Left Termination proof of /tmp/tmpeF8nix/d.pl

Left Termination of the query pattern d_in_3(g, g, a) w.r.t. the given Prolog program could successfully be proven:

0 Prolog

↳1 PrologToPrologProblemTransformerProof (⇐)

↳2 Prolog

↳3 PrologToPiTRSProof (⇐)

↳4 PiTRS

↳5 DependencyPairsProof (⇔)

↳6 PiDP

↳7 DependencyGraphProof (⇔)

↳8 AND

    ↳9 PiDP

        ↳10 UsableRulesProof (⇔)

        ↳11 PiDP

        ↳12 PiDPToQDPProof (⇔)

        ↳13 QDP

        ↳14 QDPSizeChangeProof (⇔)

        ↳15 YES

    ↳16 PiDP

        ↳17 UsableRulesProof (⇔)

        ↳18 PiDP

        ↳19 PiDPToQDPProof (⇐)

        ↳20 QDP

        ↳21 QDPOrderProof (⇔)

        ↳22 QDP

        ↳23 DependencyGraphProof (⇔)

        ↳24 QDP

        ↳25 UsableRulesProof (⇔)

        ↳26 QDP

        ↳27 QReductionProof (⇔)

        ↳28 QDP

        ↳29 QDPSizeChangeProof (⇔)

        ↳30 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).

Queries:

d(g,g,a).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: 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\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\nd(T5, T5, T3) !=? d(X7, X8, 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="16: 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), T54)\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(T79, power(T80, p(0))), div(T79, T80), T82)\n\nT79 is ground\nT80 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(isnumber(T96), d(T95, power(T95, T96), T98))\n\nT95 is ground\nT96 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: isnumber(T96)\n\nT96 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: d(T95, power(T95, T96), T98)\n\nT95 is ground\nT96 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)) | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 3 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 4\n\nT109 is ground\nT110 is ground\nd(times(T109, T110), times(T109, T110), T3) !=? d(X7, X8, 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\nd(T5, T5, T3) !=? d(X7, X8, 0)\nd(T5, T5, T3) !=? d(times(X128, X129), X130, +(times(X131, X128), times(X132, X129)))", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 0 | ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 1 | ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 2 | ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 3 | ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 4 | ?_4 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 3 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 4\n\nT109 is ground\nT110 is ground\nd(times(T109, T110), times(T109, T110), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 1 | ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 2 | ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 3 | ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 4 | ?_4 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 3 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 4\n\nT109 is ground\nT110 is ground\nd(times(T109, T110), times(T109, T110), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 1\n\nT109 is ground\nT110 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 2 | ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 3 | ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 4 | ?_4 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 3 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 4\n\nT109 is ground\nT110 is ground\nd(times(T109, T110), times(T109, T110), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ','(isnumber(T125), d(T126, times(T125, T126), T127))\n\nT125 is ground\nT126 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: isnumber(T125)\n\nT125 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: d(T126, times(T125, T126), T127)\n\nT125 is ground\nT126 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 2\n\nT109 is ground\nT110 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 3 | ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 4 | ?_4 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 3 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 4\n\nT109 is ground\nT110 is ground\nd(times(T109, T110), times(T109, T110), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(d(T154, times(times(T154, T155), T156), T159), ','(d(T155, times(times(T154, T155), T156), T160), d(T156, times(times(T154, T155), T156), T161)))\n\nT154 is ground\nT155 is ground\nT156 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: d(T154, times(times(T154, T155), T156), T159)\n\nT154 is ground\nT155 is ground\nT156 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: ','(d(T155, times(times(T154, T155), T156), T171), d(T156, times(times(T154, T155), T156), T172))\n\nT154 is ground\nT155 is ground\nT156 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: d(T155, times(times(T154, T155), T156), T171)\n\nT154 is ground\nT155 is ground\nT156 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: d(T156, times(times(T154, T155), T156), T191)\n\nT154 is ground\nT155 is ground\nT156 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 3\n\nT109 is ground\nT110 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 4 | ?_4 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 3 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 4\n\nT109 is ground\nT110 is ground\nd(times(T109, T110), times(T109, T110), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: ','(d(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230), d(T228, times(div(T226, T227), T228), T231))\n\nT226 is ground\nT227 is ground\nT228 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: d(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)\n\nT226 is ground\nT227 is ground\nT228 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: d(T228, times(div(T226, T227), T228), T239)\n\nT226 is ground\nT227 is ground\nT228 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: ','(d(T109, times(T109, T110), T113), d(T110, times(T109, T110), T114)), SCOPE: 4, CLAUSE: 4\n\nT109 is ground\nT110 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: ?_4 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 3 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 4\n\nT109 is ground\nT110 is ground\nd(times(T109, T110), times(T109, T110), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: ','(isnumber(T273), ','(d(T272, times(power(T272, T273), T274), T276), d(T274, times(power(T272, T273), T274), T277)))\n\nT272 is ground\nT273 is ground\nT274 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: isnumber(T273)\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: ','(d(T272, times(power(T272, T273), T274), T276), d(T274, times(power(T272, T273), T274), T277))\n\nT272 is ground\nT273 is ground\nT274 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: d(T272, times(power(T272, T273), T274), T276)\n\nT272 is ground\nT273 is ground\nT274 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: d(T274, times(power(T272, T273), T274), T287)\n\nT272 is ground\nT273 is ground\nT274 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 3 | d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 4\n\nT109 is ground\nT110 is ground\nd(times(T109, T110), times(T109, T110), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: d(times(T109, T110), times(T109, T110), T3), SCOPE: 1, CLAUSE: 4\n\nT109 is ground\nT110 is ground\nd(times(T109, T110), times(T109, T110), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: d(times(T309, power(T310, p(0))), div(T309, T310), T312) | d(div(T309, T310), div(T309, T310), T3), SCOPE: 1, CLAUSE: 4\n\nT309 is ground\nT310 is ground\nd(div(T309, T310), div(T309, T310), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: d(T5, T5, T3), SCOPE: 1, CLAUSE: 4\n\nT5 is ground\nd(T5, T5, T3) !=? d(X7, X8, 0)\nd(T5, T5, T3) !=? d(times(X128, X129), X130, +(times(X131, X128), times(X132, X129)))\nd(T5, T5, T3) !=? d(div(X289, X290), X291, X292)", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 0 | d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 1 | d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 2 | d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 3 | d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 4 | ?_5 | d(div(T309, T310), div(T309, T310), T3), SCOPE: 1, CLAUSE: 4\n\nT309 is ground\nT310 is ground\nd(div(T309, T310), div(T309, T310), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 1 | d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 2 | d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 3 | d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 4 | ?_5 | d(div(T309, T310), div(T309, T310), T3), SCOPE: 1, CLAUSE: 4\n\nT309 is ground\nT310 is ground\nd(div(T309, T310), div(T309, T310), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 1\n\nT309 is ground\nT310 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 2 | d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 3 | d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 4 | ?_5 | d(div(T309, T310), div(T309, T310), T3), SCOPE: 1, CLAUSE: 4\n\nT309 is ground\nT310 is ground\nd(div(T309, T310), div(T309, T310), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: isnumber(times(T323, power(T324, p(0))))\n\nT323 is ground\nT324 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 2\n\nT309 is ground\nT310 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 3 | d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 4 | ?_5 | d(div(T309, T310), div(T309, T310), T3), SCOPE: 1, CLAUSE: 4\n\nT309 is ground\nT310 is ground\nd(div(T309, T310), div(T309, T310), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: ','(d(T341, div(T341, T342), T345), d(power(T342, p(0)), div(T341, T342), T346))\n\nT341 is ground\nT342 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: d(T341, div(T341, T342), T345)\n\nT341 is ground\nT342 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: d(power(T342, p(0)), div(T341, T342), T353)\n\nT341 is ground\nT342 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: d(times(T309, power(T310, p(0))), div(T309, T310), T312), SCOPE: 5, CLAUSE: 4 | ?_5 | d(div(T309, T310), div(T309, T310), T3), SCOPE: 1, CLAUSE: 4\n\nT309 is ground\nT310 is ground\nd(div(T309, T310), div(T309, T310), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: ?_5 | d(div(T309, T310), div(T309, T310), T3), SCOPE: 1, CLAUSE: 4\n\nT309 is ground\nT310 is ground\nd(div(T309, T310), div(T309, T310), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: d(div(T309, T310), div(T309, T310), T3), SCOPE: 1, CLAUSE: 4\n\nT309 is ground\nT310 is ground\nd(div(T309, T310), div(T309, T310), T3) !=? d(X7, X8, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: ','(isnumber(T368), d(T367, power(T367, T368), T370))\n\nT367 is ground\nT368 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: ','(isnumber(T368), d(T367, power(T367, T368), T370)), SCOPE: 6, CLAUSE: 5 | ','(isnumber(T368), d(T367, power(T367, T368), T370)), SCOPE: 6, CLAUSE: 6 | ','(isnumber(T368), d(T367, power(T367, T368), T370)), SCOPE: 6, CLAUSE: 7\n\nT367 is ground\nT368 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: ','(isnumber(T368), d(T367, power(T367, T368), T370)), SCOPE: 6, CLAUSE: 5\n\nT367 is ground\nT368 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: ','(isnumber(T368), d(T367, power(T367, T368), T370)), SCOPE: 6, CLAUSE: 6 | ','(isnumber(T368), d(T367, power(T367, T368), T370)), SCOPE: 6, CLAUSE: 7\n\nT367 is ground\nT368 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: d(T367, power(T367, 0), T370)\n\nT367 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: ','(isnumber(T368), d(T367, power(T367, T368), T370)), SCOPE: 6, CLAUSE: 6\n\nT367 is ground\nT368 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(isnumber(T368), d(T367, power(T367, T368), T370)), SCOPE: 6, CLAUSE: 7\n\nT367 is ground\nT368 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(isnumber(T378), d(T367, power(T367, s(T378)), T370))\n\nT367 is ground\nT378 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: isnumber(T378)\n\nT378 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: d(T367, power(T367, s(T378)), T370)\n\nT367 is ground\nT378 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: ','(isnumber(T387), d(T367, power(T367, p(T387)), T370))\n\nT367 is ground\nT387 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: isnumber(T387)\n\nT387 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: d(T367, power(T367, p(T387)), T370)\n\nT367 is ground\nT387 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: isnumber(T396) | d(T396, T397, T3), SCOPE: 1, CLAUSE: 2 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 3 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 4\n\nT396 is ground\nT397 is ground\nd(T396, T397, 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\nd(T1, T2, T3) !=? d(X3, X3, 1)\nd(T1, T2, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: isnumber(T396), SCOPE: 7, CLAUSE: 5 | isnumber(T396), SCOPE: 7, CLAUSE: 6 | isnumber(T396), SCOPE: 7, CLAUSE: 7 | ?_7 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 2 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 3 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 4\n\nT396 is ground\nT397 is ground\nd(T396, T397, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: isnumber(T396), SCOPE: 7, CLAUSE: 5\n\nT396 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: isnumber(T396), SCOPE: 7, CLAUSE: 6 | isnumber(T396), SCOPE: 7, CLAUSE: 7 | ?_7 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 2 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 3 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 4\n\nT396 is ground\nT397 is ground\nd(T396, T397, 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(T396), SCOPE: 7, CLAUSE: 6\n\nT396 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: isnumber(T396), SCOPE: 7, CLAUSE: 7 | ?_7 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 2 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 3 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 4\n\nT396 is ground\nT397 is ground\nd(T396, T397, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: isnumber(T402)\n\nT402 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: isnumber(T396), SCOPE: 7, CLAUSE: 7\n\nT396 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: ?_7 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 2 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 3 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 4\n\nT396 is ground\nT397 is ground\nd(T396, T397, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: isnumber(T407)\n\nT407 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: d(T396, T397, T3), SCOPE: 1, CLAUSE: 2 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 3 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 4\n\nT396 is ground\nT397 is ground\nd(T396, T397, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: d(T396, T397, T3), SCOPE: 1, CLAUSE: 2\n\nT396 is ground\nT397 is ground\nd(T396, T397, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: d(T396, T397, T3), SCOPE: 1, CLAUSE: 3 | d(T396, T397, T3), SCOPE: 1, CLAUSE: 4\n\nT396 is ground\nT397 is ground\nd(T396, T397, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: ','(d(T428, T430, T433), d(T429, T430, T434))\n\nT428 is ground\nT429 is ground\nT430 is ground\nd(times(T428, T429), T430, 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(T428, T430, T433)\n\nT428 is ground\nT430 is ground\nd(times(T428, T429), T430, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: d(T429, T430, T437)\n\nT429 is ground\nT430 is ground\nd(times(T428, T429), T430, T438) !=? d(T439, T439, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: d(T396, T397, T3), SCOPE: 1, CLAUSE: 3\n\nT396 is ground\nT397 is ground\nd(T396, T397, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: d(T396, T397, T3), SCOPE: 1, CLAUSE: 4\n\nT396 is ground\nT397 is ground\nd(T396, T397, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: d(times(T460, power(T461, p(0))), T462, T464)\n\nT460 is ground\nT461 is ground\nT462 is ground\nd(div(T460, T461), T462, 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(T478), d(T477, T479, T481))\n\nT477 is ground\nT478 is ground\nT479 is ground\nd(power(T477, T478), T479, 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(T478)\n\nT478 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: d(T477, T479, T481)\n\nT477 is ground\nT479 is ground\nd(power(T477, T478), T479, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: ','(d(T489, T491, T494), d(T490, T491, T495)) | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 3 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 4\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)\nd(times(T489, T490), T491, T3) !=? d(X402, X403, 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\nd(T1, T2, T3) !=? d(X3, X3, 1)\nd(T1, T2, T3) !=? d(X402, X403, 0)\nd(T1, T2, T3) !=? d(times(X503, X504), X505, +(times(X506, X503), times(X507, X504)))", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 0 | ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 1 | ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 2 | ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 3 | ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 4 | ?_8 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 3 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 4\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)\nd(times(T489, T490), T491, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 0\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 1 | ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 2 | ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 3 | ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 4 | ?_8 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 3 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 4\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)\nd(times(T489, T490), T491, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: d(T490, T500, T501)\n\nT490 is ground\nT500 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 1\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 2 | ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 3 | ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 4 | ?_8 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 3 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 4\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)\nd(times(T489, T490), T491, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: ','(isnumber(T512), d(T490, T513, T514))\n\nT490 is ground\nT512 is ground\nT513 is ground\nd(times(T512, T490), T513, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: isnumber(T512)\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: d(T490, T513, T514)\n\nT490 is ground\nT513 is ground\nd(times(T512, T490), T513, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 2\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 3 | ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 4 | ?_8 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 3 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 4\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)\nd(times(T489, T490), T491, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: ','(d(T537, T539, T542), ','(d(T538, T539, T543), d(T490, T539, T544)))\n\nT490 is ground\nT537 is ground\nT538 is ground\nT539 is ground\nd(times(times(T537, T538), T490), T539, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: d(T537, T539, T542)\n\nT537 is ground\nT539 is ground\nd(times(times(T537, T538), T490), T539, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: ','(d(T538, T539, T547), d(T490, T539, T548))\n\nT490 is ground\nT538 is ground\nT539 is ground\nd(times(times(T537, T538), T490), T539, T549) !=? d(T550, T550, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: d(T538, T539, T547)\n\nT538 is ground\nT539 is ground\nd(times(times(T537, T538), T490), T539, T549) !=? d(T550, T550, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: d(T490, T539, T555)\n\nT490 is ground\nT539 is ground\nd(times(times(T556, T538), T490), T539, T557) !=? d(T558, T558, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 3\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 4 | ?_8 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 3 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 4\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)\nd(times(T489, T490), T491, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: ','(d(times(T579, power(T580, p(0))), T581, T583), d(T490, T581, T584))\n\nT490 is ground\nT579 is ground\nT580 is ground\nT581 is ground\nd(times(div(T579, T580), T490), T581, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: d(times(T579, power(T580, p(0))), T581, T583)\n\nT579 is ground\nT580 is ground\nT581 is ground\nd(times(div(T579, T580), T490), T581, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: d(T490, T581, T589)\n\nT490 is ground\nT581 is ground\nd(times(div(T579, T580), T490), T581, T590) !=? d(T591, T591, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: ','(d(T489, T491, T494), d(T490, T491, T495)), SCOPE: 8, CLAUSE: 4\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: ?_8 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 3 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 4\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)\nd(times(T489, T490), T491, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: ','(isnumber(T615), ','(d(T614, T616, T618), d(T490, T616, T619)))\n\nT490 is ground\nT614 is ground\nT615 is ground\nT616 is ground\nd(times(power(T614, T615), T490), T616, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: isnumber(T615)\n\nT615 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: ','(d(T614, T616, T618), d(T490, T616, T619))\n\nT490 is ground\nT614 is ground\nT616 is ground\nd(times(power(T614, T615), T490), T616, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: d(T614, T616, T618)\n\nT614 is ground\nT616 is ground\nd(times(power(T614, T615), T490), T616, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: d(T490, T616, T622)\n\nT490 is ground\nT616 is ground\nd(times(power(T614, T623), T490), T616, T624) !=? d(T625, T625, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 3 | d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 4\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)\nd(times(T489, T490), T491, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: d(times(T489, T490), T491, T3), SCOPE: 1, CLAUSE: 4\n\nT489 is ground\nT490 is ground\nT491 is ground\nd(times(T489, T490), T491, T3) !=? d(X3, X3, 1)\nd(times(T489, T490), T491, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: d(times(T634, power(T635, p(0))), T636, T638) | d(div(T634, T635), T636, T3), SCOPE: 1, CLAUSE: 4\n\nT634 is ground\nT635 is ground\nT636 is ground\nd(div(T634, T635), T636, T3) !=? d(X3, X3, 1)\nd(div(T634, T635), T636, T3) !=? d(X402, X403, 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\nd(T1, T2, T3) !=? d(X3, X3, 1)\nd(T1, T2, T3) !=? d(X402, X403, 0)\nd(T1, T2, T3) !=? d(times(X503, X504), X505, +(times(X506, X503), times(X507, X504)))\nd(T1, T2, T3) !=? d(div(X647, X648), X649, X650)", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 0 | d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 1 | d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 2 | d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 3 | d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 4 | ?_9 | d(div(T634, T635), T636, T3), SCOPE: 1, CLAUSE: 4\n\nT634 is ground\nT635 is ground\nT636 is ground\nd(div(T634, T635), T636, T3) !=? d(X3, X3, 1)\nd(div(T634, T635), T636, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 0\n\nT634 is ground\nT635 is ground\nT636 is ground\nd(div(T634, T635), T636, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 1 | d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 2 | d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 3 | d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 4 | ?_9 | d(div(T634, T635), T636, T3), SCOPE: 1, CLAUSE: 4\n\nT634 is ground\nT635 is ground\nT636 is ground\nd(div(T634, T635), T636, T3) !=? d(X3, X3, 1)\nd(div(T634, T635), T636, T3) !=? d(X402, X403, 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(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 1\n\nT634 is ground\nT635 is ground\nT636 is ground\nd(div(T634, T635), T636, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 2 | d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 3 | d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 4 | ?_9 | d(div(T634, T635), T636, T3), SCOPE: 1, CLAUSE: 4\n\nT634 is ground\nT635 is ground\nT636 is ground\nd(div(T634, T635), T636, T3) !=? d(X3, X3, 1)\nd(div(T634, T635), T636, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: isnumber(times(T661, power(T662, p(0))))\n\nT661 is ground\nT662 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 2\n\nT634 is ground\nT635 is ground\nT636 is ground\nd(div(T634, T635), T636, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 3 | d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 4 | ?_9 | d(div(T634, T635), T636, T3), SCOPE: 1, CLAUSE: 4\n\nT634 is ground\nT635 is ground\nT636 is ground\nd(div(T634, T635), T636, T3) !=? d(X3, X3, 1)\nd(div(T634, T635), T636, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: ','(d(T684, T686, T689), d(power(T685, p(0)), T686, T690))\n\nT684 is ground\nT685 is ground\nT686 is ground\nd(div(T684, T685), T686, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: d(T684, T686, T689)\n\nT684 is ground\nT686 is ground\nd(div(T684, T685), T686, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: d(power(T685, p(0)), T686, T693)\n\nT685 is ground\nT686 is ground\nd(div(T684, T685), T686, T694) !=? d(T695, T695, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: d(times(T634, power(T635, p(0))), T636, T638), SCOPE: 9, CLAUSE: 4 | ?_9 | d(div(T634, T635), T636, T3), SCOPE: 1, CLAUSE: 4\n\nT634 is ground\nT635 is ground\nT636 is ground\nd(div(T634, T635), T636, T3) !=? d(X3, X3, 1)\nd(div(T634, T635), T636, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: ?_9 | d(div(T634, T635), T636, T3), SCOPE: 1, CLAUSE: 4\n\nT634 is ground\nT635 is ground\nT636 is ground\nd(div(T634, T635), T636, T3) !=? d(X3, X3, 1)\nd(div(T634, T635), T636, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: d(div(T634, T635), T636, T3), SCOPE: 1, CLAUSE: 4\n\nT634 is ground\nT635 is ground\nT636 is ground\nd(div(T634, T635), T636, T3) !=? d(X3, X3, 1)\nd(div(T634, T635), T636, T3) !=? d(X402, X403, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: ','(isnumber(T705), d(T704, T706, T708))\n\nT704 is ground\nT705 is ground\nT706 is ground\nd(power(T704, T705), T706, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: ','(isnumber(T705), d(T704, T706, T708)), SCOPE: 10, CLAUSE: 5 | ','(isnumber(T705), d(T704, T706, T708)), SCOPE: 10, CLAUSE: 6 | ','(isnumber(T705), d(T704, T706, T708)), SCOPE: 10, CLAUSE: 7\n\nT704 is ground\nT705 is ground\nT706 is ground\nd(power(T704, T705), T706, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: ','(isnumber(T705), d(T704, T706, T708)), SCOPE: 10, CLAUSE: 5\n\nT704 is ground\nT705 is ground\nT706 is ground\nd(power(T704, T705), T706, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: ','(isnumber(T705), d(T704, T706, T708)), SCOPE: 10, CLAUSE: 6 | ','(isnumber(T705), d(T704, T706, T708)), SCOPE: 10, CLAUSE: 7\n\nT704 is ground\nT705 is ground\nT706 is ground\nd(power(T704, T705), T706, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: d(T704, T706, T708)\n\nT704 is ground\nT706 is ground\nd(power(T704, 0), T706, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: ','(isnumber(T705), d(T704, T706, T708)), SCOPE: 10, CLAUSE: 6\n\nT704 is ground\nT705 is ground\nT706 is ground\nd(power(T704, T705), T706, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: ','(isnumber(T705), d(T704, T706, T708)), SCOPE: 10, CLAUSE: 7\n\nT704 is ground\nT705 is ground\nT706 is ground\nd(power(T704, T705), T706, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: ','(isnumber(T715), d(T704, T706, T708))\n\nT704 is ground\nT706 is ground\nT715 is ground\nd(power(T704, s(T715)), T706, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: isnumber(T715)\n\nT715 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: d(T704, T706, T708)\n\nT704 is ground\nT706 is ground\nd(power(T704, s(T715)), T706, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: ','(isnumber(T720), d(T704, T706, T708))\n\nT704 is ground\nT706 is ground\nT720 is ground\nd(power(T704, p(T720)), T706, T3) !=? d(X3, X3, 1)", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: isnumber(T720)\n\nT720 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: d(T704, T706, T708)\n\nT704 is ground\nT706 is ground\nd(power(T704, p(T720)), T706, T3) !=? d(X3, X3, 1)", 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 substitution\nT1 -> 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 = lightblue];
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(X402, X403, 0) :- isnumber(X402).\nand substitution\nT1 -> T396\nX402 -> T396\nT2 -> T397\nX403 -> T397\nT3 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 231 [arrowhead = none ];
231 -> 119;

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

233 [label="EVAL with clause\nd(X7, X8, 0) :- isnumber(X7).\nand substitution\nT5 -> T7\nX7 -> T7\nX8 -> T7\nT3 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 233 [arrowhead = none ];
233 -> 6;

234 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X128, X129), X130, +(times(X131, X128), times(X132, X129))) :- ','(d(X128, X130, X132), d(X129, X130, X131)).\nand substitution\nX128 -> T109\nX129 -> T110\nT5 -> times(T109, T110)\nX130 -> times(T109, T110)\nX131 -> T114\nX132 -> T113\nT3 -> +(times(T114, T109), times(T113, T110))\nT112 -> T113\nT111 -> T114", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 236 [arrowhead = none ];
236 -> 49;

237 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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 substitution\nT7 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 240 [arrowhead = none ];
240 -> 11;

241 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X15)) :- isnumber(X15).\nand substitution\nX15 -> 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 = lightblue];
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 substitution\nT12 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 252 [arrowhead = none ];
252 -> 21;

253 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X21)) :- isnumber(X21).\nand substitution\nX21 -> 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 = lightblue];
24 -> 258 [arrowhead = none ];
258 -> 27;

259 [label="EVAL with clause\nisnumber(p(X25)) :- isnumber(X25).\nand substitution\nX25 -> 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 = lightblue];
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(X31)) :- isnumber(X31).\nand substitution\nX31 -> 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 = lightblue];
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(X53, X54), X55, +(times(X56, X53), times(X57, X54))) :- ','(d(X53, X55, X57), d(X54, X55, X56)).\nand substitution\nX53 -> T42\nX54 -> T43\nT7 -> times(T42, T43)\nX55 -> times(T42, T43)\nX56 -> T47\nX57 -> 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 = lightblue];
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:\nT46 is ground\nreplacements:\nT47 -> T54", 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 -> T54", fontsize=14, style = filled, fillcolor = lightgrey];
40 -> 276 [arrowhead = none , style=dashed];
276 -> 1[style=dashed];

277 [label="EVAL with clause\nd(div(X91, X92), X93, X94) :- d(times(X91, power(X92, p(0))), X93, X94).\nand substitution\nX91 -> T79\nX92 -> T80\nT7 -> div(T79, T80)\nX93 -> div(T79, T80)\nT3 -> T82\nX94 -> T82\nT81 -> T82", fontsize=14, style = filled, fillcolor = lightblue];
41 -> 277 [arrowhead = none ];
277 -> 43;

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

279 [label="EVAL with clause\nd(power(X111, X112), X113, times(X112, times(X114, power(X111, p(X112))))) :- ','(isnumber(X112), d(X111, X113, X114)).\nand substitution\nX111 -> T95\nX112 -> T96\nT7 -> power(T95, T96)\nX113 -> power(T95, T96)\nX114 -> T98\nT3 -> times(T96, times(T98, power(T95, p(T96))))\nT97 -> T98", fontsize=14, style = filled, fillcolor = lightblue];
42 -> 279 [arrowhead = none ];
279 -> 45;

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

281 [label="INSTANCE with matching:\nT1 -> times(T79, power(T80, p(0)))\nT2 -> div(T79, T80)\nT3 -> T82", 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", fontsize=14, style = filled, fillcolor = violet];
45 -> 283 [arrowhead = none ];
283 -> 48;

284 [label="INSTANCE with matching:\nT12 -> T96", fontsize=14, style = filled, fillcolor = lightgrey];
47 -> 284 [arrowhead = none , style=dashed];
284 -> 16[style=dashed];

285 [label="INSTANCE with matching:\nT1 -> T95\nT2 -> power(T95, T96)\nT3 -> T98", 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(X289, X290), X291, X292) :- d(times(X289, power(X290, p(0))), X291, X292).\nand substitution\nX289 -> T309\nX290 -> T310\nT5 -> div(T309, T310)\nX291 -> div(T309, T310)\nT3 -> T312\nX292 -> T312\nT311 -> T312", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 287 [arrowhead = none ];
287 -> 84;

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

289 [label="BACKTRACK\nfor clause: d(X, X, 1)because of non-unification", fontsize=14, style = filled, fillcolor = white];
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(X147, X148, 0) :- isnumber(X147).\nand substitution\nT109 -> T125\nX147 -> T125\nT110 -> T126\nX148 -> times(T125, T126)\nT113 -> 0\nT114 -> T127", fontsize=14, style = filled, fillcolor = lightblue];
53 -> 292 [arrowhead = none ];
292 -> 55;

293 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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", fontsize=14, style = filled, fillcolor = violet];
55 -> 297 [arrowhead = none ];
297 -> 58;

298 [label="INSTANCE with matching:\nT12 -> T125", fontsize=14, style = filled, fillcolor = lightgrey];
57 -> 298 [arrowhead = none , style=dashed];
298 -> 16[style=dashed];

299 [label="INSTANCE with matching:\nT1 -> T126\nT2 -> times(T125, T126)\nT3 -> T127", fontsize=14, style = filled, fillcolor = lightgrey];
58 -> 299 [arrowhead = none , style=dashed];
299 -> 1[style=dashed];

300 [label="EVAL with clause\nd(times(X175, X176), X177, +(times(X178, X175), times(X179, X176))) :- ','(d(X175, X177, X179), d(X176, X177, X178)).\nand substitution\nX175 -> T154\nX176 -> T155\nT109 -> times(T154, T155)\nT110 -> T156\nX177 -> times(times(T154, T155), T156)\nX178 -> T160\nX179 -> T159\nT113 -> +(times(T160, T154), times(T159, T155))\nT158 -> T159\nT157 -> T160\nT114 -> T161", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 300 [arrowhead = none ];
300 -> 61;

301 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT159 is ground\nreplacements:\nT160 -> T171\nT161 -> T172", fontsize=14, style = filled, fillcolor = violet];
61 -> 305 [arrowhead = none ];
305 -> 64;

306 [label="INSTANCE with matching:\nT1 -> T154\nT2 -> times(times(T154, T155), T156)\nT3 -> T159", 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:\nT171 is ground\nreplacements:\nT172 -> T191", fontsize=14, style = filled, fillcolor = violet];
64 -> 308 [arrowhead = none ];
308 -> 66;

309 [label="INSTANCE with matching:\nT1 -> T155\nT2 -> times(times(T154, T155), T156)\nT3 -> T171", fontsize=14, style = filled, fillcolor = lightgrey];
65 -> 309 [arrowhead = none , style=dashed];
309 -> 1[style=dashed];

310 [label="INSTANCE with matching:\nT1 -> T156\nT2 -> times(times(T154, T155), T156)\nT3 -> T191", fontsize=14, style = filled, fillcolor = lightgrey];
66 -> 310 [arrowhead = none , style=dashed];
310 -> 1[style=dashed];

311 [label="EVAL with clause\nd(div(X221, X222), X223, X224) :- d(times(X221, power(X222, p(0))), X223, X224).\nand substitution\nX221 -> T226\nX222 -> T227\nT109 -> div(T226, T227)\nT110 -> T228\nX223 -> times(div(T226, T227), T228)\nT113 -> T230\nX224 -> T230\nT229 -> T230\nT114 -> T231", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 311 [arrowhead = none ];
311 -> 69;

312 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT230 is ground\nreplacements:\nT231 -> T239", fontsize=14, style = filled, fillcolor = violet];
69 -> 316 [arrowhead = none ];
316 -> 72;

317 [label="INSTANCE with matching:\nT1 -> times(T226, power(T227, p(0)))\nT2 -> times(div(T226, T227), T228)\nT3 -> T230", fontsize=14, style = filled, fillcolor = lightgrey];
71 -> 317 [arrowhead = none , style=dashed];
317 -> 1[style=dashed];

318 [label="INSTANCE with matching:\nT1 -> T228\nT2 -> times(div(T226, T227), T228)\nT3 -> T239", fontsize=14, style = filled, fillcolor = lightgrey];
72 -> 318 [arrowhead = none , style=dashed];
318 -> 1[style=dashed];

319 [label="EVAL with clause\nd(power(X257, X258), X259, times(X258, times(X260, power(X257, p(X258))))) :- ','(isnumber(X258), d(X257, X259, X260)).\nand substitution\nX257 -> T272\nX258 -> T273\nT109 -> power(T272, T273)\nT110 -> T274\nX259 -> times(power(T272, T273), T274)\nX260 -> T276\nT113 -> times(T273, times(T276, power(T272, p(T273))))\nT275 -> T276\nT114 -> T277", fontsize=14, style = filled, fillcolor = lightblue];
73 -> 319 [arrowhead = none ];
319 -> 75;

320 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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", fontsize=14, style = filled, fillcolor = violet];
75 -> 323 [arrowhead = none ];
323 -> 78;

324 [label="INSTANCE with matching:\nT12 -> T273", 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:\nT276 is ground\nreplacements:\nT277 -> T287", fontsize=14, style = filled, fillcolor = violet];
78 -> 326 [arrowhead = none ];
326 -> 80;

327 [label="INSTANCE with matching:\nT1 -> T272\nT2 -> times(power(T272, T273), T274)\nT3 -> T276", fontsize=14, style = filled, fillcolor = lightgrey];
79 -> 327 [arrowhead = none , style=dashed];
327 -> 1[style=dashed];

328 [label="INSTANCE with matching:\nT1 -> T274\nT2 -> times(power(T272, T273), T274)\nT3 -> T287", 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 = white];
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 = white];
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(X370, X371), X372, times(X371, times(X373, power(X370, p(X371))))) :- ','(isnumber(X371), d(X370, X372, X373)).\nand substitution\nX370 -> T367\nX371 -> T368\nT5 -> power(T367, T368)\nX372 -> power(T367, T368)\nX373 -> T370\nT3 -> times(T368, times(T370, power(T367, p(T368))))\nT369 -> T370", fontsize=14, style = filled, fillcolor = lightblue];
85 -> 332 [arrowhead = none ];
332 -> 102;

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

334 [label="BACKTRACK\nfor clause: d(X, X, 1)because of non-unification", fontsize=14, style = filled, fillcolor = white];
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(X306, X307, 0) :- isnumber(X306).\nand substitution\nT309 -> T323\nT310 -> T324\nX306 -> times(T323, power(T324, p(0)))\nX307 -> div(T323, T324)\nT312 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
88 -> 337 [arrowhead = none ];
337 -> 90;

338 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT125 -> times(T323, power(T324, p(0)))", fontsize=14, style = filled, fillcolor = lightgrey];
90 -> 341 [arrowhead = none , style=dashed];
341 -> 57[style=dashed];

342 [label="EVAL with clause\nd(times(X332, X333), X334, +(times(X335, X332), times(X336, X333))) :- ','(d(X332, X334, X336), d(X333, X334, X335)).\nand substitution\nT309 -> T341\nX332 -> T341\nT310 -> T342\nX333 -> power(T342, p(0))\nX334 -> div(T341, T342)\nX335 -> T346\nX336 -> T345\nT312 -> +(times(T346, T341), times(T345, power(T342, p(0))))\nT344 -> T345\nT343 -> T346", fontsize=14, style = filled, fillcolor = lightblue];
92 -> 342 [arrowhead = none ];
342 -> 94;

343 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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 = white];
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:\nT345 is ground\nreplacements:\nT346 -> T353", fontsize=14, style = filled, fillcolor = violet];
94 -> 346 [arrowhead = none ];
346 -> 97;

347 [label="INSTANCE with matching:\nT1 -> T341\nT2 -> div(T341, T342)\nT3 -> T345", fontsize=14, style = filled, fillcolor = lightgrey];
96 -> 347 [arrowhead = none , style=dashed];
347 -> 1[style=dashed];

348 [label="INSTANCE with matching:\nT1 -> power(T342, p(0))\nT2 -> div(T341, T342)\nT3 -> T353", 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 = white];
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 = white];
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 substitution\nT368 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 355 [arrowhead = none ];
355 -> 107;

356 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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 -> T367\nT2 -> power(T367, 0)\nT3 -> T370", fontsize=14, style = filled, fillcolor = lightgrey];
107 -> 359 [arrowhead = none , style=dashed];
359 -> 1[style=dashed];

360 [label="EVAL with clause\nisnumber(s(X386)) :- isnumber(X386).\nand substitution\nX386 -> T378\nT368 -> s(T378)", fontsize=14, style = filled, fillcolor = lightblue];
109 -> 360 [arrowhead = none ];
360 -> 111;

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

362 [label="EVAL with clause\nisnumber(p(X394)) :- isnumber(X394).\nand substitution\nX394 -> T387\nT368 -> p(T387)", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 362 [arrowhead = none ];
362 -> 115;

363 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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", fontsize=14, style = filled, fillcolor = violet];
111 -> 365 [arrowhead = none ];
365 -> 114;

366 [label="INSTANCE with matching:\nT12 -> T378", fontsize=14, style = filled, fillcolor = lightgrey];
113 -> 366 [arrowhead = none , style=dashed];
366 -> 16[style=dashed];

367 [label="INSTANCE with matching:\nT1 -> T367\nT2 -> power(T367, s(T378))\nT3 -> T370", 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", fontsize=14, style = filled, fillcolor = violet];
115 -> 369 [arrowhead = none ];
369 -> 118;

370 [label="INSTANCE with matching:\nT12 -> T387", fontsize=14, style = filled, fillcolor = lightgrey];
117 -> 370 [arrowhead = none , style=dashed];
370 -> 16[style=dashed];

371 [label="INSTANCE with matching:\nT1 -> T367\nT2 -> power(T367, p(T387))\nT3 -> T370", 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(X503, X504), X505, +(times(X506, X503), times(X507, X504))) :- ','(d(X503, X505, X507), d(X504, X505, X506)).\nand substitution\nX503 -> T489\nX504 -> T490\nT1 -> times(T489, T490)\nT2 -> T491\nX505 -> T491\nX506 -> T495\nX507 -> T494\nT3 -> +(times(T495, T489), times(T494, T490))\nT493 -> T494\nT492 -> T495", fontsize=14, style = filled, fillcolor = lightblue];
120 -> 373 [arrowhead = none ];
373 -> 150;

374 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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 substitution\nT396 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 377 [arrowhead = none ];
377 -> 124;

378 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X410)) :- isnumber(X410).\nand substitution\nX410 -> T402\nT396 -> s(T402)", fontsize=14, style = filled, fillcolor = lightblue];
127 -> 382 [arrowhead = none ];
382 -> 129;

383 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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 -> T402", fontsize=14, style = filled, fillcolor = lightgrey];
129 -> 386 [arrowhead = none , style=dashed];
386 -> 16[style=dashed];

387 [label="EVAL with clause\nisnumber(p(X416)) :- isnumber(X416).\nand substitution\nX416 -> T407\nT396 -> p(T407)", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 387 [arrowhead = none ];
387 -> 133;

388 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT402 -> T407", fontsize=14, style = filled, fillcolor = lightgrey];
133 -> 390 [arrowhead = none , style=dashed];
390 -> 129[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(X438, X439), X440, +(times(X441, X438), times(X442, X439))) :- ','(d(X438, X440, X442), d(X439, X440, X441)).\nand substitution\nX438 -> T428\nX439 -> T429\nT396 -> times(T428, T429)\nT397 -> T430\nX440 -> T430\nX441 -> T434\nX442 -> T433\nT3 -> +(times(T434, T428), times(T433, T429))\nT432 -> T433\nT431 -> T434", fontsize=14, style = filled, fillcolor = lightblue];
136 -> 393 [arrowhead = none ];
393 -> 138;

394 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT433 is ground\nreplacements:\nT434 -> T437\nT3 -> T438\nX3 -> T439", fontsize=14, style = filled, fillcolor = violet];
138 -> 398 [arrowhead = none ];
398 -> 141;

399 [label="INSTANCE with matching:\nT1 -> T428\nT2 -> T430\nT3 -> T433", fontsize=14, style = filled, fillcolor = lightgrey];
140 -> 399 [arrowhead = none , style=dashed];
399 -> 1[style=dashed];

400 [label="INSTANCE with matching:\nT1 -> T429\nT2 -> T430\nT3 -> T437", fontsize=14, style = filled, fillcolor = lightgrey];
141 -> 400 [arrowhead = none , style=dashed];
400 -> 1[style=dashed];

401 [label="EVAL with clause\nd(div(X470, X471), X472, X473) :- d(times(X470, power(X471, p(0))), X472, X473).\nand substitution\nX470 -> T460\nX471 -> T461\nT396 -> div(T460, T461)\nT397 -> T462\nX472 -> T462\nT3 -> T464\nX473 -> T464\nT463 -> T464", fontsize=14, style = filled, fillcolor = lightblue];
142 -> 401 [arrowhead = none ];
401 -> 144;

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

403 [label="EVAL with clause\nd(power(X488, X489), X490, times(X489, times(X491, power(X488, p(X489))))) :- ','(isnumber(X489), d(X488, X490, X491)).\nand substitution\nX488 -> T477\nX489 -> T478\nT396 -> power(T477, T478)\nT397 -> T479\nX490 -> T479\nX491 -> T481\nT3 -> times(T478, times(T481, power(T477, p(T478))))\nT480 -> T481", fontsize=14, style = filled, fillcolor = lightblue];
143 -> 403 [arrowhead = none ];
403 -> 146;

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

405 [label="INSTANCE with matching:\nT1 -> times(T460, power(T461, p(0)))\nT2 -> T462\nT3 -> T464", 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", fontsize=14, style = filled, fillcolor = violet];
146 -> 407 [arrowhead = none ];
407 -> 149;

408 [label="INSTANCE with matching:\nT402 -> T478", fontsize=14, style = filled, fillcolor = lightgrey];
148 -> 408 [arrowhead = none , style=dashed];
408 -> 129[style=dashed];

409 [label="INSTANCE with matching:\nT1 -> T477\nT2 -> T479\nT3 -> T481", 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(X647, X648), X649, X650) :- d(times(X647, power(X648, p(0))), X649, X650).\nand substitution\nX647 -> T634\nX648 -> T635\nT1 -> div(T634, T635)\nT2 -> T636\nX649 -> T636\nT3 -> T638\nX650 -> T638\nT637 -> T638", fontsize=14, style = filled, fillcolor = lightblue];
151 -> 411 [arrowhead = none ];
411 -> 188;

412 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X517, X517, 1).\nand substitution\nT489 -> T500\nX517 -> T500\nT491 -> T500\nT494 -> 1\nT495 -> T501", fontsize=14, style = filled, fillcolor = lightblue];
153 -> 415 [arrowhead = none ];
415 -> 155;

416 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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 -> T490\nT2 -> T500\nT3 -> T501", fontsize=14, style = filled, fillcolor = lightgrey];
155 -> 419 [arrowhead = none , style=dashed];
419 -> 1[style=dashed];

420 [label="EVAL with clause\nd(X529, X530, 0) :- isnumber(X529).\nand substitution\nT489 -> T512\nX529 -> T512\nT491 -> T513\nX530 -> T513\nT494 -> 0\nT495 -> T514", fontsize=14, style = filled, fillcolor = lightblue];
157 -> 420 [arrowhead = none ];
420 -> 159;

421 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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", fontsize=14, style = filled, fillcolor = violet];
159 -> 425 [arrowhead = none ];
425 -> 162;

426 [label="INSTANCE with matching:\nT402 -> T512", fontsize=14, style = filled, fillcolor = lightgrey];
161 -> 426 [arrowhead = none , style=dashed];
426 -> 129[style=dashed];

427 [label="INSTANCE with matching:\nT1 -> T490\nT2 -> T513\nT3 -> T514", fontsize=14, style = filled, fillcolor = lightgrey];
162 -> 427 [arrowhead = none , style=dashed];
427 -> 1[style=dashed];

428 [label="EVAL with clause\nd(times(X555, X556), X557, +(times(X558, X555), times(X559, X556))) :- ','(d(X555, X557, X559), d(X556, X557, X558)).\nand substitution\nX555 -> T537\nX556 -> T538\nT489 -> times(T537, T538)\nT491 -> T539\nX557 -> T539\nX558 -> T543\nX559 -> T542\nT494 -> +(times(T543, T537), times(T542, T538))\nT541 -> T542\nT540 -> T543\nT495 -> T544", fontsize=14, style = filled, fillcolor = lightblue];
163 -> 428 [arrowhead = none ];
428 -> 165;

429 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT542 is ground\nreplacements:\nT543 -> T547\nT544 -> T548\nT3 -> T549\nX3 -> T550", fontsize=14, style = filled, fillcolor = violet];
165 -> 433 [arrowhead = none ];
433 -> 168;

434 [label="INSTANCE with matching:\nT1 -> T537\nT2 -> T539\nT3 -> T542", 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:\nT547 is ground\nreplacements:\nT548 -> T555\nT537 -> T556\nT549 -> T557\nT550 -> T558", fontsize=14, style = filled, fillcolor = violet];
168 -> 436 [arrowhead = none ];
436 -> 170;

437 [label="INSTANCE with matching:\nT1 -> T538\nT2 -> T539\nT3 -> T547", fontsize=14, style = filled, fillcolor = lightgrey];
169 -> 437 [arrowhead = none , style=dashed];
437 -> 1[style=dashed];

438 [label="INSTANCE with matching:\nT1 -> T490\nT2 -> T539\nT3 -> T555", fontsize=14, style = filled, fillcolor = lightgrey];
170 -> 438 [arrowhead = none , style=dashed];
438 -> 1[style=dashed];

439 [label="EVAL with clause\nd(div(X591, X592), X593, X594) :- d(times(X591, power(X592, p(0))), X593, X594).\nand substitution\nX591 -> T579\nX592 -> T580\nT489 -> div(T579, T580)\nT491 -> T581\nX593 -> T581\nT494 -> T583\nX594 -> T583\nT582 -> T583\nT495 -> T584", fontsize=14, style = filled, fillcolor = lightblue];
171 -> 439 [arrowhead = none ];
439 -> 173;

440 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT583 is ground\nreplacements:\nT584 -> T589\nT3 -> T590\nX3 -> T591", fontsize=14, style = filled, fillcolor = violet];
173 -> 444 [arrowhead = none ];
444 -> 176;

445 [label="INSTANCE with matching:\nT1 -> times(T579, power(T580, p(0)))\nT2 -> T581\nT3 -> T583", fontsize=14, style = filled, fillcolor = lightgrey];
175 -> 445 [arrowhead = none , style=dashed];
445 -> 1[style=dashed];

446 [label="INSTANCE with matching:\nT1 -> T490\nT2 -> T581\nT3 -> T589", fontsize=14, style = filled, fillcolor = lightgrey];
176 -> 446 [arrowhead = none , style=dashed];
446 -> 1[style=dashed];

447 [label="EVAL with clause\nd(power(X621, X622), X623, times(X622, times(X624, power(X621, p(X622))))) :- ','(isnumber(X622), d(X621, X623, X624)).\nand substitution\nX621 -> T614\nX622 -> T615\nT489 -> power(T614, T615)\nT491 -> T616\nX623 -> T616\nX624 -> T618\nT494 -> times(T615, times(T618, power(T614, p(T615))))\nT617 -> T618\nT495 -> T619", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 447 [arrowhead = none ];
447 -> 179;

448 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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", fontsize=14, style = filled, fillcolor = violet];
179 -> 451 [arrowhead = none ];
451 -> 182;

452 [label="INSTANCE with matching:\nT402 -> T615", fontsize=14, style = filled, fillcolor = lightgrey];
181 -> 452 [arrowhead = none , style=dashed];
452 -> 129[style=dashed];

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

454 [label="SPLIT 2\nnew knowledge:\nT618 is ground\nreplacements:\nT619 -> T622\nT615 -> T623\nT3 -> T624\nX3 -> T625", fontsize=14, style = filled, fillcolor = violet];
182 -> 454 [arrowhead = none ];
454 -> 184;

455 [label="INSTANCE with matching:\nT1 -> T614\nT2 -> T616\nT3 -> T618", fontsize=14, style = filled, fillcolor = lightgrey];
183 -> 455 [arrowhead = none , style=dashed];
455 -> 1[style=dashed];

456 [label="INSTANCE with matching:\nT1 -> T490\nT2 -> T616\nT3 -> T622", 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 = white];
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 = white];
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(X727, X728), X729, times(X728, times(X730, power(X727, p(X728))))) :- ','(isnumber(X728), d(X727, X729, X730)).\nand substitution\nX727 -> T704\nX728 -> T705\nT1 -> power(T704, T705)\nT2 -> T706\nX729 -> T706\nX730 -> T708\nT3 -> times(T705, times(T708, power(T704, p(T705))))\nT707 -> T708", fontsize=14, style = filled, fillcolor = lightblue];
189 -> 460 [arrowhead = none ];
460 -> 210;

461 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X659, X659, 1).\nand substitution\nT634 -> T647\nT635 -> T648\nX659 -> times(T647, power(T648, p(0)))\nT636 -> times(T647, power(T648, p(0)))\nT638 -> 1", fontsize=14, style = filled, fillcolor = lightblue];
191 -> 464 [arrowhead = none ];
464 -> 193;

465 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X669, X670, 0) :- isnumber(X669).\nand substitution\nT634 -> T661\nT635 -> T662\nX669 -> times(T661, power(T662, p(0)))\nT636 -> T663\nX670 -> T663\nT638 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
196 -> 469 [arrowhead = none ];
469 -> 198;

470 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT402 -> times(T661, power(T662, p(0)))", fontsize=14, style = filled, fillcolor = lightgrey];
198 -> 473 [arrowhead = none , style=dashed];
473 -> 129[style=dashed];

474 [label="EVAL with clause\nd(times(X695, X696), X697, +(times(X698, X695), times(X699, X696))) :- ','(d(X695, X697, X699), d(X696, X697, X698)).\nand substitution\nT634 -> T684\nX695 -> T684\nT635 -> T685\nX696 -> power(T685, p(0))\nT636 -> T686\nX697 -> T686\nX698 -> T690\nX699 -> T689\nT638 -> +(times(T690, T684), times(T689, power(T685, p(0))))\nT688 -> T689\nT687 -> T690", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 474 [arrowhead = none ];
474 -> 202;

475 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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 = white];
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:\nT689 is ground\nreplacements:\nT690 -> T693\nT3 -> T694\nX3 -> T695", fontsize=14, style = filled, fillcolor = violet];
202 -> 478 [arrowhead = none ];
478 -> 205;

479 [label="INSTANCE with matching:\nT1 -> T684\nT2 -> T686\nT3 -> T689", fontsize=14, style = filled, fillcolor = lightgrey];
204 -> 479 [arrowhead = none , style=dashed];
479 -> 1[style=dashed];

480 [label="INSTANCE with matching:\nT1 -> power(T685, p(0))\nT2 -> T686\nT3 -> T693", 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 = white];
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 = white];
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 substitution\nT705 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
213 -> 487 [arrowhead = none ];
487 -> 215;

488 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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 -> T704\nT2 -> T706\nT3 -> T708", fontsize=14, style = filled, fillcolor = lightgrey];
215 -> 491 [arrowhead = none , style=dashed];
491 -> 1[style=dashed];

492 [label="EVAL with clause\nisnumber(s(X741)) :- isnumber(X741).\nand substitution\nX741 -> T715\nT705 -> s(T715)", fontsize=14, style = filled, fillcolor = lightblue];
217 -> 492 [arrowhead = none ];
492 -> 219;

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

494 [label="EVAL with clause\nisnumber(p(X747)) :- isnumber(X747).\nand substitution\nX747 -> T720\nT705 -> p(T720)", fontsize=14, style = filled, fillcolor = lightblue];
218 -> 494 [arrowhead = none ];
494 -> 223;

495 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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", fontsize=14, style = filled, fillcolor = violet];
219 -> 497 [arrowhead = none ];
497 -> 222;

498 [label="INSTANCE with matching:\nT402 -> T715", fontsize=14, style = filled, fillcolor = lightgrey];
221 -> 498 [arrowhead = none , style=dashed];
498 -> 129[style=dashed];

499 [label="INSTANCE with matching:\nT1 -> T704\nT2 -> T706\nT3 -> T708", 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", fontsize=14, style = filled, fillcolor = violet];
223 -> 501 [arrowhead = none ];
501 -> 226;

502 [label="INSTANCE with matching:\nT402 -> T720", fontsize=14, style = filled, fillcolor = lightgrey];
225 -> 502 [arrowhead = none , style=dashed];
502 -> 129[style=dashed];

503 [label="INSTANCE with matching:\nT1 -> T704\nT2 -> T706\nT3 -> T708", fontsize=14, style = filled, fillcolor = lightgrey];
226 -> 503 [arrowhead = none , style=dashed];
503 -> 1[style=dashed];

}

(2) Obligation:

Clauses:

isnumber16(0).
isnumber16(s(T17)) :- isnumber16(T17).
isnumber16(p(T20)) :- isnumber16(T20).
d1(T5, T5, 1).
d1(0, 0, 0).
d1(s(T12), s(T12), 0) :- isnumber16(T12).
d1(p(T25), p(T25), 0) :- isnumber16(T25).
d1(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) :- d1(T42, times(T42, T43), T46).
d1(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43))) :- ','(d1(T42, times(T42, T43), T46), d1(T43, times(T42, T43), T54)).
d1(div(T79, T80), div(T79, T80), T82) :- d1(times(T79, power(T80, p(0))), div(T79, T80), T82).
d1(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) :- isnumber16(T96).
d1(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) :- ','(isnumber16(T96), d1(T95, power(T95, T96), T98)).
d1(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) :- isnumber16(T125).
d1(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) :- ','(isnumber16(T125), d1(T126, times(T125, T126), T127)).
d1(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) :- d1(T154, times(times(T154, T155), T156), T159).
d1(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) :- ','(d1(T154, times(times(T154, T155), T156), T159), d1(T155, times(times(T154, T155), T156), T171)).
d1(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) :- ','(d1(T154, times(times(T154, T155), T156), T159), ','(d1(T155, times(times(T154, T155), T156), T171), d1(T156, times(times(T154, T155), T156), T191))).
d1(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) :- d1(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230).
d1(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228))) :- ','(d1(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230), d1(T228, times(div(T226, T227), T228), T239)).
d1(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) :- isnumber16(T273).
d1(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) :- ','(isnumber16(T273), d1(T272, times(power(T272, T273), T274), T276)).
d1(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) :- ','(isnumber16(T273), ','(d1(T272, times(power(T272, T273), T274), T276), d1(T274, times(power(T272, T273), T274), T287))).
d1(div(T323, T324), div(T323, T324), 0) :- isnumber16(times(T323, power(T324, p(0)))).
d1(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) :- d1(T341, div(T341, T342), T345).
d1(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0))))) :- ','(d1(T341, div(T341, T342), T345), d1(power(T342, p(0)), div(T341, T342), T353)).
d1(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) :- d1(T367, power(T367, 0), T370).
d1(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) :- isnumber16(T378).
d1(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) :- ','(isnumber16(T378), d1(T367, power(T367, s(T378)), T370)).
d1(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) :- isnumber16(T387).
d1(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) :- ','(isnumber16(T387), d1(T367, power(T367, p(T387)), T370)).
d1(0, T397, 0).
d1(s(T402), T397, 0) :- isnumber16(T402).
d1(p(T407), T397, 0) :- isnumber16(T407).
d1(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) :- d1(T428, T430, T433).
d1(times(T428, T429), T430, +(times(T437, T428), times(T433, T429))) :- ','(d1(T428, T430, T433), d1(T429, T430, T437)).
d1(div(T460, T461), T462, T464) :- d1(times(T460, power(T461, p(0))), T462, T464).
d1(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) :- isnumber16(T478).
d1(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) :- ','(isnumber16(T478), d1(T477, T479, T481)).
d1(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) :- d1(T490, T500, T501).
d1(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) :- isnumber16(T512).
d1(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) :- ','(isnumber16(T512), d1(T490, T513, T514)).
d1(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) :- d1(T537, T539, T542).
d1(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490))) :- ','(d1(T537, T539, T542), d1(T538, T539, T547)).
d1(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490))) :- ','(d1(T556, T539, T542), ','(d1(T538, T539, T547), d1(T490, T539, T555))).
d1(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) :- d1(times(T579, power(T580, p(0))), T581, T583).
d1(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490))) :- ','(d1(times(T579, power(T580, p(0))), T581, T583), d1(T490, T581, T589)).
d1(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) :- isnumber16(T615).
d1(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) :- ','(isnumber16(T615), d1(T614, T616, T618)).
d1(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490))) :- ','(isnumber16(T623), ','(d1(T614, T616, T618), d1(T490, T616, T622))).
d1(div(T647, T648), times(T647, power(T648, p(0))), 1).
d1(div(T661, T662), T663, 0) :- isnumber16(times(T661, power(T662, p(0)))).
d1(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) :- d1(T684, T686, T689).
d1(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0))))) :- ','(d1(T684, T686, T689), d1(power(T685, p(0)), T686, T693)).
d1(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) :- d1(T704, T706, T708).
d1(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) :- isnumber16(T715).
d1(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) :- ','(isnumber16(T715), d1(T704, T706, T708)).
d1(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) :- isnumber16(T720).
d1(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) :- ','(isnumber16(T720), d1(T704, T706, T708)).

Queries:

d1(g,g,a).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
d1_in: (b,b,f)
isnumber16_in: (b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

d1_in_gga(T5, T5, 1) → d1_out_gga(T5, T5, 1)
d1_in_gga(0, 0, 0) → d1_out_gga(0, 0, 0)
d1_in_gga(s(T12), s(T12), 0) → U3_gga(T12, isnumber16_in_g(T12))
isnumber16_in_g(0) → isnumber16_out_g(0)
isnumber16_in_g(s(T17)) → U1_g(T17, isnumber16_in_g(T17))
isnumber16_in_g(p(T20)) → U2_g(T20, isnumber16_in_g(T20))
U2_g(T20, isnumber16_out_g(T20)) → isnumber16_out_g(p(T20))
U1_g(T17, isnumber16_out_g(T17)) → isnumber16_out_g(s(T17))
U3_gga(T12, isnumber16_out_g(T12)) → d1_out_gga(s(T12), s(T12), 0)
d1_in_gga(p(T25), p(T25), 0) → U4_gga(T25, isnumber16_in_g(T25))
U4_gga(T25, isnumber16_out_g(T25)) → d1_out_gga(p(T25), p(T25), 0)
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) → U5_gga(T42, T43, T47, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43))) → U6_gga(T42, T43, T54, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(div(T79, T80), div(T79, T80), T82) → U8_gga(T79, T80, T82, d1_in_gga(times(T79, power(T80, p(0))), div(T79, T80), T82))
d1_in_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) → U9_gga(T95, T96, T98, isnumber16_in_g(T96))
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → U10_gga(T95, T96, T98, d1_in_gga(T95, power(T95, T96), T98))
d1_in_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) → U11_gga(T125, T126, T127, isnumber16_in_g(T125))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → U12_gga(T125, T126, T127, d1_in_gga(T126, times(T125, T126), T127))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) → U13_gga(T154, T155, T156, T161, T160, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U14_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U16_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) → U19_gga(T226, T227, T228, T231, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228))) → U20_gga(T226, T227, T228, T239, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U22_gga(T272, T273, T274, T277, T276, isnumber16_in_g(T273))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → U23_gga(T272, T273, T274, T277, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U24_gga(T272, T273, T274, T287, T276, isnumber16_in_g(T273))
U24_gga(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → U25_gga(T272, T273, T274, T287, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
d1_in_gga(div(T323, T324), div(T323, T324), 0) → U27_gga(T323, T324, isnumber16_in_g(times(T323, power(T324, p(0)))))
U27_gga(T323, T324, isnumber16_out_g(times(T323, power(T324, p(0))))) → d1_out_gga(div(T323, T324), div(T323, T324), 0)
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) → U28_gga(T341, T342, T346, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0))))) → U29_gga(T341, T342, T353, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) → U31_gga(T367, T370, d1_in_gga(T367, power(T367, 0), T370))
d1_in_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) → U32_gga(T367, T378, T370, isnumber16_in_g(T378))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → U33_gga(T367, T378, T370, d1_in_gga(T367, power(T367, s(T378)), T370))
d1_in_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) → U34_gga(T367, T387, T370, isnumber16_in_g(T387))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → U35_gga(T367, T387, T370, d1_in_gga(T367, power(T367, p(T387)), T370))
d1_in_gga(0, T397, 0) → d1_out_gga(0, T397, 0)
d1_in_gga(s(T402), T397, 0) → U36_gga(T402, T397, isnumber16_in_g(T402))
U36_gga(T402, T397, isnumber16_out_g(T402)) → d1_out_gga(s(T402), T397, 0)
d1_in_gga(p(T407), T397, 0) → U37_gga(T407, T397, isnumber16_in_g(T407))
U37_gga(T407, T397, isnumber16_out_g(T407)) → d1_out_gga(p(T407), T397, 0)
d1_in_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) → U38_gga(T428, T429, T430, T434, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429))) → U39_gga(T428, T429, T430, T437, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(div(T460, T461), T462, T464) → U41_gga(T460, T461, T462, T464, d1_in_gga(times(T460, power(T461, p(0))), T462, T464))
d1_in_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) → U42_gga(T477, T478, T479, T481, isnumber16_in_g(T478))
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → U43_gga(T477, T478, T479, T481, d1_in_gga(T477, T479, T481))
d1_in_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) → U44_gga(T500, T490, T501, d1_in_gga(T490, T500, T501))
d1_in_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) → U45_gga(T512, T490, T513, T514, isnumber16_in_g(T512))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → U46_gga(T512, T490, T513, T514, d1_in_gga(T490, T513, T514))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) → U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490))) → U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490))) → U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T556, T539, T542))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) → U53_gga(T579, T580, T490, T581, T584, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490))) → U54_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) → U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_in_g(T615))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → U57_gga(T614, T615, T490, T616, T619, T618, d1_in_gga(T614, T616, T618))
d1_in_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490))) → U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_in_g(T623))
U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → U59_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T614, T616, T618))
d1_in_gga(div(T647, T648), times(T647, power(T648, p(0))), 1) → d1_out_gga(div(T647, T648), times(T647, power(T648, p(0))), 1)
d1_in_gga(div(T661, T662), T663, 0) → U61_gga(T661, T662, T663, isnumber16_in_g(times(T661, power(T662, p(0)))))
U61_gga(T661, T662, T663, isnumber16_out_g(times(T661, power(T662, p(0))))) → d1_out_gga(div(T661, T662), T663, 0)
d1_in_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) → U62_gga(T684, T685, T686, T690, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0))))) → U63_gga(T684, T685, T686, T693, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) → U65_gga(T704, T706, T708, d1_in_gga(T704, T706, T708))
d1_in_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) → U66_gga(T704, T715, T706, T708, isnumber16_in_g(T715))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → U67_gga(T704, T715, T706, T708, d1_in_gga(T704, T706, T708))
d1_in_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) → U68_gga(T704, T720, T706, T708, isnumber16_in_g(T720))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → U69_gga(T704, T720, T706, T708, d1_in_gga(T704, T706, T708))
U69_gga(T704, T720, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U67_gga(T704, T715, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U65_gga(T704, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0)))))
U63_gga(T684, T685, T686, T693, T689, d1_out_gga(T684, T686, T689)) → U64_gga(T684, T685, T686, T693, T689, d1_in_gga(power(T685, p(0)), T686, T693))
U64_gga(T684, T685, T686, T693, T689, d1_out_gga(power(T685, p(0)), T686, T693)) → d1_out_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0)))))
U62_gga(T684, T685, T686, T690, T689, d1_out_gga(T684, T686, T689)) → d1_out_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0)))))
U59_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T614, T616, T618)) → U60_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T490, T616, T622))
U60_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T490, T616, T622)) → d1_out_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490)))
U57_gga(T614, T615, T490, T616, T619, T618, d1_out_gga(T614, T616, T618)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U54_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → U55_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(T490, T581, T589))
U55_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(T490, T581, T589)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490)))
U53_gga(T579, T580, T490, T581, T584, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490)))
U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T538, T539, T547))
U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T538, T539, T547)) → U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T490, T539, T555))
U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T490, T539, T555)) → d1_out_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490)))
U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T537, T539, T542)) → U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T538, T539, T547))
U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T538, T539, T547)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490)))
U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_out_gga(T537, T539, T542)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490)))
U46_gga(T512, T490, T513, T514, d1_out_gga(T490, T513, T514)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U44_gga(T500, T490, T501, d1_out_gga(T490, T500, T501)) → d1_out_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490)))
U43_gga(T477, T478, T479, T481, d1_out_gga(T477, T479, T481)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U41_gga(T460, T461, T462, T464, d1_out_gga(times(T460, power(T461, p(0))), T462, T464)) → d1_out_gga(div(T460, T461), T462, T464)
U39_gga(T428, T429, T430, T437, T433, d1_out_gga(T428, T430, T433)) → U40_gga(T428, T429, T430, T437, T433, d1_in_gga(T429, T430, T437))
U40_gga(T428, T429, T430, T437, T433, d1_out_gga(T429, T430, T437)) → d1_out_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429)))
U38_gga(T428, T429, T430, T434, T433, d1_out_gga(T428, T430, T433)) → d1_out_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429)))
U35_gga(T367, T387, T370, d1_out_gga(T367, power(T367, p(T387)), T370)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U33_gga(T367, T378, T370, d1_out_gga(T367, power(T367, s(T378)), T370)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U31_gga(T367, T370, d1_out_gga(T367, power(T367, 0), T370)) → d1_out_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0)))))
U29_gga(T341, T342, T353, T345, d1_out_gga(T341, div(T341, T342), T345)) → U30_gga(T341, T342, T353, T345, d1_in_gga(power(T342, p(0)), div(T341, T342), T353))
U30_gga(T341, T342, T353, T345, d1_out_gga(power(T342, p(0)), div(T341, T342), T353)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0)))))
U28_gga(T341, T342, T346, T345, d1_out_gga(T341, div(T341, T342), T345)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0)))))
U25_gga(T272, T273, T274, T287, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → U26_gga(T272, T273, T274, T287, T276, d1_in_gga(T274, times(power(T272, T273), T274), T287))
U26_gga(T272, T273, T274, T287, T276, d1_out_gga(T274, times(power(T272, T273), T274), T287)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U23_gga(T272, T273, T274, T277, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U20_gga(T226, T227, T228, T239, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → U21_gga(T226, T227, T228, T239, T230, d1_in_gga(T228, times(div(T226, T227), T228), T239))
U21_gga(T226, T227, T228, T239, T230, d1_out_gga(T228, times(div(T226, T227), T228), T239)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228)))
U19_gga(T226, T227, T228, T231, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228)))
U16_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U17_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U17_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → U18_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T156, times(times(T154, T155), T156), T191))
U18_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T156, times(times(T154, T155), T156), T191)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U14_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U15_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U15_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U13_gga(T154, T155, T156, T161, T160, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156)))
U12_gga(T125, T126, T127, d1_out_gga(T126, times(T125, T126), T127)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U10_gga(T95, T96, T98, d1_out_gga(T95, power(T95, T96), T98)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U8_gga(T79, T80, T82, d1_out_gga(times(T79, power(T80, p(0))), div(T79, T80), T82)) → d1_out_gga(div(T79, T80), div(T79, T80), T82)
U6_gga(T42, T43, T54, T46, d1_out_gga(T42, times(T42, T43), T46)) → U7_gga(T42, T43, T54, T46, d1_in_gga(T43, times(T42, T43), T54))
U7_gga(T42, T43, T54, T46, d1_out_gga(T43, times(T42, T43), T54)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43)))
U5_gga(T42, T43, T47, T46, d1_out_gga(T42, times(T42, T43), T46)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43)))

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

d1_in_gga(T5, T5, 1) → d1_out_gga(T5, T5, 1)
d1_in_gga(0, 0, 0) → d1_out_gga(0, 0, 0)
d1_in_gga(s(T12), s(T12), 0) → U3_gga(T12, isnumber16_in_g(T12))
isnumber16_in_g(0) → isnumber16_out_g(0)
isnumber16_in_g(s(T17)) → U1_g(T17, isnumber16_in_g(T17))
isnumber16_in_g(p(T20)) → U2_g(T20, isnumber16_in_g(T20))
U2_g(T20, isnumber16_out_g(T20)) → isnumber16_out_g(p(T20))
U1_g(T17, isnumber16_out_g(T17)) → isnumber16_out_g(s(T17))
U3_gga(T12, isnumber16_out_g(T12)) → d1_out_gga(s(T12), s(T12), 0)
d1_in_gga(p(T25), p(T25), 0) → U4_gga(T25, isnumber16_in_g(T25))
U4_gga(T25, isnumber16_out_g(T25)) → d1_out_gga(p(T25), p(T25), 0)
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) → U5_gga(T42, T43, T47, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43))) → U6_gga(T42, T43, T54, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(div(T79, T80), div(T79, T80), T82) → U8_gga(T79, T80, T82, d1_in_gga(times(T79, power(T80, p(0))), div(T79, T80), T82))
d1_in_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) → U9_gga(T95, T96, T98, isnumber16_in_g(T96))
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → U10_gga(T95, T96, T98, d1_in_gga(T95, power(T95, T96), T98))
d1_in_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) → U11_gga(T125, T126, T127, isnumber16_in_g(T125))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → U12_gga(T125, T126, T127, d1_in_gga(T126, times(T125, T126), T127))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) → U13_gga(T154, T155, T156, T161, T160, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U14_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U16_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) → U19_gga(T226, T227, T228, T231, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228))) → U20_gga(T226, T227, T228, T239, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U22_gga(T272, T273, T274, T277, T276, isnumber16_in_g(T273))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → U23_gga(T272, T273, T274, T277, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U24_gga(T272, T273, T274, T287, T276, isnumber16_in_g(T273))
U24_gga(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → U25_gga(T272, T273, T274, T287, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
d1_in_gga(div(T323, T324), div(T323, T324), 0) → U27_gga(T323, T324, isnumber16_in_g(times(T323, power(T324, p(0)))))
U27_gga(T323, T324, isnumber16_out_g(times(T323, power(T324, p(0))))) → d1_out_gga(div(T323, T324), div(T323, T324), 0)
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) → U28_gga(T341, T342, T346, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0))))) → U29_gga(T341, T342, T353, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) → U31_gga(T367, T370, d1_in_gga(T367, power(T367, 0), T370))
d1_in_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) → U32_gga(T367, T378, T370, isnumber16_in_g(T378))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → U33_gga(T367, T378, T370, d1_in_gga(T367, power(T367, s(T378)), T370))
d1_in_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) → U34_gga(T367, T387, T370, isnumber16_in_g(T387))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → U35_gga(T367, T387, T370, d1_in_gga(T367, power(T367, p(T387)), T370))
d1_in_gga(0, T397, 0) → d1_out_gga(0, T397, 0)
d1_in_gga(s(T402), T397, 0) → U36_gga(T402, T397, isnumber16_in_g(T402))
U36_gga(T402, T397, isnumber16_out_g(T402)) → d1_out_gga(s(T402), T397, 0)
d1_in_gga(p(T407), T397, 0) → U37_gga(T407, T397, isnumber16_in_g(T407))
U37_gga(T407, T397, isnumber16_out_g(T407)) → d1_out_gga(p(T407), T397, 0)
d1_in_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) → U38_gga(T428, T429, T430, T434, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429))) → U39_gga(T428, T429, T430, T437, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(div(T460, T461), T462, T464) → U41_gga(T460, T461, T462, T464, d1_in_gga(times(T460, power(T461, p(0))), T462, T464))
d1_in_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) → U42_gga(T477, T478, T479, T481, isnumber16_in_g(T478))
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → U43_gga(T477, T478, T479, T481, d1_in_gga(T477, T479, T481))
d1_in_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) → U44_gga(T500, T490, T501, d1_in_gga(T490, T500, T501))
d1_in_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) → U45_gga(T512, T490, T513, T514, isnumber16_in_g(T512))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → U46_gga(T512, T490, T513, T514, d1_in_gga(T490, T513, T514))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) → U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490))) → U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490))) → U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T556, T539, T542))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) → U53_gga(T579, T580, T490, T581, T584, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490))) → U54_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) → U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_in_g(T615))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → U57_gga(T614, T615, T490, T616, T619, T618, d1_in_gga(T614, T616, T618))
d1_in_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490))) → U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_in_g(T623))
U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → U59_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T614, T616, T618))
d1_in_gga(div(T647, T648), times(T647, power(T648, p(0))), 1) → d1_out_gga(div(T647, T648), times(T647, power(T648, p(0))), 1)
d1_in_gga(div(T661, T662), T663, 0) → U61_gga(T661, T662, T663, isnumber16_in_g(times(T661, power(T662, p(0)))))
U61_gga(T661, T662, T663, isnumber16_out_g(times(T661, power(T662, p(0))))) → d1_out_gga(div(T661, T662), T663, 0)
d1_in_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) → U62_gga(T684, T685, T686, T690, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0))))) → U63_gga(T684, T685, T686, T693, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) → U65_gga(T704, T706, T708, d1_in_gga(T704, T706, T708))
d1_in_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) → U66_gga(T704, T715, T706, T708, isnumber16_in_g(T715))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → U67_gga(T704, T715, T706, T708, d1_in_gga(T704, T706, T708))
d1_in_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) → U68_gga(T704, T720, T706, T708, isnumber16_in_g(T720))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → U69_gga(T704, T720, T706, T708, d1_in_gga(T704, T706, T708))
U69_gga(T704, T720, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U67_gga(T704, T715, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U65_gga(T704, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0)))))
U63_gga(T684, T685, T686, T693, T689, d1_out_gga(T684, T686, T689)) → U64_gga(T684, T685, T686, T693, T689, d1_in_gga(power(T685, p(0)), T686, T693))
U64_gga(T684, T685, T686, T693, T689, d1_out_gga(power(T685, p(0)), T686, T693)) → d1_out_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0)))))
U62_gga(T684, T685, T686, T690, T689, d1_out_gga(T684, T686, T689)) → d1_out_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0)))))
U59_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T614, T616, T618)) → U60_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T490, T616, T622))
U60_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T490, T616, T622)) → d1_out_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490)))
U57_gga(T614, T615, T490, T616, T619, T618, d1_out_gga(T614, T616, T618)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U54_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → U55_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(T490, T581, T589))
U55_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(T490, T581, T589)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490)))
U53_gga(T579, T580, T490, T581, T584, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490)))
U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T538, T539, T547))
U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T538, T539, T547)) → U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T490, T539, T555))
U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T490, T539, T555)) → d1_out_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490)))
U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T537, T539, T542)) → U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T538, T539, T547))
U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T538, T539, T547)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490)))
U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_out_gga(T537, T539, T542)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490)))
U46_gga(T512, T490, T513, T514, d1_out_gga(T490, T513, T514)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U44_gga(T500, T490, T501, d1_out_gga(T490, T500, T501)) → d1_out_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490)))
U43_gga(T477, T478, T479, T481, d1_out_gga(T477, T479, T481)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U41_gga(T460, T461, T462, T464, d1_out_gga(times(T460, power(T461, p(0))), T462, T464)) → d1_out_gga(div(T460, T461), T462, T464)
U39_gga(T428, T429, T430, T437, T433, d1_out_gga(T428, T430, T433)) → U40_gga(T428, T429, T430, T437, T433, d1_in_gga(T429, T430, T437))
U40_gga(T428, T429, T430, T437, T433, d1_out_gga(T429, T430, T437)) → d1_out_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429)))
U38_gga(T428, T429, T430, T434, T433, d1_out_gga(T428, T430, T433)) → d1_out_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429)))
U35_gga(T367, T387, T370, d1_out_gga(T367, power(T367, p(T387)), T370)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U33_gga(T367, T378, T370, d1_out_gga(T367, power(T367, s(T378)), T370)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U31_gga(T367, T370, d1_out_gga(T367, power(T367, 0), T370)) → d1_out_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0)))))
U29_gga(T341, T342, T353, T345, d1_out_gga(T341, div(T341, T342), T345)) → U30_gga(T341, T342, T353, T345, d1_in_gga(power(T342, p(0)), div(T341, T342), T353))
U30_gga(T341, T342, T353, T345, d1_out_gga(power(T342, p(0)), div(T341, T342), T353)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0)))))
U28_gga(T341, T342, T346, T345, d1_out_gga(T341, div(T341, T342), T345)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0)))))
U25_gga(T272, T273, T274, T287, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → U26_gga(T272, T273, T274, T287, T276, d1_in_gga(T274, times(power(T272, T273), T274), T287))
U26_gga(T272, T273, T274, T287, T276, d1_out_gga(T274, times(power(T272, T273), T274), T287)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U23_gga(T272, T273, T274, T277, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U20_gga(T226, T227, T228, T239, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → U21_gga(T226, T227, T228, T239, T230, d1_in_gga(T228, times(div(T226, T227), T228), T239))
U21_gga(T226, T227, T228, T239, T230, d1_out_gga(T228, times(div(T226, T227), T228), T239)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228)))
U19_gga(T226, T227, T228, T231, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228)))
U16_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U17_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U17_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → U18_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T156, times(times(T154, T155), T156), T191))
U18_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T156, times(times(T154, T155), T156), T191)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U14_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U15_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U15_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U13_gga(T154, T155, T156, T161, T160, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156)))
U12_gga(T125, T126, T127, d1_out_gga(T126, times(T125, T126), T127)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U10_gga(T95, T96, T98, d1_out_gga(T95, power(T95, T96), T98)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U8_gga(T79, T80, T82, d1_out_gga(times(T79, power(T80, p(0))), div(T79, T80), T82)) → d1_out_gga(div(T79, T80), div(T79, T80), T82)
U6_gga(T42, T43, T54, T46, d1_out_gga(T42, times(T42, T43), T46)) → U7_gga(T42, T43, T54, T46, d1_in_gga(T43, times(T42, T43), T54))
U7_gga(T42, T43, T54, T46, d1_out_gga(T43, times(T42, T43), T54)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43)))
U5_gga(T42, T43, T47, T46, d1_out_gga(T42, times(T42, T43), T46)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43)))

(5) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
The TRS P consists of the following rules:

D1_IN_GGA(s(T12), s(T12), 0) → U3_GGA(T12, isnumber16_in_g(T12))
D1_IN_GGA(s(T12), s(T12), 0) → ISNUMBER16_IN_G(T12)
ISNUMBER16_IN_G(s(T17)) → U1_G(T17, isnumber16_in_g(T17))
ISNUMBER16_IN_G(s(T17)) → ISNUMBER16_IN_G(T17)
ISNUMBER16_IN_G(p(T20)) → U2_G(T20, isnumber16_in_g(T20))
ISNUMBER16_IN_G(p(T20)) → ISNUMBER16_IN_G(T20)
D1_IN_GGA(p(T25), p(T25), 0) → U4_GGA(T25, isnumber16_in_g(T25))
D1_IN_GGA(p(T25), p(T25), 0) → ISNUMBER16_IN_G(T25)
D1_IN_GGA(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) → U5_GGA(T42, T43, T47, T46, d1_in_gga(T42, times(T42, T43), T46))
D1_IN_GGA(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) → D1_IN_GGA(T42, times(T42, T43), T46)
D1_IN_GGA(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43))) → U6_GGA(T42, T43, T54, T46, d1_in_gga(T42, times(T42, T43), T46))
D1_IN_GGA(div(T79, T80), div(T79, T80), T82) → U8_GGA(T79, T80, T82, d1_in_gga(times(T79, power(T80, p(0))), div(T79, T80), T82))
D1_IN_GGA(div(T79, T80), div(T79, T80), T82) → D1_IN_GGA(times(T79, power(T80, p(0))), div(T79, T80), T82)
D1_IN_GGA(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) → U9_GGA(T95, T96, T98, isnumber16_in_g(T96))
D1_IN_GGA(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) → ISNUMBER16_IN_G(T96)
U9_GGA(T95, T96, T98, isnumber16_out_g(T96)) → U10_GGA(T95, T96, T98, d1_in_gga(T95, power(T95, T96), T98))
U9_GGA(T95, T96, T98, isnumber16_out_g(T96)) → D1_IN_GGA(T95, power(T95, T96), T98)
D1_IN_GGA(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) → U11_GGA(T125, T126, T127, isnumber16_in_g(T125))
D1_IN_GGA(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) → ISNUMBER16_IN_G(T125)
U11_GGA(T125, T126, T127, isnumber16_out_g(T125)) → U12_GGA(T125, T126, T127, d1_in_gga(T126, times(T125, T126), T127))
U11_GGA(T125, T126, T127, isnumber16_out_g(T125)) → D1_IN_GGA(T126, times(T125, T126), T127)
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) → U13_GGA(T154, T155, T156, T161, T160, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) → D1_IN_GGA(T154, times(times(T154, T155), T156), T159)
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U14_GGA(T154, T155, T156, T172, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U16_GGA(T154, T155, T156, T191, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) → U19_GGA(T226, T227, T228, T231, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) → D1_IN_GGA(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228))) → U20_GGA(T226, T227, T228, T239, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U22_GGA(T272, T273, T274, T277, T276, isnumber16_in_g(T273))
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → ISNUMBER16_IN_G(T273)
U22_GGA(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → U23_GGA(T272, T273, T274, T277, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
U22_GGA(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → D1_IN_GGA(T272, times(power(T272, T273), T274), T276)
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U24_GGA(T272, T273, T274, T287, T276, isnumber16_in_g(T273))
U24_GGA(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → U25_GGA(T272, T273, T274, T287, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
U24_GGA(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → D1_IN_GGA(T272, times(power(T272, T273), T274), T276)
D1_IN_GGA(div(T323, T324), div(T323, T324), 0) → U27_GGA(T323, T324, isnumber16_in_g(times(T323, power(T324, p(0)))))
D1_IN_GGA(div(T323, T324), div(T323, T324), 0) → ISNUMBER16_IN_G(times(T323, power(T324, p(0))))
D1_IN_GGA(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) → U28_GGA(T341, T342, T346, T345, d1_in_gga(T341, div(T341, T342), T345))
D1_IN_GGA(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) → D1_IN_GGA(T341, div(T341, T342), T345)
D1_IN_GGA(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0))))) → U29_GGA(T341, T342, T353, T345, d1_in_gga(T341, div(T341, T342), T345))
D1_IN_GGA(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) → U31_GGA(T367, T370, d1_in_gga(T367, power(T367, 0), T370))
D1_IN_GGA(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) → D1_IN_GGA(T367, power(T367, 0), T370)
D1_IN_GGA(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) → U32_GGA(T367, T378, T370, isnumber16_in_g(T378))
D1_IN_GGA(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) → ISNUMBER16_IN_G(T378)
U32_GGA(T367, T378, T370, isnumber16_out_g(T378)) → U33_GGA(T367, T378, T370, d1_in_gga(T367, power(T367, s(T378)), T370))
U32_GGA(T367, T378, T370, isnumber16_out_g(T378)) → D1_IN_GGA(T367, power(T367, s(T378)), T370)
D1_IN_GGA(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) → U34_GGA(T367, T387, T370, isnumber16_in_g(T387))
D1_IN_GGA(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) → ISNUMBER16_IN_G(T387)
U34_GGA(T367, T387, T370, isnumber16_out_g(T387)) → U35_GGA(T367, T387, T370, d1_in_gga(T367, power(T367, p(T387)), T370))
U34_GGA(T367, T387, T370, isnumber16_out_g(T387)) → D1_IN_GGA(T367, power(T367, p(T387)), T370)
D1_IN_GGA(s(T402), T397, 0) → U36_GGA(T402, T397, isnumber16_in_g(T402))
D1_IN_GGA(s(T402), T397, 0) → ISNUMBER16_IN_G(T402)
D1_IN_GGA(p(T407), T397, 0) → U37_GGA(T407, T397, isnumber16_in_g(T407))
D1_IN_GGA(p(T407), T397, 0) → ISNUMBER16_IN_G(T407)
D1_IN_GGA(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) → U38_GGA(T428, T429, T430, T434, T433, d1_in_gga(T428, T430, T433))
D1_IN_GGA(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) → D1_IN_GGA(T428, T430, T433)
D1_IN_GGA(times(T428, T429), T430, +(times(T437, T428), times(T433, T429))) → U39_GGA(T428, T429, T430, T437, T433, d1_in_gga(T428, T430, T433))
D1_IN_GGA(div(T460, T461), T462, T464) → U41_GGA(T460, T461, T462, T464, d1_in_gga(times(T460, power(T461, p(0))), T462, T464))
D1_IN_GGA(div(T460, T461), T462, T464) → D1_IN_GGA(times(T460, power(T461, p(0))), T462, T464)
D1_IN_GGA(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) → U42_GGA(T477, T478, T479, T481, isnumber16_in_g(T478))
D1_IN_GGA(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) → ISNUMBER16_IN_G(T478)
U42_GGA(T477, T478, T479, T481, isnumber16_out_g(T478)) → U43_GGA(T477, T478, T479, T481, d1_in_gga(T477, T479, T481))
U42_GGA(T477, T478, T479, T481, isnumber16_out_g(T478)) → D1_IN_GGA(T477, T479, T481)
D1_IN_GGA(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) → U44_GGA(T500, T490, T501, d1_in_gga(T490, T500, T501))
D1_IN_GGA(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) → D1_IN_GGA(T490, T500, T501)
D1_IN_GGA(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) → U45_GGA(T512, T490, T513, T514, isnumber16_in_g(T512))
D1_IN_GGA(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) → ISNUMBER16_IN_G(T512)
U45_GGA(T512, T490, T513, T514, isnumber16_out_g(T512)) → U46_GGA(T512, T490, T513, T514, d1_in_gga(T490, T513, T514))
U45_GGA(T512, T490, T513, T514, isnumber16_out_g(T512)) → D1_IN_GGA(T490, T513, T514)
D1_IN_GGA(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) → U47_GGA(T537, T538, T490, T539, T544, T543, T542, d1_in_gga(T537, T539, T542))
D1_IN_GGA(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) → D1_IN_GGA(T537, T539, T542)
D1_IN_GGA(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490))) → U48_GGA(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T537, T539, T542))
D1_IN_GGA(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490))) → U50_GGA(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T556, T539, T542))
D1_IN_GGA(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) → U53_GGA(T579, T580, T490, T581, T584, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
D1_IN_GGA(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) → D1_IN_GGA(times(T579, power(T580, p(0))), T581, T583)
D1_IN_GGA(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490))) → U54_GGA(T579, T580, T490, T581, T589, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
D1_IN_GGA(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) → U56_GGA(T614, T615, T490, T616, T619, T618, isnumber16_in_g(T615))
D1_IN_GGA(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) → ISNUMBER16_IN_G(T615)
U56_GGA(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → U57_GGA(T614, T615, T490, T616, T619, T618, d1_in_gga(T614, T616, T618))
U56_GGA(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → D1_IN_GGA(T614, T616, T618)
D1_IN_GGA(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490))) → U58_GGA(T614, T623, T490, T616, T622, T618, isnumber16_in_g(T623))
U58_GGA(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → U59_GGA(T614, T623, T490, T616, T622, T618, d1_in_gga(T614, T616, T618))
U58_GGA(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → D1_IN_GGA(T614, T616, T618)
D1_IN_GGA(div(T661, T662), T663, 0) → U61_GGA(T661, T662, T663, isnumber16_in_g(times(T661, power(T662, p(0)))))
D1_IN_GGA(div(T661, T662), T663, 0) → ISNUMBER16_IN_G(times(T661, power(T662, p(0))))
D1_IN_GGA(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) → U62_GGA(T684, T685, T686, T690, T689, d1_in_gga(T684, T686, T689))
D1_IN_GGA(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) → D1_IN_GGA(T684, T686, T689)
D1_IN_GGA(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0))))) → U63_GGA(T684, T685, T686, T693, T689, d1_in_gga(T684, T686, T689))
D1_IN_GGA(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) → U65_GGA(T704, T706, T708, d1_in_gga(T704, T706, T708))
D1_IN_GGA(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) → D1_IN_GGA(T704, T706, T708)
D1_IN_GGA(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) → U66_GGA(T704, T715, T706, T708, isnumber16_in_g(T715))
D1_IN_GGA(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) → ISNUMBER16_IN_G(T715)
U66_GGA(T704, T715, T706, T708, isnumber16_out_g(T715)) → U67_GGA(T704, T715, T706, T708, d1_in_gga(T704, T706, T708))
U66_GGA(T704, T715, T706, T708, isnumber16_out_g(T715)) → D1_IN_GGA(T704, T706, T708)
D1_IN_GGA(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) → U68_GGA(T704, T720, T706, T708, isnumber16_in_g(T720))
D1_IN_GGA(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) → ISNUMBER16_IN_G(T720)
U68_GGA(T704, T720, T706, T708, isnumber16_out_g(T720)) → U69_GGA(T704, T720, T706, T708, d1_in_gga(T704, T706, T708))
U68_GGA(T704, T720, T706, T708, isnumber16_out_g(T720)) → D1_IN_GGA(T704, T706, T708)
U63_GGA(T684, T685, T686, T693, T689, d1_out_gga(T684, T686, T689)) → U64_GGA(T684, T685, T686, T693, T689, d1_in_gga(power(T685, p(0)), T686, T693))
U63_GGA(T684, T685, T686, T693, T689, d1_out_gga(T684, T686, T689)) → D1_IN_GGA(power(T685, p(0)), T686, T693)
U59_GGA(T614, T623, T490, T616, T622, T618, d1_out_gga(T614, T616, T618)) → U60_GGA(T614, T623, T490, T616, T622, T618, d1_in_gga(T490, T616, T622))
U59_GGA(T614, T623, T490, T616, T622, T618, d1_out_gga(T614, T616, T618)) → D1_IN_GGA(T490, T616, T622)
U54_GGA(T579, T580, T490, T581, T589, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → U55_GGA(T579, T580, T490, T581, T589, T583, d1_in_gga(T490, T581, T589))
U54_GGA(T579, T580, T490, T581, T589, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → D1_IN_GGA(T490, T581, T589)
U50_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → U51_GGA(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T538, T539, T547))
U50_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → D1_IN_GGA(T538, T539, T547)
U51_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T538, T539, T547)) → U52_GGA(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T490, T539, T555))
U51_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T538, T539, T547)) → D1_IN_GGA(T490, T539, T555)
U48_GGA(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T537, T539, T542)) → U49_GGA(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T538, T539, T547))
U48_GGA(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T537, T539, T542)) → D1_IN_GGA(T538, T539, T547)
U39_GGA(T428, T429, T430, T437, T433, d1_out_gga(T428, T430, T433)) → U40_GGA(T428, T429, T430, T437, T433, d1_in_gga(T429, T430, T437))
U39_GGA(T428, T429, T430, T437, T433, d1_out_gga(T428, T430, T433)) → D1_IN_GGA(T429, T430, T437)
U29_GGA(T341, T342, T353, T345, d1_out_gga(T341, div(T341, T342), T345)) → U30_GGA(T341, T342, T353, T345, d1_in_gga(power(T342, p(0)), div(T341, T342), T353))
U29_GGA(T341, T342, T353, T345, d1_out_gga(T341, div(T341, T342), T345)) → D1_IN_GGA(power(T342, p(0)), div(T341, T342), T353)
U25_GGA(T272, T273, T274, T287, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → U26_GGA(T272, T273, T274, T287, T276, d1_in_gga(T274, times(power(T272, T273), T274), T287))
U25_GGA(T272, T273, T274, T287, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → D1_IN_GGA(T274, times(power(T272, T273), T274), T287)
U20_GGA(T226, T227, T228, T239, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → U21_GGA(T226, T227, T228, T239, T230, d1_in_gga(T228, times(div(T226, T227), T228), T239))
U20_GGA(T226, T227, T228, T239, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → D1_IN_GGA(T228, times(div(T226, T227), T228), T239)
U16_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U17_GGA(T154, T155, T156, T191, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U16_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → D1_IN_GGA(T155, times(times(T154, T155), T156), T171)
U17_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → U18_GGA(T154, T155, T156, T191, T171, T159, d1_in_gga(T156, times(times(T154, T155), T156), T191))
U17_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → D1_IN_GGA(T156, times(times(T154, T155), T156), T191)
U14_GGA(T154, T155, T156, T172, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U15_GGA(T154, T155, T156, T172, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U14_GGA(T154, T155, T156, T172, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → D1_IN_GGA(T155, times(times(T154, T155), T156), T171)
U6_GGA(T42, T43, T54, T46, d1_out_gga(T42, times(T42, T43), T46)) → U7_GGA(T42, T43, T54, T46, d1_in_gga(T43, times(T42, T43), T54))
U6_GGA(T42, T43, T54, T46, d1_out_gga(T42, times(T42, T43), T46)) → D1_IN_GGA(T43, times(T42, T43), T54)

The TRS R consists of the following rules:

d1_in_gga(T5, T5, 1) → d1_out_gga(T5, T5, 1)
d1_in_gga(0, 0, 0) → d1_out_gga(0, 0, 0)
d1_in_gga(s(T12), s(T12), 0) → U3_gga(T12, isnumber16_in_g(T12))
isnumber16_in_g(0) → isnumber16_out_g(0)
isnumber16_in_g(s(T17)) → U1_g(T17, isnumber16_in_g(T17))
isnumber16_in_g(p(T20)) → U2_g(T20, isnumber16_in_g(T20))
U2_g(T20, isnumber16_out_g(T20)) → isnumber16_out_g(p(T20))
U1_g(T17, isnumber16_out_g(T17)) → isnumber16_out_g(s(T17))
U3_gga(T12, isnumber16_out_g(T12)) → d1_out_gga(s(T12), s(T12), 0)
d1_in_gga(p(T25), p(T25), 0) → U4_gga(T25, isnumber16_in_g(T25))
U4_gga(T25, isnumber16_out_g(T25)) → d1_out_gga(p(T25), p(T25), 0)
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) → U5_gga(T42, T43, T47, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43))) → U6_gga(T42, T43, T54, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(div(T79, T80), div(T79, T80), T82) → U8_gga(T79, T80, T82, d1_in_gga(times(T79, power(T80, p(0))), div(T79, T80), T82))
d1_in_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) → U9_gga(T95, T96, T98, isnumber16_in_g(T96))
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → U10_gga(T95, T96, T98, d1_in_gga(T95, power(T95, T96), T98))
d1_in_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) → U11_gga(T125, T126, T127, isnumber16_in_g(T125))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → U12_gga(T125, T126, T127, d1_in_gga(T126, times(T125, T126), T127))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) → U13_gga(T154, T155, T156, T161, T160, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U14_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U16_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) → U19_gga(T226, T227, T228, T231, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228))) → U20_gga(T226, T227, T228, T239, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U22_gga(T272, T273, T274, T277, T276, isnumber16_in_g(T273))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → U23_gga(T272, T273, T274, T277, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U24_gga(T272, T273, T274, T287, T276, isnumber16_in_g(T273))
U24_gga(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → U25_gga(T272, T273, T274, T287, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
d1_in_gga(div(T323, T324), div(T323, T324), 0) → U27_gga(T323, T324, isnumber16_in_g(times(T323, power(T324, p(0)))))
U27_gga(T323, T324, isnumber16_out_g(times(T323, power(T324, p(0))))) → d1_out_gga(div(T323, T324), div(T323, T324), 0)
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) → U28_gga(T341, T342, T346, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0))))) → U29_gga(T341, T342, T353, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) → U31_gga(T367, T370, d1_in_gga(T367, power(T367, 0), T370))
d1_in_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) → U32_gga(T367, T378, T370, isnumber16_in_g(T378))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → U33_gga(T367, T378, T370, d1_in_gga(T367, power(T367, s(T378)), T370))
d1_in_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) → U34_gga(T367, T387, T370, isnumber16_in_g(T387))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → U35_gga(T367, T387, T370, d1_in_gga(T367, power(T367, p(T387)), T370))
d1_in_gga(0, T397, 0) → d1_out_gga(0, T397, 0)
d1_in_gga(s(T402), T397, 0) → U36_gga(T402, T397, isnumber16_in_g(T402))
U36_gga(T402, T397, isnumber16_out_g(T402)) → d1_out_gga(s(T402), T397, 0)
d1_in_gga(p(T407), T397, 0) → U37_gga(T407, T397, isnumber16_in_g(T407))
U37_gga(T407, T397, isnumber16_out_g(T407)) → d1_out_gga(p(T407), T397, 0)
d1_in_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) → U38_gga(T428, T429, T430, T434, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429))) → U39_gga(T428, T429, T430, T437, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(div(T460, T461), T462, T464) → U41_gga(T460, T461, T462, T464, d1_in_gga(times(T460, power(T461, p(0))), T462, T464))
d1_in_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) → U42_gga(T477, T478, T479, T481, isnumber16_in_g(T478))
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → U43_gga(T477, T478, T479, T481, d1_in_gga(T477, T479, T481))
d1_in_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) → U44_gga(T500, T490, T501, d1_in_gga(T490, T500, T501))
d1_in_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) → U45_gga(T512, T490, T513, T514, isnumber16_in_g(T512))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → U46_gga(T512, T490, T513, T514, d1_in_gga(T490, T513, T514))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) → U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490))) → U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490))) → U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T556, T539, T542))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) → U53_gga(T579, T580, T490, T581, T584, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490))) → U54_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) → U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_in_g(T615))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → U57_gga(T614, T615, T490, T616, T619, T618, d1_in_gga(T614, T616, T618))
d1_in_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490))) → U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_in_g(T623))
U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → U59_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T614, T616, T618))
d1_in_gga(div(T647, T648), times(T647, power(T648, p(0))), 1) → d1_out_gga(div(T647, T648), times(T647, power(T648, p(0))), 1)
d1_in_gga(div(T661, T662), T663, 0) → U61_gga(T661, T662, T663, isnumber16_in_g(times(T661, power(T662, p(0)))))
U61_gga(T661, T662, T663, isnumber16_out_g(times(T661, power(T662, p(0))))) → d1_out_gga(div(T661, T662), T663, 0)
d1_in_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) → U62_gga(T684, T685, T686, T690, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0))))) → U63_gga(T684, T685, T686, T693, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) → U65_gga(T704, T706, T708, d1_in_gga(T704, T706, T708))
d1_in_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) → U66_gga(T704, T715, T706, T708, isnumber16_in_g(T715))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → U67_gga(T704, T715, T706, T708, d1_in_gga(T704, T706, T708))
d1_in_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) → U68_gga(T704, T720, T706, T708, isnumber16_in_g(T720))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → U69_gga(T704, T720, T706, T708, d1_in_gga(T704, T706, T708))
U69_gga(T704, T720, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U67_gga(T704, T715, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U65_gga(T704, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0)))))
U63_gga(T684, T685, T686, T693, T689, d1_out_gga(T684, T686, T689)) → U64_gga(T684, T685, T686, T693, T689, d1_in_gga(power(T685, p(0)), T686, T693))
U64_gga(T684, T685, T686, T693, T689, d1_out_gga(power(T685, p(0)), T686, T693)) → d1_out_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0)))))
U62_gga(T684, T685, T686, T690, T689, d1_out_gga(T684, T686, T689)) → d1_out_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0)))))
U59_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T614, T616, T618)) → U60_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T490, T616, T622))
U60_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T490, T616, T622)) → d1_out_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490)))
U57_gga(T614, T615, T490, T616, T619, T618, d1_out_gga(T614, T616, T618)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U54_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → U55_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(T490, T581, T589))
U55_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(T490, T581, T589)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490)))
U53_gga(T579, T580, T490, T581, T584, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490)))
U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T538, T539, T547))
U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T538, T539, T547)) → U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T490, T539, T555))
U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T490, T539, T555)) → d1_out_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490)))
U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T537, T539, T542)) → U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T538, T539, T547))
U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T538, T539, T547)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490)))
U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_out_gga(T537, T539, T542)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490)))
U46_gga(T512, T490, T513, T514, d1_out_gga(T490, T513, T514)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U44_gga(T500, T490, T501, d1_out_gga(T490, T500, T501)) → d1_out_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490)))
U43_gga(T477, T478, T479, T481, d1_out_gga(T477, T479, T481)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U41_gga(T460, T461, T462, T464, d1_out_gga(times(T460, power(T461, p(0))), T462, T464)) → d1_out_gga(div(T460, T461), T462, T464)
U39_gga(T428, T429, T430, T437, T433, d1_out_gga(T428, T430, T433)) → U40_gga(T428, T429, T430, T437, T433, d1_in_gga(T429, T430, T437))
U40_gga(T428, T429, T430, T437, T433, d1_out_gga(T429, T430, T437)) → d1_out_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429)))
U38_gga(T428, T429, T430, T434, T433, d1_out_gga(T428, T430, T433)) → d1_out_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429)))
U35_gga(T367, T387, T370, d1_out_gga(T367, power(T367, p(T387)), T370)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U33_gga(T367, T378, T370, d1_out_gga(T367, power(T367, s(T378)), T370)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U31_gga(T367, T370, d1_out_gga(T367, power(T367, 0), T370)) → d1_out_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0)))))
U29_gga(T341, T342, T353, T345, d1_out_gga(T341, div(T341, T342), T345)) → U30_gga(T341, T342, T353, T345, d1_in_gga(power(T342, p(0)), div(T341, T342), T353))
U30_gga(T341, T342, T353, T345, d1_out_gga(power(T342, p(0)), div(T341, T342), T353)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0)))))
U28_gga(T341, T342, T346, T345, d1_out_gga(T341, div(T341, T342), T345)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0)))))
U25_gga(T272, T273, T274, T287, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → U26_gga(T272, T273, T274, T287, T276, d1_in_gga(T274, times(power(T272, T273), T274), T287))
U26_gga(T272, T273, T274, T287, T276, d1_out_gga(T274, times(power(T272, T273), T274), T287)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U23_gga(T272, T273, T274, T277, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U20_gga(T226, T227, T228, T239, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → U21_gga(T226, T227, T228, T239, T230, d1_in_gga(T228, times(div(T226, T227), T228), T239))
U21_gga(T226, T227, T228, T239, T230, d1_out_gga(T228, times(div(T226, T227), T228), T239)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228)))
U19_gga(T226, T227, T228, T231, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228)))
U16_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U17_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U17_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → U18_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T156, times(times(T154, T155), T156), T191))
U18_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T156, times(times(T154, T155), T156), T191)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U14_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U15_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U15_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U13_gga(T154, T155, T156, T161, T160, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156)))
U12_gga(T125, T126, T127, d1_out_gga(T126, times(T125, T126), T127)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U10_gga(T95, T96, T98, d1_out_gga(T95, power(T95, T96), T98)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U8_gga(T79, T80, T82, d1_out_gga(times(T79, power(T80, p(0))), div(T79, T80), T82)) → d1_out_gga(div(T79, T80), div(T79, T80), T82)
U6_gga(T42, T43, T54, T46, d1_out_gga(T42, times(T42, T43), T46)) → U7_gga(T42, T43, T54, T46, d1_in_gga(T43, times(T42, T43), T54))
U7_gga(T42, T43, T54, T46, d1_out_gga(T43, times(T42, T43), T54)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43)))
U5_gga(T42, T43, T47, T46, d1_out_gga(T42, times(T42, T43), T46)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43)))

The argument filtering Pi contains the following mapping:
d1_in_gga(x1, x2, x3) = d1_in_gga(x1, x2)
d1_out_gga(x1, x2, x3) = d1_out_gga
0 = 0
s(x1) = s(x1)
U3_gga(x1, x2) = U3_gga(x2)
isnumber16_in_g(x1) = isnumber16_in_g(x1)
isnumber16_out_g(x1) = isnumber16_out_g
U1_g(x1, x2) = U1_g(x2)
p(x1) = p(x1)
U2_g(x1, x2) = U2_g(x2)
U4_gga(x1, x2) = U4_gga(x2)
times(x1, x2) = times(x1, x2)
U5_gga(x1, x2, x3, x4, x5) = U5_gga(x5)
U6_gga(x1, x2, x3, x4, x5) = U6_gga(x1, x2, x5)
div(x1, x2) = div(x1, x2)
U8_gga(x1, x2, x3, x4) = U8_gga(x4)
power(x1, x2) = power(x1, x2)
U9_gga(x1, x2, x3, x4) = U9_gga(x1, x2, x4)
U10_gga(x1, x2, x3, x4) = U10_gga(x4)
U11_gga(x1, x2, x3, x4) = U11_gga(x1, x2, x4)
U12_gga(x1, x2, x3, x4) = U12_gga(x4)
U13_gga(x1, x2, x3, x4, x5, x6, x7) = U13_gga(x7)
U14_gga(x1, x2, x3, x4, x5, x6, x7) = U14_gga(x1, x2, x3, x7)
U16_gga(x1, x2, x3, x4, x5, x6, x7) = U16_gga(x1, x2, x3, x7)
U19_gga(x1, x2, x3, x4, x5, x6) = U19_gga(x6)
U20_gga(x1, x2, x3, x4, x5, x6) = U20_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(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)
U27_gga(x1, x2, x3) = U27_gga(x3)
U28_gga(x1, x2, x3, x4, x5) = U28_gga(x5)
U29_gga(x1, x2, x3, x4, x5) = U29_gga(x1, x2, x5)
U31_gga(x1, x2, x3) = U31_gga(x3)
U32_gga(x1, x2, x3, x4) = U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3, x4) = U33_gga(x4)
U34_gga(x1, x2, x3, x4) = U34_gga(x1, x2, x4)
U35_gga(x1, x2, x3, x4) = U35_gga(x4)
U36_gga(x1, x2, x3) = U36_gga(x3)
U37_gga(x1, x2, x3) = U37_gga(x3)
U38_gga(x1, x2, x3, x4, x5, x6) = U38_gga(x6)
U39_gga(x1, x2, x3, x4, x5, x6) = U39_gga(x2, x3, x6)
U41_gga(x1, x2, x3, x4, x5) = U41_gga(x5)
U42_gga(x1, x2, x3, x4, x5) = U42_gga(x1, x3, x5)
U43_gga(x1, x2, x3, x4, x5) = U43_gga(x5)
U44_gga(x1, x2, x3, x4) = U44_gga(x4)
U45_gga(x1, x2, x3, x4, x5) = U45_gga(x2, x3, x5)
U46_gga(x1, x2, x3, x4, x5) = U46_gga(x5)
U47_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U47_gga(x8)
U48_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U48_gga(x2, x4, x8)
U50_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U50_gga(x2, x3, x4, x8)
U53_gga(x1, x2, x3, x4, x5, x6, x7) = U53_gga(x7)
U54_gga(x1, x2, x3, x4, x5, x6, x7) = U54_gga(x3, x4, x7)
U56_gga(x1, x2, x3, x4, x5, x6, x7) = U56_gga(x1, x4, x7)
U57_gga(x1, x2, x3, x4, x5, x6, x7) = U57_gga(x7)
U58_gga(x1, x2, x3, x4, x5, x6, x7) = U58_gga(x1, x3, x4, x7)
U59_gga(x1, x2, x3, x4, x5, x6, x7) = U59_gga(x3, x4, x7)
U61_gga(x1, x2, x3, x4) = U61_gga(x4)
U62_gga(x1, x2, x3, x4, x5, x6) = U62_gga(x6)
U63_gga(x1, x2, x3, x4, x5, x6) = U63_gga(x2, x3, x6)
U65_gga(x1, x2, x3, x4) = U65_gga(x4)
U66_gga(x1, x2, x3, x4, x5) = U66_gga(x1, x3, x5)
U67_gga(x1, x2, x3, x4, x5) = U67_gga(x5)
U68_gga(x1, x2, x3, x4, x5) = U68_gga(x1, x3, x5)
U69_gga(x1, x2, x3, x4, x5) = U69_gga(x5)
U64_gga(x1, x2, x3, x4, x5, x6) = U64_gga(x6)
U60_gga(x1, x2, x3, x4, x5, x6, x7) = U60_gga(x7)
U55_gga(x1, x2, x3, x4, x5, x6, x7) = U55_gga(x7)
U51_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U51_gga(x3, x4, x8)
U52_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U52_gga(x8)
U49_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U49_gga(x8)
U40_gga(x1, x2, x3, x4, x5, x6) = U40_gga(x6)
U30_gga(x1, x2, x3, x4, x5) = U30_gga(x5)
U26_gga(x1, x2, x3, x4, x5, x6) = U26_gga(x6)
U21_gga(x1, x2, x3, x4, x5, x6) = U21_gga(x6)
U17_gga(x1, x2, x3, x4, x5, x6, x7) = U17_gga(x1, x2, x3, x7)
U18_gga(x1, x2, x3, x4, x5, x6, x7) = U18_gga(x7)
U15_gga(x1, x2, x3, x4, x5, x6, x7) = U15_gga(x7)
U7_gga(x1, x2, x3, x4, x5) = U7_gga(x5)
D1_IN_GGA(x1, x2, x3) = D1_IN_GGA(x1, x2)
U3_GGA(x1, x2) = U3_GGA(x2)
ISNUMBER16_IN_G(x1) = ISNUMBER16_IN_G(x1)
U1_G(x1, x2) = U1_G(x2)
U2_G(x1, x2) = U2_G(x2)
U4_GGA(x1, x2) = U4_GGA(x2)
U5_GGA(x1, x2, x3, x4, x5) = U5_GGA(x5)
U6_GGA(x1, x2, x3, x4, x5) = U6_GGA(x1, x2, x5)
U8_GGA(x1, x2, x3, x4) = U8_GGA(x4)
U9_GGA(x1, x2, x3, x4) = U9_GGA(x1, x2, x4)
U10_GGA(x1, x2, x3, x4) = U10_GGA(x4)
U11_GGA(x1, x2, x3, x4) = U11_GGA(x1, x2, x4)
U12_GGA(x1, x2, x3, x4) = U12_GGA(x4)
U13_GGA(x1, x2, x3, x4, x5, x6, x7) = U13_GGA(x7)
U14_GGA(x1, x2, x3, x4, x5, x6, x7) = U14_GGA(x1, x2, x3, x7)
U16_GGA(x1, x2, x3, x4, x5, x6, x7) = U16_GGA(x1, x2, x3, x7)
U19_GGA(x1, x2, x3, x4, x5, x6) = U19_GGA(x6)
U20_GGA(x1, x2, x3, x4, x5, x6) = U20_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(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)
U27_GGA(x1, x2, x3) = U27_GGA(x3)
U28_GGA(x1, x2, x3, x4, x5) = U28_GGA(x5)
U29_GGA(x1, x2, x3, x4, x5) = U29_GGA(x1, x2, x5)
U31_GGA(x1, x2, x3) = U31_GGA(x3)
U32_GGA(x1, x2, x3, x4) = U32_GGA(x1, x2, x4)
U33_GGA(x1, x2, x3, x4) = U33_GGA(x4)
U34_GGA(x1, x2, x3, x4) = U34_GGA(x1, x2, x4)
U35_GGA(x1, x2, x3, x4) = U35_GGA(x4)
U36_GGA(x1, x2, x3) = U36_GGA(x3)
U37_GGA(x1, x2, x3) = U37_GGA(x3)
U38_GGA(x1, x2, x3, x4, x5, x6) = U38_GGA(x6)
U39_GGA(x1, x2, x3, x4, x5, x6) = U39_GGA(x2, x3, x6)
U41_GGA(x1, x2, x3, x4, x5) = U41_GGA(x5)
U42_GGA(x1, x2, x3, x4, x5) = U42_GGA(x1, x3, x5)
U43_GGA(x1, x2, x3, x4, x5) = U43_GGA(x5)
U44_GGA(x1, x2, x3, x4) = U44_GGA(x4)
U45_GGA(x1, x2, x3, x4, x5) = U45_GGA(x2, x3, x5)
U46_GGA(x1, x2, x3, x4, x5) = U46_GGA(x5)
U47_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U47_GGA(x8)
U48_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U48_GGA(x2, x4, x8)
U50_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U50_GGA(x2, x3, x4, x8)
U53_GGA(x1, x2, x3, x4, x5, x6, x7) = U53_GGA(x7)
U54_GGA(x1, x2, x3, x4, x5, x6, x7) = U54_GGA(x3, x4, x7)
U56_GGA(x1, x2, x3, x4, x5, x6, x7) = U56_GGA(x1, x4, x7)
U57_GGA(x1, x2, x3, x4, x5, x6, x7) = U57_GGA(x7)
U58_GGA(x1, x2, x3, x4, x5, x6, x7) = U58_GGA(x1, x3, x4, x7)
U59_GGA(x1, x2, x3, x4, x5, x6, x7) = U59_GGA(x3, x4, x7)
U61_GGA(x1, x2, x3, x4) = U61_GGA(x4)
U62_GGA(x1, x2, x3, x4, x5, x6) = U62_GGA(x6)
U63_GGA(x1, x2, x3, x4, x5, x6) = U63_GGA(x2, x3, x6)
U65_GGA(x1, x2, x3, x4) = U65_GGA(x4)
U66_GGA(x1, x2, x3, x4, x5) = U66_GGA(x1, x3, x5)
U67_GGA(x1, x2, x3, x4, x5) = U67_GGA(x5)
U68_GGA(x1, x2, x3, x4, x5) = U68_GGA(x1, x3, x5)
U69_GGA(x1, x2, x3, x4, x5) = U69_GGA(x5)
U64_GGA(x1, x2, x3, x4, x5, x6) = U64_GGA(x6)
U60_GGA(x1, x2, x3, x4, x5, x6, x7) = U60_GGA(x7)
U55_GGA(x1, x2, x3, x4, x5, x6, x7) = U55_GGA(x7)
U51_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U51_GGA(x3, x4, x8)
U52_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U52_GGA(x8)
U49_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U49_GGA(x8)
U40_GGA(x1, x2, x3, x4, x5, x6) = U40_GGA(x6)
U30_GGA(x1, x2, x3, x4, x5) = U30_GGA(x5)
U26_GGA(x1, x2, x3, x4, x5, x6) = U26_GGA(x6)
U21_GGA(x1, x2, x3, x4, x5, x6) = U21_GGA(x6)
U17_GGA(x1, x2, x3, x4, x5, x6, x7) = U17_GGA(x1, x2, x3, x7)
U18_GGA(x1, x2, x3, x4, x5, x6, x7) = U18_GGA(x7)
U15_GGA(x1, x2, x3, x4, x5, x6, x7) = U15_GGA(x7)
U7_GGA(x1, x2, x3, x4, x5) = U7_GGA(x5)

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

(6) Obligation:

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

D1_IN_GGA(s(T12), s(T12), 0) → U3_GGA(T12, isnumber16_in_g(T12))
D1_IN_GGA(s(T12), s(T12), 0) → ISNUMBER16_IN_G(T12)
ISNUMBER16_IN_G(s(T17)) → U1_G(T17, isnumber16_in_g(T17))
ISNUMBER16_IN_G(s(T17)) → ISNUMBER16_IN_G(T17)
ISNUMBER16_IN_G(p(T20)) → U2_G(T20, isnumber16_in_g(T20))
ISNUMBER16_IN_G(p(T20)) → ISNUMBER16_IN_G(T20)
D1_IN_GGA(p(T25), p(T25), 0) → U4_GGA(T25, isnumber16_in_g(T25))
D1_IN_GGA(p(T25), p(T25), 0) → ISNUMBER16_IN_G(T25)
D1_IN_GGA(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) → U5_GGA(T42, T43, T47, T46, d1_in_gga(T42, times(T42, T43), T46))
D1_IN_GGA(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) → D1_IN_GGA(T42, times(T42, T43), T46)
D1_IN_GGA(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43))) → U6_GGA(T42, T43, T54, T46, d1_in_gga(T42, times(T42, T43), T46))
D1_IN_GGA(div(T79, T80), div(T79, T80), T82) → U8_GGA(T79, T80, T82, d1_in_gga(times(T79, power(T80, p(0))), div(T79, T80), T82))
D1_IN_GGA(div(T79, T80), div(T79, T80), T82) → D1_IN_GGA(times(T79, power(T80, p(0))), div(T79, T80), T82)
D1_IN_GGA(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) → U9_GGA(T95, T96, T98, isnumber16_in_g(T96))
D1_IN_GGA(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) → ISNUMBER16_IN_G(T96)
U9_GGA(T95, T96, T98, isnumber16_out_g(T96)) → U10_GGA(T95, T96, T98, d1_in_gga(T95, power(T95, T96), T98))
U9_GGA(T95, T96, T98, isnumber16_out_g(T96)) → D1_IN_GGA(T95, power(T95, T96), T98)
D1_IN_GGA(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) → U11_GGA(T125, T126, T127, isnumber16_in_g(T125))
D1_IN_GGA(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) → ISNUMBER16_IN_G(T125)
U11_GGA(T125, T126, T127, isnumber16_out_g(T125)) → U12_GGA(T125, T126, T127, d1_in_gga(T126, times(T125, T126), T127))
U11_GGA(T125, T126, T127, isnumber16_out_g(T125)) → D1_IN_GGA(T126, times(T125, T126), T127)
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) → U13_GGA(T154, T155, T156, T161, T160, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) → D1_IN_GGA(T154, times(times(T154, T155), T156), T159)
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U14_GGA(T154, T155, T156, T172, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U16_GGA(T154, T155, T156, T191, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) → U19_GGA(T226, T227, T228, T231, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) → D1_IN_GGA(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228))) → U20_GGA(T226, T227, T228, T239, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U22_GGA(T272, T273, T274, T277, T276, isnumber16_in_g(T273))
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → ISNUMBER16_IN_G(T273)
U22_GGA(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → U23_GGA(T272, T273, T274, T277, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
U22_GGA(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → D1_IN_GGA(T272, times(power(T272, T273), T274), T276)
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U24_GGA(T272, T273, T274, T287, T276, isnumber16_in_g(T273))
U24_GGA(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → U25_GGA(T272, T273, T274, T287, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
U24_GGA(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → D1_IN_GGA(T272, times(power(T272, T273), T274), T276)
D1_IN_GGA(div(T323, T324), div(T323, T324), 0) → U27_GGA(T323, T324, isnumber16_in_g(times(T323, power(T324, p(0)))))
D1_IN_GGA(div(T323, T324), div(T323, T324), 0) → ISNUMBER16_IN_G(times(T323, power(T324, p(0))))
D1_IN_GGA(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) → U28_GGA(T341, T342, T346, T345, d1_in_gga(T341, div(T341, T342), T345))
D1_IN_GGA(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) → D1_IN_GGA(T341, div(T341, T342), T345)
D1_IN_GGA(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0))))) → U29_GGA(T341, T342, T353, T345, d1_in_gga(T341, div(T341, T342), T345))
D1_IN_GGA(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) → U31_GGA(T367, T370, d1_in_gga(T367, power(T367, 0), T370))
D1_IN_GGA(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) → D1_IN_GGA(T367, power(T367, 0), T370)
D1_IN_GGA(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) → U32_GGA(T367, T378, T370, isnumber16_in_g(T378))
D1_IN_GGA(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) → ISNUMBER16_IN_G(T378)
U32_GGA(T367, T378, T370, isnumber16_out_g(T378)) → U33_GGA(T367, T378, T370, d1_in_gga(T367, power(T367, s(T378)), T370))
U32_GGA(T367, T378, T370, isnumber16_out_g(T378)) → D1_IN_GGA(T367, power(T367, s(T378)), T370)
D1_IN_GGA(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) → U34_GGA(T367, T387, T370, isnumber16_in_g(T387))
D1_IN_GGA(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) → ISNUMBER16_IN_G(T387)
U34_GGA(T367, T387, T370, isnumber16_out_g(T387)) → U35_GGA(T367, T387, T370, d1_in_gga(T367, power(T367, p(T387)), T370))
U34_GGA(T367, T387, T370, isnumber16_out_g(T387)) → D1_IN_GGA(T367, power(T367, p(T387)), T370)
D1_IN_GGA(s(T402), T397, 0) → U36_GGA(T402, T397, isnumber16_in_g(T402))
D1_IN_GGA(s(T402), T397, 0) → ISNUMBER16_IN_G(T402)
D1_IN_GGA(p(T407), T397, 0) → U37_GGA(T407, T397, isnumber16_in_g(T407))
D1_IN_GGA(p(T407), T397, 0) → ISNUMBER16_IN_G(T407)
D1_IN_GGA(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) → U38_GGA(T428, T429, T430, T434, T433, d1_in_gga(T428, T430, T433))
D1_IN_GGA(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) → D1_IN_GGA(T428, T430, T433)
D1_IN_GGA(times(T428, T429), T430, +(times(T437, T428), times(T433, T429))) → U39_GGA(T428, T429, T430, T437, T433, d1_in_gga(T428, T430, T433))
D1_IN_GGA(div(T460, T461), T462, T464) → U41_GGA(T460, T461, T462, T464, d1_in_gga(times(T460, power(T461, p(0))), T462, T464))
D1_IN_GGA(div(T460, T461), T462, T464) → D1_IN_GGA(times(T460, power(T461, p(0))), T462, T464)
D1_IN_GGA(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) → U42_GGA(T477, T478, T479, T481, isnumber16_in_g(T478))
D1_IN_GGA(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) → ISNUMBER16_IN_G(T478)
U42_GGA(T477, T478, T479, T481, isnumber16_out_g(T478)) → U43_GGA(T477, T478, T479, T481, d1_in_gga(T477, T479, T481))
U42_GGA(T477, T478, T479, T481, isnumber16_out_g(T478)) → D1_IN_GGA(T477, T479, T481)
D1_IN_GGA(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) → U44_GGA(T500, T490, T501, d1_in_gga(T490, T500, T501))
D1_IN_GGA(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) → D1_IN_GGA(T490, T500, T501)
D1_IN_GGA(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) → U45_GGA(T512, T490, T513, T514, isnumber16_in_g(T512))
D1_IN_GGA(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) → ISNUMBER16_IN_G(T512)
U45_GGA(T512, T490, T513, T514, isnumber16_out_g(T512)) → U46_GGA(T512, T490, T513, T514, d1_in_gga(T490, T513, T514))
U45_GGA(T512, T490, T513, T514, isnumber16_out_g(T512)) → D1_IN_GGA(T490, T513, T514)
D1_IN_GGA(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) → U47_GGA(T537, T538, T490, T539, T544, T543, T542, d1_in_gga(T537, T539, T542))
D1_IN_GGA(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) → D1_IN_GGA(T537, T539, T542)
D1_IN_GGA(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490))) → U48_GGA(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T537, T539, T542))
D1_IN_GGA(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490))) → U50_GGA(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T556, T539, T542))
D1_IN_GGA(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) → U53_GGA(T579, T580, T490, T581, T584, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
D1_IN_GGA(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) → D1_IN_GGA(times(T579, power(T580, p(0))), T581, T583)
D1_IN_GGA(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490))) → U54_GGA(T579, T580, T490, T581, T589, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
D1_IN_GGA(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) → U56_GGA(T614, T615, T490, T616, T619, T618, isnumber16_in_g(T615))
D1_IN_GGA(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) → ISNUMBER16_IN_G(T615)
U56_GGA(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → U57_GGA(T614, T615, T490, T616, T619, T618, d1_in_gga(T614, T616, T618))
U56_GGA(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → D1_IN_GGA(T614, T616, T618)
D1_IN_GGA(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490))) → U58_GGA(T614, T623, T490, T616, T622, T618, isnumber16_in_g(T623))
U58_GGA(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → U59_GGA(T614, T623, T490, T616, T622, T618, d1_in_gga(T614, T616, T618))
U58_GGA(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → D1_IN_GGA(T614, T616, T618)
D1_IN_GGA(div(T661, T662), T663, 0) → U61_GGA(T661, T662, T663, isnumber16_in_g(times(T661, power(T662, p(0)))))
D1_IN_GGA(div(T661, T662), T663, 0) → ISNUMBER16_IN_G(times(T661, power(T662, p(0))))
D1_IN_GGA(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) → U62_GGA(T684, T685, T686, T690, T689, d1_in_gga(T684, T686, T689))
D1_IN_GGA(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) → D1_IN_GGA(T684, T686, T689)
D1_IN_GGA(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0))))) → U63_GGA(T684, T685, T686, T693, T689, d1_in_gga(T684, T686, T689))
D1_IN_GGA(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) → U65_GGA(T704, T706, T708, d1_in_gga(T704, T706, T708))
D1_IN_GGA(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) → D1_IN_GGA(T704, T706, T708)
D1_IN_GGA(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) → U66_GGA(T704, T715, T706, T708, isnumber16_in_g(T715))
D1_IN_GGA(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) → ISNUMBER16_IN_G(T715)
U66_GGA(T704, T715, T706, T708, isnumber16_out_g(T715)) → U67_GGA(T704, T715, T706, T708, d1_in_gga(T704, T706, T708))
U66_GGA(T704, T715, T706, T708, isnumber16_out_g(T715)) → D1_IN_GGA(T704, T706, T708)
D1_IN_GGA(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) → U68_GGA(T704, T720, T706, T708, isnumber16_in_g(T720))
D1_IN_GGA(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) → ISNUMBER16_IN_G(T720)
U68_GGA(T704, T720, T706, T708, isnumber16_out_g(T720)) → U69_GGA(T704, T720, T706, T708, d1_in_gga(T704, T706, T708))
U68_GGA(T704, T720, T706, T708, isnumber16_out_g(T720)) → D1_IN_GGA(T704, T706, T708)
U63_GGA(T684, T685, T686, T693, T689, d1_out_gga(T684, T686, T689)) → U64_GGA(T684, T685, T686, T693, T689, d1_in_gga(power(T685, p(0)), T686, T693))
U63_GGA(T684, T685, T686, T693, T689, d1_out_gga(T684, T686, T689)) → D1_IN_GGA(power(T685, p(0)), T686, T693)
U59_GGA(T614, T623, T490, T616, T622, T618, d1_out_gga(T614, T616, T618)) → U60_GGA(T614, T623, T490, T616, T622, T618, d1_in_gga(T490, T616, T622))
U59_GGA(T614, T623, T490, T616, T622, T618, d1_out_gga(T614, T616, T618)) → D1_IN_GGA(T490, T616, T622)
U54_GGA(T579, T580, T490, T581, T589, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → U55_GGA(T579, T580, T490, T581, T589, T583, d1_in_gga(T490, T581, T589))
U54_GGA(T579, T580, T490, T581, T589, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → D1_IN_GGA(T490, T581, T589)
U50_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → U51_GGA(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T538, T539, T547))
U50_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → D1_IN_GGA(T538, T539, T547)
U51_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T538, T539, T547)) → U52_GGA(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T490, T539, T555))
U51_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T538, T539, T547)) → D1_IN_GGA(T490, T539, T555)
U48_GGA(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T537, T539, T542)) → U49_GGA(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T538, T539, T547))
U48_GGA(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T537, T539, T542)) → D1_IN_GGA(T538, T539, T547)
U39_GGA(T428, T429, T430, T437, T433, d1_out_gga(T428, T430, T433)) → U40_GGA(T428, T429, T430, T437, T433, d1_in_gga(T429, T430, T437))
U39_GGA(T428, T429, T430, T437, T433, d1_out_gga(T428, T430, T433)) → D1_IN_GGA(T429, T430, T437)
U29_GGA(T341, T342, T353, T345, d1_out_gga(T341, div(T341, T342), T345)) → U30_GGA(T341, T342, T353, T345, d1_in_gga(power(T342, p(0)), div(T341, T342), T353))
U29_GGA(T341, T342, T353, T345, d1_out_gga(T341, div(T341, T342), T345)) → D1_IN_GGA(power(T342, p(0)), div(T341, T342), T353)
U25_GGA(T272, T273, T274, T287, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → U26_GGA(T272, T273, T274, T287, T276, d1_in_gga(T274, times(power(T272, T273), T274), T287))
U25_GGA(T272, T273, T274, T287, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → D1_IN_GGA(T274, times(power(T272, T273), T274), T287)
U20_GGA(T226, T227, T228, T239, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → U21_GGA(T226, T227, T228, T239, T230, d1_in_gga(T228, times(div(T226, T227), T228), T239))
U20_GGA(T226, T227, T228, T239, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → D1_IN_GGA(T228, times(div(T226, T227), T228), T239)
U16_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U17_GGA(T154, T155, T156, T191, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U16_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → D1_IN_GGA(T155, times(times(T154, T155), T156), T171)
U17_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → U18_GGA(T154, T155, T156, T191, T171, T159, d1_in_gga(T156, times(times(T154, T155), T156), T191))
U17_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → D1_IN_GGA(T156, times(times(T154, T155), T156), T191)
U14_GGA(T154, T155, T156, T172, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U15_GGA(T154, T155, T156, T172, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U14_GGA(T154, T155, T156, T172, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → D1_IN_GGA(T155, times(times(T154, T155), T156), T171)
U6_GGA(T42, T43, T54, T46, d1_out_gga(T42, times(T42, T43), T46)) → U7_GGA(T42, T43, T54, T46, d1_in_gga(T43, times(T42, T43), T54))
U6_GGA(T42, T43, T54, T46, d1_out_gga(T42, times(T42, T43), T46)) → D1_IN_GGA(T43, times(T42, T43), T54)

The TRS R consists of the following rules:

d1_in_gga(T5, T5, 1) → d1_out_gga(T5, T5, 1)
d1_in_gga(0, 0, 0) → d1_out_gga(0, 0, 0)
d1_in_gga(s(T12), s(T12), 0) → U3_gga(T12, isnumber16_in_g(T12))
isnumber16_in_g(0) → isnumber16_out_g(0)
isnumber16_in_g(s(T17)) → U1_g(T17, isnumber16_in_g(T17))
isnumber16_in_g(p(T20)) → U2_g(T20, isnumber16_in_g(T20))
U2_g(T20, isnumber16_out_g(T20)) → isnumber16_out_g(p(T20))
U1_g(T17, isnumber16_out_g(T17)) → isnumber16_out_g(s(T17))
U3_gga(T12, isnumber16_out_g(T12)) → d1_out_gga(s(T12), s(T12), 0)
d1_in_gga(p(T25), p(T25), 0) → U4_gga(T25, isnumber16_in_g(T25))
U4_gga(T25, isnumber16_out_g(T25)) → d1_out_gga(p(T25), p(T25), 0)
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) → U5_gga(T42, T43, T47, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43))) → U6_gga(T42, T43, T54, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(div(T79, T80), div(T79, T80), T82) → U8_gga(T79, T80, T82, d1_in_gga(times(T79, power(T80, p(0))), div(T79, T80), T82))
d1_in_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) → U9_gga(T95, T96, T98, isnumber16_in_g(T96))
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → U10_gga(T95, T96, T98, d1_in_gga(T95, power(T95, T96), T98))
d1_in_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) → U11_gga(T125, T126, T127, isnumber16_in_g(T125))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → U12_gga(T125, T126, T127, d1_in_gga(T126, times(T125, T126), T127))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) → U13_gga(T154, T155, T156, T161, T160, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U14_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U16_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) → U19_gga(T226, T227, T228, T231, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228))) → U20_gga(T226, T227, T228, T239, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U22_gga(T272, T273, T274, T277, T276, isnumber16_in_g(T273))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → U23_gga(T272, T273, T274, T277, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U24_gga(T272, T273, T274, T287, T276, isnumber16_in_g(T273))
U24_gga(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → U25_gga(T272, T273, T274, T287, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
d1_in_gga(div(T323, T324), div(T323, T324), 0) → U27_gga(T323, T324, isnumber16_in_g(times(T323, power(T324, p(0)))))
U27_gga(T323, T324, isnumber16_out_g(times(T323, power(T324, p(0))))) → d1_out_gga(div(T323, T324), div(T323, T324), 0)
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) → U28_gga(T341, T342, T346, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0))))) → U29_gga(T341, T342, T353, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) → U31_gga(T367, T370, d1_in_gga(T367, power(T367, 0), T370))
d1_in_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) → U32_gga(T367, T378, T370, isnumber16_in_g(T378))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → U33_gga(T367, T378, T370, d1_in_gga(T367, power(T367, s(T378)), T370))
d1_in_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) → U34_gga(T367, T387, T370, isnumber16_in_g(T387))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → U35_gga(T367, T387, T370, d1_in_gga(T367, power(T367, p(T387)), T370))
d1_in_gga(0, T397, 0) → d1_out_gga(0, T397, 0)
d1_in_gga(s(T402), T397, 0) → U36_gga(T402, T397, isnumber16_in_g(T402))
U36_gga(T402, T397, isnumber16_out_g(T402)) → d1_out_gga(s(T402), T397, 0)
d1_in_gga(p(T407), T397, 0) → U37_gga(T407, T397, isnumber16_in_g(T407))
U37_gga(T407, T397, isnumber16_out_g(T407)) → d1_out_gga(p(T407), T397, 0)
d1_in_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) → U38_gga(T428, T429, T430, T434, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429))) → U39_gga(T428, T429, T430, T437, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(div(T460, T461), T462, T464) → U41_gga(T460, T461, T462, T464, d1_in_gga(times(T460, power(T461, p(0))), T462, T464))
d1_in_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) → U42_gga(T477, T478, T479, T481, isnumber16_in_g(T478))
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → U43_gga(T477, T478, T479, T481, d1_in_gga(T477, T479, T481))
d1_in_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) → U44_gga(T500, T490, T501, d1_in_gga(T490, T500, T501))
d1_in_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) → U45_gga(T512, T490, T513, T514, isnumber16_in_g(T512))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → U46_gga(T512, T490, T513, T514, d1_in_gga(T490, T513, T514))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) → U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490))) → U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490))) → U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T556, T539, T542))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) → U53_gga(T579, T580, T490, T581, T584, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490))) → U54_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) → U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_in_g(T615))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → U57_gga(T614, T615, T490, T616, T619, T618, d1_in_gga(T614, T616, T618))
d1_in_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490))) → U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_in_g(T623))
U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → U59_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T614, T616, T618))
d1_in_gga(div(T647, T648), times(T647, power(T648, p(0))), 1) → d1_out_gga(div(T647, T648), times(T647, power(T648, p(0))), 1)
d1_in_gga(div(T661, T662), T663, 0) → U61_gga(T661, T662, T663, isnumber16_in_g(times(T661, power(T662, p(0)))))
U61_gga(T661, T662, T663, isnumber16_out_g(times(T661, power(T662, p(0))))) → d1_out_gga(div(T661, T662), T663, 0)
d1_in_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) → U62_gga(T684, T685, T686, T690, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0))))) → U63_gga(T684, T685, T686, T693, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) → U65_gga(T704, T706, T708, d1_in_gga(T704, T706, T708))
d1_in_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) → U66_gga(T704, T715, T706, T708, isnumber16_in_g(T715))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → U67_gga(T704, T715, T706, T708, d1_in_gga(T704, T706, T708))
d1_in_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) → U68_gga(T704, T720, T706, T708, isnumber16_in_g(T720))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → U69_gga(T704, T720, T706, T708, d1_in_gga(T704, T706, T708))
U69_gga(T704, T720, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U67_gga(T704, T715, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U65_gga(T704, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0)))))
U63_gga(T684, T685, T686, T693, T689, d1_out_gga(T684, T686, T689)) → U64_gga(T684, T685, T686, T693, T689, d1_in_gga(power(T685, p(0)), T686, T693))
U64_gga(T684, T685, T686, T693, T689, d1_out_gga(power(T685, p(0)), T686, T693)) → d1_out_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0)))))
U62_gga(T684, T685, T686, T690, T689, d1_out_gga(T684, T686, T689)) → d1_out_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0)))))
U59_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T614, T616, T618)) → U60_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T490, T616, T622))
U60_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T490, T616, T622)) → d1_out_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490)))
U57_gga(T614, T615, T490, T616, T619, T618, d1_out_gga(T614, T616, T618)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U54_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → U55_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(T490, T581, T589))
U55_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(T490, T581, T589)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490)))
U53_gga(T579, T580, T490, T581, T584, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490)))
U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T538, T539, T547))
U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T538, T539, T547)) → U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T490, T539, T555))
U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T490, T539, T555)) → d1_out_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490)))
U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T537, T539, T542)) → U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T538, T539, T547))
U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T538, T539, T547)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490)))
U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_out_gga(T537, T539, T542)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490)))
U46_gga(T512, T490, T513, T514, d1_out_gga(T490, T513, T514)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U44_gga(T500, T490, T501, d1_out_gga(T490, T500, T501)) → d1_out_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490)))
U43_gga(T477, T478, T479, T481, d1_out_gga(T477, T479, T481)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U41_gga(T460, T461, T462, T464, d1_out_gga(times(T460, power(T461, p(0))), T462, T464)) → d1_out_gga(div(T460, T461), T462, T464)
U39_gga(T428, T429, T430, T437, T433, d1_out_gga(T428, T430, T433)) → U40_gga(T428, T429, T430, T437, T433, d1_in_gga(T429, T430, T437))
U40_gga(T428, T429, T430, T437, T433, d1_out_gga(T429, T430, T437)) → d1_out_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429)))
U38_gga(T428, T429, T430, T434, T433, d1_out_gga(T428, T430, T433)) → d1_out_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429)))
U35_gga(T367, T387, T370, d1_out_gga(T367, power(T367, p(T387)), T370)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U33_gga(T367, T378, T370, d1_out_gga(T367, power(T367, s(T378)), T370)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U31_gga(T367, T370, d1_out_gga(T367, power(T367, 0), T370)) → d1_out_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0)))))
U29_gga(T341, T342, T353, T345, d1_out_gga(T341, div(T341, T342), T345)) → U30_gga(T341, T342, T353, T345, d1_in_gga(power(T342, p(0)), div(T341, T342), T353))
U30_gga(T341, T342, T353, T345, d1_out_gga(power(T342, p(0)), div(T341, T342), T353)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0)))))
U28_gga(T341, T342, T346, T345, d1_out_gga(T341, div(T341, T342), T345)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0)))))
U25_gga(T272, T273, T274, T287, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → U26_gga(T272, T273, T274, T287, T276, d1_in_gga(T274, times(power(T272, T273), T274), T287))
U26_gga(T272, T273, T274, T287, T276, d1_out_gga(T274, times(power(T272, T273), T274), T287)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U23_gga(T272, T273, T274, T277, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U20_gga(T226, T227, T228, T239, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → U21_gga(T226, T227, T228, T239, T230, d1_in_gga(T228, times(div(T226, T227), T228), T239))
U21_gga(T226, T227, T228, T239, T230, d1_out_gga(T228, times(div(T226, T227), T228), T239)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228)))
U19_gga(T226, T227, T228, T231, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228)))
U16_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U17_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U17_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → U18_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T156, times(times(T154, T155), T156), T191))
U18_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T156, times(times(T154, T155), T156), T191)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U14_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U15_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U15_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U13_gga(T154, T155, T156, T161, T160, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156)))
U12_gga(T125, T126, T127, d1_out_gga(T126, times(T125, T126), T127)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U10_gga(T95, T96, T98, d1_out_gga(T95, power(T95, T96), T98)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U8_gga(T79, T80, T82, d1_out_gga(times(T79, power(T80, p(0))), div(T79, T80), T82)) → d1_out_gga(div(T79, T80), div(T79, T80), T82)
U6_gga(T42, T43, T54, T46, d1_out_gga(T42, times(T42, T43), T46)) → U7_gga(T42, T43, T54, T46, d1_in_gga(T43, times(T42, T43), T54))
U7_gga(T42, T43, T54, T46, d1_out_gga(T43, times(T42, T43), T54)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43)))
U5_gga(T42, T43, T47, T46, d1_out_gga(T42, times(T42, T43), T46)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43)))

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 2 SCCs with 59 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

ISNUMBER16_IN_G(p(T20)) → ISNUMBER16_IN_G(T20)
ISNUMBER16_IN_G(s(T17)) → ISNUMBER16_IN_G(T17)

The TRS R consists of the following rules:

d1_in_gga(T5, T5, 1) → d1_out_gga(T5, T5, 1)
d1_in_gga(0, 0, 0) → d1_out_gga(0, 0, 0)
d1_in_gga(s(T12), s(T12), 0) → U3_gga(T12, isnumber16_in_g(T12))
isnumber16_in_g(0) → isnumber16_out_g(0)
isnumber16_in_g(s(T17)) → U1_g(T17, isnumber16_in_g(T17))
isnumber16_in_g(p(T20)) → U2_g(T20, isnumber16_in_g(T20))
U2_g(T20, isnumber16_out_g(T20)) → isnumber16_out_g(p(T20))
U1_g(T17, isnumber16_out_g(T17)) → isnumber16_out_g(s(T17))
U3_gga(T12, isnumber16_out_g(T12)) → d1_out_gga(s(T12), s(T12), 0)
d1_in_gga(p(T25), p(T25), 0) → U4_gga(T25, isnumber16_in_g(T25))
U4_gga(T25, isnumber16_out_g(T25)) → d1_out_gga(p(T25), p(T25), 0)
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) → U5_gga(T42, T43, T47, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43))) → U6_gga(T42, T43, T54, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(div(T79, T80), div(T79, T80), T82) → U8_gga(T79, T80, T82, d1_in_gga(times(T79, power(T80, p(0))), div(T79, T80), T82))
d1_in_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) → U9_gga(T95, T96, T98, isnumber16_in_g(T96))
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → U10_gga(T95, T96, T98, d1_in_gga(T95, power(T95, T96), T98))
d1_in_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) → U11_gga(T125, T126, T127, isnumber16_in_g(T125))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → U12_gga(T125, T126, T127, d1_in_gga(T126, times(T125, T126), T127))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) → U13_gga(T154, T155, T156, T161, T160, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U14_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U16_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) → U19_gga(T226, T227, T228, T231, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228))) → U20_gga(T226, T227, T228, T239, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U22_gga(T272, T273, T274, T277, T276, isnumber16_in_g(T273))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → U23_gga(T272, T273, T274, T277, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U24_gga(T272, T273, T274, T287, T276, isnumber16_in_g(T273))
U24_gga(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → U25_gga(T272, T273, T274, T287, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
d1_in_gga(div(T323, T324), div(T323, T324), 0) → U27_gga(T323, T324, isnumber16_in_g(times(T323, power(T324, p(0)))))
U27_gga(T323, T324, isnumber16_out_g(times(T323, power(T324, p(0))))) → d1_out_gga(div(T323, T324), div(T323, T324), 0)
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) → U28_gga(T341, T342, T346, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0))))) → U29_gga(T341, T342, T353, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) → U31_gga(T367, T370, d1_in_gga(T367, power(T367, 0), T370))
d1_in_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) → U32_gga(T367, T378, T370, isnumber16_in_g(T378))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → U33_gga(T367, T378, T370, d1_in_gga(T367, power(T367, s(T378)), T370))
d1_in_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) → U34_gga(T367, T387, T370, isnumber16_in_g(T387))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → U35_gga(T367, T387, T370, d1_in_gga(T367, power(T367, p(T387)), T370))
d1_in_gga(0, T397, 0) → d1_out_gga(0, T397, 0)
d1_in_gga(s(T402), T397, 0) → U36_gga(T402, T397, isnumber16_in_g(T402))
U36_gga(T402, T397, isnumber16_out_g(T402)) → d1_out_gga(s(T402), T397, 0)
d1_in_gga(p(T407), T397, 0) → U37_gga(T407, T397, isnumber16_in_g(T407))
U37_gga(T407, T397, isnumber16_out_g(T407)) → d1_out_gga(p(T407), T397, 0)
d1_in_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) → U38_gga(T428, T429, T430, T434, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429))) → U39_gga(T428, T429, T430, T437, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(div(T460, T461), T462, T464) → U41_gga(T460, T461, T462, T464, d1_in_gga(times(T460, power(T461, p(0))), T462, T464))
d1_in_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) → U42_gga(T477, T478, T479, T481, isnumber16_in_g(T478))
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → U43_gga(T477, T478, T479, T481, d1_in_gga(T477, T479, T481))
d1_in_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) → U44_gga(T500, T490, T501, d1_in_gga(T490, T500, T501))
d1_in_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) → U45_gga(T512, T490, T513, T514, isnumber16_in_g(T512))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → U46_gga(T512, T490, T513, T514, d1_in_gga(T490, T513, T514))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) → U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490))) → U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490))) → U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T556, T539, T542))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) → U53_gga(T579, T580, T490, T581, T584, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490))) → U54_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) → U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_in_g(T615))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → U57_gga(T614, T615, T490, T616, T619, T618, d1_in_gga(T614, T616, T618))
d1_in_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490))) → U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_in_g(T623))
U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → U59_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T614, T616, T618))
d1_in_gga(div(T647, T648), times(T647, power(T648, p(0))), 1) → d1_out_gga(div(T647, T648), times(T647, power(T648, p(0))), 1)
d1_in_gga(div(T661, T662), T663, 0) → U61_gga(T661, T662, T663, isnumber16_in_g(times(T661, power(T662, p(0)))))
U61_gga(T661, T662, T663, isnumber16_out_g(times(T661, power(T662, p(0))))) → d1_out_gga(div(T661, T662), T663, 0)
d1_in_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) → U62_gga(T684, T685, T686, T690, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0))))) → U63_gga(T684, T685, T686, T693, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) → U65_gga(T704, T706, T708, d1_in_gga(T704, T706, T708))
d1_in_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) → U66_gga(T704, T715, T706, T708, isnumber16_in_g(T715))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → U67_gga(T704, T715, T706, T708, d1_in_gga(T704, T706, T708))
d1_in_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) → U68_gga(T704, T720, T706, T708, isnumber16_in_g(T720))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → U69_gga(T704, T720, T706, T708, d1_in_gga(T704, T706, T708))
U69_gga(T704, T720, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U67_gga(T704, T715, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U65_gga(T704, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0)))))
U63_gga(T684, T685, T686, T693, T689, d1_out_gga(T684, T686, T689)) → U64_gga(T684, T685, T686, T693, T689, d1_in_gga(power(T685, p(0)), T686, T693))
U64_gga(T684, T685, T686, T693, T689, d1_out_gga(power(T685, p(0)), T686, T693)) → d1_out_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0)))))
U62_gga(T684, T685, T686, T690, T689, d1_out_gga(T684, T686, T689)) → d1_out_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0)))))
U59_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T614, T616, T618)) → U60_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T490, T616, T622))
U60_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T490, T616, T622)) → d1_out_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490)))
U57_gga(T614, T615, T490, T616, T619, T618, d1_out_gga(T614, T616, T618)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U54_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → U55_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(T490, T581, T589))
U55_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(T490, T581, T589)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490)))
U53_gga(T579, T580, T490, T581, T584, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490)))
U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T538, T539, T547))
U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T538, T539, T547)) → U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T490, T539, T555))
U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T490, T539, T555)) → d1_out_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490)))
U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T537, T539, T542)) → U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T538, T539, T547))
U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T538, T539, T547)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490)))
U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_out_gga(T537, T539, T542)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490)))
U46_gga(T512, T490, T513, T514, d1_out_gga(T490, T513, T514)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U44_gga(T500, T490, T501, d1_out_gga(T490, T500, T501)) → d1_out_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490)))
U43_gga(T477, T478, T479, T481, d1_out_gga(T477, T479, T481)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U41_gga(T460, T461, T462, T464, d1_out_gga(times(T460, power(T461, p(0))), T462, T464)) → d1_out_gga(div(T460, T461), T462, T464)
U39_gga(T428, T429, T430, T437, T433, d1_out_gga(T428, T430, T433)) → U40_gga(T428, T429, T430, T437, T433, d1_in_gga(T429, T430, T437))
U40_gga(T428, T429, T430, T437, T433, d1_out_gga(T429, T430, T437)) → d1_out_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429)))
U38_gga(T428, T429, T430, T434, T433, d1_out_gga(T428, T430, T433)) → d1_out_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429)))
U35_gga(T367, T387, T370, d1_out_gga(T367, power(T367, p(T387)), T370)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U33_gga(T367, T378, T370, d1_out_gga(T367, power(T367, s(T378)), T370)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U31_gga(T367, T370, d1_out_gga(T367, power(T367, 0), T370)) → d1_out_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0)))))
U29_gga(T341, T342, T353, T345, d1_out_gga(T341, div(T341, T342), T345)) → U30_gga(T341, T342, T353, T345, d1_in_gga(power(T342, p(0)), div(T341, T342), T353))
U30_gga(T341, T342, T353, T345, d1_out_gga(power(T342, p(0)), div(T341, T342), T353)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0)))))
U28_gga(T341, T342, T346, T345, d1_out_gga(T341, div(T341, T342), T345)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0)))))
U25_gga(T272, T273, T274, T287, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → U26_gga(T272, T273, T274, T287, T276, d1_in_gga(T274, times(power(T272, T273), T274), T287))
U26_gga(T272, T273, T274, T287, T276, d1_out_gga(T274, times(power(T272, T273), T274), T287)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U23_gga(T272, T273, T274, T277, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U20_gga(T226, T227, T228, T239, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → U21_gga(T226, T227, T228, T239, T230, d1_in_gga(T228, times(div(T226, T227), T228), T239))
U21_gga(T226, T227, T228, T239, T230, d1_out_gga(T228, times(div(T226, T227), T228), T239)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228)))
U19_gga(T226, T227, T228, T231, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228)))
U16_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U17_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U17_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → U18_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T156, times(times(T154, T155), T156), T191))
U18_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T156, times(times(T154, T155), T156), T191)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U14_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U15_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U15_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U13_gga(T154, T155, T156, T161, T160, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156)))
U12_gga(T125, T126, T127, d1_out_gga(T126, times(T125, T126), T127)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U10_gga(T95, T96, T98, d1_out_gga(T95, power(T95, T96), T98)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U8_gga(T79, T80, T82, d1_out_gga(times(T79, power(T80, p(0))), div(T79, T80), T82)) → d1_out_gga(div(T79, T80), div(T79, T80), T82)
U6_gga(T42, T43, T54, T46, d1_out_gga(T42, times(T42, T43), T46)) → U7_gga(T42, T43, T54, T46, d1_in_gga(T43, times(T42, T43), T54))
U7_gga(T42, T43, T54, T46, d1_out_gga(T43, times(T42, T43), T54)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43)))
U5_gga(T42, T43, T47, T46, d1_out_gga(T42, times(T42, T43), T46)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43)))

(10) UsableRulesProof (EQUIVALENT transformation)

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

(11) Obligation:

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

ISNUMBER16_IN_G(p(T20)) → ISNUMBER16_IN_G(T20)
ISNUMBER16_IN_G(s(T17)) → ISNUMBER16_IN_G(T17)

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

(12) PiDPToQDPProof (EQUIVALENT transformation)

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

(13) Obligation:

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

ISNUMBER16_IN_G(p(T20)) → ISNUMBER16_IN_G(T20)
ISNUMBER16_IN_G(s(T17)) → ISNUMBER16_IN_G(T17)

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

(14) 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:

ISNUMBER16_IN_G(p(T20)) → ISNUMBER16_IN_G(T20)
The graph contains the following edges 1 > 1
ISNUMBER16_IN_G(s(T17)) → ISNUMBER16_IN_G(T17)
The graph contains the following edges 1 > 1

(15) YES

(16) Obligation:

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

D1_IN_GGA(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) → D1_IN_GGA(T42, times(T42, T43), T46)
D1_IN_GGA(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43))) → U6_GGA(T42, T43, T54, T46, d1_in_gga(T42, times(T42, T43), T46))
U6_GGA(T42, T43, T54, T46, d1_out_gga(T42, times(T42, T43), T46)) → D1_IN_GGA(T43, times(T42, T43), T54)
D1_IN_GGA(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) → U11_GGA(T125, T126, T127, isnumber16_in_g(T125))
U11_GGA(T125, T126, T127, isnumber16_out_g(T125)) → D1_IN_GGA(T126, times(T125, T126), T127)
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) → D1_IN_GGA(T154, times(times(T154, T155), T156), T159)
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U14_GGA(T154, T155, T156, T172, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
U14_GGA(T154, T155, T156, T172, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → D1_IN_GGA(T155, times(times(T154, T155), T156), T171)
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U16_GGA(T154, T155, T156, T191, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
U16_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U17_GGA(T154, T155, T156, T191, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U17_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → D1_IN_GGA(T156, times(times(T154, T155), T156), T191)
D1_IN_GGA(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) → D1_IN_GGA(T428, T430, T433)
D1_IN_GGA(div(T79, T80), div(T79, T80), T82) → D1_IN_GGA(times(T79, power(T80, p(0))), div(T79, T80), T82)
D1_IN_GGA(times(T428, T429), T430, +(times(T437, T428), times(T433, T429))) → U39_GGA(T428, T429, T430, T437, T433, d1_in_gga(T428, T430, T433))
U39_GGA(T428, T429, T430, T437, T433, d1_out_gga(T428, T430, T433)) → D1_IN_GGA(T429, T430, T437)
D1_IN_GGA(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) → U9_GGA(T95, T96, T98, isnumber16_in_g(T96))
U9_GGA(T95, T96, T98, isnumber16_out_g(T96)) → D1_IN_GGA(T95, power(T95, T96), T98)
D1_IN_GGA(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) → D1_IN_GGA(T367, power(T367, 0), T370)
D1_IN_GGA(div(T460, T461), T462, T464) → D1_IN_GGA(times(T460, power(T461, p(0))), T462, T464)
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) → D1_IN_GGA(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228))) → U20_GGA(T226, T227, T228, T239, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
U20_GGA(T226, T227, T228, T239, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → D1_IN_GGA(T228, times(div(T226, T227), T228), T239)
D1_IN_GGA(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) → U42_GGA(T477, T478, T479, T481, isnumber16_in_g(T478))
U42_GGA(T477, T478, T479, T481, isnumber16_out_g(T478)) → D1_IN_GGA(T477, T479, T481)
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U22_GGA(T272, T273, T274, T277, T276, isnumber16_in_g(T273))
U22_GGA(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → D1_IN_GGA(T272, times(power(T272, T273), T274), T276)
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U24_GGA(T272, T273, T274, T287, T276, isnumber16_in_g(T273))
U24_GGA(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → U25_GGA(T272, T273, T274, T287, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
U25_GGA(T272, T273, T274, T287, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → D1_IN_GGA(T274, times(power(T272, T273), T274), T287)
D1_IN_GGA(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) → D1_IN_GGA(T490, T500, T501)
D1_IN_GGA(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) → D1_IN_GGA(T341, div(T341, T342), T345)
D1_IN_GGA(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0))))) → U29_GGA(T341, T342, T353, T345, d1_in_gga(T341, div(T341, T342), T345))
U29_GGA(T341, T342, T353, T345, d1_out_gga(T341, div(T341, T342), T345)) → D1_IN_GGA(power(T342, p(0)), div(T341, T342), T353)
D1_IN_GGA(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) → U68_GGA(T704, T720, T706, T708, isnumber16_in_g(T720))
U68_GGA(T704, T720, T706, T708, isnumber16_out_g(T720)) → D1_IN_GGA(T704, T706, T708)
D1_IN_GGA(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) → U32_GGA(T367, T378, T370, isnumber16_in_g(T378))
U32_GGA(T367, T378, T370, isnumber16_out_g(T378)) → D1_IN_GGA(T367, power(T367, s(T378)), T370)
D1_IN_GGA(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) → U45_GGA(T512, T490, T513, T514, isnumber16_in_g(T512))
U45_GGA(T512, T490, T513, T514, isnumber16_out_g(T512)) → D1_IN_GGA(T490, T513, T514)
D1_IN_GGA(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) → U34_GGA(T367, T387, T370, isnumber16_in_g(T387))
U34_GGA(T367, T387, T370, isnumber16_out_g(T387)) → D1_IN_GGA(T367, power(T367, p(T387)), T370)
D1_IN_GGA(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) → D1_IN_GGA(T537, T539, T542)
D1_IN_GGA(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490))) → U48_GGA(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T537, T539, T542))
U48_GGA(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T537, T539, T542)) → D1_IN_GGA(T538, T539, T547)
D1_IN_GGA(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490))) → U50_GGA(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T556, T539, T542))
U50_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → U51_GGA(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T538, T539, T547))
U51_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T538, T539, T547)) → D1_IN_GGA(T490, T539, T555)
D1_IN_GGA(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) → D1_IN_GGA(times(T579, power(T580, p(0))), T581, T583)
D1_IN_GGA(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490))) → U54_GGA(T579, T580, T490, T581, T589, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
U54_GGA(T579, T580, T490, T581, T589, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → D1_IN_GGA(T490, T581, T589)
D1_IN_GGA(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) → U56_GGA(T614, T615, T490, T616, T619, T618, isnumber16_in_g(T615))
U56_GGA(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → D1_IN_GGA(T614, T616, T618)
D1_IN_GGA(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490))) → U58_GGA(T614, T623, T490, T616, T622, T618, isnumber16_in_g(T623))
U58_GGA(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → U59_GGA(T614, T623, T490, T616, T622, T618, d1_in_gga(T614, T616, T618))
U59_GGA(T614, T623, T490, T616, T622, T618, d1_out_gga(T614, T616, T618)) → D1_IN_GGA(T490, T616, T622)
D1_IN_GGA(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) → D1_IN_GGA(T684, T686, T689)
D1_IN_GGA(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0))))) → U63_GGA(T684, T685, T686, T693, T689, d1_in_gga(T684, T686, T689))
U63_GGA(T684, T685, T686, T693, T689, d1_out_gga(T684, T686, T689)) → D1_IN_GGA(power(T685, p(0)), T686, T693)
D1_IN_GGA(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) → D1_IN_GGA(T704, T706, T708)
D1_IN_GGA(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) → U66_GGA(T704, T715, T706, T708, isnumber16_in_g(T715))
U66_GGA(T704, T715, T706, T708, isnumber16_out_g(T715)) → D1_IN_GGA(T704, T706, T708)
U58_GGA(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → D1_IN_GGA(T614, T616, T618)
U50_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → D1_IN_GGA(T538, T539, T547)
U24_GGA(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → D1_IN_GGA(T272, times(power(T272, T273), T274), T276)
U16_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → D1_IN_GGA(T155, times(times(T154, T155), T156), T171)

The TRS R consists of the following rules:

d1_in_gga(T5, T5, 1) → d1_out_gga(T5, T5, 1)
d1_in_gga(0, 0, 0) → d1_out_gga(0, 0, 0)
d1_in_gga(s(T12), s(T12), 0) → U3_gga(T12, isnumber16_in_g(T12))
isnumber16_in_g(0) → isnumber16_out_g(0)
isnumber16_in_g(s(T17)) → U1_g(T17, isnumber16_in_g(T17))
isnumber16_in_g(p(T20)) → U2_g(T20, isnumber16_in_g(T20))
U2_g(T20, isnumber16_out_g(T20)) → isnumber16_out_g(p(T20))
U1_g(T17, isnumber16_out_g(T17)) → isnumber16_out_g(s(T17))
U3_gga(T12, isnumber16_out_g(T12)) → d1_out_gga(s(T12), s(T12), 0)
d1_in_gga(p(T25), p(T25), 0) → U4_gga(T25, isnumber16_in_g(T25))
U4_gga(T25, isnumber16_out_g(T25)) → d1_out_gga(p(T25), p(T25), 0)
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) → U5_gga(T42, T43, T47, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43))) → U6_gga(T42, T43, T54, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(div(T79, T80), div(T79, T80), T82) → U8_gga(T79, T80, T82, d1_in_gga(times(T79, power(T80, p(0))), div(T79, T80), T82))
d1_in_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) → U9_gga(T95, T96, T98, isnumber16_in_g(T96))
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → U10_gga(T95, T96, T98, d1_in_gga(T95, power(T95, T96), T98))
d1_in_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) → U11_gga(T125, T126, T127, isnumber16_in_g(T125))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → U12_gga(T125, T126, T127, d1_in_gga(T126, times(T125, T126), T127))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) → U13_gga(T154, T155, T156, T161, T160, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U14_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U16_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) → U19_gga(T226, T227, T228, T231, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228))) → U20_gga(T226, T227, T228, T239, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U22_gga(T272, T273, T274, T277, T276, isnumber16_in_g(T273))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → U23_gga(T272, T273, T274, T277, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U24_gga(T272, T273, T274, T287, T276, isnumber16_in_g(T273))
U24_gga(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → U25_gga(T272, T273, T274, T287, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
d1_in_gga(div(T323, T324), div(T323, T324), 0) → U27_gga(T323, T324, isnumber16_in_g(times(T323, power(T324, p(0)))))
U27_gga(T323, T324, isnumber16_out_g(times(T323, power(T324, p(0))))) → d1_out_gga(div(T323, T324), div(T323, T324), 0)
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) → U28_gga(T341, T342, T346, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0))))) → U29_gga(T341, T342, T353, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) → U31_gga(T367, T370, d1_in_gga(T367, power(T367, 0), T370))
d1_in_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) → U32_gga(T367, T378, T370, isnumber16_in_g(T378))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → U33_gga(T367, T378, T370, d1_in_gga(T367, power(T367, s(T378)), T370))
d1_in_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) → U34_gga(T367, T387, T370, isnumber16_in_g(T387))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → U35_gga(T367, T387, T370, d1_in_gga(T367, power(T367, p(T387)), T370))
d1_in_gga(0, T397, 0) → d1_out_gga(0, T397, 0)
d1_in_gga(s(T402), T397, 0) → U36_gga(T402, T397, isnumber16_in_g(T402))
U36_gga(T402, T397, isnumber16_out_g(T402)) → d1_out_gga(s(T402), T397, 0)
d1_in_gga(p(T407), T397, 0) → U37_gga(T407, T397, isnumber16_in_g(T407))
U37_gga(T407, T397, isnumber16_out_g(T407)) → d1_out_gga(p(T407), T397, 0)
d1_in_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) → U38_gga(T428, T429, T430, T434, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429))) → U39_gga(T428, T429, T430, T437, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(div(T460, T461), T462, T464) → U41_gga(T460, T461, T462, T464, d1_in_gga(times(T460, power(T461, p(0))), T462, T464))
d1_in_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) → U42_gga(T477, T478, T479, T481, isnumber16_in_g(T478))
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → U43_gga(T477, T478, T479, T481, d1_in_gga(T477, T479, T481))
d1_in_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) → U44_gga(T500, T490, T501, d1_in_gga(T490, T500, T501))
d1_in_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) → U45_gga(T512, T490, T513, T514, isnumber16_in_g(T512))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → U46_gga(T512, T490, T513, T514, d1_in_gga(T490, T513, T514))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) → U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490))) → U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490))) → U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T556, T539, T542))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) → U53_gga(T579, T580, T490, T581, T584, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490))) → U54_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) → U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_in_g(T615))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → U57_gga(T614, T615, T490, T616, T619, T618, d1_in_gga(T614, T616, T618))
d1_in_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490))) → U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_in_g(T623))
U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → U59_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T614, T616, T618))
d1_in_gga(div(T647, T648), times(T647, power(T648, p(0))), 1) → d1_out_gga(div(T647, T648), times(T647, power(T648, p(0))), 1)
d1_in_gga(div(T661, T662), T663, 0) → U61_gga(T661, T662, T663, isnumber16_in_g(times(T661, power(T662, p(0)))))
U61_gga(T661, T662, T663, isnumber16_out_g(times(T661, power(T662, p(0))))) → d1_out_gga(div(T661, T662), T663, 0)
d1_in_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) → U62_gga(T684, T685, T686, T690, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0))))) → U63_gga(T684, T685, T686, T693, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) → U65_gga(T704, T706, T708, d1_in_gga(T704, T706, T708))
d1_in_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) → U66_gga(T704, T715, T706, T708, isnumber16_in_g(T715))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → U67_gga(T704, T715, T706, T708, d1_in_gga(T704, T706, T708))
d1_in_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) → U68_gga(T704, T720, T706, T708, isnumber16_in_g(T720))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → U69_gga(T704, T720, T706, T708, d1_in_gga(T704, T706, T708))
U69_gga(T704, T720, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U67_gga(T704, T715, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U65_gga(T704, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0)))))
U63_gga(T684, T685, T686, T693, T689, d1_out_gga(T684, T686, T689)) → U64_gga(T684, T685, T686, T693, T689, d1_in_gga(power(T685, p(0)), T686, T693))
U64_gga(T684, T685, T686, T693, T689, d1_out_gga(power(T685, p(0)), T686, T693)) → d1_out_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0)))))
U62_gga(T684, T685, T686, T690, T689, d1_out_gga(T684, T686, T689)) → d1_out_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0)))))
U59_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T614, T616, T618)) → U60_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T490, T616, T622))
U60_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T490, T616, T622)) → d1_out_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490)))
U57_gga(T614, T615, T490, T616, T619, T618, d1_out_gga(T614, T616, T618)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U54_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → U55_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(T490, T581, T589))
U55_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(T490, T581, T589)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490)))
U53_gga(T579, T580, T490, T581, T584, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490)))
U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T538, T539, T547))
U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T538, T539, T547)) → U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T490, T539, T555))
U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T490, T539, T555)) → d1_out_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490)))
U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T537, T539, T542)) → U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T538, T539, T547))
U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T538, T539, T547)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490)))
U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_out_gga(T537, T539, T542)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490)))
U46_gga(T512, T490, T513, T514, d1_out_gga(T490, T513, T514)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U44_gga(T500, T490, T501, d1_out_gga(T490, T500, T501)) → d1_out_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490)))
U43_gga(T477, T478, T479, T481, d1_out_gga(T477, T479, T481)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U41_gga(T460, T461, T462, T464, d1_out_gga(times(T460, power(T461, p(0))), T462, T464)) → d1_out_gga(div(T460, T461), T462, T464)
U39_gga(T428, T429, T430, T437, T433, d1_out_gga(T428, T430, T433)) → U40_gga(T428, T429, T430, T437, T433, d1_in_gga(T429, T430, T437))
U40_gga(T428, T429, T430, T437, T433, d1_out_gga(T429, T430, T437)) → d1_out_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429)))
U38_gga(T428, T429, T430, T434, T433, d1_out_gga(T428, T430, T433)) → d1_out_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429)))
U35_gga(T367, T387, T370, d1_out_gga(T367, power(T367, p(T387)), T370)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U33_gga(T367, T378, T370, d1_out_gga(T367, power(T367, s(T378)), T370)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U31_gga(T367, T370, d1_out_gga(T367, power(T367, 0), T370)) → d1_out_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0)))))
U29_gga(T341, T342, T353, T345, d1_out_gga(T341, div(T341, T342), T345)) → U30_gga(T341, T342, T353, T345, d1_in_gga(power(T342, p(0)), div(T341, T342), T353))
U30_gga(T341, T342, T353, T345, d1_out_gga(power(T342, p(0)), div(T341, T342), T353)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0)))))
U28_gga(T341, T342, T346, T345, d1_out_gga(T341, div(T341, T342), T345)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0)))))
U25_gga(T272, T273, T274, T287, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → U26_gga(T272, T273, T274, T287, T276, d1_in_gga(T274, times(power(T272, T273), T274), T287))
U26_gga(T272, T273, T274, T287, T276, d1_out_gga(T274, times(power(T272, T273), T274), T287)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U23_gga(T272, T273, T274, T277, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U20_gga(T226, T227, T228, T239, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → U21_gga(T226, T227, T228, T239, T230, d1_in_gga(T228, times(div(T226, T227), T228), T239))
U21_gga(T226, T227, T228, T239, T230, d1_out_gga(T228, times(div(T226, T227), T228), T239)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228)))
U19_gga(T226, T227, T228, T231, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228)))
U16_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U17_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U17_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → U18_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T156, times(times(T154, T155), T156), T191))
U18_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T156, times(times(T154, T155), T156), T191)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U14_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U15_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U15_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U13_gga(T154, T155, T156, T161, T160, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156)))
U12_gga(T125, T126, T127, d1_out_gga(T126, times(T125, T126), T127)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U10_gga(T95, T96, T98, d1_out_gga(T95, power(T95, T96), T98)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U8_gga(T79, T80, T82, d1_out_gga(times(T79, power(T80, p(0))), div(T79, T80), T82)) → d1_out_gga(div(T79, T80), div(T79, T80), T82)
U6_gga(T42, T43, T54, T46, d1_out_gga(T42, times(T42, T43), T46)) → U7_gga(T42, T43, T54, T46, d1_in_gga(T43, times(T42, T43), T54))
U7_gga(T42, T43, T54, T46, d1_out_gga(T43, times(T42, T43), T54)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43)))
U5_gga(T42, T43, T47, T46, d1_out_gga(T42, times(T42, T43), T46)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43)))

The argument filtering Pi contains the following mapping:
d1_in_gga(x1, x2, x3) = d1_in_gga(x1, x2)
d1_out_gga(x1, x2, x3) = d1_out_gga
0 = 0
s(x1) = s(x1)
U3_gga(x1, x2) = U3_gga(x2)
isnumber16_in_g(x1) = isnumber16_in_g(x1)
isnumber16_out_g(x1) = isnumber16_out_g
U1_g(x1, x2) = U1_g(x2)
p(x1) = p(x1)
U2_g(x1, x2) = U2_g(x2)
U4_gga(x1, x2) = U4_gga(x2)
times(x1, x2) = times(x1, x2)
U5_gga(x1, x2, x3, x4, x5) = U5_gga(x5)
U6_gga(x1, x2, x3, x4, x5) = U6_gga(x1, x2, x5)
div(x1, x2) = div(x1, x2)
U8_gga(x1, x2, x3, x4) = U8_gga(x4)
power(x1, x2) = power(x1, x2)
U9_gga(x1, x2, x3, x4) = U9_gga(x1, x2, x4)
U10_gga(x1, x2, x3, x4) = U10_gga(x4)
U11_gga(x1, x2, x3, x4) = U11_gga(x1, x2, x4)
U12_gga(x1, x2, x3, x4) = U12_gga(x4)
U13_gga(x1, x2, x3, x4, x5, x6, x7) = U13_gga(x7)
U14_gga(x1, x2, x3, x4, x5, x6, x7) = U14_gga(x1, x2, x3, x7)
U16_gga(x1, x2, x3, x4, x5, x6, x7) = U16_gga(x1, x2, x3, x7)
U19_gga(x1, x2, x3, x4, x5, x6) = U19_gga(x6)
U20_gga(x1, x2, x3, x4, x5, x6) = U20_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(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)
U27_gga(x1, x2, x3) = U27_gga(x3)
U28_gga(x1, x2, x3, x4, x5) = U28_gga(x5)
U29_gga(x1, x2, x3, x4, x5) = U29_gga(x1, x2, x5)
U31_gga(x1, x2, x3) = U31_gga(x3)
U32_gga(x1, x2, x3, x4) = U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3, x4) = U33_gga(x4)
U34_gga(x1, x2, x3, x4) = U34_gga(x1, x2, x4)
U35_gga(x1, x2, x3, x4) = U35_gga(x4)
U36_gga(x1, x2, x3) = U36_gga(x3)
U37_gga(x1, x2, x3) = U37_gga(x3)
U38_gga(x1, x2, x3, x4, x5, x6) = U38_gga(x6)
U39_gga(x1, x2, x3, x4, x5, x6) = U39_gga(x2, x3, x6)
U41_gga(x1, x2, x3, x4, x5) = U41_gga(x5)
U42_gga(x1, x2, x3, x4, x5) = U42_gga(x1, x3, x5)
U43_gga(x1, x2, x3, x4, x5) = U43_gga(x5)
U44_gga(x1, x2, x3, x4) = U44_gga(x4)
U45_gga(x1, x2, x3, x4, x5) = U45_gga(x2, x3, x5)
U46_gga(x1, x2, x3, x4, x5) = U46_gga(x5)
U47_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U47_gga(x8)
U48_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U48_gga(x2, x4, x8)
U50_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U50_gga(x2, x3, x4, x8)
U53_gga(x1, x2, x3, x4, x5, x6, x7) = U53_gga(x7)
U54_gga(x1, x2, x3, x4, x5, x6, x7) = U54_gga(x3, x4, x7)
U56_gga(x1, x2, x3, x4, x5, x6, x7) = U56_gga(x1, x4, x7)
U57_gga(x1, x2, x3, x4, x5, x6, x7) = U57_gga(x7)
U58_gga(x1, x2, x3, x4, x5, x6, x7) = U58_gga(x1, x3, x4, x7)
U59_gga(x1, x2, x3, x4, x5, x6, x7) = U59_gga(x3, x4, x7)
U61_gga(x1, x2, x3, x4) = U61_gga(x4)
U62_gga(x1, x2, x3, x4, x5, x6) = U62_gga(x6)
U63_gga(x1, x2, x3, x4, x5, x6) = U63_gga(x2, x3, x6)
U65_gga(x1, x2, x3, x4) = U65_gga(x4)
U66_gga(x1, x2, x3, x4, x5) = U66_gga(x1, x3, x5)
U67_gga(x1, x2, x3, x4, x5) = U67_gga(x5)
U68_gga(x1, x2, x3, x4, x5) = U68_gga(x1, x3, x5)
U69_gga(x1, x2, x3, x4, x5) = U69_gga(x5)
U64_gga(x1, x2, x3, x4, x5, x6) = U64_gga(x6)
U60_gga(x1, x2, x3, x4, x5, x6, x7) = U60_gga(x7)
U55_gga(x1, x2, x3, x4, x5, x6, x7) = U55_gga(x7)
U51_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U51_gga(x3, x4, x8)
U52_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U52_gga(x8)
U49_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U49_gga(x8)
U40_gga(x1, x2, x3, x4, x5, x6) = U40_gga(x6)
U30_gga(x1, x2, x3, x4, x5) = U30_gga(x5)
U26_gga(x1, x2, x3, x4, x5, x6) = U26_gga(x6)
U21_gga(x1, x2, x3, x4, x5, x6) = U21_gga(x6)
U17_gga(x1, x2, x3, x4, x5, x6, x7) = U17_gga(x1, x2, x3, x7)
U18_gga(x1, x2, x3, x4, x5, x6, x7) = U18_gga(x7)
U15_gga(x1, x2, x3, x4, x5, x6, x7) = U15_gga(x7)
U7_gga(x1, x2, x3, x4, x5) = U7_gga(x5)
D1_IN_GGA(x1, x2, x3) = D1_IN_GGA(x1, x2)
U6_GGA(x1, x2, x3, x4, x5) = U6_GGA(x1, x2, x5)
U9_GGA(x1, x2, x3, x4) = U9_GGA(x1, x2, x4)
U11_GGA(x1, x2, x3, x4) = U11_GGA(x1, x2, x4)
U14_GGA(x1, x2, x3, x4, x5, x6, x7) = U14_GGA(x1, x2, x3, x7)
U16_GGA(x1, x2, x3, x4, x5, x6, x7) = U16_GGA(x1, x2, x3, x7)
U20_GGA(x1, x2, x3, x4, x5, x6) = U20_GGA(x1, x2, x3, x6)
U22_GGA(x1, x2, x3, x4, x5, x6) = U22_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)
U29_GGA(x1, x2, x3, x4, x5) = U29_GGA(x1, x2, x5)
U32_GGA(x1, x2, x3, x4) = U32_GGA(x1, x2, x4)
U34_GGA(x1, x2, x3, x4) = U34_GGA(x1, x2, x4)
U39_GGA(x1, x2, x3, x4, x5, x6) = U39_GGA(x2, x3, x6)
U42_GGA(x1, x2, x3, x4, x5) = U42_GGA(x1, x3, x5)
U45_GGA(x1, x2, x3, x4, x5) = U45_GGA(x2, x3, x5)
U48_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U48_GGA(x2, x4, x8)
U50_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U50_GGA(x2, x3, x4, x8)
U54_GGA(x1, x2, x3, x4, x5, x6, x7) = U54_GGA(x3, x4, x7)
U56_GGA(x1, x2, x3, x4, x5, x6, x7) = U56_GGA(x1, x4, x7)
U58_GGA(x1, x2, x3, x4, x5, x6, x7) = U58_GGA(x1, x3, x4, x7)
U59_GGA(x1, x2, x3, x4, x5, x6, x7) = U59_GGA(x3, x4, x7)
U63_GGA(x1, x2, x3, x4, x5, x6) = U63_GGA(x2, x3, x6)
U66_GGA(x1, x2, x3, x4, x5) = U66_GGA(x1, x3, x5)
U68_GGA(x1, x2, x3, x4, x5) = U68_GGA(x1, x3, x5)
U51_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U51_GGA(x3, x4, x8)
U17_GGA(x1, x2, x3, x4, x5, x6, x7) = U17_GGA(x1, x2, x3, x7)

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

(17) UsableRulesProof (EQUIVALENT transformation)

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

(18) Obligation:

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

D1_IN_GGA(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) → D1_IN_GGA(T42, times(T42, T43), T46)
D1_IN_GGA(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43))) → U6_GGA(T42, T43, T54, T46, d1_in_gga(T42, times(T42, T43), T46))
U6_GGA(T42, T43, T54, T46, d1_out_gga(T42, times(T42, T43), T46)) → D1_IN_GGA(T43, times(T42, T43), T54)
D1_IN_GGA(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) → U11_GGA(T125, T126, T127, isnumber16_in_g(T125))
U11_GGA(T125, T126, T127, isnumber16_out_g(T125)) → D1_IN_GGA(T126, times(T125, T126), T127)
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) → D1_IN_GGA(T154, times(times(T154, T155), T156), T159)
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U14_GGA(T154, T155, T156, T172, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
U14_GGA(T154, T155, T156, T172, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → D1_IN_GGA(T155, times(times(T154, T155), T156), T171)
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U16_GGA(T154, T155, T156, T191, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
U16_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U17_GGA(T154, T155, T156, T191, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U17_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → D1_IN_GGA(T156, times(times(T154, T155), T156), T191)
D1_IN_GGA(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) → D1_IN_GGA(T428, T430, T433)
D1_IN_GGA(div(T79, T80), div(T79, T80), T82) → D1_IN_GGA(times(T79, power(T80, p(0))), div(T79, T80), T82)
D1_IN_GGA(times(T428, T429), T430, +(times(T437, T428), times(T433, T429))) → U39_GGA(T428, T429, T430, T437, T433, d1_in_gga(T428, T430, T433))
U39_GGA(T428, T429, T430, T437, T433, d1_out_gga(T428, T430, T433)) → D1_IN_GGA(T429, T430, T437)
D1_IN_GGA(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) → U9_GGA(T95, T96, T98, isnumber16_in_g(T96))
U9_GGA(T95, T96, T98, isnumber16_out_g(T96)) → D1_IN_GGA(T95, power(T95, T96), T98)
D1_IN_GGA(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) → D1_IN_GGA(T367, power(T367, 0), T370)
D1_IN_GGA(div(T460, T461), T462, T464) → D1_IN_GGA(times(T460, power(T461, p(0))), T462, T464)
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) → D1_IN_GGA(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228))) → U20_GGA(T226, T227, T228, T239, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
U20_GGA(T226, T227, T228, T239, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → D1_IN_GGA(T228, times(div(T226, T227), T228), T239)
D1_IN_GGA(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) → U42_GGA(T477, T478, T479, T481, isnumber16_in_g(T478))
U42_GGA(T477, T478, T479, T481, isnumber16_out_g(T478)) → D1_IN_GGA(T477, T479, T481)
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U22_GGA(T272, T273, T274, T277, T276, isnumber16_in_g(T273))
U22_GGA(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → D1_IN_GGA(T272, times(power(T272, T273), T274), T276)
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U24_GGA(T272, T273, T274, T287, T276, isnumber16_in_g(T273))
U24_GGA(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → U25_GGA(T272, T273, T274, T287, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
U25_GGA(T272, T273, T274, T287, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → D1_IN_GGA(T274, times(power(T272, T273), T274), T287)
D1_IN_GGA(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) → D1_IN_GGA(T490, T500, T501)
D1_IN_GGA(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) → D1_IN_GGA(T341, div(T341, T342), T345)
D1_IN_GGA(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0))))) → U29_GGA(T341, T342, T353, T345, d1_in_gga(T341, div(T341, T342), T345))
U29_GGA(T341, T342, T353, T345, d1_out_gga(T341, div(T341, T342), T345)) → D1_IN_GGA(power(T342, p(0)), div(T341, T342), T353)
D1_IN_GGA(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) → U68_GGA(T704, T720, T706, T708, isnumber16_in_g(T720))
U68_GGA(T704, T720, T706, T708, isnumber16_out_g(T720)) → D1_IN_GGA(T704, T706, T708)
D1_IN_GGA(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) → U32_GGA(T367, T378, T370, isnumber16_in_g(T378))
U32_GGA(T367, T378, T370, isnumber16_out_g(T378)) → D1_IN_GGA(T367, power(T367, s(T378)), T370)
D1_IN_GGA(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) → U45_GGA(T512, T490, T513, T514, isnumber16_in_g(T512))
U45_GGA(T512, T490, T513, T514, isnumber16_out_g(T512)) → D1_IN_GGA(T490, T513, T514)
D1_IN_GGA(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) → U34_GGA(T367, T387, T370, isnumber16_in_g(T387))
U34_GGA(T367, T387, T370, isnumber16_out_g(T387)) → D1_IN_GGA(T367, power(T367, p(T387)), T370)
D1_IN_GGA(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) → D1_IN_GGA(T537, T539, T542)
D1_IN_GGA(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490))) → U48_GGA(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T537, T539, T542))
U48_GGA(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T537, T539, T542)) → D1_IN_GGA(T538, T539, T547)
D1_IN_GGA(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490))) → U50_GGA(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T556, T539, T542))
U50_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → U51_GGA(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T538, T539, T547))
U51_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T538, T539, T547)) → D1_IN_GGA(T490, T539, T555)
D1_IN_GGA(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) → D1_IN_GGA(times(T579, power(T580, p(0))), T581, T583)
D1_IN_GGA(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490))) → U54_GGA(T579, T580, T490, T581, T589, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
U54_GGA(T579, T580, T490, T581, T589, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → D1_IN_GGA(T490, T581, T589)
D1_IN_GGA(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) → U56_GGA(T614, T615, T490, T616, T619, T618, isnumber16_in_g(T615))
U56_GGA(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → D1_IN_GGA(T614, T616, T618)
D1_IN_GGA(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490))) → U58_GGA(T614, T623, T490, T616, T622, T618, isnumber16_in_g(T623))
U58_GGA(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → U59_GGA(T614, T623, T490, T616, T622, T618, d1_in_gga(T614, T616, T618))
U59_GGA(T614, T623, T490, T616, T622, T618, d1_out_gga(T614, T616, T618)) → D1_IN_GGA(T490, T616, T622)
D1_IN_GGA(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) → D1_IN_GGA(T684, T686, T689)
D1_IN_GGA(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0))))) → U63_GGA(T684, T685, T686, T693, T689, d1_in_gga(T684, T686, T689))
U63_GGA(T684, T685, T686, T693, T689, d1_out_gga(T684, T686, T689)) → D1_IN_GGA(power(T685, p(0)), T686, T693)
D1_IN_GGA(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) → D1_IN_GGA(T704, T706, T708)
D1_IN_GGA(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) → U66_GGA(T704, T715, T706, T708, isnumber16_in_g(T715))
U66_GGA(T704, T715, T706, T708, isnumber16_out_g(T715)) → D1_IN_GGA(T704, T706, T708)
U58_GGA(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → D1_IN_GGA(T614, T616, T618)
U50_GGA(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → D1_IN_GGA(T538, T539, T547)
U24_GGA(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → D1_IN_GGA(T272, times(power(T272, T273), T274), T276)
U16_GGA(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → D1_IN_GGA(T155, times(times(T154, T155), T156), T171)

The TRS R consists of the following rules:

d1_in_gga(T5, T5, 1) → d1_out_gga(T5, T5, 1)
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43))) → U5_gga(T42, T43, T47, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43))) → U6_gga(T42, T43, T54, T46, d1_in_gga(T42, times(T42, T43), T46))
d1_in_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126))) → U11_gga(T125, T126, T127, isnumber16_in_g(T125))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156))) → U13_gga(T154, T155, T156, T161, T160, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U14_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156))) → U16_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T154, times(times(T154, T155), T156), T159))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228))) → U19_gga(T226, T227, T228, T231, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228))) → U20_gga(T226, T227, T228, T239, T230, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U22_gga(T272, T273, T274, T277, T276, isnumber16_in_g(T273))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274))) → U24_gga(T272, T273, T274, T287, T276, isnumber16_in_g(T273))
d1_in_gga(0, T397, 0) → d1_out_gga(0, T397, 0)
d1_in_gga(s(T402), T397, 0) → U36_gga(T402, T397, isnumber16_in_g(T402))
d1_in_gga(p(T407), T397, 0) → U37_gga(T407, T397, isnumber16_in_g(T407))
d1_in_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429))) → U38_gga(T428, T429, T430, T434, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429))) → U39_gga(T428, T429, T430, T437, T433, d1_in_gga(T428, T430, T433))
d1_in_gga(div(T460, T461), T462, T464) → U41_gga(T460, T461, T462, T464, d1_in_gga(times(T460, power(T461, p(0))), T462, T464))
d1_in_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478))))) → U42_gga(T477, T478, T479, T481, isnumber16_in_g(T478))
d1_in_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490))) → U44_gga(T500, T490, T501, d1_in_gga(T490, T500, T501))
d1_in_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490))) → U45_gga(T512, T490, T513, T514, isnumber16_in_g(T512))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490))) → U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490))) → U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T537, T539, T542))
d1_in_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490))) → U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T556, T539, T542))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490))) → U53_gga(T579, T580, T490, T581, T584, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490))) → U54_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(times(T579, power(T580, p(0))), T581, T583))
d1_in_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490))) → U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_in_g(T615))
d1_in_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490))) → U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_in_g(T623))
d1_in_gga(div(T647, T648), times(T647, power(T648, p(0))), 1) → d1_out_gga(div(T647, T648), times(T647, power(T648, p(0))), 1)
d1_in_gga(div(T661, T662), T663, 0) → U61_gga(T661, T662, T663, isnumber16_in_g(times(T661, power(T662, p(0)))))
d1_in_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0))))) → U62_gga(T684, T685, T686, T690, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0))))) → U63_gga(T684, T685, T686, T693, T689, d1_in_gga(T684, T686, T689))
d1_in_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0))))) → U65_gga(T704, T706, T708, d1_in_gga(T704, T706, T708))
d1_in_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715)))))) → U66_gga(T704, T715, T706, T708, isnumber16_in_g(T715))
d1_in_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720)))))) → U68_gga(T704, T720, T706, T708, isnumber16_in_g(T720))
isnumber16_in_g(0) → isnumber16_out_g(0)
isnumber16_in_g(s(T17)) → U1_g(T17, isnumber16_in_g(T17))
isnumber16_in_g(p(T20)) → U2_g(T20, isnumber16_in_g(T20))
d1_in_gga(0, 0, 0) → d1_out_gga(0, 0, 0)
d1_in_gga(s(T12), s(T12), 0) → U3_gga(T12, isnumber16_in_g(T12))
d1_in_gga(p(T25), p(T25), 0) → U4_gga(T25, isnumber16_in_g(T25))
d1_in_gga(div(T79, T80), div(T79, T80), T82) → U8_gga(T79, T80, T82, d1_in_gga(times(T79, power(T80, p(0))), div(T79, T80), T82))
d1_in_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96))))) → U9_gga(T95, T96, T98, isnumber16_in_g(T96))
d1_in_gga(div(T323, T324), div(T323, T324), 0) → U27_gga(T323, T324, isnumber16_in_g(times(T323, power(T324, p(0)))))
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0))))) → U28_gga(T341, T342, T346, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0))))) → U29_gga(T341, T342, T353, T345, d1_in_gga(T341, div(T341, T342), T345))
d1_in_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0))))) → U31_gga(T367, T370, d1_in_gga(T367, power(T367, 0), T370))
d1_in_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378)))))) → U32_gga(T367, T378, T370, isnumber16_in_g(T378))
d1_in_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387)))))) → U34_gga(T367, T387, T370, isnumber16_in_g(T387))
U5_gga(T42, T43, T47, T46, d1_out_gga(T42, times(T42, T43), T46)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T47, T42), times(T46, T43)))
U6_gga(T42, T43, T54, T46, d1_out_gga(T42, times(T42, T43), T46)) → U7_gga(T42, T43, T54, T46, d1_in_gga(T43, times(T42, T43), T54))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U11_gga(T125, T126, T127, isnumber16_out_g(T125)) → U12_gga(T125, T126, T127, d1_in_gga(T126, times(T125, T126), T127))
U13_gga(T154, T155, T156, T161, T160, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T161, times(T154, T155)), times(+(times(T160, T154), times(T159, T155)), T156)))
U14_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U15_gga(T154, T155, T156, T172, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U16_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T154, times(times(T154, T155), T156), T159)) → U17_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T155, times(times(T154, T155), T156), T171))
U19_gga(T226, T227, T228, T231, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T231, div(T226, T227)), times(T230, T228)))
U20_gga(T226, T227, T228, T239, T230, d1_out_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228), T230)) → U21_gga(T226, T227, T228, T239, T230, d1_in_gga(T228, times(div(T226, T227), T228), T239))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U22_gga(T272, T273, T274, T277, T276, isnumber16_out_g(T273)) → U23_gga(T272, T273, T274, T277, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
U24_gga(T272, T273, T274, T287, T276, isnumber16_out_g(T273)) → U25_gga(T272, T273, T274, T287, T276, d1_in_gga(T272, times(power(T272, T273), T274), T276))
U36_gga(T402, T397, isnumber16_out_g(T402)) → d1_out_gga(s(T402), T397, 0)
U37_gga(T407, T397, isnumber16_out_g(T407)) → d1_out_gga(p(T407), T397, 0)
U38_gga(T428, T429, T430, T434, T433, d1_out_gga(T428, T430, T433)) → d1_out_gga(times(T428, T429), T430, +(times(T434, T428), times(T433, T429)))
U39_gga(T428, T429, T430, T437, T433, d1_out_gga(T428, T430, T433)) → U40_gga(T428, T429, T430, T437, T433, d1_in_gga(T429, T430, T437))
U41_gga(T460, T461, T462, T464, d1_out_gga(times(T460, power(T461, p(0))), T462, T464)) → d1_out_gga(div(T460, T461), T462, T464)
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U42_gga(T477, T478, T479, T481, isnumber16_out_g(T478)) → U43_gga(T477, T478, T479, T481, d1_in_gga(T477, T479, T481))
U44_gga(T500, T490, T501, d1_out_gga(T490, T500, T501)) → d1_out_gga(times(T500, T490), T500, +(times(T501, T500), times(1, T490)))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U45_gga(T512, T490, T513, T514, isnumber16_out_g(T512)) → U46_gga(T512, T490, T513, T514, d1_in_gga(T490, T513, T514))
U47_gga(T537, T538, T490, T539, T544, T543, T542, d1_out_gga(T537, T539, T542)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T544, times(T537, T538)), times(+(times(T543, T537), times(T542, T538)), T490)))
U48_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T537, T539, T542)) → U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_in_gga(T538, T539, T547))
U50_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T556, T539, T542)) → U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T538, T539, T547))
U53_gga(T579, T580, T490, T581, T584, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T584, div(T579, T580)), times(T583, T490)))
U54_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(times(T579, power(T580, p(0))), T581, T583)) → U55_gga(T579, T580, T490, T581, T589, T583, d1_in_gga(T490, T581, T589))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U56_gga(T614, T615, T490, T616, T619, T618, isnumber16_out_g(T615)) → U57_gga(T614, T615, T490, T616, T619, T618, d1_in_gga(T614, T616, T618))
U58_gga(T614, T623, T490, T616, T622, T618, isnumber16_out_g(T623)) → U59_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T614, T616, T618))
U62_gga(T684, T685, T686, T690, T689, d1_out_gga(T684, T686, T689)) → d1_out_gga(div(T684, T685), T686, +(times(T690, T684), times(T689, power(T685, p(0)))))
U63_gga(T684, T685, T686, T693, T689, d1_out_gga(T684, T686, T689)) → U64_gga(T684, T685, T686, T693, T689, d1_in_gga(power(T685, p(0)), T686, T693))
U65_gga(T704, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, 0), T706, times(0, times(T708, power(T704, p(0)))))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U66_gga(T704, T715, T706, T708, isnumber16_out_g(T715)) → U67_gga(T704, T715, T706, T708, d1_in_gga(T704, T706, T708))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U68_gga(T704, T720, T706, T708, isnumber16_out_g(T720)) → U69_gga(T704, T720, T706, T708, d1_in_gga(T704, T706, T708))
U1_g(T17, isnumber16_out_g(T17)) → isnumber16_out_g(s(T17))
U2_g(T20, isnumber16_out_g(T20)) → isnumber16_out_g(p(T20))
U3_gga(T12, isnumber16_out_g(T12)) → d1_out_gga(s(T12), s(T12), 0)
U4_gga(T25, isnumber16_out_g(T25)) → d1_out_gga(p(T25), p(T25), 0)
U8_gga(T79, T80, T82, d1_out_gga(times(T79, power(T80, p(0))), div(T79, T80), T82)) → d1_out_gga(div(T79, T80), div(T79, T80), T82)
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U9_gga(T95, T96, T98, isnumber16_out_g(T96)) → U10_gga(T95, T96, T98, d1_in_gga(T95, power(T95, T96), T98))
U28_gga(T341, T342, T346, T345, d1_out_gga(T341, div(T341, T342), T345)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T346, T341), times(T345, power(T342, p(0)))))
U29_gga(T341, T342, T353, T345, d1_out_gga(T341, div(T341, T342), T345)) → U30_gga(T341, T342, T353, T345, d1_in_gga(power(T342, p(0)), div(T341, T342), T353))
U31_gga(T367, T370, d1_out_gga(T367, power(T367, 0), T370)) → d1_out_gga(power(T367, 0), power(T367, 0), times(0, times(T370, power(T367, p(0)))))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U32_gga(T367, T378, T370, isnumber16_out_g(T378)) → U33_gga(T367, T378, T370, d1_in_gga(T367, power(T367, s(T378)), T370))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U34_gga(T367, T387, T370, isnumber16_out_g(T387)) → U35_gga(T367, T387, T370, d1_in_gga(T367, power(T367, p(T387)), T370))
U7_gga(T42, T43, T54, T46, d1_out_gga(T43, times(T42, T43), T54)) → d1_out_gga(times(T42, T43), times(T42, T43), +(times(T54, T42), times(T46, T43)))
U12_gga(T125, T126, T127, d1_out_gga(T126, times(T125, T126), T127)) → d1_out_gga(times(T125, T126), times(T125, T126), +(times(T127, T125), times(0, T126)))
U15_gga(T154, T155, T156, T172, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T172, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U17_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T155, times(times(T154, T155), T156), T171)) → U18_gga(T154, T155, T156, T191, T171, T159, d1_in_gga(T156, times(times(T154, T155), T156), T191))
U21_gga(T226, T227, T228, T239, T230, d1_out_gga(T228, times(div(T226, T227), T228), T239)) → d1_out_gga(times(div(T226, T227), T228), times(div(T226, T227), T228), +(times(T239, div(T226, T227)), times(T230, T228)))
U23_gga(T272, T273, T274, T277, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T277, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U25_gga(T272, T273, T274, T287, T276, d1_out_gga(T272, times(power(T272, T273), T274), T276)) → U26_gga(T272, T273, T274, T287, T276, d1_in_gga(T274, times(power(T272, T273), T274), T287))
U40_gga(T428, T429, T430, T437, T433, d1_out_gga(T429, T430, T437)) → d1_out_gga(times(T428, T429), T430, +(times(T437, T428), times(T433, T429)))
U43_gga(T477, T478, T479, T481, d1_out_gga(T477, T479, T481)) → d1_out_gga(power(T477, T478), T479, times(T478, times(T481, power(T477, p(T478)))))
U46_gga(T512, T490, T513, T514, d1_out_gga(T490, T513, T514)) → d1_out_gga(times(T512, T490), T513, +(times(T514, T512), times(0, T490)))
U49_gga(T537, T538, T490, T539, T548, T547, T542, d1_out_gga(T538, T539, T547)) → d1_out_gga(times(times(T537, T538), T490), T539, +(times(T548, times(T537, T538)), times(+(times(T547, T537), times(T542, T538)), T490)))
U51_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T538, T539, T547)) → U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_in_gga(T490, T539, T555))
U55_gga(T579, T580, T490, T581, T589, T583, d1_out_gga(T490, T581, T589)) → d1_out_gga(times(div(T579, T580), T490), T581, +(times(T589, div(T579, T580)), times(T583, T490)))
U57_gga(T614, T615, T490, T616, T619, T618, d1_out_gga(T614, T616, T618)) → d1_out_gga(times(power(T614, T615), T490), T616, +(times(T619, power(T614, T615)), times(times(T615, times(T618, power(T614, p(T615)))), T490)))
U59_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T614, T616, T618)) → U60_gga(T614, T623, T490, T616, T622, T618, d1_in_gga(T490, T616, T622))
U64_gga(T684, T685, T686, T693, T689, d1_out_gga(power(T685, p(0)), T686, T693)) → d1_out_gga(div(T684, T685), T686, +(times(T693, T684), times(T689, power(T685, p(0)))))
U67_gga(T704, T715, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, s(T715)), T706, times(s(T715), times(T708, power(T704, p(s(T715))))))
U69_gga(T704, T720, T706, T708, d1_out_gga(T704, T706, T708)) → d1_out_gga(power(T704, p(T720)), T706, times(p(T720), times(T708, power(T704, p(p(T720))))))
U10_gga(T95, T96, T98, d1_out_gga(T95, power(T95, T96), T98)) → d1_out_gga(power(T95, T96), power(T95, T96), times(T96, times(T98, power(T95, p(T96)))))
U30_gga(T341, T342, T353, T345, d1_out_gga(power(T342, p(0)), div(T341, T342), T353)) → d1_out_gga(div(T341, T342), div(T341, T342), +(times(T353, T341), times(T345, power(T342, p(0)))))
U33_gga(T367, T378, T370, d1_out_gga(T367, power(T367, s(T378)), T370)) → d1_out_gga(power(T367, s(T378)), power(T367, s(T378)), times(s(T378), times(T370, power(T367, p(s(T378))))))
U35_gga(T367, T387, T370, d1_out_gga(T367, power(T367, p(T387)), T370)) → d1_out_gga(power(T367, p(T387)), power(T367, p(T387)), times(p(T387), times(T370, power(T367, p(p(T387))))))
U18_gga(T154, T155, T156, T191, T171, T159, d1_out_gga(T156, times(times(T154, T155), T156), T191)) → d1_out_gga(times(times(T154, T155), T156), times(times(T154, T155), T156), +(times(T191, times(T154, T155)), times(+(times(T171, T154), times(T159, T155)), T156)))
U26_gga(T272, T273, T274, T287, T276, d1_out_gga(T274, times(power(T272, T273), T274), T287)) → d1_out_gga(times(power(T272, T273), T274), times(power(T272, T273), T274), +(times(T287, power(T272, T273)), times(times(T273, times(T276, power(T272, p(T273)))), T274)))
U52_gga(T556, T538, T490, T539, T555, T547, T542, d1_out_gga(T490, T539, T555)) → d1_out_gga(times(times(T556, T538), T490), T539, +(times(T555, times(T556, T538)), times(+(times(T547, T556), times(T542, T538)), T490)))
U60_gga(T614, T623, T490, T616, T622, T618, d1_out_gga(T490, T616, T622)) → d1_out_gga(times(power(T614, T623), T490), T616, +(times(T622, power(T614, T623)), times(times(T623, times(T618, power(T614, p(T623)))), T490)))

The argument filtering Pi contains the following mapping:
d1_in_gga(x1, x2, x3) = d1_in_gga(x1, x2)
d1_out_gga(x1, x2, x3) = d1_out_gga
0 = 0
s(x1) = s(x1)
U3_gga(x1, x2) = U3_gga(x2)
isnumber16_in_g(x1) = isnumber16_in_g(x1)
isnumber16_out_g(x1) = isnumber16_out_g
U1_g(x1, x2) = U1_g(x2)
p(x1) = p(x1)
U2_g(x1, x2) = U2_g(x2)
U4_gga(x1, x2) = U4_gga(x2)
times(x1, x2) = times(x1, x2)
U5_gga(x1, x2, x3, x4, x5) = U5_gga(x5)
U6_gga(x1, x2, x3, x4, x5) = U6_gga(x1, x2, x5)
div(x1, x2) = div(x1, x2)
U8_gga(x1, x2, x3, x4) = U8_gga(x4)
power(x1, x2) = power(x1, x2)
U9_gga(x1, x2, x3, x4) = U9_gga(x1, x2, x4)
U10_gga(x1, x2, x3, x4) = U10_gga(x4)
U11_gga(x1, x2, x3, x4) = U11_gga(x1, x2, x4)
U12_gga(x1, x2, x3, x4) = U12_gga(x4)
U13_gga(x1, x2, x3, x4, x5, x6, x7) = U13_gga(x7)
U14_gga(x1, x2, x3, x4, x5, x6, x7) = U14_gga(x1, x2, x3, x7)
U16_gga(x1, x2, x3, x4, x5, x6, x7) = U16_gga(x1, x2, x3, x7)
U19_gga(x1, x2, x3, x4, x5, x6) = U19_gga(x6)
U20_gga(x1, x2, x3, x4, x5, x6) = U20_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(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)
U27_gga(x1, x2, x3) = U27_gga(x3)
U28_gga(x1, x2, x3, x4, x5) = U28_gga(x5)
U29_gga(x1, x2, x3, x4, x5) = U29_gga(x1, x2, x5)
U31_gga(x1, x2, x3) = U31_gga(x3)
U32_gga(x1, x2, x3, x4) = U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3, x4) = U33_gga(x4)
U34_gga(x1, x2, x3, x4) = U34_gga(x1, x2, x4)
U35_gga(x1, x2, x3, x4) = U35_gga(x4)
U36_gga(x1, x2, x3) = U36_gga(x3)
U37_gga(x1, x2, x3) = U37_gga(x3)
U38_gga(x1, x2, x3, x4, x5, x6) = U38_gga(x6)
U39_gga(x1, x2, x3, x4, x5, x6) = U39_gga(x2, x3, x6)
U41_gga(x1, x2, x3, x4, x5) = U41_gga(x5)
U42_gga(x1, x2, x3, x4, x5) = U42_gga(x1, x3, x5)
U43_gga(x1, x2, x3, x4, x5) = U43_gga(x5)
U44_gga(x1, x2, x3, x4) = U44_gga(x4)
U45_gga(x1, x2, x3, x4, x5) = U45_gga(x2, x3, x5)
U46_gga(x1, x2, x3, x4, x5) = U46_gga(x5)
U47_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U47_gga(x8)
U48_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U48_gga(x2, x4, x8)
U50_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U50_gga(x2, x3, x4, x8)
U53_gga(x1, x2, x3, x4, x5, x6, x7) = U53_gga(x7)
U54_gga(x1, x2, x3, x4, x5, x6, x7) = U54_gga(x3, x4, x7)
U56_gga(x1, x2, x3, x4, x5, x6, x7) = U56_gga(x1, x4, x7)
U57_gga(x1, x2, x3, x4, x5, x6, x7) = U57_gga(x7)
U58_gga(x1, x2, x3, x4, x5, x6, x7) = U58_gga(x1, x3, x4, x7)
U59_gga(x1, x2, x3, x4, x5, x6, x7) = U59_gga(x3, x4, x7)
U61_gga(x1, x2, x3, x4) = U61_gga(x4)
U62_gga(x1, x2, x3, x4, x5, x6) = U62_gga(x6)
U63_gga(x1, x2, x3, x4, x5, x6) = U63_gga(x2, x3, x6)
U65_gga(x1, x2, x3, x4) = U65_gga(x4)
U66_gga(x1, x2, x3, x4, x5) = U66_gga(x1, x3, x5)
U67_gga(x1, x2, x3, x4, x5) = U67_gga(x5)
U68_gga(x1, x2, x3, x4, x5) = U68_gga(x1, x3, x5)
U69_gga(x1, x2, x3, x4, x5) = U69_gga(x5)
U64_gga(x1, x2, x3, x4, x5, x6) = U64_gga(x6)
U60_gga(x1, x2, x3, x4, x5, x6, x7) = U60_gga(x7)
U55_gga(x1, x2, x3, x4, x5, x6, x7) = U55_gga(x7)
U51_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U51_gga(x3, x4, x8)
U52_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U52_gga(x8)
U49_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U49_gga(x8)
U40_gga(x1, x2, x3, x4, x5, x6) = U40_gga(x6)
U30_gga(x1, x2, x3, x4, x5) = U30_gga(x5)
U26_gga(x1, x2, x3, x4, x5, x6) = U26_gga(x6)
U21_gga(x1, x2, x3, x4, x5, x6) = U21_gga(x6)
U17_gga(x1, x2, x3, x4, x5, x6, x7) = U17_gga(x1, x2, x3, x7)
U18_gga(x1, x2, x3, x4, x5, x6, x7) = U18_gga(x7)
U15_gga(x1, x2, x3, x4, x5, x6, x7) = U15_gga(x7)
U7_gga(x1, x2, x3, x4, x5) = U7_gga(x5)
D1_IN_GGA(x1, x2, x3) = D1_IN_GGA(x1, x2)
U6_GGA(x1, x2, x3, x4, x5) = U6_GGA(x1, x2, x5)
U9_GGA(x1, x2, x3, x4) = U9_GGA(x1, x2, x4)
U11_GGA(x1, x2, x3, x4) = U11_GGA(x1, x2, x4)
U14_GGA(x1, x2, x3, x4, x5, x6, x7) = U14_GGA(x1, x2, x3, x7)
U16_GGA(x1, x2, x3, x4, x5, x6, x7) = U16_GGA(x1, x2, x3, x7)
U20_GGA(x1, x2, x3, x4, x5, x6) = U20_GGA(x1, x2, x3, x6)
U22_GGA(x1, x2, x3, x4, x5, x6) = U22_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)
U29_GGA(x1, x2, x3, x4, x5) = U29_GGA(x1, x2, x5)
U32_GGA(x1, x2, x3, x4) = U32_GGA(x1, x2, x4)
U34_GGA(x1, x2, x3, x4) = U34_GGA(x1, x2, x4)
U39_GGA(x1, x2, x3, x4, x5, x6) = U39_GGA(x2, x3, x6)
U42_GGA(x1, x2, x3, x4, x5) = U42_GGA(x1, x3, x5)
U45_GGA(x1, x2, x3, x4, x5) = U45_GGA(x2, x3, x5)
U48_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U48_GGA(x2, x4, x8)
U50_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U50_GGA(x2, x3, x4, x8)
U54_GGA(x1, x2, x3, x4, x5, x6, x7) = U54_GGA(x3, x4, x7)
U56_GGA(x1, x2, x3, x4, x5, x6, x7) = U56_GGA(x1, x4, x7)
U58_GGA(x1, x2, x3, x4, x5, x6, x7) = U58_GGA(x1, x3, x4, x7)
U59_GGA(x1, x2, x3, x4, x5, x6, x7) = U59_GGA(x3, x4, x7)
U63_GGA(x1, x2, x3, x4, x5, x6) = U63_GGA(x2, x3, x6)
U66_GGA(x1, x2, x3, x4, x5) = U66_GGA(x1, x3, x5)
U68_GGA(x1, x2, x3, x4, x5) = U68_GGA(x1, x3, x5)
U51_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U51_GGA(x3, x4, x8)
U17_GGA(x1, x2, x3, x4, x5, x6, x7) = U17_GGA(x1, x2, x3, x7)

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

(19) PiDPToQDPProof (SOUND transformation)

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

(20) Obligation:

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

D1_IN_GGA(times(T42, T43), times(T42, T43)) → D1_IN_GGA(T42, times(T42, T43))
D1_IN_GGA(times(T42, T43), times(T42, T43)) → U6_GGA(T42, T43, d1_in_gga(T42, times(T42, T43)))
U6_GGA(T42, T43, d1_out_gga) → D1_IN_GGA(T43, times(T42, T43))
D1_IN_GGA(times(T125, T126), times(T125, T126)) → U11_GGA(T125, T126, isnumber16_in_g(T125))
U11_GGA(T125, T126, isnumber16_out_g) → D1_IN_GGA(T126, times(T125, T126))
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156)) → D1_IN_GGA(T154, times(times(T154, T155), T156))
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156)) → U14_GGA(T154, T155, T156, d1_in_gga(T154, times(times(T154, T155), T156)))
U14_GGA(T154, T155, T156, d1_out_gga) → D1_IN_GGA(T155, times(times(T154, T155), T156))
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156)) → U16_GGA(T154, T155, T156, d1_in_gga(T154, times(times(T154, T155), T156)))
U16_GGA(T154, T155, T156, d1_out_gga) → U17_GGA(T154, T155, T156, d1_in_gga(T155, times(times(T154, T155), T156)))
U17_GGA(T154, T155, T156, d1_out_gga) → D1_IN_GGA(T156, times(times(T154, T155), T156))
D1_IN_GGA(times(T428, T429), T430) → D1_IN_GGA(T428, T430)
D1_IN_GGA(div(T79, T80), div(T79, T80)) → D1_IN_GGA(times(T79, power(T80, p(0))), div(T79, T80))
D1_IN_GGA(times(T428, T429), T430) → U39_GGA(T429, T430, d1_in_gga(T428, T430))
U39_GGA(T429, T430, d1_out_gga) → D1_IN_GGA(T429, T430)
D1_IN_GGA(power(T95, T96), power(T95, T96)) → U9_GGA(T95, T96, isnumber16_in_g(T96))
U9_GGA(T95, T96, isnumber16_out_g) → D1_IN_GGA(T95, power(T95, T96))
D1_IN_GGA(power(T367, 0), power(T367, 0)) → D1_IN_GGA(T367, power(T367, 0))
D1_IN_GGA(div(T460, T461), T462) → D1_IN_GGA(times(T460, power(T461, p(0))), T462)
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228)) → D1_IN_GGA(times(T226, power(T227, p(0))), times(div(T226, T227), T228))
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228)) → U20_GGA(T226, T227, T228, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228)))
U20_GGA(T226, T227, T228, d1_out_gga) → D1_IN_GGA(T228, times(div(T226, T227), T228))
D1_IN_GGA(power(T477, T478), T479) → U42_GGA(T477, T479, isnumber16_in_g(T478))
U42_GGA(T477, T479, isnumber16_out_g) → D1_IN_GGA(T477, T479)
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274)) → U22_GGA(T272, T273, T274, isnumber16_in_g(T273))
U22_GGA(T272, T273, T274, isnumber16_out_g) → D1_IN_GGA(T272, times(power(T272, T273), T274))
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274)) → U24_GGA(T272, T273, T274, isnumber16_in_g(T273))
U24_GGA(T272, T273, T274, isnumber16_out_g) → U25_GGA(T272, T273, T274, d1_in_gga(T272, times(power(T272, T273), T274)))
U25_GGA(T272, T273, T274, d1_out_gga) → D1_IN_GGA(T274, times(power(T272, T273), T274))
D1_IN_GGA(times(T500, T490), T500) → D1_IN_GGA(T490, T500)
D1_IN_GGA(div(T341, T342), div(T341, T342)) → D1_IN_GGA(T341, div(T341, T342))
D1_IN_GGA(div(T341, T342), div(T341, T342)) → U29_GGA(T341, T342, d1_in_gga(T341, div(T341, T342)))
U29_GGA(T341, T342, d1_out_gga) → D1_IN_GGA(power(T342, p(0)), div(T341, T342))
D1_IN_GGA(power(T704, p(T720)), T706) → U68_GGA(T704, T706, isnumber16_in_g(T720))
U68_GGA(T704, T706, isnumber16_out_g) → D1_IN_GGA(T704, T706)
D1_IN_GGA(power(T367, s(T378)), power(T367, s(T378))) → U32_GGA(T367, T378, isnumber16_in_g(T378))
U32_GGA(T367, T378, isnumber16_out_g) → D1_IN_GGA(T367, power(T367, s(T378)))
D1_IN_GGA(times(T512, T490), T513) → U45_GGA(T490, T513, isnumber16_in_g(T512))
U45_GGA(T490, T513, isnumber16_out_g) → D1_IN_GGA(T490, T513)
D1_IN_GGA(power(T367, p(T387)), power(T367, p(T387))) → U34_GGA(T367, T387, isnumber16_in_g(T387))
U34_GGA(T367, T387, isnumber16_out_g) → D1_IN_GGA(T367, power(T367, p(T387)))
D1_IN_GGA(times(times(T537, T538), T490), T539) → D1_IN_GGA(T537, T539)
D1_IN_GGA(times(times(T537, T538), T490), T539) → U48_GGA(T538, T539, d1_in_gga(T537, T539))
U48_GGA(T538, T539, d1_out_gga) → D1_IN_GGA(T538, T539)
D1_IN_GGA(times(times(T556, T538), T490), T539) → U50_GGA(T538, T490, T539, d1_in_gga(T556, T539))
U50_GGA(T538, T490, T539, d1_out_gga) → U51_GGA(T490, T539, d1_in_gga(T538, T539))
U51_GGA(T490, T539, d1_out_gga) → D1_IN_GGA(T490, T539)
D1_IN_GGA(times(div(T579, T580), T490), T581) → D1_IN_GGA(times(T579, power(T580, p(0))), T581)
D1_IN_GGA(times(div(T579, T580), T490), T581) → U54_GGA(T490, T581, d1_in_gga(times(T579, power(T580, p(0))), T581))
U54_GGA(T490, T581, d1_out_gga) → D1_IN_GGA(T490, T581)
D1_IN_GGA(times(power(T614, T615), T490), T616) → U56_GGA(T614, T616, isnumber16_in_g(T615))
U56_GGA(T614, T616, isnumber16_out_g) → D1_IN_GGA(T614, T616)
D1_IN_GGA(times(power(T614, T623), T490), T616) → U58_GGA(T614, T490, T616, isnumber16_in_g(T623))
U58_GGA(T614, T490, T616, isnumber16_out_g) → U59_GGA(T490, T616, d1_in_gga(T614, T616))
U59_GGA(T490, T616, d1_out_gga) → D1_IN_GGA(T490, T616)
D1_IN_GGA(div(T684, T685), T686) → D1_IN_GGA(T684, T686)
D1_IN_GGA(div(T684, T685), T686) → U63_GGA(T685, T686, d1_in_gga(T684, T686))
U63_GGA(T685, T686, d1_out_gga) → D1_IN_GGA(power(T685, p(0)), T686)
D1_IN_GGA(power(T704, 0), T706) → D1_IN_GGA(T704, T706)
D1_IN_GGA(power(T704, s(T715)), T706) → U66_GGA(T704, T706, isnumber16_in_g(T715))
U66_GGA(T704, T706, isnumber16_out_g) → D1_IN_GGA(T704, T706)
U58_GGA(T614, T490, T616, isnumber16_out_g) → D1_IN_GGA(T614, T616)
U50_GGA(T538, T490, T539, d1_out_gga) → D1_IN_GGA(T538, T539)
U24_GGA(T272, T273, T274, isnumber16_out_g) → D1_IN_GGA(T272, times(power(T272, T273), T274))
U16_GGA(T154, T155, T156, d1_out_gga) → D1_IN_GGA(T155, times(times(T154, T155), T156))

The TRS R consists of the following rules:

d1_in_gga(T5, T5) → d1_out_gga
d1_in_gga(times(T42, T43), times(T42, T43)) → U5_gga(d1_in_gga(T42, times(T42, T43)))
d1_in_gga(times(T42, T43), times(T42, T43)) → U6_gga(T42, T43, d1_in_gga(T42, times(T42, T43)))
d1_in_gga(times(T125, T126), times(T125, T126)) → U11_gga(T125, T126, isnumber16_in_g(T125))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156)) → U13_gga(d1_in_gga(T154, times(times(T154, T155), T156)))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156)) → U14_gga(T154, T155, T156, d1_in_gga(T154, times(times(T154, T155), T156)))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156)) → U16_gga(T154, T155, T156, d1_in_gga(T154, times(times(T154, T155), T156)))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228)) → U19_gga(d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228)))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228)) → U20_gga(T226, T227, T228, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228)))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274)) → U22_gga(T272, T273, T274, isnumber16_in_g(T273))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274)) → U24_gga(T272, T273, T274, isnumber16_in_g(T273))
d1_in_gga(0, T397) → d1_out_gga
d1_in_gga(s(T402), T397) → U36_gga(isnumber16_in_g(T402))
d1_in_gga(p(T407), T397) → U37_gga(isnumber16_in_g(T407))
d1_in_gga(times(T428, T429), T430) → U38_gga(d1_in_gga(T428, T430))
d1_in_gga(times(T428, T429), T430) → U39_gga(T429, T430, d1_in_gga(T428, T430))
d1_in_gga(div(T460, T461), T462) → U41_gga(d1_in_gga(times(T460, power(T461, p(0))), T462))
d1_in_gga(power(T477, T478), T479) → U42_gga(T477, T479, isnumber16_in_g(T478))
d1_in_gga(times(T500, T490), T500) → U44_gga(d1_in_gga(T490, T500))
d1_in_gga(times(T512, T490), T513) → U45_gga(T490, T513, isnumber16_in_g(T512))
d1_in_gga(times(times(T537, T538), T490), T539) → U47_gga(d1_in_gga(T537, T539))
d1_in_gga(times(times(T537, T538), T490), T539) → U48_gga(T538, T539, d1_in_gga(T537, T539))
d1_in_gga(times(times(T556, T538), T490), T539) → U50_gga(T538, T490, T539, d1_in_gga(T556, T539))
d1_in_gga(times(div(T579, T580), T490), T581) → U53_gga(d1_in_gga(times(T579, power(T580, p(0))), T581))
d1_in_gga(times(div(T579, T580), T490), T581) → U54_gga(T490, T581, d1_in_gga(times(T579, power(T580, p(0))), T581))
d1_in_gga(times(power(T614, T615), T490), T616) → U56_gga(T614, T616, isnumber16_in_g(T615))
d1_in_gga(times(power(T614, T623), T490), T616) → U58_gga(T614, T490, T616, isnumber16_in_g(T623))
d1_in_gga(div(T647, T648), times(T647, power(T648, p(0)))) → d1_out_gga
d1_in_gga(div(T661, T662), T663) → U61_gga(isnumber16_in_g(times(T661, power(T662, p(0)))))
d1_in_gga(div(T684, T685), T686) → U62_gga(d1_in_gga(T684, T686))
d1_in_gga(div(T684, T685), T686) → U63_gga(T685, T686, d1_in_gga(T684, T686))
d1_in_gga(power(T704, 0), T706) → U65_gga(d1_in_gga(T704, T706))
d1_in_gga(power(T704, s(T715)), T706) → U66_gga(T704, T706, isnumber16_in_g(T715))
d1_in_gga(power(T704, p(T720)), T706) → U68_gga(T704, T706, isnumber16_in_g(T720))
isnumber16_in_g(0) → isnumber16_out_g
isnumber16_in_g(s(T17)) → U1_g(isnumber16_in_g(T17))
isnumber16_in_g(p(T20)) → U2_g(isnumber16_in_g(T20))
d1_in_gga(0, 0) → d1_out_gga
d1_in_gga(s(T12), s(T12)) → U3_gga(isnumber16_in_g(T12))
d1_in_gga(p(T25), p(T25)) → U4_gga(isnumber16_in_g(T25))
d1_in_gga(div(T79, T80), div(T79, T80)) → U8_gga(d1_in_gga(times(T79, power(T80, p(0))), div(T79, T80)))
d1_in_gga(power(T95, T96), power(T95, T96)) → U9_gga(T95, T96, isnumber16_in_g(T96))
d1_in_gga(div(T323, T324), div(T323, T324)) → U27_gga(isnumber16_in_g(times(T323, power(T324, p(0)))))
d1_in_gga(div(T341, T342), div(T341, T342)) → U28_gga(d1_in_gga(T341, div(T341, T342)))
d1_in_gga(div(T341, T342), div(T341, T342)) → U29_gga(T341, T342, d1_in_gga(T341, div(T341, T342)))
d1_in_gga(power(T367, 0), power(T367, 0)) → U31_gga(d1_in_gga(T367, power(T367, 0)))
d1_in_gga(power(T367, s(T378)), power(T367, s(T378))) → U32_gga(T367, T378, isnumber16_in_g(T378))
d1_in_gga(power(T367, p(T387)), power(T367, p(T387))) → U34_gga(T367, T387, isnumber16_in_g(T387))
U5_gga(d1_out_gga) → d1_out_gga
U6_gga(T42, T43, d1_out_gga) → U7_gga(d1_in_gga(T43, times(T42, T43)))
U11_gga(T125, T126, isnumber16_out_g) → d1_out_gga
U11_gga(T125, T126, isnumber16_out_g) → U12_gga(d1_in_gga(T126, times(T125, T126)))
U13_gga(d1_out_gga) → d1_out_gga
U14_gga(T154, T155, T156, d1_out_gga) → U15_gga(d1_in_gga(T155, times(times(T154, T155), T156)))
U16_gga(T154, T155, T156, d1_out_gga) → U17_gga(T154, T155, T156, d1_in_gga(T155, times(times(T154, T155), T156)))
U19_gga(d1_out_gga) → d1_out_gga
U20_gga(T226, T227, T228, d1_out_gga) → U21_gga(d1_in_gga(T228, times(div(T226, T227), T228)))
U22_gga(T272, T273, T274, isnumber16_out_g) → d1_out_gga
U22_gga(T272, T273, T274, isnumber16_out_g) → U23_gga(d1_in_gga(T272, times(power(T272, T273), T274)))
U24_gga(T272, T273, T274, isnumber16_out_g) → U25_gga(T272, T273, T274, d1_in_gga(T272, times(power(T272, T273), T274)))
U36_gga(isnumber16_out_g) → d1_out_gga
U37_gga(isnumber16_out_g) → d1_out_gga
U38_gga(d1_out_gga) → d1_out_gga
U39_gga(T429, T430, d1_out_gga) → U40_gga(d1_in_gga(T429, T430))
U41_gga(d1_out_gga) → d1_out_gga
U42_gga(T477, T479, isnumber16_out_g) → d1_out_gga
U42_gga(T477, T479, isnumber16_out_g) → U43_gga(d1_in_gga(T477, T479))
U44_gga(d1_out_gga) → d1_out_gga
U45_gga(T490, T513, isnumber16_out_g) → d1_out_gga
U45_gga(T490, T513, isnumber16_out_g) → U46_gga(d1_in_gga(T490, T513))
U47_gga(d1_out_gga) → d1_out_gga
U48_gga(T538, T539, d1_out_gga) → U49_gga(d1_in_gga(T538, T539))
U50_gga(T538, T490, T539, d1_out_gga) → U51_gga(T490, T539, d1_in_gga(T538, T539))
U53_gga(d1_out_gga) → d1_out_gga
U54_gga(T490, T581, d1_out_gga) → U55_gga(d1_in_gga(T490, T581))
U56_gga(T614, T616, isnumber16_out_g) → d1_out_gga
U56_gga(T614, T616, isnumber16_out_g) → U57_gga(d1_in_gga(T614, T616))
U58_gga(T614, T490, T616, isnumber16_out_g) → U59_gga(T490, T616, d1_in_gga(T614, T616))
U62_gga(d1_out_gga) → d1_out_gga
U63_gga(T685, T686, d1_out_gga) → U64_gga(d1_in_gga(power(T685, p(0)), T686))
U65_gga(d1_out_gga) → d1_out_gga
U66_gga(T704, T706, isnumber16_out_g) → d1_out_gga
U66_gga(T704, T706, isnumber16_out_g) → U67_gga(d1_in_gga(T704, T706))
U68_gga(T704, T706, isnumber16_out_g) → d1_out_gga
U68_gga(T704, T706, isnumber16_out_g) → U69_gga(d1_in_gga(T704, T706))
U1_g(isnumber16_out_g) → isnumber16_out_g
U2_g(isnumber16_out_g) → isnumber16_out_g
U3_gga(isnumber16_out_g) → d1_out_gga
U4_gga(isnumber16_out_g) → d1_out_gga
U8_gga(d1_out_gga) → d1_out_gga
U9_gga(T95, T96, isnumber16_out_g) → d1_out_gga
U9_gga(T95, T96, isnumber16_out_g) → U10_gga(d1_in_gga(T95, power(T95, T96)))
U28_gga(d1_out_gga) → d1_out_gga
U29_gga(T341, T342, d1_out_gga) → U30_gga(d1_in_gga(power(T342, p(0)), div(T341, T342)))
U31_gga(d1_out_gga) → d1_out_gga
U32_gga(T367, T378, isnumber16_out_g) → d1_out_gga
U32_gga(T367, T378, isnumber16_out_g) → U33_gga(d1_in_gga(T367, power(T367, s(T378))))
U34_gga(T367, T387, isnumber16_out_g) → d1_out_gga
U34_gga(T367, T387, isnumber16_out_g) → U35_gga(d1_in_gga(T367, power(T367, p(T387))))
U7_gga(d1_out_gga) → d1_out_gga
U12_gga(d1_out_gga) → d1_out_gga
U15_gga(d1_out_gga) → d1_out_gga
U17_gga(T154, T155, T156, d1_out_gga) → U18_gga(d1_in_gga(T156, times(times(T154, T155), T156)))
U21_gga(d1_out_gga) → d1_out_gga
U23_gga(d1_out_gga) → d1_out_gga
U25_gga(T272, T273, T274, d1_out_gga) → U26_gga(d1_in_gga(T274, times(power(T272, T273), T274)))
U40_gga(d1_out_gga) → d1_out_gga
U43_gga(d1_out_gga) → d1_out_gga
U46_gga(d1_out_gga) → d1_out_gga
U49_gga(d1_out_gga) → d1_out_gga
U51_gga(T490, T539, d1_out_gga) → U52_gga(d1_in_gga(T490, T539))
U55_gga(d1_out_gga) → d1_out_gga
U57_gga(d1_out_gga) → d1_out_gga
U59_gga(T490, T616, d1_out_gga) → U60_gga(d1_in_gga(T490, T616))
U64_gga(d1_out_gga) → d1_out_gga
U67_gga(d1_out_gga) → d1_out_gga
U69_gga(d1_out_gga) → d1_out_gga
U10_gga(d1_out_gga) → d1_out_gga
U30_gga(d1_out_gga) → d1_out_gga
U33_gga(d1_out_gga) → d1_out_gga
U35_gga(d1_out_gga) → d1_out_gga
U18_gga(d1_out_gga) → d1_out_gga
U26_gga(d1_out_gga) → d1_out_gga
U52_gga(d1_out_gga) → d1_out_gga
U60_gga(d1_out_gga) → d1_out_gga

The set Q consists of the following terms:

d1_in_gga(x0, x1)
isnumber16_in_g(x0)
U5_gga(x0)
U6_gga(x0, x1, x2)
U11_gga(x0, x1, x2)
U13_gga(x0)
U14_gga(x0, x1, x2, x3)
U16_gga(x0, x1, x2, x3)
U19_gga(x0)
U20_gga(x0, x1, x2, x3)
U22_gga(x0, x1, x2, x3)
U24_gga(x0, x1, x2, x3)
U36_gga(x0)
U37_gga(x0)
U38_gga(x0)
U39_gga(x0, x1, x2)
U41_gga(x0)
U42_gga(x0, x1, x2)
U44_gga(x0)
U45_gga(x0, x1, x2)
U47_gga(x0)
U48_gga(x0, x1, x2)
U50_gga(x0, x1, x2, x3)
U53_gga(x0)
U54_gga(x0, x1, x2)
U56_gga(x0, x1, x2)
U58_gga(x0, x1, x2, x3)
U62_gga(x0)
U63_gga(x0, x1, x2)
U65_gga(x0)
U66_gga(x0, x1, x2)
U68_gga(x0, x1, x2)
U1_g(x0)
U2_g(x0)
U3_gga(x0)
U4_gga(x0)
U8_gga(x0)
U9_gga(x0, x1, x2)
U28_gga(x0)
U29_gga(x0, x1, x2)
U31_gga(x0)
U32_gga(x0, x1, x2)
U34_gga(x0, x1, x2)
U7_gga(x0)
U12_gga(x0)
U15_gga(x0)
U17_gga(x0, x1, x2, x3)
U21_gga(x0)
U23_gga(x0)
U25_gga(x0, x1, x2, x3)
U40_gga(x0)
U43_gga(x0)
U46_gga(x0)
U49_gga(x0)
U51_gga(x0, x1, x2)
U55_gga(x0)
U57_gga(x0)
U59_gga(x0, x1, x2)
U64_gga(x0)
U67_gga(x0)
U69_gga(x0)
U10_gga(x0)
U30_gga(x0)
U33_gga(x0)
U35_gga(x0)
U18_gga(x0)
U26_gga(x0)
U52_gga(x0)
U60_gga(x0)

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

(21) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

D1_IN_GGA(times(T42, T43), times(T42, T43)) → D1_IN_GGA(T42, times(T42, T43))
D1_IN_GGA(times(T42, T43), times(T42, T43)) → U6_GGA(T42, T43, d1_in_gga(T42, times(T42, T43)))
D1_IN_GGA(times(T125, T126), times(T125, T126)) → U11_GGA(T125, T126, isnumber16_in_g(T125))
U11_GGA(T125, T126, isnumber16_out_g) → D1_IN_GGA(T126, times(T125, T126))
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156)) → D1_IN_GGA(T154, times(times(T154, T155), T156))
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156)) → U14_GGA(T154, T155, T156, d1_in_gga(T154, times(times(T154, T155), T156)))
D1_IN_GGA(times(times(T154, T155), T156), times(times(T154, T155), T156)) → U16_GGA(T154, T155, T156, d1_in_gga(T154, times(times(T154, T155), T156)))
D1_IN_GGA(times(T428, T429), T430) → D1_IN_GGA(T428, T430)
D1_IN_GGA(times(T428, T429), T430) → U39_GGA(T429, T430, d1_in_gga(T428, T430))
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228)) → D1_IN_GGA(times(T226, power(T227, p(0))), times(div(T226, T227), T228))
D1_IN_GGA(times(div(T226, T227), T228), times(div(T226, T227), T228)) → U20_GGA(T226, T227, T228, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228)))
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274)) → U22_GGA(T272, T273, T274, isnumber16_in_g(T273))
D1_IN_GGA(times(power(T272, T273), T274), times(power(T272, T273), T274)) → U24_GGA(T272, T273, T274, isnumber16_in_g(T273))
D1_IN_GGA(times(T500, T490), T500) → D1_IN_GGA(T490, T500)
D1_IN_GGA(div(T341, T342), div(T341, T342)) → D1_IN_GGA(T341, div(T341, T342))
D1_IN_GGA(div(T341, T342), div(T341, T342)) → U29_GGA(T341, T342, d1_in_gga(T341, div(T341, T342)))
D1_IN_GGA(times(T512, T490), T513) → U45_GGA(T490, T513, isnumber16_in_g(T512))
U45_GGA(T490, T513, isnumber16_out_g) → D1_IN_GGA(T490, T513)
D1_IN_GGA(times(times(T537, T538), T490), T539) → D1_IN_GGA(T537, T539)
D1_IN_GGA(times(times(T537, T538), T490), T539) → U48_GGA(T538, T539, d1_in_gga(T537, T539))
D1_IN_GGA(times(times(T556, T538), T490), T539) → U50_GGA(T538, T490, T539, d1_in_gga(T556, T539))
D1_IN_GGA(times(div(T579, T580), T490), T581) → D1_IN_GGA(times(T579, power(T580, p(0))), T581)
D1_IN_GGA(times(div(T579, T580), T490), T581) → U54_GGA(T490, T581, d1_in_gga(times(T579, power(T580, p(0))), T581))
D1_IN_GGA(times(power(T614, T615), T490), T616) → U56_GGA(T614, T616, isnumber16_in_g(T615))
D1_IN_GGA(times(power(T614, T623), T490), T616) → U58_GGA(T614, T490, T616, isnumber16_in_g(T623))
D1_IN_GGA(div(T684, T685), T686) → D1_IN_GGA(T684, T686)
D1_IN_GGA(div(T684, T685), T686) → U63_GGA(T685, T686, d1_in_gga(T684, T686))

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

POL(0) = 1
POL(D1_IN_GGA(x₁, x₂)) = 1 + x₁
POL(U10_gga(x₁)) = 0
POL(U11_GGA(x₁, x₂, x₃)) = 1 + x₂ + x₃
POL(U11_gga(x₁, x₂, x₃)) = 0
POL(U12_gga(x₁)) = 0
POL(U13_gga(x₁)) = 0
POL(U14_GGA(x₁, x₂, x₃, x₄)) = 1 + x₁ + x₂ + x₃
POL(U14_gga(x₁, x₂, x₃, x₄)) = 0
POL(U15_gga(x₁)) = 0
POL(U16_GGA(x₁, x₂, x₃, x₄)) = 1 + x₁ + x₂ + x₃
POL(U16_gga(x₁, x₂, x₃, x₄)) = 0
POL(U17_GGA(x₁, x₂, x₃, x₄)) = 1 + x₁ + x₂ + x₃
POL(U17_gga(x₁, x₂, x₃, x₄)) = 0
POL(U18_gga(x₁)) = 0
POL(U19_gga(x₁)) = 0
POL(U1_g(x₁)) = 1 + x₁
POL(U20_GGA(x₁, x₂, x₃, x₄)) = 1 + x₁ + x₂ + x₃
POL(U20_gga(x₁, x₂, x₃, x₄)) = 0
POL(U21_gga(x₁)) = 0
POL(U22_GGA(x₁, x₂, x₃, x₄)) = 1 + x₁
POL(U22_gga(x₁, x₂, x₃, x₄)) = 0
POL(U23_gga(x₁)) = 0
POL(U24_GGA(x₁, x₂, x₃, x₄)) = 1 + x₁ + x₃
POL(U24_gga(x₁, x₂, x₃, x₄)) = 0
POL(U25_GGA(x₁, x₂, x₃, x₄)) = 1 + x₁ + x₃
POL(U25_gga(x₁, x₂, x₃, x₄)) = 0
POL(U26_gga(x₁)) = 0
POL(U27_gga(x₁)) = 0
POL(U28_gga(x₁)) = 0
POL(U29_GGA(x₁, x₂, x₃)) = 1 + x₁ + x₂
POL(U29_gga(x₁, x₂, x₃)) = 0
POL(U2_g(x₁)) = 1
POL(U30_gga(x₁)) = 0
POL(U31_gga(x₁)) = 0
POL(U32_GGA(x₁, x₂, x₃)) = 1 + x₁
POL(U32_gga(x₁, x₂, x₃)) = 0
POL(U33_gga(x₁)) = 0
POL(U34_GGA(x₁, x₂, x₃)) = 1 + x₁
POL(U34_gga(x₁, x₂, x₃)) = 0
POL(U35_gga(x₁)) = 0
POL(U36_gga(x₁)) = 0
POL(U37_gga(x₁)) = 0
POL(U38_gga(x₁)) = 0
POL(U39_GGA(x₁, x₂, x₃)) = 1 + x₁
POL(U39_gga(x₁, x₂, x₃)) = 0
POL(U3_gga(x₁)) = 0
POL(U40_gga(x₁)) = 0
POL(U41_gga(x₁)) = 0
POL(U42_GGA(x₁, x₂, x₃)) = 1 + x₁
POL(U42_gga(x₁, x₂, x₃)) = 0
POL(U43_gga(x₁)) = 0
POL(U44_gga(x₁)) = 0
POL(U45_GGA(x₁, x₂, x₃)) = 1 + x₁ + x₃
POL(U45_gga(x₁, x₂, x₃)) = 0
POL(U46_gga(x₁)) = 0
POL(U47_gga(x₁)) = 0
POL(U48_GGA(x₁, x₂, x₃)) = 1 + x₁
POL(U48_gga(x₁, x₂, x₃)) = 0
POL(U49_gga(x₁)) = 0
POL(U4_gga(x₁)) = 0
POL(U50_GGA(x₁, x₂, x₃, x₄)) = 1 + x₁ + x₂
POL(U50_gga(x₁, x₂, x₃, x₄)) = 0
POL(U51_GGA(x₁, x₂, x₃)) = 1 + x₁
POL(U51_gga(x₁, x₂, x₃)) = 0
POL(U52_gga(x₁)) = 0
POL(U53_gga(x₁)) = 0
POL(U54_GGA(x₁, x₂, x₃)) = 1 + x₁
POL(U54_gga(x₁, x₂, x₃)) = 0
POL(U55_gga(x₁)) = 0
POL(U56_GGA(x₁, x₂, x₃)) = 1 + x₁
POL(U56_gga(x₁, x₂, x₃)) = 0
POL(U57_gga(x₁)) = 0
POL(U58_GGA(x₁, x₂, x₃, x₄)) = 1 + x₁ + x₂
POL(U58_gga(x₁, x₂, x₃, x₄)) = 0
POL(U59_GGA(x₁, x₂, x₃)) = 1 + x₁
POL(U59_gga(x₁, x₂, x₃)) = 0
POL(U5_gga(x₁)) = 0
POL(U60_gga(x₁)) = 0
POL(U61_gga(x₁)) = 0
POL(U62_gga(x₁)) = 0
POL(U63_GGA(x₁, x₂, x₃)) = 1 + x₁
POL(U63_gga(x₁, x₂, x₃)) = 0
POL(U64_gga(x₁)) = 0
POL(U65_gga(x₁)) = 0
POL(U66_GGA(x₁, x₂, x₃)) = 1 + x₁
POL(U66_gga(x₁, x₂, x₃)) = 0
POL(U67_gga(x₁)) = 0
POL(U68_GGA(x₁, x₂, x₃)) = 1 + x₁
POL(U68_gga(x₁, x₂, x₃)) = 0
POL(U69_gga(x₁)) = 0
POL(U6_GGA(x₁, x₂, x₃)) = 1 + x₁ + x₂
POL(U6_gga(x₁, x₂, x₃)) = 0
POL(U7_gga(x₁)) = 0
POL(U8_gga(x₁)) = 0
POL(U9_GGA(x₁, x₂, x₃)) = 1 + x₁
POL(U9_gga(x₁, x₂, x₃)) = 0
POL(d1_in_gga(x₁, x₂)) = 0
POL(d1_out_gga) = 0
POL(div(x₁, x₂)) = 1 + x₁ + x₂
POL(isnumber16_in_g(x₁)) = x₁
POL(isnumber16_out_g) = 1
POL(p(x₁)) = 1
POL(power(x₁, x₂)) = x₁
POL(s(x₁)) = 1 + x₁
POL(times(x₁, x₂)) = 1 + x₁ + x₂

The following usable rules [FROCOS05] were oriented:

isnumber16_in_g(0) → isnumber16_out_g
isnumber16_in_g(s(T17)) → U1_g(isnumber16_in_g(T17))
isnumber16_in_g(p(T20)) → U2_g(isnumber16_in_g(T20))
U2_g(isnumber16_out_g) → isnumber16_out_g
U1_g(isnumber16_out_g) → isnumber16_out_g

(22) Obligation:

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

U6_GGA(T42, T43, d1_out_gga) → D1_IN_GGA(T43, times(T42, T43))
U14_GGA(T154, T155, T156, d1_out_gga) → D1_IN_GGA(T155, times(times(T154, T155), T156))
U16_GGA(T154, T155, T156, d1_out_gga) → U17_GGA(T154, T155, T156, d1_in_gga(T155, times(times(T154, T155), T156)))
U17_GGA(T154, T155, T156, d1_out_gga) → D1_IN_GGA(T156, times(times(T154, T155), T156))
D1_IN_GGA(div(T79, T80), div(T79, T80)) → D1_IN_GGA(times(T79, power(T80, p(0))), div(T79, T80))
U39_GGA(T429, T430, d1_out_gga) → D1_IN_GGA(T429, T430)
D1_IN_GGA(power(T95, T96), power(T95, T96)) → U9_GGA(T95, T96, isnumber16_in_g(T96))
U9_GGA(T95, T96, isnumber16_out_g) → D1_IN_GGA(T95, power(T95, T96))
D1_IN_GGA(power(T367, 0), power(T367, 0)) → D1_IN_GGA(T367, power(T367, 0))
D1_IN_GGA(div(T460, T461), T462) → D1_IN_GGA(times(T460, power(T461, p(0))), T462)
U20_GGA(T226, T227, T228, d1_out_gga) → D1_IN_GGA(T228, times(div(T226, T227), T228))
D1_IN_GGA(power(T477, T478), T479) → U42_GGA(T477, T479, isnumber16_in_g(T478))
U42_GGA(T477, T479, isnumber16_out_g) → D1_IN_GGA(T477, T479)
U22_GGA(T272, T273, T274, isnumber16_out_g) → D1_IN_GGA(T272, times(power(T272, T273), T274))
U24_GGA(T272, T273, T274, isnumber16_out_g) → U25_GGA(T272, T273, T274, d1_in_gga(T272, times(power(T272, T273), T274)))
U25_GGA(T272, T273, T274, d1_out_gga) → D1_IN_GGA(T274, times(power(T272, T273), T274))
U29_GGA(T341, T342, d1_out_gga) → D1_IN_GGA(power(T342, p(0)), div(T341, T342))
D1_IN_GGA(power(T704, p(T720)), T706) → U68_GGA(T704, T706, isnumber16_in_g(T720))
U68_GGA(T704, T706, isnumber16_out_g) → D1_IN_GGA(T704, T706)
D1_IN_GGA(power(T367, s(T378)), power(T367, s(T378))) → U32_GGA(T367, T378, isnumber16_in_g(T378))
U32_GGA(T367, T378, isnumber16_out_g) → D1_IN_GGA(T367, power(T367, s(T378)))
D1_IN_GGA(power(T367, p(T387)), power(T367, p(T387))) → U34_GGA(T367, T387, isnumber16_in_g(T387))
U34_GGA(T367, T387, isnumber16_out_g) → D1_IN_GGA(T367, power(T367, p(T387)))
U48_GGA(T538, T539, d1_out_gga) → D1_IN_GGA(T538, T539)
U50_GGA(T538, T490, T539, d1_out_gga) → U51_GGA(T490, T539, d1_in_gga(T538, T539))
U51_GGA(T490, T539, d1_out_gga) → D1_IN_GGA(T490, T539)
U54_GGA(T490, T581, d1_out_gga) → D1_IN_GGA(T490, T581)
U56_GGA(T614, T616, isnumber16_out_g) → D1_IN_GGA(T614, T616)
U58_GGA(T614, T490, T616, isnumber16_out_g) → U59_GGA(T490, T616, d1_in_gga(T614, T616))
U59_GGA(T490, T616, d1_out_gga) → D1_IN_GGA(T490, T616)
U63_GGA(T685, T686, d1_out_gga) → D1_IN_GGA(power(T685, p(0)), T686)
D1_IN_GGA(power(T704, 0), T706) → D1_IN_GGA(T704, T706)
D1_IN_GGA(power(T704, s(T715)), T706) → U66_GGA(T704, T706, isnumber16_in_g(T715))
U66_GGA(T704, T706, isnumber16_out_g) → D1_IN_GGA(T704, T706)
U58_GGA(T614, T490, T616, isnumber16_out_g) → D1_IN_GGA(T614, T616)
U50_GGA(T538, T490, T539, d1_out_gga) → D1_IN_GGA(T538, T539)
U24_GGA(T272, T273, T274, isnumber16_out_g) → D1_IN_GGA(T272, times(power(T272, T273), T274))
U16_GGA(T154, T155, T156, d1_out_gga) → D1_IN_GGA(T155, times(times(T154, T155), T156))

The TRS R consists of the following rules:

d1_in_gga(T5, T5) → d1_out_gga
d1_in_gga(times(T42, T43), times(T42, T43)) → U5_gga(d1_in_gga(T42, times(T42, T43)))
d1_in_gga(times(T42, T43), times(T42, T43)) → U6_gga(T42, T43, d1_in_gga(T42, times(T42, T43)))
d1_in_gga(times(T125, T126), times(T125, T126)) → U11_gga(T125, T126, isnumber16_in_g(T125))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156)) → U13_gga(d1_in_gga(T154, times(times(T154, T155), T156)))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156)) → U14_gga(T154, T155, T156, d1_in_gga(T154, times(times(T154, T155), T156)))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156)) → U16_gga(T154, T155, T156, d1_in_gga(T154, times(times(T154, T155), T156)))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228)) → U19_gga(d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228)))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228)) → U20_gga(T226, T227, T228, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228)))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274)) → U22_gga(T272, T273, T274, isnumber16_in_g(T273))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274)) → U24_gga(T272, T273, T274, isnumber16_in_g(T273))
d1_in_gga(0, T397) → d1_out_gga
d1_in_gga(s(T402), T397) → U36_gga(isnumber16_in_g(T402))
d1_in_gga(p(T407), T397) → U37_gga(isnumber16_in_g(T407))
d1_in_gga(times(T428, T429), T430) → U38_gga(d1_in_gga(T428, T430))
d1_in_gga(times(T428, T429), T430) → U39_gga(T429, T430, d1_in_gga(T428, T430))
d1_in_gga(div(T460, T461), T462) → U41_gga(d1_in_gga(times(T460, power(T461, p(0))), T462))
d1_in_gga(power(T477, T478), T479) → U42_gga(T477, T479, isnumber16_in_g(T478))
d1_in_gga(times(T500, T490), T500) → U44_gga(d1_in_gga(T490, T500))
d1_in_gga(times(T512, T490), T513) → U45_gga(T490, T513, isnumber16_in_g(T512))
d1_in_gga(times(times(T537, T538), T490), T539) → U47_gga(d1_in_gga(T537, T539))
d1_in_gga(times(times(T537, T538), T490), T539) → U48_gga(T538, T539, d1_in_gga(T537, T539))
d1_in_gga(times(times(T556, T538), T490), T539) → U50_gga(T538, T490, T539, d1_in_gga(T556, T539))
d1_in_gga(times(div(T579, T580), T490), T581) → U53_gga(d1_in_gga(times(T579, power(T580, p(0))), T581))
d1_in_gga(times(div(T579, T580), T490), T581) → U54_gga(T490, T581, d1_in_gga(times(T579, power(T580, p(0))), T581))
d1_in_gga(times(power(T614, T615), T490), T616) → U56_gga(T614, T616, isnumber16_in_g(T615))
d1_in_gga(times(power(T614, T623), T490), T616) → U58_gga(T614, T490, T616, isnumber16_in_g(T623))
d1_in_gga(div(T647, T648), times(T647, power(T648, p(0)))) → d1_out_gga
d1_in_gga(div(T661, T662), T663) → U61_gga(isnumber16_in_g(times(T661, power(T662, p(0)))))
d1_in_gga(div(T684, T685), T686) → U62_gga(d1_in_gga(T684, T686))
d1_in_gga(div(T684, T685), T686) → U63_gga(T685, T686, d1_in_gga(T684, T686))
d1_in_gga(power(T704, 0), T706) → U65_gga(d1_in_gga(T704, T706))
d1_in_gga(power(T704, s(T715)), T706) → U66_gga(T704, T706, isnumber16_in_g(T715))
d1_in_gga(power(T704, p(T720)), T706) → U68_gga(T704, T706, isnumber16_in_g(T720))
isnumber16_in_g(0) → isnumber16_out_g
isnumber16_in_g(s(T17)) → U1_g(isnumber16_in_g(T17))
isnumber16_in_g(p(T20)) → U2_g(isnumber16_in_g(T20))
d1_in_gga(0, 0) → d1_out_gga
d1_in_gga(s(T12), s(T12)) → U3_gga(isnumber16_in_g(T12))
d1_in_gga(p(T25), p(T25)) → U4_gga(isnumber16_in_g(T25))
d1_in_gga(div(T79, T80), div(T79, T80)) → U8_gga(d1_in_gga(times(T79, power(T80, p(0))), div(T79, T80)))
d1_in_gga(power(T95, T96), power(T95, T96)) → U9_gga(T95, T96, isnumber16_in_g(T96))
d1_in_gga(div(T323, T324), div(T323, T324)) → U27_gga(isnumber16_in_g(times(T323, power(T324, p(0)))))
d1_in_gga(div(T341, T342), div(T341, T342)) → U28_gga(d1_in_gga(T341, div(T341, T342)))
d1_in_gga(div(T341, T342), div(T341, T342)) → U29_gga(T341, T342, d1_in_gga(T341, div(T341, T342)))
d1_in_gga(power(T367, 0), power(T367, 0)) → U31_gga(d1_in_gga(T367, power(T367, 0)))
d1_in_gga(power(T367, s(T378)), power(T367, s(T378))) → U32_gga(T367, T378, isnumber16_in_g(T378))
d1_in_gga(power(T367, p(T387)), power(T367, p(T387))) → U34_gga(T367, T387, isnumber16_in_g(T387))
U5_gga(d1_out_gga) → d1_out_gga
U6_gga(T42, T43, d1_out_gga) → U7_gga(d1_in_gga(T43, times(T42, T43)))
U11_gga(T125, T126, isnumber16_out_g) → d1_out_gga
U11_gga(T125, T126, isnumber16_out_g) → U12_gga(d1_in_gga(T126, times(T125, T126)))
U13_gga(d1_out_gga) → d1_out_gga
U14_gga(T154, T155, T156, d1_out_gga) → U15_gga(d1_in_gga(T155, times(times(T154, T155), T156)))
U16_gga(T154, T155, T156, d1_out_gga) → U17_gga(T154, T155, T156, d1_in_gga(T155, times(times(T154, T155), T156)))
U19_gga(d1_out_gga) → d1_out_gga
U20_gga(T226, T227, T228, d1_out_gga) → U21_gga(d1_in_gga(T228, times(div(T226, T227), T228)))
U22_gga(T272, T273, T274, isnumber16_out_g) → d1_out_gga
U22_gga(T272, T273, T274, isnumber16_out_g) → U23_gga(d1_in_gga(T272, times(power(T272, T273), T274)))
U24_gga(T272, T273, T274, isnumber16_out_g) → U25_gga(T272, T273, T274, d1_in_gga(T272, times(power(T272, T273), T274)))
U36_gga(isnumber16_out_g) → d1_out_gga
U37_gga(isnumber16_out_g) → d1_out_gga
U38_gga(d1_out_gga) → d1_out_gga
U39_gga(T429, T430, d1_out_gga) → U40_gga(d1_in_gga(T429, T430))
U41_gga(d1_out_gga) → d1_out_gga
U42_gga(T477, T479, isnumber16_out_g) → d1_out_gga
U42_gga(T477, T479, isnumber16_out_g) → U43_gga(d1_in_gga(T477, T479))
U44_gga(d1_out_gga) → d1_out_gga
U45_gga(T490, T513, isnumber16_out_g) → d1_out_gga
U45_gga(T490, T513, isnumber16_out_g) → U46_gga(d1_in_gga(T490, T513))
U47_gga(d1_out_gga) → d1_out_gga
U48_gga(T538, T539, d1_out_gga) → U49_gga(d1_in_gga(T538, T539))
U50_gga(T538, T490, T539, d1_out_gga) → U51_gga(T490, T539, d1_in_gga(T538, T539))
U53_gga(d1_out_gga) → d1_out_gga
U54_gga(T490, T581, d1_out_gga) → U55_gga(d1_in_gga(T490, T581))
U56_gga(T614, T616, isnumber16_out_g) → d1_out_gga
U56_gga(T614, T616, isnumber16_out_g) → U57_gga(d1_in_gga(T614, T616))
U58_gga(T614, T490, T616, isnumber16_out_g) → U59_gga(T490, T616, d1_in_gga(T614, T616))
U62_gga(d1_out_gga) → d1_out_gga
U63_gga(T685, T686, d1_out_gga) → U64_gga(d1_in_gga(power(T685, p(0)), T686))
U65_gga(d1_out_gga) → d1_out_gga
U66_gga(T704, T706, isnumber16_out_g) → d1_out_gga
U66_gga(T704, T706, isnumber16_out_g) → U67_gga(d1_in_gga(T704, T706))
U68_gga(T704, T706, isnumber16_out_g) → d1_out_gga
U68_gga(T704, T706, isnumber16_out_g) → U69_gga(d1_in_gga(T704, T706))
U1_g(isnumber16_out_g) → isnumber16_out_g
U2_g(isnumber16_out_g) → isnumber16_out_g
U3_gga(isnumber16_out_g) → d1_out_gga
U4_gga(isnumber16_out_g) → d1_out_gga
U8_gga(d1_out_gga) → d1_out_gga
U9_gga(T95, T96, isnumber16_out_g) → d1_out_gga
U9_gga(T95, T96, isnumber16_out_g) → U10_gga(d1_in_gga(T95, power(T95, T96)))
U28_gga(d1_out_gga) → d1_out_gga
U29_gga(T341, T342, d1_out_gga) → U30_gga(d1_in_gga(power(T342, p(0)), div(T341, T342)))
U31_gga(d1_out_gga) → d1_out_gga
U32_gga(T367, T378, isnumber16_out_g) → d1_out_gga
U32_gga(T367, T378, isnumber16_out_g) → U33_gga(d1_in_gga(T367, power(T367, s(T378))))
U34_gga(T367, T387, isnumber16_out_g) → d1_out_gga
U34_gga(T367, T387, isnumber16_out_g) → U35_gga(d1_in_gga(T367, power(T367, p(T387))))
U7_gga(d1_out_gga) → d1_out_gga
U12_gga(d1_out_gga) → d1_out_gga
U15_gga(d1_out_gga) → d1_out_gga
U17_gga(T154, T155, T156, d1_out_gga) → U18_gga(d1_in_gga(T156, times(times(T154, T155), T156)))
U21_gga(d1_out_gga) → d1_out_gga
U23_gga(d1_out_gga) → d1_out_gga
U25_gga(T272, T273, T274, d1_out_gga) → U26_gga(d1_in_gga(T274, times(power(T272, T273), T274)))
U40_gga(d1_out_gga) → d1_out_gga
U43_gga(d1_out_gga) → d1_out_gga
U46_gga(d1_out_gga) → d1_out_gga
U49_gga(d1_out_gga) → d1_out_gga
U51_gga(T490, T539, d1_out_gga) → U52_gga(d1_in_gga(T490, T539))
U55_gga(d1_out_gga) → d1_out_gga
U57_gga(d1_out_gga) → d1_out_gga
U59_gga(T490, T616, d1_out_gga) → U60_gga(d1_in_gga(T490, T616))
U64_gga(d1_out_gga) → d1_out_gga
U67_gga(d1_out_gga) → d1_out_gga
U69_gga(d1_out_gga) → d1_out_gga
U10_gga(d1_out_gga) → d1_out_gga
U30_gga(d1_out_gga) → d1_out_gga
U33_gga(d1_out_gga) → d1_out_gga
U35_gga(d1_out_gga) → d1_out_gga
U18_gga(d1_out_gga) → d1_out_gga
U26_gga(d1_out_gga) → d1_out_gga
U52_gga(d1_out_gga) → d1_out_gga
U60_gga(d1_out_gga) → d1_out_gga

The set Q consists of the following terms:

d1_in_gga(x0, x1)
isnumber16_in_g(x0)
U5_gga(x0)
U6_gga(x0, x1, x2)
U11_gga(x0, x1, x2)
U13_gga(x0)
U14_gga(x0, x1, x2, x3)
U16_gga(x0, x1, x2, x3)
U19_gga(x0)
U20_gga(x0, x1, x2, x3)
U22_gga(x0, x1, x2, x3)
U24_gga(x0, x1, x2, x3)
U36_gga(x0)
U37_gga(x0)
U38_gga(x0)
U39_gga(x0, x1, x2)
U41_gga(x0)
U42_gga(x0, x1, x2)
U44_gga(x0)
U45_gga(x0, x1, x2)
U47_gga(x0)
U48_gga(x0, x1, x2)
U50_gga(x0, x1, x2, x3)
U53_gga(x0)
U54_gga(x0, x1, x2)
U56_gga(x0, x1, x2)
U58_gga(x0, x1, x2, x3)
U62_gga(x0)
U63_gga(x0, x1, x2)
U65_gga(x0)
U66_gga(x0, x1, x2)
U68_gga(x0, x1, x2)
U1_g(x0)
U2_g(x0)
U3_gga(x0)
U4_gga(x0)
U8_gga(x0)
U9_gga(x0, x1, x2)
U28_gga(x0)
U29_gga(x0, x1, x2)
U31_gga(x0)
U32_gga(x0, x1, x2)
U34_gga(x0, x1, x2)
U7_gga(x0)
U12_gga(x0)
U15_gga(x0)
U17_gga(x0, x1, x2, x3)
U21_gga(x0)
U23_gga(x0)
U25_gga(x0, x1, x2, x3)
U40_gga(x0)
U43_gga(x0)
U46_gga(x0)
U49_gga(x0)
U51_gga(x0, x1, x2)
U55_gga(x0)
U57_gga(x0)
U59_gga(x0, x1, x2)
U64_gga(x0)
U67_gga(x0)
U69_gga(x0)
U10_gga(x0)
U30_gga(x0)
U33_gga(x0)
U35_gga(x0)
U18_gga(x0)
U26_gga(x0)
U52_gga(x0)
U60_gga(x0)

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

(23) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 24 less nodes.

(24) Obligation:

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

D1_IN_GGA(power(T95, T96), power(T95, T96)) → U9_GGA(T95, T96, isnumber16_in_g(T96))
U9_GGA(T95, T96, isnumber16_out_g) → D1_IN_GGA(T95, power(T95, T96))
D1_IN_GGA(power(T477, T478), T479) → U42_GGA(T477, T479, isnumber16_in_g(T478))
U42_GGA(T477, T479, isnumber16_out_g) → D1_IN_GGA(T477, T479)
D1_IN_GGA(power(T367, 0), power(T367, 0)) → D1_IN_GGA(T367, power(T367, 0))
D1_IN_GGA(power(T704, p(T720)), T706) → U68_GGA(T704, T706, isnumber16_in_g(T720))
U68_GGA(T704, T706, isnumber16_out_g) → D1_IN_GGA(T704, T706)
D1_IN_GGA(power(T367, s(T378)), power(T367, s(T378))) → U32_GGA(T367, T378, isnumber16_in_g(T378))
U32_GGA(T367, T378, isnumber16_out_g) → D1_IN_GGA(T367, power(T367, s(T378)))
D1_IN_GGA(power(T704, 0), T706) → D1_IN_GGA(T704, T706)
D1_IN_GGA(power(T367, p(T387)), power(T367, p(T387))) → U34_GGA(T367, T387, isnumber16_in_g(T387))
U34_GGA(T367, T387, isnumber16_out_g) → D1_IN_GGA(T367, power(T367, p(T387)))
D1_IN_GGA(power(T704, s(T715)), T706) → U66_GGA(T704, T706, isnumber16_in_g(T715))
U66_GGA(T704, T706, isnumber16_out_g) → D1_IN_GGA(T704, T706)

The TRS R consists of the following rules:

d1_in_gga(T5, T5) → d1_out_gga
d1_in_gga(times(T42, T43), times(T42, T43)) → U5_gga(d1_in_gga(T42, times(T42, T43)))
d1_in_gga(times(T42, T43), times(T42, T43)) → U6_gga(T42, T43, d1_in_gga(T42, times(T42, T43)))
d1_in_gga(times(T125, T126), times(T125, T126)) → U11_gga(T125, T126, isnumber16_in_g(T125))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156)) → U13_gga(d1_in_gga(T154, times(times(T154, T155), T156)))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156)) → U14_gga(T154, T155, T156, d1_in_gga(T154, times(times(T154, T155), T156)))
d1_in_gga(times(times(T154, T155), T156), times(times(T154, T155), T156)) → U16_gga(T154, T155, T156, d1_in_gga(T154, times(times(T154, T155), T156)))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228)) → U19_gga(d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228)))
d1_in_gga(times(div(T226, T227), T228), times(div(T226, T227), T228)) → U20_gga(T226, T227, T228, d1_in_gga(times(T226, power(T227, p(0))), times(div(T226, T227), T228)))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274)) → U22_gga(T272, T273, T274, isnumber16_in_g(T273))
d1_in_gga(times(power(T272, T273), T274), times(power(T272, T273), T274)) → U24_gga(T272, T273, T274, isnumber16_in_g(T273))
d1_in_gga(0, T397) → d1_out_gga
d1_in_gga(s(T402), T397) → U36_gga(isnumber16_in_g(T402))
d1_in_gga(p(T407), T397) → U37_gga(isnumber16_in_g(T407))
d1_in_gga(times(T428, T429), T430) → U38_gga(d1_in_gga(T428, T430))
d1_in_gga(times(T428, T429), T430) → U39_gga(T429, T430, d1_in_gga(T428, T430))
d1_in_gga(div(T460, T461), T462) → U41_gga(d1_in_gga(times(T460, power(T461, p(0))), T462))
d1_in_gga(power(T477, T478), T479) → U42_gga(T477, T479, isnumber16_in_g(T478))
d1_in_gga(times(T500, T490), T500) → U44_gga(d1_in_gga(T490, T500))
d1_in_gga(times(T512, T490), T513) → U45_gga(T490, T513, isnumber16_in_g(T512))
d1_in_gga(times(times(T537, T538), T490), T539) → U47_gga(d1_in_gga(T537, T539))
d1_in_gga(times(times(T537, T538), T490), T539) → U48_gga(T538, T539, d1_in_gga(T537, T539))
d1_in_gga(times(times(T556, T538), T490), T539) → U50_gga(T538, T490, T539, d1_in_gga(T556, T539))
d1_in_gga(times(div(T579, T580), T490), T581) → U53_gga(d1_in_gga(times(T579, power(T580, p(0))), T581))
d1_in_gga(times(div(T579, T580), T490), T581) → U54_gga(T490, T581, d1_in_gga(times(T579, power(T580, p(0))), T581))
d1_in_gga(times(power(T614, T615), T490), T616) → U56_gga(T614, T616, isnumber16_in_g(T615))
d1_in_gga(times(power(T614, T623), T490), T616) → U58_gga(T614, T490, T616, isnumber16_in_g(T623))
d1_in_gga(div(T647, T648), times(T647, power(T648, p(0)))) → d1_out_gga
d1_in_gga(div(T661, T662), T663) → U61_gga(isnumber16_in_g(times(T661, power(T662, p(0)))))
d1_in_gga(div(T684, T685), T686) → U62_gga(d1_in_gga(T684, T686))
d1_in_gga(div(T684, T685), T686) → U63_gga(T685, T686, d1_in_gga(T684, T686))
d1_in_gga(power(T704, 0), T706) → U65_gga(d1_in_gga(T704, T706))
d1_in_gga(power(T704, s(T715)), T706) → U66_gga(T704, T706, isnumber16_in_g(T715))
d1_in_gga(power(T704, p(T720)), T706) → U68_gga(T704, T706, isnumber16_in_g(T720))
isnumber16_in_g(0) → isnumber16_out_g
isnumber16_in_g(s(T17)) → U1_g(isnumber16_in_g(T17))
isnumber16_in_g(p(T20)) → U2_g(isnumber16_in_g(T20))
d1_in_gga(0, 0) → d1_out_gga
d1_in_gga(s(T12), s(T12)) → U3_gga(isnumber16_in_g(T12))
d1_in_gga(p(T25), p(T25)) → U4_gga(isnumber16_in_g(T25))
d1_in_gga(div(T79, T80), div(T79, T80)) → U8_gga(d1_in_gga(times(T79, power(T80, p(0))), div(T79, T80)))
d1_in_gga(power(T95, T96), power(T95, T96)) → U9_gga(T95, T96, isnumber16_in_g(T96))
d1_in_gga(div(T323, T324), div(T323, T324)) → U27_gga(isnumber16_in_g(times(T323, power(T324, p(0)))))
d1_in_gga(div(T341, T342), div(T341, T342)) → U28_gga(d1_in_gga(T341, div(T341, T342)))
d1_in_gga(div(T341, T342), div(T341, T342)) → U29_gga(T341, T342, d1_in_gga(T341, div(T341, T342)))
d1_in_gga(power(T367, 0), power(T367, 0)) → U31_gga(d1_in_gga(T367, power(T367, 0)))
d1_in_gga(power(T367, s(T378)), power(T367, s(T378))) → U32_gga(T367, T378, isnumber16_in_g(T378))
d1_in_gga(power(T367, p(T387)), power(T367, p(T387))) → U34_gga(T367, T387, isnumber16_in_g(T387))
U5_gga(d1_out_gga) → d1_out_gga
U6_gga(T42, T43, d1_out_gga) → U7_gga(d1_in_gga(T43, times(T42, T43)))
U11_gga(T125, T126, isnumber16_out_g) → d1_out_gga
U11_gga(T125, T126, isnumber16_out_g) → U12_gga(d1_in_gga(T126, times(T125, T126)))
U13_gga(d1_out_gga) → d1_out_gga
U14_gga(T154, T155, T156, d1_out_gga) → U15_gga(d1_in_gga(T155, times(times(T154, T155), T156)))
U16_gga(T154, T155, T156, d1_out_gga) → U17_gga(T154, T155, T156, d1_in_gga(T155, times(times(T154, T155), T156)))
U19_gga(d1_out_gga) → d1_out_gga
U20_gga(T226, T227, T228, d1_out_gga) → U21_gga(d1_in_gga(T228, times(div(T226, T227), T228)))
U22_gga(T272, T273, T274, isnumber16_out_g) → d1_out_gga
U22_gga(T272, T273, T274, isnumber16_out_g) → U23_gga(d1_in_gga(T272, times(power(T272, T273), T274)))
U24_gga(T272, T273, T274, isnumber16_out_g) → U25_gga(T272, T273, T274, d1_in_gga(T272, times(power(T272, T273), T274)))
U36_gga(isnumber16_out_g) → d1_out_gga
U37_gga(isnumber16_out_g) → d1_out_gga
U38_gga(d1_out_gga) → d1_out_gga
U39_gga(T429, T430, d1_out_gga) → U40_gga(d1_in_gga(T429, T430))
U41_gga(d1_out_gga) → d1_out_gga
U42_gga(T477, T479, isnumber16_out_g) → d1_out_gga
U42_gga(T477, T479, isnumber16_out_g) → U43_gga(d1_in_gga(T477, T479))
U44_gga(d1_out_gga) → d1_out_gga
U45_gga(T490, T513, isnumber16_out_g) → d1_out_gga
U45_gga(T490, T513, isnumber16_out_g) → U46_gga(d1_in_gga(T490, T513))
U47_gga(d1_out_gga) → d1_out_gga
U48_gga(T538, T539, d1_out_gga) → U49_gga(d1_in_gga(T538, T539))
U50_gga(T538, T490, T539, d1_out_gga) → U51_gga(T490, T539, d1_in_gga(T538, T539))
U53_gga(d1_out_gga) → d1_out_gga
U54_gga(T490, T581, d1_out_gga) → U55_gga(d1_in_gga(T490, T581))
U56_gga(T614, T616, isnumber16_out_g) → d1_out_gga
U56_gga(T614, T616, isnumber16_out_g) → U57_gga(d1_in_gga(T614, T616))
U58_gga(T614, T490, T616, isnumber16_out_g) → U59_gga(T490, T616, d1_in_gga(T614, T616))
U62_gga(d1_out_gga) → d1_out_gga
U63_gga(T685, T686, d1_out_gga) → U64_gga(d1_in_gga(power(T685, p(0)), T686))
U65_gga(d1_out_gga) → d1_out_gga
U66_gga(T704, T706, isnumber16_out_g) → d1_out_gga
U66_gga(T704, T706, isnumber16_out_g) → U67_gga(d1_in_gga(T704, T706))
U68_gga(T704, T706, isnumber16_out_g) → d1_out_gga
U68_gga(T704, T706, isnumber16_out_g) → U69_gga(d1_in_gga(T704, T706))
U1_g(isnumber16_out_g) → isnumber16_out_g
U2_g(isnumber16_out_g) → isnumber16_out_g
U3_gga(isnumber16_out_g) → d1_out_gga
U4_gga(isnumber16_out_g) → d1_out_gga
U8_gga(d1_out_gga) → d1_out_gga
U9_gga(T95, T96, isnumber16_out_g) → d1_out_gga
U9_gga(T95, T96, isnumber16_out_g) → U10_gga(d1_in_gga(T95, power(T95, T96)))
U28_gga(d1_out_gga) → d1_out_gga
U29_gga(T341, T342, d1_out_gga) → U30_gga(d1_in_gga(power(T342, p(0)), div(T341, T342)))
U31_gga(d1_out_gga) → d1_out_gga
U32_gga(T367, T378, isnumber16_out_g) → d1_out_gga
U32_gga(T367, T378, isnumber16_out_g) → U33_gga(d1_in_gga(T367, power(T367, s(T378))))
U34_gga(T367, T387, isnumber16_out_g) → d1_out_gga
U34_gga(T367, T387, isnumber16_out_g) → U35_gga(d1_in_gga(T367, power(T367, p(T387))))
U7_gga(d1_out_gga) → d1_out_gga
U12_gga(d1_out_gga) → d1_out_gga
U15_gga(d1_out_gga) → d1_out_gga
U17_gga(T154, T155, T156, d1_out_gga) → U18_gga(d1_in_gga(T156, times(times(T154, T155), T156)))
U21_gga(d1_out_gga) → d1_out_gga
U23_gga(d1_out_gga) → d1_out_gga
U25_gga(T272, T273, T274, d1_out_gga) → U26_gga(d1_in_gga(T274, times(power(T272, T273), T274)))
U40_gga(d1_out_gga) → d1_out_gga
U43_gga(d1_out_gga) → d1_out_gga
U46_gga(d1_out_gga) → d1_out_gga
U49_gga(d1_out_gga) → d1_out_gga
U51_gga(T490, T539, d1_out_gga) → U52_gga(d1_in_gga(T490, T539))
U55_gga(d1_out_gga) → d1_out_gga
U57_gga(d1_out_gga) → d1_out_gga
U59_gga(T490, T616, d1_out_gga) → U60_gga(d1_in_gga(T490, T616))
U64_gga(d1_out_gga) → d1_out_gga
U67_gga(d1_out_gga) → d1_out_gga
U69_gga(d1_out_gga) → d1_out_gga
U10_gga(d1_out_gga) → d1_out_gga
U30_gga(d1_out_gga) → d1_out_gga
U33_gga(d1_out_gga) → d1_out_gga
U35_gga(d1_out_gga) → d1_out_gga
U18_gga(d1_out_gga) → d1_out_gga
U26_gga(d1_out_gga) → d1_out_gga
U52_gga(d1_out_gga) → d1_out_gga
U60_gga(d1_out_gga) → d1_out_gga

The set Q consists of the following terms:

d1_in_gga(x0, x1)
isnumber16_in_g(x0)
U5_gga(x0)
U6_gga(x0, x1, x2)
U11_gga(x0, x1, x2)
U13_gga(x0)
U14_gga(x0, x1, x2, x3)
U16_gga(x0, x1, x2, x3)
U19_gga(x0)
U20_gga(x0, x1, x2, x3)
U22_gga(x0, x1, x2, x3)
U24_gga(x0, x1, x2, x3)
U36_gga(x0)
U37_gga(x0)
U38_gga(x0)
U39_gga(x0, x1, x2)
U41_gga(x0)
U42_gga(x0, x1, x2)
U44_gga(x0)
U45_gga(x0, x1, x2)
U47_gga(x0)
U48_gga(x0, x1, x2)
U50_gga(x0, x1, x2, x3)
U53_gga(x0)
U54_gga(x0, x1, x2)
U56_gga(x0, x1, x2)
U58_gga(x0, x1, x2, x3)
U62_gga(x0)
U63_gga(x0, x1, x2)
U65_gga(x0)
U66_gga(x0, x1, x2)
U68_gga(x0, x1, x2)
U1_g(x0)
U2_g(x0)
U3_gga(x0)
U4_gga(x0)
U8_gga(x0)
U9_gga(x0, x1, x2)
U28_gga(x0)
U29_gga(x0, x1, x2)
U31_gga(x0)
U32_gga(x0, x1, x2)
U34_gga(x0, x1, x2)
U7_gga(x0)
U12_gga(x0)
U15_gga(x0)
U17_gga(x0, x1, x2, x3)
U21_gga(x0)
U23_gga(x0)
U25_gga(x0, x1, x2, x3)
U40_gga(x0)
U43_gga(x0)
U46_gga(x0)
U49_gga(x0)
U51_gga(x0, x1, x2)
U55_gga(x0)
U57_gga(x0)
U59_gga(x0, x1, x2)
U64_gga(x0)
U67_gga(x0)
U69_gga(x0)
U10_gga(x0)
U30_gga(x0)
U33_gga(x0)
U35_gga(x0)
U18_gga(x0)
U26_gga(x0)
U52_gga(x0)
U60_gga(x0)

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

(25) 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.

(26) Obligation:

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

D1_IN_GGA(power(T95, T96), power(T95, T96)) → U9_GGA(T95, T96, isnumber16_in_g(T96))
U9_GGA(T95, T96, isnumber16_out_g) → D1_IN_GGA(T95, power(T95, T96))
D1_IN_GGA(power(T477, T478), T479) → U42_GGA(T477, T479, isnumber16_in_g(T478))
U42_GGA(T477, T479, isnumber16_out_g) → D1_IN_GGA(T477, T479)
D1_IN_GGA(power(T367, 0), power(T367, 0)) → D1_IN_GGA(T367, power(T367, 0))
D1_IN_GGA(power(T704, p(T720)), T706) → U68_GGA(T704, T706, isnumber16_in_g(T720))
U68_GGA(T704, T706, isnumber16_out_g) → D1_IN_GGA(T704, T706)
D1_IN_GGA(power(T367, s(T378)), power(T367, s(T378))) → U32_GGA(T367, T378, isnumber16_in_g(T378))
U32_GGA(T367, T378, isnumber16_out_g) → D1_IN_GGA(T367, power(T367, s(T378)))
D1_IN_GGA(power(T704, 0), T706) → D1_IN_GGA(T704, T706)
D1_IN_GGA(power(T367, p(T387)), power(T367, p(T387))) → U34_GGA(T367, T387, isnumber16_in_g(T387))
U34_GGA(T367, T387, isnumber16_out_g) → D1_IN_GGA(T367, power(T367, p(T387)))
D1_IN_GGA(power(T704, s(T715)), T706) → U66_GGA(T704, T706, isnumber16_in_g(T715))
U66_GGA(T704, T706, isnumber16_out_g) → D1_IN_GGA(T704, T706)

The TRS R consists of the following rules:

isnumber16_in_g(0) → isnumber16_out_g
isnumber16_in_g(s(T17)) → U1_g(isnumber16_in_g(T17))
isnumber16_in_g(p(T20)) → U2_g(isnumber16_in_g(T20))
U2_g(isnumber16_out_g) → isnumber16_out_g
U1_g(isnumber16_out_g) → isnumber16_out_g

The set Q consists of the following terms:

d1_in_gga(x0, x1)
isnumber16_in_g(x0)
U5_gga(x0)
U6_gga(x0, x1, x2)
U11_gga(x0, x1, x2)
U13_gga(x0)
U14_gga(x0, x1, x2, x3)
U16_gga(x0, x1, x2, x3)
U19_gga(x0)
U20_gga(x0, x1, x2, x3)
U22_gga(x0, x1, x2, x3)
U24_gga(x0, x1, x2, x3)
U36_gga(x0)
U37_gga(x0)
U38_gga(x0)
U39_gga(x0, x1, x2)
U41_gga(x0)
U42_gga(x0, x1, x2)
U44_gga(x0)
U45_gga(x0, x1, x2)
U47_gga(x0)
U48_gga(x0, x1, x2)
U50_gga(x0, x1, x2, x3)
U53_gga(x0)
U54_gga(x0, x1, x2)
U56_gga(x0, x1, x2)
U58_gga(x0, x1, x2, x3)
U62_gga(x0)
U63_gga(x0, x1, x2)
U65_gga(x0)
U66_gga(x0, x1, x2)
U68_gga(x0, x1, x2)
U1_g(x0)
U2_g(x0)
U3_gga(x0)
U4_gga(x0)
U8_gga(x0)
U9_gga(x0, x1, x2)
U28_gga(x0)
U29_gga(x0, x1, x2)
U31_gga(x0)
U32_gga(x0, x1, x2)
U34_gga(x0, x1, x2)
U7_gga(x0)
U12_gga(x0)
U15_gga(x0)
U17_gga(x0, x1, x2, x3)
U21_gga(x0)
U23_gga(x0)
U25_gga(x0, x1, x2, x3)
U40_gga(x0)
U43_gga(x0)
U46_gga(x0)
U49_gga(x0)
U51_gga(x0, x1, x2)
U55_gga(x0)
U57_gga(x0)
U59_gga(x0, x1, x2)
U64_gga(x0)
U67_gga(x0)
U69_gga(x0)
U10_gga(x0)
U30_gga(x0)
U33_gga(x0)
U35_gga(x0)
U18_gga(x0)
U26_gga(x0)
U52_gga(x0)
U60_gga(x0)

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

(27) 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].

d1_in_gga(x0, x1)
U5_gga(x0)
U6_gga(x0, x1, x2)
U11_gga(x0, x1, x2)
U13_gga(x0)
U14_gga(x0, x1, x2, x3)
U16_gga(x0, x1, x2, x3)
U19_gga(x0)
U20_gga(x0, x1, x2, x3)
U22_gga(x0, x1, x2, x3)
U24_gga(x0, x1, x2, x3)
U36_gga(x0)
U37_gga(x0)
U38_gga(x0)
U39_gga(x0, x1, x2)
U41_gga(x0)
U42_gga(x0, x1, x2)
U44_gga(x0)
U45_gga(x0, x1, x2)
U47_gga(x0)
U48_gga(x0, x1, x2)
U50_gga(x0, x1, x2, x3)
U53_gga(x0)
U54_gga(x0, x1, x2)
U56_gga(x0, x1, x2)
U58_gga(x0, x1, x2, x3)
U62_gga(x0)
U63_gga(x0, x1, x2)
U65_gga(x0)
U66_gga(x0, x1, x2)
U68_gga(x0, x1, x2)
U3_gga(x0)
U4_gga(x0)
U8_gga(x0)
U9_gga(x0, x1, x2)
U28_gga(x0)
U29_gga(x0, x1, x2)
U31_gga(x0)
U32_gga(x0, x1, x2)
U34_gga(x0, x1, x2)
U7_gga(x0)
U12_gga(x0)
U15_gga(x0)
U17_gga(x0, x1, x2, x3)
U21_gga(x0)
U23_gga(x0)
U25_gga(x0, x1, x2, x3)
U40_gga(x0)
U43_gga(x0)
U46_gga(x0)
U49_gga(x0)
U51_gga(x0, x1, x2)
U55_gga(x0)
U57_gga(x0)
U59_gga(x0, x1, x2)
U64_gga(x0)
U67_gga(x0)
U69_gga(x0)
U10_gga(x0)
U30_gga(x0)
U33_gga(x0)
U35_gga(x0)
U18_gga(x0)
U26_gga(x0)
U52_gga(x0)
U60_gga(x0)

(28) Obligation:

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

D1_IN_GGA(power(T95, T96), power(T95, T96)) → U9_GGA(T95, T96, isnumber16_in_g(T96))
U9_GGA(T95, T96, isnumber16_out_g) → D1_IN_GGA(T95, power(T95, T96))
D1_IN_GGA(power(T477, T478), T479) → U42_GGA(T477, T479, isnumber16_in_g(T478))
U42_GGA(T477, T479, isnumber16_out_g) → D1_IN_GGA(T477, T479)
D1_IN_GGA(power(T367, 0), power(T367, 0)) → D1_IN_GGA(T367, power(T367, 0))
D1_IN_GGA(power(T704, p(T720)), T706) → U68_GGA(T704, T706, isnumber16_in_g(T720))
U68_GGA(T704, T706, isnumber16_out_g) → D1_IN_GGA(T704, T706)
D1_IN_GGA(power(T367, s(T378)), power(T367, s(T378))) → U32_GGA(T367, T378, isnumber16_in_g(T378))
U32_GGA(T367, T378, isnumber16_out_g) → D1_IN_GGA(T367, power(T367, s(T378)))
D1_IN_GGA(power(T704, 0), T706) → D1_IN_GGA(T704, T706)
D1_IN_GGA(power(T367, p(T387)), power(T367, p(T387))) → U34_GGA(T367, T387, isnumber16_in_g(T387))
U34_GGA(T367, T387, isnumber16_out_g) → D1_IN_GGA(T367, power(T367, p(T387)))
D1_IN_GGA(power(T704, s(T715)), T706) → U66_GGA(T704, T706, isnumber16_in_g(T715))
U66_GGA(T704, T706, isnumber16_out_g) → D1_IN_GGA(T704, T706)

The TRS R consists of the following rules:

isnumber16_in_g(0) → isnumber16_out_g
isnumber16_in_g(s(T17)) → U1_g(isnumber16_in_g(T17))
isnumber16_in_g(p(T20)) → U2_g(isnumber16_in_g(T20))
U2_g(isnumber16_out_g) → isnumber16_out_g
U1_g(isnumber16_out_g) → isnumber16_out_g

The set Q consists of the following terms:

isnumber16_in_g(x0)
U1_g(x0)
U2_g(x0)

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

(29) 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:

U9_GGA(T95, T96, isnumber16_out_g) → D1_IN_GGA(T95, power(T95, T96))
The graph contains the following edges 1 >= 1
D1_IN_GGA(power(T704, 0), T706) → D1_IN_GGA(T704, T706)
The graph contains the following edges 1 > 1, 2 >= 2
D1_IN_GGA(power(T95, T96), power(T95, T96)) → U9_GGA(T95, T96, isnumber16_in_g(T96))
The graph contains the following edges 1 > 1, 2 > 1, 1 > 2, 2 > 2
U42_GGA(T477, T479, isnumber16_out_g) → D1_IN_GGA(T477, T479)
The graph contains the following edges 1 >= 1, 2 >= 2
D1_IN_GGA(power(T477, T478), T479) → U42_GGA(T477, T479, isnumber16_in_g(T478))
The graph contains the following edges 1 > 1, 2 >= 2
D1_IN_GGA(power(T367, 0), power(T367, 0)) → D1_IN_GGA(T367, power(T367, 0))
The graph contains the following edges 1 > 1, 2 > 1, 1 >= 2, 2 >= 2
U68_GGA(T704, T706, isnumber16_out_g) → D1_IN_GGA(T704, T706)
The graph contains the following edges 1 >= 1, 2 >= 2
U66_GGA(T704, T706, isnumber16_out_g) → D1_IN_GGA(T704, T706)
The graph contains the following edges 1 >= 1, 2 >= 2
D1_IN_GGA(power(T704, p(T720)), T706) → U68_GGA(T704, T706, isnumber16_in_g(T720))
The graph contains the following edges 1 > 1, 2 >= 2
D1_IN_GGA(power(T704, s(T715)), T706) → U66_GGA(T704, T706, isnumber16_in_g(T715))
The graph contains the following edges 1 > 1, 2 >= 2
U32_GGA(T367, T378, isnumber16_out_g) → D1_IN_GGA(T367, power(T367, s(T378)))
The graph contains the following edges 1 >= 1
U34_GGA(T367, T387, isnumber16_out_g) → D1_IN_GGA(T367, power(T367, p(T387)))
The graph contains the following edges 1 >= 1
D1_IN_GGA(power(T367, s(T378)), power(T367, s(T378))) → U32_GGA(T367, T378, isnumber16_in_g(T378))
The graph contains the following edges 1 > 1, 2 > 1, 1 > 2, 2 > 2
D1_IN_GGA(power(T367, p(T387)), power(T367, p(T387))) → U34_GGA(T367, T387, isnumber16_in_g(T387))
The graph contains the following edges 1 > 1, 2 > 1, 1 > 2, 2 > 2

(0) Obligation:

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) PrologToPiTRSProof (SOUND transformation)

(4) Obligation:

(5) DependencyPairsProof (EQUIVALENT transformation)

(6) Obligation:

(7) DependencyGraphProof (EQUIVALENT transformation)

(8) Complex Obligation (AND)

(9) Obligation:

(10) UsableRulesProof (EQUIVALENT transformation)

(11) Obligation:

(12) PiDPToQDPProof (EQUIVALENT transformation)

(13) Obligation:

(14) QDPSizeChangeProof (EQUIVALENT transformation)

(15) YES

(16) Obligation:

(17) UsableRulesProof (EQUIVALENT transformation)

(18) Obligation:

(19) PiDPToQDPProof (SOUND transformation)

(20) Obligation:

(21) QDPOrderProof (EQUIVALENT transformation)

(22) Obligation:

(23) DependencyGraphProof (EQUIVALENT transformation)

(24) Obligation:

(25) UsableRulesProof (EQUIVALENT transformation)

(26) Obligation:

(27) QReductionProof (EQUIVALENT transformation)

(28) Obligation:

(29) QDPSizeChangeProof (EQUIVALENT transformation)

(30) YES