), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: d(T241, times(power(T239, T240), T241), T251)\n\nT239 is ground\nT240 is ground\nT241 is ground\nX6 is free\nX7 is free\nd(times(power(T239, T240), T241), times(power(T239, T240), T241), T252) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 3 | d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nT100 is ground\nX6 is free\nX7 is free\nd(times(T99, T100), times(T99, T100), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: d(times(T99, T100), times(T99, T100), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nT100 is ground\nX6 is free\nX7 is free\nd(times(T99, T100), times(T99, T100), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: d(times(T268, power(T269, p(0))), div(T268, T269), T271) | d(div(T268, T269), div(T268, T269), T3), SCOPE: 1, CLAUSE: 4\n\nT268 is ground\nT269 is ground\nX6 is free\nX7 is free\nd(div(T268, T269), div(T268, T269), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: d(T5, T5, T3), SCOPE: 1, CLAUSE: 4\n\nT5 is ground\nX6 is free\nX7 is free\nX98 is free\nX99 is free\nX100 is free\nX101 is free\nX102 is free\nX215 is free\nX216 is free\nX217 is free\nX218 is free\nd(T5, T5, T3) !=? d(X6, X7, 0)\nd(T5, T5, T3) !=? d(times(X98, X99), X100, +(times(X101, X98), times(X102, X99)))\nd(T5, T5, T3) !=? d(div(X215, X216), X217, X218)", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 0 | d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 1 | d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 2 | d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 3 | d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 4 | ?_5 | d(div(T268, T269), div(T268, T269), T3), SCOPE: 1, CLAUSE: 4\n\nT268 is ground\nT269 is ground\nX6 is free\nX7 is free\nd(div(T268, T269), div(T268, T269), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 1 | d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 2 | d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 3 | d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 4 | ?_5 | d(div(T268, T269), div(T268, T269), T3), SCOPE: 1, CLAUSE: 4\n\nT268 is ground\nT269 is ground\nX6 is free\nX7 is free\nd(div(T268, T269), div(T268, T269), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 1\n\nT268 is ground\nT269 is ground\nX6 is free\nX7 is free\nd(div(T268, T269), div(T268, T269), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 2 | d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 3 | d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 4 | ?_5 | d(div(T268, T269), div(T268, T269), T3), SCOPE: 1, CLAUSE: 4\n\nT268 is ground\nT269 is ground\nX6 is free\nX7 is free\nd(div(T268, T269), div(T268, T269), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: isnumber(times(T282, power(T283, p(0))))\n\nT282 is ground\nT283 is ground\nX6 is free\nX7 is free\nd(div(T282, T283), div(T282, T283), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 2\n\nT268 is ground\nT269 is ground\nX6 is free\nX7 is free\nd(div(T268, T269), div(T268, T269), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 3 | d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 4 | ?_5 | d(div(T268, T269), div(T268, T269), T3), SCOPE: 1, CLAUSE: 4\n\nT268 is ground\nT269 is ground\nX6 is free\nX7 is free\nd(div(T268, T269), div(T268, T269), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: ','(d(T300, div(T300, T301), T304), d(power(T301, p(0)), div(T300, T301), T305))\n\nT300 is ground\nT301 is ground\nX6 is free\nX7 is free\nd(div(T300, T301), div(T300, T301), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: d(T300, div(T300, T301), T304)\n\nT300 is ground\nT301 is ground\nX6 is free\nX7 is free\nd(div(T300, T301), div(T300, T301), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: d(power(T301, p(0)), div(T300, T301), T310)\n\nT300 is ground\nT301 is ground\nX6 is free\nX7 is free\nd(div(T300, T301), div(T300, T301), T311) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: d(times(T268, power(T269, p(0))), div(T268, T269), T271), SCOPE: 5, CLAUSE: 4 | ?_5 | d(div(T268, T269), div(T268, T269), T3), SCOPE: 1, CLAUSE: 4\n\nT268 is ground\nT269 is ground\nX6 is free\nX7 is free\nd(div(T268, T269), div(T268, T269), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: ?_5 | d(div(T268, T269), div(T268, T269), T3), SCOPE: 1, CLAUSE: 4\n\nT268 is ground\nT269 is ground\nX6 is free\nX7 is free\nd(div(T268, T269), div(T268, T269), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: d(div(T268, T269), div(T268, T269), T3), SCOPE: 1, CLAUSE: 4\n\nT268 is ground\nT269 is ground\nX6 is free\nX7 is free\nd(div(T268, T269), div(T268, T269), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: ','(isnumber(T322), d(T321, power(T321, T322), T324))\n\nT321 is ground\nT322 is ground\nX6 is free\nX7 is free\nd(power(T321, T322), power(T321, T322), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: ','(isnumber(T322), d(T321, power(T321, T322), T324)), SCOPE: 6, CLAUSE: 5 | ','(isnumber(T322), d(T321, power(T321, T322), T324)), SCOPE: 6, CLAUSE: 6 | ','(isnumber(T322), d(T321, power(T321, T322), T324)), SCOPE: 6, CLAUSE: 7\n\nT321 is ground\nT322 is ground\nX6 is free\nX7 is free\nd(power(T321, T322), power(T321, T322), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: ','(isnumber(T322), d(T321, power(T321, T322), T324)), SCOPE: 6, CLAUSE: 5\n\nT321 is ground\nT322 is ground\nX6 is free\nX7 is free\nd(power(T321, T322), power(T321, T322), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: ','(isnumber(T322), d(T321, power(T321, T322), T324)), SCOPE: 6, CLAUSE: 6 | ','(isnumber(T322), d(T321, power(T321, T322), T324)), SCOPE: 6, CLAUSE: 7\n\nT321 is ground\nT322 is ground\nX6 is free\nX7 is free\nd(power(T321, T322), power(T321, T322), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: d(T321, power(T321, 0), T324)\n\nT321 is ground\nX6 is free\nX7 is free\nd(power(T321, 0), power(T321, 0), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: ','(isnumber(T322), d(T321, power(T321, T322), T324)), SCOPE: 6, CLAUSE: 6\n\nT321 is ground\nT322 is ground\nX6 is free\nX7 is free\nd(power(T321, T322), power(T321, T322), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(isnumber(T322), d(T321, power(T321, T322), T324)), SCOPE: 6, CLAUSE: 7\n\nT321 is ground\nT322 is ground\nX6 is free\nX7 is free\nd(power(T321, T322), power(T321, T322), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(isnumber(T331), d(T321, power(T321, s(T331)), T324))\n\nT321 is ground\nT331 is ground\nX6 is free\nX7 is free\nd(power(T321, s(T331)), power(T321, s(T331)), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: isnumber(T331)\n\nT321 is ground\nT331 is ground\nX6 is free\nX7 is free\nd(power(T321, s(T331)), power(T321, s(T331)), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: d(T321, power(T321, s(T331)), T324)\n\nT321 is ground\nT331 is ground\nX6 is free\nX7 is free\nd(power(T321, s(T331)), power(T321, s(T331)), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: ','(isnumber(T338), d(T321, power(T321, p(T338)), T324))\n\nT321 is ground\nT338 is ground\nX6 is free\nX7 is free\nd(power(T321, p(T338)), power(T321, p(T338)), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: isnumber(T338)\n\nT321 is ground\nT338 is ground\nX6 is free\nX7 is free\nd(power(T321, p(T338)), power(T321, p(T338)), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: d(T321, power(T321, p(T338)), T324)\n\nT321 is ground\nT338 is ground\nX6 is free\nX7 is free\nd(power(T321, p(T338)), power(T321, p(T338)), T3) !=? d(X6, X7, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: isnumber(T345) | d(T345, T346, T3), SCOPE: 1, CLAUSE: 2 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 3 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 4\n\nT345 is ground\nT346 is ground\nX3 is free\nd(T345, T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: d(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | d(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | d(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT2 is ground\nX3 is free\nX297 is free\nX298 is free\nd(T1, T2, T3) !=? d(X3, X3, 1)\nd(T1, T2, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: isnumber(T345), SCOPE: 7, CLAUSE: 5 | isnumber(T345), SCOPE: 7, CLAUSE: 6 | isnumber(T345), SCOPE: 7, CLAUSE: 7 | ?_7 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 2 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 3 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 4\n\nT345 is ground\nT346 is ground\nX3 is free\nd(T345, T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: isnumber(T345), SCOPE: 7, CLAUSE: 5\n\nT345 is ground\nT346 is ground\nX3 is free\nd(T345, T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: isnumber(T345), SCOPE: 7, CLAUSE: 6 | isnumber(T345), SCOPE: 7, CLAUSE: 7 | ?_7 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 2 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 3 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 4\n\nT345 is ground\nT346 is ground\nX3 is free\nd(T345, T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: isnumber(T345), SCOPE: 7, CLAUSE: 6\n\nT345 is ground\nT346 is ground\nX3 is free\nd(T345, T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: isnumber(T345), SCOPE: 7, CLAUSE: 7 | ?_7 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 2 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 3 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 4\n\nT345 is ground\nT346 is ground\nX3 is free\nd(T345, T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: isnumber(T351)\n\nT346 is ground\nT351 is ground\nX3 is free\nd(s(T351), T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: isnumber(T345), SCOPE: 7, CLAUSE: 7\n\nT345 is ground\nT346 is ground\nX3 is free\nd(T345, T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: ?_7 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 2 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 3 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 4\n\nT345 is ground\nT346 is ground\nX3 is free\nd(T345, T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: isnumber(T356)\n\nT346 is ground\nT356 is ground\nX3 is free\nd(p(T356), T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: d(T345, T346, T3), SCOPE: 1, CLAUSE: 2 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 3 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 4\n\nT345 is ground\nT346 is ground\nX3 is free\nd(T345, T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: d(T345, T346, T3), SCOPE: 1, CLAUSE: 2\n\nT345 is ground\nT346 is ground\nX3 is free\nd(T345, T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: d(T345, T346, T3), SCOPE: 1, CLAUSE: 3 | d(T345, T346, T3), SCOPE: 1, CLAUSE: 4\n\nT345 is ground\nT346 is ground\nX3 is free\nd(T345, T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: ','(d(T377, T379, T382), d(T378, T379, T383))\n\nT377 is ground\nT378 is ground\nT379 is ground\nX3 is free\nd(times(T377, T378), T379, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: d(T377, T379, T382)\n\nT377 is ground\nT378 is ground\nT379 is ground\nX3 is free\nd(times(T377, T378), T379, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: d(T378, T379, T386)\n\nT377 is ground\nT378 is ground\nT379 is ground\nX3 is free\nd(times(T377, T378), T379, T387) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: d(T345, T346, T3), SCOPE: 1, CLAUSE: 3\n\nT345 is ground\nT346 is ground\nX3 is free\nd(T345, T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: d(T345, T346, T3), SCOPE: 1, CLAUSE: 4\n\nT345 is ground\nT346 is ground\nX3 is free\nd(T345, T346, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: d(times(T408, power(T409, p(0))), T410, T412)\n\nT408 is ground\nT409 is ground\nT410 is ground\nX3 is free\nd(div(T408, T409), T410, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: ','(isnumber(T426), d(T425, T427, T429))\n\nT425 is ground\nT426 is ground\nT427 is ground\nX3 is free\nd(power(T425, T426), T427, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: isnumber(T426)\n\nT425 is ground\nT426 is ground\nT427 is ground\nX3 is free\nd(power(T425, T426), T427, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: d(T425, T427, T429)\n\nT425 is ground\nT426 is ground\nT427 is ground\nX3 is free\nd(power(T425, T426), T427, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: ','(d(T437, T439, T442), d(T438, T439, T443)) | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 3 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 4\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: d(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | d(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT2 is ground\nX3 is free\nX297 is free\nX298 is free\nX381 is free\nX382 is free\nX383 is free\nX384 is free\nX385 is free\nd(T1, T2, T3) !=? d(X3, X3, 1)\nd(T1, T2, T3) !=? d(X297, X298, 0)\nd(T1, T2, T3) !=? d(times(X381, X382), X383, +(times(X384, X381), times(X385, X382)))", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 0 | ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 1 | ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 2 | ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 3 | ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 4 | ?_8 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 3 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 4\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 0\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 1 | ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 2 | ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 3 | ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 4 | ?_8 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 3 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 4\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: d(T438, T448, T449)\n\nT438 is ground\nT448 is ground\nX297 is free\nX298 is free\nd(times(T448, T438), T448, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 1\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 2 | ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 3 | ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 4 | ?_8 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 3 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 4\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: ','(isnumber(T460), d(T438, T461, T462))\n\nT438 is ground\nT460 is ground\nT461 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T460, T438), T461, T3) !=? d(X3, X3, 1)\nd(times(T460, T438), T461, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: isnumber(T460)\n\nT438 is ground\nT460 is ground\nT461 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T460, T438), T461, T3) !=? d(X3, X3, 1)\nd(times(T460, T438), T461, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: d(T438, T461, T462)\n\nT438 is ground\nT460 is ground\nT461 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T460, T438), T461, T3) !=? d(X3, X3, 1)\nd(times(T460, T438), T461, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 2\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 3 | ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 4 | ?_8 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 3 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 4\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: ','(','(d(T485, T487, T490), d(T486, T487, T491)), d(T438, T487, T492))\n\nT438 is ground\nT485 is ground\nT486 is ground\nT487 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(times(T485, T486), T438), T487, T3) !=? d(X3, X3, 1)\nd(times(times(T485, T486), T438), T487, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: d(T485, T487, T490)\n\nT438 is ground\nT485 is ground\nT486 is ground\nT487 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(times(T485, T486), T438), T487, T3) !=? d(X3, X3, 1)\nd(times(times(T485, T486), T438), T487, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: ','(d(T486, T487, T495), d(T438, T487, T496))\n\nT438 is ground\nT485 is ground\nT486 is ground\nT487 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(times(T485, T486), T438), T487, T497) !=? d(X3, X3, 1)\nd(times(times(T485, T486), T438), T487, T497) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: d(T486, T487, T495)\n\nT438 is ground\nT485 is ground\nT486 is ground\nT487 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(times(T485, T486), T438), T487, T497) !=? d(X3, X3, 1)\nd(times(times(T485, T486), T438), T487, T497) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: d(T438, T487, T502)\n\nT438 is ground\nT485 is ground\nT486 is ground\nT487 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(times(T485, T486), T438), T487, T503) !=? d(X3, X3, 1)\nd(times(times(T485, T486), T438), T487, T503) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 3\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 4 | ?_8 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 3 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 4\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: ','(d(times(T524, power(T525, p(0))), T526, T528), d(T438, T526, T529))\n\nT438 is ground\nT524 is ground\nT525 is ground\nT526 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(div(T524, T525), T438), T526, T3) !=? d(X3, X3, 1)\nd(times(div(T524, T525), T438), T526, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: d(times(T524, power(T525, p(0))), T526, T528)\n\nT438 is ground\nT524 is ground\nT525 is ground\nT526 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(div(T524, T525), T438), T526, T3) !=? d(X3, X3, 1)\nd(times(div(T524, T525), T438), T526, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: d(T438, T526, T534)\n\nT438 is ground\nT524 is ground\nT525 is ground\nT526 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(div(T524, T525), T438), T526, T535) !=? d(X3, X3, 1)\nd(times(div(T524, T525), T438), T526, T535) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: ','(d(T437, T439, T442), d(T438, T439, T443)), SCOPE: 8, CLAUSE: 4\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: ?_8 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 3 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 4\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: ','(','(isnumber(T559), d(T558, T560, T562)), d(T438, T560, T563))\n\nT438 is ground\nT558 is ground\nT559 is ground\nT560 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(power(T558, T559), T438), T560, T3) !=? d(X3, X3, 1)\nd(times(power(T558, T559), T438), T560, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: isnumber(T559)\n\nT438 is ground\nT558 is ground\nT559 is ground\nT560 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(power(T558, T559), T438), T560, T3) !=? d(X3, X3, 1)\nd(times(power(T558, T559), T438), T560, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: ','(d(T558, T560, T562), d(T438, T560, T563))\n\nT438 is ground\nT558 is ground\nT559 is ground\nT560 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(power(T558, T559), T438), T560, T3) !=? d(X3, X3, 1)\nd(times(power(T558, T559), T438), T560, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: d(T558, T560, T562)\n\nT438 is ground\nT558 is ground\nT559 is ground\nT560 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(power(T558, T559), T438), T560, T3) !=? d(X3, X3, 1)\nd(times(power(T558, T559), T438), T560, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: d(T438, T560, T566)\n\nT438 is ground\nT558 is ground\nT559 is ground\nT560 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(power(T558, T559), T438), T560, T567) !=? d(X3, X3, 1)\nd(times(power(T558, T559), T438), T560, T567) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 3 | d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 4\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: d(times(T437, T438), T439, T3), SCOPE: 1, CLAUSE: 4\n\nT437 is ground\nT438 is ground\nT439 is ground\nX3 is free\nX297 is free\nX298 is free\nd(times(T437, T438), T439, T3) !=? d(X3, X3, 1)\nd(times(T437, T438), T439, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: d(times(T576, power(T577, p(0))), T578, T580) | d(div(T576, T577), T578, T3), SCOPE: 1, CLAUSE: 4\n\nT576 is ground\nT577 is ground\nT578 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T576, T577), T578, T3) !=? d(X3, X3, 1)\nd(div(T576, T577), T578, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: d(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT2 is ground\nX3 is free\nX297 is free\nX298 is free\nX381 is free\nX382 is free\nX383 is free\nX384 is free\nX385 is free\nX504 is free\nX505 is free\nX506 is free\nX507 is free\nd(T1, T2, T3) !=? d(X3, X3, 1)\nd(T1, T2, T3) !=? d(X297, X298, 0)\nd(T1, T2, T3) !=? d(times(X381, X382), X383, +(times(X384, X381), times(X385, X382)))\nd(T1, T2, T3) !=? d(div(X504, X505), X506, X507)", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 0 | d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 1 | d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 2 | d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 3 | d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 4 | ?_9 | d(div(T576, T577), T578, T3), SCOPE: 1, CLAUSE: 4\n\nT576 is ground\nT577 is ground\nT578 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T576, T577), T578, T3) !=? d(X3, X3, 1)\nd(div(T576, T577), T578, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 0\n\nT576 is ground\nT577 is ground\nT578 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T576, T577), T578, T3) !=? d(X3, X3, 1)\nd(div(T576, T577), T578, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 1 | d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 2 | d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 3 | d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 4 | ?_9 | d(div(T576, T577), T578, T3), SCOPE: 1, CLAUSE: 4\n\nT576 is ground\nT577 is ground\nT578 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T576, T577), T578, T3) !=? d(X3, X3, 1)\nd(div(T576, T577), T578, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 1\n\nT576 is ground\nT577 is ground\nT578 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T576, T577), T578, T3) !=? d(X3, X3, 1)\nd(div(T576, T577), T578, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 2 | d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 3 | d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 4 | ?_9 | d(div(T576, T577), T578, T3), SCOPE: 1, CLAUSE: 4\n\nT576 is ground\nT577 is ground\nT578 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T576, T577), T578, T3) !=? d(X3, X3, 1)\nd(div(T576, T577), T578, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: isnumber(times(T603, power(T604, p(0))))\n\nT603 is ground\nT604 is ground\nT605 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T603, T604), T605, T3) !=? d(X3, X3, 1)\nd(div(T603, T604), T605, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 2\n\nT576 is ground\nT577 is ground\nT578 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T576, T577), T578, T3) !=? d(X3, X3, 1)\nd(div(T576, T577), T578, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 3 | d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 4 | ?_9 | d(div(T576, T577), T578, T3), SCOPE: 1, CLAUSE: 4\n\nT576 is ground\nT577 is ground\nT578 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T576, T577), T578, T3) !=? d(X3, X3, 1)\nd(div(T576, T577), T578, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: ','(d(T626, T628, T631), d(power(T627, p(0)), T628, T632))\n\nT626 is ground\nT627 is ground\nT628 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T626, T627), T628, T3) !=? d(X3, X3, 1)\nd(div(T626, T627), T628, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: d(T626, T628, T631)\n\nT626 is ground\nT627 is ground\nT628 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T626, T627), T628, T3) !=? d(X3, X3, 1)\nd(div(T626, T627), T628, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: d(power(T627, p(0)), T628, T635)\n\nT626 is ground\nT627 is ground\nT628 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T626, T627), T628, T636) !=? d(X3, X3, 1)\nd(div(T626, T627), T628, T636) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: d(times(T576, power(T577, p(0))), T578, T580), SCOPE: 9, CLAUSE: 4 | ?_9 | d(div(T576, T577), T578, T3), SCOPE: 1, CLAUSE: 4\n\nT576 is ground\nT577 is ground\nT578 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T576, T577), T578, T3) !=? d(X3, X3, 1)\nd(div(T576, T577), T578, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: ?_9 | d(div(T576, T577), T578, T3), SCOPE: 1, CLAUSE: 4\n\nT576 is ground\nT577 is ground\nT578 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T576, T577), T578, T3) !=? d(X3, X3, 1)\nd(div(T576, T577), T578, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: d(div(T576, T577), T578, T3), SCOPE: 1, CLAUSE: 4\n\nT576 is ground\nT577 is ground\nT578 is ground\nX3 is free\nX297 is free\nX298 is free\nd(div(T576, T577), T578, T3) !=? d(X3, X3, 1)\nd(div(T576, T577), T578, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: ','(isnumber(T646), d(T645, T647, T649))\n\nT645 is ground\nT646 is ground\nT647 is ground\nX3 is free\nX297 is free\nX298 is free\nd(power(T645, T646), T647, T3) !=? d(X3, X3, 1)\nd(power(T645, T646), T647, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: ','(isnumber(T646), d(T645, T647, T649)), SCOPE: 10, CLAUSE: 5 | ','(isnumber(T646), d(T645, T647, T649)), SCOPE: 10, CLAUSE: 6 | ','(isnumber(T646), d(T645, T647, T649)), SCOPE: 10, CLAUSE: 7\n\nT645 is ground\nT646 is ground\nT647 is ground\nX3 is free\nX297 is free\nX298 is free\nd(power(T645, T646), T647, T3) !=? d(X3, X3, 1)\nd(power(T645, T646), T647, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: ','(isnumber(T646), d(T645, T647, T649)), SCOPE: 10, CLAUSE: 5\n\nT645 is ground\nT646 is ground\nT647 is ground\nX3 is free\nX297 is free\nX298 is free\nd(power(T645, T646), T647, T3) !=? d(X3, X3, 1)\nd(power(T645, T646), T647, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: ','(isnumber(T646), d(T645, T647, T649)), SCOPE: 10, CLAUSE: 6 | ','(isnumber(T646), d(T645, T647, T649)), SCOPE: 10, CLAUSE: 7\n\nT645 is ground\nT646 is ground\nT647 is ground\nX3 is free\nX297 is free\nX298 is free\nd(power(T645, T646), T647, T3) !=? d(X3, X3, 1)\nd(power(T645, T646), T647, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: d(T645, T647, T649)\n\nT645 is ground\nT647 is ground\nX3 is free\nX297 is free\nX298 is free\nd(power(T645, 0), T647, T3) !=? d(X3, X3, 1)\nd(power(T645, 0), T647, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: ','(isnumber(T646), d(T645, T647, T649)), SCOPE: 10, CLAUSE: 6\n\nT645 is ground\nT646 is ground\nT647 is ground\nX3 is free\nX297 is free\nX298 is free\nd(power(T645, T646), T647, T3) !=? d(X3, X3, 1)\nd(power(T645, T646), T647, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: ','(isnumber(T646), d(T645, T647, T649)), SCOPE: 10, CLAUSE: 7\n\nT645 is ground\nT646 is ground\nT647 is ground\nX3 is free\nX297 is free\nX298 is free\nd(power(T645, T646), T647, T3) !=? d(X3, X3, 1)\nd(power(T645, T646), T647, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: ','(isnumber(T656), d(T645, T647, T649))\n\nT645 is ground\nT647 is ground\nT656 is ground\nX3 is free\nX297 is free\nX298 is free\nd(power(T645, s(T656)), T647, T3) !=? d(X3, X3, 1)\nd(power(T645, s(T656)), T647, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: isnumber(T656)\n\nT645 is ground\nT647 is ground\nT656 is ground\nX3 is free\nX297 is free\nX298 is free\nd(power(T645, s(T656)), T647, T3) !=? d(X3, X3, 1)\nd(power(T645, s(T656)), T647, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: d(T645, T647, T649)\n\nT645 is ground\nT647 is ground\nT656 is ground\nX3 is free\nX297 is free\nX298 is free\nd(power(T645, s(T656)), T647, T3) !=? d(X3, X3, 1)\nd(power(T645, s(T656)), T647, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: ','(isnumber(T661), d(T645, T647, T649))\n\nT645 is ground\nT647 is ground\nT661 is ground\nX3 is free\nX297 is free\nX298 is free\nd(power(T645, p(T661)), T647, T3) !=? d(X3, X3, 1)\nd(power(T645, p(T661)), T647, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: isnumber(T661)\n\nT645 is ground\nT647 is ground\nT661 is ground\nX3 is free\nX297 is free\nX298 is free\nd(power(T645, p(T661)), T647, T3) !=? d(X3, X3, 1)\nd(power(T645, p(T661)), T647, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: d(T645, T647, T649)\n\nT645 is ground\nT647 is ground\nT661 is ground\nX3 is free\nX297 is free\nX298 is free\nd(power(T645, p(T661)), T647, T3) !=? d(X3, X3, 1)\nd(power(T645, p(T661)), T647, T3) !=? d(X297, X298, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 227 [arrowhead = none ];
227 -> 2;

228 [label="EVAL with clause\nd(X3, X3, 1).\nand substitutionT1 -> T5,\nX3 -> T5,\nT2 -> T5,\nT3 -> 1", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 228 [arrowhead = none ];
228 -> 3;

229 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2 -> 229 [arrowhead = none ];
229 -> 4;

230 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 230 [arrowhead = none ];
230 -> 5;

231 [label="EVAL with clause\nd(X297, X298, 0) :- isnumber(X297).\nand substitutionT1 -> T345,\nX297 -> T345,\nT2 -> T346,\nX298 -> T346,\nT3 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 231 [arrowhead = none ];
231 -> 119;

232 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 232 [arrowhead = none ];
232 -> 120;

233 [label="EVAL with clause\nd(X6, X7, 0) :- isnumber(X6).\nand substitutionT5 -> T7,\nX6 -> T7,\nX7 -> T7,\nT3 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 233 [arrowhead = none ];
233 -> 6;

234 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 234 [arrowhead = none ];
234 -> 7;

235 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
6 -> 235 [arrowhead = none ];
235 -> 8;

236 [label="EVAL with clause\nd(times(X98, X99), X100, +(times(X101, X98), times(X102, X99))) :- ','(d(X98, X100, X102), d(X99, X100, X101)).\nand substitutionX98 -> T99,\nX99 -> T100,\nT5 -> times(T99, T100),\nX100 -> times(T99, T100),\nX101 -> T104,\nX102 -> T103,\nT3 -> +(times(T104, T99), times(T103, T100)),\nT102 -> T103,\nT101 -> T104", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 236 [arrowhead = none ];
236 -> 49;

237 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 237 [arrowhead = none ];
237 -> 50;

238 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
8 -> 238 [arrowhead = none ];
238 -> 9;

239 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
8 -> 239 [arrowhead = none ];
239 -> 10;

240 [label="EVAL with clause\nisnumber(0).\nand substitutionT7 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 240 [arrowhead = none ];
240 -> 11;

241 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 241 [arrowhead = none ];
241 -> 12;

242 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
10 -> 242 [arrowhead = none ];
242 -> 14;

243 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
10 -> 243 [arrowhead = none ];
243 -> 15;

244 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 244 [arrowhead = none ];
244 -> 13;

245 [label="EVAL with clause\nisnumber(s(X12)) :- isnumber(X12).\nand substitutionX12 -> T12,\nT7 -> s(T12)", fontsize=14, style = filled, fillcolor = lightblue];
14 -> 245 [arrowhead = none ];
245 -> 16;

246 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
14 -> 246 [arrowhead = none ];
246 -> 17;

247 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
15 -> 247 [arrowhead = none ];
247 -> 30;

248 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
15 -> 248 [arrowhead = none ];
248 -> 31;

249 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
16 -> 249 [arrowhead = none ];
249 -> 18;

250 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
18 -> 250 [arrowhead = none ];
250 -> 19;

251 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
18 -> 251 [arrowhead = none ];
251 -> 20;

252 [label="EVAL with clause\nisnumber(0).\nand substitutionT12 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 252 [arrowhead = none ];
252 -> 21;

253 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
19 -> 253 [arrowhead = none ];
253 -> 22;

254 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
20 -> 254 [arrowhead = none ];
254 -> 24;

255 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
20 -> 255 [arrowhead = none ];
255 -> 25;

256 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
21 -> 256 [arrowhead = none ];
256 -> 23;

257 [label="EVAL with clause\nisnumber(s(X17)) :- isnumber(X17).\nand substitutionX17 -> T17,\nT12 -> s(T17)", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 257 [arrowhead = none ];
257 -> 26;

258 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 258 [arrowhead = none ];
258 -> 27;

259 [label="EVAL with clause\nisnumber(p(X20)) :- isnumber(X20).\nand substitutionX20 -> T20,\nT12 -> p(T20)", fontsize=14, style = filled, fillcolor = lightblue];
25 -> 259 [arrowhead = none ];
259 -> 28;

260 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
25 -> 260 [arrowhead = none ];
260 -> 29;

261 [label="INSTANCE with matching:\nT12 -> T17", fontsize=14, style = filled, fillcolor = lightgrey];
26 -> 261 [arrowhead = none , style=dashed];
261 -> 16[style=dashed];

262 [label="INSTANCE with matching:\nT12 -> T20", fontsize=14, style = filled, fillcolor = lightgrey];
28 -> 262 [arrowhead = none , style=dashed];
262 -> 16[style=dashed];

263 [label="EVAL with clause\nisnumber(p(X25)) :- isnumber(X25).\nand substitutionX25 -> T25,\nT7 -> p(T25)", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 263 [arrowhead = none ];
263 -> 32;

264 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 264 [arrowhead = none ];
264 -> 33;

265 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
31 -> 265 [arrowhead = none ];
265 -> 34;

266 [label="INSTANCE with matching:\nT12 -> T25", fontsize=14, style = filled, fillcolor = lightgrey];
32 -> 266 [arrowhead = none , style=dashed];
266 -> 16[style=dashed];

267 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
34 -> 267 [arrowhead = none ];
267 -> 35;

268 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
34 -> 268 [arrowhead = none ];
268 -> 36;

269 [label="EVAL with clause\nd(times(X46, X47), X48, +(times(X49, X46), times(X50, X47))) :- ','(d(X46, X48, X50), d(X47, X48, X49)).\nand substitutionX46 -> T42,\nX47 -> T43,\nT7 -> times(T42, T43),\nX48 -> times(T42, T43),\nX49 -> T47,\nX50 -> T46,\nT3 -> +(times(T47, T42), times(T46, T43)),\nT45 -> T46,\nT44 -> T47", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 269 [arrowhead = none ];
269 -> 37;

270 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
35 -> 270 [arrowhead = none ];
270 -> 38;

271 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
36 -> 271 [arrowhead = none ];
271 -> 41;

272 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
36 -> 272 [arrowhead = none ];
272 -> 42;

273 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
37 -> 273 [arrowhead = none ];
273 -> 39;

274 [label="SPLIT 2\nnew knowledge:\nT42 is ground\nT43 is ground\nT46 is ground\nreplacements:T47 -> T52", fontsize=14, style = filled, fillcolor = violet];
37 -> 274 [arrowhead = none ];
274 -> 40;

275 [label="INSTANCE with matching:\nT1 -> T42\nT2 -> times(T42, T43)\nT3 -> T46", fontsize=14, style = filled, fillcolor = lightgrey];
39 -> 275 [arrowhead = none , style=dashed];
275 -> 1[style=dashed];

276 [label="INSTANCE with matching:\nT1 -> T43\nT2 -> times(T42, T43)\nT3 -> T52", fontsize=14, style = filled, fillcolor = lightgrey];
40 -> 276 [arrowhead = none , style=dashed];
276 -> 1[style=dashed];

277 [label="EVAL with clause\nd(div(X73, X74), X75, X76) :- d(times(X73, power(X74, p(0))), X75, X76).\nand substitutionX73 -> T73,\nX74 -> T74,\nT7 -> div(T73, T74),\nX75 -> div(T73, T74),\nT3 -> T76,\nX76 -> T76,\nT75 -> T76", fontsize=14, style = filled, fillcolor = lightblue];
41 -> 277 [arrowhead = none ];
277 -> 43;

278 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 278 [arrowhead = none ];
278 -> 44;

279 [label="EVAL with clause\nd(power(X87, X88), X89, times(X88, times(X90, power(X87, p(X88))))) :- ','(isnumber(X88), d(X87, X89, X90)).\nand substitutionX87 -> T87,\nX88 -> T88,\nT7 -> power(T87, T88),\nX89 -> power(T87, T88),\nX90 -> T90,\nT3 -> times(T88, times(T90, power(T87, p(T88)))),\nT89 -> T90", fontsize=14, style = filled, fillcolor = lightblue];
42 -> 279 [arrowhead = none ];
279 -> 45;

280 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
42 -> 280 [arrowhead = none ];
280 -> 46;

281 [label="INSTANCE with matching:\nT1 -> times(T73, power(T74, p(0)))\nT2 -> div(T73, T74)\nT3 -> T76", fontsize=14, style = filled, fillcolor = lightgrey];
43 -> 281 [arrowhead = none , style=dashed];
281 -> 1[style=dashed];

282 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
45 -> 282 [arrowhead = none ];
282 -> 47;

283 [label="SPLIT 2\nnew knowledge:\nT88 is ground", fontsize=14, style = filled, fillcolor = violet];
45 -> 283 [arrowhead = none ];
283 -> 48;

284 [label="INSTANCE with matching:\nT12 -> T88", fontsize=14, style = filled, fillcolor = lightgrey];
47 -> 284 [arrowhead = none , style=dashed];
284 -> 16[style=dashed];

285 [label="INSTANCE with matching:\nT1 -> T87\nT2 -> power(T87, T88)\nT3 -> T90", fontsize=14, style = filled, fillcolor = lightgrey];
48 -> 285 [arrowhead = none , style=dashed];
285 -> 1[style=dashed];

286 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
49 -> 286 [arrowhead = none ];
286 -> 51;

287 [label="EVAL with clause\nd(div(X215, X216), X217, X218) :- d(times(X215, power(X216, p(0))), X217, X218).\nand substitutionX215 -> T268,\nX216 -> T269,\nT5 -> div(T268, T269),\nX217 -> div(T268, T269),\nT3 -> T271,\nX218 -> T271,\nT270 -> T271", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 287 [arrowhead = none ];
287 -> 84;

288 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
50 -> 288 [arrowhead = none ];
288 -> 85;

289 [label="BACKTRACK\nfor clause: d(X, X, 1)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
51 -> 289 [arrowhead = none ];
289 -> 52;

290 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
52 -> 290 [arrowhead = none ];
290 -> 53;

291 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
52 -> 291 [arrowhead = none ];
291 -> 54;

292 [label="EVAL with clause\nd(X112, X113, 0) :- isnumber(X112).\nand substitutionT99 -> T115,\nX112 -> T115,\nT100 -> T116,\nX113 -> times(T115, T116),\nT103 -> 0,\nT104 -> T117", fontsize=14, style = filled, fillcolor = lightblue];
53 -> 292 [arrowhead = none ];
292 -> 55;

293 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
53 -> 293 [arrowhead = none ];
293 -> 56;

294 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
54 -> 294 [arrowhead = none ];
294 -> 59;

295 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
54 -> 295 [arrowhead = none ];
295 -> 60;

296 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
55 -> 296 [arrowhead = none ];
296 -> 57;

297 [label="SPLIT 2\nnew knowledge:\nT115 is ground", fontsize=14, style = filled, fillcolor = violet];
55 -> 297 [arrowhead = none ];
297 -> 58;

298 [label="INSTANCE with matching:\nT12 -> T115", fontsize=14, style = filled, fillcolor = lightgrey];
57 -> 298 [arrowhead = none , style=dashed];
298 -> 16[style=dashed];

299 [label="INSTANCE with matching:\nT1 -> T116\nT2 -> times(T115, T116)\nT3 -> T117", fontsize=14, style = filled, fillcolor = lightgrey];
58 -> 299 [arrowhead = none , style=dashed];
299 -> 1[style=dashed];

300 [label="EVAL with clause\nd(times(X136, X137), X138, +(times(X139, X136), times(X140, X137))) :- ','(d(X136, X138, X140), d(X137, X138, X139)).\nand substitutionX136 -> T142,\nX137 -> T143,\nT99 -> times(T142, T143),\nT100 -> T144,\nX138 -> times(times(T142, T143), T144),\nX139 -> T148,\nX140 -> T147,\nT103 -> +(times(T148, T142), times(T147, T143)),\nT146 -> T147,\nT145 -> T148,\nT104 -> T149", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 300 [arrowhead = none ];
300 -> 61;

301 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
59 -> 301 [arrowhead = none ];
301 -> 62;

302 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
60 -> 302 [arrowhead = none ];
302 -> 67;

303 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
60 -> 303 [arrowhead = none ];
303 -> 68;

304 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
61 -> 304 [arrowhead = none ];
304 -> 63;

305 [label="SPLIT 2\nnew knowledge:\nT142 is ground\nT143 is ground\nT144 is ground\nT147 is ground\nreplacements:T148 -> T156,\nT149 -> T157,\nT3 -> T158", fontsize=14, style = filled, fillcolor = violet];
61 -> 305 [arrowhead = none ];
305 -> 64;

306 [label="INSTANCE with matching:\nT1 -> T142\nT2 -> times(times(T142, T143), T144)\nT3 -> T147", fontsize=14, style = filled, fillcolor = lightgrey];
63 -> 306 [arrowhead = none , style=dashed];
306 -> 1[style=dashed];

307 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
64 -> 307 [arrowhead = none ];
307 -> 65;

308 [label="SPLIT 2\nnew knowledge:\nT143 is ground\nT142 is ground\nT144 is ground\nT156 is ground\nreplacements:T157 -> T171,\nT158 -> T172", fontsize=14, style = filled, fillcolor = violet];
64 -> 308 [arrowhead = none ];
308 -> 66;

309 [label="INSTANCE with matching:\nT1 -> T143\nT2 -> times(times(T142, T143), T144)\nT3 -> T156", fontsize=14, style = filled, fillcolor = lightgrey];
65 -> 309 [arrowhead = none , style=dashed];
309 -> 1[style=dashed];

310 [label="INSTANCE with matching:\nT1 -> T144\nT2 -> times(times(T142, T143), T144)\nT3 -> T171", fontsize=14, style = filled, fillcolor = lightgrey];
66 -> 310 [arrowhead = none , style=dashed];
310 -> 1[style=dashed];

311 [label="EVAL with clause\nd(div(X167, X168), X169, X170) :- d(times(X167, power(X168, p(0))), X169, X170).\nand substitutionX167 -> T201,\nX168 -> T202,\nT99 -> div(T201, T202),\nT100 -> T203,\nX169 -> times(div(T201, T202), T203),\nT103 -> T205,\nX170 -> T205,\nT204 -> T205,\nT104 -> T206", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 311 [arrowhead = none ];
311 -> 69;

312 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
67 -> 312 [arrowhead = none ];
312 -> 70;

313 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
68 -> 313 [arrowhead = none ];
313 -> 73;

314 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
68 -> 314 [arrowhead = none ];
314 -> 74;

315 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
69 -> 315 [arrowhead = none ];
315 -> 71;

316 [label="SPLIT 2\nnew knowledge:\nT201 is ground\nT202 is ground\nT203 is ground\nT205 is ground\nreplacements:T206 -> T211,\nT3 -> T212", fontsize=14, style = filled, fillcolor = violet];
69 -> 316 [arrowhead = none ];
316 -> 72;

317 [label="INSTANCE with matching:\nT1 -> times(T201, power(T202, p(0)))\nT2 -> times(div(T201, T202), T203)\nT3 -> T205", fontsize=14, style = filled, fillcolor = lightgrey];
71 -> 317 [arrowhead = none , style=dashed];
317 -> 1[style=dashed];

318 [label="INSTANCE with matching:\nT1 -> T203\nT2 -> times(div(T201, T202), T203)\nT3 -> T211", fontsize=14, style = filled, fillcolor = lightgrey];
72 -> 318 [arrowhead = none , style=dashed];
318 -> 1[style=dashed];

319 [label="EVAL with clause\nd(power(X193, X194), X195, times(X194, times(X196, power(X193, p(X194))))) :- ','(isnumber(X194), d(X193, X195, X196)).\nand substitutionX193 -> T239,\nX194 -> T240,\nT99 -> power(T239, T240),\nT100 -> T241,\nX195 -> times(power(T239, T240), T241),\nX196 -> T243,\nT103 -> times(T240, times(T243, power(T239, p(T240)))),\nT242 -> T243,\nT104 -> T244", fontsize=14, style = filled, fillcolor = lightblue];
73 -> 319 [arrowhead = none ];
319 -> 75;

320 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
73 -> 320 [arrowhead = none ];
320 -> 76;

321 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
74 -> 321 [arrowhead = none ];
321 -> 81;

322 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
75 -> 322 [arrowhead = none ];
322 -> 77;

323 [label="SPLIT 2\nnew knowledge:\nT240 is ground", fontsize=14, style = filled, fillcolor = violet];
75 -> 323 [arrowhead = none ];
323 -> 78;

324 [label="INSTANCE with matching:\nT12 -> T240", fontsize=14, style = filled, fillcolor = lightgrey];
77 -> 324 [arrowhead = none , style=dashed];
324 -> 16[style=dashed];

325 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
78 -> 325 [arrowhead = none ];
325 -> 79;

326 [label="SPLIT 2\nnew knowledge:\nT239 is ground\nT240 is ground\nT241 is ground\nT243 is ground\nreplacements:T244 -> T251,\nT3 -> T252", fontsize=14, style = filled, fillcolor = violet];
78 -> 326 [arrowhead = none ];
326 -> 80;

327 [label="INSTANCE with matching:\nT1 -> T239\nT2 -> times(power(T239, T240), T241)\nT3 -> T243", fontsize=14, style = filled, fillcolor = lightgrey];
79 -> 327 [arrowhead = none , style=dashed];
327 -> 1[style=dashed];

328 [label="INSTANCE with matching:\nT1 -> T241\nT2 -> times(power(T239, T240), T241)\nT3 -> T251", fontsize=14, style = filled, fillcolor = lightgrey];
80 -> 328 [arrowhead = none , style=dashed];
328 -> 1[style=dashed];

329 [label="BACKTRACK\nfor clause: d(div(U, V), X, W) :- d(times(U, power(V, p(0))), X, W)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
81 -> 329 [arrowhead = none ];
329 -> 82;

330 [label="BACKTRACK\nfor clause: d(power(U, V), X, times(V, times(W, power(U, p(V))))) :- ','(isnumber(V), d(U, X, W))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
82 -> 330 [arrowhead = none ];
330 -> 83;

331 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
84 -> 331 [arrowhead = none ];
331 -> 86;

332 [label="EVAL with clause\nd(power(X277, X278), X279, times(X278, times(X280, power(X277, p(X278))))) :- ','(isnumber(X278), d(X277, X279, X280)).\nand substitutionX277 -> T321,\nX278 -> T322,\nT5 -> power(T321, T322),\nX279 -> power(T321, T322),\nX280 -> T324,\nT3 -> times(T322, times(T324, power(T321, p(T322)))),\nT323 -> T324", fontsize=14, style = filled, fillcolor = lightblue];
85 -> 332 [arrowhead = none ];
332 -> 102;

333 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
85 -> 333 [arrowhead = none ];
333 -> 103;

334 [label="BACKTRACK\nfor clause: d(X, X, 1)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
86 -> 334 [arrowhead = none ];
334 -> 87;

335 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
87 -> 335 [arrowhead = none ];
335 -> 88;

336 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
87 -> 336 [arrowhead = none ];
336 -> 89;

337 [label="EVAL with clause\nd(X228, X229, 0) :- isnumber(X228).\nand substitutionT268 -> T282,\nT269 -> T283,\nX228 -> times(T282, power(T283, p(0))),\nX229 -> div(T282, T283),\nT271 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
88 -> 337 [arrowhead = none ];
337 -> 90;

338 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
88 -> 338 [arrowhead = none ];
338 -> 91;

339 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
89 -> 339 [arrowhead = none ];
339 -> 92;

340 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
89 -> 340 [arrowhead = none ];
340 -> 93;

341 [label="INSTANCE with matching:\nT12 -> times(T282, power(T283, p(0)))", fontsize=14, style = filled, fillcolor = lightgrey];
90 -> 341 [arrowhead = none , style=dashed];
341 -> 16[style=dashed];

342 [label="EVAL with clause\nd(times(X250, X251), X252, +(times(X253, X250), times(X254, X251))) :- ','(d(X250, X252, X254), d(X251, X252, X253)).\nand substitutionT268 -> T300,\nX250 -> T300,\nT269 -> T301,\nX251 -> power(T301, p(0)),\nX252 -> div(T300, T301),\nX253 -> T305,\nX254 -> T304,\nT271 -> +(times(T305, T300), times(T304, power(T301, p(0)))),\nT303 -> T304,\nT302 -> T305", fontsize=14, style = filled, fillcolor = lightblue];
92 -> 342 [arrowhead = none ];
342 -> 94;

343 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
92 -> 343 [arrowhead = none ];
343 -> 95;

344 [label="BACKTRACK\nfor clause: d(div(U, V), X, W) :- d(times(U, power(V, p(0))), X, W)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
93 -> 344 [arrowhead = none ];
344 -> 98;

345 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
94 -> 345 [arrowhead = none ];
345 -> 96;

346 [label="SPLIT 2\nnew knowledge:\nT300 is ground\nT301 is ground\nT304 is ground\nreplacements:T305 -> T310,\nT3 -> T311", fontsize=14, style = filled, fillcolor = violet];
94 -> 346 [arrowhead = none ];
346 -> 97;

347 [label="INSTANCE with matching:\nT1 -> T300\nT2 -> div(T300, T301)\nT3 -> T304", fontsize=14, style = filled, fillcolor = lightgrey];
96 -> 347 [arrowhead = none , style=dashed];
347 -> 1[style=dashed];

348 [label="INSTANCE with matching:\nT1 -> power(T301, p(0))\nT2 -> div(T300, T301)\nT3 -> T310", fontsize=14, style = filled, fillcolor = lightgrey];
97 -> 348 [arrowhead = none , style=dashed];
348 -> 1[style=dashed];

349 [label="BACKTRACK\nfor clause: d(power(U, V), X, times(V, times(W, power(U, p(V))))) :- ','(isnumber(V), d(U, X, W))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
98 -> 349 [arrowhead = none ];
349 -> 99;

350 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
99 -> 350 [arrowhead = none ];
350 -> 100;

351 [label="BACKTRACK\nfor clause: d(power(U, V), X, times(V, times(W, power(U, p(V))))) :- ','(isnumber(V), d(U, X, W))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
100 -> 351 [arrowhead = none ];
351 -> 101;

352 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
102 -> 352 [arrowhead = none ];
352 -> 104;

353 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
104 -> 353 [arrowhead = none ];
353 -> 105;

354 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
104 -> 354 [arrowhead = none ];
354 -> 106;

355 [label="EVAL with clause\nisnumber(0).\nand substitutionT322 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 355 [arrowhead = none ];
355 -> 107;

356 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
105 -> 356 [arrowhead = none ];
356 -> 108;

357 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
106 -> 357 [arrowhead = none ];
357 -> 109;

358 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
106 -> 358 [arrowhead = none ];
358 -> 110;

359 [label="INSTANCE with matching:\nT1 -> T321\nT2 -> power(T321, 0)\nT3 -> T324", fontsize=14, style = filled, fillcolor = lightgrey];
107 -> 359 [arrowhead = none , style=dashed];
359 -> 1[style=dashed];

360 [label="EVAL with clause\nisnumber(s(X287)) :- isnumber(X287).\nand substitutionX287 -> T331,\nT322 -> s(T331)", fontsize=14, style = filled, fillcolor = lightblue];
109 -> 360 [arrowhead = none ];
360 -> 111;

361 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
109 -> 361 [arrowhead = none ];
361 -> 112;

362 [label="EVAL with clause\nisnumber(p(X292)) :- isnumber(X292).\nand substitutionX292 -> T338,\nT322 -> p(T338)", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 362 [arrowhead = none ];
362 -> 115;

363 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
110 -> 363 [arrowhead = none ];
363 -> 116;

364 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
111 -> 364 [arrowhead = none ];
364 -> 113;

365 [label="SPLIT 2\nnew knowledge:\nT331 is ground", fontsize=14, style = filled, fillcolor = violet];
111 -> 365 [arrowhead = none ];
365 -> 114;

366 [label="INSTANCE with matching:\nT12 -> T331", fontsize=14, style = filled, fillcolor = lightgrey];
113 -> 366 [arrowhead = none , style=dashed];
366 -> 16[style=dashed];

367 [label="INSTANCE with matching:\nT1 -> T321\nT2 -> power(T321, s(T331))\nT3 -> T324", fontsize=14, style = filled, fillcolor = lightgrey];
114 -> 367 [arrowhead = none , style=dashed];
367 -> 1[style=dashed];

368 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
115 -> 368 [arrowhead = none ];
368 -> 117;

369 [label="SPLIT 2\nnew knowledge:\nT338 is ground", fontsize=14, style = filled, fillcolor = violet];
115 -> 369 [arrowhead = none ];
369 -> 118;

370 [label="INSTANCE with matching:\nT12 -> T338", fontsize=14, style = filled, fillcolor = lightgrey];
117 -> 370 [arrowhead = none , style=dashed];
370 -> 16[style=dashed];

371 [label="INSTANCE with matching:\nT1 -> T321\nT2 -> power(T321, p(T338))\nT3 -> T324", fontsize=14, style = filled, fillcolor = lightgrey];
118 -> 371 [arrowhead = none , style=dashed];
371 -> 1[style=dashed];

372 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
119 -> 372 [arrowhead = none ];
372 -> 121;

373 [label="EVAL with clause\nd(times(X381, X382), X383, +(times(X384, X381), times(X385, X382))) :- ','(d(X381, X383, X385), d(X382, X383, X384)).\nand substitutionX381 -> T437,\nX382 -> T438,\nT1 -> times(T437, T438),\nT2 -> T439,\nX383 -> T439,\nX384 -> T443,\nX385 -> T442,\nT3 -> +(times(T443, T437), times(T442, T438)),\nT441 -> T442,\nT440 -> T443", fontsize=14, style = filled, fillcolor = lightblue];
120 -> 373 [arrowhead = none ];
373 -> 150;

374 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
120 -> 374 [arrowhead = none ];
374 -> 151;

375 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
121 -> 375 [arrowhead = none ];
375 -> 122;

376 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
121 -> 376 [arrowhead = none ];
376 -> 123;

377 [label="EVAL with clause\nisnumber(0).\nand substitutionT345 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 377 [arrowhead = none ];
377 -> 124;

378 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
122 -> 378 [arrowhead = none ];
378 -> 125;

379 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
123 -> 379 [arrowhead = none ];
379 -> 127;

380 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
123 -> 380 [arrowhead = none ];
380 -> 128;

381 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
124 -> 381 [arrowhead = none ];
381 -> 126;

382 [label="EVAL with clause\nisnumber(s(X303)) :- isnumber(X303).\nand substitutionX303 -> T351,\nT345 -> s(T351)", fontsize=14, style = filled, fillcolor = lightblue];
127 -> 382 [arrowhead = none ];
382 -> 129;

383 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
127 -> 383 [arrowhead = none ];
383 -> 130;

384 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
128 -> 384 [arrowhead = none ];
384 -> 131;

385 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
128 -> 385 [arrowhead = none ];
385 -> 132;

386 [label="INSTANCE with matching:\nT12 -> T351", fontsize=14, style = filled, fillcolor = lightgrey];
129 -> 386 [arrowhead = none , style=dashed];
386 -> 16[style=dashed];

387 [label="EVAL with clause\nisnumber(p(X308)) :- isnumber(X308).\nand substitutionX308 -> T356,\nT345 -> p(T356)", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 387 [arrowhead = none ];
387 -> 133;

388 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
131 -> 388 [arrowhead = none ];
388 -> 134;

389 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
132 -> 389 [arrowhead = none ];
389 -> 135;

390 [label="INSTANCE with matching:\nT12 -> T356", fontsize=14, style = filled, fillcolor = lightgrey];
133 -> 390 [arrowhead = none , style=dashed];
390 -> 16[style=dashed];

391 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
135 -> 391 [arrowhead = none ];
391 -> 136;

392 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
135 -> 392 [arrowhead = none ];
392 -> 137;

393 [label="EVAL with clause\nd(times(X329, X330), X331, +(times(X332, X329), times(X333, X330))) :- ','(d(X329, X331, X333), d(X330, X331, X332)).\nand substitutionX329 -> T377,\nX330 -> T378,\nT345 -> times(T377, T378),\nT346 -> T379,\nX331 -> T379,\nX332 -> T383,\nX333 -> T382,\nT3 -> +(times(T383, T377), times(T382, T378)),\nT381 -> T382,\nT380 -> T383", fontsize=14, style = filled, fillcolor = lightblue];
136 -> 393 [arrowhead = none ];
393 -> 138;

394 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
136 -> 394 [arrowhead = none ];
394 -> 139;

395 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
137 -> 395 [arrowhead = none ];
395 -> 142;

396 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
137 -> 396 [arrowhead = none ];
396 -> 143;

397 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
138 -> 397 [arrowhead = none ];
397 -> 140;

398 [label="SPLIT 2\nnew knowledge:\nT377 is ground\nT379 is ground\nT382 is ground\nreplacements:T383 -> T386,\nT3 -> T387", fontsize=14, style = filled, fillcolor = violet];
138 -> 398 [arrowhead = none ];
398 -> 141;

399 [label="INSTANCE with matching:\nT1 -> T377\nT2 -> T379\nT3 -> T382", fontsize=14, style = filled, fillcolor = lightgrey];
140 -> 399 [arrowhead = none , style=dashed];
399 -> 1[style=dashed];

400 [label="INSTANCE with matching:\nT1 -> T378\nT2 -> T379\nT3 -> T386", fontsize=14, style = filled, fillcolor = lightgrey];
141 -> 400 [arrowhead = none , style=dashed];
400 -> 1[style=dashed];

401 [label="EVAL with clause\nd(div(X356, X357), X358, X359) :- d(times(X356, power(X357, p(0))), X358, X359).\nand substitutionX356 -> T408,\nX357 -> T409,\nT345 -> div(T408, T409),\nT346 -> T410,\nX358 -> T410,\nT3 -> T412,\nX359 -> T412,\nT411 -> T412", fontsize=14, style = filled, fillcolor = lightblue];
142 -> 401 [arrowhead = none ];
401 -> 144;

402 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
142 -> 402 [arrowhead = none ];
402 -> 145;

403 [label="EVAL with clause\nd(power(X370, X371), X372, times(X371, times(X373, power(X370, p(X371))))) :- ','(isnumber(X371), d(X370, X372, X373)).\nand substitutionX370 -> T425,\nX371 -> T426,\nT345 -> power(T425, T426),\nT346 -> T427,\nX372 -> T427,\nX373 -> T429,\nT3 -> times(T426, times(T429, power(T425, p(T426)))),\nT428 -> T429", fontsize=14, style = filled, fillcolor = lightblue];
143 -> 403 [arrowhead = none ];
403 -> 146;

404 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
143 -> 404 [arrowhead = none ];
404 -> 147;

405 [label="INSTANCE with matching:\nT1 -> times(T408, power(T409, p(0)))\nT2 -> T410\nT3 -> T412", fontsize=14, style = filled, fillcolor = lightgrey];
144 -> 405 [arrowhead = none , style=dashed];
405 -> 1[style=dashed];

406 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
146 -> 406 [arrowhead = none ];
406 -> 148;

407 [label="SPLIT 2\nnew knowledge:\nT426 is ground", fontsize=14, style = filled, fillcolor = violet];
146 -> 407 [arrowhead = none ];
407 -> 149;

408 [label="INSTANCE with matching:\nT12 -> T426", fontsize=14, style = filled, fillcolor = lightgrey];
148 -> 408 [arrowhead = none , style=dashed];
408 -> 16[style=dashed];

409 [label="INSTANCE with matching:\nT1 -> T425\nT2 -> T427\nT3 -> T429", fontsize=14, style = filled, fillcolor = lightgrey];
149 -> 409 [arrowhead = none , style=dashed];
409 -> 1[style=dashed];

410 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
150 -> 410 [arrowhead = none ];
410 -> 152;

411 [label="EVAL with clause\nd(div(X504, X505), X506, X507) :- d(times(X504, power(X505, p(0))), X506, X507).\nand substitutionX504 -> T576,\nX505 -> T577,\nT1 -> div(T576, T577),\nT2 -> T578,\nX506 -> T578,\nT3 -> T580,\nX507 -> T580,\nT579 -> T580", fontsize=14, style = filled, fillcolor = lightblue];
151 -> 411 [arrowhead = none ];
411 -> 188;

412 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
151 -> 412 [arrowhead = none ];
412 -> 189;

413 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
152 -> 413 [arrowhead = none ];
413 -> 153;

414 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
152 -> 414 [arrowhead = none ];
414 -> 154;

415 [label="EVAL with clause\nd(X390, X390, 1).\nand substitutionT437 -> T448,\nX390 -> T448,\nT439 -> T448,\nT442 -> 1,\nT443 -> T449", fontsize=14, style = filled, fillcolor = lightblue];
153 -> 415 [arrowhead = none ];
415 -> 155;

416 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
153 -> 416 [arrowhead = none ];
416 -> 156;

417 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 417 [arrowhead = none ];
417 -> 157;

418 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 418 [arrowhead = none ];
418 -> 158;

419 [label="INSTANCE with matching:\nT1 -> T438\nT2 -> T448\nT3 -> T449", fontsize=14, style = filled, fillcolor = lightgrey];
155 -> 419 [arrowhead = none , style=dashed];
419 -> 1[style=dashed];

420 [label="EVAL with clause\nd(X401, X402, 0) :- isnumber(X401).\nand substitutionT437 -> T460,\nX401 -> T460,\nT439 -> T461,\nX402 -> T461,\nT442 -> 0,\nT443 -> T462", fontsize=14, style = filled, fillcolor = lightblue];
157 -> 420 [arrowhead = none ];
420 -> 159;

421 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
157 -> 421 [arrowhead = none ];
421 -> 160;

422 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
158 -> 422 [arrowhead = none ];
422 -> 163;

423 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
158 -> 423 [arrowhead = none ];
423 -> 164;

424 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
159 -> 424 [arrowhead = none ];
424 -> 161;

425 [label="SPLIT 2\nnew knowledge:\nT460 is ground", fontsize=14, style = filled, fillcolor = violet];
159 -> 425 [arrowhead = none ];
425 -> 162;

426 [label="INSTANCE with matching:\nT12 -> T460", fontsize=14, style = filled, fillcolor = lightgrey];
161 -> 426 [arrowhead = none , style=dashed];
426 -> 16[style=dashed];

427 [label="INSTANCE with matching:\nT1 -> T438\nT2 -> T461\nT3 -> T462", fontsize=14, style = filled, fillcolor = lightgrey];
162 -> 427 [arrowhead = none , style=dashed];
427 -> 1[style=dashed];

428 [label="EVAL with clause\nd(times(X425, X426), X427, +(times(X428, X425), times(X429, X426))) :- ','(d(X425, X427, X429), d(X426, X427, X428)).\nand substitutionX425 -> T485,\nX426 -> T486,\nT437 -> times(T485, T486),\nT439 -> T487,\nX427 -> T487,\nX428 -> T491,\nX429 -> T490,\nT442 -> +(times(T491, T485), times(T490, T486)),\nT489 -> T490,\nT488 -> T491,\nT443 -> T492", fontsize=14, style = filled, fillcolor = lightblue];
163 -> 428 [arrowhead = none ];
428 -> 165;

429 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
163 -> 429 [arrowhead = none ];
429 -> 166;

430 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
164 -> 430 [arrowhead = none ];
430 -> 171;

431 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
164 -> 431 [arrowhead = none ];
431 -> 172;

432 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
165 -> 432 [arrowhead = none ];
432 -> 167;

433 [label="SPLIT 2\nnew knowledge:\nT485 is ground\nT487 is ground\nT490 is ground\nreplacements:T491 -> T495,\nT492 -> T496,\nT3 -> T497", fontsize=14, style = filled, fillcolor = violet];
165 -> 433 [arrowhead = none ];
433 -> 168;

434 [label="INSTANCE with matching:\nT1 -> T485\nT2 -> T487\nT3 -> T490", fontsize=14, style = filled, fillcolor = lightgrey];
167 -> 434 [arrowhead = none , style=dashed];
434 -> 1[style=dashed];

435 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
168 -> 435 [arrowhead = none ];
435 -> 169;

436 [label="SPLIT 2\nnew knowledge:\nT486 is ground\nT487 is ground\nT495 is ground\nreplacements:T496 -> T502,\nT497 -> T503", fontsize=14, style = filled, fillcolor = violet];
168 -> 436 [arrowhead = none ];
436 -> 170;

437 [label="INSTANCE with matching:\nT1 -> T486\nT2 -> T487\nT3 -> T495", fontsize=14, style = filled, fillcolor = lightgrey];
169 -> 437 [arrowhead = none , style=dashed];
437 -> 1[style=dashed];

438 [label="INSTANCE with matching:\nT1 -> T438\nT2 -> T487\nT3 -> T502", fontsize=14, style = filled, fillcolor = lightgrey];
170 -> 438 [arrowhead = none , style=dashed];
438 -> 1[style=dashed];

439 [label="EVAL with clause\nd(div(X456, X457), X458, X459) :- d(times(X456, power(X457, p(0))), X458, X459).\nand substitutionX456 -> T524,\nX457 -> T525,\nT437 -> div(T524, T525),\nT439 -> T526,\nX458 -> T526,\nT442 -> T528,\nX459 -> T528,\nT527 -> T528,\nT443 -> T529", fontsize=14, style = filled, fillcolor = lightblue];
171 -> 439 [arrowhead = none ];
439 -> 173;

440 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
171 -> 440 [arrowhead = none ];
440 -> 174;

441 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
172 -> 441 [arrowhead = none ];
441 -> 177;

442 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
172 -> 442 [arrowhead = none ];
442 -> 178;

443 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
173 -> 443 [arrowhead = none ];
443 -> 175;

444 [label="SPLIT 2\nnew knowledge:\nT524 is ground\nT525 is ground\nT526 is ground\nT528 is ground\nreplacements:T529 -> T534,\nT3 -> T535", fontsize=14, style = filled, fillcolor = violet];
173 -> 444 [arrowhead = none ];
444 -> 176;

445 [label="INSTANCE with matching:\nT1 -> times(T524, power(T525, p(0)))\nT2 -> T526\nT3 -> T528", fontsize=14, style = filled, fillcolor = lightgrey];
175 -> 445 [arrowhead = none , style=dashed];
445 -> 1[style=dashed];

446 [label="INSTANCE with matching:\nT1 -> T438\nT2 -> T526\nT3 -> T534", fontsize=14, style = filled, fillcolor = lightgrey];
176 -> 446 [arrowhead = none , style=dashed];
446 -> 1[style=dashed];

447 [label="EVAL with clause\nd(power(X482, X483), X484, times(X483, times(X485, power(X482, p(X483))))) :- ','(isnumber(X483), d(X482, X484, X485)).\nand substitutionX482 -> T558,\nX483 -> T559,\nT437 -> power(T558, T559),\nT439 -> T560,\nX484 -> T560,\nX485 -> T562,\nT442 -> times(T559, times(T562, power(T558, p(T559)))),\nT561 -> T562,\nT443 -> T563", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 447 [arrowhead = none ];
447 -> 179;

448 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
177 -> 448 [arrowhead = none ];
448 -> 180;

449 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
178 -> 449 [arrowhead = none ];
449 -> 185;

450 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
179 -> 450 [arrowhead = none ];
450 -> 181;

451 [label="SPLIT 2\nnew knowledge:\nT559 is ground", fontsize=14, style = filled, fillcolor = violet];
179 -> 451 [arrowhead = none ];
451 -> 182;

452 [label="INSTANCE with matching:\nT12 -> T559", fontsize=14, style = filled, fillcolor = lightgrey];
181 -> 452 [arrowhead = none , style=dashed];
452 -> 16[style=dashed];

453 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
182 -> 453 [arrowhead = none ];
453 -> 183;

454 [label="SPLIT 2\nnew knowledge:\nT558 is ground\nT560 is ground\nT562 is ground\nreplacements:T563 -> T566,\nT3 -> T567", fontsize=14, style = filled, fillcolor = violet];
182 -> 454 [arrowhead = none ];
454 -> 184;

455 [label="INSTANCE with matching:\nT1 -> T558\nT2 -> T560\nT3 -> T562", fontsize=14, style = filled, fillcolor = lightgrey];
183 -> 455 [arrowhead = none , style=dashed];
455 -> 1[style=dashed];

456 [label="INSTANCE with matching:\nT1 -> T438\nT2 -> T560\nT3 -> T566", fontsize=14, style = filled, fillcolor = lightgrey];
184 -> 456 [arrowhead = none , style=dashed];
456 -> 1[style=dashed];

457 [label="BACKTRACK\nfor clause: d(div(U, V), X, W) :- d(times(U, power(V, p(0))), X, W)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
185 -> 457 [arrowhead = none ];
457 -> 186;

458 [label="BACKTRACK\nfor clause: d(power(U, V), X, times(V, times(W, power(U, p(V))))) :- ','(isnumber(V), d(U, X, W))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
186 -> 458 [arrowhead = none ];
458 -> 187;

459 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
188 -> 459 [arrowhead = none ];
459 -> 190;

460 [label="EVAL with clause\nd(power(X570, X571), X572, times(X571, times(X573, power(X570, p(X571))))) :- ','(isnumber(X571), d(X570, X572, X573)).\nand substitutionX570 -> T645,\nX571 -> T646,\nT1 -> power(T645, T646),\nT2 -> T647,\nX572 -> T647,\nX573 -> T649,\nT3 -> times(T646, times(T649, power(T645, p(T646)))),\nT648 -> T649", fontsize=14, style = filled, fillcolor = lightblue];
189 -> 460 [arrowhead = none ];
460 -> 210;

461 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
189 -> 461 [arrowhead = none ];
461 -> 211;

462 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
190 -> 462 [arrowhead = none ];
462 -> 191;

463 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
190 -> 463 [arrowhead = none ];
463 -> 192;

464 [label="EVAL with clause\nd(X512, X512, 1).\nand substitutionT576 -> T589,\nT577 -> T590,\nX512 -> times(T589, power(T590, p(0))),\nT578 -> times(T589, power(T590, p(0))),\nT580 -> 1", fontsize=14, style = filled, fillcolor = lightblue];
191 -> 464 [arrowhead = none ];
464 -> 193;

465 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
191 -> 465 [arrowhead = none ];
465 -> 194;

466 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
192 -> 466 [arrowhead = none ];
466 -> 196;

467 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
192 -> 467 [arrowhead = none ];
467 -> 197;

468 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
193 -> 468 [arrowhead = none ];
468 -> 195;

469 [label="EVAL with clause\nd(X521, X522, 0) :- isnumber(X521).\nand substitutionT576 -> T603,\nT577 -> T604,\nX521 -> times(T603, power(T604, p(0))),\nT578 -> T605,\nX522 -> T605,\nT580 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
196 -> 469 [arrowhead = none ];
469 -> 198;

470 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
196 -> 470 [arrowhead = none ];
470 -> 199;

471 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
197 -> 471 [arrowhead = none ];
471 -> 200;

472 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
197 -> 472 [arrowhead = none ];
472 -> 201;

473 [label="INSTANCE with matching:\nT12 -> times(T603, power(T604, p(0)))", fontsize=14, style = filled, fillcolor = lightgrey];
198 -> 473 [arrowhead = none , style=dashed];
473 -> 16[style=dashed];

474 [label="EVAL with clause\nd(times(X543, X544), X545, +(times(X546, X543), times(X547, X544))) :- ','(d(X543, X545, X547), d(X544, X545, X546)).\nand substitutionT576 -> T626,\nX543 -> T626,\nT577 -> T627,\nX544 -> power(T627, p(0)),\nT578 -> T628,\nX545 -> T628,\nX546 -> T632,\nX547 -> T631,\nT580 -> +(times(T632, T626), times(T631, power(T627, p(0)))),\nT630 -> T631,\nT629 -> T632", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 474 [arrowhead = none ];
474 -> 202;

475 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
200 -> 475 [arrowhead = none ];
475 -> 203;

476 [label="BACKTRACK\nfor clause: d(div(U, V), X, W) :- d(times(U, power(V, p(0))), X, W)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
201 -> 476 [arrowhead = none ];
476 -> 206;

477 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
202 -> 477 [arrowhead = none ];
477 -> 204;

478 [label="SPLIT 2\nnew knowledge:\nT626 is ground\nT628 is ground\nT631 is ground\nreplacements:T632 -> T635,\nT3 -> T636", fontsize=14, style = filled, fillcolor = violet];
202 -> 478 [arrowhead = none ];
478 -> 205;

479 [label="INSTANCE with matching:\nT1 -> T626\nT2 -> T628\nT3 -> T631", fontsize=14, style = filled, fillcolor = lightgrey];
204 -> 479 [arrowhead = none , style=dashed];
479 -> 1[style=dashed];

480 [label="INSTANCE with matching:\nT1 -> power(T627, p(0))\nT2 -> T628\nT3 -> T635", fontsize=14, style = filled, fillcolor = lightgrey];
205 -> 480 [arrowhead = none , style=dashed];
480 -> 1[style=dashed];

481 [label="BACKTRACK\nfor clause: d(power(U, V), X, times(V, times(W, power(U, p(V))))) :- ','(isnumber(V), d(U, X, W))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
206 -> 481 [arrowhead = none ];
481 -> 207;

482 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
207 -> 482 [arrowhead = none ];
482 -> 208;

483 [label="BACKTRACK\nfor clause: d(power(U, V), X, times(V, times(W, power(U, p(V))))) :- ','(isnumber(V), d(U, X, W))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
208 -> 483 [arrowhead = none ];
483 -> 209;

484 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
210 -> 484 [arrowhead = none ];
484 -> 212;

485 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
212 -> 485 [arrowhead = none ];
485 -> 213;

486 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
212 -> 486 [arrowhead = none ];
486 -> 214;

487 [label="EVAL with clause\nisnumber(0).\nand substitutionT646 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
213 -> 487 [arrowhead = none ];
487 -> 215;

488 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
213 -> 488 [arrowhead = none ];
488 -> 216;

489 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
214 -> 489 [arrowhead = none ];
489 -> 217;

490 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
214 -> 490 [arrowhead = none ];
490 -> 218;

491 [label="INSTANCE with matching:\nT1 -> T645\nT2 -> T647\nT3 -> T649", fontsize=14, style = filled, fillcolor = lightgrey];
215 -> 491 [arrowhead = none , style=dashed];
491 -> 1[style=dashed];

492 [label="EVAL with clause\nisnumber(s(X580)) :- isnumber(X580).\nand substitutionX580 -> T656,\nT646 -> s(T656)", fontsize=14, style = filled, fillcolor = lightblue];
217 -> 492 [arrowhead = none ];
492 -> 219;

493 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
217 -> 493 [arrowhead = none ];
493 -> 220;

494 [label="EVAL with clause\nisnumber(p(X585)) :- isnumber(X585).\nand substitutionX585 -> T661,\nT646 -> p(T661)", fontsize=14, style = filled, fillcolor = lightblue];
218 -> 494 [arrowhead = none ];
494 -> 223;

495 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
218 -> 495 [arrowhead = none ];
495 -> 224;

496 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
219 -> 496 [arrowhead = none ];
496 -> 221;

497 [label="SPLIT 2\nnew knowledge:\nT656 is ground", fontsize=14, style = filled, fillcolor = violet];
219 -> 497 [arrowhead = none ];
497 -> 222;

498 [label="INSTANCE with matching:\nT12 -> T656", fontsize=14, style = filled, fillcolor = lightgrey];
221 -> 498 [arrowhead = none , style=dashed];
498 -> 16[style=dashed];

499 [label="INSTANCE with matching:\nT1 -> T645\nT2 -> T647\nT3 -> T649", fontsize=14, style = filled, fillcolor = lightgrey];
222 -> 499 [arrowhead = none , style=dashed];
499 -> 1[style=dashed];

500 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
223 -> 500 [arrowhead = none ];
500 -> 225;

501 [label="SPLIT 2\nnew knowledge:\nT661 is ground", fontsize=14, style = filled, fillcolor = violet];
223 -> 501 [arrowhead = none ];
501 -> 226;

502 [label="INSTANCE with matching:\nT12 -> T661", fontsize=14, style = filled, fillcolor = lightgrey];
225 -> 502 [arrowhead = none , style=dashed];
502 -> 16[style=dashed];

503 [label="INSTANCE with matching:\nT1 -> T645\nT2 -> T647\nT3 -> T649", fontsize=14, style = filled, fillcolor = lightgrey];
226 -> 503 [arrowhead = none , style=dashed];
503 -> 1[style=dashed];

}

(2) Obligation:

Triples:

isnumberA(s(X1)) :- isnumberA(X1).
isnumberA(p(X1)) :- isnumberA(X1).
dB(s(X1), s(X1), 0) :- isnumberA(X1).
dB(p(X1), p(X1), 0) :- isnumberA(X1).
dB(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) :- dB(X1, times(X1, X2), X4).
dB(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) :- ','(dcB(X1, times(X1, X2), X4), dB(X2, times(X1, X2), X3)).
dB(div(X1, X2), div(X1, X2), X3) :- dB(times(X1, power(X2, p(0))), div(X1, X2), X3).
dB(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) :- isnumberA(X2).
dB(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) :- ','(isnumbercA(X2), dB(X1, power(X1, X2), X3)).
dB(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) :- isnumberA(X1).
dB(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) :- ','(isnumbercA(X1), dB(X2, times(X1, X2), X3)).
dB(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) :- dB(X1, times(times(X1, X2), X3), X6).
dB(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) :- ','(dcB(X1, times(times(X1, X2), X3), X6), dB(X2, times(times(X1, X2), X3), X5)).
dB(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) :- ','(dcB(X1, times(times(X1, X2), X3), X6), ','(dcB(X2, times(times(X1, X2), X3), X5), dB(X3, times(times(X1, X2), X3), X4))).
dB(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) :- dB(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5).
dB(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) :- ','(dcB(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5), dB(X3, times(div(X1, X2), X3), X4)).
dB(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) :- isnumberA(X2).
dB(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) :- ','(isnumbercA(X2), dB(X1, times(power(X1, X2), X3), X5)).
dB(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) :- ','(isnumbercA(X2), ','(dcB(X1, times(power(X1, X2), X3), X5), dB(X3, times(power(X1, X2), X3), X4))).
dB(div(X1, X2), div(X1, X2), 0) :- isnumberA(times(X1, power(X2, p(0)))).
dB(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) :- dB(X1, div(X1, X2), X4).
dB(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) :- ','(dcB(X1, div(X1, X2), X4), dB(power(X2, p(0)), div(X1, X2), X3)).
dB(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0))))) :- dB(X1, power(X1, 0), X2).
dB(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) :- isnumberA(X2).
dB(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) :- ','(isnumbercA(X2), dB(X1, power(X1, s(X2)), X3)).
dB(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) :- isnumberA(X2).
dB(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) :- ','(isnumbercA(X2), dB(X1, power(X1, p(X2)), X3)).
dB(s(X1), X2, 0) :- isnumberA(X1).
dB(p(X1), X2, 0) :- isnumberA(X1).
dB(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) :- dB(X1, X3, X5).
dB(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) :- ','(dcB(X1, X3, X5), dB(X2, X3, X4)).
dB(div(X1, X2), X3, X4) :- dB(times(X1, power(X2, p(0))), X3, X4).
dB(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) :- isnumberA(X2).
dB(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) :- ','(isnumbercA(X2), dB(X1, X3, X4)).
dB(times(X1, X2), X1, +(times(X3, X1), times(1, X2))) :- dB(X2, X1, X3).
dB(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) :- isnumberA(X1).
dB(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) :- ','(isnumbercA(X1), dB(X2, X3, X4)).
dB(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) :- dB(X1, X4, X7).
dB(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) :- ','(dcB(X1, X4, X7), dB(X2, X4, X6)).
dB(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) :- ','(dcB(X1, X4, X7), ','(dcB(X2, X4, X6), dB(X3, X4, X5))).
dB(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) :- dB(times(X1, power(X2, p(0))), X4, X6).
dB(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) :- ','(dcB(times(X1, power(X2, p(0))), X4, X6), dB(X3, X4, X5)).
dB(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) :- isnumberA(X2).
dB(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) :- ','(isnumbercA(X2), dB(X1, X4, X6)).
dB(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) :- ','(isnumbercA(X2), ','(dcB(X1, X4, X6), dB(X3, X4, X5))).
dB(div(X1, X2), X3, 0) :- isnumberA(times(X1, power(X2, p(0)))).
dB(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) :- dB(X1, X3, X5).
dB(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) :- ','(dcB(X1, X3, X5), dB(power(X2, p(0)), X3, X4)).
dB(power(X1, 0), X2, times(0, times(X3, power(X1, p(0))))) :- dB(X1, X2, X3).
dB(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) :- isnumberA(X2).
dB(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) :- ','(isnumbercA(X2), dB(X1, X3, X4)).
dB(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) :- isnumberA(X2).
dB(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) :- ','(isnumbercA(X2), dB(X1, X3, X4)).

Clauses:

isnumbercA(0).
isnumbercA(s(X1)) :- isnumbercA(X1).
isnumbercA(p(X1)) :- isnumbercA(X1).
dcB(X1, X1, 1).
dcB(0, 0, 0).
dcB(s(X1), s(X1), 0) :- isnumbercA(X1).
dcB(p(X1), p(X1), 0) :- isnumbercA(X1).
dcB(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) :- ','(dcB(X1, times(X1, X2), X4), dcB(X2, times(X1, X2), X3)).
dcB(div(X1, X2), div(X1, X2), X3) :- dcB(times(X1, power(X2, p(0))), div(X1, X2), X3).
dcB(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) :- ','(isnumbercA(X2), dcB(X1, power(X1, X2), X3)).
dcB(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) :- ','(isnumbercA(X1), dcB(X2, times(X1, X2), X3)).
dcB(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) :- ','(dcB(X1, times(times(X1, X2), X3), X6), ','(dcB(X2, times(times(X1, X2), X3), X5), dcB(X3, times(times(X1, X2), X3), X4))).
dcB(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) :- ','(dcB(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5), dcB(X3, times(div(X1, X2), X3), X4)).
dcB(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) :- ','(isnumbercA(X2), ','(dcB(X1, times(power(X1, X2), X3), X5), dcB(X3, times(power(X1, X2), X3), X4))).
dcB(div(X1, X2), div(X1, X2), 0) :- isnumbercA(times(X1, power(X2, p(0)))).
dcB(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) :- ','(dcB(X1, div(X1, X2), X4), dcB(power(X2, p(0)), div(X1, X2), X3)).
dcB(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0))))) :- dcB(X1, power(X1, 0), X2).
dcB(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) :- ','(isnumbercA(X2), dcB(X1, power(X1, s(X2)), X3)).
dcB(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) :- ','(isnumbercA(X2), dcB(X1, power(X1, p(X2)), X3)).
dcB(0, X1, 0).
dcB(s(X1), X2, 0) :- isnumbercA(X1).
dcB(p(X1), X2, 0) :- isnumbercA(X1).
dcB(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) :- ','(dcB(X1, X3, X5), dcB(X2, X3, X4)).
dcB(div(X1, X2), X3, X4) :- dcB(times(X1, power(X2, p(0))), X3, X4).
dcB(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) :- ','(isnumbercA(X2), dcB(X1, X3, X4)).
dcB(times(X1, X2), X1, +(times(X3, X1), times(1, X2))) :- dcB(X2, X1, X3).
dcB(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) :- ','(isnumbercA(X1), dcB(X2, X3, X4)).
dcB(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) :- ','(dcB(X1, X4, X7), ','(dcB(X2, X4, X6), dcB(X3, X4, X5))).
dcB(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) :- ','(dcB(times(X1, power(X2, p(0))), X4, X6), dcB(X3, X4, X5)).
dcB(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) :- ','(isnumbercA(X2), ','(dcB(X1, X4, X6), dcB(X3, X4, X5))).
dcB(div(X1, X2), times(X1, power(X2, p(0))), 1).
dcB(div(X1, X2), X3, 0) :- isnumbercA(times(X1, power(X2, p(0)))).
dcB(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) :- ','(dcB(X1, X3, X5), dcB(power(X2, p(0)), X3, X4)).
dcB(power(X1, 0), X2, times(0, times(X3, power(X1, p(0))))) :- dcB(X1, X2, X3).
dcB(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) :- ','(isnumbercA(X2), dcB(X1, X3, X4)).
dcB(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) :- ','(isnumbercA(X2), dcB(X1, X3, X4)).

Afs:

dB(x1, x2, x3) = dB(x1, x2)

(3) TriplesToPiDPProof (SOUND transformation)

We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes:
dB_in: (b,b,f)
isnumberA_in: (b)
dcB_in: (b,b,f)
isnumbercA_in: (b)
Transforming TRIPLES into the following Term Rewriting System:
Pi DP problem:
The TRS P consists of the following rules:

DB_IN_GGA(s(X1), s(X1), 0) → U3_GGA(X1, isnumberA_in_g(X1))
DB_IN_GGA(s(X1), s(X1), 0) → ISNUMBERA_IN_G(X1)
ISNUMBERA_IN_G(s(X1)) → U1_G(X1, isnumberA_in_g(X1))
ISNUMBERA_IN_G(s(X1)) → ISNUMBERA_IN_G(X1)
ISNUMBERA_IN_G(p(X1)) → U2_G(X1, isnumberA_in_g(X1))
ISNUMBERA_IN_G(p(X1)) → ISNUMBERA_IN_G(X1)
DB_IN_GGA(p(X1), p(X1), 0) → U4_GGA(X1, isnumberA_in_g(X1))
DB_IN_GGA(p(X1), p(X1), 0) → ISNUMBERA_IN_G(X1)
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → U5_GGA(X1, X2, X3, X4, dB_in_gga(X1, times(X1, X2), X4))
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → DB_IN_GGA(X1, times(X1, X2), X4)
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → U6_GGA(X1, X2, X3, X4, dcB_in_gga(X1, times(X1, X2), X4))
U6_GGA(X1, X2, X3, X4, dcB_out_gga(X1, times(X1, X2), X4)) → U7_GGA(X1, X2, X3, X4, dB_in_gga(X2, times(X1, X2), X3))
U6_GGA(X1, X2, X3, X4, dcB_out_gga(X1, times(X1, X2), X4)) → DB_IN_GGA(X2, times(X1, X2), X3)
DB_IN_GGA(div(X1, X2), div(X1, X2), X3) → U8_GGA(X1, X2, X3, dB_in_gga(times(X1, power(X2, p(0))), div(X1, X2), X3))
DB_IN_GGA(div(X1, X2), div(X1, X2), X3) → DB_IN_GGA(times(X1, power(X2, p(0))), div(X1, X2), X3)
DB_IN_GGA(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) → U9_GGA(X1, X2, X3, isnumberA_in_g(X2))
DB_IN_GGA(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) → U10_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U10_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → U11_GGA(X1, X2, X3, dB_in_gga(X1, power(X1, X2), X3))
U10_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, X2), X3)
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) → U12_GGA(X1, X2, X3, isnumberA_in_g(X1))
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) → ISNUMBERA_IN_G(X1)
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) → U13_GGA(X1, X2, X3, isnumbercA_in_g(X1))
U13_GGA(X1, X2, X3, isnumbercA_out_g(X1)) → U14_GGA(X1, X2, X3, dB_in_gga(X2, times(X1, X2), X3))
U13_GGA(X1, X2, X3, isnumbercA_out_g(X1)) → DB_IN_GGA(X2, times(X1, X2), X3)
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → U15_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(X1, times(times(X1, X2), X3), X6))
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → DB_IN_GGA(X1, times(times(X1, X2), X3), X6)
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → U16_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, times(times(X1, X2), X3), X6))
U16_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U17_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(X2, times(times(X1, X2), X3), X5))
U16_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → DB_IN_GGA(X2, times(times(X1, X2), X3), X5)
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → U20_GGA(X1, X2, X3, X4, X5, dB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5))
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → DB_IN_GGA(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → U21_GGA(X1, X2, X3, X4, X5, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5))
U21_GGA(X1, X2, X3, X4, X5, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → U22_GGA(X1, X2, X3, X4, X5, dB_in_gga(X3, times(div(X1, X2), X3), X4))
U21_GGA(X1, X2, X3, X4, X5, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(div(X1, X2), X3), X4)
DB_IN_GGA(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) → U23_GGA(X1, X2, X3, X4, X5, isnumberA_in_g(X2))
DB_IN_GGA(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) → U24_GGA(X1, X2, X3, X4, X5, isnumbercA_in_g(X2))
U24_GGA(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → U25_GGA(X1, X2, X3, X4, X5, dB_in_gga(X1, times(power(X1, X2), X3), X5))
U24_GGA(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, times(power(X1, X2), X3), X5)
DB_IN_GGA(div(X1, X2), div(X1, X2), 0) → U28_GGA(X1, X2, isnumberA_in_g(times(X1, power(X2, p(0)))))
DB_IN_GGA(div(X1, X2), div(X1, X2), 0) → ISNUMBERA_IN_G(times(X1, power(X2, p(0))))
DB_IN_GGA(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → U29_GGA(X1, X2, X3, X4, dB_in_gga(X1, div(X1, X2), X4))
DB_IN_GGA(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → DB_IN_GGA(X1, div(X1, X2), X4)
DB_IN_GGA(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → U30_GGA(X1, X2, X3, X4, dcB_in_gga(X1, div(X1, X2), X4))
U30_GGA(X1, X2, X3, X4, dcB_out_gga(X1, div(X1, X2), X4)) → U31_GGA(X1, X2, X3, X4, dB_in_gga(power(X2, p(0)), div(X1, X2), X3))
U30_GGA(X1, X2, X3, X4, dcB_out_gga(X1, div(X1, X2), X4)) → DB_IN_GGA(power(X2, p(0)), div(X1, X2), X3)
DB_IN_GGA(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0))))) → U32_GGA(X1, X2, dB_in_gga(X1, power(X1, 0), X2))
DB_IN_GGA(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0))))) → DB_IN_GGA(X1, power(X1, 0), X2)
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) → U33_GGA(X1, X2, X3, isnumberA_in_g(X2))
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) → U34_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U34_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → U35_GGA(X1, X2, X3, dB_in_gga(X1, power(X1, s(X2)), X3))
U34_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, s(X2)), X3)
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) → U36_GGA(X1, X2, X3, isnumberA_in_g(X2))
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) → U37_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U37_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → U38_GGA(X1, X2, X3, dB_in_gga(X1, power(X1, p(X2)), X3))
U37_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, p(X2)), X3)
DB_IN_GGA(s(X1), X2, 0) → U39_GGA(X1, X2, isnumberA_in_g(X1))
DB_IN_GGA(s(X1), X2, 0) → ISNUMBERA_IN_G(X1)
DB_IN_GGA(p(X1), X2, 0) → U40_GGA(X1, X2, isnumberA_in_g(X1))
DB_IN_GGA(p(X1), X2, 0) → ISNUMBERA_IN_G(X1)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → U41_GGA(X1, X2, X3, X4, X5, dB_in_gga(X1, X3, X5))
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → DB_IN_GGA(X1, X3, X5)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → U42_GGA(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
U42_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U43_GGA(X1, X2, X3, X4, X5, dB_in_gga(X2, X3, X4))
U42_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → DB_IN_GGA(X2, X3, X4)
DB_IN_GGA(div(X1, X2), X3, X4) → U44_GGA(X1, X2, X3, X4, dB_in_gga(times(X1, power(X2, p(0))), X3, X4))
DB_IN_GGA(div(X1, X2), X3, X4) → DB_IN_GGA(times(X1, power(X2, p(0))), X3, X4)
DB_IN_GGA(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) → U45_GGA(X1, X2, X3, X4, isnumberA_in_g(X2))
DB_IN_GGA(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) → U46_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
U46_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U47_GGA(X1, X2, X3, X4, dB_in_gga(X1, X3, X4))
U46_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3, X4)
DB_IN_GGA(times(X1, X2), X1, +(times(X3, X1), times(1, X2))) → U48_GGA(X1, X2, X3, dB_in_gga(X2, X1, X3))
DB_IN_GGA(times(X1, X2), X1, +(times(X3, X1), times(1, X2))) → DB_IN_GGA(X2, X1, X3)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) → U49_GGA(X1, X2, X3, X4, isnumberA_in_g(X1))
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) → ISNUMBERA_IN_G(X1)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) → U50_GGA(X1, X2, X3, X4, isnumbercA_in_g(X1))
U50_GGA(X1, X2, X3, X4, isnumbercA_out_g(X1)) → U51_GGA(X1, X2, X3, X4, dB_in_gga(X2, X3, X4))
U50_GGA(X1, X2, X3, X4, isnumbercA_out_g(X1)) → DB_IN_GGA(X2, X3, X4)
DB_IN_GGA(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → U52_GGA(X1, X2, X3, X4, X5, X6, X7, dB_in_gga(X1, X4, X7))
DB_IN_GGA(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → DB_IN_GGA(X1, X4, X7)
DB_IN_GGA(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X1, X4, X7))
U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → U54_GGA(X1, X2, X3, X4, X5, X6, X7, dB_in_gga(X2, X4, X6))
U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → DB_IN_GGA(X2, X4, X6)
DB_IN_GGA(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → U57_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(times(X1, power(X2, p(0))), X4, X6))
DB_IN_GGA(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → DB_IN_GGA(times(X1, power(X2, p(0))), X4, X6)
DB_IN_GGA(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → U58_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(times(X1, power(X2, p(0))), X4, X6))
U58_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → U59_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(X3, X4, X5))
U58_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → DB_IN_GGA(X3, X4, X5)
DB_IN_GGA(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) → U60_GGA(X1, X2, X3, X4, X5, X6, isnumberA_in_g(X2))
DB_IN_GGA(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) → U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_in_g(X2))
U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → U62_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(X1, X4, X6))
U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X4, X6)
DB_IN_GGA(div(X1, X2), X3, 0) → U65_GGA(X1, X2, X3, isnumberA_in_g(times(X1, power(X2, p(0)))))
DB_IN_GGA(div(X1, X2), X3, 0) → ISNUMBERA_IN_G(times(X1, power(X2, p(0))))
DB_IN_GGA(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → U66_GGA(X1, X2, X3, X4, X5, dB_in_gga(X1, X3, X5))
DB_IN_GGA(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → DB_IN_GGA(X1, X3, X5)
DB_IN_GGA(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → U67_GGA(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
U67_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U68_GGA(X1, X2, X3, X4, X5, dB_in_gga(power(X2, p(0)), X3, X4))
U67_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → DB_IN_GGA(power(X2, p(0)), X3, X4)
DB_IN_GGA(power(X1, 0), X2, times(0, times(X3, power(X1, p(0))))) → U69_GGA(X1, X2, X3, dB_in_gga(X1, X2, X3))
DB_IN_GGA(power(X1, 0), X2, times(0, times(X3, power(X1, p(0))))) → DB_IN_GGA(X1, X2, X3)
DB_IN_GGA(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) → U70_GGA(X1, X2, X3, X4, isnumberA_in_g(X2))
DB_IN_GGA(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) → U71_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
U71_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U72_GGA(X1, X2, X3, X4, dB_in_gga(X1, X3, X4))
U71_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3, X4)
DB_IN_GGA(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) → U73_GGA(X1, X2, X3, X4, isnumberA_in_g(X2))
DB_IN_GGA(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) → U74_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
U74_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U75_GGA(X1, X2, X3, X4, dB_in_gga(X1, X3, X4))
U74_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3, X4)
U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → U63_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, X4, X6))
U63_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, X4, X6)) → U64_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(X3, X4, X5))
U63_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, X4, X6)) → DB_IN_GGA(X3, X4, X5)
U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → U55_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X2, X4, X6))
U55_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X2, X4, X6)) → U56_GGA(X1, X2, X3, X4, X5, X6, X7, dB_in_gga(X3, X4, X5))
U55_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X2, X4, X6)) → DB_IN_GGA(X3, X4, X5)
U24_GGA(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → U26_GGA(X1, X2, X3, X4, X5, dcB_in_gga(X1, times(power(X1, X2), X3), X5))
U26_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → U27_GGA(X1, X2, X3, X4, X5, dB_in_gga(X3, times(power(X1, X2), X3), X4))
U26_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(power(X1, X2), X3), X4)
U16_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U18_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(X2, times(times(X1, X2), X3), X5))
U18_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → U19_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(X3, times(times(X1, X2), X3), X4))
U18_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(times(X1, X2), X3), X4)

The TRS R consists of the following rules:

dcB_in_gga(X1, X1, 1) → dcB_out_gga(X1, X1, 1)
dcB_in_gga(0, 0, 0) → dcB_out_gga(0, 0, 0)
dcB_in_gga(s(X1), s(X1), 0) → U79_gga(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(0) → isnumbercA_out_g(0)
isnumbercA_in_g(s(X1)) → U77_g(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(p(X1)) → U78_g(X1, isnumbercA_in_g(X1))
U78_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(p(X1))
U77_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(s(X1))
U79_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), s(X1), 0)
dcB_in_gga(p(X1), p(X1), 0) → U80_gga(X1, isnumbercA_in_g(X1))
U80_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), p(X1), 0)
dcB_in_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → U81_gga(X1, X2, X3, X4, dcB_in_gga(X1, times(X1, X2), X4))
dcB_in_gga(div(X1, X2), div(X1, X2), X3) → U83_gga(X1, X2, X3, dcB_in_gga(times(X1, power(X2, p(0))), div(X1, X2), X3))
dcB_in_gga(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) → U84_gga(X1, X2, X3, isnumbercA_in_g(X2))
U84_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U85_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, X2), X3))
dcB_in_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) → U86_gga(X1, X2, X3, isnumbercA_in_g(X1))
U86_gga(X1, X2, X3, isnumbercA_out_g(X1)) → U87_gga(X1, X2, X3, dcB_in_gga(X2, times(X1, X2), X3))
dcB_in_gga(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → U88_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, times(times(X1, X2), X3), X6))
dcB_in_gga(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → U91_gga(X1, X2, X3, X4, X5, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5))
dcB_in_gga(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) → U93_gga(X1, X2, X3, X4, X5, isnumbercA_in_g(X2))
U93_gga(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → U94_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, times(power(X1, X2), X3), X5))
dcB_in_gga(div(X1, X2), div(X1, X2), 0) → U96_gga(X1, X2, isnumbercA_in_g(times(X1, power(X2, p(0)))))
U96_gga(X1, X2, isnumbercA_out_g(times(X1, power(X2, p(0))))) → dcB_out_gga(div(X1, X2), div(X1, X2), 0)
dcB_in_gga(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → U97_gga(X1, X2, X3, X4, dcB_in_gga(X1, div(X1, X2), X4))
dcB_in_gga(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0))))) → U99_gga(X1, X2, dcB_in_gga(X1, power(X1, 0), X2))
dcB_in_gga(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) → U100_gga(X1, X2, X3, isnumbercA_in_g(X2))
U100_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U101_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, s(X2)), X3))
dcB_in_gga(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) → U102_gga(X1, X2, X3, isnumbercA_in_g(X2))
U102_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U103_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, p(X2)), X3))
dcB_in_gga(0, X1, 0) → dcB_out_gga(0, X1, 0)
dcB_in_gga(s(X1), X2, 0) → U104_gga(X1, X2, isnumbercA_in_g(X1))
U104_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), X2, 0)
dcB_in_gga(p(X1), X2, 0) → U105_gga(X1, X2, isnumbercA_in_g(X1))
U105_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), X2, 0)
dcB_in_gga(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → U106_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
dcB_in_gga(div(X1, X2), X3, X4) → U108_gga(X1, X2, X3, X4, dcB_in_gga(times(X1, power(X2, p(0))), X3, X4))
dcB_in_gga(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) → U109_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
U109_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U110_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
dcB_in_gga(times(X1, X2), X1, +(times(X3, X1), times(1, X2))) → U111_gga(X1, X2, X3, dcB_in_gga(X2, X1, X3))
dcB_in_gga(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) → U112_gga(X1, X2, X3, X4, isnumbercA_in_g(X1))
U112_gga(X1, X2, X3, X4, isnumbercA_out_g(X1)) → U113_gga(X1, X2, X3, X4, dcB_in_gga(X2, X3, X4))
dcB_in_gga(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → U114_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X1, X4, X7))
dcB_in_gga(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → U117_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(times(X1, power(X2, p(0))), X4, X6))
dcB_in_gga(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) → U119_gga(X1, X2, X3, X4, X5, X6, isnumbercA_in_g(X2))
U119_gga(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → U120_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, X4, X6))
dcB_in_gga(div(X1, X2), times(X1, power(X2, p(0))), 1) → dcB_out_gga(div(X1, X2), times(X1, power(X2, p(0))), 1)
dcB_in_gga(div(X1, X2), X3, 0) → U122_gga(X1, X2, X3, isnumbercA_in_g(times(X1, power(X2, p(0)))))
U122_gga(X1, X2, X3, isnumbercA_out_g(times(X1, power(X2, p(0))))) → dcB_out_gga(div(X1, X2), X3, 0)
dcB_in_gga(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → U123_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
dcB_in_gga(power(X1, 0), X2, times(0, times(X3, power(X1, p(0))))) → U125_gga(X1, X2, X3, dcB_in_gga(X1, X2, X3))
dcB_in_gga(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) → U126_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
U126_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U127_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
dcB_in_gga(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) → U128_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
U128_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U129_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
U129_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2))))))
U127_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2))))))
U125_gga(X1, X2, X3, dcB_out_gga(X1, X2, X3)) → dcB_out_gga(power(X1, 0), X2, times(0, times(X3, power(X1, p(0)))))
U123_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U124_gga(X1, X2, X3, X4, X5, dcB_in_gga(power(X2, p(0)), X3, X4))
U124_gga(X1, X2, X3, X4, X5, dcB_out_gga(power(X2, p(0)), X3, X4)) → dcB_out_gga(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0)))))
U120_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, X4, X6)) → U121_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, X4, X5))
U121_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3)))
U117_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → U118_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, X4, X5))
U118_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3)))
U114_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → U115_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X2, X4, X6))
U115_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X2, X4, X6)) → U116_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X3, X4, X5))
U116_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3)))
U113_gga(X1, X2, X3, X4, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(0, X2)))
U111_gga(X1, X2, X3, dcB_out_gga(X2, X1, X3)) → dcB_out_gga(times(X1, X2), X1, +(times(X3, X1), times(1, X2)))
U110_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2)))))
U108_gga(X1, X2, X3, X4, dcB_out_gga(times(X1, power(X2, p(0))), X3, X4)) → dcB_out_gga(div(X1, X2), X3, X4)
U106_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U107_gga(X1, X2, X3, X4, X5, dcB_in_gga(X2, X3, X4))
U107_gga(X1, X2, X3, X4, X5, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(X5, X2)))
U103_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, p(X2)), X3)) → dcB_out_gga(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2))))))
U101_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, s(X2)), X3)) → dcB_out_gga(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2))))))
U99_gga(X1, X2, dcB_out_gga(X1, power(X1, 0), X2)) → dcB_out_gga(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0)))))
U97_gga(X1, X2, X3, X4, dcB_out_gga(X1, div(X1, X2), X4)) → U98_gga(X1, X2, X3, X4, dcB_in_gga(power(X2, p(0)), div(X1, X2), X3))
U98_gga(X1, X2, X3, X4, dcB_out_gga(power(X2, p(0)), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0)))))
U94_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → U95_gga(X1, X2, X3, X4, X5, dcB_in_gga(X3, times(power(X1, X2), X3), X4))
U95_gga(X1, X2, X3, X4, X5, dcB_out_gga(X3, times(power(X1, X2), X3), X4)) → dcB_out_gga(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3)))
U91_gga(X1, X2, X3, X4, X5, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → U92_gga(X1, X2, X3, X4, X5, dcB_in_gga(X3, times(div(X1, X2), X3), X4))
U92_gga(X1, X2, X3, X4, X5, dcB_out_gga(X3, times(div(X1, X2), X3), X4)) → dcB_out_gga(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3)))
U88_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U89_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X2, times(times(X1, X2), X3), X5))
U89_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → U90_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, times(times(X1, X2), X3), X4))
U90_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, times(times(X1, X2), X3), X4)) → dcB_out_gga(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3)))
U87_gga(X1, X2, X3, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2)))
U85_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, X2), X3)) → dcB_out_gga(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2)))))
U83_gga(X1, X2, X3, dcB_out_gga(times(X1, power(X2, p(0))), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), X3)
U81_gga(X1, X2, X3, X4, dcB_out_gga(X1, times(X1, X2), X4)) → U82_gga(X1, X2, X3, X4, dcB_in_gga(X2, times(X1, X2), X3))
U82_gga(X1, X2, X3, X4, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2)))

The argument filtering Pi contains the following mapping:
dB_in_gga(x1, x2, x3) = dB_in_gga(x1, x2)
s(x1) = s(x1)
isnumberA_in_g(x1) = isnumberA_in_g(x1)
p(x1) = p(x1)
times(x1, x2) = times(x1, x2)
dcB_in_gga(x1, x2, x3) = dcB_in_gga(x1, x2)
dcB_out_gga(x1, x2, x3) = dcB_out_gga(x1, x2, x3)
0 = 0
U79_gga(x1, x2) = U79_gga(x1, x2)
isnumbercA_in_g(x1) = isnumbercA_in_g(x1)
isnumbercA_out_g(x1) = isnumbercA_out_g(x1)
U77_g(x1, x2) = U77_g(x1, x2)
U78_g(x1, x2) = U78_g(x1, x2)
U80_gga(x1, x2) = U80_gga(x1, x2)
U81_gga(x1, x2, x3, x4, x5) = U81_gga(x1, x2, x5)
div(x1, x2) = div(x1, x2)
U83_gga(x1, x2, x3, x4) = U83_gga(x1, x2, x4)
power(x1, x2) = power(x1, x2)
U84_gga(x1, x2, x3, x4) = U84_gga(x1, x2, x4)
U85_gga(x1, x2, x3, x4) = U85_gga(x1, x2, x4)
U86_gga(x1, x2, x3, x4) = U86_gga(x1, x2, x4)
U87_gga(x1, x2, x3, x4) = U87_gga(x1, x2, x4)
U88_gga(x1, x2, x3, x4, x5, x6, x7) = U88_gga(x1, x2, x3, x7)
U91_gga(x1, x2, x3, x4, x5, x6) = U91_gga(x1, x2, x3, x6)
U93_gga(x1, x2, x3, x4, x5, x6) = U93_gga(x1, x2, x3, x6)
U94_gga(x1, x2, x3, x4, x5, x6) = U94_gga(x1, x2, x3, x6)
U96_gga(x1, x2, x3) = U96_gga(x1, x2, x3)
U97_gga(x1, x2, x3, x4, x5) = U97_gga(x1, x2, x5)
U99_gga(x1, x2, x3) = U99_gga(x1, x3)
U100_gga(x1, x2, x3, x4) = U100_gga(x1, x2, x4)
U101_gga(x1, x2, x3, x4) = U101_gga(x1, x2, x4)
U102_gga(x1, x2, x3, x4) = U102_gga(x1, x2, x4)
U103_gga(x1, x2, x3, x4) = U103_gga(x1, x2, x4)
U104_gga(x1, x2, x3) = U104_gga(x1, x2, x3)
U105_gga(x1, x2, x3) = U105_gga(x1, x2, x3)
U106_gga(x1, x2, x3, x4, x5, x6) = U106_gga(x1, x2, x3, x6)
U108_gga(x1, x2, x3, x4, x5) = U108_gga(x1, x2, x3, x5)
U109_gga(x1, x2, x3, x4, x5) = U109_gga(x1, x2, x3, x5)
U110_gga(x1, x2, x3, x4, x5) = U110_gga(x1, x2, x3, x5)
U111_gga(x1, x2, x3, x4) = U111_gga(x1, x2, x4)
U112_gga(x1, x2, x3, x4, x5) = U112_gga(x1, x2, x3, x5)
U113_gga(x1, x2, x3, x4, x5) = U113_gga(x1, x2, x3, x5)
U114_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U114_gga(x1, x2, x3, x4, x8)
U117_gga(x1, x2, x3, x4, x5, x6, x7) = U117_gga(x1, x2, x3, x4, x7)
U119_gga(x1, x2, x3, x4, x5, x6, x7) = U119_gga(x1, x2, x3, x4, x7)
U120_gga(x1, x2, x3, x4, x5, x6, x7) = U120_gga(x1, x2, x3, x4, x7)
U122_gga(x1, x2, x3, x4) = U122_gga(x1, x2, x3, x4)
U123_gga(x1, x2, x3, x4, x5, x6) = U123_gga(x1, x2, x3, x6)
U125_gga(x1, x2, x3, x4) = U125_gga(x1, x2, x4)
U126_gga(x1, x2, x3, x4, x5) = U126_gga(x1, x2, x3, x5)
U127_gga(x1, x2, x3, x4, x5) = U127_gga(x1, x2, x3, x5)
U128_gga(x1, x2, x3, x4, x5) = U128_gga(x1, x2, x3, x5)
U129_gga(x1, x2, x3, x4, x5) = U129_gga(x1, x2, x3, x5)
U124_gga(x1, x2, x3, x4, x5, x6) = U124_gga(x1, x2, x3, x5, x6)
U121_gga(x1, x2, x3, x4, x5, x6, x7) = U121_gga(x1, x2, x3, x4, x6, x7)
U118_gga(x1, x2, x3, x4, x5, x6, x7) = U118_gga(x1, x2, x3, x4, x6, x7)
U115_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U115_gga(x1, x2, x3, x4, x7, x8)
U116_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U116_gga(x1, x2, x3, x4, x6, x7, x8)
U107_gga(x1, x2, x3, x4, x5, x6) = U107_gga(x1, x2, x3, x5, x6)
U98_gga(x1, x2, x3, x4, x5) = U98_gga(x1, x2, x4, x5)
U95_gga(x1, x2, x3, x4, x5, x6) = U95_gga(x1, x2, x3, x5, x6)
U92_gga(x1, x2, x3, x4, x5, x6) = U92_gga(x1, x2, x3, x5, x6)
U89_gga(x1, x2, x3, x4, x5, x6, x7) = U89_gga(x1, x2, x3, x6, x7)
U90_gga(x1, x2, x3, x4, x5, x6, x7) = U90_gga(x1, x2, x3, x5, x6, x7)
U82_gga(x1, x2, x3, x4, x5) = U82_gga(x1, x2, x4, x5)
+(x1, x2) = +(x1, x2)
1 = 1
DB_IN_GGA(x1, x2, x3) = DB_IN_GGA(x1, x2)
U3_GGA(x1, x2) = U3_GGA(x1, x2)
ISNUMBERA_IN_G(x1) = ISNUMBERA_IN_G(x1)
U1_G(x1, x2) = U1_G(x1, x2)
U2_G(x1, x2) = U2_G(x1, x2)
U4_GGA(x1, x2) = U4_GGA(x1, x2)
U5_GGA(x1, x2, x3, x4, x5) = U5_GGA(x1, x2, x5)
U6_GGA(x1, x2, x3, x4, x5) = U6_GGA(x1, x2, x5)
U7_GGA(x1, x2, x3, x4, x5) = U7_GGA(x1, x2, x5)
U8_GGA(x1, x2, x3, x4) = U8_GGA(x1, x2, x4)
U9_GGA(x1, x2, x3, x4) = U9_GGA(x1, x2, x4)
U10_GGA(x1, x2, x3, x4) = U10_GGA(x1, x2, x4)
U11_GGA(x1, x2, x3, x4) = U11_GGA(x1, x2, x4)
U12_GGA(x1, x2, x3, x4) = U12_GGA(x1, x2, x4)
U13_GGA(x1, x2, x3, x4) = U13_GGA(x1, x2, x4)
U14_GGA(x1, x2, x3, x4) = U14_GGA(x1, x2, x4)
U15_GGA(x1, x2, x3, x4, x5, x6, x7) = U15_GGA(x1, x2, x3, x7)
U16_GGA(x1, x2, x3, x4, x5, x6, x7) = U16_GGA(x1, x2, x3, x7)
U17_GGA(x1, x2, x3, x4, x5, x6, x7) = U17_GGA(x1, x2, x3, x7)
U20_GGA(x1, x2, x3, x4, x5, x6) = U20_GGA(x1, x2, x3, x6)
U21_GGA(x1, x2, x3, x4, x5, x6) = U21_GGA(x1, x2, x3, x6)
U22_GGA(x1, x2, x3, x4, x5, x6) = U22_GGA(x1, x2, x3, x6)
U23_GGA(x1, x2, x3, x4, x5, x6) = U23_GGA(x1, x2, x3, x6)
U24_GGA(x1, x2, x3, x4, x5, x6) = U24_GGA(x1, x2, x3, x6)
U25_GGA(x1, x2, x3, x4, x5, x6) = U25_GGA(x1, x2, x3, x6)
U28_GGA(x1, x2, x3) = U28_GGA(x1, x2, x3)
U29_GGA(x1, x2, x3, x4, x5) = U29_GGA(x1, x2, x5)
U30_GGA(x1, x2, x3, x4, x5) = U30_GGA(x1, x2, x5)
U31_GGA(x1, x2, x3, x4, x5) = U31_GGA(x1, x2, x5)
U32_GGA(x1, x2, x3) = U32_GGA(x1, x3)
U33_GGA(x1, x2, x3, x4) = U33_GGA(x1, x2, x4)
U34_GGA(x1, x2, x3, x4) = U34_GGA(x1, x2, x4)
U35_GGA(x1, x2, x3, x4) = U35_GGA(x1, x2, x4)
U36_GGA(x1, x2, x3, x4) = U36_GGA(x1, x2, x4)
U37_GGA(x1, x2, x3, x4) = U37_GGA(x1, x2, x4)
U38_GGA(x1, x2, x3, x4) = U38_GGA(x1, x2, x4)
U39_GGA(x1, x2, x3) = U39_GGA(x1, x2, x3)
U40_GGA(x1, x2, x3) = U40_GGA(x1, x2, x3)
U41_GGA(x1, x2, x3, x4, x5, x6) = U41_GGA(x1, x2, x3, x6)
U42_GGA(x1, x2, x3, x4, x5, x6) = U42_GGA(x1, x2, x3, x6)
U43_GGA(x1, x2, x3, x4, x5, x6) = U43_GGA(x1, x2, x3, x6)
U44_GGA(x1, x2, x3, x4, x5) = U44_GGA(x1, x2, x3, x5)
U45_GGA(x1, x2, x3, x4, x5) = U45_GGA(x1, x2, x3, x5)
U46_GGA(x1, x2, x3, x4, x5) = U46_GGA(x1, x2, x3, x5)
U47_GGA(x1, x2, x3, x4, x5) = U47_GGA(x1, x2, x3, x5)
U48_GGA(x1, x2, x3, x4) = U48_GGA(x1, x2, x4)
U49_GGA(x1, x2, x3, x4, x5) = U49_GGA(x1, x2, x3, x5)
U50_GGA(x1, x2, x3, x4, x5) = U50_GGA(x1, x2, x3, x5)
U51_GGA(x1, x2, x3, x4, x5) = U51_GGA(x1, x2, x3, x5)
U52_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U52_GGA(x1, x2, x3, x4, x8)
U53_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U53_GGA(x1, x2, x3, x4, x8)
U54_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U54_GGA(x1, x2, x3, x4, x8)
U57_GGA(x1, x2, x3, x4, x5, x6, x7) = U57_GGA(x1, x2, x3, x4, x7)
U58_GGA(x1, x2, x3, x4, x5, x6, x7) = U58_GGA(x1, x2, x3, x4, x7)
U59_GGA(x1, x2, x3, x4, x5, x6, x7) = U59_GGA(x1, x2, x3, x4, x7)
U60_GGA(x1, x2, x3, x4, x5, x6, x7) = U60_GGA(x1, x2, x3, x4, x7)
U61_GGA(x1, x2, x3, x4, x5, x6, x7) = U61_GGA(x1, x2, x3, x4, x7)
U62_GGA(x1, x2, x3, x4, x5, x6, x7) = U62_GGA(x1, x2, x3, x4, x7)
U65_GGA(x1, x2, x3, x4) = U65_GGA(x1, x2, x3, x4)
U66_GGA(x1, x2, x3, x4, x5, x6) = U66_GGA(x1, x2, x3, x6)
U67_GGA(x1, x2, x3, x4, x5, x6) = U67_GGA(x1, x2, x3, x6)
U68_GGA(x1, x2, x3, x4, x5, x6) = U68_GGA(x1, x2, x3, x6)
U69_GGA(x1, x2, x3, x4) = U69_GGA(x1, x2, x4)
U70_GGA(x1, x2, x3, x4, x5) = U70_GGA(x1, x2, x3, x5)
U71_GGA(x1, x2, x3, x4, x5) = U71_GGA(x1, x2, x3, x5)
U72_GGA(x1, x2, x3, x4, x5) = U72_GGA(x1, x2, x3, x5)
U73_GGA(x1, x2, x3, x4, x5) = U73_GGA(x1, x2, x3, x5)
U74_GGA(x1, x2, x3, x4, x5) = U74_GGA(x1, x2, x3, x5)
U75_GGA(x1, x2, x3, x4, x5) = U75_GGA(x1, x2, x3, x5)
U63_GGA(x1, x2, x3, x4, x5, x6, x7) = U63_GGA(x1, x2, x3, x4, x7)
U64_GGA(x1, x2, x3, x4, x5, x6, x7) = U64_GGA(x1, x2, x3, x4, x7)
U55_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U55_GGA(x1, x2, x3, x4, x8)
U56_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U56_GGA(x1, x2, x3, x4, x8)
U26_GGA(x1, x2, x3, x4, x5, x6) = U26_GGA(x1, x2, x3, x6)
U27_GGA(x1, x2, x3, x4, x5, x6) = U27_GGA(x1, x2, x3, x6)
U18_GGA(x1, x2, x3, x4, x5, x6, x7) = U18_GGA(x1, x2, x3, x7)
U19_GGA(x1, x2, x3, x4, x5, x6, x7) = U19_GGA(x1, x2, x3, x7)

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

Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES

(4) Obligation:

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

DB_IN_GGA(s(X1), s(X1), 0) → U3_GGA(X1, isnumberA_in_g(X1))
DB_IN_GGA(s(X1), s(X1), 0) → ISNUMBERA_IN_G(X1)
ISNUMBERA_IN_G(s(X1)) → U1_G(X1, isnumberA_in_g(X1))
ISNUMBERA_IN_G(s(X1)) → ISNUMBERA_IN_G(X1)
ISNUMBERA_IN_G(p(X1)) → U2_G(X1, isnumberA_in_g(X1))
ISNUMBERA_IN_G(p(X1)) → ISNUMBERA_IN_G(X1)
DB_IN_GGA(p(X1), p(X1), 0) → U4_GGA(X1, isnumberA_in_g(X1))
DB_IN_GGA(p(X1), p(X1), 0) → ISNUMBERA_IN_G(X1)
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → U5_GGA(X1, X2, X3, X4, dB_in_gga(X1, times(X1, X2), X4))
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → DB_IN_GGA(X1, times(X1, X2), X4)
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → U6_GGA(X1, X2, X3, X4, dcB_in_gga(X1, times(X1, X2), X4))
U6_GGA(X1, X2, X3, X4, dcB_out_gga(X1, times(X1, X2), X4)) → U7_GGA(X1, X2, X3, X4, dB_in_gga(X2, times(X1, X2), X3))
U6_GGA(X1, X2, X3, X4, dcB_out_gga(X1, times(X1, X2), X4)) → DB_IN_GGA(X2, times(X1, X2), X3)
DB_IN_GGA(div(X1, X2), div(X1, X2), X3) → U8_GGA(X1, X2, X3, dB_in_gga(times(X1, power(X2, p(0))), div(X1, X2), X3))
DB_IN_GGA(div(X1, X2), div(X1, X2), X3) → DB_IN_GGA(times(X1, power(X2, p(0))), div(X1, X2), X3)
DB_IN_GGA(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) → U9_GGA(X1, X2, X3, isnumberA_in_g(X2))
DB_IN_GGA(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) → U10_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U10_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → U11_GGA(X1, X2, X3, dB_in_gga(X1, power(X1, X2), X3))
U10_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, X2), X3)
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) → U12_GGA(X1, X2, X3, isnumberA_in_g(X1))
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) → ISNUMBERA_IN_G(X1)
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) → U13_GGA(X1, X2, X3, isnumbercA_in_g(X1))
U13_GGA(X1, X2, X3, isnumbercA_out_g(X1)) → U14_GGA(X1, X2, X3, dB_in_gga(X2, times(X1, X2), X3))
U13_GGA(X1, X2, X3, isnumbercA_out_g(X1)) → DB_IN_GGA(X2, times(X1, X2), X3)
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → U15_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(X1, times(times(X1, X2), X3), X6))
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → DB_IN_GGA(X1, times(times(X1, X2), X3), X6)
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → U16_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, times(times(X1, X2), X3), X6))
U16_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U17_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(X2, times(times(X1, X2), X3), X5))
U16_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → DB_IN_GGA(X2, times(times(X1, X2), X3), X5)
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → U20_GGA(X1, X2, X3, X4, X5, dB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5))
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → DB_IN_GGA(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → U21_GGA(X1, X2, X3, X4, X5, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5))
U21_GGA(X1, X2, X3, X4, X5, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → U22_GGA(X1, X2, X3, X4, X5, dB_in_gga(X3, times(div(X1, X2), X3), X4))
U21_GGA(X1, X2, X3, X4, X5, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(div(X1, X2), X3), X4)
DB_IN_GGA(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) → U23_GGA(X1, X2, X3, X4, X5, isnumberA_in_g(X2))
DB_IN_GGA(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) → U24_GGA(X1, X2, X3, X4, X5, isnumbercA_in_g(X2))
U24_GGA(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → U25_GGA(X1, X2, X3, X4, X5, dB_in_gga(X1, times(power(X1, X2), X3), X5))
U24_GGA(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, times(power(X1, X2), X3), X5)
DB_IN_GGA(div(X1, X2), div(X1, X2), 0) → U28_GGA(X1, X2, isnumberA_in_g(times(X1, power(X2, p(0)))))
DB_IN_GGA(div(X1, X2), div(X1, X2), 0) → ISNUMBERA_IN_G(times(X1, power(X2, p(0))))
DB_IN_GGA(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → U29_GGA(X1, X2, X3, X4, dB_in_gga(X1, div(X1, X2), X4))
DB_IN_GGA(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → DB_IN_GGA(X1, div(X1, X2), X4)
DB_IN_GGA(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → U30_GGA(X1, X2, X3, X4, dcB_in_gga(X1, div(X1, X2), X4))
U30_GGA(X1, X2, X3, X4, dcB_out_gga(X1, div(X1, X2), X4)) → U31_GGA(X1, X2, X3, X4, dB_in_gga(power(X2, p(0)), div(X1, X2), X3))
U30_GGA(X1, X2, X3, X4, dcB_out_gga(X1, div(X1, X2), X4)) → DB_IN_GGA(power(X2, p(0)), div(X1, X2), X3)
DB_IN_GGA(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0))))) → U32_GGA(X1, X2, dB_in_gga(X1, power(X1, 0), X2))
DB_IN_GGA(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0))))) → DB_IN_GGA(X1, power(X1, 0), X2)
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) → U33_GGA(X1, X2, X3, isnumberA_in_g(X2))
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) → U34_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U34_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → U35_GGA(X1, X2, X3, dB_in_gga(X1, power(X1, s(X2)), X3))
U34_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, s(X2)), X3)
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) → U36_GGA(X1, X2, X3, isnumberA_in_g(X2))
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) → U37_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U37_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → U38_GGA(X1, X2, X3, dB_in_gga(X1, power(X1, p(X2)), X3))
U37_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, p(X2)), X3)
DB_IN_GGA(s(X1), X2, 0) → U39_GGA(X1, X2, isnumberA_in_g(X1))
DB_IN_GGA(s(X1), X2, 0) → ISNUMBERA_IN_G(X1)
DB_IN_GGA(p(X1), X2, 0) → U40_GGA(X1, X2, isnumberA_in_g(X1))
DB_IN_GGA(p(X1), X2, 0) → ISNUMBERA_IN_G(X1)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → U41_GGA(X1, X2, X3, X4, X5, dB_in_gga(X1, X3, X5))
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → DB_IN_GGA(X1, X3, X5)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → U42_GGA(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
U42_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U43_GGA(X1, X2, X3, X4, X5, dB_in_gga(X2, X3, X4))
U42_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → DB_IN_GGA(X2, X3, X4)
DB_IN_GGA(div(X1, X2), X3, X4) → U44_GGA(X1, X2, X3, X4, dB_in_gga(times(X1, power(X2, p(0))), X3, X4))
DB_IN_GGA(div(X1, X2), X3, X4) → DB_IN_GGA(times(X1, power(X2, p(0))), X3, X4)
DB_IN_GGA(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) → U45_GGA(X1, X2, X3, X4, isnumberA_in_g(X2))
DB_IN_GGA(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) → U46_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
U46_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U47_GGA(X1, X2, X3, X4, dB_in_gga(X1, X3, X4))
U46_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3, X4)
DB_IN_GGA(times(X1, X2), X1, +(times(X3, X1), times(1, X2))) → U48_GGA(X1, X2, X3, dB_in_gga(X2, X1, X3))
DB_IN_GGA(times(X1, X2), X1, +(times(X3, X1), times(1, X2))) → DB_IN_GGA(X2, X1, X3)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) → U49_GGA(X1, X2, X3, X4, isnumberA_in_g(X1))
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) → ISNUMBERA_IN_G(X1)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) → U50_GGA(X1, X2, X3, X4, isnumbercA_in_g(X1))
U50_GGA(X1, X2, X3, X4, isnumbercA_out_g(X1)) → U51_GGA(X1, X2, X3, X4, dB_in_gga(X2, X3, X4))
U50_GGA(X1, X2, X3, X4, isnumbercA_out_g(X1)) → DB_IN_GGA(X2, X3, X4)
DB_IN_GGA(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → U52_GGA(X1, X2, X3, X4, X5, X6, X7, dB_in_gga(X1, X4, X7))
DB_IN_GGA(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → DB_IN_GGA(X1, X4, X7)
DB_IN_GGA(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X1, X4, X7))
U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → U54_GGA(X1, X2, X3, X4, X5, X6, X7, dB_in_gga(X2, X4, X6))
U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → DB_IN_GGA(X2, X4, X6)
DB_IN_GGA(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → U57_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(times(X1, power(X2, p(0))), X4, X6))
DB_IN_GGA(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → DB_IN_GGA(times(X1, power(X2, p(0))), X4, X6)
DB_IN_GGA(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → U58_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(times(X1, power(X2, p(0))), X4, X6))
U58_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → U59_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(X3, X4, X5))
U58_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → DB_IN_GGA(X3, X4, X5)
DB_IN_GGA(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) → U60_GGA(X1, X2, X3, X4, X5, X6, isnumberA_in_g(X2))
DB_IN_GGA(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) → U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_in_g(X2))
U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → U62_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(X1, X4, X6))
U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X4, X6)
DB_IN_GGA(div(X1, X2), X3, 0) → U65_GGA(X1, X2, X3, isnumberA_in_g(times(X1, power(X2, p(0)))))
DB_IN_GGA(div(X1, X2), X3, 0) → ISNUMBERA_IN_G(times(X1, power(X2, p(0))))
DB_IN_GGA(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → U66_GGA(X1, X2, X3, X4, X5, dB_in_gga(X1, X3, X5))
DB_IN_GGA(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → DB_IN_GGA(X1, X3, X5)
DB_IN_GGA(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → U67_GGA(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
U67_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U68_GGA(X1, X2, X3, X4, X5, dB_in_gga(power(X2, p(0)), X3, X4))
U67_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → DB_IN_GGA(power(X2, p(0)), X3, X4)
DB_IN_GGA(power(X1, 0), X2, times(0, times(X3, power(X1, p(0))))) → U69_GGA(X1, X2, X3, dB_in_gga(X1, X2, X3))
DB_IN_GGA(power(X1, 0), X2, times(0, times(X3, power(X1, p(0))))) → DB_IN_GGA(X1, X2, X3)
DB_IN_GGA(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) → U70_GGA(X1, X2, X3, X4, isnumberA_in_g(X2))
DB_IN_GGA(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) → U71_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
U71_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U72_GGA(X1, X2, X3, X4, dB_in_gga(X1, X3, X4))
U71_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3, X4)
DB_IN_GGA(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) → U73_GGA(X1, X2, X3, X4, isnumberA_in_g(X2))
DB_IN_GGA(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) → ISNUMBERA_IN_G(X2)
DB_IN_GGA(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) → U74_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
U74_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U75_GGA(X1, X2, X3, X4, dB_in_gga(X1, X3, X4))
U74_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3, X4)
U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → U63_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, X4, X6))
U63_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, X4, X6)) → U64_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(X3, X4, X5))
U63_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, X4, X6)) → DB_IN_GGA(X3, X4, X5)
U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → U55_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X2, X4, X6))
U55_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X2, X4, X6)) → U56_GGA(X1, X2, X3, X4, X5, X6, X7, dB_in_gga(X3, X4, X5))
U55_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X2, X4, X6)) → DB_IN_GGA(X3, X4, X5)
U24_GGA(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → U26_GGA(X1, X2, X3, X4, X5, dcB_in_gga(X1, times(power(X1, X2), X3), X5))
U26_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → U27_GGA(X1, X2, X3, X4, X5, dB_in_gga(X3, times(power(X1, X2), X3), X4))
U26_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(power(X1, X2), X3), X4)
U16_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U18_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(X2, times(times(X1, X2), X3), X5))
U18_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → U19_GGA(X1, X2, X3, X4, X5, X6, dB_in_gga(X3, times(times(X1, X2), X3), X4))
U18_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(times(X1, X2), X3), X4)

The TRS R consists of the following rules:

dcB_in_gga(X1, X1, 1) → dcB_out_gga(X1, X1, 1)
dcB_in_gga(0, 0, 0) → dcB_out_gga(0, 0, 0)
dcB_in_gga(s(X1), s(X1), 0) → U79_gga(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(0) → isnumbercA_out_g(0)
isnumbercA_in_g(s(X1)) → U77_g(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(p(X1)) → U78_g(X1, isnumbercA_in_g(X1))
U78_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(p(X1))
U77_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(s(X1))
U79_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), s(X1), 0)
dcB_in_gga(p(X1), p(X1), 0) → U80_gga(X1, isnumbercA_in_g(X1))
U80_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), p(X1), 0)
dcB_in_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → U81_gga(X1, X2, X3, X4, dcB_in_gga(X1, times(X1, X2), X4))
dcB_in_gga(div(X1, X2), div(X1, X2), X3) → U83_gga(X1, X2, X3, dcB_in_gga(times(X1, power(X2, p(0))), div(X1, X2), X3))
dcB_in_gga(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) → U84_gga(X1, X2, X3, isnumbercA_in_g(X2))
U84_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U85_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, X2), X3))
dcB_in_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) → U86_gga(X1, X2, X3, isnumbercA_in_g(X1))
U86_gga(X1, X2, X3, isnumbercA_out_g(X1)) → U87_gga(X1, X2, X3, dcB_in_gga(X2, times(X1, X2), X3))
dcB_in_gga(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → U88_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, times(times(X1, X2), X3), X6))
dcB_in_gga(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → U91_gga(X1, X2, X3, X4, X5, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5))
dcB_in_gga(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) → U93_gga(X1, X2, X3, X4, X5, isnumbercA_in_g(X2))
U93_gga(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → U94_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, times(power(X1, X2), X3), X5))
dcB_in_gga(div(X1, X2), div(X1, X2), 0) → U96_gga(X1, X2, isnumbercA_in_g(times(X1, power(X2, p(0)))))
U96_gga(X1, X2, isnumbercA_out_g(times(X1, power(X2, p(0))))) → dcB_out_gga(div(X1, X2), div(X1, X2), 0)
dcB_in_gga(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → U97_gga(X1, X2, X3, X4, dcB_in_gga(X1, div(X1, X2), X4))
dcB_in_gga(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0))))) → U99_gga(X1, X2, dcB_in_gga(X1, power(X1, 0), X2))
dcB_in_gga(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) → U100_gga(X1, X2, X3, isnumbercA_in_g(X2))
U100_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U101_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, s(X2)), X3))
dcB_in_gga(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) → U102_gga(X1, X2, X3, isnumbercA_in_g(X2))
U102_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U103_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, p(X2)), X3))
dcB_in_gga(0, X1, 0) → dcB_out_gga(0, X1, 0)
dcB_in_gga(s(X1), X2, 0) → U104_gga(X1, X2, isnumbercA_in_g(X1))
U104_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), X2, 0)
dcB_in_gga(p(X1), X2, 0) → U105_gga(X1, X2, isnumbercA_in_g(X1))
U105_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), X2, 0)
dcB_in_gga(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → U106_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
dcB_in_gga(div(X1, X2), X3, X4) → U108_gga(X1, X2, X3, X4, dcB_in_gga(times(X1, power(X2, p(0))), X3, X4))
dcB_in_gga(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) → U109_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
U109_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U110_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
dcB_in_gga(times(X1, X2), X1, +(times(X3, X1), times(1, X2))) → U111_gga(X1, X2, X3, dcB_in_gga(X2, X1, X3))
dcB_in_gga(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) → U112_gga(X1, X2, X3, X4, isnumbercA_in_g(X1))
U112_gga(X1, X2, X3, X4, isnumbercA_out_g(X1)) → U113_gga(X1, X2, X3, X4, dcB_in_gga(X2, X3, X4))
dcB_in_gga(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → U114_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X1, X4, X7))
dcB_in_gga(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → U117_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(times(X1, power(X2, p(0))), X4, X6))
dcB_in_gga(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) → U119_gga(X1, X2, X3, X4, X5, X6, isnumbercA_in_g(X2))
U119_gga(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → U120_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, X4, X6))
dcB_in_gga(div(X1, X2), times(X1, power(X2, p(0))), 1) → dcB_out_gga(div(X1, X2), times(X1, power(X2, p(0))), 1)
dcB_in_gga(div(X1, X2), X3, 0) → U122_gga(X1, X2, X3, isnumbercA_in_g(times(X1, power(X2, p(0)))))
U122_gga(X1, X2, X3, isnumbercA_out_g(times(X1, power(X2, p(0))))) → dcB_out_gga(div(X1, X2), X3, 0)
dcB_in_gga(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → U123_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
dcB_in_gga(power(X1, 0), X2, times(0, times(X3, power(X1, p(0))))) → U125_gga(X1, X2, X3, dcB_in_gga(X1, X2, X3))
dcB_in_gga(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) → U126_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
U126_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U127_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
dcB_in_gga(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) → U128_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
U128_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U129_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
U129_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2))))))
U127_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2))))))
U125_gga(X1, X2, X3, dcB_out_gga(X1, X2, X3)) → dcB_out_gga(power(X1, 0), X2, times(0, times(X3, power(X1, p(0)))))
U123_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U124_gga(X1, X2, X3, X4, X5, dcB_in_gga(power(X2, p(0)), X3, X4))
U124_gga(X1, X2, X3, X4, X5, dcB_out_gga(power(X2, p(0)), X3, X4)) → dcB_out_gga(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0)))))
U120_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, X4, X6)) → U121_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, X4, X5))
U121_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3)))
U117_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → U118_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, X4, X5))
U118_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3)))
U114_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → U115_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X2, X4, X6))
U115_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X2, X4, X6)) → U116_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X3, X4, X5))
U116_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3)))
U113_gga(X1, X2, X3, X4, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(0, X2)))
U111_gga(X1, X2, X3, dcB_out_gga(X2, X1, X3)) → dcB_out_gga(times(X1, X2), X1, +(times(X3, X1), times(1, X2)))
U110_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2)))))
U108_gga(X1, X2, X3, X4, dcB_out_gga(times(X1, power(X2, p(0))), X3, X4)) → dcB_out_gga(div(X1, X2), X3, X4)
U106_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U107_gga(X1, X2, X3, X4, X5, dcB_in_gga(X2, X3, X4))
U107_gga(X1, X2, X3, X4, X5, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(X5, X2)))
U103_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, p(X2)), X3)) → dcB_out_gga(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2))))))
U101_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, s(X2)), X3)) → dcB_out_gga(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2))))))
U99_gga(X1, X2, dcB_out_gga(X1, power(X1, 0), X2)) → dcB_out_gga(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0)))))
U97_gga(X1, X2, X3, X4, dcB_out_gga(X1, div(X1, X2), X4)) → U98_gga(X1, X2, X3, X4, dcB_in_gga(power(X2, p(0)), div(X1, X2), X3))
U98_gga(X1, X2, X3, X4, dcB_out_gga(power(X2, p(0)), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0)))))
U94_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → U95_gga(X1, X2, X3, X4, X5, dcB_in_gga(X3, times(power(X1, X2), X3), X4))
U95_gga(X1, X2, X3, X4, X5, dcB_out_gga(X3, times(power(X1, X2), X3), X4)) → dcB_out_gga(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3)))
U91_gga(X1, X2, X3, X4, X5, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → U92_gga(X1, X2, X3, X4, X5, dcB_in_gga(X3, times(div(X1, X2), X3), X4))
U92_gga(X1, X2, X3, X4, X5, dcB_out_gga(X3, times(div(X1, X2), X3), X4)) → dcB_out_gga(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3)))
U88_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U89_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X2, times(times(X1, X2), X3), X5))
U89_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → U90_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, times(times(X1, X2), X3), X4))
U90_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, times(times(X1, X2), X3), X4)) → dcB_out_gga(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3)))
U87_gga(X1, X2, X3, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2)))
U85_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, X2), X3)) → dcB_out_gga(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2)))))
U83_gga(X1, X2, X3, dcB_out_gga(times(X1, power(X2, p(0))), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), X3)
U81_gga(X1, X2, X3, X4, dcB_out_gga(X1, times(X1, X2), X4)) → U82_gga(X1, X2, X3, X4, dcB_in_gga(X2, times(X1, X2), X3))
U82_gga(X1, X2, X3, X4, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2)))

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 2 SCCs with 69 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

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

ISNUMBERA_IN_G(p(X1)) → ISNUMBERA_IN_G(X1)
ISNUMBERA_IN_G(s(X1)) → ISNUMBERA_IN_G(X1)

The TRS R consists of the following rules:

dcB_in_gga(X1, X1, 1) → dcB_out_gga(X1, X1, 1)
dcB_in_gga(0, 0, 0) → dcB_out_gga(0, 0, 0)
dcB_in_gga(s(X1), s(X1), 0) → U79_gga(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(0) → isnumbercA_out_g(0)
isnumbercA_in_g(s(X1)) → U77_g(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(p(X1)) → U78_g(X1, isnumbercA_in_g(X1))
U78_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(p(X1))
U77_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(s(X1))
U79_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), s(X1), 0)
dcB_in_gga(p(X1), p(X1), 0) → U80_gga(X1, isnumbercA_in_g(X1))
U80_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), p(X1), 0)
dcB_in_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → U81_gga(X1, X2, X3, X4, dcB_in_gga(X1, times(X1, X2), X4))
dcB_in_gga(div(X1, X2), div(X1, X2), X3) → U83_gga(X1, X2, X3, dcB_in_gga(times(X1, power(X2, p(0))), div(X1, X2), X3))
dcB_in_gga(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) → U84_gga(X1, X2, X3, isnumbercA_in_g(X2))
U84_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U85_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, X2), X3))
dcB_in_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) → U86_gga(X1, X2, X3, isnumbercA_in_g(X1))
U86_gga(X1, X2, X3, isnumbercA_out_g(X1)) → U87_gga(X1, X2, X3, dcB_in_gga(X2, times(X1, X2), X3))
dcB_in_gga(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → U88_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, times(times(X1, X2), X3), X6))
dcB_in_gga(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → U91_gga(X1, X2, X3, X4, X5, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5))
dcB_in_gga(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) → U93_gga(X1, X2, X3, X4, X5, isnumbercA_in_g(X2))
U93_gga(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → U94_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, times(power(X1, X2), X3), X5))
dcB_in_gga(div(X1, X2), div(X1, X2), 0) → U96_gga(X1, X2, isnumbercA_in_g(times(X1, power(X2, p(0)))))
U96_gga(X1, X2, isnumbercA_out_g(times(X1, power(X2, p(0))))) → dcB_out_gga(div(X1, X2), div(X1, X2), 0)
dcB_in_gga(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → U97_gga(X1, X2, X3, X4, dcB_in_gga(X1, div(X1, X2), X4))
dcB_in_gga(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0))))) → U99_gga(X1, X2, dcB_in_gga(X1, power(X1, 0), X2))
dcB_in_gga(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) → U100_gga(X1, X2, X3, isnumbercA_in_g(X2))
U100_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U101_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, s(X2)), X3))
dcB_in_gga(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) → U102_gga(X1, X2, X3, isnumbercA_in_g(X2))
U102_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U103_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, p(X2)), X3))
dcB_in_gga(0, X1, 0) → dcB_out_gga(0, X1, 0)
dcB_in_gga(s(X1), X2, 0) → U104_gga(X1, X2, isnumbercA_in_g(X1))
U104_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), X2, 0)
dcB_in_gga(p(X1), X2, 0) → U105_gga(X1, X2, isnumbercA_in_g(X1))
U105_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), X2, 0)
dcB_in_gga(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → U106_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
dcB_in_gga(div(X1, X2), X3, X4) → U108_gga(X1, X2, X3, X4, dcB_in_gga(times(X1, power(X2, p(0))), X3, X4))
dcB_in_gga(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) → U109_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
U109_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U110_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
dcB_in_gga(times(X1, X2), X1, +(times(X3, X1), times(1, X2))) → U111_gga(X1, X2, X3, dcB_in_gga(X2, X1, X3))
dcB_in_gga(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) → U112_gga(X1, X2, X3, X4, isnumbercA_in_g(X1))
U112_gga(X1, X2, X3, X4, isnumbercA_out_g(X1)) → U113_gga(X1, X2, X3, X4, dcB_in_gga(X2, X3, X4))
dcB_in_gga(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → U114_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X1, X4, X7))
dcB_in_gga(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → U117_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(times(X1, power(X2, p(0))), X4, X6))
dcB_in_gga(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) → U119_gga(X1, X2, X3, X4, X5, X6, isnumbercA_in_g(X2))
U119_gga(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → U120_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, X4, X6))
dcB_in_gga(div(X1, X2), times(X1, power(X2, p(0))), 1) → dcB_out_gga(div(X1, X2), times(X1, power(X2, p(0))), 1)
dcB_in_gga(div(X1, X2), X3, 0) → U122_gga(X1, X2, X3, isnumbercA_in_g(times(X1, power(X2, p(0)))))
U122_gga(X1, X2, X3, isnumbercA_out_g(times(X1, power(X2, p(0))))) → dcB_out_gga(div(X1, X2), X3, 0)
dcB_in_gga(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → U123_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
dcB_in_gga(power(X1, 0), X2, times(0, times(X3, power(X1, p(0))))) → U125_gga(X1, X2, X3, dcB_in_gga(X1, X2, X3))
dcB_in_gga(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) → U126_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
U126_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U127_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
dcB_in_gga(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) → U128_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
U128_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U129_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
U129_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2))))))
U127_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2))))))
U125_gga(X1, X2, X3, dcB_out_gga(X1, X2, X3)) → dcB_out_gga(power(X1, 0), X2, times(0, times(X3, power(X1, p(0)))))
U123_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U124_gga(X1, X2, X3, X4, X5, dcB_in_gga(power(X2, p(0)), X3, X4))
U124_gga(X1, X2, X3, X4, X5, dcB_out_gga(power(X2, p(0)), X3, X4)) → dcB_out_gga(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0)))))
U120_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, X4, X6)) → U121_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, X4, X5))
U121_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3)))
U117_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → U118_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, X4, X5))
U118_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3)))
U114_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → U115_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X2, X4, X6))
U115_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X2, X4, X6)) → U116_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X3, X4, X5))
U116_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3)))
U113_gga(X1, X2, X3, X4, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(0, X2)))
U111_gga(X1, X2, X3, dcB_out_gga(X2, X1, X3)) → dcB_out_gga(times(X1, X2), X1, +(times(X3, X1), times(1, X2)))
U110_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2)))))
U108_gga(X1, X2, X3, X4, dcB_out_gga(times(X1, power(X2, p(0))), X3, X4)) → dcB_out_gga(div(X1, X2), X3, X4)
U106_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U107_gga(X1, X2, X3, X4, X5, dcB_in_gga(X2, X3, X4))
U107_gga(X1, X2, X3, X4, X5, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(X5, X2)))
U103_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, p(X2)), X3)) → dcB_out_gga(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2))))))
U101_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, s(X2)), X3)) → dcB_out_gga(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2))))))
U99_gga(X1, X2, dcB_out_gga(X1, power(X1, 0), X2)) → dcB_out_gga(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0)))))
U97_gga(X1, X2, X3, X4, dcB_out_gga(X1, div(X1, X2), X4)) → U98_gga(X1, X2, X3, X4, dcB_in_gga(power(X2, p(0)), div(X1, X2), X3))
U98_gga(X1, X2, X3, X4, dcB_out_gga(power(X2, p(0)), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0)))))
U94_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → U95_gga(X1, X2, X3, X4, X5, dcB_in_gga(X3, times(power(X1, X2), X3), X4))
U95_gga(X1, X2, X3, X4, X5, dcB_out_gga(X3, times(power(X1, X2), X3), X4)) → dcB_out_gga(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3)))
U91_gga(X1, X2, X3, X4, X5, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → U92_gga(X1, X2, X3, X4, X5, dcB_in_gga(X3, times(div(X1, X2), X3), X4))
U92_gga(X1, X2, X3, X4, X5, dcB_out_gga(X3, times(div(X1, X2), X3), X4)) → dcB_out_gga(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3)))
U88_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U89_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X2, times(times(X1, X2), X3), X5))
U89_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → U90_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, times(times(X1, X2), X3), X4))
U90_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, times(times(X1, X2), X3), X4)) → dcB_out_gga(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3)))
U87_gga(X1, X2, X3, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2)))
U85_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, X2), X3)) → dcB_out_gga(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2)))))
U83_gga(X1, X2, X3, dcB_out_gga(times(X1, power(X2, p(0))), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), X3)
U81_gga(X1, X2, X3, X4, dcB_out_gga(X1, times(X1, X2), X4)) → U82_gga(X1, X2, X3, X4, dcB_in_gga(X2, times(X1, X2), X3))
U82_gga(X1, X2, X3, X4, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2)))

The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
p(x1) = p(x1)
times(x1, x2) = times(x1, x2)
dcB_in_gga(x1, x2, x3) = dcB_in_gga(x1, x2)
dcB_out_gga(x1, x2, x3) = dcB_out_gga(x1, x2, x3)
0 = 0
U79_gga(x1, x2) = U79_gga(x1, x2)
isnumbercA_in_g(x1) = isnumbercA_in_g(x1)
isnumbercA_out_g(x1) = isnumbercA_out_g(x1)
U77_g(x1, x2) = U77_g(x1, x2)
U78_g(x1, x2) = U78_g(x1, x2)
U80_gga(x1, x2) = U80_gga(x1, x2)
U81_gga(x1, x2, x3, x4, x5) = U81_gga(x1, x2, x5)
div(x1, x2) = div(x1, x2)
U83_gga(x1, x2, x3, x4) = U83_gga(x1, x2, x4)
power(x1, x2) = power(x1, x2)
U84_gga(x1, x2, x3, x4) = U84_gga(x1, x2, x4)
U85_gga(x1, x2, x3, x4) = U85_gga(x1, x2, x4)
U86_gga(x1, x2, x3, x4) = U86_gga(x1, x2, x4)
U87_gga(x1, x2, x3, x4) = U87_gga(x1, x2, x4)
U88_gga(x1, x2, x3, x4, x5, x6, x7) = U88_gga(x1, x2, x3, x7)
U91_gga(x1, x2, x3, x4, x5, x6) = U91_gga(x1, x2, x3, x6)
U93_gga(x1, x2, x3, x4, x5, x6) = U93_gga(x1, x2, x3, x6)
U94_gga(x1, x2, x3, x4, x5, x6) = U94_gga(x1, x2, x3, x6)
U96_gga(x1, x2, x3) = U96_gga(x1, x2, x3)
U97_gga(x1, x2, x3, x4, x5) = U97_gga(x1, x2, x5)
U99_gga(x1, x2, x3) = U99_gga(x1, x3)
U100_gga(x1, x2, x3, x4) = U100_gga(x1, x2, x4)
U101_gga(x1, x2, x3, x4) = U101_gga(x1, x2, x4)
U102_gga(x1, x2, x3, x4) = U102_gga(x1, x2, x4)
U103_gga(x1, x2, x3, x4) = U103_gga(x1, x2, x4)
U104_gga(x1, x2, x3) = U104_gga(x1, x2, x3)
U105_gga(x1, x2, x3) = U105_gga(x1, x2, x3)
U106_gga(x1, x2, x3, x4, x5, x6) = U106_gga(x1, x2, x3, x6)
U108_gga(x1, x2, x3, x4, x5) = U108_gga(x1, x2, x3, x5)
U109_gga(x1, x2, x3, x4, x5) = U109_gga(x1, x2, x3, x5)
U110_gga(x1, x2, x3, x4, x5) = U110_gga(x1, x2, x3, x5)
U111_gga(x1, x2, x3, x4) = U111_gga(x1, x2, x4)
U112_gga(x1, x2, x3, x4, x5) = U112_gga(x1, x2, x3, x5)
U113_gga(x1, x2, x3, x4, x5) = U113_gga(x1, x2, x3, x5)
U114_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U114_gga(x1, x2, x3, x4, x8)
U117_gga(x1, x2, x3, x4, x5, x6, x7) = U117_gga(x1, x2, x3, x4, x7)
U119_gga(x1, x2, x3, x4, x5, x6, x7) = U119_gga(x1, x2, x3, x4, x7)
U120_gga(x1, x2, x3, x4, x5, x6, x7) = U120_gga(x1, x2, x3, x4, x7)
U122_gga(x1, x2, x3, x4) = U122_gga(x1, x2, x3, x4)
U123_gga(x1, x2, x3, x4, x5, x6) = U123_gga(x1, x2, x3, x6)
U125_gga(x1, x2, x3, x4) = U125_gga(x1, x2, x4)
U126_gga(x1, x2, x3, x4, x5) = U126_gga(x1, x2, x3, x5)
U127_gga(x1, x2, x3, x4, x5) = U127_gga(x1, x2, x3, x5)
U128_gga(x1, x2, x3, x4, x5) = U128_gga(x1, x2, x3, x5)
U129_gga(x1, x2, x3, x4, x5) = U129_gga(x1, x2, x3, x5)
U124_gga(x1, x2, x3, x4, x5, x6) = U124_gga(x1, x2, x3, x5, x6)
U121_gga(x1, x2, x3, x4, x5, x6, x7) = U121_gga(x1, x2, x3, x4, x6, x7)
U118_gga(x1, x2, x3, x4, x5, x6, x7) = U118_gga(x1, x2, x3, x4, x6, x7)
U115_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U115_gga(x1, x2, x3, x4, x7, x8)
U116_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U116_gga(x1, x2, x3, x4, x6, x7, x8)
U107_gga(x1, x2, x3, x4, x5, x6) = U107_gga(x1, x2, x3, x5, x6)
U98_gga(x1, x2, x3, x4, x5) = U98_gga(x1, x2, x4, x5)
U95_gga(x1, x2, x3, x4, x5, x6) = U95_gga(x1, x2, x3, x5, x6)
U92_gga(x1, x2, x3, x4, x5, x6) = U92_gga(x1, x2, x3, x5, x6)
U89_gga(x1, x2, x3, x4, x5, x6, x7) = U89_gga(x1, x2, x3, x6, x7)
U90_gga(x1, x2, x3, x4, x5, x6, x7) = U90_gga(x1, x2, x3, x5, x6, x7)
U82_gga(x1, x2, x3, x4, x5) = U82_gga(x1, x2, x4, x5)
+(x1, x2) = +(x1, x2)
1 = 1
ISNUMBERA_IN_G(x1) = ISNUMBERA_IN_G(x1)

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

(8) UsableRulesProof (EQUIVALENT transformation)

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

(9) Obligation:

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

ISNUMBERA_IN_G(p(X1)) → ISNUMBERA_IN_G(X1)
ISNUMBERA_IN_G(s(X1)) → ISNUMBERA_IN_G(X1)

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

(10) PiDPToQDPProof (EQUIVALENT 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:

ISNUMBERA_IN_G(p(X1)) → ISNUMBERA_IN_G(X1)
ISNUMBERA_IN_G(s(X1)) → ISNUMBERA_IN_G(X1)

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:

ISNUMBERA_IN_G(p(X1)) → ISNUMBERA_IN_G(X1)
The graph contains the following edges 1 > 1
ISNUMBERA_IN_G(s(X1)) → ISNUMBERA_IN_G(X1)
The graph contains the following edges 1 > 1

(13) YES

(14) Obligation:

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

DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → DB_IN_GGA(X1, times(X1, X2), X4)
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → U6_GGA(X1, X2, X3, X4, dcB_in_gga(X1, times(X1, X2), X4))
U6_GGA(X1, X2, X3, X4, dcB_out_gga(X1, times(X1, X2), X4)) → DB_IN_GGA(X2, times(X1, X2), X3)
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) → U13_GGA(X1, X2, X3, isnumbercA_in_g(X1))
U13_GGA(X1, X2, X3, isnumbercA_out_g(X1)) → DB_IN_GGA(X2, times(X1, X2), X3)
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → DB_IN_GGA(X1, times(times(X1, X2), X3), X6)
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → U16_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, times(times(X1, X2), X3), X6))
U16_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → DB_IN_GGA(X2, times(times(X1, X2), X3), X5)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → DB_IN_GGA(X1, X3, X5)
DB_IN_GGA(div(X1, X2), div(X1, X2), X3) → DB_IN_GGA(times(X1, power(X2, p(0))), div(X1, X2), X3)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → U42_GGA(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
U42_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → DB_IN_GGA(X2, X3, X4)
DB_IN_GGA(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) → U10_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U10_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, X2), X3)
DB_IN_GGA(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0))))) → DB_IN_GGA(X1, power(X1, 0), X2)
DB_IN_GGA(div(X1, X2), X3, X4) → DB_IN_GGA(times(X1, power(X2, p(0))), X3, X4)
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → DB_IN_GGA(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → U21_GGA(X1, X2, X3, X4, X5, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5))
U21_GGA(X1, X2, X3, X4, X5, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(div(X1, X2), X3), X4)
DB_IN_GGA(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) → U46_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
U46_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3, X4)
DB_IN_GGA(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) → U24_GGA(X1, X2, X3, X4, X5, isnumbercA_in_g(X2))
U24_GGA(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, times(power(X1, X2), X3), X5)
DB_IN_GGA(times(X1, X2), X1, +(times(X3, X1), times(1, X2))) → DB_IN_GGA(X2, X1, X3)
DB_IN_GGA(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → DB_IN_GGA(X1, div(X1, X2), X4)
DB_IN_GGA(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → U30_GGA(X1, X2, X3, X4, dcB_in_gga(X1, div(X1, X2), X4))
U30_GGA(X1, X2, X3, X4, dcB_out_gga(X1, div(X1, X2), X4)) → DB_IN_GGA(power(X2, p(0)), div(X1, X2), X3)
DB_IN_GGA(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) → U74_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
U74_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3, X4)
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) → U34_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U34_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, s(X2)), X3)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) → U50_GGA(X1, X2, X3, X4, isnumbercA_in_g(X1))
U50_GGA(X1, X2, X3, X4, isnumbercA_out_g(X1)) → DB_IN_GGA(X2, X3, X4)
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) → U37_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U37_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, p(X2)), X3)
DB_IN_GGA(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → DB_IN_GGA(X1, X4, X7)
DB_IN_GGA(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X1, X4, X7))
U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → DB_IN_GGA(X2, X4, X6)
DB_IN_GGA(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → DB_IN_GGA(times(X1, power(X2, p(0))), X4, X6)
DB_IN_GGA(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → U58_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(times(X1, power(X2, p(0))), X4, X6))
U58_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → DB_IN_GGA(X3, X4, X5)
DB_IN_GGA(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) → U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_in_g(X2))
U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X4, X6)
DB_IN_GGA(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → DB_IN_GGA(X1, X3, X5)
DB_IN_GGA(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → U67_GGA(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
U67_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → DB_IN_GGA(power(X2, p(0)), X3, X4)
DB_IN_GGA(power(X1, 0), X2, times(0, times(X3, power(X1, p(0))))) → DB_IN_GGA(X1, X2, X3)
DB_IN_GGA(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) → U71_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
U71_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3, X4)
U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → U63_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, X4, X6))
U63_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, X4, X6)) → DB_IN_GGA(X3, X4, X5)
U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → U55_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X2, X4, X6))
U55_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X2, X4, X6)) → DB_IN_GGA(X3, X4, X5)
U24_GGA(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → U26_GGA(X1, X2, X3, X4, X5, dcB_in_gga(X1, times(power(X1, X2), X3), X5))
U26_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(power(X1, X2), X3), X4)
U16_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U18_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(X2, times(times(X1, X2), X3), X5))
U18_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(times(X1, X2), X3), X4)

The TRS R consists of the following rules:

dcB_in_gga(X1, X1, 1) → dcB_out_gga(X1, X1, 1)
dcB_in_gga(0, 0, 0) → dcB_out_gga(0, 0, 0)
dcB_in_gga(s(X1), s(X1), 0) → U79_gga(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(0) → isnumbercA_out_g(0)
isnumbercA_in_g(s(X1)) → U77_g(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(p(X1)) → U78_g(X1, isnumbercA_in_g(X1))
U78_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(p(X1))
U77_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(s(X1))
U79_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), s(X1), 0)
dcB_in_gga(p(X1), p(X1), 0) → U80_gga(X1, isnumbercA_in_g(X1))
U80_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), p(X1), 0)
dcB_in_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → U81_gga(X1, X2, X3, X4, dcB_in_gga(X1, times(X1, X2), X4))
dcB_in_gga(div(X1, X2), div(X1, X2), X3) → U83_gga(X1, X2, X3, dcB_in_gga(times(X1, power(X2, p(0))), div(X1, X2), X3))
dcB_in_gga(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) → U84_gga(X1, X2, X3, isnumbercA_in_g(X2))
U84_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U85_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, X2), X3))
dcB_in_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) → U86_gga(X1, X2, X3, isnumbercA_in_g(X1))
U86_gga(X1, X2, X3, isnumbercA_out_g(X1)) → U87_gga(X1, X2, X3, dcB_in_gga(X2, times(X1, X2), X3))
dcB_in_gga(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → U88_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, times(times(X1, X2), X3), X6))
dcB_in_gga(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → U91_gga(X1, X2, X3, X4, X5, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5))
dcB_in_gga(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) → U93_gga(X1, X2, X3, X4, X5, isnumbercA_in_g(X2))
U93_gga(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → U94_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, times(power(X1, X2), X3), X5))
dcB_in_gga(div(X1, X2), div(X1, X2), 0) → U96_gga(X1, X2, isnumbercA_in_g(times(X1, power(X2, p(0)))))
U96_gga(X1, X2, isnumbercA_out_g(times(X1, power(X2, p(0))))) → dcB_out_gga(div(X1, X2), div(X1, X2), 0)
dcB_in_gga(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → U97_gga(X1, X2, X3, X4, dcB_in_gga(X1, div(X1, X2), X4))
dcB_in_gga(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0))))) → U99_gga(X1, X2, dcB_in_gga(X1, power(X1, 0), X2))
dcB_in_gga(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) → U100_gga(X1, X2, X3, isnumbercA_in_g(X2))
U100_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U101_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, s(X2)), X3))
dcB_in_gga(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) → U102_gga(X1, X2, X3, isnumbercA_in_g(X2))
U102_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U103_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, p(X2)), X3))
dcB_in_gga(0, X1, 0) → dcB_out_gga(0, X1, 0)
dcB_in_gga(s(X1), X2, 0) → U104_gga(X1, X2, isnumbercA_in_g(X1))
U104_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), X2, 0)
dcB_in_gga(p(X1), X2, 0) → U105_gga(X1, X2, isnumbercA_in_g(X1))
U105_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), X2, 0)
dcB_in_gga(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → U106_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
dcB_in_gga(div(X1, X2), X3, X4) → U108_gga(X1, X2, X3, X4, dcB_in_gga(times(X1, power(X2, p(0))), X3, X4))
dcB_in_gga(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) → U109_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
U109_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U110_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
dcB_in_gga(times(X1, X2), X1, +(times(X3, X1), times(1, X2))) → U111_gga(X1, X2, X3, dcB_in_gga(X2, X1, X3))
dcB_in_gga(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) → U112_gga(X1, X2, X3, X4, isnumbercA_in_g(X1))
U112_gga(X1, X2, X3, X4, isnumbercA_out_g(X1)) → U113_gga(X1, X2, X3, X4, dcB_in_gga(X2, X3, X4))
dcB_in_gga(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → U114_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X1, X4, X7))
dcB_in_gga(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → U117_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(times(X1, power(X2, p(0))), X4, X6))
dcB_in_gga(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) → U119_gga(X1, X2, X3, X4, X5, X6, isnumbercA_in_g(X2))
U119_gga(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → U120_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, X4, X6))
dcB_in_gga(div(X1, X2), times(X1, power(X2, p(0))), 1) → dcB_out_gga(div(X1, X2), times(X1, power(X2, p(0))), 1)
dcB_in_gga(div(X1, X2), X3, 0) → U122_gga(X1, X2, X3, isnumbercA_in_g(times(X1, power(X2, p(0)))))
U122_gga(X1, X2, X3, isnumbercA_out_g(times(X1, power(X2, p(0))))) → dcB_out_gga(div(X1, X2), X3, 0)
dcB_in_gga(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → U123_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
dcB_in_gga(power(X1, 0), X2, times(0, times(X3, power(X1, p(0))))) → U125_gga(X1, X2, X3, dcB_in_gga(X1, X2, X3))
dcB_in_gga(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) → U126_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
U126_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U127_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
dcB_in_gga(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) → U128_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
U128_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U129_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
U129_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2))))))
U127_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2))))))
U125_gga(X1, X2, X3, dcB_out_gga(X1, X2, X3)) → dcB_out_gga(power(X1, 0), X2, times(0, times(X3, power(X1, p(0)))))
U123_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U124_gga(X1, X2, X3, X4, X5, dcB_in_gga(power(X2, p(0)), X3, X4))
U124_gga(X1, X2, X3, X4, X5, dcB_out_gga(power(X2, p(0)), X3, X4)) → dcB_out_gga(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0)))))
U120_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, X4, X6)) → U121_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, X4, X5))
U121_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3)))
U117_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → U118_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, X4, X5))
U118_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3)))
U114_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → U115_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X2, X4, X6))
U115_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X2, X4, X6)) → U116_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X3, X4, X5))
U116_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3)))
U113_gga(X1, X2, X3, X4, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(0, X2)))
U111_gga(X1, X2, X3, dcB_out_gga(X2, X1, X3)) → dcB_out_gga(times(X1, X2), X1, +(times(X3, X1), times(1, X2)))
U110_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2)))))
U108_gga(X1, X2, X3, X4, dcB_out_gga(times(X1, power(X2, p(0))), X3, X4)) → dcB_out_gga(div(X1, X2), X3, X4)
U106_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U107_gga(X1, X2, X3, X4, X5, dcB_in_gga(X2, X3, X4))
U107_gga(X1, X2, X3, X4, X5, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(X5, X2)))
U103_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, p(X2)), X3)) → dcB_out_gga(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2))))))
U101_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, s(X2)), X3)) → dcB_out_gga(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2))))))
U99_gga(X1, X2, dcB_out_gga(X1, power(X1, 0), X2)) → dcB_out_gga(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0)))))
U97_gga(X1, X2, X3, X4, dcB_out_gga(X1, div(X1, X2), X4)) → U98_gga(X1, X2, X3, X4, dcB_in_gga(power(X2, p(0)), div(X1, X2), X3))
U98_gga(X1, X2, X3, X4, dcB_out_gga(power(X2, p(0)), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0)))))
U94_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → U95_gga(X1, X2, X3, X4, X5, dcB_in_gga(X3, times(power(X1, X2), X3), X4))
U95_gga(X1, X2, X3, X4, X5, dcB_out_gga(X3, times(power(X1, X2), X3), X4)) → dcB_out_gga(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3)))
U91_gga(X1, X2, X3, X4, X5, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → U92_gga(X1, X2, X3, X4, X5, dcB_in_gga(X3, times(div(X1, X2), X3), X4))
U92_gga(X1, X2, X3, X4, X5, dcB_out_gga(X3, times(div(X1, X2), X3), X4)) → dcB_out_gga(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3)))
U88_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U89_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X2, times(times(X1, X2), X3), X5))
U89_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → U90_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, times(times(X1, X2), X3), X4))
U90_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, times(times(X1, X2), X3), X4)) → dcB_out_gga(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3)))
U87_gga(X1, X2, X3, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2)))
U85_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, X2), X3)) → dcB_out_gga(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2)))))
U83_gga(X1, X2, X3, dcB_out_gga(times(X1, power(X2, p(0))), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), X3)
U81_gga(X1, X2, X3, X4, dcB_out_gga(X1, times(X1, X2), X4)) → U82_gga(X1, X2, X3, X4, dcB_in_gga(X2, times(X1, X2), X3))
U82_gga(X1, X2, X3, X4, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2)))

The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
p(x1) = p(x1)
times(x1, x2) = times(x1, x2)
dcB_in_gga(x1, x2, x3) = dcB_in_gga(x1, x2)
dcB_out_gga(x1, x2, x3) = dcB_out_gga(x1, x2, x3)
0 = 0
U79_gga(x1, x2) = U79_gga(x1, x2)
isnumbercA_in_g(x1) = isnumbercA_in_g(x1)
isnumbercA_out_g(x1) = isnumbercA_out_g(x1)
U77_g(x1, x2) = U77_g(x1, x2)
U78_g(x1, x2) = U78_g(x1, x2)
U80_gga(x1, x2) = U80_gga(x1, x2)
U81_gga(x1, x2, x3, x4, x5) = U81_gga(x1, x2, x5)
div(x1, x2) = div(x1, x2)
U83_gga(x1, x2, x3, x4) = U83_gga(x1, x2, x4)
power(x1, x2) = power(x1, x2)
U84_gga(x1, x2, x3, x4) = U84_gga(x1, x2, x4)
U85_gga(x1, x2, x3, x4) = U85_gga(x1, x2, x4)
U86_gga(x1, x2, x3, x4) = U86_gga(x1, x2, x4)
U87_gga(x1, x2, x3, x4) = U87_gga(x1, x2, x4)
U88_gga(x1, x2, x3, x4, x5, x6, x7) = U88_gga(x1, x2, x3, x7)
U91_gga(x1, x2, x3, x4, x5, x6) = U91_gga(x1, x2, x3, x6)
U93_gga(x1, x2, x3, x4, x5, x6) = U93_gga(x1, x2, x3, x6)
U94_gga(x1, x2, x3, x4, x5, x6) = U94_gga(x1, x2, x3, x6)
U96_gga(x1, x2, x3) = U96_gga(x1, x2, x3)
U97_gga(x1, x2, x3, x4, x5) = U97_gga(x1, x2, x5)
U99_gga(x1, x2, x3) = U99_gga(x1, x3)
U100_gga(x1, x2, x3, x4) = U100_gga(x1, x2, x4)
U101_gga(x1, x2, x3, x4) = U101_gga(x1, x2, x4)
U102_gga(x1, x2, x3, x4) = U102_gga(x1, x2, x4)
U103_gga(x1, x2, x3, x4) = U103_gga(x1, x2, x4)
U104_gga(x1, x2, x3) = U104_gga(x1, x2, x3)
U105_gga(x1, x2, x3) = U105_gga(x1, x2, x3)
U106_gga(x1, x2, x3, x4, x5, x6) = U106_gga(x1, x2, x3, x6)
U108_gga(x1, x2, x3, x4, x5) = U108_gga(x1, x2, x3, x5)
U109_gga(x1, x2, x3, x4, x5) = U109_gga(x1, x2, x3, x5)
U110_gga(x1, x2, x3, x4, x5) = U110_gga(x1, x2, x3, x5)
U111_gga(x1, x2, x3, x4) = U111_gga(x1, x2, x4)
U112_gga(x1, x2, x3, x4, x5) = U112_gga(x1, x2, x3, x5)
U113_gga(x1, x2, x3, x4, x5) = U113_gga(x1, x2, x3, x5)
U114_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U114_gga(x1, x2, x3, x4, x8)
U117_gga(x1, x2, x3, x4, x5, x6, x7) = U117_gga(x1, x2, x3, x4, x7)
U119_gga(x1, x2, x3, x4, x5, x6, x7) = U119_gga(x1, x2, x3, x4, x7)
U120_gga(x1, x2, x3, x4, x5, x6, x7) = U120_gga(x1, x2, x3, x4, x7)
U122_gga(x1, x2, x3, x4) = U122_gga(x1, x2, x3, x4)
U123_gga(x1, x2, x3, x4, x5, x6) = U123_gga(x1, x2, x3, x6)
U125_gga(x1, x2, x3, x4) = U125_gga(x1, x2, x4)
U126_gga(x1, x2, x3, x4, x5) = U126_gga(x1, x2, x3, x5)
U127_gga(x1, x2, x3, x4, x5) = U127_gga(x1, x2, x3, x5)
U128_gga(x1, x2, x3, x4, x5) = U128_gga(x1, x2, x3, x5)
U129_gga(x1, x2, x3, x4, x5) = U129_gga(x1, x2, x3, x5)
U124_gga(x1, x2, x3, x4, x5, x6) = U124_gga(x1, x2, x3, x5, x6)
U121_gga(x1, x2, x3, x4, x5, x6, x7) = U121_gga(x1, x2, x3, x4, x6, x7)
U118_gga(x1, x2, x3, x4, x5, x6, x7) = U118_gga(x1, x2, x3, x4, x6, x7)
U115_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U115_gga(x1, x2, x3, x4, x7, x8)
U116_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U116_gga(x1, x2, x3, x4, x6, x7, x8)
U107_gga(x1, x2, x3, x4, x5, x6) = U107_gga(x1, x2, x3, x5, x6)
U98_gga(x1, x2, x3, x4, x5) = U98_gga(x1, x2, x4, x5)
U95_gga(x1, x2, x3, x4, x5, x6) = U95_gga(x1, x2, x3, x5, x6)
U92_gga(x1, x2, x3, x4, x5, x6) = U92_gga(x1, x2, x3, x5, x6)
U89_gga(x1, x2, x3, x4, x5, x6, x7) = U89_gga(x1, x2, x3, x6, x7)
U90_gga(x1, x2, x3, x4, x5, x6, x7) = U90_gga(x1, x2, x3, x5, x6, x7)
U82_gga(x1, x2, x3, x4, x5) = U82_gga(x1, x2, x4, x5)
+(x1, x2) = +(x1, x2)
1 = 1
DB_IN_GGA(x1, x2, x3) = DB_IN_GGA(x1, x2)
U6_GGA(x1, x2, x3, x4, x5) = U6_GGA(x1, x2, x5)
U10_GGA(x1, x2, x3, x4) = U10_GGA(x1, x2, x4)
U13_GGA(x1, x2, x3, x4) = U13_GGA(x1, x2, x4)
U16_GGA(x1, x2, x3, x4, x5, x6, x7) = U16_GGA(x1, x2, x3, x7)
U21_GGA(x1, x2, x3, x4, x5, x6) = U21_GGA(x1, x2, x3, x6)
U24_GGA(x1, x2, x3, x4, x5, x6) = U24_GGA(x1, x2, x3, x6)
U30_GGA(x1, x2, x3, x4, x5) = U30_GGA(x1, x2, x5)
U34_GGA(x1, x2, x3, x4) = U34_GGA(x1, x2, x4)
U37_GGA(x1, x2, x3, x4) = U37_GGA(x1, x2, x4)
U42_GGA(x1, x2, x3, x4, x5, x6) = U42_GGA(x1, x2, x3, x6)
U46_GGA(x1, x2, x3, x4, x5) = U46_GGA(x1, x2, x3, x5)
U50_GGA(x1, x2, x3, x4, x5) = U50_GGA(x1, x2, x3, x5)
U53_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U53_GGA(x1, x2, x3, x4, x8)
U58_GGA(x1, x2, x3, x4, x5, x6, x7) = U58_GGA(x1, x2, x3, x4, x7)
U61_GGA(x1, x2, x3, x4, x5, x6, x7) = U61_GGA(x1, x2, x3, x4, x7)
U67_GGA(x1, x2, x3, x4, x5, x6) = U67_GGA(x1, x2, x3, x6)
U71_GGA(x1, x2, x3, x4, x5) = U71_GGA(x1, x2, x3, x5)
U74_GGA(x1, x2, x3, x4, x5) = U74_GGA(x1, x2, x3, x5)
U63_GGA(x1, x2, x3, x4, x5, x6, x7) = U63_GGA(x1, x2, x3, x4, x7)
U55_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U55_GGA(x1, x2, x3, x4, x8)
U26_GGA(x1, x2, x3, x4, x5, x6) = U26_GGA(x1, x2, x3, x6)
U18_GGA(x1, x2, x3, x4, x5, x6, x7) = U18_GGA(x1, x2, x3, x7)

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

(15) UsableRulesProof (EQUIVALENT transformation)

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

(16) Obligation:

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

DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → DB_IN_GGA(X1, times(X1, X2), X4)
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → U6_GGA(X1, X2, X3, X4, dcB_in_gga(X1, times(X1, X2), X4))
U6_GGA(X1, X2, X3, X4, dcB_out_gga(X1, times(X1, X2), X4)) → DB_IN_GGA(X2, times(X1, X2), X3)
DB_IN_GGA(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) → U13_GGA(X1, X2, X3, isnumbercA_in_g(X1))
U13_GGA(X1, X2, X3, isnumbercA_out_g(X1)) → DB_IN_GGA(X2, times(X1, X2), X3)
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → DB_IN_GGA(X1, times(times(X1, X2), X3), X6)
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → U16_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, times(times(X1, X2), X3), X6))
U16_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → DB_IN_GGA(X2, times(times(X1, X2), X3), X5)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → DB_IN_GGA(X1, X3, X5)
DB_IN_GGA(div(X1, X2), div(X1, X2), X3) → DB_IN_GGA(times(X1, power(X2, p(0))), div(X1, X2), X3)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → U42_GGA(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
U42_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → DB_IN_GGA(X2, X3, X4)
DB_IN_GGA(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) → U10_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U10_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, X2), X3)
DB_IN_GGA(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0))))) → DB_IN_GGA(X1, power(X1, 0), X2)
DB_IN_GGA(div(X1, X2), X3, X4) → DB_IN_GGA(times(X1, power(X2, p(0))), X3, X4)
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → DB_IN_GGA(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → U21_GGA(X1, X2, X3, X4, X5, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5))
U21_GGA(X1, X2, X3, X4, X5, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(div(X1, X2), X3), X4)
DB_IN_GGA(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) → U46_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
U46_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3, X4)
DB_IN_GGA(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) → U24_GGA(X1, X2, X3, X4, X5, isnumbercA_in_g(X2))
U24_GGA(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, times(power(X1, X2), X3), X5)
DB_IN_GGA(times(X1, X2), X1, +(times(X3, X1), times(1, X2))) → DB_IN_GGA(X2, X1, X3)
DB_IN_GGA(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → DB_IN_GGA(X1, div(X1, X2), X4)
DB_IN_GGA(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → U30_GGA(X1, X2, X3, X4, dcB_in_gga(X1, div(X1, X2), X4))
U30_GGA(X1, X2, X3, X4, dcB_out_gga(X1, div(X1, X2), X4)) → DB_IN_GGA(power(X2, p(0)), div(X1, X2), X3)
DB_IN_GGA(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) → U74_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
U74_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3, X4)
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) → U34_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U34_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, s(X2)), X3)
DB_IN_GGA(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) → U50_GGA(X1, X2, X3, X4, isnumbercA_in_g(X1))
U50_GGA(X1, X2, X3, X4, isnumbercA_out_g(X1)) → DB_IN_GGA(X2, X3, X4)
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) → U37_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U37_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, p(X2)), X3)
DB_IN_GGA(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → DB_IN_GGA(X1, X4, X7)
DB_IN_GGA(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X1, X4, X7))
U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → DB_IN_GGA(X2, X4, X6)
DB_IN_GGA(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → DB_IN_GGA(times(X1, power(X2, p(0))), X4, X6)
DB_IN_GGA(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → U58_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(times(X1, power(X2, p(0))), X4, X6))
U58_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → DB_IN_GGA(X3, X4, X5)
DB_IN_GGA(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) → U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_in_g(X2))
U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X4, X6)
DB_IN_GGA(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → DB_IN_GGA(X1, X3, X5)
DB_IN_GGA(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → U67_GGA(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
U67_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → DB_IN_GGA(power(X2, p(0)), X3, X4)
DB_IN_GGA(power(X1, 0), X2, times(0, times(X3, power(X1, p(0))))) → DB_IN_GGA(X1, X2, X3)
DB_IN_GGA(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) → U71_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
U71_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3, X4)
U61_GGA(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → U63_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, X4, X6))
U63_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, X4, X6)) → DB_IN_GGA(X3, X4, X5)
U53_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → U55_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X2, X4, X6))
U55_GGA(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X2, X4, X6)) → DB_IN_GGA(X3, X4, X5)
U24_GGA(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → U26_GGA(X1, X2, X3, X4, X5, dcB_in_gga(X1, times(power(X1, X2), X3), X5))
U26_GGA(X1, X2, X3, X4, X5, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(power(X1, X2), X3), X4)
U16_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U18_GGA(X1, X2, X3, X4, X5, X6, dcB_in_gga(X2, times(times(X1, X2), X3), X5))
U18_GGA(X1, X2, X3, X4, X5, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(times(X1, X2), X3), X4)

The TRS R consists of the following rules:

dcB_in_gga(X1, X1, 1) → dcB_out_gga(X1, X1, 1)
dcB_in_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2))) → U81_gga(X1, X2, X3, X4, dcB_in_gga(X1, times(X1, X2), X4))
dcB_in_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2))) → U86_gga(X1, X2, X3, isnumbercA_in_g(X1))
dcB_in_gga(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3))) → U88_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, times(times(X1, X2), X3), X6))
dcB_in_gga(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3))) → U91_gga(X1, X2, X3, X4, X5, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5))
dcB_in_gga(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3))) → U93_gga(X1, X2, X3, X4, X5, isnumbercA_in_g(X2))
dcB_in_gga(0, X1, 0) → dcB_out_gga(0, X1, 0)
dcB_in_gga(s(X1), X2, 0) → U104_gga(X1, X2, isnumbercA_in_g(X1))
dcB_in_gga(p(X1), X2, 0) → U105_gga(X1, X2, isnumbercA_in_g(X1))
dcB_in_gga(times(X1, X2), X3, +(times(X4, X1), times(X5, X2))) → U106_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
dcB_in_gga(div(X1, X2), X3, X4) → U108_gga(X1, X2, X3, X4, dcB_in_gga(times(X1, power(X2, p(0))), X3, X4))
dcB_in_gga(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2))))) → U109_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
dcB_in_gga(times(X1, X2), X1, +(times(X3, X1), times(1, X2))) → U111_gga(X1, X2, X3, dcB_in_gga(X2, X1, X3))
dcB_in_gga(times(X1, X2), X3, +(times(X4, X1), times(0, X2))) → U112_gga(X1, X2, X3, X4, isnumbercA_in_g(X1))
dcB_in_gga(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3))) → U114_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X1, X4, X7))
dcB_in_gga(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3))) → U117_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(times(X1, power(X2, p(0))), X4, X6))
dcB_in_gga(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3))) → U119_gga(X1, X2, X3, X4, X5, X6, isnumbercA_in_g(X2))
dcB_in_gga(div(X1, X2), times(X1, power(X2, p(0))), 1) → dcB_out_gga(div(X1, X2), times(X1, power(X2, p(0))), 1)
dcB_in_gga(div(X1, X2), X3, 0) → U122_gga(X1, X2, X3, isnumbercA_in_g(times(X1, power(X2, p(0)))))
dcB_in_gga(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0))))) → U123_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, X3, X5))
dcB_in_gga(power(X1, 0), X2, times(0, times(X3, power(X1, p(0))))) → U125_gga(X1, X2, X3, dcB_in_gga(X1, X2, X3))
dcB_in_gga(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2)))))) → U126_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
dcB_in_gga(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2)))))) → U128_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
isnumbercA_in_g(0) → isnumbercA_out_g(0)
isnumbercA_in_g(s(X1)) → U77_g(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(p(X1)) → U78_g(X1, isnumbercA_in_g(X1))
dcB_in_gga(0, 0, 0) → dcB_out_gga(0, 0, 0)
dcB_in_gga(s(X1), s(X1), 0) → U79_gga(X1, isnumbercA_in_g(X1))
dcB_in_gga(p(X1), p(X1), 0) → U80_gga(X1, isnumbercA_in_g(X1))
dcB_in_gga(div(X1, X2), div(X1, X2), X3) → U83_gga(X1, X2, X3, dcB_in_gga(times(X1, power(X2, p(0))), div(X1, X2), X3))
dcB_in_gga(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2))))) → U84_gga(X1, X2, X3, isnumbercA_in_g(X2))
dcB_in_gga(div(X1, X2), div(X1, X2), 0) → U96_gga(X1, X2, isnumbercA_in_g(times(X1, power(X2, p(0)))))
dcB_in_gga(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0))))) → U97_gga(X1, X2, X3, X4, dcB_in_gga(X1, div(X1, X2), X4))
dcB_in_gga(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0))))) → U99_gga(X1, X2, dcB_in_gga(X1, power(X1, 0), X2))
dcB_in_gga(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2)))))) → U100_gga(X1, X2, X3, isnumbercA_in_g(X2))
dcB_in_gga(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2)))))) → U102_gga(X1, X2, X3, isnumbercA_in_g(X2))
U81_gga(X1, X2, X3, X4, dcB_out_gga(X1, times(X1, X2), X4)) → U82_gga(X1, X2, X3, X4, dcB_in_gga(X2, times(X1, X2), X3))
U86_gga(X1, X2, X3, isnumbercA_out_g(X1)) → U87_gga(X1, X2, X3, dcB_in_gga(X2, times(X1, X2), X3))
U88_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U89_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X2, times(times(X1, X2), X3), X5))
U91_gga(X1, X2, X3, X4, X5, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → U92_gga(X1, X2, X3, X4, X5, dcB_in_gga(X3, times(div(X1, X2), X3), X4))
U93_gga(X1, X2, X3, X4, X5, isnumbercA_out_g(X2)) → U94_gga(X1, X2, X3, X4, X5, dcB_in_gga(X1, times(power(X1, X2), X3), X5))
U104_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), X2, 0)
U105_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), X2, 0)
U106_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U107_gga(X1, X2, X3, X4, X5, dcB_in_gga(X2, X3, X4))
U108_gga(X1, X2, X3, X4, dcB_out_gga(times(X1, power(X2, p(0))), X3, X4)) → dcB_out_gga(div(X1, X2), X3, X4)
U109_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U110_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
U111_gga(X1, X2, X3, dcB_out_gga(X2, X1, X3)) → dcB_out_gga(times(X1, X2), X1, +(times(X3, X1), times(1, X2)))
U112_gga(X1, X2, X3, X4, isnumbercA_out_g(X1)) → U113_gga(X1, X2, X3, X4, dcB_in_gga(X2, X3, X4))
U114_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X1, X4, X7)) → U115_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X2, X4, X6))
U117_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → U118_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, X4, X5))
U119_gga(X1, X2, X3, X4, X5, X6, isnumbercA_out_g(X2)) → U120_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X1, X4, X6))
U123_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, X3, X5)) → U124_gga(X1, X2, X3, X4, X5, dcB_in_gga(power(X2, p(0)), X3, X4))
U125_gga(X1, X2, X3, dcB_out_gga(X1, X2, X3)) → dcB_out_gga(power(X1, 0), X2, times(0, times(X3, power(X1, p(0)))))
U126_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U127_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
U128_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U129_gga(X1, X2, X3, X4, dcB_in_gga(X1, X3, X4))
U77_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(s(X1))
U78_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(p(X1))
U79_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), s(X1), 0)
U80_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), p(X1), 0)
U83_gga(X1, X2, X3, dcB_out_gga(times(X1, power(X2, p(0))), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), X3)
U84_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U85_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, X2), X3))
U97_gga(X1, X2, X3, X4, dcB_out_gga(X1, div(X1, X2), X4)) → U98_gga(X1, X2, X3, X4, dcB_in_gga(power(X2, p(0)), div(X1, X2), X3))
U99_gga(X1, X2, dcB_out_gga(X1, power(X1, 0), X2)) → dcB_out_gga(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0)))))
U100_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U101_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, s(X2)), X3))
U102_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U103_gga(X1, X2, X3, dcB_in_gga(X1, power(X1, p(X2)), X3))
U82_gga(X1, X2, X3, X4, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2)))
U87_gga(X1, X2, X3, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2)))
U89_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → U90_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, times(times(X1, X2), X3), X4))
U92_gga(X1, X2, X3, X4, X5, dcB_out_gga(X3, times(div(X1, X2), X3), X4)) → dcB_out_gga(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3)))
U94_gga(X1, X2, X3, X4, X5, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → U95_gga(X1, X2, X3, X4, X5, dcB_in_gga(X3, times(power(X1, X2), X3), X4))
U107_gga(X1, X2, X3, X4, X5, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(X5, X2)))
U110_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2)))))
U113_gga(X1, X2, X3, X4, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(0, X2)))
U115_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X2, X4, X6)) → U116_gga(X1, X2, X3, X4, X5, X6, X7, dcB_in_gga(X3, X4, X5))
U118_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3)))
U120_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X1, X4, X6)) → U121_gga(X1, X2, X3, X4, X5, X6, dcB_in_gga(X3, X4, X5))
U124_gga(X1, X2, X3, X4, X5, dcB_out_gga(power(X2, p(0)), X3, X4)) → dcB_out_gga(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0)))))
U127_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2))))))
U129_gga(X1, X2, X3, X4, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2))))))
U85_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, X2), X3)) → dcB_out_gga(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2)))))
U98_gga(X1, X2, X3, X4, dcB_out_gga(power(X2, p(0)), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0)))))
U101_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, s(X2)), X3)) → dcB_out_gga(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2))))))
U103_gga(X1, X2, X3, dcB_out_gga(X1, power(X1, p(X2)), X3)) → dcB_out_gga(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2))))))
U90_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, times(times(X1, X2), X3), X4)) → dcB_out_gga(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3)))
U95_gga(X1, X2, X3, X4, X5, dcB_out_gga(X3, times(power(X1, X2), X3), X4)) → dcB_out_gga(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3)))
U116_gga(X1, X2, X3, X4, X5, X6, X7, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3)))
U121_gga(X1, X2, X3, X4, X5, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3)))

The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
p(x1) = p(x1)
times(x1, x2) = times(x1, x2)
dcB_in_gga(x1, x2, x3) = dcB_in_gga(x1, x2)
dcB_out_gga(x1, x2, x3) = dcB_out_gga(x1, x2, x3)
0 = 0
U79_gga(x1, x2) = U79_gga(x1, x2)
isnumbercA_in_g(x1) = isnumbercA_in_g(x1)
isnumbercA_out_g(x1) = isnumbercA_out_g(x1)
U77_g(x1, x2) = U77_g(x1, x2)
U78_g(x1, x2) = U78_g(x1, x2)
U80_gga(x1, x2) = U80_gga(x1, x2)
U81_gga(x1, x2, x3, x4, x5) = U81_gga(x1, x2, x5)
div(x1, x2) = div(x1, x2)
U83_gga(x1, x2, x3, x4) = U83_gga(x1, x2, x4)
power(x1, x2) = power(x1, x2)
U84_gga(x1, x2, x3, x4) = U84_gga(x1, x2, x4)
U85_gga(x1, x2, x3, x4) = U85_gga(x1, x2, x4)
U86_gga(x1, x2, x3, x4) = U86_gga(x1, x2, x4)
U87_gga(x1, x2, x3, x4) = U87_gga(x1, x2, x4)
U88_gga(x1, x2, x3, x4, x5, x6, x7) = U88_gga(x1, x2, x3, x7)
U91_gga(x1, x2, x3, x4, x5, x6) = U91_gga(x1, x2, x3, x6)
U93_gga(x1, x2, x3, x4, x5, x6) = U93_gga(x1, x2, x3, x6)
U94_gga(x1, x2, x3, x4, x5, x6) = U94_gga(x1, x2, x3, x6)
U96_gga(x1, x2, x3) = U96_gga(x1, x2, x3)
U97_gga(x1, x2, x3, x4, x5) = U97_gga(x1, x2, x5)
U99_gga(x1, x2, x3) = U99_gga(x1, x3)
U100_gga(x1, x2, x3, x4) = U100_gga(x1, x2, x4)
U101_gga(x1, x2, x3, x4) = U101_gga(x1, x2, x4)
U102_gga(x1, x2, x3, x4) = U102_gga(x1, x2, x4)
U103_gga(x1, x2, x3, x4) = U103_gga(x1, x2, x4)
U104_gga(x1, x2, x3) = U104_gga(x1, x2, x3)
U105_gga(x1, x2, x3) = U105_gga(x1, x2, x3)
U106_gga(x1, x2, x3, x4, x5, x6) = U106_gga(x1, x2, x3, x6)
U108_gga(x1, x2, x3, x4, x5) = U108_gga(x1, x2, x3, x5)
U109_gga(x1, x2, x3, x4, x5) = U109_gga(x1, x2, x3, x5)
U110_gga(x1, x2, x3, x4, x5) = U110_gga(x1, x2, x3, x5)
U111_gga(x1, x2, x3, x4) = U111_gga(x1, x2, x4)
U112_gga(x1, x2, x3, x4, x5) = U112_gga(x1, x2, x3, x5)
U113_gga(x1, x2, x3, x4, x5) = U113_gga(x1, x2, x3, x5)
U114_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U114_gga(x1, x2, x3, x4, x8)
U117_gga(x1, x2, x3, x4, x5, x6, x7) = U117_gga(x1, x2, x3, x4, x7)
U119_gga(x1, x2, x3, x4, x5, x6, x7) = U119_gga(x1, x2, x3, x4, x7)
U120_gga(x1, x2, x3, x4, x5, x6, x7) = U120_gga(x1, x2, x3, x4, x7)
U122_gga(x1, x2, x3, x4) = U122_gga(x1, x2, x3, x4)
U123_gga(x1, x2, x3, x4, x5, x6) = U123_gga(x1, x2, x3, x6)
U125_gga(x1, x2, x3, x4) = U125_gga(x1, x2, x4)
U126_gga(x1, x2, x3, x4, x5) = U126_gga(x1, x2, x3, x5)
U127_gga(x1, x2, x3, x4, x5) = U127_gga(x1, x2, x3, x5)
U128_gga(x1, x2, x3, x4, x5) = U128_gga(x1, x2, x3, x5)
U129_gga(x1, x2, x3, x4, x5) = U129_gga(x1, x2, x3, x5)
U124_gga(x1, x2, x3, x4, x5, x6) = U124_gga(x1, x2, x3, x5, x6)
U121_gga(x1, x2, x3, x4, x5, x6, x7) = U121_gga(x1, x2, x3, x4, x6, x7)
U118_gga(x1, x2, x3, x4, x5, x6, x7) = U118_gga(x1, x2, x3, x4, x6, x7)
U115_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U115_gga(x1, x2, x3, x4, x7, x8)
U116_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U116_gga(x1, x2, x3, x4, x6, x7, x8)
U107_gga(x1, x2, x3, x4, x5, x6) = U107_gga(x1, x2, x3, x5, x6)
U98_gga(x1, x2, x3, x4, x5) = U98_gga(x1, x2, x4, x5)
U95_gga(x1, x2, x3, x4, x5, x6) = U95_gga(x1, x2, x3, x5, x6)
U92_gga(x1, x2, x3, x4, x5, x6) = U92_gga(x1, x2, x3, x5, x6)
U89_gga(x1, x2, x3, x4, x5, x6, x7) = U89_gga(x1, x2, x3, x6, x7)
U90_gga(x1, x2, x3, x4, x5, x6, x7) = U90_gga(x1, x2, x3, x5, x6, x7)
U82_gga(x1, x2, x3, x4, x5) = U82_gga(x1, x2, x4, x5)
+(x1, x2) = +(x1, x2)
1 = 1
DB_IN_GGA(x1, x2, x3) = DB_IN_GGA(x1, x2)
U6_GGA(x1, x2, x3, x4, x5) = U6_GGA(x1, x2, x5)
U10_GGA(x1, x2, x3, x4) = U10_GGA(x1, x2, x4)
U13_GGA(x1, x2, x3, x4) = U13_GGA(x1, x2, x4)
U16_GGA(x1, x2, x3, x4, x5, x6, x7) = U16_GGA(x1, x2, x3, x7)
U21_GGA(x1, x2, x3, x4, x5, x6) = U21_GGA(x1, x2, x3, x6)
U24_GGA(x1, x2, x3, x4, x5, x6) = U24_GGA(x1, x2, x3, x6)
U30_GGA(x1, x2, x3, x4, x5) = U30_GGA(x1, x2, x5)
U34_GGA(x1, x2, x3, x4) = U34_GGA(x1, x2, x4)
U37_GGA(x1, x2, x3, x4) = U37_GGA(x1, x2, x4)
U42_GGA(x1, x2, x3, x4, x5, x6) = U42_GGA(x1, x2, x3, x6)
U46_GGA(x1, x2, x3, x4, x5) = U46_GGA(x1, x2, x3, x5)
U50_GGA(x1, x2, x3, x4, x5) = U50_GGA(x1, x2, x3, x5)
U53_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U53_GGA(x1, x2, x3, x4, x8)
U58_GGA(x1, x2, x3, x4, x5, x6, x7) = U58_GGA(x1, x2, x3, x4, x7)
U61_GGA(x1, x2, x3, x4, x5, x6, x7) = U61_GGA(x1, x2, x3, x4, x7)
U67_GGA(x1, x2, x3, x4, x5, x6) = U67_GGA(x1, x2, x3, x6)
U71_GGA(x1, x2, x3, x4, x5) = U71_GGA(x1, x2, x3, x5)
U74_GGA(x1, x2, x3, x4, x5) = U74_GGA(x1, x2, x3, x5)
U63_GGA(x1, x2, x3, x4, x5, x6, x7) = U63_GGA(x1, x2, x3, x4, x7)
U55_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U55_GGA(x1, x2, x3, x4, x8)
U26_GGA(x1, x2, x3, x4, x5, x6) = U26_GGA(x1, x2, x3, x6)
U18_GGA(x1, x2, x3, x4, x5, x6, x7) = U18_GGA(x1, x2, x3, x7)

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:

DB_IN_GGA(times(X1, X2), times(X1, X2)) → DB_IN_GGA(X1, times(X1, X2))
DB_IN_GGA(times(X1, X2), times(X1, X2)) → U6_GGA(X1, X2, dcB_in_gga(X1, times(X1, X2)))
U6_GGA(X1, X2, dcB_out_gga(X1, times(X1, X2), X4)) → DB_IN_GGA(X2, times(X1, X2))
DB_IN_GGA(times(X1, X2), times(X1, X2)) → U13_GGA(X1, X2, isnumbercA_in_g(X1))
U13_GGA(X1, X2, isnumbercA_out_g(X1)) → DB_IN_GGA(X2, times(X1, X2))
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3)) → DB_IN_GGA(X1, times(times(X1, X2), X3))
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3)) → U16_GGA(X1, X2, X3, dcB_in_gga(X1, times(times(X1, X2), X3)))
U16_GGA(X1, X2, X3, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → DB_IN_GGA(X2, times(times(X1, X2), X3))
DB_IN_GGA(times(X1, X2), X3) → DB_IN_GGA(X1, X3)
DB_IN_GGA(div(X1, X2), div(X1, X2)) → DB_IN_GGA(times(X1, power(X2, p(0))), div(X1, X2))
DB_IN_GGA(times(X1, X2), X3) → U42_GGA(X1, X2, X3, dcB_in_gga(X1, X3))
U42_GGA(X1, X2, X3, dcB_out_gga(X1, X3, X5)) → DB_IN_GGA(X2, X3)
DB_IN_GGA(power(X1, X2), power(X1, X2)) → U10_GGA(X1, X2, isnumbercA_in_g(X2))
U10_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, X2))
DB_IN_GGA(power(X1, 0), power(X1, 0)) → DB_IN_GGA(X1, power(X1, 0))
DB_IN_GGA(div(X1, X2), X3) → DB_IN_GGA(times(X1, power(X2, p(0))), X3)
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3)) → DB_IN_GGA(times(X1, power(X2, p(0))), times(div(X1, X2), X3))
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3)) → U21_GGA(X1, X2, X3, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3)))
U21_GGA(X1, X2, X3, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(div(X1, X2), X3))
DB_IN_GGA(power(X1, X2), X3) → U46_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U46_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
DB_IN_GGA(times(power(X1, X2), X3), times(power(X1, X2), X3)) → U24_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U24_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, times(power(X1, X2), X3))
DB_IN_GGA(times(X1, X2), X1) → DB_IN_GGA(X2, X1)
DB_IN_GGA(div(X1, X2), div(X1, X2)) → DB_IN_GGA(X1, div(X1, X2))
DB_IN_GGA(div(X1, X2), div(X1, X2)) → U30_GGA(X1, X2, dcB_in_gga(X1, div(X1, X2)))
U30_GGA(X1, X2, dcB_out_gga(X1, div(X1, X2), X4)) → DB_IN_GGA(power(X2, p(0)), div(X1, X2))
DB_IN_GGA(power(X1, p(X2)), X3) → U74_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U74_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2))) → U34_GGA(X1, X2, isnumbercA_in_g(X2))
U34_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, s(X2)))
DB_IN_GGA(times(X1, X2), X3) → U50_GGA(X1, X2, X3, isnumbercA_in_g(X1))
U50_GGA(X1, X2, X3, isnumbercA_out_g(X1)) → DB_IN_GGA(X2, X3)
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2))) → U37_GGA(X1, X2, isnumbercA_in_g(X2))
U37_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, p(X2)))
DB_IN_GGA(times(times(X1, X2), X3), X4) → DB_IN_GGA(X1, X4)
DB_IN_GGA(times(times(X1, X2), X3), X4) → U53_GGA(X1, X2, X3, X4, dcB_in_gga(X1, X4))
U53_GGA(X1, X2, X3, X4, dcB_out_gga(X1, X4, X7)) → DB_IN_GGA(X2, X4)
DB_IN_GGA(times(div(X1, X2), X3), X4) → DB_IN_GGA(times(X1, power(X2, p(0))), X4)
DB_IN_GGA(times(div(X1, X2), X3), X4) → U58_GGA(X1, X2, X3, X4, dcB_in_gga(times(X1, power(X2, p(0))), X4))
U58_GGA(X1, X2, X3, X4, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → DB_IN_GGA(X3, X4)
DB_IN_GGA(times(power(X1, X2), X3), X4) → U61_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
U61_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X4)
DB_IN_GGA(div(X1, X2), X3) → DB_IN_GGA(X1, X3)
DB_IN_GGA(div(X1, X2), X3) → U67_GGA(X1, X2, X3, dcB_in_gga(X1, X3))
U67_GGA(X1, X2, X3, dcB_out_gga(X1, X3, X5)) → DB_IN_GGA(power(X2, p(0)), X3)
DB_IN_GGA(power(X1, 0), X2) → DB_IN_GGA(X1, X2)
DB_IN_GGA(power(X1, s(X2)), X3) → U71_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U71_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
U61_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U63_GGA(X1, X2, X3, X4, dcB_in_gga(X1, X4))
U63_GGA(X1, X2, X3, X4, dcB_out_gga(X1, X4, X6)) → DB_IN_GGA(X3, X4)
U53_GGA(X1, X2, X3, X4, dcB_out_gga(X1, X4, X7)) → U55_GGA(X1, X2, X3, X4, dcB_in_gga(X2, X4))
U55_GGA(X1, X2, X3, X4, dcB_out_gga(X2, X4, X6)) → DB_IN_GGA(X3, X4)
U24_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → U26_GGA(X1, X2, X3, dcB_in_gga(X1, times(power(X1, X2), X3)))
U26_GGA(X1, X2, X3, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(power(X1, X2), X3))
U16_GGA(X1, X2, X3, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U18_GGA(X1, X2, X3, dcB_in_gga(X2, times(times(X1, X2), X3)))
U18_GGA(X1, X2, X3, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(times(X1, X2), X3))

The TRS R consists of the following rules:

dcB_in_gga(X1, X1) → dcB_out_gga(X1, X1, 1)
dcB_in_gga(times(X1, X2), times(X1, X2)) → U81_gga(X1, X2, dcB_in_gga(X1, times(X1, X2)))
dcB_in_gga(times(X1, X2), times(X1, X2)) → U86_gga(X1, X2, isnumbercA_in_g(X1))
dcB_in_gga(times(times(X1, X2), X3), times(times(X1, X2), X3)) → U88_gga(X1, X2, X3, dcB_in_gga(X1, times(times(X1, X2), X3)))
dcB_in_gga(times(div(X1, X2), X3), times(div(X1, X2), X3)) → U91_gga(X1, X2, X3, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3)))
dcB_in_gga(times(power(X1, X2), X3), times(power(X1, X2), X3)) → U93_gga(X1, X2, X3, isnumbercA_in_g(X2))
dcB_in_gga(0, X1) → dcB_out_gga(0, X1, 0)
dcB_in_gga(s(X1), X2) → U104_gga(X1, X2, isnumbercA_in_g(X1))
dcB_in_gga(p(X1), X2) → U105_gga(X1, X2, isnumbercA_in_g(X1))
dcB_in_gga(times(X1, X2), X3) → U106_gga(X1, X2, X3, dcB_in_gga(X1, X3))
dcB_in_gga(div(X1, X2), X3) → U108_gga(X1, X2, X3, dcB_in_gga(times(X1, power(X2, p(0))), X3))
dcB_in_gga(power(X1, X2), X3) → U109_gga(X1, X2, X3, isnumbercA_in_g(X2))
dcB_in_gga(times(X1, X2), X1) → U111_gga(X1, X2, dcB_in_gga(X2, X1))
dcB_in_gga(times(X1, X2), X3) → U112_gga(X1, X2, X3, isnumbercA_in_g(X1))
dcB_in_gga(times(times(X1, X2), X3), X4) → U114_gga(X1, X2, X3, X4, dcB_in_gga(X1, X4))
dcB_in_gga(times(div(X1, X2), X3), X4) → U117_gga(X1, X2, X3, X4, dcB_in_gga(times(X1, power(X2, p(0))), X4))
dcB_in_gga(times(power(X1, X2), X3), X4) → U119_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
dcB_in_gga(div(X1, X2), times(X1, power(X2, p(0)))) → dcB_out_gga(div(X1, X2), times(X1, power(X2, p(0))), 1)
dcB_in_gga(div(X1, X2), X3) → U122_gga(X1, X2, X3, isnumbercA_in_g(times(X1, power(X2, p(0)))))
dcB_in_gga(div(X1, X2), X3) → U123_gga(X1, X2, X3, dcB_in_gga(X1, X3))
dcB_in_gga(power(X1, 0), X2) → U125_gga(X1, X2, dcB_in_gga(X1, X2))
dcB_in_gga(power(X1, s(X2)), X3) → U126_gga(X1, X2, X3, isnumbercA_in_g(X2))
dcB_in_gga(power(X1, p(X2)), X3) → U128_gga(X1, X2, X3, isnumbercA_in_g(X2))
isnumbercA_in_g(0) → isnumbercA_out_g(0)
isnumbercA_in_g(s(X1)) → U77_g(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(p(X1)) → U78_g(X1, isnumbercA_in_g(X1))
dcB_in_gga(0, 0) → dcB_out_gga(0, 0, 0)
dcB_in_gga(s(X1), s(X1)) → U79_gga(X1, isnumbercA_in_g(X1))
dcB_in_gga(p(X1), p(X1)) → U80_gga(X1, isnumbercA_in_g(X1))
dcB_in_gga(div(X1, X2), div(X1, X2)) → U83_gga(X1, X2, dcB_in_gga(times(X1, power(X2, p(0))), div(X1, X2)))
dcB_in_gga(power(X1, X2), power(X1, X2)) → U84_gga(X1, X2, isnumbercA_in_g(X2))
dcB_in_gga(div(X1, X2), div(X1, X2)) → U96_gga(X1, X2, isnumbercA_in_g(times(X1, power(X2, p(0)))))
dcB_in_gga(div(X1, X2), div(X1, X2)) → U97_gga(X1, X2, dcB_in_gga(X1, div(X1, X2)))
dcB_in_gga(power(X1, 0), power(X1, 0)) → U99_gga(X1, dcB_in_gga(X1, power(X1, 0)))
dcB_in_gga(power(X1, s(X2)), power(X1, s(X2))) → U100_gga(X1, X2, isnumbercA_in_g(X2))
dcB_in_gga(power(X1, p(X2)), power(X1, p(X2))) → U102_gga(X1, X2, isnumbercA_in_g(X2))
U81_gga(X1, X2, dcB_out_gga(X1, times(X1, X2), X4)) → U82_gga(X1, X2, X4, dcB_in_gga(X2, times(X1, X2)))
U86_gga(X1, X2, isnumbercA_out_g(X1)) → U87_gga(X1, X2, dcB_in_gga(X2, times(X1, X2)))
U88_gga(X1, X2, X3, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U89_gga(X1, X2, X3, X6, dcB_in_gga(X2, times(times(X1, X2), X3)))
U91_gga(X1, X2, X3, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → U92_gga(X1, X2, X3, X5, dcB_in_gga(X3, times(div(X1, X2), X3)))
U93_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U94_gga(X1, X2, X3, dcB_in_gga(X1, times(power(X1, X2), X3)))
U104_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), X2, 0)
U105_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), X2, 0)
U106_gga(X1, X2, X3, dcB_out_gga(X1, X3, X5)) → U107_gga(X1, X2, X3, X5, dcB_in_gga(X2, X3))
U108_gga(X1, X2, X3, dcB_out_gga(times(X1, power(X2, p(0))), X3, X4)) → dcB_out_gga(div(X1, X2), X3, X4)
U109_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U110_gga(X1, X2, X3, dcB_in_gga(X1, X3))
U111_gga(X1, X2, dcB_out_gga(X2, X1, X3)) → dcB_out_gga(times(X1, X2), X1, +(times(X3, X1), times(1, X2)))
U112_gga(X1, X2, X3, isnumbercA_out_g(X1)) → U113_gga(X1, X2, X3, dcB_in_gga(X2, X3))
U114_gga(X1, X2, X3, X4, dcB_out_gga(X1, X4, X7)) → U115_gga(X1, X2, X3, X4, X7, dcB_in_gga(X2, X4))
U117_gga(X1, X2, X3, X4, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → U118_gga(X1, X2, X3, X4, X6, dcB_in_gga(X3, X4))
U119_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U120_gga(X1, X2, X3, X4, dcB_in_gga(X1, X4))
U123_gga(X1, X2, X3, dcB_out_gga(X1, X3, X5)) → U124_gga(X1, X2, X3, X5, dcB_in_gga(power(X2, p(0)), X3))
U125_gga(X1, X2, dcB_out_gga(X1, X2, X3)) → dcB_out_gga(power(X1, 0), X2, times(0, times(X3, power(X1, p(0)))))
U126_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U127_gga(X1, X2, X3, dcB_in_gga(X1, X3))
U128_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U129_gga(X1, X2, X3, dcB_in_gga(X1, X3))
U77_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(s(X1))
U78_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(p(X1))
U79_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), s(X1), 0)
U80_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), p(X1), 0)
U83_gga(X1, X2, dcB_out_gga(times(X1, power(X2, p(0))), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), X3)
U84_gga(X1, X2, isnumbercA_out_g(X2)) → U85_gga(X1, X2, dcB_in_gga(X1, power(X1, X2)))
U97_gga(X1, X2, dcB_out_gga(X1, div(X1, X2), X4)) → U98_gga(X1, X2, X4, dcB_in_gga(power(X2, p(0)), div(X1, X2)))
U99_gga(X1, dcB_out_gga(X1, power(X1, 0), X2)) → dcB_out_gga(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0)))))
U100_gga(X1, X2, isnumbercA_out_g(X2)) → U101_gga(X1, X2, dcB_in_gga(X1, power(X1, s(X2))))
U102_gga(X1, X2, isnumbercA_out_g(X2)) → U103_gga(X1, X2, dcB_in_gga(X1, power(X1, p(X2))))
U82_gga(X1, X2, X4, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2)))
U87_gga(X1, X2, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2)))
U89_gga(X1, X2, X3, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → U90_gga(X1, X2, X3, X5, X6, dcB_in_gga(X3, times(times(X1, X2), X3)))
U92_gga(X1, X2, X3, X5, dcB_out_gga(X3, times(div(X1, X2), X3), X4)) → dcB_out_gga(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3)))
U94_gga(X1, X2, X3, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → U95_gga(X1, X2, X3, X5, dcB_in_gga(X3, times(power(X1, X2), X3)))
U107_gga(X1, X2, X3, X5, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(X5, X2)))
U110_gga(X1, X2, X3, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2)))))
U113_gga(X1, X2, X3, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(0, X2)))
U115_gga(X1, X2, X3, X4, X7, dcB_out_gga(X2, X4, X6)) → U116_gga(X1, X2, X3, X4, X6, X7, dcB_in_gga(X3, X4))
U118_gga(X1, X2, X3, X4, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3)))
U120_gga(X1, X2, X3, X4, dcB_out_gga(X1, X4, X6)) → U121_gga(X1, X2, X3, X4, X6, dcB_in_gga(X3, X4))
U124_gga(X1, X2, X3, X5, dcB_out_gga(power(X2, p(0)), X3, X4)) → dcB_out_gga(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0)))))
U127_gga(X1, X2, X3, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2))))))
U129_gga(X1, X2, X3, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2))))))
U85_gga(X1, X2, dcB_out_gga(X1, power(X1, X2), X3)) → dcB_out_gga(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2)))))
U98_gga(X1, X2, X4, dcB_out_gga(power(X2, p(0)), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0)))))
U101_gga(X1, X2, dcB_out_gga(X1, power(X1, s(X2)), X3)) → dcB_out_gga(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2))))))
U103_gga(X1, X2, dcB_out_gga(X1, power(X1, p(X2)), X3)) → dcB_out_gga(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2))))))
U90_gga(X1, X2, X3, X5, X6, dcB_out_gga(X3, times(times(X1, X2), X3), X4)) → dcB_out_gga(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3)))
U95_gga(X1, X2, X3, X5, dcB_out_gga(X3, times(power(X1, X2), X3), X4)) → dcB_out_gga(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3)))
U116_gga(X1, X2, X3, X4, X6, X7, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3)))
U121_gga(X1, X2, X3, X4, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3)))

The set Q consists of the following terms:

dcB_in_gga(x0, x1)
isnumbercA_in_g(x0)
U81_gga(x0, x1, x2)
U86_gga(x0, x1, x2)
U88_gga(x0, x1, x2, x3)
U91_gga(x0, x1, x2, x3)
U93_gga(x0, x1, x2, x3)
U104_gga(x0, x1, x2)
U105_gga(x0, x1, x2)
U106_gga(x0, x1, x2, x3)
U108_gga(x0, x1, x2, x3)
U109_gga(x0, x1, x2, x3)
U111_gga(x0, x1, x2)
U112_gga(x0, x1, x2, x3)
U114_gga(x0, x1, x2, x3, x4)
U117_gga(x0, x1, x2, x3, x4)
U119_gga(x0, x1, x2, x3, x4)
U123_gga(x0, x1, x2, x3)
U125_gga(x0, x1, x2)
U126_gga(x0, x1, x2, x3)
U128_gga(x0, x1, x2, x3)
U77_g(x0, x1)
U78_g(x0, x1)
U79_gga(x0, x1)
U80_gga(x0, x1)
U83_gga(x0, x1, x2)
U84_gga(x0, x1, x2)
U97_gga(x0, x1, x2)
U99_gga(x0, x1)
U100_gga(x0, x1, x2)
U102_gga(x0, x1, x2)
U82_gga(x0, x1, x2, x3)
U87_gga(x0, x1, x2)
U89_gga(x0, x1, x2, x3, x4)
U92_gga(x0, x1, x2, x3, x4)
U94_gga(x0, x1, x2, x3)
U107_gga(x0, x1, x2, x3, x4)
U110_gga(x0, x1, x2, x3)
U113_gga(x0, x1, x2, x3)
U115_gga(x0, x1, x2, x3, x4, x5)
U118_gga(x0, x1, x2, x3, x4, x5)
U120_gga(x0, x1, x2, x3, x4)
U124_gga(x0, x1, x2, x3, x4)
U127_gga(x0, x1, x2, x3)
U129_gga(x0, x1, x2, x3)
U85_gga(x0, x1, x2)
U98_gga(x0, x1, x2, x3)
U101_gga(x0, x1, x2)
U103_gga(x0, x1, x2)
U90_gga(x0, x1, x2, x3, x4, x5)
U95_gga(x0, x1, x2, x3, x4)
U116_gga(x0, x1, x2, x3, x4, x5, x6)
U121_gga(x0, x1, x2, x3, x4, x5)

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

(19) QDPOrderProof (EQUIVALENT transformation)

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

The following pairs can be oriented strictly and are deleted.

DB_IN_GGA(times(X1, X2), times(X1, X2)) → DB_IN_GGA(X1, times(X1, X2))
DB_IN_GGA(times(X1, X2), times(X1, X2)) → U6_GGA(X1, X2, dcB_in_gga(X1, times(X1, X2)))
DB_IN_GGA(times(X1, X2), times(X1, X2)) → U13_GGA(X1, X2, isnumbercA_in_g(X1))
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3)) → DB_IN_GGA(X1, times(times(X1, X2), X3))
DB_IN_GGA(times(times(X1, X2), X3), times(times(X1, X2), X3)) → U16_GGA(X1, X2, X3, dcB_in_gga(X1, times(times(X1, X2), X3)))
U16_GGA(X1, X2, X3, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → DB_IN_GGA(X2, times(times(X1, X2), X3))
DB_IN_GGA(times(X1, X2), X3) → DB_IN_GGA(X1, X3)
DB_IN_GGA(times(X1, X2), X3) → U42_GGA(X1, X2, X3, dcB_in_gga(X1, X3))
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3)) → DB_IN_GGA(times(X1, power(X2, p(0))), times(div(X1, X2), X3))
DB_IN_GGA(times(div(X1, X2), X3), times(div(X1, X2), X3)) → U21_GGA(X1, X2, X3, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3)))
U24_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, times(power(X1, X2), X3))
DB_IN_GGA(times(X1, X2), X1) → DB_IN_GGA(X2, X1)
DB_IN_GGA(div(X1, X2), div(X1, X2)) → DB_IN_GGA(X1, div(X1, X2))
DB_IN_GGA(div(X1, X2), div(X1, X2)) → U30_GGA(X1, X2, dcB_in_gga(X1, div(X1, X2)))
DB_IN_GGA(times(X1, X2), X3) → U50_GGA(X1, X2, X3, isnumbercA_in_g(X1))
DB_IN_GGA(times(times(X1, X2), X3), X4) → DB_IN_GGA(X1, X4)
DB_IN_GGA(times(times(X1, X2), X3), X4) → U53_GGA(X1, X2, X3, X4, dcB_in_gga(X1, X4))
U53_GGA(X1, X2, X3, X4, dcB_out_gga(X1, X4, X7)) → DB_IN_GGA(X2, X4)
DB_IN_GGA(times(div(X1, X2), X3), X4) → DB_IN_GGA(times(X1, power(X2, p(0))), X4)
DB_IN_GGA(times(div(X1, X2), X3), X4) → U58_GGA(X1, X2, X3, X4, dcB_in_gga(times(X1, power(X2, p(0))), X4))
U58_GGA(X1, X2, X3, X4, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → DB_IN_GGA(X3, X4)
DB_IN_GGA(times(power(X1, X2), X3), X4) → U61_GGA(X1, X2, X3, X4, isnumbercA_in_g(X2))
DB_IN_GGA(div(X1, X2), X3) → DB_IN_GGA(X1, X3)
U67_GGA(X1, X2, X3, dcB_out_gga(X1, X3, X5)) → DB_IN_GGA(power(X2, p(0)), X3)
U55_GGA(X1, X2, X3, X4, dcB_out_gga(X2, X4, X6)) → DB_IN_GGA(X3, X4)
U26_GGA(X1, X2, X3, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(power(X1, X2), X3))
U16_GGA(X1, X2, X3, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U18_GGA(X1, X2, X3, dcB_in_gga(X2, times(times(X1, X2), X3)))

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

POL(+(x₁, x₂)) = 0
POL(0) = 0
POL(1) = 0
POL(DB_IN_GGA(x₁, x₂)) = x₁
POL(U100_gga(x₁, x₂, x₃)) = 0
POL(U101_gga(x₁, x₂, x₃)) = 0
POL(U102_gga(x₁, x₂, x₃)) = 0
POL(U103_gga(x₁, x₂, x₃)) = 0
POL(U104_gga(x₁, x₂, x₃)) = 0
POL(U105_gga(x₁, x₂, x₃)) = 0
POL(U106_gga(x₁, x₂, x₃, x₄)) = 0
POL(U107_gga(x₁, x₂, x₃, x₄, x₅)) = 0
POL(U108_gga(x₁, x₂, x₃, x₄)) = 0
POL(U109_gga(x₁, x₂, x₃, x₄)) = 0
POL(U10_GGA(x₁, x₂, x₃)) = x₁
POL(U110_gga(x₁, x₂, x₃, x₄)) = 0
POL(U111_gga(x₁, x₂, x₃)) = 0
POL(U112_gga(x₁, x₂, x₃, x₄)) = 0
POL(U113_gga(x₁, x₂, x₃, x₄)) = 0
POL(U114_gga(x₁, x₂, x₃, x₄, x₅)) = 0
POL(U115_gga(x₁, x₂, x₃, x₄, x₅, x₆)) = 0
POL(U116_gga(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = 0
POL(U117_gga(x₁, x₂, x₃, x₄, x₅)) = 0
POL(U118_gga(x₁, x₂, x₃, x₄, x₅, x₆)) = 0
POL(U119_gga(x₁, x₂, x₃, x₄, x₅)) = 0
POL(U120_gga(x₁, x₂, x₃, x₄, x₅)) = 0
POL(U121_gga(x₁, x₂, x₃, x₄, x₅, x₆)) = 0
POL(U122_gga(x₁, x₂, x₃, x₄)) = 0
POL(U123_gga(x₁, x₂, x₃, x₄)) = 0
POL(U124_gga(x₁, x₂, x₃, x₄, x₅)) = 0
POL(U125_gga(x₁, x₂, x₃)) = 0
POL(U126_gga(x₁, x₂, x₃, x₄)) = 0
POL(U127_gga(x₁, x₂, x₃, x₄)) = 0
POL(U128_gga(x₁, x₂, x₃, x₄)) = 0
POL(U129_gga(x₁, x₂, x₃, x₄)) = 0
POL(U13_GGA(x₁, x₂, x₃)) = x₁ + x₂
POL(U16_GGA(x₁, x₂, x₃, x₄)) = 1 + x₂ + x₃
POL(U18_GGA(x₁, x₂, x₃, x₄)) = x₂ + x₃
POL(U21_GGA(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₃
POL(U24_GGA(x₁, x₂, x₃, x₄)) = 1 + x₁ + x₃
POL(U26_GGA(x₁, x₂, x₃, x₄)) = 1 + x₁ + x₃
POL(U30_GGA(x₁, x₂, x₃)) = x₁ + x₂
POL(U34_GGA(x₁, x₂, x₃)) = x₁
POL(U37_GGA(x₁, x₂, x₃)) = x₁
POL(U42_GGA(x₁, x₂, x₃, x₄)) = x₂
POL(U46_GGA(x₁, x₂, x₃, x₄)) = x₁
POL(U50_GGA(x₁, x₂, x₃, x₄)) = x₂
POL(U53_GGA(x₁, x₂, x₃, x₄, x₅)) = 1 + x₁ + x₂ + x₃
POL(U55_GGA(x₁, x₂, x₃, x₄, x₅)) = 1 + x₃
POL(U58_GGA(x₁, x₂, x₃, x₄, x₅)) = 1 + x₃
POL(U61_GGA(x₁, x₂, x₃, x₄, x₅)) = x₁ + x₃
POL(U63_GGA(x₁, x₂, x₃, x₄, x₅)) = x₃
POL(U67_GGA(x₁, x₂, x₃, x₄)) = 1 + x₂
POL(U6_GGA(x₁, x₂, x₃)) = x₁ + x₂
POL(U71_GGA(x₁, x₂, x₃, x₄)) = x₁
POL(U74_GGA(x₁, x₂, x₃, x₄)) = x₁
POL(U77_g(x₁, x₂)) = 0
POL(U78_g(x₁, x₂)) = 0
POL(U79_gga(x₁, x₂)) = 0
POL(U80_gga(x₁, x₂)) = 0
POL(U81_gga(x₁, x₂, x₃)) = 0
POL(U82_gga(x₁, x₂, x₃, x₄)) = 0
POL(U83_gga(x₁, x₂, x₃)) = 0
POL(U84_gga(x₁, x₂, x₃)) = 0
POL(U85_gga(x₁, x₂, x₃)) = 0
POL(U86_gga(x₁, x₂, x₃)) = 0
POL(U87_gga(x₁, x₂, x₃)) = 0
POL(U88_gga(x₁, x₂, x₃, x₄)) = 0
POL(U89_gga(x₁, x₂, x₃, x₄, x₅)) = 0
POL(U90_gga(x₁, x₂, x₃, x₄, x₅, x₆)) = 0
POL(U91_gga(x₁, x₂, x₃, x₄)) = 0
POL(U92_gga(x₁, x₂, x₃, x₄, x₅)) = 0
POL(U93_gga(x₁, x₂, x₃, x₄)) = 0
POL(U94_gga(x₁, x₂, x₃, x₄)) = 0
POL(U95_gga(x₁, x₂, x₃, x₄, x₅)) = 0
POL(U96_gga(x₁, x₂, x₃)) = 0
POL(U97_gga(x₁, x₂, x₃)) = 0
POL(U98_gga(x₁, x₂, x₃, x₄)) = 0
POL(U99_gga(x₁, x₂)) = 0
POL(dcB_in_gga(x₁, x₂)) = 0
POL(dcB_out_gga(x₁, x₂, x₃)) = 0
POL(div(x₁, x₂)) = 1 + x₁ + x₂
POL(isnumbercA_in_g(x₁)) = 0
POL(isnumbercA_out_g(x₁)) = 0
POL(p(x₁)) = 0
POL(power(x₁, x₂)) = x₁
POL(s(x₁)) = 0
POL(times(x₁, x₂)) = 1 + x₁ + x₂

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
none

(20) Obligation:

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

U6_GGA(X1, X2, dcB_out_gga(X1, times(X1, X2), X4)) → DB_IN_GGA(X2, times(X1, X2))
U13_GGA(X1, X2, isnumbercA_out_g(X1)) → DB_IN_GGA(X2, times(X1, X2))
DB_IN_GGA(div(X1, X2), div(X1, X2)) → DB_IN_GGA(times(X1, power(X2, p(0))), div(X1, X2))
U42_GGA(X1, X2, X3, dcB_out_gga(X1, X3, X5)) → DB_IN_GGA(X2, X3)
DB_IN_GGA(power(X1, X2), power(X1, X2)) → U10_GGA(X1, X2, isnumbercA_in_g(X2))
U10_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, X2))
DB_IN_GGA(power(X1, 0), power(X1, 0)) → DB_IN_GGA(X1, power(X1, 0))
DB_IN_GGA(div(X1, X2), X3) → DB_IN_GGA(times(X1, power(X2, p(0))), X3)
U21_GGA(X1, X2, X3, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(div(X1, X2), X3))
DB_IN_GGA(power(X1, X2), X3) → U46_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U46_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
DB_IN_GGA(times(power(X1, X2), X3), times(power(X1, X2), X3)) → U24_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U30_GGA(X1, X2, dcB_out_gga(X1, div(X1, X2), X4)) → DB_IN_GGA(power(X2, p(0)), div(X1, X2))
DB_IN_GGA(power(X1, p(X2)), X3) → U74_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U74_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2))) → U34_GGA(X1, X2, isnumbercA_in_g(X2))
U34_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, s(X2)))
U50_GGA(X1, X2, X3, isnumbercA_out_g(X1)) → DB_IN_GGA(X2, X3)
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2))) → U37_GGA(X1, X2, isnumbercA_in_g(X2))
U37_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, p(X2)))
U61_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X4)
DB_IN_GGA(div(X1, X2), X3) → U67_GGA(X1, X2, X3, dcB_in_gga(X1, X3))
DB_IN_GGA(power(X1, 0), X2) → DB_IN_GGA(X1, X2)
DB_IN_GGA(power(X1, s(X2)), X3) → U71_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U71_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
U61_GGA(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U63_GGA(X1, X2, X3, X4, dcB_in_gga(X1, X4))
U63_GGA(X1, X2, X3, X4, dcB_out_gga(X1, X4, X6)) → DB_IN_GGA(X3, X4)
U53_GGA(X1, X2, X3, X4, dcB_out_gga(X1, X4, X7)) → U55_GGA(X1, X2, X3, X4, dcB_in_gga(X2, X4))
U24_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → U26_GGA(X1, X2, X3, dcB_in_gga(X1, times(power(X1, X2), X3)))
U18_GGA(X1, X2, X3, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → DB_IN_GGA(X3, times(times(X1, X2), X3))

The TRS R consists of the following rules:

dcB_in_gga(X1, X1) → dcB_out_gga(X1, X1, 1)
dcB_in_gga(times(X1, X2), times(X1, X2)) → U81_gga(X1, X2, dcB_in_gga(X1, times(X1, X2)))
dcB_in_gga(times(X1, X2), times(X1, X2)) → U86_gga(X1, X2, isnumbercA_in_g(X1))
dcB_in_gga(times(times(X1, X2), X3), times(times(X1, X2), X3)) → U88_gga(X1, X2, X3, dcB_in_gga(X1, times(times(X1, X2), X3)))
dcB_in_gga(times(div(X1, X2), X3), times(div(X1, X2), X3)) → U91_gga(X1, X2, X3, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3)))
dcB_in_gga(times(power(X1, X2), X3), times(power(X1, X2), X3)) → U93_gga(X1, X2, X3, isnumbercA_in_g(X2))
dcB_in_gga(0, X1) → dcB_out_gga(0, X1, 0)
dcB_in_gga(s(X1), X2) → U104_gga(X1, X2, isnumbercA_in_g(X1))
dcB_in_gga(p(X1), X2) → U105_gga(X1, X2, isnumbercA_in_g(X1))
dcB_in_gga(times(X1, X2), X3) → U106_gga(X1, X2, X3, dcB_in_gga(X1, X3))
dcB_in_gga(div(X1, X2), X3) → U108_gga(X1, X2, X3, dcB_in_gga(times(X1, power(X2, p(0))), X3))
dcB_in_gga(power(X1, X2), X3) → U109_gga(X1, X2, X3, isnumbercA_in_g(X2))
dcB_in_gga(times(X1, X2), X1) → U111_gga(X1, X2, dcB_in_gga(X2, X1))
dcB_in_gga(times(X1, X2), X3) → U112_gga(X1, X2, X3, isnumbercA_in_g(X1))
dcB_in_gga(times(times(X1, X2), X3), X4) → U114_gga(X1, X2, X3, X4, dcB_in_gga(X1, X4))
dcB_in_gga(times(div(X1, X2), X3), X4) → U117_gga(X1, X2, X3, X4, dcB_in_gga(times(X1, power(X2, p(0))), X4))
dcB_in_gga(times(power(X1, X2), X3), X4) → U119_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
dcB_in_gga(div(X1, X2), times(X1, power(X2, p(0)))) → dcB_out_gga(div(X1, X2), times(X1, power(X2, p(0))), 1)
dcB_in_gga(div(X1, X2), X3) → U122_gga(X1, X2, X3, isnumbercA_in_g(times(X1, power(X2, p(0)))))
dcB_in_gga(div(X1, X2), X3) → U123_gga(X1, X2, X3, dcB_in_gga(X1, X3))
dcB_in_gga(power(X1, 0), X2) → U125_gga(X1, X2, dcB_in_gga(X1, X2))
dcB_in_gga(power(X1, s(X2)), X3) → U126_gga(X1, X2, X3, isnumbercA_in_g(X2))
dcB_in_gga(power(X1, p(X2)), X3) → U128_gga(X1, X2, X3, isnumbercA_in_g(X2))
isnumbercA_in_g(0) → isnumbercA_out_g(0)
isnumbercA_in_g(s(X1)) → U77_g(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(p(X1)) → U78_g(X1, isnumbercA_in_g(X1))
dcB_in_gga(0, 0) → dcB_out_gga(0, 0, 0)
dcB_in_gga(s(X1), s(X1)) → U79_gga(X1, isnumbercA_in_g(X1))
dcB_in_gga(p(X1), p(X1)) → U80_gga(X1, isnumbercA_in_g(X1))
dcB_in_gga(div(X1, X2), div(X1, X2)) → U83_gga(X1, X2, dcB_in_gga(times(X1, power(X2, p(0))), div(X1, X2)))
dcB_in_gga(power(X1, X2), power(X1, X2)) → U84_gga(X1, X2, isnumbercA_in_g(X2))
dcB_in_gga(div(X1, X2), div(X1, X2)) → U96_gga(X1, X2, isnumbercA_in_g(times(X1, power(X2, p(0)))))
dcB_in_gga(div(X1, X2), div(X1, X2)) → U97_gga(X1, X2, dcB_in_gga(X1, div(X1, X2)))
dcB_in_gga(power(X1, 0), power(X1, 0)) → U99_gga(X1, dcB_in_gga(X1, power(X1, 0)))
dcB_in_gga(power(X1, s(X2)), power(X1, s(X2))) → U100_gga(X1, X2, isnumbercA_in_g(X2))
dcB_in_gga(power(X1, p(X2)), power(X1, p(X2))) → U102_gga(X1, X2, isnumbercA_in_g(X2))
U81_gga(X1, X2, dcB_out_gga(X1, times(X1, X2), X4)) → U82_gga(X1, X2, X4, dcB_in_gga(X2, times(X1, X2)))
U86_gga(X1, X2, isnumbercA_out_g(X1)) → U87_gga(X1, X2, dcB_in_gga(X2, times(X1, X2)))
U88_gga(X1, X2, X3, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U89_gga(X1, X2, X3, X6, dcB_in_gga(X2, times(times(X1, X2), X3)))
U91_gga(X1, X2, X3, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → U92_gga(X1, X2, X3, X5, dcB_in_gga(X3, times(div(X1, X2), X3)))
U93_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U94_gga(X1, X2, X3, dcB_in_gga(X1, times(power(X1, X2), X3)))
U104_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), X2, 0)
U105_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), X2, 0)
U106_gga(X1, X2, X3, dcB_out_gga(X1, X3, X5)) → U107_gga(X1, X2, X3, X5, dcB_in_gga(X2, X3))
U108_gga(X1, X2, X3, dcB_out_gga(times(X1, power(X2, p(0))), X3, X4)) → dcB_out_gga(div(X1, X2), X3, X4)
U109_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U110_gga(X1, X2, X3, dcB_in_gga(X1, X3))
U111_gga(X1, X2, dcB_out_gga(X2, X1, X3)) → dcB_out_gga(times(X1, X2), X1, +(times(X3, X1), times(1, X2)))
U112_gga(X1, X2, X3, isnumbercA_out_g(X1)) → U113_gga(X1, X2, X3, dcB_in_gga(X2, X3))
U114_gga(X1, X2, X3, X4, dcB_out_gga(X1, X4, X7)) → U115_gga(X1, X2, X3, X4, X7, dcB_in_gga(X2, X4))
U117_gga(X1, X2, X3, X4, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → U118_gga(X1, X2, X3, X4, X6, dcB_in_gga(X3, X4))
U119_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U120_gga(X1, X2, X3, X4, dcB_in_gga(X1, X4))
U123_gga(X1, X2, X3, dcB_out_gga(X1, X3, X5)) → U124_gga(X1, X2, X3, X5, dcB_in_gga(power(X2, p(0)), X3))
U125_gga(X1, X2, dcB_out_gga(X1, X2, X3)) → dcB_out_gga(power(X1, 0), X2, times(0, times(X3, power(X1, p(0)))))
U126_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U127_gga(X1, X2, X3, dcB_in_gga(X1, X3))
U128_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U129_gga(X1, X2, X3, dcB_in_gga(X1, X3))
U77_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(s(X1))
U78_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(p(X1))
U79_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), s(X1), 0)
U80_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), p(X1), 0)
U83_gga(X1, X2, dcB_out_gga(times(X1, power(X2, p(0))), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), X3)
U84_gga(X1, X2, isnumbercA_out_g(X2)) → U85_gga(X1, X2, dcB_in_gga(X1, power(X1, X2)))
U97_gga(X1, X2, dcB_out_gga(X1, div(X1, X2), X4)) → U98_gga(X1, X2, X4, dcB_in_gga(power(X2, p(0)), div(X1, X2)))
U99_gga(X1, dcB_out_gga(X1, power(X1, 0), X2)) → dcB_out_gga(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0)))))
U100_gga(X1, X2, isnumbercA_out_g(X2)) → U101_gga(X1, X2, dcB_in_gga(X1, power(X1, s(X2))))
U102_gga(X1, X2, isnumbercA_out_g(X2)) → U103_gga(X1, X2, dcB_in_gga(X1, power(X1, p(X2))))
U82_gga(X1, X2, X4, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2)))
U87_gga(X1, X2, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2)))
U89_gga(X1, X2, X3, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → U90_gga(X1, X2, X3, X5, X6, dcB_in_gga(X3, times(times(X1, X2), X3)))
U92_gga(X1, X2, X3, X5, dcB_out_gga(X3, times(div(X1, X2), X3), X4)) → dcB_out_gga(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3)))
U94_gga(X1, X2, X3, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → U95_gga(X1, X2, X3, X5, dcB_in_gga(X3, times(power(X1, X2), X3)))
U107_gga(X1, X2, X3, X5, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(X5, X2)))
U110_gga(X1, X2, X3, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2)))))
U113_gga(X1, X2, X3, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(0, X2)))
U115_gga(X1, X2, X3, X4, X7, dcB_out_gga(X2, X4, X6)) → U116_gga(X1, X2, X3, X4, X6, X7, dcB_in_gga(X3, X4))
U118_gga(X1, X2, X3, X4, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3)))
U120_gga(X1, X2, X3, X4, dcB_out_gga(X1, X4, X6)) → U121_gga(X1, X2, X3, X4, X6, dcB_in_gga(X3, X4))
U124_gga(X1, X2, X3, X5, dcB_out_gga(power(X2, p(0)), X3, X4)) → dcB_out_gga(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0)))))
U127_gga(X1, X2, X3, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2))))))
U129_gga(X1, X2, X3, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2))))))
U85_gga(X1, X2, dcB_out_gga(X1, power(X1, X2), X3)) → dcB_out_gga(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2)))))
U98_gga(X1, X2, X4, dcB_out_gga(power(X2, p(0)), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0)))))
U101_gga(X1, X2, dcB_out_gga(X1, power(X1, s(X2)), X3)) → dcB_out_gga(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2))))))
U103_gga(X1, X2, dcB_out_gga(X1, power(X1, p(X2)), X3)) → dcB_out_gga(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2))))))
U90_gga(X1, X2, X3, X5, X6, dcB_out_gga(X3, times(times(X1, X2), X3), X4)) → dcB_out_gga(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3)))
U95_gga(X1, X2, X3, X5, dcB_out_gga(X3, times(power(X1, X2), X3), X4)) → dcB_out_gga(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3)))
U116_gga(X1, X2, X3, X4, X6, X7, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3)))
U121_gga(X1, X2, X3, X4, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3)))

The set Q consists of the following terms:

dcB_in_gga(x0, x1)
isnumbercA_in_g(x0)
U81_gga(x0, x1, x2)
U86_gga(x0, x1, x2)
U88_gga(x0, x1, x2, x3)
U91_gga(x0, x1, x2, x3)
U93_gga(x0, x1, x2, x3)
U104_gga(x0, x1, x2)
U105_gga(x0, x1, x2)
U106_gga(x0, x1, x2, x3)
U108_gga(x0, x1, x2, x3)
U109_gga(x0, x1, x2, x3)
U111_gga(x0, x1, x2)
U112_gga(x0, x1, x2, x3)
U114_gga(x0, x1, x2, x3, x4)
U117_gga(x0, x1, x2, x3, x4)
U119_gga(x0, x1, x2, x3, x4)
U123_gga(x0, x1, x2, x3)
U125_gga(x0, x1, x2)
U126_gga(x0, x1, x2, x3)
U128_gga(x0, x1, x2, x3)
U77_g(x0, x1)
U78_g(x0, x1)
U79_gga(x0, x1)
U80_gga(x0, x1)
U83_gga(x0, x1, x2)
U84_gga(x0, x1, x2)
U97_gga(x0, x1, x2)
U99_gga(x0, x1)
U100_gga(x0, x1, x2)
U102_gga(x0, x1, x2)
U82_gga(x0, x1, x2, x3)
U87_gga(x0, x1, x2)
U89_gga(x0, x1, x2, x3, x4)
U92_gga(x0, x1, x2, x3, x4)
U94_gga(x0, x1, x2, x3)
U107_gga(x0, x1, x2, x3, x4)
U110_gga(x0, x1, x2, x3)
U113_gga(x0, x1, x2, x3)
U115_gga(x0, x1, x2, x3, x4, x5)
U118_gga(x0, x1, x2, x3, x4, x5)
U120_gga(x0, x1, x2, x3, x4)
U124_gga(x0, x1, x2, x3, x4)
U127_gga(x0, x1, x2, x3)
U129_gga(x0, x1, x2, x3)
U85_gga(x0, x1, x2)
U98_gga(x0, x1, x2, x3)
U101_gga(x0, x1, x2)
U103_gga(x0, x1, x2)
U90_gga(x0, x1, x2, x3, x4, x5)
U95_gga(x0, x1, x2, x3, x4)
U116_gga(x0, x1, x2, x3, x4, x5, x6)
U121_gga(x0, x1, x2, x3, x4, x5)

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

(21) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 16 less nodes.

(22) Obligation:

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

DB_IN_GGA(power(X1, X2), power(X1, X2)) → U10_GGA(X1, X2, isnumbercA_in_g(X2))
U10_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, X2))
DB_IN_GGA(power(X1, X2), X3) → U46_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U46_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
DB_IN_GGA(power(X1, 0), power(X1, 0)) → DB_IN_GGA(X1, power(X1, 0))
DB_IN_GGA(power(X1, p(X2)), X3) → U74_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U74_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2))) → U34_GGA(X1, X2, isnumbercA_in_g(X2))
U34_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, s(X2)))
DB_IN_GGA(power(X1, 0), X2) → DB_IN_GGA(X1, X2)
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2))) → U37_GGA(X1, X2, isnumbercA_in_g(X2))
U37_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, p(X2)))
DB_IN_GGA(power(X1, s(X2)), X3) → U71_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U71_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)

The TRS R consists of the following rules:

dcB_in_gga(X1, X1) → dcB_out_gga(X1, X1, 1)
dcB_in_gga(times(X1, X2), times(X1, X2)) → U81_gga(X1, X2, dcB_in_gga(X1, times(X1, X2)))
dcB_in_gga(times(X1, X2), times(X1, X2)) → U86_gga(X1, X2, isnumbercA_in_g(X1))
dcB_in_gga(times(times(X1, X2), X3), times(times(X1, X2), X3)) → U88_gga(X1, X2, X3, dcB_in_gga(X1, times(times(X1, X2), X3)))
dcB_in_gga(times(div(X1, X2), X3), times(div(X1, X2), X3)) → U91_gga(X1, X2, X3, dcB_in_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3)))
dcB_in_gga(times(power(X1, X2), X3), times(power(X1, X2), X3)) → U93_gga(X1, X2, X3, isnumbercA_in_g(X2))
dcB_in_gga(0, X1) → dcB_out_gga(0, X1, 0)
dcB_in_gga(s(X1), X2) → U104_gga(X1, X2, isnumbercA_in_g(X1))
dcB_in_gga(p(X1), X2) → U105_gga(X1, X2, isnumbercA_in_g(X1))
dcB_in_gga(times(X1, X2), X3) → U106_gga(X1, X2, X3, dcB_in_gga(X1, X3))
dcB_in_gga(div(X1, X2), X3) → U108_gga(X1, X2, X3, dcB_in_gga(times(X1, power(X2, p(0))), X3))
dcB_in_gga(power(X1, X2), X3) → U109_gga(X1, X2, X3, isnumbercA_in_g(X2))
dcB_in_gga(times(X1, X2), X1) → U111_gga(X1, X2, dcB_in_gga(X2, X1))
dcB_in_gga(times(X1, X2), X3) → U112_gga(X1, X2, X3, isnumbercA_in_g(X1))
dcB_in_gga(times(times(X1, X2), X3), X4) → U114_gga(X1, X2, X3, X4, dcB_in_gga(X1, X4))
dcB_in_gga(times(div(X1, X2), X3), X4) → U117_gga(X1, X2, X3, X4, dcB_in_gga(times(X1, power(X2, p(0))), X4))
dcB_in_gga(times(power(X1, X2), X3), X4) → U119_gga(X1, X2, X3, X4, isnumbercA_in_g(X2))
dcB_in_gga(div(X1, X2), times(X1, power(X2, p(0)))) → dcB_out_gga(div(X1, X2), times(X1, power(X2, p(0))), 1)
dcB_in_gga(div(X1, X2), X3) → U122_gga(X1, X2, X3, isnumbercA_in_g(times(X1, power(X2, p(0)))))
dcB_in_gga(div(X1, X2), X3) → U123_gga(X1, X2, X3, dcB_in_gga(X1, X3))
dcB_in_gga(power(X1, 0), X2) → U125_gga(X1, X2, dcB_in_gga(X1, X2))
dcB_in_gga(power(X1, s(X2)), X3) → U126_gga(X1, X2, X3, isnumbercA_in_g(X2))
dcB_in_gga(power(X1, p(X2)), X3) → U128_gga(X1, X2, X3, isnumbercA_in_g(X2))
isnumbercA_in_g(0) → isnumbercA_out_g(0)
isnumbercA_in_g(s(X1)) → U77_g(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(p(X1)) → U78_g(X1, isnumbercA_in_g(X1))
dcB_in_gga(0, 0) → dcB_out_gga(0, 0, 0)
dcB_in_gga(s(X1), s(X1)) → U79_gga(X1, isnumbercA_in_g(X1))
dcB_in_gga(p(X1), p(X1)) → U80_gga(X1, isnumbercA_in_g(X1))
dcB_in_gga(div(X1, X2), div(X1, X2)) → U83_gga(X1, X2, dcB_in_gga(times(X1, power(X2, p(0))), div(X1, X2)))
dcB_in_gga(power(X1, X2), power(X1, X2)) → U84_gga(X1, X2, isnumbercA_in_g(X2))
dcB_in_gga(div(X1, X2), div(X1, X2)) → U96_gga(X1, X2, isnumbercA_in_g(times(X1, power(X2, p(0)))))
dcB_in_gga(div(X1, X2), div(X1, X2)) → U97_gga(X1, X2, dcB_in_gga(X1, div(X1, X2)))
dcB_in_gga(power(X1, 0), power(X1, 0)) → U99_gga(X1, dcB_in_gga(X1, power(X1, 0)))
dcB_in_gga(power(X1, s(X2)), power(X1, s(X2))) → U100_gga(X1, X2, isnumbercA_in_g(X2))
dcB_in_gga(power(X1, p(X2)), power(X1, p(X2))) → U102_gga(X1, X2, isnumbercA_in_g(X2))
U81_gga(X1, X2, dcB_out_gga(X1, times(X1, X2), X4)) → U82_gga(X1, X2, X4, dcB_in_gga(X2, times(X1, X2)))
U86_gga(X1, X2, isnumbercA_out_g(X1)) → U87_gga(X1, X2, dcB_in_gga(X2, times(X1, X2)))
U88_gga(X1, X2, X3, dcB_out_gga(X1, times(times(X1, X2), X3), X6)) → U89_gga(X1, X2, X3, X6, dcB_in_gga(X2, times(times(X1, X2), X3)))
U91_gga(X1, X2, X3, dcB_out_gga(times(X1, power(X2, p(0))), times(div(X1, X2), X3), X5)) → U92_gga(X1, X2, X3, X5, dcB_in_gga(X3, times(div(X1, X2), X3)))
U93_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U94_gga(X1, X2, X3, dcB_in_gga(X1, times(power(X1, X2), X3)))
U104_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), X2, 0)
U105_gga(X1, X2, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), X2, 0)
U106_gga(X1, X2, X3, dcB_out_gga(X1, X3, X5)) → U107_gga(X1, X2, X3, X5, dcB_in_gga(X2, X3))
U108_gga(X1, X2, X3, dcB_out_gga(times(X1, power(X2, p(0))), X3, X4)) → dcB_out_gga(div(X1, X2), X3, X4)
U109_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U110_gga(X1, X2, X3, dcB_in_gga(X1, X3))
U111_gga(X1, X2, dcB_out_gga(X2, X1, X3)) → dcB_out_gga(times(X1, X2), X1, +(times(X3, X1), times(1, X2)))
U112_gga(X1, X2, X3, isnumbercA_out_g(X1)) → U113_gga(X1, X2, X3, dcB_in_gga(X2, X3))
U114_gga(X1, X2, X3, X4, dcB_out_gga(X1, X4, X7)) → U115_gga(X1, X2, X3, X4, X7, dcB_in_gga(X2, X4))
U117_gga(X1, X2, X3, X4, dcB_out_gga(times(X1, power(X2, p(0))), X4, X6)) → U118_gga(X1, X2, X3, X4, X6, dcB_in_gga(X3, X4))
U119_gga(X1, X2, X3, X4, isnumbercA_out_g(X2)) → U120_gga(X1, X2, X3, X4, dcB_in_gga(X1, X4))
U123_gga(X1, X2, X3, dcB_out_gga(X1, X3, X5)) → U124_gga(X1, X2, X3, X5, dcB_in_gga(power(X2, p(0)), X3))
U125_gga(X1, X2, dcB_out_gga(X1, X2, X3)) → dcB_out_gga(power(X1, 0), X2, times(0, times(X3, power(X1, p(0)))))
U126_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U127_gga(X1, X2, X3, dcB_in_gga(X1, X3))
U128_gga(X1, X2, X3, isnumbercA_out_g(X2)) → U129_gga(X1, X2, X3, dcB_in_gga(X1, X3))
U77_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(s(X1))
U78_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(p(X1))
U79_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(s(X1), s(X1), 0)
U80_gga(X1, isnumbercA_out_g(X1)) → dcB_out_gga(p(X1), p(X1), 0)
U83_gga(X1, X2, dcB_out_gga(times(X1, power(X2, p(0))), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), X3)
U84_gga(X1, X2, isnumbercA_out_g(X2)) → U85_gga(X1, X2, dcB_in_gga(X1, power(X1, X2)))
U97_gga(X1, X2, dcB_out_gga(X1, div(X1, X2), X4)) → U98_gga(X1, X2, X4, dcB_in_gga(power(X2, p(0)), div(X1, X2)))
U99_gga(X1, dcB_out_gga(X1, power(X1, 0), X2)) → dcB_out_gga(power(X1, 0), power(X1, 0), times(0, times(X2, power(X1, p(0)))))
U100_gga(X1, X2, isnumbercA_out_g(X2)) → U101_gga(X1, X2, dcB_in_gga(X1, power(X1, s(X2))))
U102_gga(X1, X2, isnumbercA_out_g(X2)) → U103_gga(X1, X2, dcB_in_gga(X1, power(X1, p(X2))))
U82_gga(X1, X2, X4, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(X4, X2)))
U87_gga(X1, X2, dcB_out_gga(X2, times(X1, X2), X3)) → dcB_out_gga(times(X1, X2), times(X1, X2), +(times(X3, X1), times(0, X2)))
U89_gga(X1, X2, X3, X6, dcB_out_gga(X2, times(times(X1, X2), X3), X5)) → U90_gga(X1, X2, X3, X5, X6, dcB_in_gga(X3, times(times(X1, X2), X3)))
U92_gga(X1, X2, X3, X5, dcB_out_gga(X3, times(div(X1, X2), X3), X4)) → dcB_out_gga(times(div(X1, X2), X3), times(div(X1, X2), X3), +(times(X4, div(X1, X2)), times(X5, X3)))
U94_gga(X1, X2, X3, dcB_out_gga(X1, times(power(X1, X2), X3), X5)) → U95_gga(X1, X2, X3, X5, dcB_in_gga(X3, times(power(X1, X2), X3)))
U107_gga(X1, X2, X3, X5, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(X5, X2)))
U110_gga(X1, X2, X3, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, X2), X3, times(X2, times(X4, power(X1, p(X2)))))
U113_gga(X1, X2, X3, dcB_out_gga(X2, X3, X4)) → dcB_out_gga(times(X1, X2), X3, +(times(X4, X1), times(0, X2)))
U115_gga(X1, X2, X3, X4, X7, dcB_out_gga(X2, X4, X6)) → U116_gga(X1, X2, X3, X4, X6, X7, dcB_in_gga(X3, X4))
U118_gga(X1, X2, X3, X4, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(div(X1, X2), X3), X4, +(times(X5, div(X1, X2)), times(X6, X3)))
U120_gga(X1, X2, X3, X4, dcB_out_gga(X1, X4, X6)) → U121_gga(X1, X2, X3, X4, X6, dcB_in_gga(X3, X4))
U124_gga(X1, X2, X3, X5, dcB_out_gga(power(X2, p(0)), X3, X4)) → dcB_out_gga(div(X1, X2), X3, +(times(X4, X1), times(X5, power(X2, p(0)))))
U127_gga(X1, X2, X3, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, s(X2)), X3, times(s(X2), times(X4, power(X1, p(s(X2))))))
U129_gga(X1, X2, X3, dcB_out_gga(X1, X3, X4)) → dcB_out_gga(power(X1, p(X2)), X3, times(p(X2), times(X4, power(X1, p(p(X2))))))
U85_gga(X1, X2, dcB_out_gga(X1, power(X1, X2), X3)) → dcB_out_gga(power(X1, X2), power(X1, X2), times(X2, times(X3, power(X1, p(X2)))))
U98_gga(X1, X2, X4, dcB_out_gga(power(X2, p(0)), div(X1, X2), X3)) → dcB_out_gga(div(X1, X2), div(X1, X2), +(times(X3, X1), times(X4, power(X2, p(0)))))
U101_gga(X1, X2, dcB_out_gga(X1, power(X1, s(X2)), X3)) → dcB_out_gga(power(X1, s(X2)), power(X1, s(X2)), times(s(X2), times(X3, power(X1, p(s(X2))))))
U103_gga(X1, X2, dcB_out_gga(X1, power(X1, p(X2)), X3)) → dcB_out_gga(power(X1, p(X2)), power(X1, p(X2)), times(p(X2), times(X3, power(X1, p(p(X2))))))
U90_gga(X1, X2, X3, X5, X6, dcB_out_gga(X3, times(times(X1, X2), X3), X4)) → dcB_out_gga(times(times(X1, X2), X3), times(times(X1, X2), X3), +(times(X4, times(X1, X2)), times(+(times(X5, X1), times(X6, X2)), X3)))
U95_gga(X1, X2, X3, X5, dcB_out_gga(X3, times(power(X1, X2), X3), X4)) → dcB_out_gga(times(power(X1, X2), X3), times(power(X1, X2), X3), +(times(X4, power(X1, X2)), times(times(X2, times(X5, power(X1, p(X2)))), X3)))
U116_gga(X1, X2, X3, X4, X6, X7, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(times(X1, X2), X3), X4, +(times(X5, times(X1, X2)), times(+(times(X6, X1), times(X7, X2)), X3)))
U121_gga(X1, X2, X3, X4, X6, dcB_out_gga(X3, X4, X5)) → dcB_out_gga(times(power(X1, X2), X3), X4, +(times(X5, power(X1, X2)), times(times(X2, times(X6, power(X1, p(X2)))), X3)))

The set Q consists of the following terms:

dcB_in_gga(x0, x1)
isnumbercA_in_g(x0)
U81_gga(x0, x1, x2)
U86_gga(x0, x1, x2)
U88_gga(x0, x1, x2, x3)
U91_gga(x0, x1, x2, x3)
U93_gga(x0, x1, x2, x3)
U104_gga(x0, x1, x2)
U105_gga(x0, x1, x2)
U106_gga(x0, x1, x2, x3)
U108_gga(x0, x1, x2, x3)
U109_gga(x0, x1, x2, x3)
U111_gga(x0, x1, x2)
U112_gga(x0, x1, x2, x3)
U114_gga(x0, x1, x2, x3, x4)
U117_gga(x0, x1, x2, x3, x4)
U119_gga(x0, x1, x2, x3, x4)
U123_gga(x0, x1, x2, x3)
U125_gga(x0, x1, x2)
U126_gga(x0, x1, x2, x3)
U128_gga(x0, x1, x2, x3)
U77_g(x0, x1)
U78_g(x0, x1)
U79_gga(x0, x1)
U80_gga(x0, x1)
U83_gga(x0, x1, x2)
U84_gga(x0, x1, x2)
U97_gga(x0, x1, x2)
U99_gga(x0, x1)
U100_gga(x0, x1, x2)
U102_gga(x0, x1, x2)
U82_gga(x0, x1, x2, x3)
U87_gga(x0, x1, x2)
U89_gga(x0, x1, x2, x3, x4)
U92_gga(x0, x1, x2, x3, x4)
U94_gga(x0, x1, x2, x3)
U107_gga(x0, x1, x2, x3, x4)
U110_gga(x0, x1, x2, x3)
U113_gga(x0, x1, x2, x3)
U115_gga(x0, x1, x2, x3, x4, x5)
U118_gga(x0, x1, x2, x3, x4, x5)
U120_gga(x0, x1, x2, x3, x4)
U124_gga(x0, x1, x2, x3, x4)
U127_gga(x0, x1, x2, x3)
U129_gga(x0, x1, x2, x3)
U85_gga(x0, x1, x2)
U98_gga(x0, x1, x2, x3)
U101_gga(x0, x1, x2)
U103_gga(x0, x1, x2)
U90_gga(x0, x1, x2, x3, x4, x5)
U95_gga(x0, x1, x2, x3, x4)
U116_gga(x0, x1, x2, x3, x4, x5, x6)
U121_gga(x0, x1, x2, x3, x4, x5)

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

(23) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

(24) Obligation:

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

DB_IN_GGA(power(X1, X2), power(X1, X2)) → U10_GGA(X1, X2, isnumbercA_in_g(X2))
U10_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, X2))
DB_IN_GGA(power(X1, X2), X3) → U46_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U46_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
DB_IN_GGA(power(X1, 0), power(X1, 0)) → DB_IN_GGA(X1, power(X1, 0))
DB_IN_GGA(power(X1, p(X2)), X3) → U74_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U74_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2))) → U34_GGA(X1, X2, isnumbercA_in_g(X2))
U34_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, s(X2)))
DB_IN_GGA(power(X1, 0), X2) → DB_IN_GGA(X1, X2)
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2))) → U37_GGA(X1, X2, isnumbercA_in_g(X2))
U37_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, p(X2)))
DB_IN_GGA(power(X1, s(X2)), X3) → U71_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U71_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)

The TRS R consists of the following rules:

isnumbercA_in_g(0) → isnumbercA_out_g(0)
isnumbercA_in_g(s(X1)) → U77_g(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(p(X1)) → U78_g(X1, isnumbercA_in_g(X1))
U78_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(p(X1))
U77_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(s(X1))

The set Q consists of the following terms:

dcB_in_gga(x0, x1)
isnumbercA_in_g(x0)
U81_gga(x0, x1, x2)
U86_gga(x0, x1, x2)
U88_gga(x0, x1, x2, x3)
U91_gga(x0, x1, x2, x3)
U93_gga(x0, x1, x2, x3)
U104_gga(x0, x1, x2)
U105_gga(x0, x1, x2)
U106_gga(x0, x1, x2, x3)
U108_gga(x0, x1, x2, x3)
U109_gga(x0, x1, x2, x3)
U111_gga(x0, x1, x2)
U112_gga(x0, x1, x2, x3)
U114_gga(x0, x1, x2, x3, x4)
U117_gga(x0, x1, x2, x3, x4)
U119_gga(x0, x1, x2, x3, x4)
U123_gga(x0, x1, x2, x3)
U125_gga(x0, x1, x2)
U126_gga(x0, x1, x2, x3)
U128_gga(x0, x1, x2, x3)
U77_g(x0, x1)
U78_g(x0, x1)
U79_gga(x0, x1)
U80_gga(x0, x1)
U83_gga(x0, x1, x2)
U84_gga(x0, x1, x2)
U97_gga(x0, x1, x2)
U99_gga(x0, x1)
U100_gga(x0, x1, x2)
U102_gga(x0, x1, x2)
U82_gga(x0, x1, x2, x3)
U87_gga(x0, x1, x2)
U89_gga(x0, x1, x2, x3, x4)
U92_gga(x0, x1, x2, x3, x4)
U94_gga(x0, x1, x2, x3)
U107_gga(x0, x1, x2, x3, x4)
U110_gga(x0, x1, x2, x3)
U113_gga(x0, x1, x2, x3)
U115_gga(x0, x1, x2, x3, x4, x5)
U118_gga(x0, x1, x2, x3, x4, x5)
U120_gga(x0, x1, x2, x3, x4)
U124_gga(x0, x1, x2, x3, x4)
U127_gga(x0, x1, x2, x3)
U129_gga(x0, x1, x2, x3)
U85_gga(x0, x1, x2)
U98_gga(x0, x1, x2, x3)
U101_gga(x0, x1, x2)
U103_gga(x0, x1, x2)
U90_gga(x0, x1, x2, x3, x4, x5)
U95_gga(x0, x1, x2, x3, x4)
U116_gga(x0, x1, x2, x3, x4, x5, x6)
U121_gga(x0, x1, x2, x3, x4, x5)

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

(25) QReductionProof (EQUIVALENT transformation)

We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].

dcB_in_gga(x0, x1)
U81_gga(x0, x1, x2)
U86_gga(x0, x1, x2)
U88_gga(x0, x1, x2, x3)
U91_gga(x0, x1, x2, x3)
U93_gga(x0, x1, x2, x3)
U104_gga(x0, x1, x2)
U105_gga(x0, x1, x2)
U106_gga(x0, x1, x2, x3)
U108_gga(x0, x1, x2, x3)
U109_gga(x0, x1, x2, x3)
U111_gga(x0, x1, x2)
U112_gga(x0, x1, x2, x3)
U114_gga(x0, x1, x2, x3, x4)
U117_gga(x0, x1, x2, x3, x4)
U119_gga(x0, x1, x2, x3, x4)
U123_gga(x0, x1, x2, x3)
U125_gga(x0, x1, x2)
U126_gga(x0, x1, x2, x3)
U128_gga(x0, x1, x2, x3)
U79_gga(x0, x1)
U80_gga(x0, x1)
U83_gga(x0, x1, x2)
U84_gga(x0, x1, x2)
U97_gga(x0, x1, x2)
U99_gga(x0, x1)
U100_gga(x0, x1, x2)
U102_gga(x0, x1, x2)
U82_gga(x0, x1, x2, x3)
U87_gga(x0, x1, x2)
U89_gga(x0, x1, x2, x3, x4)
U92_gga(x0, x1, x2, x3, x4)
U94_gga(x0, x1, x2, x3)
U107_gga(x0, x1, x2, x3, x4)
U110_gga(x0, x1, x2, x3)
U113_gga(x0, x1, x2, x3)
U115_gga(x0, x1, x2, x3, x4, x5)
U118_gga(x0, x1, x2, x3, x4, x5)
U120_gga(x0, x1, x2, x3, x4)
U124_gga(x0, x1, x2, x3, x4)
U127_gga(x0, x1, x2, x3)
U129_gga(x0, x1, x2, x3)
U85_gga(x0, x1, x2)
U98_gga(x0, x1, x2, x3)
U101_gga(x0, x1, x2)
U103_gga(x0, x1, x2)
U90_gga(x0, x1, x2, x3, x4, x5)
U95_gga(x0, x1, x2, x3, x4)
U116_gga(x0, x1, x2, x3, x4, x5, x6)
U121_gga(x0, x1, x2, x3, x4, x5)

(26) Obligation:

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

DB_IN_GGA(power(X1, X2), power(X1, X2)) → U10_GGA(X1, X2, isnumbercA_in_g(X2))
U10_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, X2))
DB_IN_GGA(power(X1, X2), X3) → U46_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U46_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
DB_IN_GGA(power(X1, 0), power(X1, 0)) → DB_IN_GGA(X1, power(X1, 0))
DB_IN_GGA(power(X1, p(X2)), X3) → U74_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U74_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2))) → U34_GGA(X1, X2, isnumbercA_in_g(X2))
U34_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, s(X2)))
DB_IN_GGA(power(X1, 0), X2) → DB_IN_GGA(X1, X2)
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2))) → U37_GGA(X1, X2, isnumbercA_in_g(X2))
U37_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, p(X2)))
DB_IN_GGA(power(X1, s(X2)), X3) → U71_GGA(X1, X2, X3, isnumbercA_in_g(X2))
U71_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)

The TRS R consists of the following rules:

isnumbercA_in_g(0) → isnumbercA_out_g(0)
isnumbercA_in_g(s(X1)) → U77_g(X1, isnumbercA_in_g(X1))
isnumbercA_in_g(p(X1)) → U78_g(X1, isnumbercA_in_g(X1))
U78_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(p(X1))
U77_g(X1, isnumbercA_out_g(X1)) → isnumbercA_out_g(s(X1))

The set Q consists of the following terms:

isnumbercA_in_g(x0)
U77_g(x0, x1)
U78_g(x0, x1)

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

(27) 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:

U10_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, X2))
The graph contains the following edges 1 >= 1
DB_IN_GGA(power(X1, 0), X2) → DB_IN_GGA(X1, X2)
The graph contains the following edges 1 > 1, 2 >= 2
DB_IN_GGA(power(X1, X2), power(X1, X2)) → U10_GGA(X1, X2, isnumbercA_in_g(X2))
The graph contains the following edges 1 > 1, 2 > 1, 1 > 2, 2 > 2
U46_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
The graph contains the following edges 1 >= 1, 3 >= 2
DB_IN_GGA(power(X1, X2), X3) → U46_GGA(X1, X2, X3, isnumbercA_in_g(X2))
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3
DB_IN_GGA(power(X1, 0), power(X1, 0)) → DB_IN_GGA(X1, power(X1, 0))
The graph contains the following edges 1 > 1, 2 > 1, 1 >= 2, 2 >= 2
U74_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
The graph contains the following edges 1 >= 1, 3 >= 2
U71_GGA(X1, X2, X3, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, X3)
The graph contains the following edges 1 >= 1, 3 >= 2
DB_IN_GGA(power(X1, p(X2)), X3) → U74_GGA(X1, X2, X3, isnumbercA_in_g(X2))
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3
DB_IN_GGA(power(X1, s(X2)), X3) → U71_GGA(X1, X2, X3, isnumbercA_in_g(X2))
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3
U34_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, s(X2)))
The graph contains the following edges 1 >= 1
U37_GGA(X1, X2, isnumbercA_out_g(X2)) → DB_IN_GGA(X1, power(X1, p(X2)))
The graph contains the following edges 1 >= 1
DB_IN_GGA(power(X1, s(X2)), power(X1, s(X2))) → U34_GGA(X1, X2, isnumbercA_in_g(X2))
The graph contains the following edges 1 > 1, 2 > 1, 1 > 2, 2 > 2
DB_IN_GGA(power(X1, p(X2)), power(X1, p(X2))) → U37_GGA(X1, X2, isnumbercA_in_g(X2))
The graph contains the following edges 1 > 1, 2 > 1, 1 > 2, 2 > 2

(0) Obligation:

(1) PrologToDTProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) TriplesToPiDPProof (SOUND transformation)

(4) Obligation:

(5) DependencyGraphProof (EQUIVALENT transformation)

(6) Complex Obligation (AND)

(7) Obligation:

(8) UsableRulesProof (EQUIVALENT transformation)

(9) Obligation:

(10) PiDPToQDPProof (EQUIVALENT transformation)

(11) Obligation:

(12) QDPSizeChangeProof (EQUIVALENT transformation)

(13) YES

(14) Obligation:

(15) UsableRulesProof (EQUIVALENT transformation)

(16) Obligation:

(17) PiDPToQDPProof (SOUND transformation)

(18) Obligation:

(19) QDPOrderProof (EQUIVALENT transformation)

(20) Obligation:

(21) DependencyGraphProof (EQUIVALENT transformation)

(22) Obligation:

(23) UsableRulesProof (EQUIVALENT transformation)

(24) Obligation:

(25) QReductionProof (EQUIVALENT transformation)

(26) Obligation:

(27) QDPSizeChangeProof (EQUIVALENT transformation)

(28) YES