Left Termination of the query pattern times_in_3(g, g, a) w.r.t. the given Prolog program could not be shown:

(0) Obligation:

Clauses:

times(X, Y, Z) :- mult(X, Y, 0, Z).
mult(0, Y, 0, Z) :- ','(!, eq(Z, 0)).
mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z)).
mult(X, Y, W, s(Z)) :- ','(p(W, P), mult(X, Y, P, Z)).
p(0, 0).
p(s(X), X).
eq(X, X).

Queries:

times(g,g,a).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: times(T1, T2, T3)\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: times(T1, T2, T3), SCOPE: 1, CLAUSE: 0\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: mult(T4, T5, 0, T7)\n\nT4 is ground\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: mult(T4, T5, 0, T7), SCOPE: 2, CLAUSE: 1 | mult(T4, T5, 0, T7), SCOPE: 2, CLAUSE: 2 | mult(T4, T5, 0, T7), SCOPE: 2, CLAUSE: 3 | ?_2\n\nT4 is ground\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: ','(!_2, eq(T10, 0)) | mult(0, T8, 0, T7), SCOPE: 2, CLAUSE: 2 | mult(0, T8, 0, T7), SCOPE: 2, CLAUSE: 3 | ?_2\n\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: mult(T4, T5, 0, T7), SCOPE: 2, CLAUSE: 2 | mult(T4, T5, 0, T7), SCOPE: 2, CLAUSE: 3 | ?_2\n\nT4 is ground\nT5 is ground\nX9 is free; \nX10 is free; \nmult(T4, T5, 0, T7) !=? mult(0, X9, 0, X10)", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: eq(T10, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: eq(T10, 0), SCOPE: 3, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: \n\nX12 is free", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: ','(!_2, mult(T12, T13, T13, T15)) | mult(s(T12), T13, 0, T7), SCOPE: 2, CLAUSE: 3 | ?_2\n\nT12 is ground\nT13 is ground\nX9 is free; \nX10 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: mult(T4, T5, 0, T7), SCOPE: 2, CLAUSE: 3\n\nT4 is ground\nT5 is ground\nX9 is free; \nX10 is free; \nX16 is free; \nX17 is free; \nX18 is free; \nmult(T4, T5, 0, T7) !=? mult(0, X9, 0, X10)\nmult(T4, T5, 0, T7) !=? mult(s(X16), X17, 0, X18)", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: mult(T12, T13, T13, T15)\n\nT12 is ground\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: mult(T12, T13, T13, T15), SCOPE: 4, CLAUSE: 1 | mult(T12, T13, T13, T15), SCOPE: 4, CLAUSE: 2 | mult(T12, T13, T13, T15), SCOPE: 4, CLAUSE: 3 | ?_4\n\nT12 is ground\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(!_4, eq(T18, 0)) | mult(0, 0, 0, T15), SCOPE: 4, CLAUSE: 2 | mult(0, 0, 0, T15), SCOPE: 4, CLAUSE: 3 | ?_4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: mult(T12, T13, T13, T15), SCOPE: 4, CLAUSE: 2 | mult(T12, T13, T13, T15), SCOPE: 4, CLAUSE: 3 | ?_4\n\nT12 is ground\nT13 is ground\nX21 is free; \nX22 is free; \nmult(T12, T13, T13, T15) !=? mult(0, X21, 0, X22)", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: eq(T18, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: eq(T18, 0), SCOPE: 5, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: \n\nX24 is free", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: ','(!_4, mult(T20, 0, 0, T23)) | mult(s(T20), 0, 0, T15), SCOPE: 4, CLAUSE: 3 | ?_4\n\nT20 is ground\nX21 is free; \nX22 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: mult(T12, T13, T13, T15), SCOPE: 4, CLAUSE: 3\n\nT12 is ground\nT13 is ground\nX21 is free; \nX22 is free; \nX28 is free; \nX29 is free; \nX30 is free; \nmult(T12, T13, T13, T15) !=? mult(0, X21, 0, X22)\nmult(T12, T13, T13, T15) !=? mult(s(X28), X29, 0, X30)", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: mult(T20, 0, 0, T23)\n\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: mult(T20, 0, 0, T23), SCOPE: 6, CLAUSE: 1 | mult(T20, 0, 0, T23), SCOPE: 6, CLAUSE: 2 | mult(T20, 0, 0, T23), SCOPE: 6, CLAUSE: 3 | ?_6\n\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: ','(!_6, eq(T25, 0)) | mult(0, 0, 0, T23), SCOPE: 6, CLAUSE: 2 | mult(0, 0, 0, T23), SCOPE: 6, CLAUSE: 3 | ?_6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: mult(T20, 0, 0, T23), SCOPE: 6, CLAUSE: 2 | mult(T20, 0, 0, T23), SCOPE: 6, CLAUSE: 3 | ?_6\n\nT20 is ground\nX33 is free; \nX34 is free; \nmult(T20, 0, 0, T23) !=? mult(0, X33, 0, X34)", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: eq(T25, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: eq(T25, 0), SCOPE: 7, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: \n\nX36 is free", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: ','(!_6, mult(T27, 0, 0, T29)) | mult(s(T27), 0, 0, T23), SCOPE: 6, CLAUSE: 3 | ?_6\n\nT27 is ground\nX33 is free; \nX34 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: mult(T20, 0, 0, T23), SCOPE: 6, CLAUSE: 3\n\nT20 is ground\nX33 is free; \nX34 is free; \nX40 is free; \nX41 is free; \nX42 is free; \nmult(T20, 0, 0, T23) !=? mult(0, X33, 0, X34)\nmult(T20, 0, 0, T23) !=? mult(s(X40), X41, 0, X42)", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: mult(T27, 0, 0, T29)\n\nT27 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(p(0, X51), mult(T30, 0, X51, T32))\n\nT30 is ground\nX33 is free; \nX34 is free; \nX40 is free; \nX41 is free; \nX42 is free; \nX51 is free; \nmult(T30, 0, 0, T23) !=? mult(0, X33, 0, X34)\nmult(T30, 0, 0, T23) !=? mult(s(X40), X41, 0, X42)", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: \n\nX33 is free\nX34 is free; \nX40 is free; \nX41 is free; \nX42 is free; \nX47 is free; \nX48 is free; \nX49 is free; \nX50 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: ','(p(0, X51), mult(T30, 0, X51, T32)), SCOPE: 8, CLAUSE: 4 | ','(p(0, X51), mult(T30, 0, X51, T32)), SCOPE: 8, CLAUSE: 5\n\nT30 is ground\nX33 is free; \nX34 is free; \nX40 is free; \nX41 is free; \nX42 is free; \nX51 is free; \nmult(T30, 0, 0, T23) !=? mult(0, X33, 0, X34)\nmult(T30, 0, 0, T23) !=? mult(s(X40), X41, 0, X42)", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: mult(T30, 0, 0, T32) | ','(p(0, X51), mult(T30, 0, X51, T32)), SCOPE: 8, CLAUSE: 5\n\nT30 is ground\nX33 is free; \nX34 is free; \nX40 is free; \nX41 is free; \nX42 is free; \nX51 is free; \nmult(T30, 0, 0, T23) !=? mult(0, X33, 0, X34)\nmult(T30, 0, 0, T23) !=? mult(s(X40), X41, 0, X42)", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: mult(T30, 0, 0, T32)\n\nT30 is ground\nX33 is free; \nX34 is free; \nX40 is free; \nX41 is free; \nX42 is free; \nmult(T30, 0, 0, T23) !=? mult(0, X33, 0, X34)\nmult(T30, 0, 0, T23) !=? mult(s(X40), X41, 0, X42)", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: ','(p(0, X51), mult(T30, 0, X51, T32)), SCOPE: 8, CLAUSE: 5\n\nT30 is ground\nX33 is free; \nX34 is free; \nX40 is free; \nX41 is free; \nX42 is free; \nX51 is free; \nmult(T30, 0, 0, T23) !=? mult(0, X33, 0, X34)\nmult(T30, 0, 0, T23) !=? mult(s(X40), X41, 0, X42)", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: \n\nX33 is free\nX34 is free; \nX40 is free; \nX41 is free; \nX42 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ','(p(T34, X61), mult(T33, T34, X61, T36))\n\nT33 is ground\nT34 is ground\nX21 is free; \nX22 is free; \nX28 is free; \nX29 is free; \nX30 is free; \nX61 is free; \nmult(T33, T34, T34, T15) !=? mult(0, X21, 0, X22)\nmult(T33, T34, T34, T15) !=? mult(s(X28), X29, 0, X30)", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: \n\nX21 is free\nX22 is free; \nX28 is free; \nX29 is free; \nX30 is free; \nX57 is free; \nX58 is free; \nX59 is free; \nX60 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: ','(p(T34, X61), mult(T33, T34, X61, T36)), SCOPE: 9, CLAUSE: 4 | ','(p(T34, X61), mult(T33, T34, X61, T36)), SCOPE: 9, CLAUSE: 5\n\nT33 is ground\nT34 is ground\nX21 is free; \nX22 is free; \nX28 is free; \nX29 is free; \nX30 is free; \nX61 is free; \nmult(T33, T34, T34, T15) !=? mult(0, X21, 0, X22)\nmult(T33, T34, T34, T15) !=? mult(s(X28), X29, 0, X30)", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: mult(T33, 0, 0, T36) | ','(p(0, X61), mult(T33, 0, X61, T36)), SCOPE: 9, CLAUSE: 5\n\nT33 is ground\nX21 is free; \nX22 is free; \nX28 is free; \nX29 is free; \nX30 is free; \nX61 is free; \nmult(T33, 0, 0, T15) !=? mult(0, X21, 0, X22)\nmult(T33, 0, 0, T15) !=? mult(s(X28), X29, 0, X30)", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: ','(p(T34, X61), mult(T33, T34, X61, T36)), SCOPE: 9, CLAUSE: 5\n\nT33 is ground\nT34 is ground\nX21 is free; \nX22 is free; \nX28 is free; \nX29 is free; \nX30 is free; \nX61 is free; \nmult(T33, T34, T34, T15) !=? mult(0, X21, 0, X22)\nmult(T33, T34, T34, T15) !=? mult(s(X28), X29, 0, X30)\np(T34, X61) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: mult(T33, 0, 0, T36)\n\nT33 is ground\nX21 is free; \nX22 is free; \nX28 is free; \nX29 is free; \nX30 is free; \nmult(T33, 0, 0, T15) !=? mult(0, X21, 0, X22)\nmult(T33, 0, 0, T15) !=? mult(s(X28), X29, 0, X30)", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(p(0, X61), mult(T33, 0, X61, T36)), SCOPE: 9, CLAUSE: 5\n\nT33 is ground\nX21 is free; \nX22 is free; \nX28 is free; \nX29 is free; \nX30 is free; \nX61 is free; \nmult(T33, 0, 0, T15) !=? mult(0, X21, 0, X22)\nmult(T33, 0, 0, T15) !=? mult(s(X28), X29, 0, X30)", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\nX21 is free\nX22 is free; \nX28 is free; \nX29 is free; \nX30 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: mult(T33, s(T37), T37, T36)\n\nT33 is ground\nT37 is ground\nX21 is free; \nX22 is free; \nX28 is free; \nX29 is free; \nX30 is free; \nX61 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: \n\nX21 is free\nX22 is free; \nX28 is free; \nX29 is free; \nX30 is free; \nX61 is free; \nX64 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: mult(T33, s(T37), T37, T36), SCOPE: 10, CLAUSE: 1 | mult(T33, s(T37), T37, T36), SCOPE: 10, CLAUSE: 2 | mult(T33, s(T37), T37, T36), SCOPE: 10, CLAUSE: 3 | ?_10\n\nT33 is ground\nT37 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ','(!_10, eq(T40, 0)) | mult(0, s(0), 0, T36), SCOPE: 10, CLAUSE: 2 | mult(0, s(0), 0, T36), SCOPE: 10, CLAUSE: 3 | ?_10\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: mult(T33, s(T37), T37, T36), SCOPE: 10, CLAUSE: 2 | mult(T33, s(T37), T37, T36), SCOPE: 10, CLAUSE: 3 | ?_10\n\nT33 is ground\nT37 is ground\nX67 is free; \nX68 is free; \nmult(T33, s(T37), T37, T36) !=? mult(0, X67, 0, X68)", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: eq(T40, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: eq(T40, 0), SCOPE: 11, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: \n\nX70 is free", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: ','(!_10, mult(T42, s(0), s(0), T45)) | mult(s(T42), s(0), 0, T36), SCOPE: 10, CLAUSE: 3 | ?_10\n\nT42 is ground\nX67 is free; \nX68 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: mult(T33, s(T37), T37, T36), SCOPE: 10, CLAUSE: 3\n\nT33 is ground\nT37 is ground\nX67 is free; \nX68 is free; \nX74 is free; \nX75 is free; \nX76 is free; \nmult(T33, s(T37), T37, T36) !=? mult(0, X67, 0, X68)\nmult(T33, s(T37), T37, T36) !=? mult(s(X74), X75, 0, X76)", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: mult(T42, s(0), s(0), T45)\n\nT42 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: mult(T42, s(0), s(0), T45), SCOPE: 12, CLAUSE: 1 | mult(T42, s(0), s(0), T45), SCOPE: 12, CLAUSE: 2 | mult(T42, s(0), s(0), T45), SCOPE: 12, CLAUSE: 3 | ?_12\n\nT42 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: mult(T42, s(0), s(0), T45), SCOPE: 12, CLAUSE: 2 | mult(T42, s(0), s(0), T45), SCOPE: 12, CLAUSE: 3 | ?_12\n\nT42 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: mult(T42, s(0), s(0), T45), SCOPE: 12, CLAUSE: 3\n\nT42 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(p(s(0), X90), mult(T46, s(0), X90, T48))\n\nT46 is ground\nX90 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: \n\nX86 is free\nX87 is free; \nX88 is free; \nX89 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: ','(p(s(0), X90), mult(T46, s(0), X90, T48)), SCOPE: 13, CLAUSE: 4 | ','(p(s(0), X90), mult(T46, s(0), X90, T48)), SCOPE: 13, CLAUSE: 5\n\nT46 is ground\nX90 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: ','(p(s(0), X90), mult(T46, s(0), X90, T48)), SCOPE: 13, CLAUSE: 5\n\nT46 is ground\nX90 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: mult(T46, s(0), 0, T48)\n\nT46 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: mult(T46, s(0), 0, T48), SCOPE: 14, CLAUSE: 1 | mult(T46, s(0), 0, T48), SCOPE: 14, CLAUSE: 2 | mult(T46, s(0), 0, T48), SCOPE: 14, CLAUSE: 3 | ?_14\n\nT46 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: ','(!_14, eq(T50, 0)) | mult(0, s(0), 0, T48), SCOPE: 14, CLAUSE: 2 | mult(0, s(0), 0, T48), SCOPE: 14, CLAUSE: 3 | ?_14\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: mult(T46, s(0), 0, T48), SCOPE: 14, CLAUSE: 2 | mult(T46, s(0), 0, T48), SCOPE: 14, CLAUSE: 3 | ?_14\n\nT46 is ground\nX95 is free; \nX96 is free; \nmult(T46, s(0), 0, T48) !=? mult(0, X95, 0, X96)", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: eq(T50, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: eq(T50, 0), SCOPE: 15, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: \n\nX98 is free", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: ','(!_14, mult(T52, s(0), s(0), T54)) | mult(s(T52), s(0), 0, T48), SCOPE: 14, CLAUSE: 3 | ?_14\n\nT52 is ground\nX95 is free; \nX96 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: mult(T46, s(0), 0, T48), SCOPE: 14, CLAUSE: 3\n\nT46 is ground\nX95 is free; \nX96 is free; \nX102 is free; \nX103 is free; \nX104 is free; \nmult(T46, s(0), 0, T48) !=? mult(0, X95, 0, X96)\nmult(T46, s(0), 0, T48) !=? mult(s(X102), X103, 0, X104)", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: mult(T52, s(0), s(0), T54)\n\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: ','(p(0, X113), mult(T55, s(0), X113, T57))\n\nT55 is ground\nX95 is free; \nX96 is free; \nX102 is free; \nX103 is free; \nX104 is free; \nX113 is free; \nmult(T55, s(0), 0, T48) !=? mult(0, X95, 0, X96)\nmult(T55, s(0), 0, T48) !=? mult(s(X102), X103, 0, X104)", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: \n\nX95 is free\nX96 is free; \nX102 is free; \nX103 is free; \nX104 is free; \nX109 is free; \nX110 is free; \nX111 is free; \nX112 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: ','(p(0, X113), mult(T55, s(0), X113, T57)), SCOPE: 16, CLAUSE: 4 | ','(p(0, X113), mult(T55, s(0), X113, T57)), SCOPE: 16, CLAUSE: 5\n\nT55 is ground\nX95 is free; \nX96 is free; \nX102 is free; \nX103 is free; \nX104 is free; \nX113 is free; \nmult(T55, s(0), 0, T48) !=? mult(0, X95, 0, X96)\nmult(T55, s(0), 0, T48) !=? mult(s(X102), X103, 0, X104)", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: mult(T55, s(0), 0, T57) | ','(p(0, X113), mult(T55, s(0), X113, T57)), SCOPE: 16, CLAUSE: 5\n\nT55 is ground\nX95 is free; \nX96 is free; \nX102 is free; \nX103 is free; \nX104 is free; \nX113 is free; \nmult(T55, s(0), 0, T48) !=? mult(0, X95, 0, X96)\nmult(T55, s(0), 0, T48) !=? mult(s(X102), X103, 0, X104)", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: mult(T55, s(0), 0, T57)\n\nT55 is ground\nX95 is free; \nX96 is free; \nX102 is free; \nX103 is free; \nX104 is free; \nmult(T55, s(0), 0, T48) !=? mult(0, X95, 0, X96)\nmult(T55, s(0), 0, T48) !=? mult(s(X102), X103, 0, X104)", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: ','(p(0, X113), mult(T55, s(0), X113, T57)), SCOPE: 16, CLAUSE: 5\n\nT55 is ground\nX95 is free; \nX96 is free; \nX102 is free; \nX103 is free; \nX104 is free; \nX113 is free; \nmult(T55, s(0), 0, T48) !=? mult(0, X95, 0, X96)\nmult(T55, s(0), 0, T48) !=? mult(s(X102), X103, 0, X104)", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: \n\nX95 is free\nX96 is free; \nX102 is free; \nX103 is free; \nX104 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: ','(p(T59, X123), mult(T58, s(T59), X123, T61))\n\nT58 is ground\nT59 is ground\nX67 is free; \nX68 is free; \nX74 is free; \nX75 is free; \nX76 is free; \nX123 is free; \nmult(T58, s(T59), T59, T36) !=? mult(0, X67, 0, X68)\nmult(T58, s(T59), T59, T36) !=? mult(s(X74), X75, 0, X76)", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: \n\nX67 is free\nX68 is free; \nX74 is free; \nX75 is free; \nX76 is free; \nX119 is free; \nX120 is free; \nX121 is free; \nX122 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: ','(p(T59, X123), mult(T58, s(T59), X123, T61)), SCOPE: 17, CLAUSE: 4 | ','(p(T59, X123), mult(T58, s(T59), X123, T61)), SCOPE: 17, CLAUSE: 5\n\nT58 is ground\nT59 is ground\nX67 is free; \nX68 is free; \nX74 is free; \nX75 is free; \nX76 is free; \nX123 is free; \nmult(T58, s(T59), T59, T36) !=? mult(0, X67, 0, X68)\nmult(T58, s(T59), T59, T36) !=? mult(s(X74), X75, 0, X76)", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: mult(T58, s(0), 0, T61) | ','(p(0, X123), mult(T58, s(0), X123, T61)), SCOPE: 17, CLAUSE: 5\n\nT58 is ground\nX67 is free; \nX68 is free; \nX74 is free; \nX75 is free; \nX76 is free; \nX123 is free; \nmult(T58, s(0), 0, T36) !=? mult(0, X67, 0, X68)\nmult(T58, s(0), 0, T36) !=? mult(s(X74), X75, 0, X76)", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: ','(p(T59, X123), mult(T58, s(T59), X123, T61)), SCOPE: 17, CLAUSE: 5\n\nT58 is ground\nT59 is ground\nX67 is free; \nX68 is free; \nX74 is free; \nX75 is free; \nX76 is free; \nX123 is free; \nmult(T58, s(T59), T59, T36) !=? mult(0, X67, 0, X68)\nmult(T58, s(T59), T59, T36) !=? mult(s(X74), X75, 0, X76)\np(T59, X123) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: mult(T58, s(0), 0, T61)\n\nT58 is ground\nX67 is free; \nX68 is free; \nX74 is free; \nX75 is free; \nX76 is free; \nmult(T58, s(0), 0, T36) !=? mult(0, X67, 0, X68)\nmult(T58, s(0), 0, T36) !=? mult(s(X74), X75, 0, X76)", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: ','(p(0, X123), mult(T58, s(0), X123, T61)), SCOPE: 17, CLAUSE: 5\n\nT58 is ground\nX67 is free; \nX68 is free; \nX74 is free; \nX75 is free; \nX76 is free; \nX123 is free; \nmult(T58, s(0), 0, T36) !=? mult(0, X67, 0, X68)\nmult(T58, s(0), 0, T36) !=? mult(s(X74), X75, 0, X76)", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: \n\nX67 is free\nX68 is free; \nX74 is free; \nX75 is free; \nX76 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: mult(T58, s(s(T62)), T62, T61)\n\nT58 is ground\nT62 is ground\nX67 is free; \nX68 is free; \nX74 is free; \nX75 is free; \nX76 is free; \nX123 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: \n\nX67 is free\nX68 is free; \nX74 is free; \nX75 is free; \nX76 is free; \nX123 is free; \nX126 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: mult(T58, s(s(T62)), T62, T61), SCOPE: 18, CLAUSE: 1 | mult(T58, s(s(T62)), T62, T61), SCOPE: 18, CLAUSE: 2 | mult(T58, s(s(T62)), T62, T61), SCOPE: 18, CLAUSE: 3 | ?_18\n\nT58 is ground\nT62 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: ','(!_18, eq(T65, 0)) | mult(0, s(s(0)), 0, T61), SCOPE: 18, CLAUSE: 2 | mult(0, s(s(0)), 0, T61), SCOPE: 18, CLAUSE: 3 | ?_18\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: mult(T58, s(s(T62)), T62, T61), SCOPE: 18, CLAUSE: 2 | mult(T58, s(s(T62)), T62, T61), SCOPE: 18, CLAUSE: 3 | ?_18\n\nT58 is ground\nT62 is ground\nX129 is free; \nX130 is free; \nmult(T58, s(s(T62)), T62, T61) !=? mult(0, X129, 0, X130)", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: eq(T65, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: eq(T65, 0), SCOPE: 19, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: \n\nX132 is free", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: ','(!_18, mult(T67, s(s(0)), s(s(0)), T70)) | mult(s(T67), s(s(0)), 0, T61), SCOPE: 18, CLAUSE: 3 | ?_18\n\nT67 is ground\nX129 is free; \nX130 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: mult(T58, s(s(T62)), T62, T61), SCOPE: 18, CLAUSE: 3\n\nT58 is ground\nT62 is ground\nX129 is free; \nX130 is free; \nX136 is free; \nX137 is free; \nX138 is free; \nmult(T58, s(s(T62)), T62, T61) !=? mult(0, X129, 0, X130)\nmult(T58, s(s(T62)), T62, T61) !=? mult(s(X136), X137, 0, X138)", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: mult(T67, s(s(0)), s(s(0)), T70)\n\nT67 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: mult(T67, s(s(0)), s(s(0)), T70), SCOPE: 20, CLAUSE: 1 | mult(T67, s(s(0)), s(s(0)), T70), SCOPE: 20, CLAUSE: 2 | mult(T67, s(s(0)), s(s(0)), T70), SCOPE: 20, CLAUSE: 3 | ?_20\n\nT67 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: mult(T67, s(s(0)), s(s(0)), T70), SCOPE: 20, CLAUSE: 2 | mult(T67, s(s(0)), s(s(0)), T70), SCOPE: 20, CLAUSE: 3 | ?_20\n\nT67 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: mult(T67, s(s(0)), s(s(0)), T70), SCOPE: 20, CLAUSE: 3\n\nT67 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: ','(p(s(s(0)), X152), mult(T71, s(s(0)), X152, T73))\n\nT71 is ground\nX152 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: \n\nX148 is free\nX149 is free; \nX150 is free; \nX151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: ','(p(s(s(0)), X152), mult(T71, s(s(0)), X152, T73)), SCOPE: 21, CLAUSE: 4 | ','(p(s(s(0)), X152), mult(T71, s(s(0)), X152, T73)), SCOPE: 21, CLAUSE: 5\n\nT71 is ground\nX152 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: ','(p(s(s(0)), X152), mult(T71, s(s(0)), X152, T73)), SCOPE: 21, CLAUSE: 5\n\nT71 is ground\nX152 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: mult(T71, s(s(0)), s(0), T73)\n\nT71 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: mult(T71, s(s(0)), s(0), T73), SCOPE: 22, CLAUSE: 1 | mult(T71, s(s(0)), s(0), T73), SCOPE: 22, CLAUSE: 2 | mult(T71, s(s(0)), s(0), T73), SCOPE: 22, CLAUSE: 3 | ?_22\n\nT71 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: mult(T71, s(s(0)), s(0), T73), SCOPE: 22, CLAUSE: 2 | mult(T71, s(s(0)), s(0), T73), SCOPE: 22, CLAUSE: 3 | ?_22\n\nT71 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: mult(T71, s(s(0)), s(0), T73), SCOPE: 22, CLAUSE: 3\n\nT71 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: ','(p(s(0), X168), mult(T74, s(s(0)), X168, T76))\n\nT74 is ground\nX168 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: \n\nX164 is free\nX165 is free; \nX166 is free; \nX167 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: ','(p(s(0), X168), mult(T74, s(s(0)), X168, T76)), SCOPE: 23, CLAUSE: 4 | ','(p(s(0), X168), mult(T74, s(s(0)), X168, T76)), SCOPE: 23, CLAUSE: 5\n\nT74 is ground\nX168 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: ','(p(s(0), X168), mult(T74, s(s(0)), X168, T76)), SCOPE: 23, CLAUSE: 5\n\nT74 is ground\nX168 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: mult(T74, s(s(0)), 0, T76)\n\nT74 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: mult(T74, s(s(0)), 0, T76), SCOPE: 24, CLAUSE: 1 | mult(T74, s(s(0)), 0, T76), SCOPE: 24, CLAUSE: 2 | mult(T74, s(s(0)), 0, T76), SCOPE: 24, CLAUSE: 3 | ?_24\n\nT74 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: ','(!_24, eq(T78, 0)) | mult(0, s(s(0)), 0, T76), SCOPE: 24, CLAUSE: 2 | mult(0, s(s(0)), 0, T76), SCOPE: 24, CLAUSE: 3 | ?_24\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: mult(T74, s(s(0)), 0, T76), SCOPE: 24, CLAUSE: 2 | mult(T74, s(s(0)), 0, T76), SCOPE: 24, CLAUSE: 3 | ?_24\n\nT74 is ground\nX173 is free; \nX174 is free; \nmult(T74, s(s(0)), 0, T76) !=? mult(0, X173, 0, X174)", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: eq(T78, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: eq(T78, 0), SCOPE: 25, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: \n\nX176 is free", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: ','(!_24, mult(T80, s(s(0)), s(s(0)), T82)) | mult(s(T80), s(s(0)), 0, T76), SCOPE: 24, CLAUSE: 3 | ?_24\n\nT80 is ground\nX173 is free; \nX174 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: mult(T74, s(s(0)), 0, T76), SCOPE: 24, CLAUSE: 3\n\nT74 is ground\nX173 is free; \nX174 is free; \nX180 is free; \nX181 is free; \nX182 is free; \nmult(T74, s(s(0)), 0, T76) !=? mult(0, X173, 0, X174)\nmult(T74, s(s(0)), 0, T76) !=? mult(s(X180), X181, 0, X182)", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: mult(T80, s(s(0)), s(s(0)), T82)\n\nT80 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: ','(p(0, X191), mult(T83, s(s(0)), X191, T85))\n\nT83 is ground\nX173 is free; \nX174 is free; \nX180 is free; \nX181 is free; \nX182 is free; \nX191 is free; \nmult(T83, s(s(0)), 0, T76) !=? mult(0, X173, 0, X174)\nmult(T83, s(s(0)), 0, T76) !=? mult(s(X180), X181, 0, X182)", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: \n\nX173 is free\nX174 is free; \nX180 is free; \nX181 is free; \nX182 is free; \nX187 is free; \nX188 is free; \nX189 is free; \nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: ','(p(0, X191), mult(T83, s(s(0)), X191, T85)), SCOPE: 26, CLAUSE: 4 | ','(p(0, X191), mult(T83, s(s(0)), X191, T85)), SCOPE: 26, CLAUSE: 5\n\nT83 is ground\nX173 is free; \nX174 is free; \nX180 is free; \nX181 is free; \nX182 is free; \nX191 is free; \nmult(T83, s(s(0)), 0, T76) !=? mult(0, X173, 0, X174)\nmult(T83, s(s(0)), 0, T76) !=? mult(s(X180), X181, 0, X182)", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: mult(T83, s(s(0)), 0, T85) | ','(p(0, X191), mult(T83, s(s(0)), X191, T85)), SCOPE: 26, CLAUSE: 5\n\nT83 is ground\nX173 is free; \nX174 is free; \nX180 is free; \nX181 is free; \nX182 is free; \nX191 is free; \nmult(T83, s(s(0)), 0, T76) !=? mult(0, X173, 0, X174)\nmult(T83, s(s(0)), 0, T76) !=? mult(s(X180), X181, 0, X182)", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: mult(T83, s(s(0)), 0, T85)\n\nT83 is ground\nX173 is free; \nX174 is free; \nX180 is free; \nX181 is free; \nX182 is free; \nmult(T83, s(s(0)), 0, T76) !=? mult(0, X173, 0, X174)\nmult(T83, s(s(0)), 0, T76) !=? mult(s(X180), X181, 0, X182)", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: ','(p(0, X191), mult(T83, s(s(0)), X191, T85)), SCOPE: 26, CLAUSE: 5\n\nT83 is ground\nX173 is free; \nX174 is free; \nX180 is free; \nX181 is free; \nX182 is free; \nX191 is free; \nmult(T83, s(s(0)), 0, T76) !=? mult(0, X173, 0, X174)\nmult(T83, s(s(0)), 0, T76) !=? mult(s(X180), X181, 0, X182)", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: \n\nX173 is free\nX174 is free; \nX180 is free; \nX181 is free; \nX182 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: ','(p(T87, X201), mult(T86, s(s(T87)), X201, T89))\n\nT86 is ground\nT87 is ground\nX129 is free; \nX130 is free; \nX136 is free; \nX137 is free; \nX138 is free; \nX201 is free; \nmult(T86, s(s(T87)), T87, T61) !=? mult(0, X129, 0, X130)\nmult(T86, s(s(T87)), T87, T61) !=? mult(s(X136), X137, 0, X138)", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: \n\nX129 is free\nX130 is free; \nX136 is free; \nX137 is free; \nX138 is free; \nX197 is free; \nX198 is free; \nX199 is free; \nX200 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: ','(p(T87, X201), mult(T86, s(s(T87)), X201, T89)), SCOPE: 27, CLAUSE: 4 | ','(p(T87, X201), mult(T86, s(s(T87)), X201, T89)), SCOPE: 27, CLAUSE: 5\n\nT86 is ground\nT87 is ground\nX129 is free; \nX130 is free; \nX136 is free; \nX137 is free; \nX138 is free; \nX201 is free; \nmult(T86, s(s(T87)), T87, T61) !=? mult(0, X129, 0, X130)\nmult(T86, s(s(T87)), T87, T61) !=? mult(s(X136), X137, 0, X138)", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: mult(T86, s(s(0)), 0, T89) | ','(p(0, X201), mult(T86, s(s(0)), X201, T89)), SCOPE: 27, CLAUSE: 5\n\nT86 is ground\nX129 is free; \nX130 is free; \nX136 is free; \nX137 is free; \nX138 is free; \nX201 is free; \nmult(T86, s(s(0)), 0, T61) !=? mult(0, X129, 0, X130)\nmult(T86, s(s(0)), 0, T61) !=? mult(s(X136), X137, 0, X138)", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: ','(p(T87, X201), mult(T86, s(s(T87)), X201, T89)), SCOPE: 27, CLAUSE: 5\n\nT86 is ground\nT87 is ground\nX129 is free; \nX130 is free; \nX136 is free; \nX137 is free; \nX138 is free; \nX201 is free; \nmult(T86, s(s(T87)), T87, T61) !=? mult(0, X129, 0, X130)\nmult(T86, s(s(T87)), T87, T61) !=? mult(s(X136), X137, 0, X138)\np(T87, X201) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: mult(T86, s(s(0)), 0, T89)\n\nT86 is ground\nX129 is free; \nX130 is free; \nX136 is free; \nX137 is free; \nX138 is free; \nmult(T86, s(s(0)), 0, T61) !=? mult(0, X129, 0, X130)\nmult(T86, s(s(0)), 0, T61) !=? mult(s(X136), X137, 0, X138)", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: ','(p(0, X201), mult(T86, s(s(0)), X201, T89)), SCOPE: 27, CLAUSE: 5\n\nT86 is ground\nX129 is free; \nX130 is free; \nX136 is free; \nX137 is free; \nX138 is free; \nX201 is free; \nmult(T86, s(s(0)), 0, T61) !=? mult(0, X129, 0, X130)\nmult(T86, s(s(0)), 0, T61) !=? mult(s(X136), X137, 0, X138)", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: \n\nX129 is free\nX130 is free; \nX136 is free; \nX137 is free; \nX138 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: mult(T86, s(s(s(T90))), T90, T89)\n\nT86 is ground\nT90 is ground\nX129 is free; \nX130 is free; \nX136 is free; \nX137 is free; \nX138 is free; \nX201 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: \n\nX129 is free\nX130 is free; \nX136 is free; \nX137 is free; \nX138 is free; \nX201 is free; \nX204 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: mult(T86, s(s(s(T90))), T90, T89), SCOPE: 28, CLAUSE: 1 | mult(T86, s(s(s(T90))), T90, T89), SCOPE: 28, CLAUSE: 2 | mult(T86, s(s(s(T90))), T90, T89), SCOPE: 28, CLAUSE: 3 | ?_28\n\nT86 is ground\nT90 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: ','(!_28, eq(T93, 0)) | mult(0, s(s(s(0))), 0, T89), SCOPE: 28, CLAUSE: 2 | mult(0, s(s(s(0))), 0, T89), SCOPE: 28, CLAUSE: 3 | ?_28\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: mult(T86, s(s(s(T90))), T90, T89), SCOPE: 28, CLAUSE: 2 | mult(T86, s(s(s(T90))), T90, T89), SCOPE: 28, CLAUSE: 3 | ?_28\n\nT86 is ground\nT90 is ground\nX207 is free; \nX208 is free; \nmult(T86, s(s(s(T90))), T90, T89) !=? mult(0, X207, 0, X208)", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: eq(T93, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: eq(T93, 0), SCOPE: 29, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: \n\nX210 is free", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: ','(!_28, mult(T95, s(s(s(0))), s(s(s(0))), T98)) | mult(s(T95), s(s(s(0))), 0, T89), SCOPE: 28, CLAUSE: 3 | ?_28\n\nT95 is ground\nX207 is free; \nX208 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: mult(T86, s(s(s(T90))), T90, T89), SCOPE: 28, CLAUSE: 3\n\nT86 is ground\nT90 is ground\nX207 is free; \nX208 is free; \nX214 is free; \nX215 is free; \nX216 is free; \nmult(T86, s(s(s(T90))), T90, T89) !=? mult(0, X207, 0, X208)\nmult(T86, s(s(s(T90))), T90, T89) !=? mult(s(X214), X215, 0, X216)", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: mult(T95, s(s(s(0))), s(s(s(0))), T98)\n\nT95 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: mult(T95, s(s(s(0))), s(s(s(0))), T98), SCOPE: 30, CLAUSE: 1 | mult(T95, s(s(s(0))), s(s(s(0))), T98), SCOPE: 30, CLAUSE: 2 | mult(T95, s(s(s(0))), s(s(s(0))), T98), SCOPE: 30, CLAUSE: 3 | ?_30\n\nT95 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: mult(T95, s(s(s(0))), s(s(s(0))), T98), SCOPE: 30, CLAUSE: 2 | mult(T95, s(s(s(0))), s(s(s(0))), T98), SCOPE: 30, CLAUSE: 3 | ?_30\n\nT95 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: mult(T95, s(s(s(0))), s(s(s(0))), T98), SCOPE: 30, CLAUSE: 3\n\nT95 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: ','(p(s(s(s(0))), X230), mult(T99, s(s(s(0))), X230, T101))\n\nT99 is ground\nX230 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: \n\nX226 is free\nX227 is free; \nX228 is free; \nX229 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: ','(p(s(s(s(0))), X230), mult(T99, s(s(s(0))), X230, T101)), SCOPE: 31, CLAUSE: 4 | ','(p(s(s(s(0))), X230), mult(T99, s(s(s(0))), X230, T101)), SCOPE: 31, CLAUSE: 5\n\nT99 is ground\nX230 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: ','(p(s(s(s(0))), X230), mult(T99, s(s(s(0))), X230, T101)), SCOPE: 31, CLAUSE: 5\n\nT99 is ground\nX230 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: mult(T99, s(s(s(0))), s(s(0)), T101)\n\nT99 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: mult(T99, s(s(s(0))), s(s(0)), T101), SCOPE: 32, CLAUSE: 1 | mult(T99, s(s(s(0))), s(s(0)), T101), SCOPE: 32, CLAUSE: 2 | mult(T99, s(s(s(0))), s(s(0)), T101), SCOPE: 32, CLAUSE: 3 | ?_32\n\nT99 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: mult(T99, s(s(s(0))), s(s(0)), T101), SCOPE: 32, CLAUSE: 2 | mult(T99, s(s(s(0))), s(s(0)), T101), SCOPE: 32, CLAUSE: 3 | ?_32\n\nT99 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: mult(T99, s(s(s(0))), s(s(0)), T101), SCOPE: 32, CLAUSE: 3\n\nT99 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: ','(p(s(s(0)), X246), mult(T102, s(s(s(0))), X246, T104))\n\nT102 is ground\nX246 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: \n\nX242 is free\nX243 is free; \nX244 is free; \nX245 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: ','(p(s(s(0)), X246), mult(T102, s(s(s(0))), X246, T104)), SCOPE: 33, CLAUSE: 4 | ','(p(s(s(0)), X246), mult(T102, s(s(s(0))), X246, T104)), SCOPE: 33, CLAUSE: 5\n\nT102 is ground\nX246 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: ','(p(s(s(0)), X246), mult(T102, s(s(s(0))), X246, T104)), SCOPE: 33, CLAUSE: 5\n\nT102 is ground\nX246 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: mult(T102, s(s(s(0))), s(0), T104)\n\nT102 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: mult(T102, s(s(s(0))), s(0), T104), SCOPE: 34, CLAUSE: 1 | mult(T102, s(s(s(0))), s(0), T104), SCOPE: 34, CLAUSE: 2 | mult(T102, s(s(s(0))), s(0), T104), SCOPE: 34, CLAUSE: 3 | ?_34\n\nT102 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: mult(T102, s(s(s(0))), s(0), T104), SCOPE: 34, CLAUSE: 2 | mult(T102, s(s(s(0))), s(0), T104), SCOPE: 34, CLAUSE: 3 | ?_34\n\nT102 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: mult(T102, s(s(s(0))), s(0), T104), SCOPE: 34, CLAUSE: 3\n\nT102 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: ','(p(s(0), X262), mult(T105, s(s(s(0))), X262, T107))\n\nT105 is ground\nX262 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: \n\nX258 is free\nX259 is free; \nX260 is free; \nX261 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: ','(p(s(0), X262), mult(T105, s(s(s(0))), X262, T107)), SCOPE: 35, CLAUSE: 4 | ','(p(s(0), X262), mult(T105, s(s(s(0))), X262, T107)), SCOPE: 35, CLAUSE: 5\n\nT105 is ground\nX262 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: ','(p(s(0), X262), mult(T105, s(s(s(0))), X262, T107)), SCOPE: 35, CLAUSE: 5\n\nT105 is ground\nX262 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: mult(T105, s(s(s(0))), 0, T107)\n\nT105 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: mult(T105, s(s(s(0))), 0, T107), SCOPE: 36, CLAUSE: 1 | mult(T105, s(s(s(0))), 0, T107), SCOPE: 36, CLAUSE: 2 | mult(T105, s(s(s(0))), 0, T107), SCOPE: 36, CLAUSE: 3 | ?_36\n\nT105 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: ','(!_36, eq(T109, 0)) | mult(0, s(s(s(0))), 0, T107), SCOPE: 36, CLAUSE: 2 | mult(0, s(s(s(0))), 0, T107), SCOPE: 36, CLAUSE: 3 | ?_36\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: mult(T105, s(s(s(0))), 0, T107), SCOPE: 36, CLAUSE: 2 | mult(T105, s(s(s(0))), 0, T107), SCOPE: 36, CLAUSE: 3 | ?_36\n\nT105 is ground\nX267 is free; \nX268 is free; \nmult(T105, s(s(s(0))), 0, T107) !=? mult(0, X267, 0, X268)", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: eq(T109, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: eq(T109, 0), SCOPE: 37, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: \n\nX270 is free", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: ','(!_36, mult(T111, s(s(s(0))), s(s(s(0))), T113)) | mult(s(T111), s(s(s(0))), 0, T107), SCOPE: 36, CLAUSE: 3 | ?_36\n\nT111 is ground\nX267 is free; \nX268 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: mult(T105, s(s(s(0))), 0, T107), SCOPE: 36, CLAUSE: 3\n\nT105 is ground\nX267 is free; \nX268 is free; \nX274 is free; \nX275 is free; \nX276 is free; \nmult(T105, s(s(s(0))), 0, T107) !=? mult(0, X267, 0, X268)\nmult(T105, s(s(s(0))), 0, T107) !=? mult(s(X274), X275, 0, X276)", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: mult(T111, s(s(s(0))), s(s(s(0))), T113)\n\nT111 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: ','(p(0, X285), mult(T114, s(s(s(0))), X285, T116))\n\nT114 is ground\nX267 is free; \nX268 is free; \nX274 is free; \nX275 is free; \nX276 is free; \nX285 is free; \nmult(T114, s(s(s(0))), 0, T107) !=? mult(0, X267, 0, X268)\nmult(T114, s(s(s(0))), 0, T107) !=? mult(s(X274), X275, 0, X276)", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: \n\nX267 is free\nX268 is free; \nX274 is free; \nX275 is free; \nX276 is free; \nX281 is free; \nX282 is free; \nX283 is free; \nX284 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: ','(p(0, X285), mult(T114, s(s(s(0))), X285, T116)), SCOPE: 38, CLAUSE: 4 | ','(p(0, X285), mult(T114, s(s(s(0))), X285, T116)), SCOPE: 38, CLAUSE: 5\n\nT114 is ground\nX267 is free; \nX268 is free; \nX274 is free; \nX275 is free; \nX276 is free; \nX285 is free; \nmult(T114, s(s(s(0))), 0, T107) !=? mult(0, X267, 0, X268)\nmult(T114, s(s(s(0))), 0, T107) !=? mult(s(X274), X275, 0, X276)", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: mult(T114, s(s(s(0))), 0, T116) | ','(p(0, X285), mult(T114, s(s(s(0))), X285, T116)), SCOPE: 38, CLAUSE: 5\n\nT114 is ground\nX267 is free; \nX268 is free; \nX274 is free; \nX275 is free; \nX276 is free; \nX285 is free; \nmult(T114, s(s(s(0))), 0, T107) !=? mult(0, X267, 0, X268)\nmult(T114, s(s(s(0))), 0, T107) !=? mult(s(X274), X275, 0, X276)", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: mult(T114, s(s(s(0))), 0, T116)\n\nT114 is ground\nX267 is free; \nX268 is free; \nX274 is free; \nX275 is free; \nX276 is free; \nmult(T114, s(s(s(0))), 0, T107) !=? mult(0, X267, 0, X268)\nmult(T114, s(s(s(0))), 0, T107) !=? mult(s(X274), X275, 0, X276)", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: ','(p(0, X285), mult(T114, s(s(s(0))), X285, T116)), SCOPE: 38, CLAUSE: 5\n\nT114 is ground\nX267 is free; \nX268 is free; \nX274 is free; \nX275 is free; \nX276 is free; \nX285 is free; \nmult(T114, s(s(s(0))), 0, T107) !=? mult(0, X267, 0, X268)\nmult(T114, s(s(s(0))), 0, T107) !=? mult(s(X274), X275, 0, X276)", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: \n\nX267 is free\nX268 is free; \nX274 is free; \nX275 is free; \nX276 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: ','(p(T118, X295), mult(T117, s(s(s(T118))), X295, T120))\n\nT117 is ground\nT118 is ground\nX207 is free; \nX208 is free; \nX214 is free; \nX215 is free; \nX216 is free; \nX295 is free; \nmult(T117, s(s(s(T118))), T118, T89) !=? mult(0, X207, 0, X208)\nmult(T117, s(s(s(T118))), T118, T89) !=? mult(s(X214), X215, 0, X216)", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: \n\nX207 is free\nX208 is free; \nX214 is free; \nX215 is free; \nX216 is free; \nX291 is free; \nX292 is free; \nX293 is free; \nX294 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: ','(p(T118, X295), mult(T117, s(s(s(T118))), X295, T120)), SCOPE: 39, CLAUSE: 4 | ','(p(T118, X295), mult(T117, s(s(s(T118))), X295, T120)), SCOPE: 39, CLAUSE: 5\n\nT117 is ground\nT118 is ground\nX207 is free; \nX208 is free; \nX214 is free; \nX215 is free; \nX216 is free; \nX295 is free; \nmult(T117, s(s(s(T118))), T118, T89) !=? mult(0, X207, 0, X208)\nmult(T117, s(s(s(T118))), T118, T89) !=? mult(s(X214), X215, 0, X216)", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: mult(T117, s(s(s(0))), 0, T120) | ','(p(0, X295), mult(T117, s(s(s(0))), X295, T120)), SCOPE: 39, CLAUSE: 5\n\nT117 is ground\nX207 is free; \nX208 is free; \nX214 is free; \nX215 is free; \nX216 is free; \nX295 is free; \nmult(T117, s(s(s(0))), 0, T89) !=? mult(0, X207, 0, X208)\nmult(T117, s(s(s(0))), 0, T89) !=? mult(s(X214), X215, 0, X216)", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: ','(p(T118, X295), mult(T117, s(s(s(T118))), X295, T120)), SCOPE: 39, CLAUSE: 5\n\nT117 is ground\nT118 is ground\nX207 is free; \nX208 is free; \nX214 is free; \nX215 is free; \nX216 is free; \nX295 is free; \nmult(T117, s(s(s(T118))), T118, T89) !=? mult(0, X207, 0, X208)\nmult(T117, s(s(s(T118))), T118, T89) !=? mult(s(X214), X215, 0, X216)\np(T118, X295) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: mult(T117, s(s(s(0))), 0, T120)\n\nT117 is ground\nX207 is free; \nX208 is free; \nX214 is free; \nX215 is free; \nX216 is free; \nmult(T117, s(s(s(0))), 0, T89) !=? mult(0, X207, 0, X208)\nmult(T117, s(s(s(0))), 0, T89) !=? mult(s(X214), X215, 0, X216)", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: ','(p(0, X295), mult(T117, s(s(s(0))), X295, T120)), SCOPE: 39, CLAUSE: 5\n\nT117 is ground\nX207 is free; \nX208 is free; \nX214 is free; \nX215 is free; \nX216 is free; \nX295 is free; \nmult(T117, s(s(s(0))), 0, T89) !=? mult(0, X207, 0, X208)\nmult(T117, s(s(s(0))), 0, T89) !=? mult(s(X214), X215, 0, X216)", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: \n\nX207 is free\nX208 is free; \nX214 is free; \nX215 is free; \nX216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: mult(T117, s(s(s(s(T121)))), T121, T120)\n\nT117 is ground\nT121 is ground\nX207 is free; \nX208 is free; \nX214 is free; \nX215 is free; \nX216 is free; \nX295 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: \n\nX207 is free\nX208 is free; \nX214 is free; \nX215 is free; \nX216 is free; \nX295 is free; \nX298 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: mult(T117, s(s(s(s(T121)))), T121, T120), SCOPE: 40, CLAUSE: 1 | mult(T117, s(s(s(s(T121)))), T121, T120), SCOPE: 40, CLAUSE: 2 | mult(T117, s(s(s(s(T121)))), T121, T120), SCOPE: 40, CLAUSE: 3 | ?_40\n\nT117 is ground\nT121 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: ','(!_40, eq(T124, 0)) | mult(0, s(s(s(s(0)))), 0, T120), SCOPE: 40, CLAUSE: 2 | mult(0, s(s(s(s(0)))), 0, T120), SCOPE: 40, CLAUSE: 3 | ?_40\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: mult(T117, s(s(s(s(T121)))), T121, T120), SCOPE: 40, CLAUSE: 2 | mult(T117, s(s(s(s(T121)))), T121, T120), SCOPE: 40, CLAUSE: 3 | ?_40\n\nT117 is ground\nT121 is ground\nX301 is free; \nX302 is free; \nmult(T117, s(s(s(s(T121)))), T121, T120) !=? mult(0, X301, 0, X302)", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: eq(T124, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: eq(T124, 0), SCOPE: 41, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: \n\nX304 is free", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="227: ','(!_40, mult(T126, s(s(s(s(0)))), s(s(s(s(0)))), T129)) | mult(s(T126), s(s(s(s(0)))), 0, T120), SCOPE: 40, CLAUSE: 3 | ?_40\n\nT126 is ground\nX301 is free; \nX302 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: mult(T117, s(s(s(s(T121)))), T121, T120), SCOPE: 40, CLAUSE: 3\n\nT117 is ground\nT121 is ground\nX301 is free; \nX302 is free; \nX308 is free; \nX309 is free; \nX310 is free; \nmult(T117, s(s(s(s(T121)))), T121, T120) !=? mult(0, X301, 0, X302)\nmult(T117, s(s(s(s(T121)))), T121, T120) !=? mult(s(X308), X309, 0, X310)", fontsize=16, style=filled, fillcolor=lightyellow];
229 [label="229: mult(T126, s(s(s(s(0)))), s(s(s(s(0)))), T129)\n\nT126 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: mult(T126, s(s(s(s(0)))), s(s(s(s(0)))), T129), SCOPE: 42, CLAUSE: 1 | mult(T126, s(s(s(s(0)))), s(s(s(s(0)))), T129), SCOPE: 42, CLAUSE: 2 | mult(T126, s(s(s(s(0)))), s(s(s(s(0)))), T129), SCOPE: 42, CLAUSE: 3 | ?_42\n\nT126 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
231 [label="231: mult(T126, s(s(s(s(0)))), s(s(s(s(0)))), T129), SCOPE: 42, CLAUSE: 2 | mult(T126, s(s(s(s(0)))), s(s(s(s(0)))), T129), SCOPE: 42, CLAUSE: 3 | ?_42\n\nT126 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: mult(T126, s(s(s(s(0)))), s(s(s(s(0)))), T129), SCOPE: 42, CLAUSE: 3\n\nT126 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: ','(p(s(s(s(s(0)))), X324), mult(T130, s(s(s(s(0)))), X324, T132))\n\nT130 is ground\nX324 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
234 [label="234: \n\nX320 is free\nX321 is free; \nX322 is free; \nX323 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
235 [label="235: ','(p(s(s(s(s(0)))), X324), mult(T130, s(s(s(s(0)))), X324, T132)), SCOPE: 43, CLAUSE: 4 | ','(p(s(s(s(s(0)))), X324), mult(T130, s(s(s(s(0)))), X324, T132)), SCOPE: 43, CLAUSE: 5\n\nT130 is ground\nX324 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
236 [label="236: ','(p(s(s(s(s(0)))), X324), mult(T130, s(s(s(s(0)))), X324, T132)), SCOPE: 43, CLAUSE: 5\n\nT130 is ground\nX324 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: mult(T130, s(s(s(s(0)))), s(s(s(0))), T132)\n\nT130 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
238 [label="238: mult(T130, s(s(s(s(0)))), s(s(s(0))), T132), SCOPE: 44, CLAUSE: 1 | mult(T130, s(s(s(s(0)))), s(s(s(0))), T132), SCOPE: 44, CLAUSE: 2 | mult(T130, s(s(s(s(0)))), s(s(s(0))), T132), SCOPE: 44, CLAUSE: 3 | ?_44\n\nT130 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
239 [label="239: mult(T130, s(s(s(s(0)))), s(s(s(0))), T132), SCOPE: 44, CLAUSE: 2 | mult(T130, s(s(s(s(0)))), s(s(s(0))), T132), SCOPE: 44, CLAUSE: 3 | ?_44\n\nT130 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
240 [label="240: mult(T130, s(s(s(s(0)))), s(s(s(0))), T132), SCOPE: 44, CLAUSE: 3\n\nT130 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
241 [label="241: ','(p(s(s(s(0))), X340), mult(T133, s(s(s(s(0)))), X340, T135))\n\nT133 is ground\nX340 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
242 [label="242: \n\nX336 is free\nX337 is free; \nX338 is free; \nX339 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
243 [label="243: ','(p(s(s(s(0))), X340), mult(T133, s(s(s(s(0)))), X340, T135)), SCOPE: 45, CLAUSE: 4 | ','(p(s(s(s(0))), X340), mult(T133, s(s(s(s(0)))), X340, T135)), SCOPE: 45, CLAUSE: 5\n\nT133 is ground\nX340 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
244 [label="244: ','(p(s(s(s(0))), X340), mult(T133, s(s(s(s(0)))), X340, T135)), SCOPE: 45, CLAUSE: 5\n\nT133 is ground\nX340 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
245 [label="245: mult(T133, s(s(s(s(0)))), s(s(0)), T135)\n\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
246 [label="246: mult(T133, s(s(s(s(0)))), s(s(0)), T135), SCOPE: 46, CLAUSE: 1 | mult(T133, s(s(s(s(0)))), s(s(0)), T135), SCOPE: 46, CLAUSE: 2 | mult(T133, s(s(s(s(0)))), s(s(0)), T135), SCOPE: 46, CLAUSE: 3 | ?_46\n\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
247 [label="247: mult(T133, s(s(s(s(0)))), s(s(0)), T135), SCOPE: 46, CLAUSE: 2 | mult(T133, s(s(s(s(0)))), s(s(0)), T135), SCOPE: 46, CLAUSE: 3 | ?_46\n\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="248: mult(T133, s(s(s(s(0)))), s(s(0)), T135), SCOPE: 46, CLAUSE: 3\n\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
249 [label="249: ','(p(s(s(0)), X356), mult(T136, s(s(s(s(0)))), X356, T138))\n\nT136 is ground\nX356 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="250: \n\nX352 is free\nX353 is free; \nX354 is free; \nX355 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
251 [label="251: ','(p(s(s(0)), X356), mult(T136, s(s(s(s(0)))), X356, T138)), SCOPE: 47, CLAUSE: 4 | ','(p(s(s(0)), X356), mult(T136, s(s(s(s(0)))), X356, T138)), SCOPE: 47, CLAUSE: 5\n\nT136 is ground\nX356 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
252 [label="252: ','(p(s(s(0)), X356), mult(T136, s(s(s(s(0)))), X356, T138)), SCOPE: 47, CLAUSE: 5\n\nT136 is ground\nX356 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="253: mult(T136, s(s(s(s(0)))), s(0), T138)\n\nT136 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
254 [label="254: mult(T136, s(s(s(s(0)))), s(0), T138), SCOPE: 48, CLAUSE: 1 | mult(T136, s(s(s(s(0)))), s(0), T138), SCOPE: 48, CLAUSE: 2 | mult(T136, s(s(s(s(0)))), s(0), T138), SCOPE: 48, CLAUSE: 3 | ?_48\n\nT136 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
255 [label="255: mult(T136, s(s(s(s(0)))), s(0), T138), SCOPE: 48, CLAUSE: 2 | mult(T136, s(s(s(s(0)))), s(0), T138), SCOPE: 48, CLAUSE: 3 | ?_48\n\nT136 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
256 [label="256: mult(T136, s(s(s(s(0)))), s(0), T138), SCOPE: 48, CLAUSE: 3\n\nT136 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
257 [label="257: ','(p(s(0), X372), mult(T139, s(s(s(s(0)))), X372, T141))\n\nT139 is ground\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="258: \n\nX368 is free\nX369 is free; \nX370 is free; \nX371 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="259: ','(p(s(0), X372), mult(T139, s(s(s(s(0)))), X372, T141)), SCOPE: 49, CLAUSE: 4 | ','(p(s(0), X372), mult(T139, s(s(s(s(0)))), X372, T141)), SCOPE: 49, CLAUSE: 5\n\nT139 is ground\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
260 [label="260: ','(p(s(0), X372), mult(T139, s(s(s(s(0)))), X372, T141)), SCOPE: 49, CLAUSE: 5\n\nT139 is ground\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
261 [label="261: mult(T139, s(s(s(s(0)))), 0, T141)\n\nT139 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
262 [label="262: mult(T139, s(s(s(s(0)))), 0, T141), SCOPE: 50, CLAUSE: 1 | mult(T139, s(s(s(s(0)))), 0, T141), SCOPE: 50, CLAUSE: 2 | mult(T139, s(s(s(s(0)))), 0, T141), SCOPE: 50, CLAUSE: 3 | ?_50\n\nT139 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: ','(!_50, eq(T143, 0)) | mult(0, s(s(s(s(0)))), 0, T141), SCOPE: 50, CLAUSE: 2 | mult(0, s(s(s(s(0)))), 0, T141), SCOPE: 50, CLAUSE: 3 | ?_50\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: mult(T139, s(s(s(s(0)))), 0, T141), SCOPE: 50, CLAUSE: 2 | mult(T139, s(s(s(s(0)))), 0, T141), SCOPE: 50, CLAUSE: 3 | ?_50\n\nT139 is ground\nX377 is free; \nX378 is free; \nmult(T139, s(s(s(s(0)))), 0, T141) !=? mult(0, X377, 0, X378)", fontsize=16, style=filled, fillcolor=lightyellow];
265 [label="265: eq(T143, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
266 [label="266: eq(T143, 0), SCOPE: 51, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="267: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
268 [label="268: \n\nX380 is free", fontsize=16, style=filled, fillcolor=lightyellow];
269 [label="269: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="270: ','(!_50, mult(T145, s(s(s(s(0)))), s(s(s(s(0)))), T147)) | mult(s(T145), s(s(s(s(0)))), 0, T141), SCOPE: 50, CLAUSE: 3 | ?_50\n\nT145 is ground\nX377 is free; \nX378 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
271 [label="271: mult(T139, s(s(s(s(0)))), 0, T141), SCOPE: 50, CLAUSE: 3\n\nT139 is ground\nX377 is free; \nX378 is free; \nX384 is free; \nX385 is free; \nX386 is free; \nmult(T139, s(s(s(s(0)))), 0, T141) !=? mult(0, X377, 0, X378)\nmult(T139, s(s(s(s(0)))), 0, T141) !=? mult(s(X384), X385, 0, X386)", fontsize=16, style=filled, fillcolor=lightyellow];
272 [label="272: mult(T145, s(s(s(s(0)))), s(s(s(s(0)))), T147)\n\nT145 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
273 [label="273: ','(p(0, X395), mult(T148, s(s(s(s(0)))), X395, T150))\n\nT148 is ground\nX377 is free; \nX378 is free; \nX384 is free; \nX385 is free; \nX386 is free; \nX395 is free; \nmult(T148, s(s(s(s(0)))), 0, T141) !=? mult(0, X377, 0, X378)\nmult(T148, s(s(s(s(0)))), 0, T141) !=? mult(s(X384), X385, 0, X386)", fontsize=16, style=filled, fillcolor=lightyellow];
274 [label="274: \n\nX377 is free\nX378 is free; \nX384 is free; \nX385 is free; \nX386 is free; \nX391 is free; \nX392 is free; \nX393 is free; \nX394 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
275 [label="275: ','(p(0, X395), mult(T148, s(s(s(s(0)))), X395, T150)), SCOPE: 52, CLAUSE: 4 | ','(p(0, X395), mult(T148, s(s(s(s(0)))), X395, T150)), SCOPE: 52, CLAUSE: 5\n\nT148 is ground\nX377 is free; \nX378 is free; \nX384 is free; \nX385 is free; \nX386 is free; \nX395 is free; \nmult(T148, s(s(s(s(0)))), 0, T141) !=? mult(0, X377, 0, X378)\nmult(T148, s(s(s(s(0)))), 0, T141) !=? mult(s(X384), X385, 0, X386)", fontsize=16, style=filled, fillcolor=lightyellow];
276 [label="276: mult(T148, s(s(s(s(0)))), 0, T150) | ','(p(0, X395), mult(T148, s(s(s(s(0)))), X395, T150)), SCOPE: 52, CLAUSE: 5\n\nT148 is ground\nX377 is free; \nX378 is free; \nX384 is free; \nX385 is free; \nX386 is free; \nX395 is free; \nmult(T148, s(s(s(s(0)))), 0, T141) !=? mult(0, X377, 0, X378)\nmult(T148, s(s(s(s(0)))), 0, T141) !=? mult(s(X384), X385, 0, X386)", fontsize=16, style=filled, fillcolor=lightyellow];
277 [label="277: mult(T148, s(s(s(s(0)))), 0, T150)\n\nT148 is ground\nX377 is free; \nX378 is free; \nX384 is free; \nX385 is free; \nX386 is free; \nmult(T148, s(s(s(s(0)))), 0, T141) !=? mult(0, X377, 0, X378)\nmult(T148, s(s(s(s(0)))), 0, T141) !=? mult(s(X384), X385, 0, X386)", fontsize=16, style=filled, fillcolor=lightyellow];
278 [label="278: ','(p(0, X395), mult(T148, s(s(s(s(0)))), X395, T150)), SCOPE: 52, CLAUSE: 5\n\nT148 is ground\nX377 is free; \nX378 is free; \nX384 is free; \nX385 is free; \nX386 is free; \nX395 is free; \nmult(T148, s(s(s(s(0)))), 0, T141) !=? mult(0, X377, 0, X378)\nmult(T148, s(s(s(s(0)))), 0, T141) !=? mult(s(X384), X385, 0, X386)", fontsize=16, style=filled, fillcolor=lightyellow];
279 [label="279: \n\nX377 is free\nX378 is free; \nX384 is free; \nX385 is free; \nX386 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
280 [label="280: ','(p(T152, X405), mult(T151, s(s(s(s(T152)))), X405, T154))\n\nT151 is ground\nT152 is ground\nX301 is free; \nX302 is free; \nX308 is free; \nX309 is free; \nX310 is free; \nX405 is free; \nmult(T151, s(s(s(s(T152)))), T152, T120) !=? mult(0, X301, 0, X302)\nmult(T151, s(s(s(s(T152)))), T152, T120) !=? mult(s(X308), X309, 0, X310)", fontsize=16, style=filled, fillcolor=lightyellow];
281 [label="281: \n\nX301 is free\nX302 is free; \nX308 is free; \nX309 is free; \nX310 is free; \nX401 is free; \nX402 is free; \nX403 is free; \nX404 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
282 [label="282: ','(p(T152, X405), mult(T151, s(s(s(s(T152)))), X405, T154)), SCOPE: 53, CLAUSE: 4 | ','(p(T152, X405), mult(T151, s(s(s(s(T152)))), X405, T154)), SCOPE: 53, CLAUSE: 5\n\nT151 is ground\nT152 is ground\nX301 is free; \nX302 is free; \nX308 is free; \nX309 is free; \nX310 is free; \nX405 is free; \nmult(T151, s(s(s(s(T152)))), T152, T120) !=? mult(0, X301, 0, X302)\nmult(T151, s(s(s(s(T152)))), T152, T120) !=? mult(s(X308), X309, 0, X310)", fontsize=16, style=filled, fillcolor=lightyellow];
283 [label="283: mult(T151, s(s(s(s(0)))), 0, T154) | ','(p(0, X405), mult(T151, s(s(s(s(0)))), X405, T154)), SCOPE: 53, CLAUSE: 5\n\nT151 is ground\nX301 is free; \nX302 is free; \nX308 is free; \nX309 is free; \nX310 is free; \nX405 is free; \nmult(T151, s(s(s(s(0)))), 0, T120) !=? mult(0, X301, 0, X302)\nmult(T151, s(s(s(s(0)))), 0, T120) !=? mult(s(X308), X309, 0, X310)", fontsize=16, style=filled, fillcolor=lightyellow];
284 [label="284: ','(p(T152, X405), mult(T151, s(s(s(s(T152)))), X405, T154)), SCOPE: 53, CLAUSE: 5\n\nT151 is ground\nT152 is ground\nX301 is free; \nX302 is free; \nX308 is free; \nX309 is free; \nX310 is free; \nX405 is free; \nmult(T151, s(s(s(s(T152)))), T152, T120) !=? mult(0, X301, 0, X302)\nmult(T151, s(s(s(s(T152)))), T152, T120) !=? mult(s(X308), X309, 0, X310)\np(T152, X405) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
285 [label="285: mult(T151, s(s(s(s(0)))), 0, T154)\n\nT151 is ground\nX301 is free; \nX302 is free; \nX308 is free; \nX309 is free; \nX310 is free; \nmult(T151, s(s(s(s(0)))), 0, T120) !=? mult(0, X301, 0, X302)\nmult(T151, s(s(s(s(0)))), 0, T120) !=? mult(s(X308), X309, 0, X310)", fontsize=16, style=filled, fillcolor=lightyellow];
286 [label="286: ','(p(0, X405), mult(T151, s(s(s(s(0)))), X405, T154)), SCOPE: 53, CLAUSE: 5\n\nT151 is ground\nX301 is free; \nX302 is free; \nX308 is free; \nX309 is free; \nX310 is free; \nX405 is free; \nmult(T151, s(s(s(s(0)))), 0, T120) !=? mult(0, X301, 0, X302)\nmult(T151, s(s(s(s(0)))), 0, T120) !=? mult(s(X308), X309, 0, X310)", fontsize=16, style=filled, fillcolor=lightyellow];
287 [label="287: \n\nX301 is free\nX302 is free; \nX308 is free; \nX309 is free; \nX310 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
288 [label="288: mult(T151, s(s(s(s(s(T155))))), T155, T154)\n\nT151 is ground\nT155 is ground\nX301 is free; \nX302 is free; \nX308 is free; \nX309 is free; \nX310 is free; \nX405 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
289 [label="289: \n\nX301 is free\nX302 is free; \nX308 is free; \nX309 is free; \nX310 is free; \nX405 is free; \nX408 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
290 [label="290: mult(T151, s(s(s(s(s(T155))))), T155, T154), SCOPE: 54, CLAUSE: 1 | mult(T151, s(s(s(s(s(T155))))), T155, T154), SCOPE: 54, CLAUSE: 2 | mult(T151, s(s(s(s(s(T155))))), T155, T154), SCOPE: 54, CLAUSE: 3 | ?_54\n\nT151 is ground\nT155 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
291 [label="291: ','(!_54, eq(T158, 0)) | mult(0, s(s(s(s(s(0))))), 0, T154), SCOPE: 54, CLAUSE: 2 | mult(0, s(s(s(s(s(0))))), 0, T154), SCOPE: 54, CLAUSE: 3 | ?_54\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
292 [label="292: mult(T151, s(s(s(s(s(T155))))), T155, T154), SCOPE: 54, CLAUSE: 2 | mult(T151, s(s(s(s(s(T155))))), T155, T154), SCOPE: 54, CLAUSE: 3 | ?_54\n\nT151 is ground\nT155 is ground\nX411 is free; \nX412 is free; \nmult(T151, s(s(s(s(s(T155))))), T155, T154) !=? mult(0, X411, 0, X412)", fontsize=16, style=filled, fillcolor=lightyellow];
293 [label="293: eq(T158, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
294 [label="294: eq(T158, 0), SCOPE: 55, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
295 [label="295: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
296 [label="296: \n\nX414 is free", fontsize=16, style=filled, fillcolor=lightyellow];
297 [label="297: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
298 [label="298: ','(!_54, mult(T160, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T163)) | mult(s(T160), s(s(s(s(s(0))))), 0, T154), SCOPE: 54, CLAUSE: 3 | ?_54\n\nT160 is ground\nX411 is free; \nX412 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
299 [label="299: mult(T151, s(s(s(s(s(T155))))), T155, T154), SCOPE: 54, CLAUSE: 3\n\nT151 is ground\nT155 is ground\nX411 is free; \nX412 is free; \nX418 is free; \nX419 is free; \nX420 is free; \nmult(T151, s(s(s(s(s(T155))))), T155, T154) !=? mult(0, X411, 0, X412)\nmult(T151, s(s(s(s(s(T155))))), T155, T154) !=? mult(s(X418), X419, 0, X420)", fontsize=16, style=filled, fillcolor=lightyellow];
300 [label="300: mult(T160, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T163)\n\nT160 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
301 [label="301: mult(T160, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T163), SCOPE: 56, CLAUSE: 1 | mult(T160, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T163), SCOPE: 56, CLAUSE: 2 | mult(T160, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T163), SCOPE: 56, CLAUSE: 3 | ?_56\n\nT160 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
302 [label="302: mult(T160, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T163), SCOPE: 56, CLAUSE: 2 | mult(T160, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T163), SCOPE: 56, CLAUSE: 3 | ?_56\n\nT160 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
303 [label="303: mult(T160, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T163), SCOPE: 56, CLAUSE: 3\n\nT160 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
304 [label="304: ','(p(s(s(s(s(s(0))))), X434), mult(T164, s(s(s(s(s(0))))), X434, T166))\n\nT164 is ground\nX434 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
305 [label="305: \n\nX430 is free\nX431 is free; \nX432 is free; \nX433 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
306 [label="306: ','(p(s(s(s(s(s(0))))), X434), mult(T164, s(s(s(s(s(0))))), X434, T166)), SCOPE: 57, CLAUSE: 4 | ','(p(s(s(s(s(s(0))))), X434), mult(T164, s(s(s(s(s(0))))), X434, T166)), SCOPE: 57, CLAUSE: 5\n\nT164 is ground\nX434 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
307 [label="307: ','(p(s(s(s(s(s(0))))), X434), mult(T164, s(s(s(s(s(0))))), X434, T166)), SCOPE: 57, CLAUSE: 5\n\nT164 is ground\nX434 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
308 [label="308: mult(T164, s(s(s(s(s(0))))), s(s(s(s(0)))), T166)\n\nT164 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
309 [label="309: mult(T164, s(s(s(s(s(0))))), s(s(s(s(0)))), T166), SCOPE: 58, CLAUSE: 1 | mult(T164, s(s(s(s(s(0))))), s(s(s(s(0)))), T166), SCOPE: 58, CLAUSE: 2 | mult(T164, s(s(s(s(s(0))))), s(s(s(s(0)))), T166), SCOPE: 58, CLAUSE: 3 | ?_58\n\nT164 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
310 [label="310: mult(T164, s(s(s(s(s(0))))), s(s(s(s(0)))), T166), SCOPE: 58, CLAUSE: 2 | mult(T164, s(s(s(s(s(0))))), s(s(s(s(0)))), T166), SCOPE: 58, CLAUSE: 3 | ?_58\n\nT164 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
311 [label="311: mult(T164, s(s(s(s(s(0))))), s(s(s(s(0)))), T166), SCOPE: 58, CLAUSE: 3\n\nT164 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
312 [label="312: ','(p(s(s(s(s(0)))), X450), mult(T167, s(s(s(s(s(0))))), X450, T169))\n\nT167 is ground\nX450 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
313 [label="313: \n\nX446 is free\nX447 is free; \nX448 is free; \nX449 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
314 [label="314: ','(p(s(s(s(s(0)))), X450), mult(T167, s(s(s(s(s(0))))), X450, T169)), SCOPE: 59, CLAUSE: 4 | ','(p(s(s(s(s(0)))), X450), mult(T167, s(s(s(s(s(0))))), X450, T169)), SCOPE: 59, CLAUSE: 5\n\nT167 is ground\nX450 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
315 [label="315: ','(p(s(s(s(s(0)))), X450), mult(T167, s(s(s(s(s(0))))), X450, T169)), SCOPE: 59, CLAUSE: 5\n\nT167 is ground\nX450 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
316 [label="316: mult(T167, s(s(s(s(s(0))))), s(s(s(0))), T169)\n\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
317 [label="317: mult(T167, s(s(s(s(s(0))))), s(s(s(0))), T169), SCOPE: 60, CLAUSE: 1 | mult(T167, s(s(s(s(s(0))))), s(s(s(0))), T169), SCOPE: 60, CLAUSE: 2 | mult(T167, s(s(s(s(s(0))))), s(s(s(0))), T169), SCOPE: 60, CLAUSE: 3 | ?_60\n\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
318 [label="318: mult(T167, s(s(s(s(s(0))))), s(s(s(0))), T169), SCOPE: 60, CLAUSE: 2 | mult(T167, s(s(s(s(s(0))))), s(s(s(0))), T169), SCOPE: 60, CLAUSE: 3 | ?_60\n\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
319 [label="319: mult(T167, s(s(s(s(s(0))))), s(s(s(0))), T169), SCOPE: 60, CLAUSE: 3\n\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
320 [label="320: ','(p(s(s(s(0))), X466), mult(T170, s(s(s(s(s(0))))), X466, T172))\n\nT170 is ground\nX466 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
321 [label="321: \n\nX462 is free\nX463 is free; \nX464 is free; \nX465 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
322 [label="322: ','(p(s(s(s(0))), X466), mult(T170, s(s(s(s(s(0))))), X466, T172)), SCOPE: 61, CLAUSE: 4 | ','(p(s(s(s(0))), X466), mult(T170, s(s(s(s(s(0))))), X466, T172)), SCOPE: 61, CLAUSE: 5\n\nT170 is ground\nX466 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
323 [label="323: ','(p(s(s(s(0))), X466), mult(T170, s(s(s(s(s(0))))), X466, T172)), SCOPE: 61, CLAUSE: 5\n\nT170 is ground\nX466 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
324 [label="324: mult(T170, s(s(s(s(s(0))))), s(s(0)), T172)\n\nT170 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
325 [label="325: mult(T170, s(s(s(s(s(0))))), s(s(0)), T172), SCOPE: 62, CLAUSE: 1 | mult(T170, s(s(s(s(s(0))))), s(s(0)), T172), SCOPE: 62, CLAUSE: 2 | mult(T170, s(s(s(s(s(0))))), s(s(0)), T172), SCOPE: 62, CLAUSE: 3 | ?_62\n\nT170 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
326 [label="326: mult(T170, s(s(s(s(s(0))))), s(s(0)), T172), SCOPE: 62, CLAUSE: 2 | mult(T170, s(s(s(s(s(0))))), s(s(0)), T172), SCOPE: 62, CLAUSE: 3 | ?_62\n\nT170 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
327 [label="327: mult(T170, s(s(s(s(s(0))))), s(s(0)), T172), SCOPE: 62, CLAUSE: 3\n\nT170 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
328 [label="328: ','(p(s(s(0)), X482), mult(T173, s(s(s(s(s(0))))), X482, T175))\n\nT173 is ground\nX482 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
329 [label="329: \n\nX478 is free\nX479 is free; \nX480 is free; \nX481 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
330 [label="330: ','(p(s(s(0)), X482), mult(T173, s(s(s(s(s(0))))), X482, T175)), SCOPE: 63, CLAUSE: 4 | ','(p(s(s(0)), X482), mult(T173, s(s(s(s(s(0))))), X482, T175)), SCOPE: 63, CLAUSE: 5\n\nT173 is ground\nX482 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
331 [label="331: ','(p(s(s(0)), X482), mult(T173, s(s(s(s(s(0))))), X482, T175)), SCOPE: 63, CLAUSE: 5\n\nT173 is ground\nX482 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
332 [label="332: mult(T173, s(s(s(s(s(0))))), s(0), T175)\n\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
333 [label="333: mult(T173, s(s(s(s(s(0))))), s(0), T175), SCOPE: 64, CLAUSE: 1 | mult(T173, s(s(s(s(s(0))))), s(0), T175), SCOPE: 64, CLAUSE: 2 | mult(T173, s(s(s(s(s(0))))), s(0), T175), SCOPE: 64, CLAUSE: 3 | ?_64\n\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
334 [label="334: mult(T173, s(s(s(s(s(0))))), s(0), T175), SCOPE: 64, CLAUSE: 2 | mult(T173, s(s(s(s(s(0))))), s(0), T175), SCOPE: 64, CLAUSE: 3 | ?_64\n\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
335 [label="335: mult(T173, s(s(s(s(s(0))))), s(0), T175), SCOPE: 64, CLAUSE: 3\n\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
336 [label="336: ','(p(s(0), X498), mult(T176, s(s(s(s(s(0))))), X498, T178))\n\nT176 is ground\nX498 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
337 [label="337: \n\nX494 is free\nX495 is free; \nX496 is free; \nX497 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
338 [label="338: ','(p(s(0), X498), mult(T176, s(s(s(s(s(0))))), X498, T178)), SCOPE: 65, CLAUSE: 4 | ','(p(s(0), X498), mult(T176, s(s(s(s(s(0))))), X498, T178)), SCOPE: 65, CLAUSE: 5\n\nT176 is ground\nX498 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
339 [label="339: ','(p(s(0), X498), mult(T176, s(s(s(s(s(0))))), X498, T178)), SCOPE: 65, CLAUSE: 5\n\nT176 is ground\nX498 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
340 [label="340: mult(T176, s(s(s(s(s(0))))), 0, T178)\n\nT176 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
341 [label="341: mult(T176, s(s(s(s(s(0))))), 0, T178), SCOPE: 66, CLAUSE: 1 | mult(T176, s(s(s(s(s(0))))), 0, T178), SCOPE: 66, CLAUSE: 2 | mult(T176, s(s(s(s(s(0))))), 0, T178), SCOPE: 66, CLAUSE: 3 | ?_66\n\nT176 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
342 [label="342: ','(!_66, eq(T180, 0)) | mult(0, s(s(s(s(s(0))))), 0, T178), SCOPE: 66, CLAUSE: 2 | mult(0, s(s(s(s(s(0))))), 0, T178), SCOPE: 66, CLAUSE: 3 | ?_66\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
343 [label="343: mult(T176, s(s(s(s(s(0))))), 0, T178), SCOPE: 66, CLAUSE: 2 | mult(T176, s(s(s(s(s(0))))), 0, T178), SCOPE: 66, CLAUSE: 3 | ?_66\n\nT176 is ground\nX503 is free; \nX504 is free; \nmult(T176, s(s(s(s(s(0))))), 0, T178) !=? mult(0, X503, 0, X504)", fontsize=16, style=filled, fillcolor=lightyellow];
344 [label="344: eq(T180, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
345 [label="345: eq(T180, 0), SCOPE: 67, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
346 [label="346: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
347 [label="347: \n\nX506 is free", fontsize=16, style=filled, fillcolor=lightyellow];
348 [label="348: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
349 [label="349: ','(!_66, mult(T182, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T184)) | mult(s(T182), s(s(s(s(s(0))))), 0, T178), SCOPE: 66, CLAUSE: 3 | ?_66\n\nT182 is ground\nX503 is free; \nX504 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
350 [label="350: mult(T176, s(s(s(s(s(0))))), 0, T178), SCOPE: 66, CLAUSE: 3\n\nT176 is ground\nX503 is free; \nX504 is free; \nX510 is free; \nX511 is free; \nX512 is free; \nmult(T176, s(s(s(s(s(0))))), 0, T178) !=? mult(0, X503, 0, X504)\nmult(T176, s(s(s(s(s(0))))), 0, T178) !=? mult(s(X510), X511, 0, X512)", fontsize=16, style=filled, fillcolor=lightyellow];
351 [label="351: mult(T182, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T184)\n\nT182 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
352 [label="352: ','(p(0, X521), mult(T185, s(s(s(s(s(0))))), X521, T187))\n\nT185 is ground\nX503 is free; \nX504 is free; \nX510 is free; \nX511 is free; \nX512 is free; \nX521 is free; \nmult(T185, s(s(s(s(s(0))))), 0, T178) !=? mult(0, X503, 0, X504)\nmult(T185, s(s(s(s(s(0))))), 0, T178) !=? mult(s(X510), X511, 0, X512)", fontsize=16, style=filled, fillcolor=lightyellow];
353 [label="353: \n\nX503 is free\nX504 is free; \nX510 is free; \nX511 is free; \nX512 is free; \nX517 is free; \nX518 is free; \nX519 is free; \nX520 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
354 [label="354: ','(p(0, X521), mult(T185, s(s(s(s(s(0))))), X521, T187)), SCOPE: 68, CLAUSE: 4 | ','(p(0, X521), mult(T185, s(s(s(s(s(0))))), X521, T187)), SCOPE: 68, CLAUSE: 5\n\nT185 is ground\nX503 is free; \nX504 is free; \nX510 is free; \nX511 is free; \nX512 is free; \nX521 is free; \nmult(T185, s(s(s(s(s(0))))), 0, T178) !=? mult(0, X503, 0, X504)\nmult(T185, s(s(s(s(s(0))))), 0, T178) !=? mult(s(X510), X511, 0, X512)", fontsize=16, style=filled, fillcolor=lightyellow];
355 [label="355: mult(T185, s(s(s(s(s(0))))), 0, T187) | ','(p(0, X521), mult(T185, s(s(s(s(s(0))))), X521, T187)), SCOPE: 68, CLAUSE: 5\n\nT185 is ground\nX503 is free; \nX504 is free; \nX510 is free; \nX511 is free; \nX512 is free; \nX521 is free; \nmult(T185, s(s(s(s(s(0))))), 0, T178) !=? mult(0, X503, 0, X504)\nmult(T185, s(s(s(s(s(0))))), 0, T178) !=? mult(s(X510), X511, 0, X512)", fontsize=16, style=filled, fillcolor=lightyellow];
356 [label="356: mult(T185, s(s(s(s(s(0))))), 0, T187)\n\nT185 is ground\nX503 is free; \nX504 is free; \nX510 is free; \nX511 is free; \nX512 is free; \nmult(T185, s(s(s(s(s(0))))), 0, T178) !=? mult(0, X503, 0, X504)\nmult(T185, s(s(s(s(s(0))))), 0, T178) !=? mult(s(X510), X511, 0, X512)", fontsize=16, style=filled, fillcolor=lightyellow];
357 [label="357: ','(p(0, X521), mult(T185, s(s(s(s(s(0))))), X521, T187)), SCOPE: 68, CLAUSE: 5\n\nT185 is ground\nX503 is free; \nX504 is free; \nX510 is free; \nX511 is free; \nX512 is free; \nX521 is free; \nmult(T185, s(s(s(s(s(0))))), 0, T178) !=? mult(0, X503, 0, X504)\nmult(T185, s(s(s(s(s(0))))), 0, T178) !=? mult(s(X510), X511, 0, X512)", fontsize=16, style=filled, fillcolor=lightyellow];
358 [label="358: \n\nX503 is free\nX504 is free; \nX510 is free; \nX511 is free; \nX512 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
359 [label="359: ','(p(T189, X531), mult(T188, s(s(s(s(s(T189))))), X531, T191))\n\nT188 is ground\nT189 is ground\nX411 is free; \nX412 is free; \nX418 is free; \nX419 is free; \nX420 is free; \nX531 is free; \nmult(T188, s(s(s(s(s(T189))))), T189, T154) !=? mult(0, X411, 0, X412)\nmult(T188, s(s(s(s(s(T189))))), T189, T154) !=? mult(s(X418), X419, 0, X420)", fontsize=16, style=filled, fillcolor=lightyellow];
360 [label="360: \n\nX411 is free\nX412 is free; \nX418 is free; \nX419 is free; \nX420 is free; \nX527 is free; \nX528 is free; \nX529 is free; \nX530 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
361 [label="361: ','(p(T189, X531), mult(T188, s(s(s(s(s(T189))))), X531, T191)), SCOPE: 69, CLAUSE: 4 | ','(p(T189, X531), mult(T188, s(s(s(s(s(T189))))), X531, T191)), SCOPE: 69, CLAUSE: 5\n\nT188 is ground\nT189 is ground\nX411 is free; \nX412 is free; \nX418 is free; \nX419 is free; \nX420 is free; \nX531 is free; \nmult(T188, s(s(s(s(s(T189))))), T189, T154) !=? mult(0, X411, 0, X412)\nmult(T188, s(s(s(s(s(T189))))), T189, T154) !=? mult(s(X418), X419, 0, X420)", fontsize=16, style=filled, fillcolor=lightyellow];
362 [label="362: mult(T188, s(s(s(s(s(0))))), 0, T191) | ','(p(0, X531), mult(T188, s(s(s(s(s(0))))), X531, T191)), SCOPE: 69, CLAUSE: 5\n\nT188 is ground\nX411 is free; \nX412 is free; \nX418 is free; \nX419 is free; \nX420 is free; \nX531 is free; \nmult(T188, s(s(s(s(s(0))))), 0, T154) !=? mult(0, X411, 0, X412)\nmult(T188, s(s(s(s(s(0))))), 0, T154) !=? mult(s(X418), X419, 0, X420)", fontsize=16, style=filled, fillcolor=lightyellow];
363 [label="363: ','(p(T189, X531), mult(T188, s(s(s(s(s(T189))))), X531, T191)), SCOPE: 69, CLAUSE: 5\n\nT188 is ground\nT189 is ground\nX411 is free; \nX412 is free; \nX418 is free; \nX419 is free; \nX420 is free; \nX531 is free; \nmult(T188, s(s(s(s(s(T189))))), T189, T154) !=? mult(0, X411, 0, X412)\nmult(T188, s(s(s(s(s(T189))))), T189, T154) !=? mult(s(X418), X419, 0, X420)\np(T189, X531) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
364 [label="364: mult(T188, s(s(s(s(s(0))))), 0, T191)\n\nT188 is ground\nX411 is free; \nX412 is free; \nX418 is free; \nX419 is free; \nX420 is free; \nmult(T188, s(s(s(s(s(0))))), 0, T154) !=? mult(0, X411, 0, X412)\nmult(T188, s(s(s(s(s(0))))), 0, T154) !=? mult(s(X418), X419, 0, X420)", fontsize=16, style=filled, fillcolor=lightyellow];
365 [label="365: ','(p(0, X531), mult(T188, s(s(s(s(s(0))))), X531, T191)), SCOPE: 69, CLAUSE: 5\n\nT188 is ground\nX411 is free; \nX412 is free; \nX418 is free; \nX419 is free; \nX420 is free; \nX531 is free; \nmult(T188, s(s(s(s(s(0))))), 0, T154) !=? mult(0, X411, 0, X412)\nmult(T188, s(s(s(s(s(0))))), 0, T154) !=? mult(s(X418), X419, 0, X420)", fontsize=16, style=filled, fillcolor=lightyellow];
366 [label="366: \n\nX411 is free\nX412 is free; \nX418 is free; \nX419 is free; \nX420 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
367 [label="367: mult(T188, s(s(s(s(s(s(T192)))))), T192, T191)\n\nT188 is ground\nT192 is ground\nX411 is free; \nX412 is free; \nX418 is free; \nX419 is free; \nX420 is free; \nX531 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
368 [label="368: \n\nX411 is free\nX412 is free; \nX418 is free; \nX419 is free; \nX420 is free; \nX531 is free; \nX534 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
369 [label="369: mult(T188, s(s(s(s(s(s(T192)))))), T192, T191), SCOPE: 70, CLAUSE: 1 | mult(T188, s(s(s(s(s(s(T192)))))), T192, T191), SCOPE: 70, CLAUSE: 2 | mult(T188, s(s(s(s(s(s(T192)))))), T192, T191), SCOPE: 70, CLAUSE: 3 | ?_70\n\nT188 is ground\nT192 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
370 [label="370: ','(!_70, eq(T195, 0)) | mult(0, s(s(s(s(s(s(0)))))), 0, T191), SCOPE: 70, CLAUSE: 2 | mult(0, s(s(s(s(s(s(0)))))), 0, T191), SCOPE: 70, CLAUSE: 3 | ?_70\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
371 [label="371: mult(T188, s(s(s(s(s(s(T192)))))), T192, T191), SCOPE: 70, CLAUSE: 2 | mult(T188, s(s(s(s(s(s(T192)))))), T192, T191), SCOPE: 70, CLAUSE: 3 | ?_70\n\nT188 is ground\nT192 is ground\nX537 is free; \nX538 is free; \nmult(T188, s(s(s(s(s(s(T192)))))), T192, T191) !=? mult(0, X537, 0, X538)", fontsize=16, style=filled, fillcolor=lightyellow];
372 [label="372: eq(T195, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
373 [label="373: eq(T195, 0), SCOPE: 71, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
374 [label="374: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
375 [label="375: \n\nX540 is free", fontsize=16, style=filled, fillcolor=lightyellow];
376 [label="376: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
377 [label="377: ','(!_70, mult(T197, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T200)) | mult(s(T197), s(s(s(s(s(s(0)))))), 0, T191), SCOPE: 70, CLAUSE: 3 | ?_70\n\nT197 is ground\nX537 is free; \nX538 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
378 [label="378: mult(T188, s(s(s(s(s(s(T192)))))), T192, T191), SCOPE: 70, CLAUSE: 3\n\nT188 is ground\nT192 is ground\nX537 is free; \nX538 is free; \nX544 is free; \nX545 is free; \nX546 is free; \nmult(T188, s(s(s(s(s(s(T192)))))), T192, T191) !=? mult(0, X537, 0, X538)\nmult(T188, s(s(s(s(s(s(T192)))))), T192, T191) !=? mult(s(X544), X545, 0, X546)", fontsize=16, style=filled, fillcolor=lightyellow];
379 [label="379: mult(T197, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T200)\n\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
380 [label="380: mult(T197, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T200), SCOPE: 72, CLAUSE: 1 | mult(T197, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T200), SCOPE: 72, CLAUSE: 2 | mult(T197, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T200), SCOPE: 72, CLAUSE: 3 | ?_72\n\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
381 [label="381: mult(T197, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T200), SCOPE: 72, CLAUSE: 2 | mult(T197, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T200), SCOPE: 72, CLAUSE: 3 | ?_72\n\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
382 [label="382: mult(T197, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T200), SCOPE: 72, CLAUSE: 3\n\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
383 [label="383: ','(p(s(s(s(s(s(s(0)))))), X560), mult(T201, s(s(s(s(s(s(0)))))), X560, T203))\n\nT201 is ground\nX560 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
384 [label="384: \n\nX556 is free\nX557 is free; \nX558 is free; \nX559 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
385 [label="385: ','(p(s(s(s(s(s(s(0)))))), X560), mult(T201, s(s(s(s(s(s(0)))))), X560, T203)), SCOPE: 73, CLAUSE: 4 | ','(p(s(s(s(s(s(s(0)))))), X560), mult(T201, s(s(s(s(s(s(0)))))), X560, T203)), SCOPE: 73, CLAUSE: 5\n\nT201 is ground\nX560 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
386 [label="386: ','(p(s(s(s(s(s(s(0)))))), X560), mult(T201, s(s(s(s(s(s(0)))))), X560, T203)), SCOPE: 73, CLAUSE: 5\n\nT201 is ground\nX560 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
387 [label="387: mult(T201, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T203)\n\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
388 [label="388: mult(T201, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T203), SCOPE: 74, CLAUSE: 1 | mult(T201, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T203), SCOPE: 74, CLAUSE: 2 | mult(T201, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T203), SCOPE: 74, CLAUSE: 3 | ?_74\n\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
389 [label="389: mult(T201, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T203), SCOPE: 74, CLAUSE: 2 | mult(T201, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T203), SCOPE: 74, CLAUSE: 3 | ?_74\n\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
390 [label="390: mult(T201, s(s(s(s(s(s(0)))))), s(s(s(s(s(0))))), T203), SCOPE: 74, CLAUSE: 3\n\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
391 [label="391: ','(p(s(s(s(s(s(0))))), X576), mult(T204, s(s(s(s(s(s(0)))))), X576, T206))\n\nT204 is ground\nX576 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
392 [label="392: \n\nX572 is free\nX573 is free; \nX574 is free; \nX575 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
393 [label="393: ','(p(s(s(s(s(s(0))))), X576), mult(T204, s(s(s(s(s(s(0)))))), X576, T206)), SCOPE: 75, CLAUSE: 4 | ','(p(s(s(s(s(s(0))))), X576), mult(T204, s(s(s(s(s(s(0)))))), X576, T206)), SCOPE: 75, CLAUSE: 5\n\nT204 is ground\nX576 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
394 [label="394: ','(p(s(s(s(s(s(0))))), X576), mult(T204, s(s(s(s(s(s(0)))))), X576, T206)), SCOPE: 75, CLAUSE: 5\n\nT204 is ground\nX576 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
395 [label="395: mult(T204, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T206)\n\nT204 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
396 [label="396: mult(T204, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T206), SCOPE: 76, CLAUSE: 1 | mult(T204, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T206), SCOPE: 76, CLAUSE: 2 | mult(T204, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T206), SCOPE: 76, CLAUSE: 3 | ?_76\n\nT204 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
397 [label="397: mult(T204, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T206), SCOPE: 76, CLAUSE: 2 | mult(T204, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T206), SCOPE: 76, CLAUSE: 3 | ?_76\n\nT204 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
398 [label="398: mult(T204, s(s(s(s(s(s(0)))))), s(s(s(s(0)))), T206), SCOPE: 76, CLAUSE: 3\n\nT204 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
399 [label="399: ','(p(s(s(s(s(0)))), X592), mult(T207, s(s(s(s(s(s(0)))))), X592, T209))\n\nT207 is ground\nX592 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
400 [label="400: \n\nX588 is free\nX589 is free; \nX590 is free; \nX591 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
401 [label="401: ','(p(s(s(s(s(0)))), X592), mult(T207, s(s(s(s(s(s(0)))))), X592, T209)), SCOPE: 77, CLAUSE: 4 | ','(p(s(s(s(s(0)))), X592), mult(T207, s(s(s(s(s(s(0)))))), X592, T209)), SCOPE: 77, CLAUSE: 5\n\nT207 is ground\nX592 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
402 [label="402: ','(p(s(s(s(s(0)))), X592), mult(T207, s(s(s(s(s(s(0)))))), X592, T209)), SCOPE: 77, CLAUSE: 5\n\nT207 is ground\nX592 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
403 [label="403: mult(T207, s(s(s(s(s(s(0)))))), s(s(s(0))), T209)\n\nT207 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
404 [label="404: mult(T207, s(s(s(s(s(s(0)))))), s(s(s(0))), T209), SCOPE: 78, CLAUSE: 1 | mult(T207, s(s(s(s(s(s(0)))))), s(s(s(0))), T209), SCOPE: 78, CLAUSE: 2 | mult(T207, s(s(s(s(s(s(0)))))), s(s(s(0))), T209), SCOPE: 78, CLAUSE: 3 | ?_78\n\nT207 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
405 [label="405: mult(T207, s(s(s(s(s(s(0)))))), s(s(s(0))), T209), SCOPE: 78, CLAUSE: 2 | mult(T207, s(s(s(s(s(s(0)))))), s(s(s(0))), T209), SCOPE: 78, CLAUSE: 3 | ?_78\n\nT207 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
406 [label="406: mult(T207, s(s(s(s(s(s(0)))))), s(s(s(0))), T209), SCOPE: 78, CLAUSE: 3\n\nT207 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
407 [label="407: ','(p(s(s(s(0))), X608), mult(T210, s(s(s(s(s(s(0)))))), X608, T212))\n\nT210 is ground\nX608 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
408 [label="408: \n\nX604 is free\nX605 is free; \nX606 is free; \nX607 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
409 [label="409: ','(p(s(s(s(0))), X608), mult(T210, s(s(s(s(s(s(0)))))), X608, T212)), SCOPE: 79, CLAUSE: 4 | ','(p(s(s(s(0))), X608), mult(T210, s(s(s(s(s(s(0)))))), X608, T212)), SCOPE: 79, CLAUSE: 5\n\nT210 is ground\nX608 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
410 [label="410: ','(p(s(s(s(0))), X608), mult(T210, s(s(s(s(s(s(0)))))), X608, T212)), SCOPE: 79, CLAUSE: 5\n\nT210 is ground\nX608 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
411 [label="411: mult(T210, s(s(s(s(s(s(0)))))), s(s(0)), T212)\n\nT210 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
412 [label="412: mult(T210, s(s(s(s(s(s(0)))))), s(s(0)), T212), SCOPE: 80, CLAUSE: 1 | mult(T210, s(s(s(s(s(s(0)))))), s(s(0)), T212), SCOPE: 80, CLAUSE: 2 | mult(T210, s(s(s(s(s(s(0)))))), s(s(0)), T212), SCOPE: 80, CLAUSE: 3 | ?_80\n\nT210 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
413 [label="413: mult(T210, s(s(s(s(s(s(0)))))), s(s(0)), T212), SCOPE: 80, CLAUSE: 2 | mult(T210, s(s(s(s(s(s(0)))))), s(s(0)), T212), SCOPE: 80, CLAUSE: 3 | ?_80\n\nT210 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
414 [label="414: mult(T210, s(s(s(s(s(s(0)))))), s(s(0)), T212), SCOPE: 80, CLAUSE: 3\n\nT210 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
415 [label="415: ','(p(s(s(0)), X624), mult(T213, s(s(s(s(s(s(0)))))), X624, T215))\n\nT213 is ground\nX624 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
416 [label="416: \n\nX620 is free\nX621 is free; \nX622 is free; \nX623 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
417 [label="417: ','(p(s(s(0)), X624), mult(T213, s(s(s(s(s(s(0)))))), X624, T215)), SCOPE: 81, CLAUSE: 4 | ','(p(s(s(0)), X624), mult(T213, s(s(s(s(s(s(0)))))), X624, T215)), SCOPE: 81, CLAUSE: 5\n\nT213 is ground\nX624 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
418 [label="418: ','(p(s(s(0)), X624), mult(T213, s(s(s(s(s(s(0)))))), X624, T215)), SCOPE: 81, CLAUSE: 5\n\nT213 is ground\nX624 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
419 [label="419: mult(T213, s(s(s(s(s(s(0)))))), s(0), T215)\n\nT213 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
420 [label="420: mult(T213, s(s(s(s(s(s(0)))))), s(0), T215), SCOPE: 82, CLAUSE: 1 | mult(T213, s(s(s(s(s(s(0)))))), s(0), T215), SCOPE: 82, CLAUSE: 2 | mult(T213, s(s(s(s(s(s(0)))))), s(0), T215), SCOPE: 82, CLAUSE: 3 | ?_82\n\nT213 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
421 [label="421: mult(T213, s(s(s(s(s(s(0)))))), s(0), T215), SCOPE: 82, CLAUSE: 2 | mult(T213, s(s(s(s(s(s(0)))))), s(0), T215), SCOPE: 82, CLAUSE: 3 | ?_82\n\nT213 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
422 [label="422: mult(T213, s(s(s(s(s(s(0)))))), s(0), T215), SCOPE: 82, CLAUSE: 3\n\nT213 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
423 [label="423: ','(p(s(0), X640), mult(T216, s(s(s(s(s(s(0)))))), X640, T218))\n\nT216 is ground\nX640 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
424 [label="424: \n\nX636 is free\nX637 is free; \nX638 is free; \nX639 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
425 [label="425: ','(p(s(0), X640), mult(T216, s(s(s(s(s(s(0)))))), X640, T218)), SCOPE: 83, CLAUSE: 4 | ','(p(s(0), X640), mult(T216, s(s(s(s(s(s(0)))))), X640, T218)), SCOPE: 83, CLAUSE: 5\n\nT216 is ground\nX640 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
426 [label="426: ','(p(s(0), X640), mult(T216, s(s(s(s(s(s(0)))))), X640, T218)), SCOPE: 83, CLAUSE: 5\n\nT216 is ground\nX640 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
427 [label="427: mult(T216, s(s(s(s(s(s(0)))))), 0, T218)\n\nT216 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
428 [label="428: mult(T216, s(s(s(s(s(s(0)))))), 0, T218), SCOPE: 84, CLAUSE: 1 | mult(T216, s(s(s(s(s(s(0)))))), 0, T218), SCOPE: 84, CLAUSE: 2 | mult(T216, s(s(s(s(s(s(0)))))), 0, T218), SCOPE: 84, CLAUSE: 3 | ?_84\n\nT216 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
429 [label="429: ','(!_84, eq(T220, 0)) | mult(0, s(s(s(s(s(s(0)))))), 0, T218), SCOPE: 84, CLAUSE: 2 | mult(0, s(s(s(s(s(s(0)))))), 0, T218), SCOPE: 84, CLAUSE: 3 | ?_84\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
430 [label="430: mult(T216, s(s(s(s(s(s(0)))))), 0, T218), SCOPE: 84, CLAUSE: 2 | mult(T216, s(s(s(s(s(s(0)))))), 0, T218), SCOPE: 84, CLAUSE: 3 | ?_84\n\nT216 is ground\nX645 is free; \nX646 is free; \nmult(T216, s(s(s(s(s(s(0)))))), 0, T218) !=? mult(0, X645, 0, X646)", fontsize=16, style=filled, fillcolor=lightyellow];
431 [label="431: eq(T220, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
432 [label="432: eq(T220, 0), SCOPE: 85, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
433 [label="433: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
434 [label="434: \n\nX648 is free", fontsize=16, style=filled, fillcolor=lightyellow];
435 [label="435: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
436 [label="436: ','(!_84, mult(T222, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T224)) | mult(s(T222), s(s(s(s(s(s(0)))))), 0, T218), SCOPE: 84, CLAUSE: 3 | ?_84\n\nT222 is ground\nX645 is free; \nX646 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
437 [label="437: mult(T216, s(s(s(s(s(s(0)))))), 0, T218), SCOPE: 84, CLAUSE: 3\n\nT216 is ground\nX645 is free; \nX646 is free; \nX652 is free; \nX653 is free; \nX654 is free; \nmult(T216, s(s(s(s(s(s(0)))))), 0, T218) !=? mult(0, X645, 0, X646)\nmult(T216, s(s(s(s(s(s(0)))))), 0, T218) !=? mult(s(X652), X653, 0, X654)", fontsize=16, style=filled, fillcolor=lightyellow];
438 [label="438: mult(T222, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T224)\n\nT222 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
439 [label="439: ','(p(0, X663), mult(T225, s(s(s(s(s(s(0)))))), X663, T227))\n\nT225 is ground\nX645 is free; \nX646 is free; \nX652 is free; \nX653 is free; \nX654 is free; \nX663 is free; \nmult(T225, s(s(s(s(s(s(0)))))), 0, T218) !=? mult(0, X645, 0, X646)\nmult(T225, s(s(s(s(s(s(0)))))), 0, T218) !=? mult(s(X652), X653, 0, X654)", fontsize=16, style=filled, fillcolor=lightyellow];
440 [label="440: \n\nX645 is free\nX646 is free; \nX652 is free; \nX653 is free; \nX654 is free; \nX659 is free; \nX660 is free; \nX661 is free; \nX662 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
441 [label="441: ','(p(0, X663), mult(T225, s(s(s(s(s(s(0)))))), X663, T227)), SCOPE: 86, CLAUSE: 4 | ','(p(0, X663), mult(T225, s(s(s(s(s(s(0)))))), X663, T227)), SCOPE: 86, CLAUSE: 5\n\nT225 is ground\nX645 is free; \nX646 is free; \nX652 is free; \nX653 is free; \nX654 is free; \nX663 is free; \nmult(T225, s(s(s(s(s(s(0)))))), 0, T218) !=? mult(0, X645, 0, X646)\nmult(T225, s(s(s(s(s(s(0)))))), 0, T218) !=? mult(s(X652), X653, 0, X654)", fontsize=16, style=filled, fillcolor=lightyellow];
442 [label="442: mult(T225, s(s(s(s(s(s(0)))))), 0, T227) | ','(p(0, X663), mult(T225, s(s(s(s(s(s(0)))))), X663, T227)), SCOPE: 86, CLAUSE: 5\n\nT225 is ground\nX645 is free; \nX646 is free; \nX652 is free; \nX653 is free; \nX654 is free; \nX663 is free; \nmult(T225, s(s(s(s(s(s(0)))))), 0, T218) !=? mult(0, X645, 0, X646)\nmult(T225, s(s(s(s(s(s(0)))))), 0, T218) !=? mult(s(X652), X653, 0, X654)", fontsize=16, style=filled, fillcolor=lightyellow];
443 [label="443: mult(T225, s(s(s(s(s(s(0)))))), 0, T227)\n\nT225 is ground\nX645 is free; \nX646 is free; \nX652 is free; \nX653 is free; \nX654 is free; \nmult(T225, s(s(s(s(s(s(0)))))), 0, T218) !=? mult(0, X645, 0, X646)\nmult(T225, s(s(s(s(s(s(0)))))), 0, T218) !=? mult(s(X652), X653, 0, X654)", fontsize=16, style=filled, fillcolor=lightyellow];
444 [label="444: ','(p(0, X663), mult(T225, s(s(s(s(s(s(0)))))), X663, T227)), SCOPE: 86, CLAUSE: 5\n\nT225 is ground\nX645 is free; \nX646 is free; \nX652 is free; \nX653 is free; \nX654 is free; \nX663 is free; \nmult(T225, s(s(s(s(s(s(0)))))), 0, T218) !=? mult(0, X645, 0, X646)\nmult(T225, s(s(s(s(s(s(0)))))), 0, T218) !=? mult(s(X652), X653, 0, X654)", fontsize=16, style=filled, fillcolor=lightyellow];
445 [label="445: \n\nX645 is free\nX646 is free; \nX652 is free; \nX653 is free; \nX654 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
446 [label="446: ','(p(T229, X673), mult(T228, s(s(s(s(s(s(T229)))))), X673, T231))\n\nT228 is ground\nT229 is ground\nX537 is free; \nX538 is free; \nX544 is free; \nX545 is free; \nX546 is free; \nX673 is free; \nmult(T228, s(s(s(s(s(s(T229)))))), T229, T191) !=? mult(0, X537, 0, X538)\nmult(T228, s(s(s(s(s(s(T229)))))), T229, T191) !=? mult(s(X544), X545, 0, X546)", fontsize=16, style=filled, fillcolor=lightyellow];
447 [label="447: \n\nX537 is free\nX538 is free; \nX544 is free; \nX545 is free; \nX546 is free; \nX669 is free; \nX670 is free; \nX671 is free; \nX672 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
448 [label="448: ','(p(T229, X673), mult(T228, s(s(s(s(s(s(T229)))))), X673, T231)), SCOPE: 87, CLAUSE: 4 | ','(p(T229, X673), mult(T228, s(s(s(s(s(s(T229)))))), X673, T231)), SCOPE: 87, CLAUSE: 5\n\nT228 is ground\nT229 is ground\nX537 is free; \nX538 is free; \nX544 is free; \nX545 is free; \nX546 is free; \nX673 is free; \nmult(T228, s(s(s(s(s(s(T229)))))), T229, T191) !=? mult(0, X537, 0, X538)\nmult(T228, s(s(s(s(s(s(T229)))))), T229, T191) !=? mult(s(X544), X545, 0, X546)", fontsize=16, style=filled, fillcolor=lightyellow];
449 [label="449: mult(T228, s(s(s(s(s(s(0)))))), 0, T231) | ','(p(0, X673), mult(T228, s(s(s(s(s(s(0)))))), X673, T231)), SCOPE: 87, CLAUSE: 5\n\nT228 is ground\nX537 is free; \nX538 is free; \nX544 is free; \nX545 is free; \nX546 is free; \nX673 is free; \nmult(T228, s(s(s(s(s(s(0)))))), 0, T191) !=? mult(0, X537, 0, X538)\nmult(T228, s(s(s(s(s(s(0)))))), 0, T191) !=? mult(s(X544), X545, 0, X546)", fontsize=16, style=filled, fillcolor=lightyellow];
450 [label="450: ','(p(T229, X673), mult(T228, s(s(s(s(s(s(T229)))))), X673, T231)), SCOPE: 87, CLAUSE: 5\n\nT228 is ground\nT229 is ground\nX537 is free; \nX538 is free; \nX544 is free; \nX545 is free; \nX546 is free; \nX673 is free; \nmult(T228, s(s(s(s(s(s(T229)))))), T229, T191) !=? mult(0, X537, 0, X538)\nmult(T228, s(s(s(s(s(s(T229)))))), T229, T191) !=? mult(s(X544), X545, 0, X546)\np(T229, X673) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
451 [label="451: mult(T228, s(s(s(s(s(s(0)))))), 0, T231)\n\nT228 is ground\nX537 is free; \nX538 is free; \nX544 is free; \nX545 is free; \nX546 is free; \nmult(T228, s(s(s(s(s(s(0)))))), 0, T191) !=? mult(0, X537, 0, X538)\nmult(T228, s(s(s(s(s(s(0)))))), 0, T191) !=? mult(s(X544), X545, 0, X546)", fontsize=16, style=filled, fillcolor=lightyellow];
452 [label="452: ','(p(0, X673), mult(T228, s(s(s(s(s(s(0)))))), X673, T231)), SCOPE: 87, CLAUSE: 5\n\nT228 is ground\nX537 is free; \nX538 is free; \nX544 is free; \nX545 is free; \nX546 is free; \nX673 is free; \nmult(T228, s(s(s(s(s(s(0)))))), 0, T191) !=? mult(0, X537, 0, X538)\nmult(T228, s(s(s(s(s(s(0)))))), 0, T191) !=? mult(s(X544), X545, 0, X546)", fontsize=16, style=filled, fillcolor=lightyellow];
453 [label="453: \n\nX537 is free\nX538 is free; \nX544 is free; \nX545 is free; \nX546 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
454 [label="454: mult(T228, s(s(s(s(s(s(s(T232))))))), T232, T231)\n\nT228 is ground\nT232 is ground\nX537 is free; \nX538 is free; \nX544 is free; \nX545 is free; \nX546 is free; \nX673 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
455 [label="455: \n\nX537 is free\nX538 is free; \nX544 is free; \nX545 is free; \nX546 is free; \nX673 is free; \nX676 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
456 [label="456: mult(T228, s(T233), T232, T231)\n\nT228 is ground\nT232 is ground\nT233 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
457 [label="457: mult(T228, s(T233), T232, T231), SCOPE: 88, CLAUSE: 1 | mult(T228, s(T233), T232, T231), SCOPE: 88, CLAUSE: 2 | mult(T228, s(T233), T232, T231), SCOPE: 88, CLAUSE: 3 | ?_88\n\nT228 is ground\nT232 is ground\nT233 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
458 [label="458: ','(!_88, eq(T236, 0)) | mult(0, s(T234), 0, T231), SCOPE: 88, CLAUSE: 2 | mult(0, s(T234), 0, T231), SCOPE: 88, CLAUSE: 3 | ?_88\n\nT234 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
459 [label="459: mult(T228, s(T233), T232, T231), SCOPE: 88, CLAUSE: 2 | mult(T228, s(T233), T232, T231), SCOPE: 88, CLAUSE: 3 | ?_88\n\nT228 is ground\nT232 is ground\nT233 is ground\nX679 is free; \nX680 is free; \nmult(T228, s(T233), T232, T231) !=? mult(0, X679, 0, X680)", fontsize=16, style=filled, fillcolor=lightyellow];
460 [label="460: eq(T236, 0)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
461 [label="461: eq(T236, 0), SCOPE: 89, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
462 [label="462: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
463 [label="463: \n\nX682 is free", fontsize=16, style=filled, fillcolor=lightyellow];
464 [label="464: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
465 [label="465: ','(!_88, mult(T238, s(T239), s(T239), T241)) | mult(s(T238), s(T239), 0, T231), SCOPE: 88, CLAUSE: 3 | ?_88\n\nT238 is ground\nT239 is ground\nX679 is free; \nX680 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
466 [label="466: mult(T228, s(T233), T232, T231), SCOPE: 88, CLAUSE: 3\n\nT228 is ground\nT232 is ground\nT233 is ground\nX679 is free; \nX680 is free; \nX686 is free; \nX687 is free; \nX688 is free; \nmult(T228, s(T233), T232, T231) !=? mult(0, X679, 0, X680)\nmult(T228, s(T233), T232, T231) !=? mult(s(X686), X687, 0, X688)", fontsize=16, style=filled, fillcolor=lightyellow];
467 [label="467: mult(T238, s(T239), s(T239), T241)\n\nT238 is ground\nT239 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
468 [label="468: ','(p(T244, X697), mult(T242, s(T243), X697, T246))\n\nT242 is ground\nT243 is ground\nT244 is ground\nX679 is free; \nX680 is free; \nX686 is free; \nX687 is free; \nX688 is free; \nX697 is free; \nmult(T242, s(T243), T244, T231) !=? mult(0, X679, 0, X680)\nmult(T242, s(T243), T244, T231) !=? mult(s(X686), X687, 0, X688)", fontsize=16, style=filled, fillcolor=lightyellow];
469 [label="469: \n\nX679 is free\nX680 is free; \nX686 is free; \nX687 is free; \nX688 is free; \nX693 is free; \nX694 is free; \nX695 is free; \nX696 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
470 [label="470: ','(p(T244, X697), mult(T242, s(T243), X697, T246)), SCOPE: 90, CLAUSE: 4 | ','(p(T244, X697), mult(T242, s(T243), X697, T246)), SCOPE: 90, CLAUSE: 5\n\nT242 is ground\nT243 is ground\nT244 is ground\nX679 is free; \nX680 is free; \nX686 is free; \nX687 is free; \nX688 is free; \nX697 is free; \nmult(T242, s(T243), T244, T231) !=? mult(0, X679, 0, X680)\nmult(T242, s(T243), T244, T231) !=? mult(s(X686), X687, 0, X688)", fontsize=16, style=filled, fillcolor=lightyellow];
471 [label="471: mult(T242, s(T243), 0, T246) | ','(p(0, X697), mult(T242, s(T243), X697, T246)), SCOPE: 90, CLAUSE: 5\n\nT242 is ground\nT243 is ground\nX679 is free; \nX680 is free; \nX686 is free; \nX687 is free; \nX688 is free; \nX697 is free; \nmult(T242, s(T243), 0, T231) !=? mult(0, X679, 0, X680)\nmult(T242, s(T243), 0, T231) !=? mult(s(X686), X687, 0, X688)", fontsize=16, style=filled, fillcolor=lightyellow];
472 [label="472: ','(p(T244, X697), mult(T242, s(T243), X697, T246)), SCOPE: 90, CLAUSE: 5\n\nT242 is ground\nT243 is ground\nT244 is ground\nX679 is free; \nX680 is free; \nX686 is free; \nX687 is free; \nX688 is free; \nX697 is free; \nmult(T242, s(T243), T244, T231) !=? mult(0, X679, 0, X680)\nmult(T242, s(T243), T244, T231) !=? mult(s(X686), X687, 0, X688)\np(T244, X697) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
473 [label="473: mult(T242, s(T243), 0, T246)\n\nT242 is ground\nT243 is ground\nX679 is free; \nX680 is free; \nX686 is free; \nX687 is free; \nX688 is free; \nmult(T242, s(T243), 0, T231) !=? mult(0, X679, 0, X680)\nmult(T242, s(T243), 0, T231) !=? mult(s(X686), X687, 0, X688)", fontsize=16, style=filled, fillcolor=lightyellow];
474 [label="474: ','(p(0, X697), mult(T242, s(T243), X697, T246)), SCOPE: 90, CLAUSE: 5\n\nT242 is ground\nT243 is ground\nX679 is free; \nX680 is free; \nX686 is free; \nX687 is free; \nX688 is free; \nX697 is free; \nmult(T242, s(T243), 0, T231) !=? mult(0, X679, 0, X680)\nmult(T242, s(T243), 0, T231) !=? mult(s(X686), X687, 0, X688)", fontsize=16, style=filled, fillcolor=lightyellow];
475 [label="475: \n\nX679 is free\nX680 is free; \nX686 is free; \nX687 is free; \nX688 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
476 [label="476: mult(T242, s(T243), T247, T246)\n\nT242 is ground\nT243 is ground\nT247 is ground\nX679 is free; \nX680 is free; \nX686 is free; \nX687 is free; \nX688 is free; \nX697 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
477 [label="477: \n\nX679 is free\nX680 is free; \nX686 is free; \nX687 is free; \nX688 is free; \nX697 is free; \nX700 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
478 [label="478: ','(p(0, X709), mult(T248, T249, X709, T251))\n\nT248 is ground\nT249 is ground\nX9 is free; \nX10 is free; \nX16 is free; \nX17 is free; \nX18 is free; \nX709 is free; \nmult(T248, T249, 0, T7) !=? mult(0, X9, 0, X10)\nmult(T248, T249, 0, T7) !=? mult(s(X16), X17, 0, X18)", fontsize=16, style=filled, fillcolor=lightyellow];
479 [label="479: \n\nX9 is free\nX10 is free; \nX16 is free; \nX17 is free; \nX18 is free; \nX705 is free; \nX706 is free; \nX707 is free; \nX708 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
480 [label="480: ','(p(0, X709), mult(T248, T249, X709, T251)), SCOPE: 91, CLAUSE: 4 | ','(p(0, X709), mult(T248, T249, X709, T251)), SCOPE: 91, CLAUSE: 5\n\nT248 is ground\nT249 is ground\nX9 is free; \nX10 is free; \nX16 is free; \nX17 is free; \nX18 is free; \nX709 is free; \nmult(T248, T249, 0, T7) !=? mult(0, X9, 0, X10)\nmult(T248, T249, 0, T7) !=? mult(s(X16), X17, 0, X18)", fontsize=16, style=filled, fillcolor=lightyellow];
481 [label="481: mult(T248, T249, 0, T251) | ','(p(0, X709), mult(T248, T249, X709, T251)), SCOPE: 91, CLAUSE: 5\n\nT248 is ground\nT249 is ground\nX9 is free; \nX10 is free; \nX16 is free; \nX17 is free; \nX18 is free; \nX709 is free; \nmult(T248, T249, 0, T7) !=? mult(0, X9, 0, X10)\nmult(T248, T249, 0, T7) !=? mult(s(X16), X17, 0, X18)", fontsize=16, style=filled, fillcolor=lightyellow];
482 [label="482: mult(T248, T249, 0, T251)\n\nT248 is ground\nT249 is ground\nX9 is free; \nX10 is free; \nX16 is free; \nX17 is free; \nX18 is free; \nmult(T248, T249, 0, T7) !=? mult(0, X9, 0, X10)\nmult(T248, T249, 0, T7) !=? mult(s(X16), X17, 0, X18)", fontsize=16, style=filled, fillcolor=lightyellow];
483 [label="483: ','(p(0, X709), mult(T248, T249, X709, T251)), SCOPE: 91, CLAUSE: 5\n\nT248 is ground\nT249 is ground\nX9 is free; \nX10 is free; \nX16 is free; \nX17 is free; \nX18 is free; \nX709 is free; \nmult(T248, T249, 0, T7) !=? mult(0, X9, 0, X10)\nmult(T248, T249, 0, T7) !=? mult(s(X16), X17, 0, X18)", fontsize=16, style=filled, fillcolor=lightyellow];
484 [label="484: \n\nX9 is free\nX10 is free; \nX16 is free; \nX17 is free; \nX18 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
485 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 485 [arrowhead = none ];
485 -> 2;

486 [label="EVAL with clause\ntimes(X4, X5, X6) :- mult(X4, X5, 0, X6).\nand substitution\nT1 -> T4\nX4 -> T4\nT2 -> T5\nX5 -> T5\nT3 -> T7\nX6 -> T7\nT6 -> T7", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 486 [arrowhead = none ];
486 -> 3;

487 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 487 [arrowhead = none ];
487 -> 4;

488 [label="EVAL with clause\nmult(0, X9, 0, X10) :- ','(!, eq(X10, 0)).\nand substitution\nT4 -> 0\nT5 -> T8\nX9 -> T8\nT7 -> T10\nX10 -> T10\nT9 -> T10", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 488 [arrowhead = none ];
488 -> 5;

489 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 489 [arrowhead = none ];
489 -> 6;

490 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 490 [arrowhead = none ];
490 -> 7;

491 [label="EVAL with clause\nmult(s(X16), X17, 0, X18) :- ','(!, mult(X16, X17, X17, X18)).\nand substitution\nX16 -> T12\nT4 -> s(T12)\nT5 -> T13\nX17 -> T13\nT7 -> T15\nX18 -> T15\nT14 -> T15", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 491 [arrowhead = none ];
491 -> 12;

492 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 492 [arrowhead = none ];
492 -> 13;

493 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
7 -> 493 [arrowhead = none ];
493 -> 8;

494 [label="EVAL with clause\neq(X12, X12).\nand substitution\nT10 -> 0\nX12 -> 0\nT11 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 494 [arrowhead = none ];
494 -> 9;

495 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 495 [arrowhead = none ];
495 -> 10;

496 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 496 [arrowhead = none ];
496 -> 11;

497 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 497 [arrowhead = none ];
497 -> 14;

498 [label="EVAL with clause\nmult(X705, X706, X707, s(X708)) :- ','(p(X707, X709), mult(X705, X706, X709, X708)).\nand substitution\nT4 -> T248\nX705 -> T248\nT5 -> T249\nX706 -> T249\nX707 -> 0\nX708 -> T251\nT7 -> s(T251)\nT250 -> T251", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 498 [arrowhead = none ];
498 -> 478;

499 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 499 [arrowhead = none ];
499 -> 479;

500 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
14 -> 500 [arrowhead = none ];
500 -> 15;

501 [label="EVAL with clause\nmult(0, X21, 0, X22) :- ','(!, eq(X22, 0)).\nand substitution\nT12 -> 0\nT13 -> 0\nX21 -> 0\nT16 -> 0\nT15 -> T18\nX22 -> T18\nT17 -> T18", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 501 [arrowhead = none ];
501 -> 16;

502 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 502 [arrowhead = none ];
502 -> 17;

503 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 503 [arrowhead = none ];
503 -> 18;

504 [label="EVAL with clause\nmult(s(X28), X29, 0, X30) :- ','(!, mult(X28, X29, X29, X30)).\nand substitution\nX28 -> T20\nT12 -> s(T20)\nT13 -> 0\nX29 -> 0\nT21 -> 0\nT15 -> T23\nX30 -> T23\nT22 -> T23", fontsize=14, style = filled, fillcolor = lightblue];
17 -> 504 [arrowhead = none ];
504 -> 23;

505 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
17 -> 505 [arrowhead = none ];
505 -> 24;

506 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
18 -> 506 [arrowhead = none ];
506 -> 19;

507 [label="EVAL with clause\neq(X24, X24).\nand substitution\nT18 -> 0\nX24 -> 0\nT19 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 507 [arrowhead = none ];
507 -> 20;

508 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 508 [arrowhead = none ];
508 -> 21;

509 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 509 [arrowhead = none ];
509 -> 22;

510 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 510 [arrowhead = none ];
510 -> 25;

511 [label="EVAL with clause\nmult(X57, X58, X59, s(X60)) :- ','(p(X59, X61), mult(X57, X58, X61, X60)).\nand substitution\nT12 -> T33\nX57 -> T33\nT13 -> T34\nX58 -> T34\nX59 -> T34\nX60 -> T36\nT15 -> s(T36)\nT35 -> T36", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 511 [arrowhead = none ];
511 -> 44;

512 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 512 [arrowhead = none ];
512 -> 45;

513 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
25 -> 513 [arrowhead = none ];
513 -> 26;

514 [label="EVAL with clause\nmult(0, X33, 0, X34) :- ','(!, eq(X34, 0)).\nand substitution\nT20 -> 0\nX33 -> 0\nT23 -> T25\nX34 -> T25\nT24 -> T25", fontsize=14, style = filled, fillcolor = lightblue];
26 -> 514 [arrowhead = none ];
514 -> 27;

515 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
26 -> 515 [arrowhead = none ];
515 -> 28;

516 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
27 -> 516 [arrowhead = none ];
516 -> 29;

517 [label="EVAL with clause\nmult(s(X40), X41, 0, X42) :- ','(!, mult(X40, X41, X41, X42)).\nand substitution\nX40 -> T27\nT20 -> s(T27)\nX41 -> 0\nT23 -> T29\nX42 -> T29\nT28 -> T29", fontsize=14, style = filled, fillcolor = lightblue];
28 -> 517 [arrowhead = none ];
517 -> 34;

518 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
28 -> 518 [arrowhead = none ];
518 -> 35;

519 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
29 -> 519 [arrowhead = none ];
519 -> 30;

520 [label="EVAL with clause\neq(X36, X36).\nand substitution\nT25 -> 0\nX36 -> 0\nT26 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 520 [arrowhead = none ];
520 -> 31;

521 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 521 [arrowhead = none ];
521 -> 32;

522 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
31 -> 522 [arrowhead = none ];
522 -> 33;

523 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
34 -> 523 [arrowhead = none ];
523 -> 36;

524 [label="EVAL with clause\nmult(X47, X48, X49, s(X50)) :- ','(p(X49, X51), mult(X47, X48, X51, X50)).\nand substitution\nT20 -> T30\nX47 -> T30\nX48 -> 0\nX49 -> 0\nX50 -> T32\nT23 -> s(T32)\nT31 -> T32", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 524 [arrowhead = none ];
524 -> 37;

525 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 525 [arrowhead = none ];
525 -> 38;

526 [label="INSTANCE with matching:\nT20 -> T27\nT23 -> T29", fontsize=14, style = filled, fillcolor = lightgrey];
36 -> 526 [arrowhead = none , style=dashed];
526 -> 25[style=dashed];

527 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
37 -> 527 [arrowhead = none ];
527 -> 39;

528 [label="EVAL with clause\np(0, 0).\nand substitution\nX51 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 528 [arrowhead = none ];
528 -> 40;

529 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
40 -> 529 [arrowhead = none ];
529 -> 41;

530 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
40 -> 530 [arrowhead = none ];
530 -> 42;

531 [label="INSTANCE with matching:\nT20 -> T30\nT23 -> T32", fontsize=14, style = filled, fillcolor = lightgrey];
41 -> 531 [arrowhead = none , style=dashed];
531 -> 25[style=dashed];

532 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
42 -> 532 [arrowhead = none ];
532 -> 43;

533 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
44 -> 533 [arrowhead = none ];
533 -> 46;

534 [label="EVAL with clause\np(0, 0).\nand substitution\nT34 -> 0\nX61 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 534 [arrowhead = none ];
534 -> 47;

535 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 535 [arrowhead = none ];
535 -> 48;

536 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
47 -> 536 [arrowhead = none ];
536 -> 49;

537 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
47 -> 537 [arrowhead = none ];
537 -> 50;

538 [label="EVAL with clause\np(s(X64), X64).\nand substitution\nX64 -> T37\nT34 -> s(T37)\nX61 -> T37", fontsize=14, style = filled, fillcolor = lightblue];
48 -> 538 [arrowhead = none ];
538 -> 52;

539 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
48 -> 539 [arrowhead = none ];
539 -> 53;

540 [label="INSTANCE with matching:\nT20 -> T33\nT23 -> T36", fontsize=14, style = filled, fillcolor = lightgrey];
49 -> 540 [arrowhead = none , style=dashed];
540 -> 25[style=dashed];

541 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
50 -> 541 [arrowhead = none ];
541 -> 51;

542 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
52 -> 542 [arrowhead = none ];
542 -> 54;

543 [label="EVAL with clause\nmult(0, X67, 0, X68) :- ','(!, eq(X68, 0)).\nand substitution\nT33 -> 0\nT37 -> 0\nX67 -> s(0)\nT38 -> 0\nT36 -> T40\nX68 -> T40\nT39 -> T40", fontsize=14, style = filled, fillcolor = lightblue];
54 -> 543 [arrowhead = none ];
543 -> 55;

544 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
54 -> 544 [arrowhead = none ];
544 -> 56;

545 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
55 -> 545 [arrowhead = none ];
545 -> 57;

546 [label="EVAL with clause\nmult(s(X74), X75, 0, X76) :- ','(!, mult(X74, X75, X75, X76)).\nand substitution\nX74 -> T42\nT33 -> s(T42)\nT37 -> 0\nX75 -> s(0)\nT43 -> 0\nT36 -> T45\nX76 -> T45\nT44 -> T45", fontsize=14, style = filled, fillcolor = lightblue];
56 -> 546 [arrowhead = none ];
546 -> 62;

547 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
56 -> 547 [arrowhead = none ];
547 -> 63;

548 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
57 -> 548 [arrowhead = none ];
548 -> 58;

549 [label="EVAL with clause\neq(X70, X70).\nand substitution\nT40 -> 0\nX70 -> 0\nT41 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
58 -> 549 [arrowhead = none ];
549 -> 59;

550 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
58 -> 550 [arrowhead = none ];
550 -> 60;

551 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
59 -> 551 [arrowhead = none ];
551 -> 61;

552 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
62 -> 552 [arrowhead = none ];
552 -> 64;

553 [label="EVAL with clause\nmult(X119, X120, X121, s(X122)) :- ','(p(X121, X123), mult(X119, X120, X123, X122)).\nand substitution\nT33 -> T58\nX119 -> T58\nT37 -> T59\nX120 -> s(T59)\nX121 -> T59\nX122 -> T61\nT36 -> s(T61)\nT60 -> T61", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 553 [arrowhead = none ];
553 -> 91;

554 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 554 [arrowhead = none ];
554 -> 92;

555 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
64 -> 555 [arrowhead = none ];
555 -> 65;

556 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
65 -> 556 [arrowhead = none ];
556 -> 66;

557 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
66 -> 557 [arrowhead = none ];
557 -> 67;

558 [label="EVAL with clause\nmult(X86, X87, X88, s(X89)) :- ','(p(X88, X90), mult(X86, X87, X90, X89)).\nand substitution\nT42 -> T46\nX86 -> T46\nX87 -> s(0)\nX88 -> s(0)\nX89 -> T48\nT45 -> s(T48)\nT47 -> T48", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 558 [arrowhead = none ];
558 -> 68;

559 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 559 [arrowhead = none ];
559 -> 69;

560 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
68 -> 560 [arrowhead = none ];
560 -> 70;

561 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
70 -> 561 [arrowhead = none ];
561 -> 71;

562 [label="EVAL with clause\np(s(X92), X92).\nand substitution\nX92 -> 0\nX90 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 562 [arrowhead = none ];
562 -> 72;

563 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
72 -> 563 [arrowhead = none ];
563 -> 73;

564 [label="EVAL with clause\nmult(0, X95, 0, X96) :- ','(!, eq(X96, 0)).\nand substitution\nT46 -> 0\nX95 -> s(0)\nT48 -> T50\nX96 -> T50\nT49 -> T50", fontsize=14, style = filled, fillcolor = lightblue];
73 -> 564 [arrowhead = none ];
564 -> 74;

565 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
73 -> 565 [arrowhead = none ];
565 -> 75;

566 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
74 -> 566 [arrowhead = none ];
566 -> 76;

567 [label="EVAL with clause\nmult(s(X102), X103, 0, X104) :- ','(!, mult(X102, X103, X103, X104)).\nand substitution\nX102 -> T52\nT46 -> s(T52)\nX103 -> s(0)\nT48 -> T54\nX104 -> T54\nT53 -> T54", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 567 [arrowhead = none ];
567 -> 81;

568 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 568 [arrowhead = none ];
568 -> 82;

569 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
76 -> 569 [arrowhead = none ];
569 -> 77;

570 [label="EVAL with clause\neq(X98, X98).\nand substitution\nT50 -> 0\nX98 -> 0\nT51 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
77 -> 570 [arrowhead = none ];
570 -> 78;

571 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
77 -> 571 [arrowhead = none ];
571 -> 79;

572 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
78 -> 572 [arrowhead = none ];
572 -> 80;

573 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
81 -> 573 [arrowhead = none ];
573 -> 83;

574 [label="EVAL with clause\nmult(X109, X110, X111, s(X112)) :- ','(p(X111, X113), mult(X109, X110, X113, X112)).\nand substitution\nT46 -> T55\nX109 -> T55\nX110 -> s(0)\nX111 -> 0\nX112 -> T57\nT48 -> s(T57)\nT56 -> T57", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 574 [arrowhead = none ];
574 -> 84;

575 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 575 [arrowhead = none ];
575 -> 85;

576 [label="INSTANCE with matching:\nT42 -> T52\nT45 -> T54", fontsize=14, style = filled, fillcolor = lightgrey];
83 -> 576 [arrowhead = none , style=dashed];
576 -> 64[style=dashed];

577 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
84 -> 577 [arrowhead = none ];
577 -> 86;

578 [label="EVAL with clause\np(0, 0).\nand substitution\nX113 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 578 [arrowhead = none ];
578 -> 87;

579 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
87 -> 579 [arrowhead = none ];
579 -> 88;

580 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
87 -> 580 [arrowhead = none ];
580 -> 89;

581 [label="INSTANCE with matching:\nT46 -> T55\nT48 -> T57", fontsize=14, style = filled, fillcolor = lightgrey];
88 -> 581 [arrowhead = none , style=dashed];
581 -> 72[style=dashed];

582 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
89 -> 582 [arrowhead = none ];
582 -> 90;

583 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
91 -> 583 [arrowhead = none ];
583 -> 93;

584 [label="EVAL with clause\np(0, 0).\nand substitution\nT59 -> 0\nX123 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
93 -> 584 [arrowhead = none ];
584 -> 94;

585 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
93 -> 585 [arrowhead = none ];
585 -> 95;

586 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
94 -> 586 [arrowhead = none ];
586 -> 96;

587 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
94 -> 587 [arrowhead = none ];
587 -> 97;

588 [label="EVAL with clause\np(s(X126), X126).\nand substitution\nX126 -> T62\nT59 -> s(T62)\nX123 -> T62", fontsize=14, style = filled, fillcolor = lightblue];
95 -> 588 [arrowhead = none ];
588 -> 99;

589 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
95 -> 589 [arrowhead = none ];
589 -> 100;

590 [label="INSTANCE with matching:\nT46 -> T58\nT48 -> T61", fontsize=14, style = filled, fillcolor = lightgrey];
96 -> 590 [arrowhead = none , style=dashed];
590 -> 72[style=dashed];

591 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
97 -> 591 [arrowhead = none ];
591 -> 98;

592 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
99 -> 592 [arrowhead = none ];
592 -> 101;

593 [label="EVAL with clause\nmult(0, X129, 0, X130) :- ','(!, eq(X130, 0)).\nand substitution\nT58 -> 0\nT62 -> 0\nX129 -> s(s(0))\nT63 -> 0\nT61 -> T65\nX130 -> T65\nT64 -> T65", fontsize=14, style = filled, fillcolor = lightblue];
101 -> 593 [arrowhead = none ];
593 -> 102;

594 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
101 -> 594 [arrowhead = none ];
594 -> 103;

595 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
102 -> 595 [arrowhead = none ];
595 -> 104;

596 [label="EVAL with clause\nmult(s(X136), X137, 0, X138) :- ','(!, mult(X136, X137, X137, X138)).\nand substitution\nX136 -> T67\nT58 -> s(T67)\nT62 -> 0\nX137 -> s(s(0))\nT68 -> 0\nT61 -> T70\nX138 -> T70\nT69 -> T70", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 596 [arrowhead = none ];
596 -> 109;

597 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 597 [arrowhead = none ];
597 -> 110;

598 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
104 -> 598 [arrowhead = none ];
598 -> 105;

599 [label="EVAL with clause\neq(X132, X132).\nand substitution\nT65 -> 0\nX132 -> 0\nT66 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 599 [arrowhead = none ];
599 -> 106;

600 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 600 [arrowhead = none ];
600 -> 107;

601 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
106 -> 601 [arrowhead = none ];
601 -> 108;

602 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
109 -> 602 [arrowhead = none ];
602 -> 111;

603 [label="EVAL with clause\nmult(X197, X198, X199, s(X200)) :- ','(p(X199, X201), mult(X197, X198, X201, X200)).\nand substitution\nT58 -> T86\nX197 -> T86\nT62 -> T87\nX198 -> s(s(T87))\nX199 -> T87\nX200 -> T89\nT61 -> s(T89)\nT88 -> T89", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 603 [arrowhead = none ];
603 -> 146;

604 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 604 [arrowhead = none ];
604 -> 147;

605 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
111 -> 605 [arrowhead = none ];
605 -> 112;

606 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
112 -> 606 [arrowhead = none ];
606 -> 113;

607 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
113 -> 607 [arrowhead = none ];
607 -> 114;

608 [label="EVAL with clause\nmult(X148, X149, X150, s(X151)) :- ','(p(X150, X152), mult(X148, X149, X152, X151)).\nand substitution\nT67 -> T71\nX148 -> T71\nX149 -> s(s(0))\nX150 -> s(s(0))\nX151 -> T73\nT70 -> s(T73)\nT72 -> T73", fontsize=14, style = filled, fillcolor = lightblue];
114 -> 608 [arrowhead = none ];
608 -> 115;

609 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
114 -> 609 [arrowhead = none ];
609 -> 116;

610 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
115 -> 610 [arrowhead = none ];
610 -> 117;

611 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
117 -> 611 [arrowhead = none ];
611 -> 118;

612 [label="EVAL with clause\np(s(X154), X154).\nand substitution\nX154 -> s(0)\nX152 -> s(0)", fontsize=14, style = filled, fillcolor = lightblue];
118 -> 612 [arrowhead = none ];
612 -> 119;

613 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
119 -> 613 [arrowhead = none ];
613 -> 120;

614 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
120 -> 614 [arrowhead = none ];
614 -> 121;

615 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
121 -> 615 [arrowhead = none ];
615 -> 122;

616 [label="EVAL with clause\nmult(X164, X165, X166, s(X167)) :- ','(p(X166, X168), mult(X164, X165, X168, X167)).\nand substitution\nT71 -> T74\nX164 -> T74\nX165 -> s(s(0))\nX166 -> s(0)\nX167 -> T76\nT73 -> s(T76)\nT75 -> T76", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 616 [arrowhead = none ];
616 -> 123;

617 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 617 [arrowhead = none ];
617 -> 124;

618 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
123 -> 618 [arrowhead = none ];
618 -> 125;

619 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
125 -> 619 [arrowhead = none ];
619 -> 126;

620 [label="EVAL with clause\np(s(X170), X170).\nand substitution\nX170 -> 0\nX168 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
126 -> 620 [arrowhead = none ];
620 -> 127;

621 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
127 -> 621 [arrowhead = none ];
621 -> 128;

622 [label="EVAL with clause\nmult(0, X173, 0, X174) :- ','(!, eq(X174, 0)).\nand substitution\nT74 -> 0\nX173 -> s(s(0))\nT76 -> T78\nX174 -> T78\nT77 -> T78", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 622 [arrowhead = none ];
622 -> 129;

623 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 623 [arrowhead = none ];
623 -> 130;

624 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 624 [arrowhead = none ];
624 -> 131;

625 [label="EVAL with clause\nmult(s(X180), X181, 0, X182) :- ','(!, mult(X180, X181, X181, X182)).\nand substitution\nX180 -> T80\nT74 -> s(T80)\nX181 -> s(s(0))\nT76 -> T82\nX182 -> T82\nT81 -> T82", fontsize=14, style = filled, fillcolor = lightblue];
130 -> 625 [arrowhead = none ];
625 -> 136;

626 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
130 -> 626 [arrowhead = none ];
626 -> 137;

627 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
131 -> 627 [arrowhead = none ];
627 -> 132;

628 [label="EVAL with clause\neq(X176, X176).\nand substitution\nT78 -> 0\nX176 -> 0\nT79 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 628 [arrowhead = none ];
628 -> 133;

629 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 629 [arrowhead = none ];
629 -> 134;

630 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
133 -> 630 [arrowhead = none ];
630 -> 135;

631 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
136 -> 631 [arrowhead = none ];
631 -> 138;

632 [label="EVAL with clause\nmult(X187, X188, X189, s(X190)) :- ','(p(X189, X191), mult(X187, X188, X191, X190)).\nand substitution\nT74 -> T83\nX187 -> T83\nX188 -> s(s(0))\nX189 -> 0\nX190 -> T85\nT76 -> s(T85)\nT84 -> T85", fontsize=14, style = filled, fillcolor = lightblue];
137 -> 632 [arrowhead = none ];
632 -> 139;

633 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
137 -> 633 [arrowhead = none ];
633 -> 140;

634 [label="INSTANCE with matching:\nT67 -> T80\nT70 -> T82", fontsize=14, style = filled, fillcolor = lightgrey];
138 -> 634 [arrowhead = none , style=dashed];
634 -> 111[style=dashed];

635 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
139 -> 635 [arrowhead = none ];
635 -> 141;

636 [label="EVAL with clause\np(0, 0).\nand substitution\nX191 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
141 -> 636 [arrowhead = none ];
636 -> 142;

637 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
142 -> 637 [arrowhead = none ];
637 -> 143;

638 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
142 -> 638 [arrowhead = none ];
638 -> 144;

639 [label="INSTANCE with matching:\nT74 -> T83\nT76 -> T85", fontsize=14, style = filled, fillcolor = lightgrey];
143 -> 639 [arrowhead = none , style=dashed];
639 -> 127[style=dashed];

640 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
144 -> 640 [arrowhead = none ];
640 -> 145;

641 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
146 -> 641 [arrowhead = none ];
641 -> 148;

642 [label="EVAL with clause\np(0, 0).\nand substitution\nT87 -> 0\nX201 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
148 -> 642 [arrowhead = none ];
642 -> 149;

643 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
148 -> 643 [arrowhead = none ];
643 -> 150;

644 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
149 -> 644 [arrowhead = none ];
644 -> 151;

645 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
149 -> 645 [arrowhead = none ];
645 -> 152;

646 [label="EVAL with clause\np(s(X204), X204).\nand substitution\nX204 -> T90\nT87 -> s(T90)\nX201 -> T90", fontsize=14, style = filled, fillcolor = lightblue];
150 -> 646 [arrowhead = none ];
646 -> 154;

647 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
150 -> 647 [arrowhead = none ];
647 -> 155;

648 [label="INSTANCE with matching:\nT74 -> T86\nT76 -> T89", fontsize=14, style = filled, fillcolor = lightgrey];
151 -> 648 [arrowhead = none , style=dashed];
648 -> 127[style=dashed];

649 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
152 -> 649 [arrowhead = none ];
649 -> 153;

650 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
154 -> 650 [arrowhead = none ];
650 -> 156;

651 [label="EVAL with clause\nmult(0, X207, 0, X208) :- ','(!, eq(X208, 0)).\nand substitution\nT86 -> 0\nT90 -> 0\nX207 -> s(s(s(0)))\nT91 -> 0\nT89 -> T93\nX208 -> T93\nT92 -> T93", fontsize=14, style = filled, fillcolor = lightblue];
156 -> 651 [arrowhead = none ];
651 -> 157;

652 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
156 -> 652 [arrowhead = none ];
652 -> 158;

653 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
157 -> 653 [arrowhead = none ];
653 -> 159;

654 [label="EVAL with clause\nmult(s(X214), X215, 0, X216) :- ','(!, mult(X214, X215, X215, X216)).\nand substitution\nX214 -> T95\nT86 -> s(T95)\nT90 -> 0\nX215 -> s(s(s(0)))\nT96 -> 0\nT89 -> T98\nX216 -> T98\nT97 -> T98", fontsize=14, style = filled, fillcolor = lightblue];
158 -> 654 [arrowhead = none ];
654 -> 164;

655 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
158 -> 655 [arrowhead = none ];
655 -> 165;

656 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
159 -> 656 [arrowhead = none ];
656 -> 160;

657 [label="EVAL with clause\neq(X210, X210).\nand substitution\nT93 -> 0\nX210 -> 0\nT94 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
160 -> 657 [arrowhead = none ];
657 -> 161;

658 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
160 -> 658 [arrowhead = none ];
658 -> 162;

659 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
161 -> 659 [arrowhead = none ];
659 -> 163;

660 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
164 -> 660 [arrowhead = none ];
660 -> 166;

661 [label="EVAL with clause\nmult(X291, X292, X293, s(X294)) :- ','(p(X293, X295), mult(X291, X292, X295, X294)).\nand substitution\nT86 -> T117\nX291 -> T117\nT90 -> T118\nX292 -> s(s(s(T118)))\nX293 -> T118\nX294 -> T120\nT89 -> s(T120)\nT119 -> T120", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 661 [arrowhead = none ];
661 -> 209;

662 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 662 [arrowhead = none ];
662 -> 210;

663 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
166 -> 663 [arrowhead = none ];
663 -> 167;

664 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
167 -> 664 [arrowhead = none ];
664 -> 168;

665 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
168 -> 665 [arrowhead = none ];
665 -> 169;

666 [label="EVAL with clause\nmult(X226, X227, X228, s(X229)) :- ','(p(X228, X230), mult(X226, X227, X230, X229)).\nand substitution\nT95 -> T99\nX226 -> T99\nX227 -> s(s(s(0)))\nX228 -> s(s(s(0)))\nX229 -> T101\nT98 -> s(T101)\nT100 -> T101", fontsize=14, style = filled, fillcolor = lightblue];
169 -> 666 [arrowhead = none ];
666 -> 170;

667 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
169 -> 667 [arrowhead = none ];
667 -> 171;

668 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
170 -> 668 [arrowhead = none ];
668 -> 172;

669 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
172 -> 669 [arrowhead = none ];
669 -> 173;

670 [label="EVAL with clause\np(s(X232), X232).\nand substitution\nX232 -> s(s(0))\nX230 -> s(s(0))", fontsize=14, style = filled, fillcolor = lightblue];
173 -> 670 [arrowhead = none ];
670 -> 174;

671 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
174 -> 671 [arrowhead = none ];
671 -> 175;

672 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
175 -> 672 [arrowhead = none ];
672 -> 176;

673 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
176 -> 673 [arrowhead = none ];
673 -> 177;

674 [label="EVAL with clause\nmult(X242, X243, X244, s(X245)) :- ','(p(X244, X246), mult(X242, X243, X246, X245)).\nand substitution\nT99 -> T102\nX242 -> T102\nX243 -> s(s(s(0)))\nX244 -> s(s(0))\nX245 -> T104\nT101 -> s(T104)\nT103 -> T104", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 674 [arrowhead = none ];
674 -> 178;

675 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 675 [arrowhead = none ];
675 -> 179;

676 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
178 -> 676 [arrowhead = none ];
676 -> 180;

677 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
180 -> 677 [arrowhead = none ];
677 -> 181;

678 [label="EVAL with clause\np(s(X248), X248).\nand substitution\nX248 -> s(0)\nX246 -> s(0)", fontsize=14, style = filled, fillcolor = lightblue];
181 -> 678 [arrowhead = none ];
678 -> 182;

679 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
182 -> 679 [arrowhead = none ];
679 -> 183;

680 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
183 -> 680 [arrowhead = none ];
680 -> 184;

681 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
184 -> 681 [arrowhead = none ];
681 -> 185;

682 [label="EVAL with clause\nmult(X258, X259, X260, s(X261)) :- ','(p(X260, X262), mult(X258, X259, X262, X261)).\nand substitution\nT102 -> T105\nX258 -> T105\nX259 -> s(s(s(0)))\nX260 -> s(0)\nX261 -> T107\nT104 -> s(T107)\nT106 -> T107", fontsize=14, style = filled, fillcolor = lightblue];
185 -> 682 [arrowhead = none ];
682 -> 186;

683 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
185 -> 683 [arrowhead = none ];
683 -> 187;

684 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
186 -> 684 [arrowhead = none ];
684 -> 188;

685 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
188 -> 685 [arrowhead = none ];
685 -> 189;

686 [label="EVAL with clause\np(s(X264), X264).\nand substitution\nX264 -> 0\nX262 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
189 -> 686 [arrowhead = none ];
686 -> 190;

687 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
190 -> 687 [arrowhead = none ];
687 -> 191;

688 [label="EVAL with clause\nmult(0, X267, 0, X268) :- ','(!, eq(X268, 0)).\nand substitution\nT105 -> 0\nX267 -> s(s(s(0)))\nT107 -> T109\nX268 -> T109\nT108 -> T109", fontsize=14, style = filled, fillcolor = lightblue];
191 -> 688 [arrowhead = none ];
688 -> 192;

689 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
191 -> 689 [arrowhead = none ];
689 -> 193;

690 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
192 -> 690 [arrowhead = none ];
690 -> 194;

691 [label="EVAL with clause\nmult(s(X274), X275, 0, X276) :- ','(!, mult(X274, X275, X275, X276)).\nand substitution\nX274 -> T111\nT105 -> s(T111)\nX275 -> s(s(s(0)))\nT107 -> T113\nX276 -> T113\nT112 -> T113", fontsize=14, style = filled, fillcolor = lightblue];
193 -> 691 [arrowhead = none ];
691 -> 199;

692 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
193 -> 692 [arrowhead = none ];
692 -> 200;

693 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
194 -> 693 [arrowhead = none ];
693 -> 195;

694 [label="EVAL with clause\neq(X270, X270).\nand substitution\nT109 -> 0\nX270 -> 0\nT110 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
195 -> 694 [arrowhead = none ];
694 -> 196;

695 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
195 -> 695 [arrowhead = none ];
695 -> 197;

696 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
196 -> 696 [arrowhead = none ];
696 -> 198;

697 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
199 -> 697 [arrowhead = none ];
697 -> 201;

698 [label="EVAL with clause\nmult(X281, X282, X283, s(X284)) :- ','(p(X283, X285), mult(X281, X282, X285, X284)).\nand substitution\nT105 -> T114\nX281 -> T114\nX282 -> s(s(s(0)))\nX283 -> 0\nX284 -> T116\nT107 -> s(T116)\nT115 -> T116", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 698 [arrowhead = none ];
698 -> 202;

699 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 699 [arrowhead = none ];
699 -> 203;

700 [label="INSTANCE with matching:\nT95 -> T111\nT98 -> T113", fontsize=14, style = filled, fillcolor = lightgrey];
201 -> 700 [arrowhead = none , style=dashed];
700 -> 166[style=dashed];

701 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
202 -> 701 [arrowhead = none ];
701 -> 204;

702 [label="EVAL with clause\np(0, 0).\nand substitution\nX285 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
204 -> 702 [arrowhead = none ];
702 -> 205;

703 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
205 -> 703 [arrowhead = none ];
703 -> 206;

704 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
205 -> 704 [arrowhead = none ];
704 -> 207;

705 [label="INSTANCE with matching:\nT105 -> T114\nT107 -> T116", fontsize=14, style = filled, fillcolor = lightgrey];
206 -> 705 [arrowhead = none , style=dashed];
705 -> 190[style=dashed];

706 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
207 -> 706 [arrowhead = none ];
706 -> 208;

707 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
209 -> 707 [arrowhead = none ];
707 -> 211;

708 [label="EVAL with clause\np(0, 0).\nand substitution\nT118 -> 0\nX295 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
211 -> 708 [arrowhead = none ];
708 -> 212;

709 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
211 -> 709 [arrowhead = none ];
709 -> 213;

710 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
212 -> 710 [arrowhead = none ];
710 -> 214;

711 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
212 -> 711 [arrowhead = none ];
711 -> 215;

712 [label="EVAL with clause\np(s(X298), X298).\nand substitution\nX298 -> T121\nT118 -> s(T121)\nX295 -> T121", fontsize=14, style = filled, fillcolor = lightblue];
213 -> 712 [arrowhead = none ];
712 -> 217;

713 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
213 -> 713 [arrowhead = none ];
713 -> 218;

714 [label="INSTANCE with matching:\nT105 -> T117\nT107 -> T120", fontsize=14, style = filled, fillcolor = lightgrey];
214 -> 714 [arrowhead = none , style=dashed];
714 -> 190[style=dashed];

715 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
215 -> 715 [arrowhead = none ];
715 -> 216;

716 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
217 -> 716 [arrowhead = none ];
716 -> 219;

717 [label="EVAL with clause\nmult(0, X301, 0, X302) :- ','(!, eq(X302, 0)).\nand substitution\nT117 -> 0\nT121 -> 0\nX301 -> s(s(s(s(0))))\nT122 -> 0\nT120 -> T124\nX302 -> T124\nT123 -> T124", fontsize=14, style = filled, fillcolor = lightblue];
219 -> 717 [arrowhead = none ];
717 -> 220;

718 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
219 -> 718 [arrowhead = none ];
718 -> 221;

719 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
220 -> 719 [arrowhead = none ];
719 -> 222;

720 [label="EVAL with clause\nmult(s(X308), X309, 0, X310) :- ','(!, mult(X308, X309, X309, X310)).\nand substitution\nX308 -> T126\nT117 -> s(T126)\nT121 -> 0\nX309 -> s(s(s(s(0))))\nT127 -> 0\nT120 -> T129\nX310 -> T129\nT128 -> T129", fontsize=14, style = filled, fillcolor = lightblue];
221 -> 720 [arrowhead = none ];
720 -> 227;

721 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
221 -> 721 [arrowhead = none ];
721 -> 228;

722 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
222 -> 722 [arrowhead = none ];
722 -> 223;

723 [label="EVAL with clause\neq(X304, X304).\nand substitution\nT124 -> 0\nX304 -> 0\nT125 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
223 -> 723 [arrowhead = none ];
723 -> 224;

724 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
223 -> 724 [arrowhead = none ];
724 -> 225;

725 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
224 -> 725 [arrowhead = none ];
725 -> 226;

726 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
227 -> 726 [arrowhead = none ];
726 -> 229;

727 [label="EVAL with clause\nmult(X401, X402, X403, s(X404)) :- ','(p(X403, X405), mult(X401, X402, X405, X404)).\nand substitution\nT117 -> T151\nX401 -> T151\nT121 -> T152\nX402 -> s(s(s(s(T152))))\nX403 -> T152\nX404 -> T154\nT120 -> s(T154)\nT153 -> T154", fontsize=14, style = filled, fillcolor = lightblue];
228 -> 727 [arrowhead = none ];
727 -> 280;

728 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
228 -> 728 [arrowhead = none ];
728 -> 281;

729 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
229 -> 729 [arrowhead = none ];
729 -> 230;

730 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
230 -> 730 [arrowhead = none ];
730 -> 231;

731 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
231 -> 731 [arrowhead = none ];
731 -> 232;

732 [label="EVAL with clause\nmult(X320, X321, X322, s(X323)) :- ','(p(X322, X324), mult(X320, X321, X324, X323)).\nand substitution\nT126 -> T130\nX320 -> T130\nX321 -> s(s(s(s(0))))\nX322 -> s(s(s(s(0))))\nX323 -> T132\nT129 -> s(T132)\nT131 -> T132", fontsize=14, style = filled, fillcolor = lightblue];
232 -> 732 [arrowhead = none ];
732 -> 233;

733 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
232 -> 733 [arrowhead = none ];
733 -> 234;

734 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
233 -> 734 [arrowhead = none ];
734 -> 235;

735 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
235 -> 735 [arrowhead = none ];
735 -> 236;

736 [label="EVAL with clause\np(s(X326), X326).\nand substitution\nX326 -> s(s(s(0)))\nX324 -> s(s(s(0)))", fontsize=14, style = filled, fillcolor = lightblue];
236 -> 736 [arrowhead = none ];
736 -> 237;

737 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
237 -> 737 [arrowhead = none ];
737 -> 238;

738 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
238 -> 738 [arrowhead = none ];
738 -> 239;

739 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
239 -> 739 [arrowhead = none ];
739 -> 240;

740 [label="EVAL with clause\nmult(X336, X337, X338, s(X339)) :- ','(p(X338, X340), mult(X336, X337, X340, X339)).\nand substitution\nT130 -> T133\nX336 -> T133\nX337 -> s(s(s(s(0))))\nX338 -> s(s(s(0)))\nX339 -> T135\nT132 -> s(T135)\nT134 -> T135", fontsize=14, style = filled, fillcolor = lightblue];
240 -> 740 [arrowhead = none ];
740 -> 241;

741 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
240 -> 741 [arrowhead = none ];
741 -> 242;

742 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
241 -> 742 [arrowhead = none ];
742 -> 243;

743 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
243 -> 743 [arrowhead = none ];
743 -> 244;

744 [label="EVAL with clause\np(s(X342), X342).\nand substitution\nX342 -> s(s(0))\nX340 -> s(s(0))", fontsize=14, style = filled, fillcolor = lightblue];
244 -> 744 [arrowhead = none ];
744 -> 245;

745 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
245 -> 745 [arrowhead = none ];
745 -> 246;

746 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
246 -> 746 [arrowhead = none ];
746 -> 247;

747 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
247 -> 747 [arrowhead = none ];
747 -> 248;

748 [label="EVAL with clause\nmult(X352, X353, X354, s(X355)) :- ','(p(X354, X356), mult(X352, X353, X356, X355)).\nand substitution\nT133 -> T136\nX352 -> T136\nX353 -> s(s(s(s(0))))\nX354 -> s(s(0))\nX355 -> T138\nT135 -> s(T138)\nT137 -> T138", fontsize=14, style = filled, fillcolor = lightblue];
248 -> 748 [arrowhead = none ];
748 -> 249;

749 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
248 -> 749 [arrowhead = none ];
749 -> 250;

750 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
249 -> 750 [arrowhead = none ];
750 -> 251;

751 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
251 -> 751 [arrowhead = none ];
751 -> 252;

752 [label="EVAL with clause\np(s(X358), X358).\nand substitution\nX358 -> s(0)\nX356 -> s(0)", fontsize=14, style = filled, fillcolor = lightblue];
252 -> 752 [arrowhead = none ];
752 -> 253;

753 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
253 -> 753 [arrowhead = none ];
753 -> 254;

754 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
254 -> 754 [arrowhead = none ];
754 -> 255;

755 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
255 -> 755 [arrowhead = none ];
755 -> 256;

756 [label="EVAL with clause\nmult(X368, X369, X370, s(X371)) :- ','(p(X370, X372), mult(X368, X369, X372, X371)).\nand substitution\nT136 -> T139\nX368 -> T139\nX369 -> s(s(s(s(0))))\nX370 -> s(0)\nX371 -> T141\nT138 -> s(T141)\nT140 -> T141", fontsize=14, style = filled, fillcolor = lightblue];
256 -> 756 [arrowhead = none ];
756 -> 257;

757 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
256 -> 757 [arrowhead = none ];
757 -> 258;

758 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
257 -> 758 [arrowhead = none ];
758 -> 259;

759 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
259 -> 759 [arrowhead = none ];
759 -> 260;

760 [label="EVAL with clause\np(s(X374), X374).\nand substitution\nX374 -> 0\nX372 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
260 -> 760 [arrowhead = none ];
760 -> 261;

761 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
261 -> 761 [arrowhead = none ];
761 -> 262;

762 [label="EVAL with clause\nmult(0, X377, 0, X378) :- ','(!, eq(X378, 0)).\nand substitution\nT139 -> 0\nX377 -> s(s(s(s(0))))\nT141 -> T143\nX378 -> T143\nT142 -> T143", fontsize=14, style = filled, fillcolor = lightblue];
262 -> 762 [arrowhead = none ];
762 -> 263;

763 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
262 -> 763 [arrowhead = none ];
763 -> 264;

764 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
263 -> 764 [arrowhead = none ];
764 -> 265;

765 [label="EVAL with clause\nmult(s(X384), X385, 0, X386) :- ','(!, mult(X384, X385, X385, X386)).\nand substitution\nX384 -> T145\nT139 -> s(T145)\nX385 -> s(s(s(s(0))))\nT141 -> T147\nX386 -> T147\nT146 -> T147", fontsize=14, style = filled, fillcolor = lightblue];
264 -> 765 [arrowhead = none ];
765 -> 270;

766 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
264 -> 766 [arrowhead = none ];
766 -> 271;

767 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
265 -> 767 [arrowhead = none ];
767 -> 266;

768 [label="EVAL with clause\neq(X380, X380).\nand substitution\nT143 -> 0\nX380 -> 0\nT144 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
266 -> 768 [arrowhead = none ];
768 -> 267;

769 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
266 -> 769 [arrowhead = none ];
769 -> 268;

770 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
267 -> 770 [arrowhead = none ];
770 -> 269;

771 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
270 -> 771 [arrowhead = none ];
771 -> 272;

772 [label="EVAL with clause\nmult(X391, X392, X393, s(X394)) :- ','(p(X393, X395), mult(X391, X392, X395, X394)).\nand substitution\nT139 -> T148\nX391 -> T148\nX392 -> s(s(s(s(0))))\nX393 -> 0\nX394 -> T150\nT141 -> s(T150)\nT149 -> T150", fontsize=14, style = filled, fillcolor = lightblue];
271 -> 772 [arrowhead = none ];
772 -> 273;

773 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
271 -> 773 [arrowhead = none ];
773 -> 274;

774 [label="INSTANCE with matching:\nT126 -> T145\nT129 -> T147", fontsize=14, style = filled, fillcolor = lightgrey];
272 -> 774 [arrowhead = none , style=dashed];
774 -> 229[style=dashed];

775 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
273 -> 775 [arrowhead = none ];
775 -> 275;

776 [label="EVAL with clause\np(0, 0).\nand substitution\nX395 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
275 -> 776 [arrowhead = none ];
776 -> 276;

777 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
276 -> 777 [arrowhead = none ];
777 -> 277;

778 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
276 -> 778 [arrowhead = none ];
778 -> 278;

779 [label="INSTANCE with matching:\nT139 -> T148\nT141 -> T150", fontsize=14, style = filled, fillcolor = lightgrey];
277 -> 779 [arrowhead = none , style=dashed];
779 -> 261[style=dashed];

780 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
278 -> 780 [arrowhead = none ];
780 -> 279;

781 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
280 -> 781 [arrowhead = none ];
781 -> 282;

782 [label="EVAL with clause\np(0, 0).\nand substitution\nT152 -> 0\nX405 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
282 -> 782 [arrowhead = none ];
782 -> 283;

783 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
282 -> 783 [arrowhead = none ];
783 -> 284;

784 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
283 -> 784 [arrowhead = none ];
784 -> 285;

785 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
283 -> 785 [arrowhead = none ];
785 -> 286;

786 [label="EVAL with clause\np(s(X408), X408).\nand substitution\nX408 -> T155\nT152 -> s(T155)\nX405 -> T155", fontsize=14, style = filled, fillcolor = lightblue];
284 -> 786 [arrowhead = none ];
786 -> 288;

787 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
284 -> 787 [arrowhead = none ];
787 -> 289;

788 [label="INSTANCE with matching:\nT139 -> T151\nT141 -> T154", fontsize=14, style = filled, fillcolor = lightgrey];
285 -> 788 [arrowhead = none , style=dashed];
788 -> 261[style=dashed];

789 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
286 -> 789 [arrowhead = none ];
789 -> 287;

790 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
288 -> 790 [arrowhead = none ];
790 -> 290;

791 [label="EVAL with clause\nmult(0, X411, 0, X412) :- ','(!, eq(X412, 0)).\nand substitution\nT151 -> 0\nT155 -> 0\nX411 -> s(s(s(s(s(0)))))\nT156 -> 0\nT154 -> T158\nX412 -> T158\nT157 -> T158", fontsize=14, style = filled, fillcolor = lightblue];
290 -> 791 [arrowhead = none ];
791 -> 291;

792 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
290 -> 792 [arrowhead = none ];
792 -> 292;

793 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
291 -> 793 [arrowhead = none ];
793 -> 293;

794 [label="EVAL with clause\nmult(s(X418), X419, 0, X420) :- ','(!, mult(X418, X419, X419, X420)).\nand substitution\nX418 -> T160\nT151 -> s(T160)\nT155 -> 0\nX419 -> s(s(s(s(s(0)))))\nT161 -> 0\nT154 -> T163\nX420 -> T163\nT162 -> T163", fontsize=14, style = filled, fillcolor = lightblue];
292 -> 794 [arrowhead = none ];
794 -> 298;

795 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
292 -> 795 [arrowhead = none ];
795 -> 299;

796 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
293 -> 796 [arrowhead = none ];
796 -> 294;

797 [label="EVAL with clause\neq(X414, X414).\nand substitution\nT158 -> 0\nX414 -> 0\nT159 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
294 -> 797 [arrowhead = none ];
797 -> 295;

798 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
294 -> 798 [arrowhead = none ];
798 -> 296;

799 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
295 -> 799 [arrowhead = none ];
799 -> 297;

800 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
298 -> 800 [arrowhead = none ];
800 -> 300;

801 [label="EVAL with clause\nmult(X527, X528, X529, s(X530)) :- ','(p(X529, X531), mult(X527, X528, X531, X530)).\nand substitution\nT151 -> T188\nX527 -> T188\nT155 -> T189\nX528 -> s(s(s(s(s(T189)))))\nX529 -> T189\nX530 -> T191\nT154 -> s(T191)\nT190 -> T191", fontsize=14, style = filled, fillcolor = lightblue];
299 -> 801 [arrowhead = none ];
801 -> 359;

802 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
299 -> 802 [arrowhead = none ];
802 -> 360;

803 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
300 -> 803 [arrowhead = none ];
803 -> 301;

804 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
301 -> 804 [arrowhead = none ];
804 -> 302;

805 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
302 -> 805 [arrowhead = none ];
805 -> 303;

806 [label="EVAL with clause\nmult(X430, X431, X432, s(X433)) :- ','(p(X432, X434), mult(X430, X431, X434, X433)).\nand substitution\nT160 -> T164\nX430 -> T164\nX431 -> s(s(s(s(s(0)))))\nX432 -> s(s(s(s(s(0)))))\nX433 -> T166\nT163 -> s(T166)\nT165 -> T166", fontsize=14, style = filled, fillcolor = lightblue];
303 -> 806 [arrowhead = none ];
806 -> 304;

807 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
303 -> 807 [arrowhead = none ];
807 -> 305;

808 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
304 -> 808 [arrowhead = none ];
808 -> 306;

809 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
306 -> 809 [arrowhead = none ];
809 -> 307;

810 [label="EVAL with clause\np(s(X436), X436).\nand substitution\nX436 -> s(s(s(s(0))))\nX434 -> s(s(s(s(0))))", fontsize=14, style = filled, fillcolor = lightblue];
307 -> 810 [arrowhead = none ];
810 -> 308;

811 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
308 -> 811 [arrowhead = none ];
811 -> 309;

812 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
309 -> 812 [arrowhead = none ];
812 -> 310;

813 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
310 -> 813 [arrowhead = none ];
813 -> 311;

814 [label="EVAL with clause\nmult(X446, X447, X448, s(X449)) :- ','(p(X448, X450), mult(X446, X447, X450, X449)).\nand substitution\nT164 -> T167\nX446 -> T167\nX447 -> s(s(s(s(s(0)))))\nX448 -> s(s(s(s(0))))\nX449 -> T169\nT166 -> s(T169)\nT168 -> T169", fontsize=14, style = filled, fillcolor = lightblue];
311 -> 814 [arrowhead = none ];
814 -> 312;

815 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
311 -> 815 [arrowhead = none ];
815 -> 313;

816 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
312 -> 816 [arrowhead = none ];
816 -> 314;

817 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
314 -> 817 [arrowhead = none ];
817 -> 315;

818 [label="EVAL with clause\np(s(X452), X452).\nand substitution\nX452 -> s(s(s(0)))\nX450 -> s(s(s(0)))", fontsize=14, style = filled, fillcolor = lightblue];
315 -> 818 [arrowhead = none ];
818 -> 316;

819 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
316 -> 819 [arrowhead = none ];
819 -> 317;

820 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
317 -> 820 [arrowhead = none ];
820 -> 318;

821 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
318 -> 821 [arrowhead = none ];
821 -> 319;

822 [label="EVAL with clause\nmult(X462, X463, X464, s(X465)) :- ','(p(X464, X466), mult(X462, X463, X466, X465)).\nand substitution\nT167 -> T170\nX462 -> T170\nX463 -> s(s(s(s(s(0)))))\nX464 -> s(s(s(0)))\nX465 -> T172\nT169 -> s(T172)\nT171 -> T172", fontsize=14, style = filled, fillcolor = lightblue];
319 -> 822 [arrowhead = none ];
822 -> 320;

823 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
319 -> 823 [arrowhead = none ];
823 -> 321;

824 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
320 -> 824 [arrowhead = none ];
824 -> 322;

825 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
322 -> 825 [arrowhead = none ];
825 -> 323;

826 [label="EVAL with clause\np(s(X468), X468).\nand substitution\nX468 -> s(s(0))\nX466 -> s(s(0))", fontsize=14, style = filled, fillcolor = lightblue];
323 -> 826 [arrowhead = none ];
826 -> 324;

827 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
324 -> 827 [arrowhead = none ];
827 -> 325;

828 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
325 -> 828 [arrowhead = none ];
828 -> 326;

829 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
326 -> 829 [arrowhead = none ];
829 -> 327;

830 [label="EVAL with clause\nmult(X478, X479, X480, s(X481)) :- ','(p(X480, X482), mult(X478, X479, X482, X481)).\nand substitution\nT170 -> T173\nX478 -> T173\nX479 -> s(s(s(s(s(0)))))\nX480 -> s(s(0))\nX481 -> T175\nT172 -> s(T175)\nT174 -> T175", fontsize=14, style = filled, fillcolor = lightblue];
327 -> 830 [arrowhead = none ];
830 -> 328;

831 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
327 -> 831 [arrowhead = none ];
831 -> 329;

832 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
328 -> 832 [arrowhead = none ];
832 -> 330;

833 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
330 -> 833 [arrowhead = none ];
833 -> 331;

834 [label="EVAL with clause\np(s(X484), X484).\nand substitution\nX484 -> s(0)\nX482 -> s(0)", fontsize=14, style = filled, fillcolor = lightblue];
331 -> 834 [arrowhead = none ];
834 -> 332;

835 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
332 -> 835 [arrowhead = none ];
835 -> 333;

836 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
333 -> 836 [arrowhead = none ];
836 -> 334;

837 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
334 -> 837 [arrowhead = none ];
837 -> 335;

838 [label="EVAL with clause\nmult(X494, X495, X496, s(X497)) :- ','(p(X496, X498), mult(X494, X495, X498, X497)).\nand substitution\nT173 -> T176\nX494 -> T176\nX495 -> s(s(s(s(s(0)))))\nX496 -> s(0)\nX497 -> T178\nT175 -> s(T178)\nT177 -> T178", fontsize=14, style = filled, fillcolor = lightblue];
335 -> 838 [arrowhead = none ];
838 -> 336;

839 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
335 -> 839 [arrowhead = none ];
839 -> 337;

840 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
336 -> 840 [arrowhead = none ];
840 -> 338;

841 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
338 -> 841 [arrowhead = none ];
841 -> 339;

842 [label="EVAL with clause\np(s(X500), X500).\nand substitution\nX500 -> 0\nX498 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
339 -> 842 [arrowhead = none ];
842 -> 340;

843 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
340 -> 843 [arrowhead = none ];
843 -> 341;

844 [label="EVAL with clause\nmult(0, X503, 0, X504) :- ','(!, eq(X504, 0)).\nand substitution\nT176 -> 0\nX503 -> s(s(s(s(s(0)))))\nT178 -> T180\nX504 -> T180\nT179 -> T180", fontsize=14, style = filled, fillcolor = lightblue];
341 -> 844 [arrowhead = none ];
844 -> 342;

845 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
341 -> 845 [arrowhead = none ];
845 -> 343;

846 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
342 -> 846 [arrowhead = none ];
846 -> 344;

847 [label="EVAL with clause\nmult(s(X510), X511, 0, X512) :- ','(!, mult(X510, X511, X511, X512)).\nand substitution\nX510 -> T182\nT176 -> s(T182)\nX511 -> s(s(s(s(s(0)))))\nT178 -> T184\nX512 -> T184\nT183 -> T184", fontsize=14, style = filled, fillcolor = lightblue];
343 -> 847 [arrowhead = none ];
847 -> 349;

848 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
343 -> 848 [arrowhead = none ];
848 -> 350;

849 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
344 -> 849 [arrowhead = none ];
849 -> 345;

850 [label="EVAL with clause\neq(X506, X506).\nand substitution\nT180 -> 0\nX506 -> 0\nT181 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
345 -> 850 [arrowhead = none ];
850 -> 346;

851 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
345 -> 851 [arrowhead = none ];
851 -> 347;

852 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
346 -> 852 [arrowhead = none ];
852 -> 348;

853 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
349 -> 853 [arrowhead = none ];
853 -> 351;

854 [label="EVAL with clause\nmult(X517, X518, X519, s(X520)) :- ','(p(X519, X521), mult(X517, X518, X521, X520)).\nand substitution\nT176 -> T185\nX517 -> T185\nX518 -> s(s(s(s(s(0)))))\nX519 -> 0\nX520 -> T187\nT178 -> s(T187)\nT186 -> T187", fontsize=14, style = filled, fillcolor = lightblue];
350 -> 854 [arrowhead = none ];
854 -> 352;

855 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
350 -> 855 [arrowhead = none ];
855 -> 353;

856 [label="INSTANCE with matching:\nT160 -> T182\nT163 -> T184", fontsize=14, style = filled, fillcolor = lightgrey];
351 -> 856 [arrowhead = none , style=dashed];
856 -> 300[style=dashed];

857 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
352 -> 857 [arrowhead = none ];
857 -> 354;

858 [label="EVAL with clause\np(0, 0).\nand substitution\nX521 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
354 -> 858 [arrowhead = none ];
858 -> 355;

859 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
355 -> 859 [arrowhead = none ];
859 -> 356;

860 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
355 -> 860 [arrowhead = none ];
860 -> 357;

861 [label="INSTANCE with matching:\nT176 -> T185\nT178 -> T187", fontsize=14, style = filled, fillcolor = lightgrey];
356 -> 861 [arrowhead = none , style=dashed];
861 -> 340[style=dashed];

862 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
357 -> 862 [arrowhead = none ];
862 -> 358;

863 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
359 -> 863 [arrowhead = none ];
863 -> 361;

864 [label="EVAL with clause\np(0, 0).\nand substitution\nT189 -> 0\nX531 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
361 -> 864 [arrowhead = none ];
864 -> 362;

865 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
361 -> 865 [arrowhead = none ];
865 -> 363;

866 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
362 -> 866 [arrowhead = none ];
866 -> 364;

867 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
362 -> 867 [arrowhead = none ];
867 -> 365;

868 [label="EVAL with clause\np(s(X534), X534).\nand substitution\nX534 -> T192\nT189 -> s(T192)\nX531 -> T192", fontsize=14, style = filled, fillcolor = lightblue];
363 -> 868 [arrowhead = none ];
868 -> 367;

869 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
363 -> 869 [arrowhead = none ];
869 -> 368;

870 [label="INSTANCE with matching:\nT176 -> T188\nT178 -> T191", fontsize=14, style = filled, fillcolor = lightgrey];
364 -> 870 [arrowhead = none , style=dashed];
870 -> 340[style=dashed];

871 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
365 -> 871 [arrowhead = none ];
871 -> 366;

872 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
367 -> 872 [arrowhead = none ];
872 -> 369;

873 [label="EVAL with clause\nmult(0, X537, 0, X538) :- ','(!, eq(X538, 0)).\nand substitution\nT188 -> 0\nT192 -> 0\nX537 -> s(s(s(s(s(s(0))))))\nT193 -> 0\nT191 -> T195\nX538 -> T195\nT194 -> T195", fontsize=14, style = filled, fillcolor = lightblue];
369 -> 873 [arrowhead = none ];
873 -> 370;

874 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
369 -> 874 [arrowhead = none ];
874 -> 371;

875 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
370 -> 875 [arrowhead = none ];
875 -> 372;

876 [label="EVAL with clause\nmult(s(X544), X545, 0, X546) :- ','(!, mult(X544, X545, X545, X546)).\nand substitution\nX544 -> T197\nT188 -> s(T197)\nT192 -> 0\nX545 -> s(s(s(s(s(s(0))))))\nT198 -> 0\nT191 -> T200\nX546 -> T200\nT199 -> T200", fontsize=14, style = filled, fillcolor = lightblue];
371 -> 876 [arrowhead = none ];
876 -> 377;

877 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
371 -> 877 [arrowhead = none ];
877 -> 378;

878 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
372 -> 878 [arrowhead = none ];
878 -> 373;

879 [label="EVAL with clause\neq(X540, X540).\nand substitution\nT195 -> 0\nX540 -> 0\nT196 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
373 -> 879 [arrowhead = none ];
879 -> 374;

880 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
373 -> 880 [arrowhead = none ];
880 -> 375;

881 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
374 -> 881 [arrowhead = none ];
881 -> 376;

882 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
377 -> 882 [arrowhead = none ];
882 -> 379;

883 [label="EVAL with clause\nmult(X669, X670, X671, s(X672)) :- ','(p(X671, X673), mult(X669, X670, X673, X672)).\nand substitution\nT188 -> T228\nX669 -> T228\nT192 -> T229\nX670 -> s(s(s(s(s(s(T229))))))\nX671 -> T229\nX672 -> T231\nT191 -> s(T231)\nT230 -> T231", fontsize=14, style = filled, fillcolor = lightblue];
378 -> 883 [arrowhead = none ];
883 -> 446;

884 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
378 -> 884 [arrowhead = none ];
884 -> 447;

885 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
379 -> 885 [arrowhead = none ];
885 -> 380;

886 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
380 -> 886 [arrowhead = none ];
886 -> 381;

887 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
381 -> 887 [arrowhead = none ];
887 -> 382;

888 [label="EVAL with clause\nmult(X556, X557, X558, s(X559)) :- ','(p(X558, X560), mult(X556, X557, X560, X559)).\nand substitution\nT197 -> T201\nX556 -> T201\nX557 -> s(s(s(s(s(s(0))))))\nX558 -> s(s(s(s(s(s(0))))))\nX559 -> T203\nT200 -> s(T203)\nT202 -> T203", fontsize=14, style = filled, fillcolor = lightblue];
382 -> 888 [arrowhead = none ];
888 -> 383;

889 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
382 -> 889 [arrowhead = none ];
889 -> 384;

890 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
383 -> 890 [arrowhead = none ];
890 -> 385;

891 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
385 -> 891 [arrowhead = none ];
891 -> 386;

892 [label="EVAL with clause\np(s(X562), X562).\nand substitution\nX562 -> s(s(s(s(s(0)))))\nX560 -> s(s(s(s(s(0)))))", fontsize=14, style = filled, fillcolor = lightblue];
386 -> 892 [arrowhead = none ];
892 -> 387;

893 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
387 -> 893 [arrowhead = none ];
893 -> 388;

894 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
388 -> 894 [arrowhead = none ];
894 -> 389;

895 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
389 -> 895 [arrowhead = none ];
895 -> 390;

896 [label="EVAL with clause\nmult(X572, X573, X574, s(X575)) :- ','(p(X574, X576), mult(X572, X573, X576, X575)).\nand substitution\nT201 -> T204\nX572 -> T204\nX573 -> s(s(s(s(s(s(0))))))\nX574 -> s(s(s(s(s(0)))))\nX575 -> T206\nT203 -> s(T206)\nT205 -> T206", fontsize=14, style = filled, fillcolor = lightblue];
390 -> 896 [arrowhead = none ];
896 -> 391;

897 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
390 -> 897 [arrowhead = none ];
897 -> 392;

898 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
391 -> 898 [arrowhead = none ];
898 -> 393;

899 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
393 -> 899 [arrowhead = none ];
899 -> 394;

900 [label="EVAL with clause\np(s(X578), X578).\nand substitution\nX578 -> s(s(s(s(0))))\nX576 -> s(s(s(s(0))))", fontsize=14, style = filled, fillcolor = lightblue];
394 -> 900 [arrowhead = none ];
900 -> 395;

901 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
395 -> 901 [arrowhead = none ];
901 -> 396;

902 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
396 -> 902 [arrowhead = none ];
902 -> 397;

903 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
397 -> 903 [arrowhead = none ];
903 -> 398;

904 [label="EVAL with clause\nmult(X588, X589, X590, s(X591)) :- ','(p(X590, X592), mult(X588, X589, X592, X591)).\nand substitution\nT204 -> T207\nX588 -> T207\nX589 -> s(s(s(s(s(s(0))))))\nX590 -> s(s(s(s(0))))\nX591 -> T209\nT206 -> s(T209)\nT208 -> T209", fontsize=14, style = filled, fillcolor = lightblue];
398 -> 904 [arrowhead = none ];
904 -> 399;

905 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
398 -> 905 [arrowhead = none ];
905 -> 400;

906 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
399 -> 906 [arrowhead = none ];
906 -> 401;

907 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
401 -> 907 [arrowhead = none ];
907 -> 402;

908 [label="EVAL with clause\np(s(X594), X594).\nand substitution\nX594 -> s(s(s(0)))\nX592 -> s(s(s(0)))", fontsize=14, style = filled, fillcolor = lightblue];
402 -> 908 [arrowhead = none ];
908 -> 403;

909 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
403 -> 909 [arrowhead = none ];
909 -> 404;

910 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
404 -> 910 [arrowhead = none ];
910 -> 405;

911 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
405 -> 911 [arrowhead = none ];
911 -> 406;

912 [label="EVAL with clause\nmult(X604, X605, X606, s(X607)) :- ','(p(X606, X608), mult(X604, X605, X608, X607)).\nand substitution\nT207 -> T210\nX604 -> T210\nX605 -> s(s(s(s(s(s(0))))))\nX606 -> s(s(s(0)))\nX607 -> T212\nT209 -> s(T212)\nT211 -> T212", fontsize=14, style = filled, fillcolor = lightblue];
406 -> 912 [arrowhead = none ];
912 -> 407;

913 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
406 -> 913 [arrowhead = none ];
913 -> 408;

914 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
407 -> 914 [arrowhead = none ];
914 -> 409;

915 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
409 -> 915 [arrowhead = none ];
915 -> 410;

916 [label="EVAL with clause\np(s(X610), X610).\nand substitution\nX610 -> s(s(0))\nX608 -> s(s(0))", fontsize=14, style = filled, fillcolor = lightblue];
410 -> 916 [arrowhead = none ];
916 -> 411;

917 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
411 -> 917 [arrowhead = none ];
917 -> 412;

918 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
412 -> 918 [arrowhead = none ];
918 -> 413;

919 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
413 -> 919 [arrowhead = none ];
919 -> 414;

920 [label="EVAL with clause\nmult(X620, X621, X622, s(X623)) :- ','(p(X622, X624), mult(X620, X621, X624, X623)).\nand substitution\nT210 -> T213\nX620 -> T213\nX621 -> s(s(s(s(s(s(0))))))\nX622 -> s(s(0))\nX623 -> T215\nT212 -> s(T215)\nT214 -> T215", fontsize=14, style = filled, fillcolor = lightblue];
414 -> 920 [arrowhead = none ];
920 -> 415;

921 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
414 -> 921 [arrowhead = none ];
921 -> 416;

922 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
415 -> 922 [arrowhead = none ];
922 -> 417;

923 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
417 -> 923 [arrowhead = none ];
923 -> 418;

924 [label="EVAL with clause\np(s(X626), X626).\nand substitution\nX626 -> s(0)\nX624 -> s(0)", fontsize=14, style = filled, fillcolor = lightblue];
418 -> 924 [arrowhead = none ];
924 -> 419;

925 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
419 -> 925 [arrowhead = none ];
925 -> 420;

926 [label="BACKTRACK\nfor clause: mult(0, Y, 0, Z) :- ','(!, eq(Z, 0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
420 -> 926 [arrowhead = none ];
926 -> 421;

927 [label="BACKTRACK\nfor clause: mult(s(X), Y, 0, Z) :- ','(!, mult(X, Y, Y, Z))because of non-unification", fontsize=14, style = filled, fillcolor = white];
421 -> 927 [arrowhead = none ];
927 -> 422;

928 [label="EVAL with clause\nmult(X636, X637, X638, s(X639)) :- ','(p(X638, X640), mult(X636, X637, X640, X639)).\nand substitution\nT213 -> T216\nX636 -> T216\nX637 -> s(s(s(s(s(s(0))))))\nX638 -> s(0)\nX639 -> T218\nT215 -> s(T218)\nT217 -> T218", fontsize=14, style = filled, fillcolor = lightblue];
422 -> 928 [arrowhead = none ];
928 -> 423;

929 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
422 -> 929 [arrowhead = none ];
929 -> 424;

930 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
423 -> 930 [arrowhead = none ];
930 -> 425;

931 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
425 -> 931 [arrowhead = none ];
931 -> 426;

932 [label="EVAL with clause\np(s(X642), X642).\nand substitution\nX642 -> 0\nX640 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
426 -> 932 [arrowhead = none ];
932 -> 427;

933 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
427 -> 933 [arrowhead = none ];
933 -> 428;

934 [label="EVAL with clause\nmult(0, X645, 0, X646) :- ','(!, eq(X646, 0)).\nand substitution\nT216 -> 0\nX645 -> s(s(s(s(s(s(0))))))\nT218 -> T220\nX646 -> T220\nT219 -> T220", fontsize=14, style = filled, fillcolor = lightblue];
428 -> 934 [arrowhead = none ];
934 -> 429;

935 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
428 -> 935 [arrowhead = none ];
935 -> 430;

936 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
429 -> 936 [arrowhead = none ];
936 -> 431;

937 [label="EVAL with clause\nmult(s(X652), X653, 0, X654) :- ','(!, mult(X652, X653, X653, X654)).\nand substitution\nX652 -> T222\nT216 -> s(T222)\nX653 -> s(s(s(s(s(s(0))))))\nT218 -> T224\nX654 -> T224\nT223 -> T224", fontsize=14, style = filled, fillcolor = lightblue];
430 -> 937 [arrowhead = none ];
937 -> 436;

938 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
430 -> 938 [arrowhead = none ];
938 -> 437;

939 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
431 -> 939 [arrowhead = none ];
939 -> 432;

940 [label="EVAL with clause\neq(X648, X648).\nand substitution\nT220 -> 0\nX648 -> 0\nT221 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
432 -> 940 [arrowhead = none ];
940 -> 433;

941 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
432 -> 941 [arrowhead = none ];
941 -> 434;

942 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
433 -> 942 [arrowhead = none ];
942 -> 435;

943 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
436 -> 943 [arrowhead = none ];
943 -> 438;

944 [label="EVAL with clause\nmult(X659, X660, X661, s(X662)) :- ','(p(X661, X663), mult(X659, X660, X663, X662)).\nand substitution\nT216 -> T225\nX659 -> T225\nX660 -> s(s(s(s(s(s(0))))))\nX661 -> 0\nX662 -> T227\nT218 -> s(T227)\nT226 -> T227", fontsize=14, style = filled, fillcolor = lightblue];
437 -> 944 [arrowhead = none ];
944 -> 439;

945 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
437 -> 945 [arrowhead = none ];
945 -> 440;

946 [label="INSTANCE with matching:\nT197 -> T222\nT200 -> T224", fontsize=14, style = filled, fillcolor = lightgrey];
438 -> 946 [arrowhead = none , style=dashed];
946 -> 379[style=dashed];

947 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
439 -> 947 [arrowhead = none ];
947 -> 441;

948 [label="EVAL with clause\np(0, 0).\nand substitution\nX663 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
441 -> 948 [arrowhead = none ];
948 -> 442;

949 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
442 -> 949 [arrowhead = none ];
949 -> 443;

950 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
442 -> 950 [arrowhead = none ];
950 -> 444;

951 [label="INSTANCE with matching:\nT216 -> T225\nT218 -> T227", fontsize=14, style = filled, fillcolor = lightgrey];
443 -> 951 [arrowhead = none , style=dashed];
951 -> 427[style=dashed];

952 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
444 -> 952 [arrowhead = none ];
952 -> 445;

953 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
446 -> 953 [arrowhead = none ];
953 -> 448;

954 [label="EVAL with clause\np(0, 0).\nand substitution\nT229 -> 0\nX673 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
448 -> 954 [arrowhead = none ];
954 -> 449;

955 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
448 -> 955 [arrowhead = none ];
955 -> 450;

956 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
449 -> 956 [arrowhead = none ];
956 -> 451;

957 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
449 -> 957 [arrowhead = none ];
957 -> 452;

958 [label="EVAL with clause\np(s(X676), X676).\nand substitution\nX676 -> T232\nT229 -> s(T232)\nX673 -> T232", fontsize=14, style = filled, fillcolor = lightblue];
450 -> 958 [arrowhead = none ];
958 -> 454;

959 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
450 -> 959 [arrowhead = none ];
959 -> 455;

960 [label="INSTANCE with matching:\nT216 -> T228\nT218 -> T231", fontsize=14, style = filled, fillcolor = lightgrey];
451 -> 960 [arrowhead = none , style=dashed];
960 -> 427[style=dashed];

961 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
452 -> 961 [arrowhead = none ];
961 -> 453;

962 [label="GENERALIZATION\nT233 <-- s(s(s(s(s(s(T232))))))\n\nNew Knowledge:\nT233 is ground", fontsize=14, style = filled, fillcolor = violet];
454 -> 962 [arrowhead = none ];
962 -> 456;

963 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
456 -> 963 [arrowhead = none ];
963 -> 457;

964 [label="EVAL with clause\nmult(0, X679, 0, X680) :- ','(!, eq(X680, 0)).\nand substitution\nT228 -> 0\nT233 -> T234\nX679 -> s(T234)\nT232 -> 0\nT231 -> T236\nX680 -> T236\nT235 -> T236", fontsize=14, style = filled, fillcolor = lightblue];
457 -> 964 [arrowhead = none ];
964 -> 458;

965 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
457 -> 965 [arrowhead = none ];
965 -> 459;

966 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
458 -> 966 [arrowhead = none ];
966 -> 460;

967 [label="EVAL with clause\nmult(s(X686), X687, 0, X688) :- ','(!, mult(X686, X687, X687, X688)).\nand substitution\nX686 -> T238\nT228 -> s(T238)\nT233 -> T239\nX687 -> s(T239)\nT232 -> 0\nT231 -> T241\nX688 -> T241\nT240 -> T241", fontsize=14, style = filled, fillcolor = lightblue];
459 -> 967 [arrowhead = none ];
967 -> 465;

968 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
459 -> 968 [arrowhead = none ];
968 -> 466;

969 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
460 -> 969 [arrowhead = none ];
969 -> 461;

970 [label="EVAL with clause\neq(X682, X682).\nand substitution\nT236 -> 0\nX682 -> 0\nT237 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
461 -> 970 [arrowhead = none ];
970 -> 462;

971 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
461 -> 971 [arrowhead = none ];
971 -> 463;

972 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
462 -> 972 [arrowhead = none ];
972 -> 464;

973 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
465 -> 973 [arrowhead = none ];
973 -> 467;

974 [label="EVAL with clause\nmult(X693, X694, X695, s(X696)) :- ','(p(X695, X697), mult(X693, X694, X697, X696)).\nand substitution\nT228 -> T242\nX693 -> T242\nT233 -> T243\nX694 -> s(T243)\nT232 -> T244\nX695 -> T244\nX696 -> T246\nT231 -> s(T246)\nT245 -> T246", fontsize=14, style = filled, fillcolor = lightblue];
466 -> 974 [arrowhead = none ];
974 -> 468;

975 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
466 -> 975 [arrowhead = none ];
975 -> 469;

976 [label="INSTANCE with matching:\nT12 -> T238\nT13 -> s(T239)\nT15 -> T241", fontsize=14, style = filled, fillcolor = lightgrey];
467 -> 976 [arrowhead = none , style=dashed];
976 -> 14[style=dashed];

977 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
468 -> 977 [arrowhead = none ];
977 -> 470;

978 [label="EVAL with clause\np(0, 0).\nand substitution\nT244 -> 0\nX697 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
470 -> 978 [arrowhead = none ];
978 -> 471;

979 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
470 -> 979 [arrowhead = none ];
979 -> 472;

980 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
471 -> 980 [arrowhead = none ];
980 -> 473;

981 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
471 -> 981 [arrowhead = none ];
981 -> 474;

982 [label="EVAL with clause\np(s(X700), X700).\nand substitution\nX700 -> T247\nT244 -> s(T247)\nX697 -> T247", fontsize=14, style = filled, fillcolor = lightblue];
472 -> 982 [arrowhead = none ];
982 -> 476;

983 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
472 -> 983 [arrowhead = none ];
983 -> 477;

984 [label="INSTANCE with matching:\nT4 -> T242\nT5 -> s(T243)\nT7 -> T246", fontsize=14, style = filled, fillcolor = lightgrey];
473 -> 984 [arrowhead = none , style=dashed];
984 -> 3[style=dashed];

985 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
474 -> 985 [arrowhead = none ];
985 -> 475;

986 [label="INSTANCE with matching:\nT228 -> T242\nT233 -> T243\nT232 -> T247\nT231 -> T246", fontsize=14, style = filled, fillcolor = lightgrey];
476 -> 986 [arrowhead = none , style=dashed];
986 -> 456[style=dashed];

987 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
478 -> 987 [arrowhead = none ];
987 -> 480;

988 [label="EVAL with clause\np(0, 0).\nand substitution\nX709 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
480 -> 988 [arrowhead = none ];
988 -> 481;

989 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
481 -> 989 [arrowhead = none ];
989 -> 482;

990 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
481 -> 990 [arrowhead = none ];
990 -> 483;

991 [label="INSTANCE with matching:\nT4 -> T248\nT5 -> T249\nT7 -> T251", fontsize=14, style = filled, fillcolor = lightgrey];
482 -> 991 [arrowhead = none , style=dashed];
991 -> 3[style=dashed];

992 [label="BACKTRACK\nfor clause: p(s(X), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
483 -> 992 [arrowhead = none ];
992 -> 484;

}

(2) Obligation:

Clauses:

mult25(0, 0).
mult25(s(T27), T29) :- mult25(T27, T29).
mult25(T30, s(T32)) :- mult25(T30, T32).
mult64(0, s(0)).
mult64(s(T52), s(T54)) :- mult64(T52, T54).
mult64(T55, s(s(T57))) :- mult72(T55, T57).
mult72(0, 0).
mult72(s(T52), T54) :- mult64(T52, T54).
mult72(T55, s(T57)) :- mult72(T55, T57).
mult111(0, s(s(0))).
mult111(s(T80), s(s(T82))) :- mult111(T80, T82).
mult111(T83, s(s(s(T85)))) :- mult127(T83, T85).
mult127(0, 0).
mult127(s(T80), T82) :- mult111(T80, T82).
mult127(T83, s(T85)) :- mult127(T83, T85).
mult166(0, s(s(s(0)))).
mult166(s(T111), s(s(s(T113)))) :- mult166(T111, T113).
mult166(T114, s(s(s(s(T116))))) :- mult190(T114, T116).
mult190(0, 0).
mult190(s(T111), T113) :- mult166(T111, T113).
mult190(T114, s(T116)) :- mult190(T114, T116).
mult229(0, s(s(s(s(0))))).
mult229(s(T145), s(s(s(s(T147))))) :- mult229(T145, T147).
mult229(T148, s(s(s(s(s(T150)))))) :- mult261(T148, T150).
mult261(0, 0).
mult261(s(T145), T147) :- mult229(T145, T147).
mult261(T148, s(T150)) :- mult261(T148, T150).
mult300(0, s(s(s(s(s(0)))))).
mult300(s(T182), s(s(s(s(s(T184)))))) :- mult300(T182, T184).
mult300(T185, s(s(s(s(s(s(T187))))))) :- mult340(T185, T187).
mult340(0, 0).
mult340(s(T182), T184) :- mult300(T182, T184).
mult340(T185, s(T187)) :- mult340(T185, T187).
mult379(0, s(s(s(s(s(s(0))))))).
mult379(s(T222), s(s(s(s(s(s(T224))))))) :- mult379(T222, T224).
mult379(T225, s(s(s(s(s(s(s(T227)))))))) :- mult427(T225, T227).
mult427(0, 0).
mult427(s(T222), T224) :- mult379(T222, T224).
mult427(T225, s(T227)) :- mult427(T225, T227).
mult14(0, 0, 0).
mult14(s(0), 0, 0).
mult14(s(s(T27)), 0, T29) :- mult25(T27, T29).
mult14(s(T30), 0, s(T32)) :- mult25(T30, T32).
mult14(T33, 0, s(T36)) :- mult25(T33, T36).
mult14(0, s(0), s(0)).
mult14(s(0), s(0), s(s(0))).
mult14(s(s(T52)), s(0), s(s(T54))) :- mult64(T52, T54).
mult14(s(T55), s(0), s(s(s(T57)))) :- mult72(T55, T57).
mult14(T58, s(0), s(s(T61))) :- mult72(T58, T61).
mult14(0, s(s(0)), s(s(0))).
mult14(s(0), s(s(0)), s(s(s(s(0))))).
mult14(s(s(T80)), s(s(0)), s(s(s(s(T82))))) :- mult111(T80, T82).
mult14(s(T83), s(s(0)), s(s(s(s(s(T85)))))) :- mult127(T83, T85).
mult14(T86, s(s(0)), s(s(s(T89)))) :- mult127(T86, T89).
mult14(0, s(s(s(0))), s(s(s(0)))).
mult14(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))).
mult14(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) :- mult166(T111, T113).
mult14(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) :- mult190(T114, T116).
mult14(T117, s(s(s(0))), s(s(s(s(T120))))) :- mult190(T117, T120).
mult14(0, s(s(s(s(0)))), s(s(s(s(0))))).
mult14(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))).
mult14(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) :- mult229(T145, T147).
mult14(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) :- mult261(T148, T150).
mult14(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) :- mult261(T151, T154).
mult14(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))).
mult14(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))).
mult14(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) :- mult300(T182, T184).
mult14(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) :- mult340(T185, T187).
mult14(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) :- mult340(T188, T191).
mult14(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))).
mult14(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))).
mult14(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) :- mult379(T222, T224).
mult14(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) :- mult427(T225, T227).
mult14(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) :- mult427(T228, T231).
mult14(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))).
mult14(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) :- mult14(T238, s(T239), T241).
mult14(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) :- mult3(T242, s(T243), T246).
mult14(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) :- mult456(T242, T243, T247, T246).
mult3(0, T8, 0).
mult3(s(0), 0, 0).
mult3(s(s(0)), 0, 0).
mult3(s(s(s(T27))), 0, T29) :- mult25(T27, T29).
mult3(s(s(T30)), 0, s(T32)) :- mult25(T30, T32).
mult3(s(T33), 0, s(T36)) :- mult25(T33, T36).
mult3(s(0), s(0), s(0)).
mult3(s(s(0)), s(0), s(s(0))).
mult3(s(s(s(T52))), s(0), s(s(T54))) :- mult64(T52, T54).
mult3(s(s(T55)), s(0), s(s(s(T57)))) :- mult72(T55, T57).
mult3(s(T58), s(0), s(s(T61))) :- mult72(T58, T61).
mult3(s(0), s(s(0)), s(s(0))).
mult3(s(s(0)), s(s(0)), s(s(s(s(0))))).
mult3(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) :- mult111(T80, T82).
mult3(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) :- mult127(T83, T85).
mult3(s(T86), s(s(0)), s(s(s(T89)))) :- mult127(T86, T89).
mult3(s(0), s(s(s(0))), s(s(s(0)))).
mult3(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))).
mult3(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) :- mult166(T111, T113).
mult3(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) :- mult190(T114, T116).
mult3(s(T117), s(s(s(0))), s(s(s(s(T120))))) :- mult190(T117, T120).
mult3(s(0), s(s(s(s(0)))), s(s(s(s(0))))).
mult3(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))).
mult3(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) :- mult229(T145, T147).
mult3(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) :- mult261(T148, T150).
mult3(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) :- mult261(T151, T154).
mult3(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))).
mult3(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))).
mult3(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) :- mult300(T182, T184).
mult3(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) :- mult340(T185, T187).
mult3(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) :- mult340(T188, T191).
mult3(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))).
mult3(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))).
mult3(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) :- mult379(T222, T224).
mult3(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) :- mult427(T225, T227).
mult3(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) :- mult427(T228, T231).
mult3(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))).
mult3(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) :- mult14(T238, s(T239), T241).
mult3(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) :- mult3(T242, s(T243), T246).
mult3(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) :- mult456(T242, T243, T247, T246).
mult3(T248, T249, s(T251)) :- mult3(T248, T249, T251).
mult456(0, T234, 0, 0).
mult456(s(T238), T239, 0, T241) :- mult14(T238, s(T239), T241).
mult456(T242, T243, 0, s(T246)) :- mult3(T242, s(T243), T246).
mult456(T242, T243, s(T247), s(T246)) :- mult456(T242, T243, T247, T246).
times1(0, T8, 0).
times1(s(0), 0, 0).
times1(s(s(0)), 0, 0).
times1(s(s(s(T27))), 0, T29) :- mult25(T27, T29).
times1(s(s(T30)), 0, s(T32)) :- mult25(T30, T32).
times1(s(T33), 0, s(T36)) :- mult25(T33, T36).
times1(s(0), s(0), s(0)).
times1(s(s(0)), s(0), s(s(0))).
times1(s(s(s(T52))), s(0), s(s(T54))) :- mult64(T52, T54).
times1(s(s(T55)), s(0), s(s(s(T57)))) :- mult72(T55, T57).
times1(s(T58), s(0), s(s(T61))) :- mult72(T58, T61).
times1(s(0), s(s(0)), s(s(0))).
times1(s(s(0)), s(s(0)), s(s(s(s(0))))).
times1(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) :- mult111(T80, T82).
times1(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) :- mult127(T83, T85).
times1(s(T86), s(s(0)), s(s(s(T89)))) :- mult127(T86, T89).
times1(s(0), s(s(s(0))), s(s(s(0)))).
times1(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))).
times1(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) :- mult166(T111, T113).
times1(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) :- mult190(T114, T116).
times1(s(T117), s(s(s(0))), s(s(s(s(T120))))) :- mult190(T117, T120).
times1(s(0), s(s(s(s(0)))), s(s(s(s(0))))).
times1(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))).
times1(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) :- mult229(T145, T147).
times1(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) :- mult261(T148, T150).
times1(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) :- mult261(T151, T154).
times1(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))).
times1(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))).
times1(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) :- mult300(T182, T184).
times1(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) :- mult340(T185, T187).
times1(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) :- mult340(T188, T191).
times1(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))).
times1(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))).
times1(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) :- mult379(T222, T224).
times1(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) :- mult427(T225, T227).
times1(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) :- mult427(T228, T231).
times1(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))).
times1(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) :- mult14(T238, s(T239), T241).
times1(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) :- mult3(T242, s(T243), T246).
times1(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) :- mult456(T242, T243, T247, T246).
times1(T248, T249, s(T251)) :- mult3(T248, T249, T251).

Queries:

times1(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:
times1_in: (b,b,f)
mult25_in: (b,f)
mult64_in: (b,f)
mult72_in: (b,f)
mult111_in: (b,f)
mult127_in: (b,f)
mult166_in: (b,f)
mult190_in: (b,f)
mult229_in: (b,f)
mult261_in: (b,f)
mult300_in: (b,f)
mult340_in: (b,f)
mult379_in: (b,f)
mult427_in: (b,f)
mult14_in: (b,f,f)
mult3_in: (b,f,f) (b,b,f)
mult456_in: (b,f,f,f) (b,f,b,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)

(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:

TIMES1_IN_GGA(s(s(s(T27))), 0, T29) → U79_GGA(T27, T29, mult25_in_ga(T27, T29))
TIMES1_IN_GGA(s(s(s(T27))), 0, T29) → MULT25_IN_GA(T27, T29)
MULT25_IN_GA(s(T27), T29) → U1_GA(T27, T29, mult25_in_ga(T27, T29))
MULT25_IN_GA(s(T27), T29) → MULT25_IN_GA(T27, T29)
MULT25_IN_GA(T30, s(T32)) → U2_GA(T30, T32, mult25_in_ga(T30, T32))
MULT25_IN_GA(T30, s(T32)) → MULT25_IN_GA(T30, T32)
TIMES1_IN_GGA(s(s(T30)), 0, s(T32)) → U80_GGA(T30, T32, mult25_in_ga(T30, T32))
TIMES1_IN_GGA(s(s(T30)), 0, s(T32)) → MULT25_IN_GA(T30, T32)
TIMES1_IN_GGA(s(T33), 0, s(T36)) → U81_GGA(T33, T36, mult25_in_ga(T33, T36))
TIMES1_IN_GGA(s(T33), 0, s(T36)) → MULT25_IN_GA(T33, T36)
TIMES1_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → U82_GGA(T52, T54, mult64_in_ga(T52, T54))
TIMES1_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT64_IN_GA(s(T52), s(T54)) → U3_GA(T52, T54, mult64_in_ga(T52, T54))
MULT64_IN_GA(s(T52), s(T54)) → MULT64_IN_GA(T52, T54)
MULT64_IN_GA(T55, s(s(T57))) → U4_GA(T55, T57, mult72_in_ga(T55, T57))
MULT64_IN_GA(T55, s(s(T57))) → MULT72_IN_GA(T55, T57)
MULT72_IN_GA(s(T52), T54) → U5_GA(T52, T54, mult64_in_ga(T52, T54))
MULT72_IN_GA(s(T52), T54) → MULT64_IN_GA(T52, T54)
MULT72_IN_GA(T55, s(T57)) → U6_GA(T55, T57, mult72_in_ga(T55, T57))
MULT72_IN_GA(T55, s(T57)) → MULT72_IN_GA(T55, T57)
TIMES1_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → U83_GGA(T55, T57, mult72_in_ga(T55, T57))
TIMES1_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
TIMES1_IN_GGA(s(T58), s(0), s(s(T61))) → U84_GGA(T58, T61, mult72_in_ga(T58, T61))
TIMES1_IN_GGA(s(T58), s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
TIMES1_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_GGA(T80, T82, mult111_in_ga(T80, T82))
TIMES1_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT111_IN_GA(s(T80), s(s(T82))) → U7_GA(T80, T82, mult111_in_ga(T80, T82))
MULT111_IN_GA(s(T80), s(s(T82))) → MULT111_IN_GA(T80, T82)
MULT111_IN_GA(T83, s(s(s(T85)))) → U8_GA(T83, T85, mult127_in_ga(T83, T85))
MULT111_IN_GA(T83, s(s(s(T85)))) → MULT127_IN_GA(T83, T85)
MULT127_IN_GA(s(T80), T82) → U9_GA(T80, T82, mult111_in_ga(T80, T82))
MULT127_IN_GA(s(T80), T82) → MULT111_IN_GA(T80, T82)
MULT127_IN_GA(T83, s(T85)) → U10_GA(T83, T85, mult127_in_ga(T83, T85))
MULT127_IN_GA(T83, s(T85)) → MULT127_IN_GA(T83, T85)
TIMES1_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_GGA(T83, T85, mult127_in_ga(T83, T85))
TIMES1_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
TIMES1_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → U87_GGA(T86, T89, mult127_in_ga(T86, T89))
TIMES1_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
TIMES1_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_GGA(T111, T113, mult166_in_ga(T111, T113))
TIMES1_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT166_IN_GA(s(T111), s(s(s(T113)))) → U11_GA(T111, T113, mult166_in_ga(T111, T113))
MULT166_IN_GA(s(T111), s(s(s(T113)))) → MULT166_IN_GA(T111, T113)
MULT166_IN_GA(T114, s(s(s(s(T116))))) → U12_GA(T114, T116, mult190_in_ga(T114, T116))
MULT166_IN_GA(T114, s(s(s(s(T116))))) → MULT190_IN_GA(T114, T116)
MULT190_IN_GA(s(T111), T113) → U13_GA(T111, T113, mult166_in_ga(T111, T113))
MULT190_IN_GA(s(T111), T113) → MULT166_IN_GA(T111, T113)
MULT190_IN_GA(T114, s(T116)) → U14_GA(T114, T116, mult190_in_ga(T114, T116))
MULT190_IN_GA(T114, s(T116)) → MULT190_IN_GA(T114, T116)
TIMES1_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_GGA(T114, T116, mult190_in_ga(T114, T116))
TIMES1_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
TIMES1_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_GGA(T117, T120, mult190_in_ga(T117, T120))
TIMES1_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
TIMES1_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_GGA(T145, T147, mult229_in_ga(T145, T147))
TIMES1_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT229_IN_GA(s(T145), s(s(s(s(T147))))) → U15_GA(T145, T147, mult229_in_ga(T145, T147))
MULT229_IN_GA(s(T145), s(s(s(s(T147))))) → MULT229_IN_GA(T145, T147)
MULT229_IN_GA(T148, s(s(s(s(s(T150)))))) → U16_GA(T148, T150, mult261_in_ga(T148, T150))
MULT229_IN_GA(T148, s(s(s(s(s(T150)))))) → MULT261_IN_GA(T148, T150)
MULT261_IN_GA(s(T145), T147) → U17_GA(T145, T147, mult229_in_ga(T145, T147))
MULT261_IN_GA(s(T145), T147) → MULT229_IN_GA(T145, T147)
MULT261_IN_GA(T148, s(T150)) → U18_GA(T148, T150, mult261_in_ga(T148, T150))
MULT261_IN_GA(T148, s(T150)) → MULT261_IN_GA(T148, T150)
TIMES1_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_GGA(T148, T150, mult261_in_ga(T148, T150))
TIMES1_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
TIMES1_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_GGA(T151, T154, mult261_in_ga(T151, T154))
TIMES1_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
TIMES1_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_GGA(T182, T184, mult300_in_ga(T182, T184))
TIMES1_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT300_IN_GA(s(T182), s(s(s(s(s(T184)))))) → U19_GA(T182, T184, mult300_in_ga(T182, T184))
MULT300_IN_GA(s(T182), s(s(s(s(s(T184)))))) → MULT300_IN_GA(T182, T184)
MULT300_IN_GA(T185, s(s(s(s(s(s(T187))))))) → U20_GA(T185, T187, mult340_in_ga(T185, T187))
MULT300_IN_GA(T185, s(s(s(s(s(s(T187))))))) → MULT340_IN_GA(T185, T187)
MULT340_IN_GA(s(T182), T184) → U21_GA(T182, T184, mult300_in_ga(T182, T184))
MULT340_IN_GA(s(T182), T184) → MULT300_IN_GA(T182, T184)
MULT340_IN_GA(T185, s(T187)) → U22_GA(T185, T187, mult340_in_ga(T185, T187))
MULT340_IN_GA(T185, s(T187)) → MULT340_IN_GA(T185, T187)
TIMES1_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_GGA(T185, T187, mult340_in_ga(T185, T187))
TIMES1_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
TIMES1_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_GGA(T188, T191, mult340_in_ga(T188, T191))
TIMES1_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
TIMES1_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_GGA(T222, T224, mult379_in_ga(T222, T224))
TIMES1_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT379_IN_GA(s(T222), s(s(s(s(s(s(T224))))))) → U23_GA(T222, T224, mult379_in_ga(T222, T224))
MULT379_IN_GA(s(T222), s(s(s(s(s(s(T224))))))) → MULT379_IN_GA(T222, T224)
MULT379_IN_GA(T225, s(s(s(s(s(s(s(T227)))))))) → U24_GA(T225, T227, mult427_in_ga(T225, T227))
MULT379_IN_GA(T225, s(s(s(s(s(s(s(T227)))))))) → MULT427_IN_GA(T225, T227)
MULT427_IN_GA(s(T222), T224) → U25_GA(T222, T224, mult379_in_ga(T222, T224))
MULT427_IN_GA(s(T222), T224) → MULT379_IN_GA(T222, T224)
MULT427_IN_GA(T225, s(T227)) → U26_GA(T225, T227, mult427_in_ga(T225, T227))
MULT427_IN_GA(T225, s(T227)) → MULT427_IN_GA(T225, T227)
TIMES1_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_GGA(T225, T227, mult427_in_ga(T225, T227))
TIMES1_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
TIMES1_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_GGA(T228, T231, mult427_in_ga(T228, T231))
TIMES1_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
TIMES1_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_GGA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
TIMES1_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(s(s(T27)), 0, T29) → U27_GAA(T27, T29, mult25_in_ga(T27, T29))
MULT14_IN_GAA(s(s(T27)), 0, T29) → MULT25_IN_GA(T27, T29)
MULT14_IN_GAA(s(T30), 0, s(T32)) → U28_GAA(T30, T32, mult25_in_ga(T30, T32))
MULT14_IN_GAA(s(T30), 0, s(T32)) → MULT25_IN_GA(T30, T32)
MULT14_IN_GAA(T33, 0, s(T36)) → U29_GAA(T33, T36, mult25_in_ga(T33, T36))
MULT14_IN_GAA(T33, 0, s(T36)) → MULT25_IN_GA(T33, T36)
MULT14_IN_GAA(s(s(T52)), s(0), s(s(T54))) → U30_GAA(T52, T54, mult64_in_ga(T52, T54))
MULT14_IN_GAA(s(s(T52)), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT14_IN_GAA(s(T55), s(0), s(s(s(T57)))) → U31_GAA(T55, T57, mult72_in_ga(T55, T57))
MULT14_IN_GAA(s(T55), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
MULT14_IN_GAA(T58, s(0), s(s(T61))) → U32_GAA(T58, T61, mult72_in_ga(T58, T61))
MULT14_IN_GAA(T58, s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
MULT14_IN_GAA(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_GAA(T80, T82, mult111_in_ga(T80, T82))
MULT14_IN_GAA(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT14_IN_GAA(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_GAA(T83, T85, mult127_in_ga(T83, T85))
MULT14_IN_GAA(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
MULT14_IN_GAA(T86, s(s(0)), s(s(s(T89)))) → U35_GAA(T86, T89, mult127_in_ga(T86, T89))
MULT14_IN_GAA(T86, s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
MULT14_IN_GAA(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_GAA(T111, T113, mult166_in_ga(T111, T113))
MULT14_IN_GAA(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT14_IN_GAA(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_GAA(T114, T116, mult190_in_ga(T114, T116))
MULT14_IN_GAA(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
MULT14_IN_GAA(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_GAA(T117, T120, mult190_in_ga(T117, T120))
MULT14_IN_GAA(T117, s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
MULT14_IN_GAA(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_GAA(T145, T147, mult229_in_ga(T145, T147))
MULT14_IN_GAA(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT14_IN_GAA(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_GAA(T148, T150, mult261_in_ga(T148, T150))
MULT14_IN_GAA(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
MULT14_IN_GAA(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_GAA(T151, T154, mult261_in_ga(T151, T154))
MULT14_IN_GAA(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
MULT14_IN_GAA(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_GAA(T182, T184, mult300_in_ga(T182, T184))
MULT14_IN_GAA(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT14_IN_GAA(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_GAA(T185, T187, mult340_in_ga(T185, T187))
MULT14_IN_GAA(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
MULT14_IN_GAA(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_GAA(T188, T191, mult340_in_ga(T188, T191))
MULT14_IN_GAA(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
MULT14_IN_GAA(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_GAA(T222, T224, mult379_in_ga(T222, T224))
MULT14_IN_GAA(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT14_IN_GAA(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_GAA(T225, T227, mult427_in_ga(T225, T227))
MULT14_IN_GAA(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
MULT14_IN_GAA(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_GAA(T228, T231, mult427_in_ga(T228, T231))
MULT14_IN_GAA(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
MULT14_IN_GAA(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_GAA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
MULT14_IN_GAA(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_GAA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(s(s(T27))), 0, T29) → U51_GAA(T27, T29, mult25_in_ga(T27, T29))
MULT3_IN_GAA(s(s(s(T27))), 0, T29) → MULT25_IN_GA(T27, T29)
MULT3_IN_GAA(s(s(T30)), 0, s(T32)) → U52_GAA(T30, T32, mult25_in_ga(T30, T32))
MULT3_IN_GAA(s(s(T30)), 0, s(T32)) → MULT25_IN_GA(T30, T32)
MULT3_IN_GAA(s(T33), 0, s(T36)) → U53_GAA(T33, T36, mult25_in_ga(T33, T36))
MULT3_IN_GAA(s(T33), 0, s(T36)) → MULT25_IN_GA(T33, T36)
MULT3_IN_GAA(s(s(s(T52))), s(0), s(s(T54))) → U54_GAA(T52, T54, mult64_in_ga(T52, T54))
MULT3_IN_GAA(s(s(s(T52))), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT3_IN_GAA(s(s(T55)), s(0), s(s(s(T57)))) → U55_GAA(T55, T57, mult72_in_ga(T55, T57))
MULT3_IN_GAA(s(s(T55)), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
MULT3_IN_GAA(s(T58), s(0), s(s(T61))) → U56_GAA(T58, T61, mult72_in_ga(T58, T61))
MULT3_IN_GAA(s(T58), s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
MULT3_IN_GAA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_GAA(T80, T82, mult111_in_ga(T80, T82))
MULT3_IN_GAA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT3_IN_GAA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_GAA(T83, T85, mult127_in_ga(T83, T85))
MULT3_IN_GAA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
MULT3_IN_GAA(s(T86), s(s(0)), s(s(s(T89)))) → U59_GAA(T86, T89, mult127_in_ga(T86, T89))
MULT3_IN_GAA(s(T86), s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
MULT3_IN_GAA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_GAA(T111, T113, mult166_in_ga(T111, T113))
MULT3_IN_GAA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT3_IN_GAA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_GAA(T114, T116, mult190_in_ga(T114, T116))
MULT3_IN_GAA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
MULT3_IN_GAA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_GAA(T117, T120, mult190_in_ga(T117, T120))
MULT3_IN_GAA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
MULT3_IN_GAA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_GAA(T145, T147, mult229_in_ga(T145, T147))
MULT3_IN_GAA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT3_IN_GAA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_GAA(T148, T150, mult261_in_ga(T148, T150))
MULT3_IN_GAA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
MULT3_IN_GAA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_GAA(T151, T154, mult261_in_ga(T151, T154))
MULT3_IN_GAA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
MULT3_IN_GAA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_GAA(T182, T184, mult300_in_ga(T182, T184))
MULT3_IN_GAA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT3_IN_GAA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_GAA(T185, T187, mult340_in_ga(T185, T187))
MULT3_IN_GAA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
MULT3_IN_GAA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_GAA(T188, T191, mult340_in_ga(T188, T191))
MULT3_IN_GAA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
MULT3_IN_GAA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_GAA(T222, T224, mult379_in_ga(T222, T224))
MULT3_IN_GAA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT3_IN_GAA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_GAA(T225, T227, mult427_in_ga(T225, T227))
MULT3_IN_GAA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
MULT3_IN_GAA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_GAA(T228, T231, mult427_in_ga(T228, T231))
MULT3_IN_GAA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
MULT3_IN_GAA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_GAA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
MULT3_IN_GAA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_GAA(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(s(T238), T239, 0, T241) → U76_GAAA(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
MULT456_IN_GAAA(s(T238), T239, 0, T241) → MULT14_IN_GAA(T238, s(T239), T241)
MULT456_IN_GAAA(T242, T243, 0, s(T246)) → U77_GAAA(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
MULT456_IN_GAAA(T242, T243, 0, s(T246)) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_GAA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_GAA(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(T242, T243, s(T247), s(T246)) → U78_GAAA(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
MULT456_IN_GAAA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT3_IN_GAA(T248, T249, s(T251)) → U75_GAA(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
MULT3_IN_GAA(T248, T249, s(T251)) → MULT3_IN_GAA(T248, T249, T251)
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_GGA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_GGA(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAGA(T242, T243, T247, T246)
MULT456_IN_GAGA(s(T238), T239, 0, T241) → U76_GAGA(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
MULT456_IN_GAGA(s(T238), T239, 0, T241) → MULT14_IN_GAA(T238, s(T239), T241)
MULT456_IN_GAGA(T242, T243, 0, s(T246)) → U77_GAGA(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
MULT456_IN_GAGA(T242, T243, 0, s(T246)) → MULT3_IN_GAA(T242, s(T243), T246)
MULT456_IN_GAGA(T242, T243, s(T247), s(T246)) → U78_GAGA(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
MULT456_IN_GAGA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAGA(T242, T243, T247, T246)
TIMES1_IN_GGA(T248, T249, s(T251)) → U103_GGA(T248, T249, T251, mult3_in_gga(T248, T249, T251))
TIMES1_IN_GGA(T248, T249, s(T251)) → MULT3_IN_GGA(T248, T249, T251)
MULT3_IN_GGA(s(s(s(T27))), 0, T29) → U51_GGA(T27, T29, mult25_in_ga(T27, T29))
MULT3_IN_GGA(s(s(s(T27))), 0, T29) → MULT25_IN_GA(T27, T29)
MULT3_IN_GGA(s(s(T30)), 0, s(T32)) → U52_GGA(T30, T32, mult25_in_ga(T30, T32))
MULT3_IN_GGA(s(s(T30)), 0, s(T32)) → MULT25_IN_GA(T30, T32)
MULT3_IN_GGA(s(T33), 0, s(T36)) → U53_GGA(T33, T36, mult25_in_ga(T33, T36))
MULT3_IN_GGA(s(T33), 0, s(T36)) → MULT25_IN_GA(T33, T36)
MULT3_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → U54_GGA(T52, T54, mult64_in_ga(T52, T54))
MULT3_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT3_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → U55_GGA(T55, T57, mult72_in_ga(T55, T57))
MULT3_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
MULT3_IN_GGA(s(T58), s(0), s(s(T61))) → U56_GGA(T58, T61, mult72_in_ga(T58, T61))
MULT3_IN_GGA(s(T58), s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
MULT3_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_GGA(T80, T82, mult111_in_ga(T80, T82))
MULT3_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT3_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_GGA(T83, T85, mult127_in_ga(T83, T85))
MULT3_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
MULT3_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → U59_GGA(T86, T89, mult127_in_ga(T86, T89))
MULT3_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
MULT3_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_GGA(T111, T113, mult166_in_ga(T111, T113))
MULT3_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT3_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_GGA(T114, T116, mult190_in_ga(T114, T116))
MULT3_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
MULT3_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_GGA(T117, T120, mult190_in_ga(T117, T120))
MULT3_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
MULT3_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_GGA(T145, T147, mult229_in_ga(T145, T147))
MULT3_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT3_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_GGA(T148, T150, mult261_in_ga(T148, T150))
MULT3_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
MULT3_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_GGA(T151, T154, mult261_in_ga(T151, T154))
MULT3_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
MULT3_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_GGA(T182, T184, mult300_in_ga(T182, T184))
MULT3_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT3_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_GGA(T185, T187, mult340_in_ga(T185, T187))
MULT3_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
MULT3_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_GGA(T188, T191, mult340_in_ga(T188, T191))
MULT3_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
MULT3_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_GGA(T222, T224, mult379_in_ga(T222, T224))
MULT3_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT3_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_GGA(T225, T227, mult427_in_ga(T225, T227))
MULT3_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
MULT3_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_GGA(T228, T231, mult427_in_ga(T228, T231))
MULT3_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
MULT3_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_GGA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
MULT3_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_GGA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_GGA(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAGA(T242, T243, T247, T246)
MULT3_IN_GGA(T248, T249, s(T251)) → U75_GGA(T248, T249, T251, mult3_in_gga(T248, T249, T251))
MULT3_IN_GGA(T248, T249, s(T251)) → MULT3_IN_GGA(T248, T249, T251)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)
TIMES1_IN_GGA(x1, x2, x3)  =  TIMES1_IN_GGA(x1, x2)
U79_GGA(x1, x2, x3)  =  U79_GGA(x3)
MULT25_IN_GA(x1, x2)  =  MULT25_IN_GA(x1)
U1_GA(x1, x2, x3)  =  U1_GA(x3)
U2_GA(x1, x2, x3)  =  U2_GA(x3)
U80_GGA(x1, x2, x3)  =  U80_GGA(x3)
U81_GGA(x1, x2, x3)  =  U81_GGA(x3)
U82_GGA(x1, x2, x3)  =  U82_GGA(x3)
MULT64_IN_GA(x1, x2)  =  MULT64_IN_GA(x1)
U3_GA(x1, x2, x3)  =  U3_GA(x3)
U4_GA(x1, x2, x3)  =  U4_GA(x3)
MULT72_IN_GA(x1, x2)  =  MULT72_IN_GA(x1)
U5_GA(x1, x2, x3)  =  U5_GA(x3)
U6_GA(x1, x2, x3)  =  U6_GA(x3)
U83_GGA(x1, x2, x3)  =  U83_GGA(x3)
U84_GGA(x1, x2, x3)  =  U84_GGA(x3)
U85_GGA(x1, x2, x3)  =  U85_GGA(x3)
MULT111_IN_GA(x1, x2)  =  MULT111_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x3)
U8_GA(x1, x2, x3)  =  U8_GA(x3)
MULT127_IN_GA(x1, x2)  =  MULT127_IN_GA(x1)
U9_GA(x1, x2, x3)  =  U9_GA(x3)
U10_GA(x1, x2, x3)  =  U10_GA(x3)
U86_GGA(x1, x2, x3)  =  U86_GGA(x3)
U87_GGA(x1, x2, x3)  =  U87_GGA(x3)
U88_GGA(x1, x2, x3)  =  U88_GGA(x3)
MULT166_IN_GA(x1, x2)  =  MULT166_IN_GA(x1)
U11_GA(x1, x2, x3)  =  U11_GA(x3)
U12_GA(x1, x2, x3)  =  U12_GA(x3)
MULT190_IN_GA(x1, x2)  =  MULT190_IN_GA(x1)
U13_GA(x1, x2, x3)  =  U13_GA(x3)
U14_GA(x1, x2, x3)  =  U14_GA(x3)
U89_GGA(x1, x2, x3)  =  U89_GGA(x3)
U90_GGA(x1, x2, x3)  =  U90_GGA(x3)
U91_GGA(x1, x2, x3)  =  U91_GGA(x3)
MULT229_IN_GA(x1, x2)  =  MULT229_IN_GA(x1)
U15_GA(x1, x2, x3)  =  U15_GA(x3)
U16_GA(x1, x2, x3)  =  U16_GA(x3)
MULT261_IN_GA(x1, x2)  =  MULT261_IN_GA(x1)
U17_GA(x1, x2, x3)  =  U17_GA(x3)
U18_GA(x1, x2, x3)  =  U18_GA(x3)
U92_GGA(x1, x2, x3)  =  U92_GGA(x3)
U93_GGA(x1, x2, x3)  =  U93_GGA(x3)
U94_GGA(x1, x2, x3)  =  U94_GGA(x3)
MULT300_IN_GA(x1, x2)  =  MULT300_IN_GA(x1)
U19_GA(x1, x2, x3)  =  U19_GA(x3)
U20_GA(x1, x2, x3)  =  U20_GA(x3)
MULT340_IN_GA(x1, x2)  =  MULT340_IN_GA(x1)
U21_GA(x1, x2, x3)  =  U21_GA(x3)
U22_GA(x1, x2, x3)  =  U22_GA(x3)
U95_GGA(x1, x2, x3)  =  U95_GGA(x3)
U96_GGA(x1, x2, x3)  =  U96_GGA(x3)
U97_GGA(x1, x2, x3)  =  U97_GGA(x3)
MULT379_IN_GA(x1, x2)  =  MULT379_IN_GA(x1)
U23_GA(x1, x2, x3)  =  U23_GA(x3)
U24_GA(x1, x2, x3)  =  U24_GA(x3)
MULT427_IN_GA(x1, x2)  =  MULT427_IN_GA(x1)
U25_GA(x1, x2, x3)  =  U25_GA(x3)
U26_GA(x1, x2, x3)  =  U26_GA(x3)
U98_GGA(x1, x2, x3)  =  U98_GGA(x3)
U99_GGA(x1, x2, x3)  =  U99_GGA(x3)
U100_GGA(x1, x2, x3)  =  U100_GGA(x3)
MULT14_IN_GAA(x1, x2, x3)  =  MULT14_IN_GAA(x1)
U27_GAA(x1, x2, x3)  =  U27_GAA(x3)
U28_GAA(x1, x2, x3)  =  U28_GAA(x3)
U29_GAA(x1, x2, x3)  =  U29_GAA(x3)
U30_GAA(x1, x2, x3)  =  U30_GAA(x3)
U31_GAA(x1, x2, x3)  =  U31_GAA(x3)
U32_GAA(x1, x2, x3)  =  U32_GAA(x3)
U33_GAA(x1, x2, x3)  =  U33_GAA(x3)
U34_GAA(x1, x2, x3)  =  U34_GAA(x3)
U35_GAA(x1, x2, x3)  =  U35_GAA(x3)
U36_GAA(x1, x2, x3)  =  U36_GAA(x3)
U37_GAA(x1, x2, x3)  =  U37_GAA(x3)
U38_GAA(x1, x2, x3)  =  U38_GAA(x3)
U39_GAA(x1, x2, x3)  =  U39_GAA(x3)
U40_GAA(x1, x2, x3)  =  U40_GAA(x3)
U41_GAA(x1, x2, x3)  =  U41_GAA(x3)
U42_GAA(x1, x2, x3)  =  U42_GAA(x3)
U43_GAA(x1, x2, x3)  =  U43_GAA(x3)
U44_GAA(x1, x2, x3)  =  U44_GAA(x3)
U45_GAA(x1, x2, x3)  =  U45_GAA(x3)
U46_GAA(x1, x2, x3)  =  U46_GAA(x3)
U47_GAA(x1, x2, x3)  =  U47_GAA(x3)
U48_GAA(x1, x2, x3)  =  U48_GAA(x3)
U49_GAA(x1, x2, x3)  =  U49_GAA(x3)
MULT3_IN_GAA(x1, x2, x3)  =  MULT3_IN_GAA(x1)
U51_GAA(x1, x2, x3)  =  U51_GAA(x3)
U52_GAA(x1, x2, x3)  =  U52_GAA(x3)
U53_GAA(x1, x2, x3)  =  U53_GAA(x3)
U54_GAA(x1, x2, x3)  =  U54_GAA(x3)
U55_GAA(x1, x2, x3)  =  U55_GAA(x3)
U56_GAA(x1, x2, x3)  =  U56_GAA(x3)
U57_GAA(x1, x2, x3)  =  U57_GAA(x3)
U58_GAA(x1, x2, x3)  =  U58_GAA(x3)
U59_GAA(x1, x2, x3)  =  U59_GAA(x3)
U60_GAA(x1, x2, x3)  =  U60_GAA(x3)
U61_GAA(x1, x2, x3)  =  U61_GAA(x3)
U62_GAA(x1, x2, x3)  =  U62_GAA(x3)
U63_GAA(x1, x2, x3)  =  U63_GAA(x3)
U64_GAA(x1, x2, x3)  =  U64_GAA(x3)
U65_GAA(x1, x2, x3)  =  U65_GAA(x3)
U66_GAA(x1, x2, x3)  =  U66_GAA(x3)
U67_GAA(x1, x2, x3)  =  U67_GAA(x3)
U68_GAA(x1, x2, x3)  =  U68_GAA(x3)
U69_GAA(x1, x2, x3)  =  U69_GAA(x3)
U70_GAA(x1, x2, x3)  =  U70_GAA(x3)
U71_GAA(x1, x2, x3)  =  U71_GAA(x3)
U72_GAA(x1, x2, x3)  =  U72_GAA(x3)
U50_GAA(x1, x2, x3, x4)  =  U50_GAA(x4)
MULT456_IN_GAAA(x1, x2, x3, x4)  =  MULT456_IN_GAAA(x1)
U76_GAAA(x1, x2, x3, x4)  =  U76_GAAA(x4)
U77_GAAA(x1, x2, x3, x4)  =  U77_GAAA(x4)
U73_GAA(x1, x2, x3)  =  U73_GAA(x3)
U74_GAA(x1, x2, x3, x4)  =  U74_GAA(x4)
U78_GAAA(x1, x2, x3, x4, x5)  =  U78_GAAA(x5)
U75_GAA(x1, x2, x3, x4)  =  U75_GAA(x4)
U101_GGA(x1, x2, x3)  =  U101_GGA(x3)
U102_GGA(x1, x2, x3, x4)  =  U102_GGA(x4)
MULT456_IN_GAGA(x1, x2, x3, x4)  =  MULT456_IN_GAGA(x1, x3)
U76_GAGA(x1, x2, x3, x4)  =  U76_GAGA(x4)
U77_GAGA(x1, x2, x3, x4)  =  U77_GAGA(x4)
U78_GAGA(x1, x2, x3, x4, x5)  =  U78_GAGA(x5)
U103_GGA(x1, x2, x3, x4)  =  U103_GGA(x4)
MULT3_IN_GGA(x1, x2, x3)  =  MULT3_IN_GGA(x1, x2)
U51_GGA(x1, x2, x3)  =  U51_GGA(x3)
U52_GGA(x1, x2, x3)  =  U52_GGA(x3)
U53_GGA(x1, x2, x3)  =  U53_GGA(x3)
U54_GGA(x1, x2, x3)  =  U54_GGA(x3)
U55_GGA(x1, x2, x3)  =  U55_GGA(x3)
U56_GGA(x1, x2, x3)  =  U56_GGA(x3)
U57_GGA(x1, x2, x3)  =  U57_GGA(x3)
U58_GGA(x1, x2, x3)  =  U58_GGA(x3)
U59_GGA(x1, x2, x3)  =  U59_GGA(x3)
U60_GGA(x1, x2, x3)  =  U60_GGA(x3)
U61_GGA(x1, x2, x3)  =  U61_GGA(x3)
U62_GGA(x1, x2, x3)  =  U62_GGA(x3)
U63_GGA(x1, x2, x3)  =  U63_GGA(x3)
U64_GGA(x1, x2, x3)  =  U64_GGA(x3)
U65_GGA(x1, x2, x3)  =  U65_GGA(x3)
U66_GGA(x1, x2, x3)  =  U66_GGA(x3)
U67_GGA(x1, x2, x3)  =  U67_GGA(x3)
U68_GGA(x1, x2, x3)  =  U68_GGA(x3)
U69_GGA(x1, x2, x3)  =  U69_GGA(x3)
U70_GGA(x1, x2, x3)  =  U70_GGA(x3)
U71_GGA(x1, x2, x3)  =  U71_GGA(x3)
U72_GGA(x1, x2, x3)  =  U72_GGA(x3)
U73_GGA(x1, x2, x3)  =  U73_GGA(x3)
U74_GGA(x1, x2, x3, x4)  =  U74_GGA(x4)
U75_GGA(x1, x2, x3, x4)  =  U75_GGA(x4)

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

(6) Obligation:

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

TIMES1_IN_GGA(s(s(s(T27))), 0, T29) → U79_GGA(T27, T29, mult25_in_ga(T27, T29))
TIMES1_IN_GGA(s(s(s(T27))), 0, T29) → MULT25_IN_GA(T27, T29)
MULT25_IN_GA(s(T27), T29) → U1_GA(T27, T29, mult25_in_ga(T27, T29))
MULT25_IN_GA(s(T27), T29) → MULT25_IN_GA(T27, T29)
MULT25_IN_GA(T30, s(T32)) → U2_GA(T30, T32, mult25_in_ga(T30, T32))
MULT25_IN_GA(T30, s(T32)) → MULT25_IN_GA(T30, T32)
TIMES1_IN_GGA(s(s(T30)), 0, s(T32)) → U80_GGA(T30, T32, mult25_in_ga(T30, T32))
TIMES1_IN_GGA(s(s(T30)), 0, s(T32)) → MULT25_IN_GA(T30, T32)
TIMES1_IN_GGA(s(T33), 0, s(T36)) → U81_GGA(T33, T36, mult25_in_ga(T33, T36))
TIMES1_IN_GGA(s(T33), 0, s(T36)) → MULT25_IN_GA(T33, T36)
TIMES1_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → U82_GGA(T52, T54, mult64_in_ga(T52, T54))
TIMES1_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT64_IN_GA(s(T52), s(T54)) → U3_GA(T52, T54, mult64_in_ga(T52, T54))
MULT64_IN_GA(s(T52), s(T54)) → MULT64_IN_GA(T52, T54)
MULT64_IN_GA(T55, s(s(T57))) → U4_GA(T55, T57, mult72_in_ga(T55, T57))
MULT64_IN_GA(T55, s(s(T57))) → MULT72_IN_GA(T55, T57)
MULT72_IN_GA(s(T52), T54) → U5_GA(T52, T54, mult64_in_ga(T52, T54))
MULT72_IN_GA(s(T52), T54) → MULT64_IN_GA(T52, T54)
MULT72_IN_GA(T55, s(T57)) → U6_GA(T55, T57, mult72_in_ga(T55, T57))
MULT72_IN_GA(T55, s(T57)) → MULT72_IN_GA(T55, T57)
TIMES1_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → U83_GGA(T55, T57, mult72_in_ga(T55, T57))
TIMES1_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
TIMES1_IN_GGA(s(T58), s(0), s(s(T61))) → U84_GGA(T58, T61, mult72_in_ga(T58, T61))
TIMES1_IN_GGA(s(T58), s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
TIMES1_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_GGA(T80, T82, mult111_in_ga(T80, T82))
TIMES1_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT111_IN_GA(s(T80), s(s(T82))) → U7_GA(T80, T82, mult111_in_ga(T80, T82))
MULT111_IN_GA(s(T80), s(s(T82))) → MULT111_IN_GA(T80, T82)
MULT111_IN_GA(T83, s(s(s(T85)))) → U8_GA(T83, T85, mult127_in_ga(T83, T85))
MULT111_IN_GA(T83, s(s(s(T85)))) → MULT127_IN_GA(T83, T85)
MULT127_IN_GA(s(T80), T82) → U9_GA(T80, T82, mult111_in_ga(T80, T82))
MULT127_IN_GA(s(T80), T82) → MULT111_IN_GA(T80, T82)
MULT127_IN_GA(T83, s(T85)) → U10_GA(T83, T85, mult127_in_ga(T83, T85))
MULT127_IN_GA(T83, s(T85)) → MULT127_IN_GA(T83, T85)
TIMES1_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_GGA(T83, T85, mult127_in_ga(T83, T85))
TIMES1_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
TIMES1_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → U87_GGA(T86, T89, mult127_in_ga(T86, T89))
TIMES1_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
TIMES1_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_GGA(T111, T113, mult166_in_ga(T111, T113))
TIMES1_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT166_IN_GA(s(T111), s(s(s(T113)))) → U11_GA(T111, T113, mult166_in_ga(T111, T113))
MULT166_IN_GA(s(T111), s(s(s(T113)))) → MULT166_IN_GA(T111, T113)
MULT166_IN_GA(T114, s(s(s(s(T116))))) → U12_GA(T114, T116, mult190_in_ga(T114, T116))
MULT166_IN_GA(T114, s(s(s(s(T116))))) → MULT190_IN_GA(T114, T116)
MULT190_IN_GA(s(T111), T113) → U13_GA(T111, T113, mult166_in_ga(T111, T113))
MULT190_IN_GA(s(T111), T113) → MULT166_IN_GA(T111, T113)
MULT190_IN_GA(T114, s(T116)) → U14_GA(T114, T116, mult190_in_ga(T114, T116))
MULT190_IN_GA(T114, s(T116)) → MULT190_IN_GA(T114, T116)
TIMES1_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_GGA(T114, T116, mult190_in_ga(T114, T116))
TIMES1_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
TIMES1_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_GGA(T117, T120, mult190_in_ga(T117, T120))
TIMES1_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
TIMES1_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_GGA(T145, T147, mult229_in_ga(T145, T147))
TIMES1_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT229_IN_GA(s(T145), s(s(s(s(T147))))) → U15_GA(T145, T147, mult229_in_ga(T145, T147))
MULT229_IN_GA(s(T145), s(s(s(s(T147))))) → MULT229_IN_GA(T145, T147)
MULT229_IN_GA(T148, s(s(s(s(s(T150)))))) → U16_GA(T148, T150, mult261_in_ga(T148, T150))
MULT229_IN_GA(T148, s(s(s(s(s(T150)))))) → MULT261_IN_GA(T148, T150)
MULT261_IN_GA(s(T145), T147) → U17_GA(T145, T147, mult229_in_ga(T145, T147))
MULT261_IN_GA(s(T145), T147) → MULT229_IN_GA(T145, T147)
MULT261_IN_GA(T148, s(T150)) → U18_GA(T148, T150, mult261_in_ga(T148, T150))
MULT261_IN_GA(T148, s(T150)) → MULT261_IN_GA(T148, T150)
TIMES1_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_GGA(T148, T150, mult261_in_ga(T148, T150))
TIMES1_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
TIMES1_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_GGA(T151, T154, mult261_in_ga(T151, T154))
TIMES1_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
TIMES1_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_GGA(T182, T184, mult300_in_ga(T182, T184))
TIMES1_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT300_IN_GA(s(T182), s(s(s(s(s(T184)))))) → U19_GA(T182, T184, mult300_in_ga(T182, T184))
MULT300_IN_GA(s(T182), s(s(s(s(s(T184)))))) → MULT300_IN_GA(T182, T184)
MULT300_IN_GA(T185, s(s(s(s(s(s(T187))))))) → U20_GA(T185, T187, mult340_in_ga(T185, T187))
MULT300_IN_GA(T185, s(s(s(s(s(s(T187))))))) → MULT340_IN_GA(T185, T187)
MULT340_IN_GA(s(T182), T184) → U21_GA(T182, T184, mult300_in_ga(T182, T184))
MULT340_IN_GA(s(T182), T184) → MULT300_IN_GA(T182, T184)
MULT340_IN_GA(T185, s(T187)) → U22_GA(T185, T187, mult340_in_ga(T185, T187))
MULT340_IN_GA(T185, s(T187)) → MULT340_IN_GA(T185, T187)
TIMES1_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_GGA(T185, T187, mult340_in_ga(T185, T187))
TIMES1_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
TIMES1_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_GGA(T188, T191, mult340_in_ga(T188, T191))
TIMES1_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
TIMES1_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_GGA(T222, T224, mult379_in_ga(T222, T224))
TIMES1_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT379_IN_GA(s(T222), s(s(s(s(s(s(T224))))))) → U23_GA(T222, T224, mult379_in_ga(T222, T224))
MULT379_IN_GA(s(T222), s(s(s(s(s(s(T224))))))) → MULT379_IN_GA(T222, T224)
MULT379_IN_GA(T225, s(s(s(s(s(s(s(T227)))))))) → U24_GA(T225, T227, mult427_in_ga(T225, T227))
MULT379_IN_GA(T225, s(s(s(s(s(s(s(T227)))))))) → MULT427_IN_GA(T225, T227)
MULT427_IN_GA(s(T222), T224) → U25_GA(T222, T224, mult379_in_ga(T222, T224))
MULT427_IN_GA(s(T222), T224) → MULT379_IN_GA(T222, T224)
MULT427_IN_GA(T225, s(T227)) → U26_GA(T225, T227, mult427_in_ga(T225, T227))
MULT427_IN_GA(T225, s(T227)) → MULT427_IN_GA(T225, T227)
TIMES1_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_GGA(T225, T227, mult427_in_ga(T225, T227))
TIMES1_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
TIMES1_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_GGA(T228, T231, mult427_in_ga(T228, T231))
TIMES1_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
TIMES1_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_GGA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
TIMES1_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(s(s(T27)), 0, T29) → U27_GAA(T27, T29, mult25_in_ga(T27, T29))
MULT14_IN_GAA(s(s(T27)), 0, T29) → MULT25_IN_GA(T27, T29)
MULT14_IN_GAA(s(T30), 0, s(T32)) → U28_GAA(T30, T32, mult25_in_ga(T30, T32))
MULT14_IN_GAA(s(T30), 0, s(T32)) → MULT25_IN_GA(T30, T32)
MULT14_IN_GAA(T33, 0, s(T36)) → U29_GAA(T33, T36, mult25_in_ga(T33, T36))
MULT14_IN_GAA(T33, 0, s(T36)) → MULT25_IN_GA(T33, T36)
MULT14_IN_GAA(s(s(T52)), s(0), s(s(T54))) → U30_GAA(T52, T54, mult64_in_ga(T52, T54))
MULT14_IN_GAA(s(s(T52)), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT14_IN_GAA(s(T55), s(0), s(s(s(T57)))) → U31_GAA(T55, T57, mult72_in_ga(T55, T57))
MULT14_IN_GAA(s(T55), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
MULT14_IN_GAA(T58, s(0), s(s(T61))) → U32_GAA(T58, T61, mult72_in_ga(T58, T61))
MULT14_IN_GAA(T58, s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
MULT14_IN_GAA(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_GAA(T80, T82, mult111_in_ga(T80, T82))
MULT14_IN_GAA(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT14_IN_GAA(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_GAA(T83, T85, mult127_in_ga(T83, T85))
MULT14_IN_GAA(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
MULT14_IN_GAA(T86, s(s(0)), s(s(s(T89)))) → U35_GAA(T86, T89, mult127_in_ga(T86, T89))
MULT14_IN_GAA(T86, s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
MULT14_IN_GAA(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_GAA(T111, T113, mult166_in_ga(T111, T113))
MULT14_IN_GAA(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT14_IN_GAA(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_GAA(T114, T116, mult190_in_ga(T114, T116))
MULT14_IN_GAA(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
MULT14_IN_GAA(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_GAA(T117, T120, mult190_in_ga(T117, T120))
MULT14_IN_GAA(T117, s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
MULT14_IN_GAA(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_GAA(T145, T147, mult229_in_ga(T145, T147))
MULT14_IN_GAA(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT14_IN_GAA(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_GAA(T148, T150, mult261_in_ga(T148, T150))
MULT14_IN_GAA(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
MULT14_IN_GAA(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_GAA(T151, T154, mult261_in_ga(T151, T154))
MULT14_IN_GAA(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
MULT14_IN_GAA(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_GAA(T182, T184, mult300_in_ga(T182, T184))
MULT14_IN_GAA(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT14_IN_GAA(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_GAA(T185, T187, mult340_in_ga(T185, T187))
MULT14_IN_GAA(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
MULT14_IN_GAA(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_GAA(T188, T191, mult340_in_ga(T188, T191))
MULT14_IN_GAA(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
MULT14_IN_GAA(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_GAA(T222, T224, mult379_in_ga(T222, T224))
MULT14_IN_GAA(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT14_IN_GAA(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_GAA(T225, T227, mult427_in_ga(T225, T227))
MULT14_IN_GAA(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
MULT14_IN_GAA(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_GAA(T228, T231, mult427_in_ga(T228, T231))
MULT14_IN_GAA(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
MULT14_IN_GAA(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_GAA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
MULT14_IN_GAA(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_GAA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(s(s(T27))), 0, T29) → U51_GAA(T27, T29, mult25_in_ga(T27, T29))
MULT3_IN_GAA(s(s(s(T27))), 0, T29) → MULT25_IN_GA(T27, T29)
MULT3_IN_GAA(s(s(T30)), 0, s(T32)) → U52_GAA(T30, T32, mult25_in_ga(T30, T32))
MULT3_IN_GAA(s(s(T30)), 0, s(T32)) → MULT25_IN_GA(T30, T32)
MULT3_IN_GAA(s(T33), 0, s(T36)) → U53_GAA(T33, T36, mult25_in_ga(T33, T36))
MULT3_IN_GAA(s(T33), 0, s(T36)) → MULT25_IN_GA(T33, T36)
MULT3_IN_GAA(s(s(s(T52))), s(0), s(s(T54))) → U54_GAA(T52, T54, mult64_in_ga(T52, T54))
MULT3_IN_GAA(s(s(s(T52))), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT3_IN_GAA(s(s(T55)), s(0), s(s(s(T57)))) → U55_GAA(T55, T57, mult72_in_ga(T55, T57))
MULT3_IN_GAA(s(s(T55)), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
MULT3_IN_GAA(s(T58), s(0), s(s(T61))) → U56_GAA(T58, T61, mult72_in_ga(T58, T61))
MULT3_IN_GAA(s(T58), s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
MULT3_IN_GAA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_GAA(T80, T82, mult111_in_ga(T80, T82))
MULT3_IN_GAA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT3_IN_GAA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_GAA(T83, T85, mult127_in_ga(T83, T85))
MULT3_IN_GAA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
MULT3_IN_GAA(s(T86), s(s(0)), s(s(s(T89)))) → U59_GAA(T86, T89, mult127_in_ga(T86, T89))
MULT3_IN_GAA(s(T86), s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
MULT3_IN_GAA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_GAA(T111, T113, mult166_in_ga(T111, T113))
MULT3_IN_GAA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT3_IN_GAA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_GAA(T114, T116, mult190_in_ga(T114, T116))
MULT3_IN_GAA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
MULT3_IN_GAA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_GAA(T117, T120, mult190_in_ga(T117, T120))
MULT3_IN_GAA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
MULT3_IN_GAA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_GAA(T145, T147, mult229_in_ga(T145, T147))
MULT3_IN_GAA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT3_IN_GAA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_GAA(T148, T150, mult261_in_ga(T148, T150))
MULT3_IN_GAA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
MULT3_IN_GAA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_GAA(T151, T154, mult261_in_ga(T151, T154))
MULT3_IN_GAA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
MULT3_IN_GAA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_GAA(T182, T184, mult300_in_ga(T182, T184))
MULT3_IN_GAA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT3_IN_GAA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_GAA(T185, T187, mult340_in_ga(T185, T187))
MULT3_IN_GAA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
MULT3_IN_GAA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_GAA(T188, T191, mult340_in_ga(T188, T191))
MULT3_IN_GAA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
MULT3_IN_GAA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_GAA(T222, T224, mult379_in_ga(T222, T224))
MULT3_IN_GAA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT3_IN_GAA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_GAA(T225, T227, mult427_in_ga(T225, T227))
MULT3_IN_GAA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
MULT3_IN_GAA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_GAA(T228, T231, mult427_in_ga(T228, T231))
MULT3_IN_GAA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
MULT3_IN_GAA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_GAA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
MULT3_IN_GAA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_GAA(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(s(T238), T239, 0, T241) → U76_GAAA(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
MULT456_IN_GAAA(s(T238), T239, 0, T241) → MULT14_IN_GAA(T238, s(T239), T241)
MULT456_IN_GAAA(T242, T243, 0, s(T246)) → U77_GAAA(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
MULT456_IN_GAAA(T242, T243, 0, s(T246)) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_GAA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_GAA(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(T242, T243, s(T247), s(T246)) → U78_GAAA(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
MULT456_IN_GAAA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT3_IN_GAA(T248, T249, s(T251)) → U75_GAA(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
MULT3_IN_GAA(T248, T249, s(T251)) → MULT3_IN_GAA(T248, T249, T251)
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_GGA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_GGA(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAGA(T242, T243, T247, T246)
MULT456_IN_GAGA(s(T238), T239, 0, T241) → U76_GAGA(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
MULT456_IN_GAGA(s(T238), T239, 0, T241) → MULT14_IN_GAA(T238, s(T239), T241)
MULT456_IN_GAGA(T242, T243, 0, s(T246)) → U77_GAGA(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
MULT456_IN_GAGA(T242, T243, 0, s(T246)) → MULT3_IN_GAA(T242, s(T243), T246)
MULT456_IN_GAGA(T242, T243, s(T247), s(T246)) → U78_GAGA(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
MULT456_IN_GAGA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAGA(T242, T243, T247, T246)
TIMES1_IN_GGA(T248, T249, s(T251)) → U103_GGA(T248, T249, T251, mult3_in_gga(T248, T249, T251))
TIMES1_IN_GGA(T248, T249, s(T251)) → MULT3_IN_GGA(T248, T249, T251)
MULT3_IN_GGA(s(s(s(T27))), 0, T29) → U51_GGA(T27, T29, mult25_in_ga(T27, T29))
MULT3_IN_GGA(s(s(s(T27))), 0, T29) → MULT25_IN_GA(T27, T29)
MULT3_IN_GGA(s(s(T30)), 0, s(T32)) → U52_GGA(T30, T32, mult25_in_ga(T30, T32))
MULT3_IN_GGA(s(s(T30)), 0, s(T32)) → MULT25_IN_GA(T30, T32)
MULT3_IN_GGA(s(T33), 0, s(T36)) → U53_GGA(T33, T36, mult25_in_ga(T33, T36))
MULT3_IN_GGA(s(T33), 0, s(T36)) → MULT25_IN_GA(T33, T36)
MULT3_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → U54_GGA(T52, T54, mult64_in_ga(T52, T54))
MULT3_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT3_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → U55_GGA(T55, T57, mult72_in_ga(T55, T57))
MULT3_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
MULT3_IN_GGA(s(T58), s(0), s(s(T61))) → U56_GGA(T58, T61, mult72_in_ga(T58, T61))
MULT3_IN_GGA(s(T58), s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
MULT3_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_GGA(T80, T82, mult111_in_ga(T80, T82))
MULT3_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT3_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_GGA(T83, T85, mult127_in_ga(T83, T85))
MULT3_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
MULT3_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → U59_GGA(T86, T89, mult127_in_ga(T86, T89))
MULT3_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
MULT3_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_GGA(T111, T113, mult166_in_ga(T111, T113))
MULT3_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT3_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_GGA(T114, T116, mult190_in_ga(T114, T116))
MULT3_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
MULT3_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_GGA(T117, T120, mult190_in_ga(T117, T120))
MULT3_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
MULT3_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_GGA(T145, T147, mult229_in_ga(T145, T147))
MULT3_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT3_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_GGA(T148, T150, mult261_in_ga(T148, T150))
MULT3_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
MULT3_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_GGA(T151, T154, mult261_in_ga(T151, T154))
MULT3_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
MULT3_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_GGA(T182, T184, mult300_in_ga(T182, T184))
MULT3_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT3_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_GGA(T185, T187, mult340_in_ga(T185, T187))
MULT3_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
MULT3_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_GGA(T188, T191, mult340_in_ga(T188, T191))
MULT3_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
MULT3_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_GGA(T222, T224, mult379_in_ga(T222, T224))
MULT3_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT3_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_GGA(T225, T227, mult427_in_ga(T225, T227))
MULT3_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
MULT3_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_GGA(T228, T231, mult427_in_ga(T228, T231))
MULT3_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
MULT3_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_GGA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
MULT3_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_GGA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_GGA(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAGA(T242, T243, T247, T246)
MULT3_IN_GGA(T248, T249, s(T251)) → U75_GGA(T248, T249, T251, mult3_in_gga(T248, T249, T251))
MULT3_IN_GGA(T248, T249, s(T251)) → MULT3_IN_GGA(T248, T249, T251)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)
TIMES1_IN_GGA(x1, x2, x3)  =  TIMES1_IN_GGA(x1, x2)
U79_GGA(x1, x2, x3)  =  U79_GGA(x3)
MULT25_IN_GA(x1, x2)  =  MULT25_IN_GA(x1)
U1_GA(x1, x2, x3)  =  U1_GA(x3)
U2_GA(x1, x2, x3)  =  U2_GA(x3)
U80_GGA(x1, x2, x3)  =  U80_GGA(x3)
U81_GGA(x1, x2, x3)  =  U81_GGA(x3)
U82_GGA(x1, x2, x3)  =  U82_GGA(x3)
MULT64_IN_GA(x1, x2)  =  MULT64_IN_GA(x1)
U3_GA(x1, x2, x3)  =  U3_GA(x3)
U4_GA(x1, x2, x3)  =  U4_GA(x3)
MULT72_IN_GA(x1, x2)  =  MULT72_IN_GA(x1)
U5_GA(x1, x2, x3)  =  U5_GA(x3)
U6_GA(x1, x2, x3)  =  U6_GA(x3)
U83_GGA(x1, x2, x3)  =  U83_GGA(x3)
U84_GGA(x1, x2, x3)  =  U84_GGA(x3)
U85_GGA(x1, x2, x3)  =  U85_GGA(x3)
MULT111_IN_GA(x1, x2)  =  MULT111_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x3)
U8_GA(x1, x2, x3)  =  U8_GA(x3)
MULT127_IN_GA(x1, x2)  =  MULT127_IN_GA(x1)
U9_GA(x1, x2, x3)  =  U9_GA(x3)
U10_GA(x1, x2, x3)  =  U10_GA(x3)
U86_GGA(x1, x2, x3)  =  U86_GGA(x3)
U87_GGA(x1, x2, x3)  =  U87_GGA(x3)
U88_GGA(x1, x2, x3)  =  U88_GGA(x3)
MULT166_IN_GA(x1, x2)  =  MULT166_IN_GA(x1)
U11_GA(x1, x2, x3)  =  U11_GA(x3)
U12_GA(x1, x2, x3)  =  U12_GA(x3)
MULT190_IN_GA(x1, x2)  =  MULT190_IN_GA(x1)
U13_GA(x1, x2, x3)  =  U13_GA(x3)
U14_GA(x1, x2, x3)  =  U14_GA(x3)
U89_GGA(x1, x2, x3)  =  U89_GGA(x3)
U90_GGA(x1, x2, x3)  =  U90_GGA(x3)
U91_GGA(x1, x2, x3)  =  U91_GGA(x3)
MULT229_IN_GA(x1, x2)  =  MULT229_IN_GA(x1)
U15_GA(x1, x2, x3)  =  U15_GA(x3)
U16_GA(x1, x2, x3)  =  U16_GA(x3)
MULT261_IN_GA(x1, x2)  =  MULT261_IN_GA(x1)
U17_GA(x1, x2, x3)  =  U17_GA(x3)
U18_GA(x1, x2, x3)  =  U18_GA(x3)
U92_GGA(x1, x2, x3)  =  U92_GGA(x3)
U93_GGA(x1, x2, x3)  =  U93_GGA(x3)
U94_GGA(x1, x2, x3)  =  U94_GGA(x3)
MULT300_IN_GA(x1, x2)  =  MULT300_IN_GA(x1)
U19_GA(x1, x2, x3)  =  U19_GA(x3)
U20_GA(x1, x2, x3)  =  U20_GA(x3)
MULT340_IN_GA(x1, x2)  =  MULT340_IN_GA(x1)
U21_GA(x1, x2, x3)  =  U21_GA(x3)
U22_GA(x1, x2, x3)  =  U22_GA(x3)
U95_GGA(x1, x2, x3)  =  U95_GGA(x3)
U96_GGA(x1, x2, x3)  =  U96_GGA(x3)
U97_GGA(x1, x2, x3)  =  U97_GGA(x3)
MULT379_IN_GA(x1, x2)  =  MULT379_IN_GA(x1)
U23_GA(x1, x2, x3)  =  U23_GA(x3)
U24_GA(x1, x2, x3)  =  U24_GA(x3)
MULT427_IN_GA(x1, x2)  =  MULT427_IN_GA(x1)
U25_GA(x1, x2, x3)  =  U25_GA(x3)
U26_GA(x1, x2, x3)  =  U26_GA(x3)
U98_GGA(x1, x2, x3)  =  U98_GGA(x3)
U99_GGA(x1, x2, x3)  =  U99_GGA(x3)
U100_GGA(x1, x2, x3)  =  U100_GGA(x3)
MULT14_IN_GAA(x1, x2, x3)  =  MULT14_IN_GAA(x1)
U27_GAA(x1, x2, x3)  =  U27_GAA(x3)
U28_GAA(x1, x2, x3)  =  U28_GAA(x3)
U29_GAA(x1, x2, x3)  =  U29_GAA(x3)
U30_GAA(x1, x2, x3)  =  U30_GAA(x3)
U31_GAA(x1, x2, x3)  =  U31_GAA(x3)
U32_GAA(x1, x2, x3)  =  U32_GAA(x3)
U33_GAA(x1, x2, x3)  =  U33_GAA(x3)
U34_GAA(x1, x2, x3)  =  U34_GAA(x3)
U35_GAA(x1, x2, x3)  =  U35_GAA(x3)
U36_GAA(x1, x2, x3)  =  U36_GAA(x3)
U37_GAA(x1, x2, x3)  =  U37_GAA(x3)
U38_GAA(x1, x2, x3)  =  U38_GAA(x3)
U39_GAA(x1, x2, x3)  =  U39_GAA(x3)
U40_GAA(x1, x2, x3)  =  U40_GAA(x3)
U41_GAA(x1, x2, x3)  =  U41_GAA(x3)
U42_GAA(x1, x2, x3)  =  U42_GAA(x3)
U43_GAA(x1, x2, x3)  =  U43_GAA(x3)
U44_GAA(x1, x2, x3)  =  U44_GAA(x3)
U45_GAA(x1, x2, x3)  =  U45_GAA(x3)
U46_GAA(x1, x2, x3)  =  U46_GAA(x3)
U47_GAA(x1, x2, x3)  =  U47_GAA(x3)
U48_GAA(x1, x2, x3)  =  U48_GAA(x3)
U49_GAA(x1, x2, x3)  =  U49_GAA(x3)
MULT3_IN_GAA(x1, x2, x3)  =  MULT3_IN_GAA(x1)
U51_GAA(x1, x2, x3)  =  U51_GAA(x3)
U52_GAA(x1, x2, x3)  =  U52_GAA(x3)
U53_GAA(x1, x2, x3)  =  U53_GAA(x3)
U54_GAA(x1, x2, x3)  =  U54_GAA(x3)
U55_GAA(x1, x2, x3)  =  U55_GAA(x3)
U56_GAA(x1, x2, x3)  =  U56_GAA(x3)
U57_GAA(x1, x2, x3)  =  U57_GAA(x3)
U58_GAA(x1, x2, x3)  =  U58_GAA(x3)
U59_GAA(x1, x2, x3)  =  U59_GAA(x3)
U60_GAA(x1, x2, x3)  =  U60_GAA(x3)
U61_GAA(x1, x2, x3)  =  U61_GAA(x3)
U62_GAA(x1, x2, x3)  =  U62_GAA(x3)
U63_GAA(x1, x2, x3)  =  U63_GAA(x3)
U64_GAA(x1, x2, x3)  =  U64_GAA(x3)
U65_GAA(x1, x2, x3)  =  U65_GAA(x3)
U66_GAA(x1, x2, x3)  =  U66_GAA(x3)
U67_GAA(x1, x2, x3)  =  U67_GAA(x3)
U68_GAA(x1, x2, x3)  =  U68_GAA(x3)
U69_GAA(x1, x2, x3)  =  U69_GAA(x3)
U70_GAA(x1, x2, x3)  =  U70_GAA(x3)
U71_GAA(x1, x2, x3)  =  U71_GAA(x3)
U72_GAA(x1, x2, x3)  =  U72_GAA(x3)
U50_GAA(x1, x2, x3, x4)  =  U50_GAA(x4)
MULT456_IN_GAAA(x1, x2, x3, x4)  =  MULT456_IN_GAAA(x1)
U76_GAAA(x1, x2, x3, x4)  =  U76_GAAA(x4)
U77_GAAA(x1, x2, x3, x4)  =  U77_GAAA(x4)
U73_GAA(x1, x2, x3)  =  U73_GAA(x3)
U74_GAA(x1, x2, x3, x4)  =  U74_GAA(x4)
U78_GAAA(x1, x2, x3, x4, x5)  =  U78_GAAA(x5)
U75_GAA(x1, x2, x3, x4)  =  U75_GAA(x4)
U101_GGA(x1, x2, x3)  =  U101_GGA(x3)
U102_GGA(x1, x2, x3, x4)  =  U102_GGA(x4)
MULT456_IN_GAGA(x1, x2, x3, x4)  =  MULT456_IN_GAGA(x1, x3)
U76_GAGA(x1, x2, x3, x4)  =  U76_GAGA(x4)
U77_GAGA(x1, x2, x3, x4)  =  U77_GAGA(x4)
U78_GAGA(x1, x2, x3, x4, x5)  =  U78_GAGA(x5)
U103_GGA(x1, x2, x3, x4)  =  U103_GGA(x4)
MULT3_IN_GGA(x1, x2, x3)  =  MULT3_IN_GGA(x1, x2)
U51_GGA(x1, x2, x3)  =  U51_GGA(x3)
U52_GGA(x1, x2, x3)  =  U52_GGA(x3)
U53_GGA(x1, x2, x3)  =  U53_GGA(x3)
U54_GGA(x1, x2, x3)  =  U54_GGA(x3)
U55_GGA(x1, x2, x3)  =  U55_GGA(x3)
U56_GGA(x1, x2, x3)  =  U56_GGA(x3)
U57_GGA(x1, x2, x3)  =  U57_GGA(x3)
U58_GGA(x1, x2, x3)  =  U58_GGA(x3)
U59_GGA(x1, x2, x3)  =  U59_GGA(x3)
U60_GGA(x1, x2, x3)  =  U60_GGA(x3)
U61_GGA(x1, x2, x3)  =  U61_GGA(x3)
U62_GGA(x1, x2, x3)  =  U62_GGA(x3)
U63_GGA(x1, x2, x3)  =  U63_GGA(x3)
U64_GGA(x1, x2, x3)  =  U64_GGA(x3)
U65_GGA(x1, x2, x3)  =  U65_GGA(x3)
U66_GGA(x1, x2, x3)  =  U66_GGA(x3)
U67_GGA(x1, x2, x3)  =  U67_GGA(x3)
U68_GGA(x1, x2, x3)  =  U68_GGA(x3)
U69_GGA(x1, x2, x3)  =  U69_GGA(x3)
U70_GGA(x1, x2, x3)  =  U70_GGA(x3)
U71_GGA(x1, x2, x3)  =  U71_GGA(x3)
U72_GGA(x1, x2, x3)  =  U72_GGA(x3)
U73_GGA(x1, x2, x3)  =  U73_GGA(x3)
U74_GGA(x1, x2, x3, x4)  =  U74_GGA(x4)
U75_GGA(x1, x2, x3, x4)  =  U75_GGA(x4)

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

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 10 SCCs with 224 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

MULT379_IN_GA(T225, s(s(s(s(s(s(s(T227)))))))) → MULT427_IN_GA(T225, T227)
MULT427_IN_GA(s(T222), T224) → MULT379_IN_GA(T222, T224)
MULT379_IN_GA(s(T222), s(s(s(s(s(s(T224))))))) → MULT379_IN_GA(T222, T224)
MULT427_IN_GA(T225, s(T227)) → MULT427_IN_GA(T225, T227)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)
MULT379_IN_GA(x1, x2)  =  MULT379_IN_GA(x1)
MULT427_IN_GA(x1, x2)  =  MULT427_IN_GA(x1)

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

(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:

MULT379_IN_GA(T225, s(s(s(s(s(s(s(T227)))))))) → MULT427_IN_GA(T225, T227)
MULT427_IN_GA(s(T222), T224) → MULT379_IN_GA(T222, T224)
MULT379_IN_GA(s(T222), s(s(s(s(s(s(T224))))))) → MULT379_IN_GA(T222, T224)
MULT427_IN_GA(T225, s(T227)) → MULT427_IN_GA(T225, T227)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT379_IN_GA(x1, x2)  =  MULT379_IN_GA(x1)
MULT427_IN_GA(x1, x2)  =  MULT427_IN_GA(x1)

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

(12) PiDPToQDPProof (SOUND 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:

MULT379_IN_GA(T225) → MULT427_IN_GA(T225)
MULT427_IN_GA(s(T222)) → MULT379_IN_GA(T222)
MULT379_IN_GA(s(T222)) → MULT379_IN_GA(T222)
MULT427_IN_GA(T225) → MULT427_IN_GA(T225)

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

(14) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT379_IN_GA(T225) → MULT427_IN_GA(T225)
MULT427_IN_GA(s(T222)) → MULT379_IN_GA(T222)
MULT379_IN_GA(s(T222)) → MULT379_IN_GA(T222)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT379_IN_GA(x₁)) = 2 + x₁   
POL(MULT427_IN_GA(x₁)) = 1 + x₁   
POL(s(x₁)) = 2 + 2·x₁   

(15) Obligation:

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

MULT427_IN_GA(T225) → MULT427_IN_GA(T225)

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

(16) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT427_IN_GA(T225) evaluates to t =MULT427_IN_GA(T225)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT427_IN_GA(T225) to MULT427_IN_GA(T225).

(17) FALSE

(18) Obligation:

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

MULT300_IN_GA(T185, s(s(s(s(s(s(T187))))))) → MULT340_IN_GA(T185, T187)
MULT340_IN_GA(s(T182), T184) → MULT300_IN_GA(T182, T184)
MULT300_IN_GA(s(T182), s(s(s(s(s(T184)))))) → MULT300_IN_GA(T182, T184)
MULT340_IN_GA(T185, s(T187)) → MULT340_IN_GA(T185, T187)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)
MULT300_IN_GA(x1, x2)  =  MULT300_IN_GA(x1)
MULT340_IN_GA(x1, x2)  =  MULT340_IN_GA(x1)

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

(19) UsableRulesProof (EQUIVALENT transformation)

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

(20) Obligation:

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

MULT300_IN_GA(T185, s(s(s(s(s(s(T187))))))) → MULT340_IN_GA(T185, T187)
MULT340_IN_GA(s(T182), T184) → MULT300_IN_GA(T182, T184)
MULT300_IN_GA(s(T182), s(s(s(s(s(T184)))))) → MULT300_IN_GA(T182, T184)
MULT340_IN_GA(T185, s(T187)) → MULT340_IN_GA(T185, T187)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT300_IN_GA(x1, x2)  =  MULT300_IN_GA(x1)
MULT340_IN_GA(x1, x2)  =  MULT340_IN_GA(x1)

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

(21) PiDPToQDPProof (SOUND transformation)

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

(22) Obligation:

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

MULT300_IN_GA(T185) → MULT340_IN_GA(T185)
MULT340_IN_GA(s(T182)) → MULT300_IN_GA(T182)
MULT300_IN_GA(s(T182)) → MULT300_IN_GA(T182)
MULT340_IN_GA(T185) → MULT340_IN_GA(T185)

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

(23) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT300_IN_GA(T185) → MULT340_IN_GA(T185)
MULT340_IN_GA(s(T182)) → MULT300_IN_GA(T182)
MULT300_IN_GA(s(T182)) → MULT300_IN_GA(T182)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT300_IN_GA(x₁)) = 2 + x₁   
POL(MULT340_IN_GA(x₁)) = 1 + x₁   
POL(s(x₁)) = 2 + 2·x₁   

(24) Obligation:

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

MULT340_IN_GA(T185) → MULT340_IN_GA(T185)

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

(25) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT340_IN_GA(T185) evaluates to t =MULT340_IN_GA(T185)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT340_IN_GA(T185) to MULT340_IN_GA(T185).

(26) FALSE

(27) Obligation:

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

MULT229_IN_GA(T148, s(s(s(s(s(T150)))))) → MULT261_IN_GA(T148, T150)
MULT261_IN_GA(s(T145), T147) → MULT229_IN_GA(T145, T147)
MULT229_IN_GA(s(T145), s(s(s(s(T147))))) → MULT229_IN_GA(T145, T147)
MULT261_IN_GA(T148, s(T150)) → MULT261_IN_GA(T148, T150)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)
MULT229_IN_GA(x1, x2)  =  MULT229_IN_GA(x1)
MULT261_IN_GA(x1, x2)  =  MULT261_IN_GA(x1)

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

(28) UsableRulesProof (EQUIVALENT transformation)

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

(29) Obligation:

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

MULT229_IN_GA(T148, s(s(s(s(s(T150)))))) → MULT261_IN_GA(T148, T150)
MULT261_IN_GA(s(T145), T147) → MULT229_IN_GA(T145, T147)
MULT229_IN_GA(s(T145), s(s(s(s(T147))))) → MULT229_IN_GA(T145, T147)
MULT261_IN_GA(T148, s(T150)) → MULT261_IN_GA(T148, T150)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT229_IN_GA(x1, x2)  =  MULT229_IN_GA(x1)
MULT261_IN_GA(x1, x2)  =  MULT261_IN_GA(x1)

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

(30) PiDPToQDPProof (SOUND transformation)

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

(31) Obligation:

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

MULT229_IN_GA(T148) → MULT261_IN_GA(T148)
MULT261_IN_GA(s(T145)) → MULT229_IN_GA(T145)
MULT229_IN_GA(s(T145)) → MULT229_IN_GA(T145)
MULT261_IN_GA(T148) → MULT261_IN_GA(T148)

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

(32) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT229_IN_GA(T148) → MULT261_IN_GA(T148)
MULT261_IN_GA(s(T145)) → MULT229_IN_GA(T145)
MULT229_IN_GA(s(T145)) → MULT229_IN_GA(T145)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT229_IN_GA(x₁)) = 2 + x₁   
POL(MULT261_IN_GA(x₁)) = 1 + x₁   
POL(s(x₁)) = 2 + 2·x₁   

(33) Obligation:

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

MULT261_IN_GA(T148) → MULT261_IN_GA(T148)

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

(34) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT261_IN_GA(T148) evaluates to t =MULT261_IN_GA(T148)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT261_IN_GA(T148) to MULT261_IN_GA(T148).

(35) FALSE

(36) Obligation:

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

MULT166_IN_GA(T114, s(s(s(s(T116))))) → MULT190_IN_GA(T114, T116)
MULT190_IN_GA(s(T111), T113) → MULT166_IN_GA(T111, T113)
MULT166_IN_GA(s(T111), s(s(s(T113)))) → MULT166_IN_GA(T111, T113)
MULT190_IN_GA(T114, s(T116)) → MULT190_IN_GA(T114, T116)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)
MULT166_IN_GA(x1, x2)  =  MULT166_IN_GA(x1)
MULT190_IN_GA(x1, x2)  =  MULT190_IN_GA(x1)

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

(37) UsableRulesProof (EQUIVALENT transformation)

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

(38) Obligation:

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

MULT166_IN_GA(T114, s(s(s(s(T116))))) → MULT190_IN_GA(T114, T116)
MULT190_IN_GA(s(T111), T113) → MULT166_IN_GA(T111, T113)
MULT166_IN_GA(s(T111), s(s(s(T113)))) → MULT166_IN_GA(T111, T113)
MULT190_IN_GA(T114, s(T116)) → MULT190_IN_GA(T114, T116)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT166_IN_GA(x1, x2)  =  MULT166_IN_GA(x1)
MULT190_IN_GA(x1, x2)  =  MULT190_IN_GA(x1)

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

(39) PiDPToQDPProof (SOUND transformation)

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

(40) Obligation:

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

MULT166_IN_GA(T114) → MULT190_IN_GA(T114)
MULT190_IN_GA(s(T111)) → MULT166_IN_GA(T111)
MULT166_IN_GA(s(T111)) → MULT166_IN_GA(T111)
MULT190_IN_GA(T114) → MULT190_IN_GA(T114)

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

(41) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT166_IN_GA(T114) → MULT190_IN_GA(T114)
MULT190_IN_GA(s(T111)) → MULT166_IN_GA(T111)
MULT166_IN_GA(s(T111)) → MULT166_IN_GA(T111)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT166_IN_GA(x₁)) = 2 + x₁   
POL(MULT190_IN_GA(x₁)) = 1 + x₁   
POL(s(x₁)) = 2 + 2·x₁   

(42) Obligation:

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

MULT190_IN_GA(T114) → MULT190_IN_GA(T114)

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

(43) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT190_IN_GA(T114) evaluates to t =MULT190_IN_GA(T114)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT190_IN_GA(T114) to MULT190_IN_GA(T114).

(44) FALSE

(45) Obligation:

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

MULT111_IN_GA(T83, s(s(s(T85)))) → MULT127_IN_GA(T83, T85)
MULT127_IN_GA(s(T80), T82) → MULT111_IN_GA(T80, T82)
MULT111_IN_GA(s(T80), s(s(T82))) → MULT111_IN_GA(T80, T82)
MULT127_IN_GA(T83, s(T85)) → MULT127_IN_GA(T83, T85)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)
MULT111_IN_GA(x1, x2)  =  MULT111_IN_GA(x1)
MULT127_IN_GA(x1, x2)  =  MULT127_IN_GA(x1)

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

(46) UsableRulesProof (EQUIVALENT transformation)

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

(47) Obligation:

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

MULT111_IN_GA(T83, s(s(s(T85)))) → MULT127_IN_GA(T83, T85)
MULT127_IN_GA(s(T80), T82) → MULT111_IN_GA(T80, T82)
MULT111_IN_GA(s(T80), s(s(T82))) → MULT111_IN_GA(T80, T82)
MULT127_IN_GA(T83, s(T85)) → MULT127_IN_GA(T83, T85)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT111_IN_GA(x1, x2)  =  MULT111_IN_GA(x1)
MULT127_IN_GA(x1, x2)  =  MULT127_IN_GA(x1)

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

(48) PiDPToQDPProof (SOUND transformation)

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

(49) Obligation:

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

MULT111_IN_GA(T83) → MULT127_IN_GA(T83)
MULT127_IN_GA(s(T80)) → MULT111_IN_GA(T80)
MULT111_IN_GA(s(T80)) → MULT111_IN_GA(T80)
MULT127_IN_GA(T83) → MULT127_IN_GA(T83)

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

(50) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT111_IN_GA(T83) → MULT127_IN_GA(T83)
MULT127_IN_GA(s(T80)) → MULT111_IN_GA(T80)
MULT111_IN_GA(s(T80)) → MULT111_IN_GA(T80)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT111_IN_GA(x₁)) = 2 + x₁   
POL(MULT127_IN_GA(x₁)) = 1 + x₁   
POL(s(x₁)) = 2 + 2·x₁   

(51) Obligation:

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

MULT127_IN_GA(T83) → MULT127_IN_GA(T83)

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

(52) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT127_IN_GA(T83) evaluates to t =MULT127_IN_GA(T83)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT127_IN_GA(T83) to MULT127_IN_GA(T83).

(53) FALSE

(54) Obligation:

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

MULT64_IN_GA(T55, s(s(T57))) → MULT72_IN_GA(T55, T57)
MULT72_IN_GA(s(T52), T54) → MULT64_IN_GA(T52, T54)
MULT64_IN_GA(s(T52), s(T54)) → MULT64_IN_GA(T52, T54)
MULT72_IN_GA(T55, s(T57)) → MULT72_IN_GA(T55, T57)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)
MULT64_IN_GA(x1, x2)  =  MULT64_IN_GA(x1)
MULT72_IN_GA(x1, x2)  =  MULT72_IN_GA(x1)

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

(55) UsableRulesProof (EQUIVALENT transformation)

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

(56) Obligation:

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

MULT64_IN_GA(T55, s(s(T57))) → MULT72_IN_GA(T55, T57)
MULT72_IN_GA(s(T52), T54) → MULT64_IN_GA(T52, T54)
MULT64_IN_GA(s(T52), s(T54)) → MULT64_IN_GA(T52, T54)
MULT72_IN_GA(T55, s(T57)) → MULT72_IN_GA(T55, T57)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT64_IN_GA(x1, x2)  =  MULT64_IN_GA(x1)
MULT72_IN_GA(x1, x2)  =  MULT72_IN_GA(x1)

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

(57) PiDPToQDPProof (SOUND transformation)

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

(58) Obligation:

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

MULT64_IN_GA(T55) → MULT72_IN_GA(T55)
MULT72_IN_GA(s(T52)) → MULT64_IN_GA(T52)
MULT64_IN_GA(s(T52)) → MULT64_IN_GA(T52)
MULT72_IN_GA(T55) → MULT72_IN_GA(T55)

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

(59) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT64_IN_GA(T55) → MULT72_IN_GA(T55)
MULT72_IN_GA(s(T52)) → MULT64_IN_GA(T52)
MULT64_IN_GA(s(T52)) → MULT64_IN_GA(T52)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT64_IN_GA(x₁)) = 2 + x₁   
POL(MULT72_IN_GA(x₁)) = 1 + x₁   
POL(s(x₁)) = 2 + 2·x₁   

(60) Obligation:

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

MULT72_IN_GA(T55) → MULT72_IN_GA(T55)

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

(61) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT72_IN_GA(T55) evaluates to t =MULT72_IN_GA(T55)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT72_IN_GA(T55) to MULT72_IN_GA(T55).

(62) FALSE

(63) Obligation:

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

MULT25_IN_GA(T30, s(T32)) → MULT25_IN_GA(T30, T32)
MULT25_IN_GA(s(T27), T29) → MULT25_IN_GA(T27, T29)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)
MULT25_IN_GA(x1, x2)  =  MULT25_IN_GA(x1)

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

(64) UsableRulesProof (EQUIVALENT transformation)

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

(65) Obligation:

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

MULT25_IN_GA(T30, s(T32)) → MULT25_IN_GA(T30, T32)
MULT25_IN_GA(s(T27), T29) → MULT25_IN_GA(T27, T29)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT25_IN_GA(x1, x2)  =  MULT25_IN_GA(x1)

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

(66) PiDPToQDPProof (SOUND transformation)

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

(67) Obligation:

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

MULT25_IN_GA(T30) → MULT25_IN_GA(T30)
MULT25_IN_GA(s(T27)) → MULT25_IN_GA(T27)

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

(68) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT25_IN_GA(s(T27)) → MULT25_IN_GA(T27)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT25_IN_GA(x₁)) = 2·x₁   
POL(s(x₁)) = 2·x₁   

(69) Obligation:

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

MULT25_IN_GA(T30) → MULT25_IN_GA(T30)

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

(70) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT25_IN_GA(T30) evaluates to t =MULT25_IN_GA(T30)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT25_IN_GA(T30) to MULT25_IN_GA(T30).

(71) FALSE

(72) Obligation:

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

MULT3_IN_GAA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(s(T238), T239, 0, T241) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(T242, T243, 0, s(T246)) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(T248, T249, s(T251)) → MULT3_IN_GAA(T248, T249, T251)
MULT456_IN_GAAA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAAA(T242, T243, T247, T246)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)
MULT14_IN_GAA(x1, x2, x3)  =  MULT14_IN_GAA(x1)
MULT3_IN_GAA(x1, x2, x3)  =  MULT3_IN_GAA(x1)
MULT456_IN_GAAA(x1, x2, x3, x4)  =  MULT456_IN_GAAA(x1)

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

(73) UsableRulesProof (EQUIVALENT transformation)

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

(74) Obligation:

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

MULT3_IN_GAA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(s(T238), T239, 0, T241) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(T242, T243, 0, s(T246)) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(T248, T249, s(T251)) → MULT3_IN_GAA(T248, T249, T251)
MULT456_IN_GAAA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAAA(T242, T243, T247, T246)

R is empty.
The argument filtering Pi contains the following mapping:
0  =  0
s(x1)  =  s(x1)
MULT14_IN_GAA(x1, x2, x3)  =  MULT14_IN_GAA(x1)
MULT3_IN_GAA(x1, x2, x3)  =  MULT3_IN_GAA(x1)
MULT456_IN_GAAA(x1, x2, x3, x4)  =  MULT456_IN_GAAA(x1)

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

(75) PiDPToQDPProof (SOUND transformation)

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

(76) Obligation:

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

MULT3_IN_GAA(s(s(T238))) → MULT14_IN_GAA(T238)
MULT14_IN_GAA(s(T238)) → MULT14_IN_GAA(T238)
MULT14_IN_GAA(T242) → MULT3_IN_GAA(T242)
MULT3_IN_GAA(s(T242)) → MULT3_IN_GAA(T242)
MULT3_IN_GAA(s(T242)) → MULT456_IN_GAAA(T242)
MULT456_IN_GAAA(s(T238)) → MULT14_IN_GAA(T238)
MULT14_IN_GAA(T242) → MULT456_IN_GAAA(T242)
MULT456_IN_GAAA(T242) → MULT3_IN_GAA(T242)
MULT3_IN_GAA(T248) → MULT3_IN_GAA(T248)
MULT456_IN_GAAA(T242) → MULT456_IN_GAAA(T242)

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

(77) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT3_IN_GAA(s(s(T238))) → MULT14_IN_GAA(T238)
MULT14_IN_GAA(s(T238)) → MULT14_IN_GAA(T238)
MULT14_IN_GAA(T242) → MULT3_IN_GAA(T242)
MULT3_IN_GAA(s(T242)) → MULT3_IN_GAA(T242)
MULT3_IN_GAA(s(T242)) → MULT456_IN_GAAA(T242)
MULT456_IN_GAAA(s(T238)) → MULT14_IN_GAA(T238)
MULT14_IN_GAA(T242) → MULT456_IN_GAAA(T242)
MULT456_IN_GAAA(T242) → MULT3_IN_GAA(T242)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT14_IN_GAA(x₁)) = 2 + 2·x₁   
POL(MULT3_IN_GAA(x₁)) = x₁   
POL(MULT456_IN_GAAA(x₁)) = 1 + 2·x₁   
POL(s(x₁)) = 2 + 2·x₁   

(78) Obligation:

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

MULT3_IN_GAA(T248) → MULT3_IN_GAA(T248)
MULT456_IN_GAAA(T242) → MULT456_IN_GAAA(T242)

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

(79) DependencyGraphProof (EQUIVALENT transformation)

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

(80) Complex Obligation (AND)

(81) Obligation:

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

MULT456_IN_GAAA(T242) → MULT456_IN_GAAA(T242)

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

(82) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT456_IN_GAAA(T242) evaluates to t =MULT456_IN_GAAA(T242)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT456_IN_GAAA(T242) to MULT456_IN_GAAA(T242).

(83) FALSE

(84) Obligation:

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

MULT3_IN_GAA(T248) → MULT3_IN_GAA(T248)

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

(85) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT3_IN_GAA(T248) evaluates to t =MULT3_IN_GAA(T248)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT3_IN_GAA(T248) to MULT3_IN_GAA(T248).

(86) FALSE

(87) Obligation:

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

MULT456_IN_GAGA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAGA(T242, T243, T247, T246)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)
MULT456_IN_GAGA(x1, x2, x3, x4)  =  MULT456_IN_GAGA(x1, x3)

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

(88) UsableRulesProof (EQUIVALENT transformation)

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

(89) Obligation:

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

MULT456_IN_GAGA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAGA(T242, T243, T247, T246)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT456_IN_GAGA(x1, x2, x3, x4)  =  MULT456_IN_GAGA(x1, x3)

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

(90) PiDPToQDPProof (SOUND transformation)

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

(91) Obligation:

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

MULT456_IN_GAGA(T242, s(T247)) → MULT456_IN_GAGA(T242, T247)

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

(92) 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:

• MULT456_IN_GAGA(T242, s(T247)) → MULT456_IN_GAGA(T242, T247)
  The graph contains the following edges 1 >= 1, 2 > 2

(93) TRUE

(94) Obligation:

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

MULT3_IN_GGA(T248, T249, s(T251)) → MULT3_IN_GGA(T248, T249, T251)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x2)
U1_ga(x1, x2, x3)  =  U1_ga(x3)
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U80_gga(x1, x2, x3)  =  U80_gga(x3)
U81_gga(x1, x2, x3)  =  U81_gga(x3)
U82_gga(x1, x2, x3)  =  U82_gga(x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x2)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x2)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
U83_gga(x1, x2, x3)  =  U83_gga(x3)
U84_gga(x1, x2, x3)  =  U84_gga(x3)
U85_gga(x1, x2, x3)  =  U85_gga(x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x2)
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x2)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U86_gga(x1, x2, x3)  =  U86_gga(x3)
U87_gga(x1, x2, x3)  =  U87_gga(x3)
U88_gga(x1, x2, x3)  =  U88_gga(x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x2)
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x2)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
U14_ga(x1, x2, x3)  =  U14_ga(x3)
U89_gga(x1, x2, x3)  =  U89_gga(x3)
U90_gga(x1, x2, x3)  =  U90_gga(x3)
U91_gga(x1, x2, x3)  =  U91_gga(x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x2)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x2)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
U92_gga(x1, x2, x3)  =  U92_gga(x3)
U93_gga(x1, x2, x3)  =  U93_gga(x3)
U94_gga(x1, x2, x3)  =  U94_gga(x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x2)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U95_gga(x1, x2, x3)  =  U95_gga(x3)
U96_gga(x1, x2, x3)  =  U96_gga(x3)
U97_gga(x1, x2, x3)  =  U97_gga(x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x2)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x2)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U98_gga(x1, x2, x3)  =  U98_gga(x3)
U99_gga(x1, x2, x3)  =  U99_gga(x3)
U100_gga(x1, x2, x3)  =  U100_gga(x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x4)
U101_gga(x1, x2, x3)  =  U101_gga(x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x3)
U51_gga(x1, x2, x3)  =  U51_gga(x3)
U52_gga(x1, x2, x3)  =  U52_gga(x3)
U53_gga(x1, x2, x3)  =  U53_gga(x3)
U54_gga(x1, x2, x3)  =  U54_gga(x3)
U55_gga(x1, x2, x3)  =  U55_gga(x3)
U56_gga(x1, x2, x3)  =  U56_gga(x3)
U57_gga(x1, x2, x3)  =  U57_gga(x3)
U58_gga(x1, x2, x3)  =  U58_gga(x3)
U59_gga(x1, x2, x3)  =  U59_gga(x3)
U60_gga(x1, x2, x3)  =  U60_gga(x3)
U61_gga(x1, x2, x3)  =  U61_gga(x3)
U62_gga(x1, x2, x3)  =  U62_gga(x3)
U63_gga(x1, x2, x3)  =  U63_gga(x3)
U64_gga(x1, x2, x3)  =  U64_gga(x3)
U65_gga(x1, x2, x3)  =  U65_gga(x3)
U66_gga(x1, x2, x3)  =  U66_gga(x3)
U67_gga(x1, x2, x3)  =  U67_gga(x3)
U68_gga(x1, x2, x3)  =  U68_gga(x3)
U69_gga(x1, x2, x3)  =  U69_gga(x3)
U70_gga(x1, x2, x3)  =  U70_gga(x3)
U71_gga(x1, x2, x3)  =  U71_gga(x3)
U72_gga(x1, x2, x3)  =  U72_gga(x3)
U73_gga(x1, x2, x3)  =  U73_gga(x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x4)
MULT3_IN_GGA(x1, x2, x3)  =  MULT3_IN_GGA(x1, x2)

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

(95) UsableRulesProof (EQUIVALENT transformation)

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

(96) Obligation:

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

MULT3_IN_GGA(T248, T249, s(T251)) → MULT3_IN_GGA(T248, T249, T251)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT3_IN_GGA(x1, x2, x3)  =  MULT3_IN_GGA(x1, x2)

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

(97) PiDPToQDPProof (SOUND transformation)

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

(98) Obligation:

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

MULT3_IN_GGA(T248, T249) → MULT3_IN_GGA(T248, T249)

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

(99) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT3_IN_GGA(T248, T249) evaluates to t =MULT3_IN_GGA(T248, T249)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT3_IN_GGA(T248, T249) to MULT3_IN_GGA(T248, T249).

(100) FALSE

(101) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
times1_in: (b,b,f)
mult25_in: (b,f)
mult64_in: (b,f)
mult72_in: (b,f)
mult111_in: (b,f)
mult127_in: (b,f)
mult166_in: (b,f)
mult190_in: (b,f)
mult229_in: (b,f)
mult261_in: (b,f)
mult300_in: (b,f)
mult340_in: (b,f)
mult379_in: (b,f)
mult427_in: (b,f)
mult14_in: (b,f,f)
mult3_in: (b,f,f) (b,b,f)
mult456_in: (b,f,f,f) (b,f,b,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(102) Obligation:

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

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)

(103) 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:

TIMES1_IN_GGA(s(s(s(T27))), 0, T29) → U79_GGA(T27, T29, mult25_in_ga(T27, T29))
TIMES1_IN_GGA(s(s(s(T27))), 0, T29) → MULT25_IN_GA(T27, T29)
MULT25_IN_GA(s(T27), T29) → U1_GA(T27, T29, mult25_in_ga(T27, T29))
MULT25_IN_GA(s(T27), T29) → MULT25_IN_GA(T27, T29)
MULT25_IN_GA(T30, s(T32)) → U2_GA(T30, T32, mult25_in_ga(T30, T32))
MULT25_IN_GA(T30, s(T32)) → MULT25_IN_GA(T30, T32)
TIMES1_IN_GGA(s(s(T30)), 0, s(T32)) → U80_GGA(T30, T32, mult25_in_ga(T30, T32))
TIMES1_IN_GGA(s(s(T30)), 0, s(T32)) → MULT25_IN_GA(T30, T32)
TIMES1_IN_GGA(s(T33), 0, s(T36)) → U81_GGA(T33, T36, mult25_in_ga(T33, T36))
TIMES1_IN_GGA(s(T33), 0, s(T36)) → MULT25_IN_GA(T33, T36)
TIMES1_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → U82_GGA(T52, T54, mult64_in_ga(T52, T54))
TIMES1_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT64_IN_GA(s(T52), s(T54)) → U3_GA(T52, T54, mult64_in_ga(T52, T54))
MULT64_IN_GA(s(T52), s(T54)) → MULT64_IN_GA(T52, T54)
MULT64_IN_GA(T55, s(s(T57))) → U4_GA(T55, T57, mult72_in_ga(T55, T57))
MULT64_IN_GA(T55, s(s(T57))) → MULT72_IN_GA(T55, T57)
MULT72_IN_GA(s(T52), T54) → U5_GA(T52, T54, mult64_in_ga(T52, T54))
MULT72_IN_GA(s(T52), T54) → MULT64_IN_GA(T52, T54)
MULT72_IN_GA(T55, s(T57)) → U6_GA(T55, T57, mult72_in_ga(T55, T57))
MULT72_IN_GA(T55, s(T57)) → MULT72_IN_GA(T55, T57)
TIMES1_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → U83_GGA(T55, T57, mult72_in_ga(T55, T57))
TIMES1_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
TIMES1_IN_GGA(s(T58), s(0), s(s(T61))) → U84_GGA(T58, T61, mult72_in_ga(T58, T61))
TIMES1_IN_GGA(s(T58), s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
TIMES1_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_GGA(T80, T82, mult111_in_ga(T80, T82))
TIMES1_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT111_IN_GA(s(T80), s(s(T82))) → U7_GA(T80, T82, mult111_in_ga(T80, T82))
MULT111_IN_GA(s(T80), s(s(T82))) → MULT111_IN_GA(T80, T82)
MULT111_IN_GA(T83, s(s(s(T85)))) → U8_GA(T83, T85, mult127_in_ga(T83, T85))
MULT111_IN_GA(T83, s(s(s(T85)))) → MULT127_IN_GA(T83, T85)
MULT127_IN_GA(s(T80), T82) → U9_GA(T80, T82, mult111_in_ga(T80, T82))
MULT127_IN_GA(s(T80), T82) → MULT111_IN_GA(T80, T82)
MULT127_IN_GA(T83, s(T85)) → U10_GA(T83, T85, mult127_in_ga(T83, T85))
MULT127_IN_GA(T83, s(T85)) → MULT127_IN_GA(T83, T85)
TIMES1_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_GGA(T83, T85, mult127_in_ga(T83, T85))
TIMES1_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
TIMES1_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → U87_GGA(T86, T89, mult127_in_ga(T86, T89))
TIMES1_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
TIMES1_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_GGA(T111, T113, mult166_in_ga(T111, T113))
TIMES1_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT166_IN_GA(s(T111), s(s(s(T113)))) → U11_GA(T111, T113, mult166_in_ga(T111, T113))
MULT166_IN_GA(s(T111), s(s(s(T113)))) → MULT166_IN_GA(T111, T113)
MULT166_IN_GA(T114, s(s(s(s(T116))))) → U12_GA(T114, T116, mult190_in_ga(T114, T116))
MULT166_IN_GA(T114, s(s(s(s(T116))))) → MULT190_IN_GA(T114, T116)
MULT190_IN_GA(s(T111), T113) → U13_GA(T111, T113, mult166_in_ga(T111, T113))
MULT190_IN_GA(s(T111), T113) → MULT166_IN_GA(T111, T113)
MULT190_IN_GA(T114, s(T116)) → U14_GA(T114, T116, mult190_in_ga(T114, T116))
MULT190_IN_GA(T114, s(T116)) → MULT190_IN_GA(T114, T116)
TIMES1_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_GGA(T114, T116, mult190_in_ga(T114, T116))
TIMES1_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
TIMES1_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_GGA(T117, T120, mult190_in_ga(T117, T120))
TIMES1_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
TIMES1_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_GGA(T145, T147, mult229_in_ga(T145, T147))
TIMES1_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT229_IN_GA(s(T145), s(s(s(s(T147))))) → U15_GA(T145, T147, mult229_in_ga(T145, T147))
MULT229_IN_GA(s(T145), s(s(s(s(T147))))) → MULT229_IN_GA(T145, T147)
MULT229_IN_GA(T148, s(s(s(s(s(T150)))))) → U16_GA(T148, T150, mult261_in_ga(T148, T150))
MULT229_IN_GA(T148, s(s(s(s(s(T150)))))) → MULT261_IN_GA(T148, T150)
MULT261_IN_GA(s(T145), T147) → U17_GA(T145, T147, mult229_in_ga(T145, T147))
MULT261_IN_GA(s(T145), T147) → MULT229_IN_GA(T145, T147)
MULT261_IN_GA(T148, s(T150)) → U18_GA(T148, T150, mult261_in_ga(T148, T150))
MULT261_IN_GA(T148, s(T150)) → MULT261_IN_GA(T148, T150)
TIMES1_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_GGA(T148, T150, mult261_in_ga(T148, T150))
TIMES1_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
TIMES1_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_GGA(T151, T154, mult261_in_ga(T151, T154))
TIMES1_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
TIMES1_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_GGA(T182, T184, mult300_in_ga(T182, T184))
TIMES1_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT300_IN_GA(s(T182), s(s(s(s(s(T184)))))) → U19_GA(T182, T184, mult300_in_ga(T182, T184))
MULT300_IN_GA(s(T182), s(s(s(s(s(T184)))))) → MULT300_IN_GA(T182, T184)
MULT300_IN_GA(T185, s(s(s(s(s(s(T187))))))) → U20_GA(T185, T187, mult340_in_ga(T185, T187))
MULT300_IN_GA(T185, s(s(s(s(s(s(T187))))))) → MULT340_IN_GA(T185, T187)
MULT340_IN_GA(s(T182), T184) → U21_GA(T182, T184, mult300_in_ga(T182, T184))
MULT340_IN_GA(s(T182), T184) → MULT300_IN_GA(T182, T184)
MULT340_IN_GA(T185, s(T187)) → U22_GA(T185, T187, mult340_in_ga(T185, T187))
MULT340_IN_GA(T185, s(T187)) → MULT340_IN_GA(T185, T187)
TIMES1_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_GGA(T185, T187, mult340_in_ga(T185, T187))
TIMES1_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
TIMES1_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_GGA(T188, T191, mult340_in_ga(T188, T191))
TIMES1_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
TIMES1_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_GGA(T222, T224, mult379_in_ga(T222, T224))
TIMES1_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT379_IN_GA(s(T222), s(s(s(s(s(s(T224))))))) → U23_GA(T222, T224, mult379_in_ga(T222, T224))
MULT379_IN_GA(s(T222), s(s(s(s(s(s(T224))))))) → MULT379_IN_GA(T222, T224)
MULT379_IN_GA(T225, s(s(s(s(s(s(s(T227)))))))) → U24_GA(T225, T227, mult427_in_ga(T225, T227))
MULT379_IN_GA(T225, s(s(s(s(s(s(s(T227)))))))) → MULT427_IN_GA(T225, T227)
MULT427_IN_GA(s(T222), T224) → U25_GA(T222, T224, mult379_in_ga(T222, T224))
MULT427_IN_GA(s(T222), T224) → MULT379_IN_GA(T222, T224)
MULT427_IN_GA(T225, s(T227)) → U26_GA(T225, T227, mult427_in_ga(T225, T227))
MULT427_IN_GA(T225, s(T227)) → MULT427_IN_GA(T225, T227)
TIMES1_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_GGA(T225, T227, mult427_in_ga(T225, T227))
TIMES1_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
TIMES1_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_GGA(T228, T231, mult427_in_ga(T228, T231))
TIMES1_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
TIMES1_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_GGA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
TIMES1_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(s(s(T27)), 0, T29) → U27_GAA(T27, T29, mult25_in_ga(T27, T29))
MULT14_IN_GAA(s(s(T27)), 0, T29) → MULT25_IN_GA(T27, T29)
MULT14_IN_GAA(s(T30), 0, s(T32)) → U28_GAA(T30, T32, mult25_in_ga(T30, T32))
MULT14_IN_GAA(s(T30), 0, s(T32)) → MULT25_IN_GA(T30, T32)
MULT14_IN_GAA(T33, 0, s(T36)) → U29_GAA(T33, T36, mult25_in_ga(T33, T36))
MULT14_IN_GAA(T33, 0, s(T36)) → MULT25_IN_GA(T33, T36)
MULT14_IN_GAA(s(s(T52)), s(0), s(s(T54))) → U30_GAA(T52, T54, mult64_in_ga(T52, T54))
MULT14_IN_GAA(s(s(T52)), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT14_IN_GAA(s(T55), s(0), s(s(s(T57)))) → U31_GAA(T55, T57, mult72_in_ga(T55, T57))
MULT14_IN_GAA(s(T55), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
MULT14_IN_GAA(T58, s(0), s(s(T61))) → U32_GAA(T58, T61, mult72_in_ga(T58, T61))
MULT14_IN_GAA(T58, s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
MULT14_IN_GAA(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_GAA(T80, T82, mult111_in_ga(T80, T82))
MULT14_IN_GAA(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT14_IN_GAA(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_GAA(T83, T85, mult127_in_ga(T83, T85))
MULT14_IN_GAA(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
MULT14_IN_GAA(T86, s(s(0)), s(s(s(T89)))) → U35_GAA(T86, T89, mult127_in_ga(T86, T89))
MULT14_IN_GAA(T86, s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
MULT14_IN_GAA(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_GAA(T111, T113, mult166_in_ga(T111, T113))
MULT14_IN_GAA(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT14_IN_GAA(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_GAA(T114, T116, mult190_in_ga(T114, T116))
MULT14_IN_GAA(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
MULT14_IN_GAA(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_GAA(T117, T120, mult190_in_ga(T117, T120))
MULT14_IN_GAA(T117, s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
MULT14_IN_GAA(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_GAA(T145, T147, mult229_in_ga(T145, T147))
MULT14_IN_GAA(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT14_IN_GAA(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_GAA(T148, T150, mult261_in_ga(T148, T150))
MULT14_IN_GAA(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
MULT14_IN_GAA(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_GAA(T151, T154, mult261_in_ga(T151, T154))
MULT14_IN_GAA(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
MULT14_IN_GAA(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_GAA(T182, T184, mult300_in_ga(T182, T184))
MULT14_IN_GAA(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT14_IN_GAA(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_GAA(T185, T187, mult340_in_ga(T185, T187))
MULT14_IN_GAA(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
MULT14_IN_GAA(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_GAA(T188, T191, mult340_in_ga(T188, T191))
MULT14_IN_GAA(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
MULT14_IN_GAA(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_GAA(T222, T224, mult379_in_ga(T222, T224))
MULT14_IN_GAA(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT14_IN_GAA(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_GAA(T225, T227, mult427_in_ga(T225, T227))
MULT14_IN_GAA(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
MULT14_IN_GAA(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_GAA(T228, T231, mult427_in_ga(T228, T231))
MULT14_IN_GAA(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
MULT14_IN_GAA(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_GAA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
MULT14_IN_GAA(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_GAA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(s(s(T27))), 0, T29) → U51_GAA(T27, T29, mult25_in_ga(T27, T29))
MULT3_IN_GAA(s(s(s(T27))), 0, T29) → MULT25_IN_GA(T27, T29)
MULT3_IN_GAA(s(s(T30)), 0, s(T32)) → U52_GAA(T30, T32, mult25_in_ga(T30, T32))
MULT3_IN_GAA(s(s(T30)), 0, s(T32)) → MULT25_IN_GA(T30, T32)
MULT3_IN_GAA(s(T33), 0, s(T36)) → U53_GAA(T33, T36, mult25_in_ga(T33, T36))
MULT3_IN_GAA(s(T33), 0, s(T36)) → MULT25_IN_GA(T33, T36)
MULT3_IN_GAA(s(s(s(T52))), s(0), s(s(T54))) → U54_GAA(T52, T54, mult64_in_ga(T52, T54))
MULT3_IN_GAA(s(s(s(T52))), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT3_IN_GAA(s(s(T55)), s(0), s(s(s(T57)))) → U55_GAA(T55, T57, mult72_in_ga(T55, T57))
MULT3_IN_GAA(s(s(T55)), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
MULT3_IN_GAA(s(T58), s(0), s(s(T61))) → U56_GAA(T58, T61, mult72_in_ga(T58, T61))
MULT3_IN_GAA(s(T58), s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
MULT3_IN_GAA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_GAA(T80, T82, mult111_in_ga(T80, T82))
MULT3_IN_GAA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT3_IN_GAA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_GAA(T83, T85, mult127_in_ga(T83, T85))
MULT3_IN_GAA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
MULT3_IN_GAA(s(T86), s(s(0)), s(s(s(T89)))) → U59_GAA(T86, T89, mult127_in_ga(T86, T89))
MULT3_IN_GAA(s(T86), s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
MULT3_IN_GAA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_GAA(T111, T113, mult166_in_ga(T111, T113))
MULT3_IN_GAA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT3_IN_GAA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_GAA(T114, T116, mult190_in_ga(T114, T116))
MULT3_IN_GAA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
MULT3_IN_GAA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_GAA(T117, T120, mult190_in_ga(T117, T120))
MULT3_IN_GAA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
MULT3_IN_GAA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_GAA(T145, T147, mult229_in_ga(T145, T147))
MULT3_IN_GAA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT3_IN_GAA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_GAA(T148, T150, mult261_in_ga(T148, T150))
MULT3_IN_GAA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
MULT3_IN_GAA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_GAA(T151, T154, mult261_in_ga(T151, T154))
MULT3_IN_GAA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
MULT3_IN_GAA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_GAA(T182, T184, mult300_in_ga(T182, T184))
MULT3_IN_GAA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT3_IN_GAA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_GAA(T185, T187, mult340_in_ga(T185, T187))
MULT3_IN_GAA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
MULT3_IN_GAA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_GAA(T188, T191, mult340_in_ga(T188, T191))
MULT3_IN_GAA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
MULT3_IN_GAA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_GAA(T222, T224, mult379_in_ga(T222, T224))
MULT3_IN_GAA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT3_IN_GAA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_GAA(T225, T227, mult427_in_ga(T225, T227))
MULT3_IN_GAA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
MULT3_IN_GAA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_GAA(T228, T231, mult427_in_ga(T228, T231))
MULT3_IN_GAA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
MULT3_IN_GAA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_GAA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
MULT3_IN_GAA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_GAA(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(s(T238), T239, 0, T241) → U76_GAAA(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
MULT456_IN_GAAA(s(T238), T239, 0, T241) → MULT14_IN_GAA(T238, s(T239), T241)
MULT456_IN_GAAA(T242, T243, 0, s(T246)) → U77_GAAA(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
MULT456_IN_GAAA(T242, T243, 0, s(T246)) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_GAA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_GAA(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(T242, T243, s(T247), s(T246)) → U78_GAAA(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
MULT456_IN_GAAA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT3_IN_GAA(T248, T249, s(T251)) → U75_GAA(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
MULT3_IN_GAA(T248, T249, s(T251)) → MULT3_IN_GAA(T248, T249, T251)
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_GGA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_GGA(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAGA(T242, T243, T247, T246)
MULT456_IN_GAGA(s(T238), T239, 0, T241) → U76_GAGA(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
MULT456_IN_GAGA(s(T238), T239, 0, T241) → MULT14_IN_GAA(T238, s(T239), T241)
MULT456_IN_GAGA(T242, T243, 0, s(T246)) → U77_GAGA(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
MULT456_IN_GAGA(T242, T243, 0, s(T246)) → MULT3_IN_GAA(T242, s(T243), T246)
MULT456_IN_GAGA(T242, T243, s(T247), s(T246)) → U78_GAGA(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
MULT456_IN_GAGA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAGA(T242, T243, T247, T246)
TIMES1_IN_GGA(T248, T249, s(T251)) → U103_GGA(T248, T249, T251, mult3_in_gga(T248, T249, T251))
TIMES1_IN_GGA(T248, T249, s(T251)) → MULT3_IN_GGA(T248, T249, T251)
MULT3_IN_GGA(s(s(s(T27))), 0, T29) → U51_GGA(T27, T29, mult25_in_ga(T27, T29))
MULT3_IN_GGA(s(s(s(T27))), 0, T29) → MULT25_IN_GA(T27, T29)
MULT3_IN_GGA(s(s(T30)), 0, s(T32)) → U52_GGA(T30, T32, mult25_in_ga(T30, T32))
MULT3_IN_GGA(s(s(T30)), 0, s(T32)) → MULT25_IN_GA(T30, T32)
MULT3_IN_GGA(s(T33), 0, s(T36)) → U53_GGA(T33, T36, mult25_in_ga(T33, T36))
MULT3_IN_GGA(s(T33), 0, s(T36)) → MULT25_IN_GA(T33, T36)
MULT3_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → U54_GGA(T52, T54, mult64_in_ga(T52, T54))
MULT3_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT3_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → U55_GGA(T55, T57, mult72_in_ga(T55, T57))
MULT3_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
MULT3_IN_GGA(s(T58), s(0), s(s(T61))) → U56_GGA(T58, T61, mult72_in_ga(T58, T61))
MULT3_IN_GGA(s(T58), s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
MULT3_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_GGA(T80, T82, mult111_in_ga(T80, T82))
MULT3_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT3_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_GGA(T83, T85, mult127_in_ga(T83, T85))
MULT3_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
MULT3_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → U59_GGA(T86, T89, mult127_in_ga(T86, T89))
MULT3_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
MULT3_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_GGA(T111, T113, mult166_in_ga(T111, T113))
MULT3_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT3_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_GGA(T114, T116, mult190_in_ga(T114, T116))
MULT3_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
MULT3_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_GGA(T117, T120, mult190_in_ga(T117, T120))
MULT3_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
MULT3_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_GGA(T145, T147, mult229_in_ga(T145, T147))
MULT3_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT3_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_GGA(T148, T150, mult261_in_ga(T148, T150))
MULT3_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
MULT3_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_GGA(T151, T154, mult261_in_ga(T151, T154))
MULT3_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
MULT3_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_GGA(T182, T184, mult300_in_ga(T182, T184))
MULT3_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT3_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_GGA(T185, T187, mult340_in_ga(T185, T187))
MULT3_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
MULT3_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_GGA(T188, T191, mult340_in_ga(T188, T191))
MULT3_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
MULT3_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_GGA(T222, T224, mult379_in_ga(T222, T224))
MULT3_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT3_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_GGA(T225, T227, mult427_in_ga(T225, T227))
MULT3_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
MULT3_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_GGA(T228, T231, mult427_in_ga(T228, T231))
MULT3_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
MULT3_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_GGA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
MULT3_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_GGA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_GGA(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAGA(T242, T243, T247, T246)
MULT3_IN_GGA(T248, T249, s(T251)) → U75_GGA(T248, T249, T251, mult3_in_gga(T248, T249, T251))
MULT3_IN_GGA(T248, T249, s(T251)) → MULT3_IN_GGA(T248, T249, T251)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)
TIMES1_IN_GGA(x1, x2, x3)  =  TIMES1_IN_GGA(x1, x2)
U79_GGA(x1, x2, x3)  =  U79_GGA(x1, x3)
MULT25_IN_GA(x1, x2)  =  MULT25_IN_GA(x1)
U1_GA(x1, x2, x3)  =  U1_GA(x1, x3)
U2_GA(x1, x2, x3)  =  U2_GA(x1, x3)
U80_GGA(x1, x2, x3)  =  U80_GGA(x1, x3)
U81_GGA(x1, x2, x3)  =  U81_GGA(x1, x3)
U82_GGA(x1, x2, x3)  =  U82_GGA(x1, x3)
MULT64_IN_GA(x1, x2)  =  MULT64_IN_GA(x1)
U3_GA(x1, x2, x3)  =  U3_GA(x1, x3)
U4_GA(x1, x2, x3)  =  U4_GA(x1, x3)
MULT72_IN_GA(x1, x2)  =  MULT72_IN_GA(x1)
U5_GA(x1, x2, x3)  =  U5_GA(x1, x3)
U6_GA(x1, x2, x3)  =  U6_GA(x1, x3)
U83_GGA(x1, x2, x3)  =  U83_GGA(x1, x3)
U84_GGA(x1, x2, x3)  =  U84_GGA(x1, x3)
U85_GGA(x1, x2, x3)  =  U85_GGA(x1, x3)
MULT111_IN_GA(x1, x2)  =  MULT111_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x1, x3)
U8_GA(x1, x2, x3)  =  U8_GA(x1, x3)
MULT127_IN_GA(x1, x2)  =  MULT127_IN_GA(x1)
U9_GA(x1, x2, x3)  =  U9_GA(x1, x3)
U10_GA(x1, x2, x3)  =  U10_GA(x1, x3)
U86_GGA(x1, x2, x3)  =  U86_GGA(x1, x3)
U87_GGA(x1, x2, x3)  =  U87_GGA(x1, x3)
U88_GGA(x1, x2, x3)  =  U88_GGA(x1, x3)
MULT166_IN_GA(x1, x2)  =  MULT166_IN_GA(x1)
U11_GA(x1, x2, x3)  =  U11_GA(x1, x3)
U12_GA(x1, x2, x3)  =  U12_GA(x1, x3)
MULT190_IN_GA(x1, x2)  =  MULT190_IN_GA(x1)
U13_GA(x1, x2, x3)  =  U13_GA(x1, x3)
U14_GA(x1, x2, x3)  =  U14_GA(x1, x3)
U89_GGA(x1, x2, x3)  =  U89_GGA(x1, x3)
U90_GGA(x1, x2, x3)  =  U90_GGA(x1, x3)
U91_GGA(x1, x2, x3)  =  U91_GGA(x1, x3)
MULT229_IN_GA(x1, x2)  =  MULT229_IN_GA(x1)
U15_GA(x1, x2, x3)  =  U15_GA(x1, x3)
U16_GA(x1, x2, x3)  =  U16_GA(x1, x3)
MULT261_IN_GA(x1, x2)  =  MULT261_IN_GA(x1)
U17_GA(x1, x2, x3)  =  U17_GA(x1, x3)
U18_GA(x1, x2, x3)  =  U18_GA(x1, x3)
U92_GGA(x1, x2, x3)  =  U92_GGA(x1, x3)
U93_GGA(x1, x2, x3)  =  U93_GGA(x1, x3)
U94_GGA(x1, x2, x3)  =  U94_GGA(x1, x3)
MULT300_IN_GA(x1, x2)  =  MULT300_IN_GA(x1)
U19_GA(x1, x2, x3)  =  U19_GA(x1, x3)
U20_GA(x1, x2, x3)  =  U20_GA(x1, x3)
MULT340_IN_GA(x1, x2)  =  MULT340_IN_GA(x1)
U21_GA(x1, x2, x3)  =  U21_GA(x1, x3)
U22_GA(x1, x2, x3)  =  U22_GA(x1, x3)
U95_GGA(x1, x2, x3)  =  U95_GGA(x1, x3)
U96_GGA(x1, x2, x3)  =  U96_GGA(x1, x3)
U97_GGA(x1, x2, x3)  =  U97_GGA(x1, x3)
MULT379_IN_GA(x1, x2)  =  MULT379_IN_GA(x1)
U23_GA(x1, x2, x3)  =  U23_GA(x1, x3)
U24_GA(x1, x2, x3)  =  U24_GA(x1, x3)
MULT427_IN_GA(x1, x2)  =  MULT427_IN_GA(x1)
U25_GA(x1, x2, x3)  =  U25_GA(x1, x3)
U26_GA(x1, x2, x3)  =  U26_GA(x1, x3)
U98_GGA(x1, x2, x3)  =  U98_GGA(x1, x3)
U99_GGA(x1, x2, x3)  =  U99_GGA(x1, x3)
U100_GGA(x1, x2, x3)  =  U100_GGA(x1, x3)
MULT14_IN_GAA(x1, x2, x3)  =  MULT14_IN_GAA(x1)
U27_GAA(x1, x2, x3)  =  U27_GAA(x1, x3)
U28_GAA(x1, x2, x3)  =  U28_GAA(x1, x3)
U29_GAA(x1, x2, x3)  =  U29_GAA(x1, x3)
U30_GAA(x1, x2, x3)  =  U30_GAA(x1, x3)
U31_GAA(x1, x2, x3)  =  U31_GAA(x1, x3)
U32_GAA(x1, x2, x3)  =  U32_GAA(x1, x3)
U33_GAA(x1, x2, x3)  =  U33_GAA(x1, x3)
U34_GAA(x1, x2, x3)  =  U34_GAA(x1, x3)
U35_GAA(x1, x2, x3)  =  U35_GAA(x1, x3)
U36_GAA(x1, x2, x3)  =  U36_GAA(x1, x3)
U37_GAA(x1, x2, x3)  =  U37_GAA(x1, x3)
U38_GAA(x1, x2, x3)  =  U38_GAA(x1, x3)
U39_GAA(x1, x2, x3)  =  U39_GAA(x1, x3)
U40_GAA(x1, x2, x3)  =  U40_GAA(x1, x3)
U41_GAA(x1, x2, x3)  =  U41_GAA(x1, x3)
U42_GAA(x1, x2, x3)  =  U42_GAA(x1, x3)
U43_GAA(x1, x2, x3)  =  U43_GAA(x1, x3)
U44_GAA(x1, x2, x3)  =  U44_GAA(x1, x3)
U45_GAA(x1, x2, x3)  =  U45_GAA(x1, x3)
U46_GAA(x1, x2, x3)  =  U46_GAA(x1, x3)
U47_GAA(x1, x2, x3)  =  U47_GAA(x1, x3)
U48_GAA(x1, x2, x3)  =  U48_GAA(x1, x3)
U49_GAA(x1, x2, x3)  =  U49_GAA(x1, x3)
MULT3_IN_GAA(x1, x2, x3)  =  MULT3_IN_GAA(x1)
U51_GAA(x1, x2, x3)  =  U51_GAA(x1, x3)
U52_GAA(x1, x2, x3)  =  U52_GAA(x1, x3)
U53_GAA(x1, x2, x3)  =  U53_GAA(x1, x3)
U54_GAA(x1, x2, x3)  =  U54_GAA(x1, x3)
U55_GAA(x1, x2, x3)  =  U55_GAA(x1, x3)
U56_GAA(x1, x2, x3)  =  U56_GAA(x1, x3)
U57_GAA(x1, x2, x3)  =  U57_GAA(x1, x3)
U58_GAA(x1, x2, x3)  =  U58_GAA(x1, x3)
U59_GAA(x1, x2, x3)  =  U59_GAA(x1, x3)
U60_GAA(x1, x2, x3)  =  U60_GAA(x1, x3)
U61_GAA(x1, x2, x3)  =  U61_GAA(x1, x3)
U62_GAA(x1, x2, x3)  =  U62_GAA(x1, x3)
U63_GAA(x1, x2, x3)  =  U63_GAA(x1, x3)
U64_GAA(x1, x2, x3)  =  U64_GAA(x1, x3)
U65_GAA(x1, x2, x3)  =  U65_GAA(x1, x3)
U66_GAA(x1, x2, x3)  =  U66_GAA(x1, x3)
U67_GAA(x1, x2, x3)  =  U67_GAA(x1, x3)
U68_GAA(x1, x2, x3)  =  U68_GAA(x1, x3)
U69_GAA(x1, x2, x3)  =  U69_GAA(x1, x3)
U70_GAA(x1, x2, x3)  =  U70_GAA(x1, x3)
U71_GAA(x1, x2, x3)  =  U71_GAA(x1, x3)
U72_GAA(x1, x2, x3)  =  U72_GAA(x1, x3)
U50_GAA(x1, x2, x3, x4)  =  U50_GAA(x1, x4)
MULT456_IN_GAAA(x1, x2, x3, x4)  =  MULT456_IN_GAAA(x1)
U76_GAAA(x1, x2, x3, x4)  =  U76_GAAA(x1, x4)
U77_GAAA(x1, x2, x3, x4)  =  U77_GAAA(x1, x4)
U73_GAA(x1, x2, x3)  =  U73_GAA(x1, x3)
U74_GAA(x1, x2, x3, x4)  =  U74_GAA(x1, x4)
U78_GAAA(x1, x2, x3, x4, x5)  =  U78_GAAA(x1, x5)
U75_GAA(x1, x2, x3, x4)  =  U75_GAA(x1, x4)
U101_GGA(x1, x2, x3)  =  U101_GGA(x1, x3)
U102_GGA(x1, x2, x3, x4)  =  U102_GGA(x1, x2, x4)
MULT456_IN_GAGA(x1, x2, x3, x4)  =  MULT456_IN_GAGA(x1, x3)
U76_GAGA(x1, x2, x3, x4)  =  U76_GAGA(x1, x4)
U77_GAGA(x1, x2, x3, x4)  =  U77_GAGA(x1, x4)
U78_GAGA(x1, x2, x3, x4, x5)  =  U78_GAGA(x1, x3, x5)
U103_GGA(x1, x2, x3, x4)  =  U103_GGA(x1, x2, x4)
MULT3_IN_GGA(x1, x2, x3)  =  MULT3_IN_GGA(x1, x2)
U51_GGA(x1, x2, x3)  =  U51_GGA(x1, x3)
U52_GGA(x1, x2, x3)  =  U52_GGA(x1, x3)
U53_GGA(x1, x2, x3)  =  U53_GGA(x1, x3)
U54_GGA(x1, x2, x3)  =  U54_GGA(x1, x3)
U55_GGA(x1, x2, x3)  =  U55_GGA(x1, x3)
U56_GGA(x1, x2, x3)  =  U56_GGA(x1, x3)
U57_GGA(x1, x2, x3)  =  U57_GGA(x1, x3)
U58_GGA(x1, x2, x3)  =  U58_GGA(x1, x3)
U59_GGA(x1, x2, x3)  =  U59_GGA(x1, x3)
U60_GGA(x1, x2, x3)  =  U60_GGA(x1, x3)
U61_GGA(x1, x2, x3)  =  U61_GGA(x1, x3)
U62_GGA(x1, x2, x3)  =  U62_GGA(x1, x3)
U63_GGA(x1, x2, x3)  =  U63_GGA(x1, x3)
U64_GGA(x1, x2, x3)  =  U64_GGA(x1, x3)
U65_GGA(x1, x2, x3)  =  U65_GGA(x1, x3)
U66_GGA(x1, x2, x3)  =  U66_GGA(x1, x3)
U67_GGA(x1, x2, x3)  =  U67_GGA(x1, x3)
U68_GGA(x1, x2, x3)  =  U68_GGA(x1, x3)
U69_GGA(x1, x2, x3)  =  U69_GGA(x1, x3)
U70_GGA(x1, x2, x3)  =  U70_GGA(x1, x3)
U71_GGA(x1, x2, x3)  =  U71_GGA(x1, x3)
U72_GGA(x1, x2, x3)  =  U72_GGA(x1, x3)
U73_GGA(x1, x2, x3)  =  U73_GGA(x1, x3)
U74_GGA(x1, x2, x3, x4)  =  U74_GGA(x1, x2, x4)
U75_GGA(x1, x2, x3, x4)  =  U75_GGA(x1, x2, x4)

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

(104) Obligation:

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

TIMES1_IN_GGA(s(s(s(T27))), 0, T29) → U79_GGA(T27, T29, mult25_in_ga(T27, T29))
TIMES1_IN_GGA(s(s(s(T27))), 0, T29) → MULT25_IN_GA(T27, T29)
MULT25_IN_GA(s(T27), T29) → U1_GA(T27, T29, mult25_in_ga(T27, T29))
MULT25_IN_GA(s(T27), T29) → MULT25_IN_GA(T27, T29)
MULT25_IN_GA(T30, s(T32)) → U2_GA(T30, T32, mult25_in_ga(T30, T32))
MULT25_IN_GA(T30, s(T32)) → MULT25_IN_GA(T30, T32)
TIMES1_IN_GGA(s(s(T30)), 0, s(T32)) → U80_GGA(T30, T32, mult25_in_ga(T30, T32))
TIMES1_IN_GGA(s(s(T30)), 0, s(T32)) → MULT25_IN_GA(T30, T32)
TIMES1_IN_GGA(s(T33), 0, s(T36)) → U81_GGA(T33, T36, mult25_in_ga(T33, T36))
TIMES1_IN_GGA(s(T33), 0, s(T36)) → MULT25_IN_GA(T33, T36)
TIMES1_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → U82_GGA(T52, T54, mult64_in_ga(T52, T54))
TIMES1_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT64_IN_GA(s(T52), s(T54)) → U3_GA(T52, T54, mult64_in_ga(T52, T54))
MULT64_IN_GA(s(T52), s(T54)) → MULT64_IN_GA(T52, T54)
MULT64_IN_GA(T55, s(s(T57))) → U4_GA(T55, T57, mult72_in_ga(T55, T57))
MULT64_IN_GA(T55, s(s(T57))) → MULT72_IN_GA(T55, T57)
MULT72_IN_GA(s(T52), T54) → U5_GA(T52, T54, mult64_in_ga(T52, T54))
MULT72_IN_GA(s(T52), T54) → MULT64_IN_GA(T52, T54)
MULT72_IN_GA(T55, s(T57)) → U6_GA(T55, T57, mult72_in_ga(T55, T57))
MULT72_IN_GA(T55, s(T57)) → MULT72_IN_GA(T55, T57)
TIMES1_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → U83_GGA(T55, T57, mult72_in_ga(T55, T57))
TIMES1_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
TIMES1_IN_GGA(s(T58), s(0), s(s(T61))) → U84_GGA(T58, T61, mult72_in_ga(T58, T61))
TIMES1_IN_GGA(s(T58), s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
TIMES1_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_GGA(T80, T82, mult111_in_ga(T80, T82))
TIMES1_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT111_IN_GA(s(T80), s(s(T82))) → U7_GA(T80, T82, mult111_in_ga(T80, T82))
MULT111_IN_GA(s(T80), s(s(T82))) → MULT111_IN_GA(T80, T82)
MULT111_IN_GA(T83, s(s(s(T85)))) → U8_GA(T83, T85, mult127_in_ga(T83, T85))
MULT111_IN_GA(T83, s(s(s(T85)))) → MULT127_IN_GA(T83, T85)
MULT127_IN_GA(s(T80), T82) → U9_GA(T80, T82, mult111_in_ga(T80, T82))
MULT127_IN_GA(s(T80), T82) → MULT111_IN_GA(T80, T82)
MULT127_IN_GA(T83, s(T85)) → U10_GA(T83, T85, mult127_in_ga(T83, T85))
MULT127_IN_GA(T83, s(T85)) → MULT127_IN_GA(T83, T85)
TIMES1_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_GGA(T83, T85, mult127_in_ga(T83, T85))
TIMES1_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
TIMES1_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → U87_GGA(T86, T89, mult127_in_ga(T86, T89))
TIMES1_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
TIMES1_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_GGA(T111, T113, mult166_in_ga(T111, T113))
TIMES1_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT166_IN_GA(s(T111), s(s(s(T113)))) → U11_GA(T111, T113, mult166_in_ga(T111, T113))
MULT166_IN_GA(s(T111), s(s(s(T113)))) → MULT166_IN_GA(T111, T113)
MULT166_IN_GA(T114, s(s(s(s(T116))))) → U12_GA(T114, T116, mult190_in_ga(T114, T116))
MULT166_IN_GA(T114, s(s(s(s(T116))))) → MULT190_IN_GA(T114, T116)
MULT190_IN_GA(s(T111), T113) → U13_GA(T111, T113, mult166_in_ga(T111, T113))
MULT190_IN_GA(s(T111), T113) → MULT166_IN_GA(T111, T113)
MULT190_IN_GA(T114, s(T116)) → U14_GA(T114, T116, mult190_in_ga(T114, T116))
MULT190_IN_GA(T114, s(T116)) → MULT190_IN_GA(T114, T116)
TIMES1_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_GGA(T114, T116, mult190_in_ga(T114, T116))
TIMES1_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
TIMES1_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_GGA(T117, T120, mult190_in_ga(T117, T120))
TIMES1_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
TIMES1_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_GGA(T145, T147, mult229_in_ga(T145, T147))
TIMES1_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT229_IN_GA(s(T145), s(s(s(s(T147))))) → U15_GA(T145, T147, mult229_in_ga(T145, T147))
MULT229_IN_GA(s(T145), s(s(s(s(T147))))) → MULT229_IN_GA(T145, T147)
MULT229_IN_GA(T148, s(s(s(s(s(T150)))))) → U16_GA(T148, T150, mult261_in_ga(T148, T150))
MULT229_IN_GA(T148, s(s(s(s(s(T150)))))) → MULT261_IN_GA(T148, T150)
MULT261_IN_GA(s(T145), T147) → U17_GA(T145, T147, mult229_in_ga(T145, T147))
MULT261_IN_GA(s(T145), T147) → MULT229_IN_GA(T145, T147)
MULT261_IN_GA(T148, s(T150)) → U18_GA(T148, T150, mult261_in_ga(T148, T150))
MULT261_IN_GA(T148, s(T150)) → MULT261_IN_GA(T148, T150)
TIMES1_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_GGA(T148, T150, mult261_in_ga(T148, T150))
TIMES1_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
TIMES1_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_GGA(T151, T154, mult261_in_ga(T151, T154))
TIMES1_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
TIMES1_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_GGA(T182, T184, mult300_in_ga(T182, T184))
TIMES1_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT300_IN_GA(s(T182), s(s(s(s(s(T184)))))) → U19_GA(T182, T184, mult300_in_ga(T182, T184))
MULT300_IN_GA(s(T182), s(s(s(s(s(T184)))))) → MULT300_IN_GA(T182, T184)
MULT300_IN_GA(T185, s(s(s(s(s(s(T187))))))) → U20_GA(T185, T187, mult340_in_ga(T185, T187))
MULT300_IN_GA(T185, s(s(s(s(s(s(T187))))))) → MULT340_IN_GA(T185, T187)
MULT340_IN_GA(s(T182), T184) → U21_GA(T182, T184, mult300_in_ga(T182, T184))
MULT340_IN_GA(s(T182), T184) → MULT300_IN_GA(T182, T184)
MULT340_IN_GA(T185, s(T187)) → U22_GA(T185, T187, mult340_in_ga(T185, T187))
MULT340_IN_GA(T185, s(T187)) → MULT340_IN_GA(T185, T187)
TIMES1_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_GGA(T185, T187, mult340_in_ga(T185, T187))
TIMES1_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
TIMES1_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_GGA(T188, T191, mult340_in_ga(T188, T191))
TIMES1_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
TIMES1_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_GGA(T222, T224, mult379_in_ga(T222, T224))
TIMES1_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT379_IN_GA(s(T222), s(s(s(s(s(s(T224))))))) → U23_GA(T222, T224, mult379_in_ga(T222, T224))
MULT379_IN_GA(s(T222), s(s(s(s(s(s(T224))))))) → MULT379_IN_GA(T222, T224)
MULT379_IN_GA(T225, s(s(s(s(s(s(s(T227)))))))) → U24_GA(T225, T227, mult427_in_ga(T225, T227))
MULT379_IN_GA(T225, s(s(s(s(s(s(s(T227)))))))) → MULT427_IN_GA(T225, T227)
MULT427_IN_GA(s(T222), T224) → U25_GA(T222, T224, mult379_in_ga(T222, T224))
MULT427_IN_GA(s(T222), T224) → MULT379_IN_GA(T222, T224)
MULT427_IN_GA(T225, s(T227)) → U26_GA(T225, T227, mult427_in_ga(T225, T227))
MULT427_IN_GA(T225, s(T227)) → MULT427_IN_GA(T225, T227)
TIMES1_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_GGA(T225, T227, mult427_in_ga(T225, T227))
TIMES1_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
TIMES1_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_GGA(T228, T231, mult427_in_ga(T228, T231))
TIMES1_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
TIMES1_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_GGA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
TIMES1_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(s(s(T27)), 0, T29) → U27_GAA(T27, T29, mult25_in_ga(T27, T29))
MULT14_IN_GAA(s(s(T27)), 0, T29) → MULT25_IN_GA(T27, T29)
MULT14_IN_GAA(s(T30), 0, s(T32)) → U28_GAA(T30, T32, mult25_in_ga(T30, T32))
MULT14_IN_GAA(s(T30), 0, s(T32)) → MULT25_IN_GA(T30, T32)
MULT14_IN_GAA(T33, 0, s(T36)) → U29_GAA(T33, T36, mult25_in_ga(T33, T36))
MULT14_IN_GAA(T33, 0, s(T36)) → MULT25_IN_GA(T33, T36)
MULT14_IN_GAA(s(s(T52)), s(0), s(s(T54))) → U30_GAA(T52, T54, mult64_in_ga(T52, T54))
MULT14_IN_GAA(s(s(T52)), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT14_IN_GAA(s(T55), s(0), s(s(s(T57)))) → U31_GAA(T55, T57, mult72_in_ga(T55, T57))
MULT14_IN_GAA(s(T55), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
MULT14_IN_GAA(T58, s(0), s(s(T61))) → U32_GAA(T58, T61, mult72_in_ga(T58, T61))
MULT14_IN_GAA(T58, s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
MULT14_IN_GAA(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_GAA(T80, T82, mult111_in_ga(T80, T82))
MULT14_IN_GAA(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT14_IN_GAA(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_GAA(T83, T85, mult127_in_ga(T83, T85))
MULT14_IN_GAA(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
MULT14_IN_GAA(T86, s(s(0)), s(s(s(T89)))) → U35_GAA(T86, T89, mult127_in_ga(T86, T89))
MULT14_IN_GAA(T86, s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
MULT14_IN_GAA(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_GAA(T111, T113, mult166_in_ga(T111, T113))
MULT14_IN_GAA(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT14_IN_GAA(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_GAA(T114, T116, mult190_in_ga(T114, T116))
MULT14_IN_GAA(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
MULT14_IN_GAA(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_GAA(T117, T120, mult190_in_ga(T117, T120))
MULT14_IN_GAA(T117, s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
MULT14_IN_GAA(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_GAA(T145, T147, mult229_in_ga(T145, T147))
MULT14_IN_GAA(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT14_IN_GAA(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_GAA(T148, T150, mult261_in_ga(T148, T150))
MULT14_IN_GAA(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
MULT14_IN_GAA(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_GAA(T151, T154, mult261_in_ga(T151, T154))
MULT14_IN_GAA(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
MULT14_IN_GAA(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_GAA(T182, T184, mult300_in_ga(T182, T184))
MULT14_IN_GAA(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT14_IN_GAA(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_GAA(T185, T187, mult340_in_ga(T185, T187))
MULT14_IN_GAA(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
MULT14_IN_GAA(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_GAA(T188, T191, mult340_in_ga(T188, T191))
MULT14_IN_GAA(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
MULT14_IN_GAA(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_GAA(T222, T224, mult379_in_ga(T222, T224))
MULT14_IN_GAA(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT14_IN_GAA(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_GAA(T225, T227, mult427_in_ga(T225, T227))
MULT14_IN_GAA(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
MULT14_IN_GAA(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_GAA(T228, T231, mult427_in_ga(T228, T231))
MULT14_IN_GAA(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
MULT14_IN_GAA(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_GAA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
MULT14_IN_GAA(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_GAA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(s(s(T27))), 0, T29) → U51_GAA(T27, T29, mult25_in_ga(T27, T29))
MULT3_IN_GAA(s(s(s(T27))), 0, T29) → MULT25_IN_GA(T27, T29)
MULT3_IN_GAA(s(s(T30)), 0, s(T32)) → U52_GAA(T30, T32, mult25_in_ga(T30, T32))
MULT3_IN_GAA(s(s(T30)), 0, s(T32)) → MULT25_IN_GA(T30, T32)
MULT3_IN_GAA(s(T33), 0, s(T36)) → U53_GAA(T33, T36, mult25_in_ga(T33, T36))
MULT3_IN_GAA(s(T33), 0, s(T36)) → MULT25_IN_GA(T33, T36)
MULT3_IN_GAA(s(s(s(T52))), s(0), s(s(T54))) → U54_GAA(T52, T54, mult64_in_ga(T52, T54))
MULT3_IN_GAA(s(s(s(T52))), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT3_IN_GAA(s(s(T55)), s(0), s(s(s(T57)))) → U55_GAA(T55, T57, mult72_in_ga(T55, T57))
MULT3_IN_GAA(s(s(T55)), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
MULT3_IN_GAA(s(T58), s(0), s(s(T61))) → U56_GAA(T58, T61, mult72_in_ga(T58, T61))
MULT3_IN_GAA(s(T58), s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
MULT3_IN_GAA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_GAA(T80, T82, mult111_in_ga(T80, T82))
MULT3_IN_GAA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT3_IN_GAA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_GAA(T83, T85, mult127_in_ga(T83, T85))
MULT3_IN_GAA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
MULT3_IN_GAA(s(T86), s(s(0)), s(s(s(T89)))) → U59_GAA(T86, T89, mult127_in_ga(T86, T89))
MULT3_IN_GAA(s(T86), s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
MULT3_IN_GAA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_GAA(T111, T113, mult166_in_ga(T111, T113))
MULT3_IN_GAA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT3_IN_GAA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_GAA(T114, T116, mult190_in_ga(T114, T116))
MULT3_IN_GAA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
MULT3_IN_GAA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_GAA(T117, T120, mult190_in_ga(T117, T120))
MULT3_IN_GAA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
MULT3_IN_GAA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_GAA(T145, T147, mult229_in_ga(T145, T147))
MULT3_IN_GAA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT3_IN_GAA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_GAA(T148, T150, mult261_in_ga(T148, T150))
MULT3_IN_GAA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
MULT3_IN_GAA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_GAA(T151, T154, mult261_in_ga(T151, T154))
MULT3_IN_GAA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
MULT3_IN_GAA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_GAA(T182, T184, mult300_in_ga(T182, T184))
MULT3_IN_GAA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT3_IN_GAA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_GAA(T185, T187, mult340_in_ga(T185, T187))
MULT3_IN_GAA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
MULT3_IN_GAA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_GAA(T188, T191, mult340_in_ga(T188, T191))
MULT3_IN_GAA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
MULT3_IN_GAA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_GAA(T222, T224, mult379_in_ga(T222, T224))
MULT3_IN_GAA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT3_IN_GAA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_GAA(T225, T227, mult427_in_ga(T225, T227))
MULT3_IN_GAA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
MULT3_IN_GAA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_GAA(T228, T231, mult427_in_ga(T228, T231))
MULT3_IN_GAA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
MULT3_IN_GAA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_GAA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
MULT3_IN_GAA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_GAA(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(s(T238), T239, 0, T241) → U76_GAAA(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
MULT456_IN_GAAA(s(T238), T239, 0, T241) → MULT14_IN_GAA(T238, s(T239), T241)
MULT456_IN_GAAA(T242, T243, 0, s(T246)) → U77_GAAA(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
MULT456_IN_GAAA(T242, T243, 0, s(T246)) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_GAA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_GAA(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(T242, T243, s(T247), s(T246)) → U78_GAAA(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
MULT456_IN_GAAA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT3_IN_GAA(T248, T249, s(T251)) → U75_GAA(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
MULT3_IN_GAA(T248, T249, s(T251)) → MULT3_IN_GAA(T248, T249, T251)
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_GGA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_GGA(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
TIMES1_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAGA(T242, T243, T247, T246)
MULT456_IN_GAGA(s(T238), T239, 0, T241) → U76_GAGA(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
MULT456_IN_GAGA(s(T238), T239, 0, T241) → MULT14_IN_GAA(T238, s(T239), T241)
MULT456_IN_GAGA(T242, T243, 0, s(T246)) → U77_GAGA(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
MULT456_IN_GAGA(T242, T243, 0, s(T246)) → MULT3_IN_GAA(T242, s(T243), T246)
MULT456_IN_GAGA(T242, T243, s(T247), s(T246)) → U78_GAGA(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
MULT456_IN_GAGA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAGA(T242, T243, T247, T246)
TIMES1_IN_GGA(T248, T249, s(T251)) → U103_GGA(T248, T249, T251, mult3_in_gga(T248, T249, T251))
TIMES1_IN_GGA(T248, T249, s(T251)) → MULT3_IN_GGA(T248, T249, T251)
MULT3_IN_GGA(s(s(s(T27))), 0, T29) → U51_GGA(T27, T29, mult25_in_ga(T27, T29))
MULT3_IN_GGA(s(s(s(T27))), 0, T29) → MULT25_IN_GA(T27, T29)
MULT3_IN_GGA(s(s(T30)), 0, s(T32)) → U52_GGA(T30, T32, mult25_in_ga(T30, T32))
MULT3_IN_GGA(s(s(T30)), 0, s(T32)) → MULT25_IN_GA(T30, T32)
MULT3_IN_GGA(s(T33), 0, s(T36)) → U53_GGA(T33, T36, mult25_in_ga(T33, T36))
MULT3_IN_GGA(s(T33), 0, s(T36)) → MULT25_IN_GA(T33, T36)
MULT3_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → U54_GGA(T52, T54, mult64_in_ga(T52, T54))
MULT3_IN_GGA(s(s(s(T52))), s(0), s(s(T54))) → MULT64_IN_GA(T52, T54)
MULT3_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → U55_GGA(T55, T57, mult72_in_ga(T55, T57))
MULT3_IN_GGA(s(s(T55)), s(0), s(s(s(T57)))) → MULT72_IN_GA(T55, T57)
MULT3_IN_GGA(s(T58), s(0), s(s(T61))) → U56_GGA(T58, T61, mult72_in_ga(T58, T61))
MULT3_IN_GGA(s(T58), s(0), s(s(T61))) → MULT72_IN_GA(T58, T61)
MULT3_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_GGA(T80, T82, mult111_in_ga(T80, T82))
MULT3_IN_GGA(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → MULT111_IN_GA(T80, T82)
MULT3_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_GGA(T83, T85, mult127_in_ga(T83, T85))
MULT3_IN_GGA(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → MULT127_IN_GA(T83, T85)
MULT3_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → U59_GGA(T86, T89, mult127_in_ga(T86, T89))
MULT3_IN_GGA(s(T86), s(s(0)), s(s(s(T89)))) → MULT127_IN_GA(T86, T89)
MULT3_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_GGA(T111, T113, mult166_in_ga(T111, T113))
MULT3_IN_GGA(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → MULT166_IN_GA(T111, T113)
MULT3_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_GGA(T114, T116, mult190_in_ga(T114, T116))
MULT3_IN_GGA(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → MULT190_IN_GA(T114, T116)
MULT3_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_GGA(T117, T120, mult190_in_ga(T117, T120))
MULT3_IN_GGA(s(T117), s(s(s(0))), s(s(s(s(T120))))) → MULT190_IN_GA(T117, T120)
MULT3_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_GGA(T145, T147, mult229_in_ga(T145, T147))
MULT3_IN_GGA(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → MULT229_IN_GA(T145, T147)
MULT3_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_GGA(T148, T150, mult261_in_ga(T148, T150))
MULT3_IN_GGA(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → MULT261_IN_GA(T148, T150)
MULT3_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_GGA(T151, T154, mult261_in_ga(T151, T154))
MULT3_IN_GGA(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → MULT261_IN_GA(T151, T154)
MULT3_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_GGA(T182, T184, mult300_in_ga(T182, T184))
MULT3_IN_GGA(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → MULT300_IN_GA(T182, T184)
MULT3_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_GGA(T185, T187, mult340_in_ga(T185, T187))
MULT3_IN_GGA(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → MULT340_IN_GA(T185, T187)
MULT3_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_GGA(T188, T191, mult340_in_ga(T188, T191))
MULT3_IN_GGA(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → MULT340_IN_GA(T188, T191)
MULT3_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_GGA(T222, T224, mult379_in_ga(T222, T224))
MULT3_IN_GGA(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → MULT379_IN_GA(T222, T224)
MULT3_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_GGA(T225, T227, mult427_in_ga(T225, T227))
MULT3_IN_GGA(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → MULT427_IN_GA(T225, T227)
MULT3_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_GGA(T228, T231, mult427_in_ga(T228, T231))
MULT3_IN_GGA(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → MULT427_IN_GA(T228, T231)
MULT3_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_GGA(T238, T241, mult14_in_gaa(T238, s(T239), T241))
MULT3_IN_GGA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_GGA(T242, T246, mult3_in_gaa(T242, s(T243), T246))
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_GGA(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
MULT3_IN_GGA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAGA(T242, T243, T247, T246)
MULT3_IN_GGA(T248, T249, s(T251)) → U75_GGA(T248, T249, T251, mult3_in_gga(T248, T249, T251))
MULT3_IN_GGA(T248, T249, s(T251)) → MULT3_IN_GGA(T248, T249, T251)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)
TIMES1_IN_GGA(x1, x2, x3)  =  TIMES1_IN_GGA(x1, x2)
U79_GGA(x1, x2, x3)  =  U79_GGA(x1, x3)
MULT25_IN_GA(x1, x2)  =  MULT25_IN_GA(x1)
U1_GA(x1, x2, x3)  =  U1_GA(x1, x3)
U2_GA(x1, x2, x3)  =  U2_GA(x1, x3)
U80_GGA(x1, x2, x3)  =  U80_GGA(x1, x3)
U81_GGA(x1, x2, x3)  =  U81_GGA(x1, x3)
U82_GGA(x1, x2, x3)  =  U82_GGA(x1, x3)
MULT64_IN_GA(x1, x2)  =  MULT64_IN_GA(x1)
U3_GA(x1, x2, x3)  =  U3_GA(x1, x3)
U4_GA(x1, x2, x3)  =  U4_GA(x1, x3)
MULT72_IN_GA(x1, x2)  =  MULT72_IN_GA(x1)
U5_GA(x1, x2, x3)  =  U5_GA(x1, x3)
U6_GA(x1, x2, x3)  =  U6_GA(x1, x3)
U83_GGA(x1, x2, x3)  =  U83_GGA(x1, x3)
U84_GGA(x1, x2, x3)  =  U84_GGA(x1, x3)
U85_GGA(x1, x2, x3)  =  U85_GGA(x1, x3)
MULT111_IN_GA(x1, x2)  =  MULT111_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x1, x3)
U8_GA(x1, x2, x3)  =  U8_GA(x1, x3)
MULT127_IN_GA(x1, x2)  =  MULT127_IN_GA(x1)
U9_GA(x1, x2, x3)  =  U9_GA(x1, x3)
U10_GA(x1, x2, x3)  =  U10_GA(x1, x3)
U86_GGA(x1, x2, x3)  =  U86_GGA(x1, x3)
U87_GGA(x1, x2, x3)  =  U87_GGA(x1, x3)
U88_GGA(x1, x2, x3)  =  U88_GGA(x1, x3)
MULT166_IN_GA(x1, x2)  =  MULT166_IN_GA(x1)
U11_GA(x1, x2, x3)  =  U11_GA(x1, x3)
U12_GA(x1, x2, x3)  =  U12_GA(x1, x3)
MULT190_IN_GA(x1, x2)  =  MULT190_IN_GA(x1)
U13_GA(x1, x2, x3)  =  U13_GA(x1, x3)
U14_GA(x1, x2, x3)  =  U14_GA(x1, x3)
U89_GGA(x1, x2, x3)  =  U89_GGA(x1, x3)
U90_GGA(x1, x2, x3)  =  U90_GGA(x1, x3)
U91_GGA(x1, x2, x3)  =  U91_GGA(x1, x3)
MULT229_IN_GA(x1, x2)  =  MULT229_IN_GA(x1)
U15_GA(x1, x2, x3)  =  U15_GA(x1, x3)
U16_GA(x1, x2, x3)  =  U16_GA(x1, x3)
MULT261_IN_GA(x1, x2)  =  MULT261_IN_GA(x1)
U17_GA(x1, x2, x3)  =  U17_GA(x1, x3)
U18_GA(x1, x2, x3)  =  U18_GA(x1, x3)
U92_GGA(x1, x2, x3)  =  U92_GGA(x1, x3)
U93_GGA(x1, x2, x3)  =  U93_GGA(x1, x3)
U94_GGA(x1, x2, x3)  =  U94_GGA(x1, x3)
MULT300_IN_GA(x1, x2)  =  MULT300_IN_GA(x1)
U19_GA(x1, x2, x3)  =  U19_GA(x1, x3)
U20_GA(x1, x2, x3)  =  U20_GA(x1, x3)
MULT340_IN_GA(x1, x2)  =  MULT340_IN_GA(x1)
U21_GA(x1, x2, x3)  =  U21_GA(x1, x3)
U22_GA(x1, x2, x3)  =  U22_GA(x1, x3)
U95_GGA(x1, x2, x3)  =  U95_GGA(x1, x3)
U96_GGA(x1, x2, x3)  =  U96_GGA(x1, x3)
U97_GGA(x1, x2, x3)  =  U97_GGA(x1, x3)
MULT379_IN_GA(x1, x2)  =  MULT379_IN_GA(x1)
U23_GA(x1, x2, x3)  =  U23_GA(x1, x3)
U24_GA(x1, x2, x3)  =  U24_GA(x1, x3)
MULT427_IN_GA(x1, x2)  =  MULT427_IN_GA(x1)
U25_GA(x1, x2, x3)  =  U25_GA(x1, x3)
U26_GA(x1, x2, x3)  =  U26_GA(x1, x3)
U98_GGA(x1, x2, x3)  =  U98_GGA(x1, x3)
U99_GGA(x1, x2, x3)  =  U99_GGA(x1, x3)
U100_GGA(x1, x2, x3)  =  U100_GGA(x1, x3)
MULT14_IN_GAA(x1, x2, x3)  =  MULT14_IN_GAA(x1)
U27_GAA(x1, x2, x3)  =  U27_GAA(x1, x3)
U28_GAA(x1, x2, x3)  =  U28_GAA(x1, x3)
U29_GAA(x1, x2, x3)  =  U29_GAA(x1, x3)
U30_GAA(x1, x2, x3)  =  U30_GAA(x1, x3)
U31_GAA(x1, x2, x3)  =  U31_GAA(x1, x3)
U32_GAA(x1, x2, x3)  =  U32_GAA(x1, x3)
U33_GAA(x1, x2, x3)  =  U33_GAA(x1, x3)
U34_GAA(x1, x2, x3)  =  U34_GAA(x1, x3)
U35_GAA(x1, x2, x3)  =  U35_GAA(x1, x3)
U36_GAA(x1, x2, x3)  =  U36_GAA(x1, x3)
U37_GAA(x1, x2, x3)  =  U37_GAA(x1, x3)
U38_GAA(x1, x2, x3)  =  U38_GAA(x1, x3)
U39_GAA(x1, x2, x3)  =  U39_GAA(x1, x3)
U40_GAA(x1, x2, x3)  =  U40_GAA(x1, x3)
U41_GAA(x1, x2, x3)  =  U41_GAA(x1, x3)
U42_GAA(x1, x2, x3)  =  U42_GAA(x1, x3)
U43_GAA(x1, x2, x3)  =  U43_GAA(x1, x3)
U44_GAA(x1, x2, x3)  =  U44_GAA(x1, x3)
U45_GAA(x1, x2, x3)  =  U45_GAA(x1, x3)
U46_GAA(x1, x2, x3)  =  U46_GAA(x1, x3)
U47_GAA(x1, x2, x3)  =  U47_GAA(x1, x3)
U48_GAA(x1, x2, x3)  =  U48_GAA(x1, x3)
U49_GAA(x1, x2, x3)  =  U49_GAA(x1, x3)
MULT3_IN_GAA(x1, x2, x3)  =  MULT3_IN_GAA(x1)
U51_GAA(x1, x2, x3)  =  U51_GAA(x1, x3)
U52_GAA(x1, x2, x3)  =  U52_GAA(x1, x3)
U53_GAA(x1, x2, x3)  =  U53_GAA(x1, x3)
U54_GAA(x1, x2, x3)  =  U54_GAA(x1, x3)
U55_GAA(x1, x2, x3)  =  U55_GAA(x1, x3)
U56_GAA(x1, x2, x3)  =  U56_GAA(x1, x3)
U57_GAA(x1, x2, x3)  =  U57_GAA(x1, x3)
U58_GAA(x1, x2, x3)  =  U58_GAA(x1, x3)
U59_GAA(x1, x2, x3)  =  U59_GAA(x1, x3)
U60_GAA(x1, x2, x3)  =  U60_GAA(x1, x3)
U61_GAA(x1, x2, x3)  =  U61_GAA(x1, x3)
U62_GAA(x1, x2, x3)  =  U62_GAA(x1, x3)
U63_GAA(x1, x2, x3)  =  U63_GAA(x1, x3)
U64_GAA(x1, x2, x3)  =  U64_GAA(x1, x3)
U65_GAA(x1, x2, x3)  =  U65_GAA(x1, x3)
U66_GAA(x1, x2, x3)  =  U66_GAA(x1, x3)
U67_GAA(x1, x2, x3)  =  U67_GAA(x1, x3)
U68_GAA(x1, x2, x3)  =  U68_GAA(x1, x3)
U69_GAA(x1, x2, x3)  =  U69_GAA(x1, x3)
U70_GAA(x1, x2, x3)  =  U70_GAA(x1, x3)
U71_GAA(x1, x2, x3)  =  U71_GAA(x1, x3)
U72_GAA(x1, x2, x3)  =  U72_GAA(x1, x3)
U50_GAA(x1, x2, x3, x4)  =  U50_GAA(x1, x4)
MULT456_IN_GAAA(x1, x2, x3, x4)  =  MULT456_IN_GAAA(x1)
U76_GAAA(x1, x2, x3, x4)  =  U76_GAAA(x1, x4)
U77_GAAA(x1, x2, x3, x4)  =  U77_GAAA(x1, x4)
U73_GAA(x1, x2, x3)  =  U73_GAA(x1, x3)
U74_GAA(x1, x2, x3, x4)  =  U74_GAA(x1, x4)
U78_GAAA(x1, x2, x3, x4, x5)  =  U78_GAAA(x1, x5)
U75_GAA(x1, x2, x3, x4)  =  U75_GAA(x1, x4)
U101_GGA(x1, x2, x3)  =  U101_GGA(x1, x3)
U102_GGA(x1, x2, x3, x4)  =  U102_GGA(x1, x2, x4)
MULT456_IN_GAGA(x1, x2, x3, x4)  =  MULT456_IN_GAGA(x1, x3)
U76_GAGA(x1, x2, x3, x4)  =  U76_GAGA(x1, x4)
U77_GAGA(x1, x2, x3, x4)  =  U77_GAGA(x1, x4)
U78_GAGA(x1, x2, x3, x4, x5)  =  U78_GAGA(x1, x3, x5)
U103_GGA(x1, x2, x3, x4)  =  U103_GGA(x1, x2, x4)
MULT3_IN_GGA(x1, x2, x3)  =  MULT3_IN_GGA(x1, x2)
U51_GGA(x1, x2, x3)  =  U51_GGA(x1, x3)
U52_GGA(x1, x2, x3)  =  U52_GGA(x1, x3)
U53_GGA(x1, x2, x3)  =  U53_GGA(x1, x3)
U54_GGA(x1, x2, x3)  =  U54_GGA(x1, x3)
U55_GGA(x1, x2, x3)  =  U55_GGA(x1, x3)
U56_GGA(x1, x2, x3)  =  U56_GGA(x1, x3)
U57_GGA(x1, x2, x3)  =  U57_GGA(x1, x3)
U58_GGA(x1, x2, x3)  =  U58_GGA(x1, x3)
U59_GGA(x1, x2, x3)  =  U59_GGA(x1, x3)
U60_GGA(x1, x2, x3)  =  U60_GGA(x1, x3)
U61_GGA(x1, x2, x3)  =  U61_GGA(x1, x3)
U62_GGA(x1, x2, x3)  =  U62_GGA(x1, x3)
U63_GGA(x1, x2, x3)  =  U63_GGA(x1, x3)
U64_GGA(x1, x2, x3)  =  U64_GGA(x1, x3)
U65_GGA(x1, x2, x3)  =  U65_GGA(x1, x3)
U66_GGA(x1, x2, x3)  =  U66_GGA(x1, x3)
U67_GGA(x1, x2, x3)  =  U67_GGA(x1, x3)
U68_GGA(x1, x2, x3)  =  U68_GGA(x1, x3)
U69_GGA(x1, x2, x3)  =  U69_GGA(x1, x3)
U70_GGA(x1, x2, x3)  =  U70_GGA(x1, x3)
U71_GGA(x1, x2, x3)  =  U71_GGA(x1, x3)
U72_GGA(x1, x2, x3)  =  U72_GGA(x1, x3)
U73_GGA(x1, x2, x3)  =  U73_GGA(x1, x3)
U74_GGA(x1, x2, x3, x4)  =  U74_GGA(x1, x2, x4)
U75_GGA(x1, x2, x3, x4)  =  U75_GGA(x1, x2, x4)

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

(105) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 10 SCCs with 224 less nodes.

(106) Complex Obligation (AND)

(107) Obligation:

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

MULT379_IN_GA(T225, s(s(s(s(s(s(s(T227)))))))) → MULT427_IN_GA(T225, T227)
MULT427_IN_GA(s(T222), T224) → MULT379_IN_GA(T222, T224)
MULT379_IN_GA(s(T222), s(s(s(s(s(s(T224))))))) → MULT379_IN_GA(T222, T224)
MULT427_IN_GA(T225, s(T227)) → MULT427_IN_GA(T225, T227)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)
MULT379_IN_GA(x1, x2)  =  MULT379_IN_GA(x1)
MULT427_IN_GA(x1, x2)  =  MULT427_IN_GA(x1)

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

(108) UsableRulesProof (EQUIVALENT transformation)

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

(109) Obligation:

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

MULT379_IN_GA(T225, s(s(s(s(s(s(s(T227)))))))) → MULT427_IN_GA(T225, T227)
MULT427_IN_GA(s(T222), T224) → MULT379_IN_GA(T222, T224)
MULT379_IN_GA(s(T222), s(s(s(s(s(s(T224))))))) → MULT379_IN_GA(T222, T224)
MULT427_IN_GA(T225, s(T227)) → MULT427_IN_GA(T225, T227)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT379_IN_GA(x1, x2)  =  MULT379_IN_GA(x1)
MULT427_IN_GA(x1, x2)  =  MULT427_IN_GA(x1)

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

(110) PiDPToQDPProof (SOUND transformation)

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

(111) Obligation:

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

MULT379_IN_GA(T225) → MULT427_IN_GA(T225)
MULT427_IN_GA(s(T222)) → MULT379_IN_GA(T222)
MULT379_IN_GA(s(T222)) → MULT379_IN_GA(T222)
MULT427_IN_GA(T225) → MULT427_IN_GA(T225)

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

(112) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT379_IN_GA(T225) → MULT427_IN_GA(T225)
MULT427_IN_GA(s(T222)) → MULT379_IN_GA(T222)
MULT379_IN_GA(s(T222)) → MULT379_IN_GA(T222)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT379_IN_GA(x₁)) = 2 + x₁   
POL(MULT427_IN_GA(x₁)) = 1 + x₁   
POL(s(x₁)) = 2 + 2·x₁   

(113) Obligation:

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

MULT427_IN_GA(T225) → MULT427_IN_GA(T225)

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

(114) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT427_IN_GA(T225) evaluates to t =MULT427_IN_GA(T225)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT427_IN_GA(T225) to MULT427_IN_GA(T225).

(115) FALSE

(116) Obligation:

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

MULT300_IN_GA(T185, s(s(s(s(s(s(T187))))))) → MULT340_IN_GA(T185, T187)
MULT340_IN_GA(s(T182), T184) → MULT300_IN_GA(T182, T184)
MULT300_IN_GA(s(T182), s(s(s(s(s(T184)))))) → MULT300_IN_GA(T182, T184)
MULT340_IN_GA(T185, s(T187)) → MULT340_IN_GA(T185, T187)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)
MULT300_IN_GA(x1, x2)  =  MULT300_IN_GA(x1)
MULT340_IN_GA(x1, x2)  =  MULT340_IN_GA(x1)

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

(117) UsableRulesProof (EQUIVALENT transformation)

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

(118) Obligation:

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

MULT300_IN_GA(T185, s(s(s(s(s(s(T187))))))) → MULT340_IN_GA(T185, T187)
MULT340_IN_GA(s(T182), T184) → MULT300_IN_GA(T182, T184)
MULT300_IN_GA(s(T182), s(s(s(s(s(T184)))))) → MULT300_IN_GA(T182, T184)
MULT340_IN_GA(T185, s(T187)) → MULT340_IN_GA(T185, T187)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT300_IN_GA(x1, x2)  =  MULT300_IN_GA(x1)
MULT340_IN_GA(x1, x2)  =  MULT340_IN_GA(x1)

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

(119) PiDPToQDPProof (SOUND transformation)

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

(120) Obligation:

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

MULT300_IN_GA(T185) → MULT340_IN_GA(T185)
MULT340_IN_GA(s(T182)) → MULT300_IN_GA(T182)
MULT300_IN_GA(s(T182)) → MULT300_IN_GA(T182)
MULT340_IN_GA(T185) → MULT340_IN_GA(T185)

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

(121) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT300_IN_GA(T185) → MULT340_IN_GA(T185)
MULT340_IN_GA(s(T182)) → MULT300_IN_GA(T182)
MULT300_IN_GA(s(T182)) → MULT300_IN_GA(T182)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT300_IN_GA(x₁)) = 2 + x₁   
POL(MULT340_IN_GA(x₁)) = 1 + x₁   
POL(s(x₁)) = 2 + 2·x₁   

(122) Obligation:

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

MULT340_IN_GA(T185) → MULT340_IN_GA(T185)

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

(123) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT340_IN_GA(T185) evaluates to t =MULT340_IN_GA(T185)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT340_IN_GA(T185) to MULT340_IN_GA(T185).

(124) FALSE

(125) Obligation:

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

MULT229_IN_GA(T148, s(s(s(s(s(T150)))))) → MULT261_IN_GA(T148, T150)
MULT261_IN_GA(s(T145), T147) → MULT229_IN_GA(T145, T147)
MULT229_IN_GA(s(T145), s(s(s(s(T147))))) → MULT229_IN_GA(T145, T147)
MULT261_IN_GA(T148, s(T150)) → MULT261_IN_GA(T148, T150)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)
MULT229_IN_GA(x1, x2)  =  MULT229_IN_GA(x1)
MULT261_IN_GA(x1, x2)  =  MULT261_IN_GA(x1)

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

(126) UsableRulesProof (EQUIVALENT transformation)

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

(127) Obligation:

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

MULT229_IN_GA(T148, s(s(s(s(s(T150)))))) → MULT261_IN_GA(T148, T150)
MULT261_IN_GA(s(T145), T147) → MULT229_IN_GA(T145, T147)
MULT229_IN_GA(s(T145), s(s(s(s(T147))))) → MULT229_IN_GA(T145, T147)
MULT261_IN_GA(T148, s(T150)) → MULT261_IN_GA(T148, T150)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT229_IN_GA(x1, x2)  =  MULT229_IN_GA(x1)
MULT261_IN_GA(x1, x2)  =  MULT261_IN_GA(x1)

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

(128) PiDPToQDPProof (SOUND transformation)

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

(129) Obligation:

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

MULT229_IN_GA(T148) → MULT261_IN_GA(T148)
MULT261_IN_GA(s(T145)) → MULT229_IN_GA(T145)
MULT229_IN_GA(s(T145)) → MULT229_IN_GA(T145)
MULT261_IN_GA(T148) → MULT261_IN_GA(T148)

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

(130) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT229_IN_GA(T148) → MULT261_IN_GA(T148)
MULT261_IN_GA(s(T145)) → MULT229_IN_GA(T145)
MULT229_IN_GA(s(T145)) → MULT229_IN_GA(T145)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT229_IN_GA(x₁)) = 2 + x₁   
POL(MULT261_IN_GA(x₁)) = 1 + x₁   
POL(s(x₁)) = 2 + 2·x₁   

(131) Obligation:

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

MULT261_IN_GA(T148) → MULT261_IN_GA(T148)

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

(132) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT261_IN_GA(T148) evaluates to t =MULT261_IN_GA(T148)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT261_IN_GA(T148) to MULT261_IN_GA(T148).

(133) FALSE

(134) Obligation:

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

MULT166_IN_GA(T114, s(s(s(s(T116))))) → MULT190_IN_GA(T114, T116)
MULT190_IN_GA(s(T111), T113) → MULT166_IN_GA(T111, T113)
MULT166_IN_GA(s(T111), s(s(s(T113)))) → MULT166_IN_GA(T111, T113)
MULT190_IN_GA(T114, s(T116)) → MULT190_IN_GA(T114, T116)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)
MULT166_IN_GA(x1, x2)  =  MULT166_IN_GA(x1)
MULT190_IN_GA(x1, x2)  =  MULT190_IN_GA(x1)

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

(135) UsableRulesProof (EQUIVALENT transformation)

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

(136) Obligation:

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

MULT166_IN_GA(T114, s(s(s(s(T116))))) → MULT190_IN_GA(T114, T116)
MULT190_IN_GA(s(T111), T113) → MULT166_IN_GA(T111, T113)
MULT166_IN_GA(s(T111), s(s(s(T113)))) → MULT166_IN_GA(T111, T113)
MULT190_IN_GA(T114, s(T116)) → MULT190_IN_GA(T114, T116)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT166_IN_GA(x1, x2)  =  MULT166_IN_GA(x1)
MULT190_IN_GA(x1, x2)  =  MULT190_IN_GA(x1)

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

(137) PiDPToQDPProof (SOUND transformation)

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

(138) Obligation:

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

MULT166_IN_GA(T114) → MULT190_IN_GA(T114)
MULT190_IN_GA(s(T111)) → MULT166_IN_GA(T111)
MULT166_IN_GA(s(T111)) → MULT166_IN_GA(T111)
MULT190_IN_GA(T114) → MULT190_IN_GA(T114)

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

(139) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT166_IN_GA(T114) → MULT190_IN_GA(T114)
MULT190_IN_GA(s(T111)) → MULT166_IN_GA(T111)
MULT166_IN_GA(s(T111)) → MULT166_IN_GA(T111)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT166_IN_GA(x₁)) = 2 + x₁   
POL(MULT190_IN_GA(x₁)) = 1 + x₁   
POL(s(x₁)) = 2 + 2·x₁   

(140) Obligation:

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

MULT190_IN_GA(T114) → MULT190_IN_GA(T114)

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

(141) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT190_IN_GA(T114) evaluates to t =MULT190_IN_GA(T114)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT190_IN_GA(T114) to MULT190_IN_GA(T114).

(142) FALSE

(143) Obligation:

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

MULT111_IN_GA(T83, s(s(s(T85)))) → MULT127_IN_GA(T83, T85)
MULT127_IN_GA(s(T80), T82) → MULT111_IN_GA(T80, T82)
MULT111_IN_GA(s(T80), s(s(T82))) → MULT111_IN_GA(T80, T82)
MULT127_IN_GA(T83, s(T85)) → MULT127_IN_GA(T83, T85)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)
MULT111_IN_GA(x1, x2)  =  MULT111_IN_GA(x1)
MULT127_IN_GA(x1, x2)  =  MULT127_IN_GA(x1)

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

(144) UsableRulesProof (EQUIVALENT transformation)

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

(145) Obligation:

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

MULT111_IN_GA(T83, s(s(s(T85)))) → MULT127_IN_GA(T83, T85)
MULT127_IN_GA(s(T80), T82) → MULT111_IN_GA(T80, T82)
MULT111_IN_GA(s(T80), s(s(T82))) → MULT111_IN_GA(T80, T82)
MULT127_IN_GA(T83, s(T85)) → MULT127_IN_GA(T83, T85)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT111_IN_GA(x1, x2)  =  MULT111_IN_GA(x1)
MULT127_IN_GA(x1, x2)  =  MULT127_IN_GA(x1)

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

(146) PiDPToQDPProof (SOUND transformation)

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

(147) Obligation:

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

MULT111_IN_GA(T83) → MULT127_IN_GA(T83)
MULT127_IN_GA(s(T80)) → MULT111_IN_GA(T80)
MULT111_IN_GA(s(T80)) → MULT111_IN_GA(T80)
MULT127_IN_GA(T83) → MULT127_IN_GA(T83)

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

(148) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT111_IN_GA(T83) → MULT127_IN_GA(T83)
MULT127_IN_GA(s(T80)) → MULT111_IN_GA(T80)
MULT111_IN_GA(s(T80)) → MULT111_IN_GA(T80)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT111_IN_GA(x₁)) = 2 + x₁   
POL(MULT127_IN_GA(x₁)) = 1 + x₁   
POL(s(x₁)) = 2 + 2·x₁   

(149) Obligation:

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

MULT127_IN_GA(T83) → MULT127_IN_GA(T83)

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

(150) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT127_IN_GA(T83) evaluates to t =MULT127_IN_GA(T83)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT127_IN_GA(T83) to MULT127_IN_GA(T83).

(151) FALSE

(152) Obligation:

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

MULT64_IN_GA(T55, s(s(T57))) → MULT72_IN_GA(T55, T57)
MULT72_IN_GA(s(T52), T54) → MULT64_IN_GA(T52, T54)
MULT64_IN_GA(s(T52), s(T54)) → MULT64_IN_GA(T52, T54)
MULT72_IN_GA(T55, s(T57)) → MULT72_IN_GA(T55, T57)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)
MULT64_IN_GA(x1, x2)  =  MULT64_IN_GA(x1)
MULT72_IN_GA(x1, x2)  =  MULT72_IN_GA(x1)

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

(153) UsableRulesProof (EQUIVALENT transformation)

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

(154) Obligation:

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

MULT64_IN_GA(T55, s(s(T57))) → MULT72_IN_GA(T55, T57)
MULT72_IN_GA(s(T52), T54) → MULT64_IN_GA(T52, T54)
MULT64_IN_GA(s(T52), s(T54)) → MULT64_IN_GA(T52, T54)
MULT72_IN_GA(T55, s(T57)) → MULT72_IN_GA(T55, T57)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT64_IN_GA(x1, x2)  =  MULT64_IN_GA(x1)
MULT72_IN_GA(x1, x2)  =  MULT72_IN_GA(x1)

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

(155) PiDPToQDPProof (SOUND transformation)

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

(156) Obligation:

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

MULT64_IN_GA(T55) → MULT72_IN_GA(T55)
MULT72_IN_GA(s(T52)) → MULT64_IN_GA(T52)
MULT64_IN_GA(s(T52)) → MULT64_IN_GA(T52)
MULT72_IN_GA(T55) → MULT72_IN_GA(T55)

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

(157) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT64_IN_GA(T55) → MULT72_IN_GA(T55)
MULT72_IN_GA(s(T52)) → MULT64_IN_GA(T52)
MULT64_IN_GA(s(T52)) → MULT64_IN_GA(T52)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT64_IN_GA(x₁)) = 2 + x₁   
POL(MULT72_IN_GA(x₁)) = 1 + x₁   
POL(s(x₁)) = 2 + 2·x₁   

(158) Obligation:

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

MULT72_IN_GA(T55) → MULT72_IN_GA(T55)

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

(159) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT72_IN_GA(T55) evaluates to t =MULT72_IN_GA(T55)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT72_IN_GA(T55) to MULT72_IN_GA(T55).

(160) FALSE

(161) Obligation:

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

MULT25_IN_GA(T30, s(T32)) → MULT25_IN_GA(T30, T32)
MULT25_IN_GA(s(T27), T29) → MULT25_IN_GA(T27, T29)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)
MULT25_IN_GA(x1, x2)  =  MULT25_IN_GA(x1)

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

(162) UsableRulesProof (EQUIVALENT transformation)

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

(163) Obligation:

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

MULT25_IN_GA(T30, s(T32)) → MULT25_IN_GA(T30, T32)
MULT25_IN_GA(s(T27), T29) → MULT25_IN_GA(T27, T29)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT25_IN_GA(x1, x2)  =  MULT25_IN_GA(x1)

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

(164) PiDPToQDPProof (SOUND transformation)

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

(165) Obligation:

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

MULT25_IN_GA(T30) → MULT25_IN_GA(T30)
MULT25_IN_GA(s(T27)) → MULT25_IN_GA(T27)

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

(166) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT25_IN_GA(s(T27)) → MULT25_IN_GA(T27)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT25_IN_GA(x₁)) = 2·x₁   
POL(s(x₁)) = 2·x₁   

(167) Obligation:

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

MULT25_IN_GA(T30) → MULT25_IN_GA(T30)

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

(168) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT25_IN_GA(T30) evaluates to t =MULT25_IN_GA(T30)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT25_IN_GA(T30) to MULT25_IN_GA(T30).

(169) FALSE

(170) Obligation:

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

MULT3_IN_GAA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(s(T238), T239, 0, T241) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(T242, T243, 0, s(T246)) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(T248, T249, s(T251)) → MULT3_IN_GAA(T248, T249, T251)
MULT456_IN_GAAA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAAA(T242, T243, T247, T246)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)
MULT14_IN_GAA(x1, x2, x3)  =  MULT14_IN_GAA(x1)
MULT3_IN_GAA(x1, x2, x3)  =  MULT3_IN_GAA(x1)
MULT456_IN_GAAA(x1, x2, x3, x4)  =  MULT456_IN_GAAA(x1)

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

(171) UsableRulesProof (EQUIVALENT transformation)

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

(172) Obligation:

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

MULT3_IN_GAA(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(s(T238), T239, 0, T241) → MULT14_IN_GAA(T238, s(T239), T241)
MULT14_IN_GAA(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → MULT456_IN_GAAA(T242, T243, T247, T246)
MULT456_IN_GAAA(T242, T243, 0, s(T246)) → MULT3_IN_GAA(T242, s(T243), T246)
MULT3_IN_GAA(T248, T249, s(T251)) → MULT3_IN_GAA(T248, T249, T251)
MULT456_IN_GAAA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAAA(T242, T243, T247, T246)

R is empty.
The argument filtering Pi contains the following mapping:
0  =  0
s(x1)  =  s(x1)
MULT14_IN_GAA(x1, x2, x3)  =  MULT14_IN_GAA(x1)
MULT3_IN_GAA(x1, x2, x3)  =  MULT3_IN_GAA(x1)
MULT456_IN_GAAA(x1, x2, x3, x4)  =  MULT456_IN_GAAA(x1)

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

(173) PiDPToQDPProof (SOUND transformation)

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

(174) Obligation:

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

MULT3_IN_GAA(s(s(T238))) → MULT14_IN_GAA(T238)
MULT14_IN_GAA(s(T238)) → MULT14_IN_GAA(T238)
MULT14_IN_GAA(T242) → MULT3_IN_GAA(T242)
MULT3_IN_GAA(s(T242)) → MULT3_IN_GAA(T242)
MULT3_IN_GAA(s(T242)) → MULT456_IN_GAAA(T242)
MULT456_IN_GAAA(s(T238)) → MULT14_IN_GAA(T238)
MULT14_IN_GAA(T242) → MULT456_IN_GAAA(T242)
MULT456_IN_GAAA(T242) → MULT3_IN_GAA(T242)
MULT3_IN_GAA(T248) → MULT3_IN_GAA(T248)
MULT456_IN_GAAA(T242) → MULT456_IN_GAAA(T242)

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

(175) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

MULT3_IN_GAA(s(s(T238))) → MULT14_IN_GAA(T238)
MULT14_IN_GAA(s(T238)) → MULT14_IN_GAA(T238)
MULT14_IN_GAA(T242) → MULT3_IN_GAA(T242)
MULT3_IN_GAA(s(T242)) → MULT3_IN_GAA(T242)
MULT3_IN_GAA(s(T242)) → MULT456_IN_GAAA(T242)
MULT456_IN_GAAA(s(T238)) → MULT14_IN_GAA(T238)
MULT14_IN_GAA(T242) → MULT456_IN_GAAA(T242)
MULT456_IN_GAAA(T242) → MULT3_IN_GAA(T242)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(MULT14_IN_GAA(x₁)) = 2 + 2·x₁   
POL(MULT3_IN_GAA(x₁)) = x₁   
POL(MULT456_IN_GAAA(x₁)) = 1 + 2·x₁   
POL(s(x₁)) = 2 + 2·x₁   

(176) Obligation:

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

MULT3_IN_GAA(T248) → MULT3_IN_GAA(T248)
MULT456_IN_GAAA(T242) → MULT456_IN_GAAA(T242)

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

(177) DependencyGraphProof (EQUIVALENT transformation)

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

(178) Complex Obligation (AND)

(179) Obligation:

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

MULT456_IN_GAAA(T242) → MULT456_IN_GAAA(T242)

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

(180) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT456_IN_GAAA(T242) evaluates to t =MULT456_IN_GAAA(T242)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT456_IN_GAAA(T242) to MULT456_IN_GAAA(T242).

(181) FALSE

(182) Obligation:

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

MULT3_IN_GAA(T248) → MULT3_IN_GAA(T248)

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

(183) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT3_IN_GAA(T248) evaluates to t =MULT3_IN_GAA(T248)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT3_IN_GAA(T248) to MULT3_IN_GAA(T248).

(184) FALSE

(185) Obligation:

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

MULT456_IN_GAGA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAGA(T242, T243, T247, T246)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)
MULT456_IN_GAGA(x1, x2, x3, x4)  =  MULT456_IN_GAGA(x1, x3)

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

(186) UsableRulesProof (EQUIVALENT transformation)

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

(187) Obligation:

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

MULT456_IN_GAGA(T242, T243, s(T247), s(T246)) → MULT456_IN_GAGA(T242, T243, T247, T246)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT456_IN_GAGA(x1, x2, x3, x4)  =  MULT456_IN_GAGA(x1, x3)

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

(188) PiDPToQDPProof (SOUND transformation)

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

(189) Obligation:

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

MULT456_IN_GAGA(T242, s(T247)) → MULT456_IN_GAGA(T242, T247)

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

(190) 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:

• MULT456_IN_GAGA(T242, s(T247)) → MULT456_IN_GAGA(T242, T247)
  The graph contains the following edges 1 >= 1, 2 > 2

(191) TRUE

(192) Obligation:

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

MULT3_IN_GGA(T248, T249, s(T251)) → MULT3_IN_GGA(T248, T249, T251)

The TRS R consists of the following rules:

times1_in_gga(0, T8, 0) → times1_out_gga(0, T8, 0)
times1_in_gga(s(0), 0, 0) → times1_out_gga(s(0), 0, 0)
times1_in_gga(s(s(0)), 0, 0) → times1_out_gga(s(s(0)), 0, 0)
times1_in_gga(s(s(s(T27))), 0, T29) → U79_gga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(0, 0) → mult25_out_ga(0, 0)
mult25_in_ga(s(T27), T29) → U1_ga(T27, T29, mult25_in_ga(T27, T29))
mult25_in_ga(T30, s(T32)) → U2_ga(T30, T32, mult25_in_ga(T30, T32))
U2_ga(T30, T32, mult25_out_ga(T30, T32)) → mult25_out_ga(T30, s(T32))
U1_ga(T27, T29, mult25_out_ga(T27, T29)) → mult25_out_ga(s(T27), T29)
U79_gga(T27, T29, mult25_out_ga(T27, T29)) → times1_out_gga(s(s(s(T27))), 0, T29)
times1_in_gga(s(s(T30)), 0, s(T32)) → U80_gga(T30, T32, mult25_in_ga(T30, T32))
U80_gga(T30, T32, mult25_out_ga(T30, T32)) → times1_out_gga(s(s(T30)), 0, s(T32))
times1_in_gga(s(T33), 0, s(T36)) → U81_gga(T33, T36, mult25_in_ga(T33, T36))
U81_gga(T33, T36, mult25_out_ga(T33, T36)) → times1_out_gga(s(T33), 0, s(T36))
times1_in_gga(s(0), s(0), s(0)) → times1_out_gga(s(0), s(0), s(0))
times1_in_gga(s(s(0)), s(0), s(s(0))) → times1_out_gga(s(s(0)), s(0), s(s(0)))
times1_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U82_gga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(0, s(0)) → mult64_out_ga(0, s(0))
mult64_in_ga(s(T52), s(T54)) → U3_ga(T52, T54, mult64_in_ga(T52, T54))
mult64_in_ga(T55, s(s(T57))) → U4_ga(T55, T57, mult72_in_ga(T55, T57))
mult72_in_ga(0, 0) → mult72_out_ga(0, 0)
mult72_in_ga(s(T52), T54) → U5_ga(T52, T54, mult64_in_ga(T52, T54))
U5_ga(T52, T54, mult64_out_ga(T52, T54)) → mult72_out_ga(s(T52), T54)
mult72_in_ga(T55, s(T57)) → U6_ga(T55, T57, mult72_in_ga(T55, T57))
U6_ga(T55, T57, mult72_out_ga(T55, T57)) → mult72_out_ga(T55, s(T57))
U4_ga(T55, T57, mult72_out_ga(T55, T57)) → mult64_out_ga(T55, s(s(T57)))
U3_ga(T52, T54, mult64_out_ga(T52, T54)) → mult64_out_ga(s(T52), s(T54))
U82_gga(T52, T54, mult64_out_ga(T52, T54)) → times1_out_gga(s(s(s(T52))), s(0), s(s(T54)))
times1_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U83_gga(T55, T57, mult72_in_ga(T55, T57))
U83_gga(T55, T57, mult72_out_ga(T55, T57)) → times1_out_gga(s(s(T55)), s(0), s(s(s(T57))))
times1_in_gga(s(T58), s(0), s(s(T61))) → U84_gga(T58, T61, mult72_in_ga(T58, T61))
U84_gga(T58, T61, mult72_out_ga(T58, T61)) → times1_out_gga(s(T58), s(0), s(s(T61)))
times1_in_gga(s(0), s(s(0)), s(s(0))) → times1_out_gga(s(0), s(s(0)), s(s(0)))
times1_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → times1_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
times1_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U85_gga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(0, s(s(0))) → mult111_out_ga(0, s(s(0)))
mult111_in_ga(s(T80), s(s(T82))) → U7_ga(T80, T82, mult111_in_ga(T80, T82))
mult111_in_ga(T83, s(s(s(T85)))) → U8_ga(T83, T85, mult127_in_ga(T83, T85))
mult127_in_ga(0, 0) → mult127_out_ga(0, 0)
mult127_in_ga(s(T80), T82) → U9_ga(T80, T82, mult111_in_ga(T80, T82))
U9_ga(T80, T82, mult111_out_ga(T80, T82)) → mult127_out_ga(s(T80), T82)
mult127_in_ga(T83, s(T85)) → U10_ga(T83, T85, mult127_in_ga(T83, T85))
U10_ga(T83, T85, mult127_out_ga(T83, T85)) → mult127_out_ga(T83, s(T85))
U8_ga(T83, T85, mult127_out_ga(T83, T85)) → mult111_out_ga(T83, s(s(s(T85))))
U7_ga(T80, T82, mult111_out_ga(T80, T82)) → mult111_out_ga(s(T80), s(s(T82)))
U85_gga(T80, T82, mult111_out_ga(T80, T82)) → times1_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
times1_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U86_gga(T83, T85, mult127_in_ga(T83, T85))
U86_gga(T83, T85, mult127_out_ga(T83, T85)) → times1_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
times1_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U87_gga(T86, T89, mult127_in_ga(T86, T89))
U87_gga(T86, T89, mult127_out_ga(T86, T89)) → times1_out_gga(s(T86), s(s(0)), s(s(s(T89))))
times1_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → times1_out_gga(s(0), s(s(s(0))), s(s(s(0))))
times1_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U88_gga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(0, s(s(s(0)))) → mult166_out_ga(0, s(s(s(0))))
mult166_in_ga(s(T111), s(s(s(T113)))) → U11_ga(T111, T113, mult166_in_ga(T111, T113))
mult166_in_ga(T114, s(s(s(s(T116))))) → U12_ga(T114, T116, mult190_in_ga(T114, T116))
mult190_in_ga(0, 0) → mult190_out_ga(0, 0)
mult190_in_ga(s(T111), T113) → U13_ga(T111, T113, mult166_in_ga(T111, T113))
U13_ga(T111, T113, mult166_out_ga(T111, T113)) → mult190_out_ga(s(T111), T113)
mult190_in_ga(T114, s(T116)) → U14_ga(T114, T116, mult190_in_ga(T114, T116))
U14_ga(T114, T116, mult190_out_ga(T114, T116)) → mult190_out_ga(T114, s(T116))
U12_ga(T114, T116, mult190_out_ga(T114, T116)) → mult166_out_ga(T114, s(s(s(s(T116)))))
U11_ga(T111, T113, mult166_out_ga(T111, T113)) → mult166_out_ga(s(T111), s(s(s(T113))))
U88_gga(T111, T113, mult166_out_ga(T111, T113)) → times1_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
times1_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U89_gga(T114, T116, mult190_in_ga(T114, T116))
U89_gga(T114, T116, mult190_out_ga(T114, T116)) → times1_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
times1_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U90_gga(T117, T120, mult190_in_ga(T117, T120))
U90_gga(T117, T120, mult190_out_ga(T117, T120)) → times1_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
times1_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → times1_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
times1_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → times1_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
times1_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U91_gga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(0, s(s(s(s(0))))) → mult229_out_ga(0, s(s(s(s(0)))))
mult229_in_ga(s(T145), s(s(s(s(T147))))) → U15_ga(T145, T147, mult229_in_ga(T145, T147))
mult229_in_ga(T148, s(s(s(s(s(T150)))))) → U16_ga(T148, T150, mult261_in_ga(T148, T150))
mult261_in_ga(0, 0) → mult261_out_ga(0, 0)
mult261_in_ga(s(T145), T147) → U17_ga(T145, T147, mult229_in_ga(T145, T147))
U17_ga(T145, T147, mult229_out_ga(T145, T147)) → mult261_out_ga(s(T145), T147)
mult261_in_ga(T148, s(T150)) → U18_ga(T148, T150, mult261_in_ga(T148, T150))
U18_ga(T148, T150, mult261_out_ga(T148, T150)) → mult261_out_ga(T148, s(T150))
U16_ga(T148, T150, mult261_out_ga(T148, T150)) → mult229_out_ga(T148, s(s(s(s(s(T150))))))
U15_ga(T145, T147, mult229_out_ga(T145, T147)) → mult229_out_ga(s(T145), s(s(s(s(T147)))))
U91_gga(T145, T147, mult229_out_ga(T145, T147)) → times1_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
times1_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U92_gga(T148, T150, mult261_in_ga(T148, T150))
U92_gga(T148, T150, mult261_out_ga(T148, T150)) → times1_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
times1_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U93_gga(T151, T154, mult261_in_ga(T151, T154))
U93_gga(T151, T154, mult261_out_ga(T151, T154)) → times1_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
times1_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → times1_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
times1_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
times1_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U94_gga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(0, s(s(s(s(s(0)))))) → mult300_out_ga(0, s(s(s(s(s(0))))))
mult300_in_ga(s(T182), s(s(s(s(s(T184)))))) → U19_ga(T182, T184, mult300_in_ga(T182, T184))
mult300_in_ga(T185, s(s(s(s(s(s(T187))))))) → U20_ga(T185, T187, mult340_in_ga(T185, T187))
mult340_in_ga(0, 0) → mult340_out_ga(0, 0)
mult340_in_ga(s(T182), T184) → U21_ga(T182, T184, mult300_in_ga(T182, T184))
U21_ga(T182, T184, mult300_out_ga(T182, T184)) → mult340_out_ga(s(T182), T184)
mult340_in_ga(T185, s(T187)) → U22_ga(T185, T187, mult340_in_ga(T185, T187))
U22_ga(T185, T187, mult340_out_ga(T185, T187)) → mult340_out_ga(T185, s(T187))
U20_ga(T185, T187, mult340_out_ga(T185, T187)) → mult300_out_ga(T185, s(s(s(s(s(s(T187)))))))
U19_ga(T182, T184, mult300_out_ga(T182, T184)) → mult300_out_ga(s(T182), s(s(s(s(s(T184))))))
U94_gga(T182, T184, mult300_out_ga(T182, T184)) → times1_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
times1_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U95_gga(T185, T187, mult340_in_ga(T185, T187))
U95_gga(T185, T187, mult340_out_ga(T185, T187)) → times1_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
times1_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U96_gga(T188, T191, mult340_in_ga(T188, T191))
U96_gga(T188, T191, mult340_out_ga(T188, T191)) → times1_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
times1_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → times1_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
times1_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → times1_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
times1_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U97_gga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(0, s(s(s(s(s(s(0))))))) → mult379_out_ga(0, s(s(s(s(s(s(0)))))))
mult379_in_ga(s(T222), s(s(s(s(s(s(T224))))))) → U23_ga(T222, T224, mult379_in_ga(T222, T224))
mult379_in_ga(T225, s(s(s(s(s(s(s(T227)))))))) → U24_ga(T225, T227, mult427_in_ga(T225, T227))
mult427_in_ga(0, 0) → mult427_out_ga(0, 0)
mult427_in_ga(s(T222), T224) → U25_ga(T222, T224, mult379_in_ga(T222, T224))
U25_ga(T222, T224, mult379_out_ga(T222, T224)) → mult427_out_ga(s(T222), T224)
mult427_in_ga(T225, s(T227)) → U26_ga(T225, T227, mult427_in_ga(T225, T227))
U26_ga(T225, T227, mult427_out_ga(T225, T227)) → mult427_out_ga(T225, s(T227))
U24_ga(T225, T227, mult427_out_ga(T225, T227)) → mult379_out_ga(T225, s(s(s(s(s(s(s(T227))))))))
U23_ga(T222, T224, mult379_out_ga(T222, T224)) → mult379_out_ga(s(T222), s(s(s(s(s(s(T224)))))))
U97_gga(T222, T224, mult379_out_ga(T222, T224)) → times1_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
times1_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U98_gga(T225, T227, mult427_in_ga(T225, T227))
U98_gga(T225, T227, mult427_out_ga(T225, T227)) → times1_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
times1_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U99_gga(T228, T231, mult427_in_ga(T228, T231))
U99_gga(T228, T231, mult427_out_ga(T228, T231)) → times1_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
times1_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → times1_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
times1_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U100_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(0, 0, 0) → mult14_out_gaa(0, 0, 0)
mult14_in_gaa(s(0), 0, 0) → mult14_out_gaa(s(0), 0, 0)
mult14_in_gaa(s(s(T27)), 0, T29) → U27_gaa(T27, T29, mult25_in_ga(T27, T29))
U27_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult14_out_gaa(s(s(T27)), 0, T29)
mult14_in_gaa(s(T30), 0, s(T32)) → U28_gaa(T30, T32, mult25_in_ga(T30, T32))
U28_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult14_out_gaa(s(T30), 0, s(T32))
mult14_in_gaa(T33, 0, s(T36)) → U29_gaa(T33, T36, mult25_in_ga(T33, T36))
U29_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult14_out_gaa(T33, 0, s(T36))
mult14_in_gaa(0, s(0), s(0)) → mult14_out_gaa(0, s(0), s(0))
mult14_in_gaa(s(0), s(0), s(s(0))) → mult14_out_gaa(s(0), s(0), s(s(0)))
mult14_in_gaa(s(s(T52)), s(0), s(s(T54))) → U30_gaa(T52, T54, mult64_in_ga(T52, T54))
U30_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult14_out_gaa(s(s(T52)), s(0), s(s(T54)))
mult14_in_gaa(s(T55), s(0), s(s(s(T57)))) → U31_gaa(T55, T57, mult72_in_ga(T55, T57))
U31_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult14_out_gaa(s(T55), s(0), s(s(s(T57))))
mult14_in_gaa(T58, s(0), s(s(T61))) → U32_gaa(T58, T61, mult72_in_ga(T58, T61))
U32_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult14_out_gaa(T58, s(0), s(s(T61)))
mult14_in_gaa(0, s(s(0)), s(s(0))) → mult14_out_gaa(0, s(s(0)), s(s(0)))
mult14_in_gaa(s(0), s(s(0)), s(s(s(s(0))))) → mult14_out_gaa(s(0), s(s(0)), s(s(s(s(0)))))
mult14_in_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82))))) → U33_gaa(T80, T82, mult111_in_ga(T80, T82))
U33_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult14_out_gaa(s(s(T80)), s(s(0)), s(s(s(s(T82)))))
mult14_in_gaa(s(T83), s(s(0)), s(s(s(s(s(T85)))))) → U34_gaa(T83, T85, mult127_in_ga(T83, T85))
U34_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult14_out_gaa(s(T83), s(s(0)), s(s(s(s(s(T85))))))
mult14_in_gaa(T86, s(s(0)), s(s(s(T89)))) → U35_gaa(T86, T89, mult127_in_ga(T86, T89))
U35_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult14_out_gaa(T86, s(s(0)), s(s(s(T89))))
mult14_in_gaa(0, s(s(s(0))), s(s(s(0)))) → mult14_out_gaa(0, s(s(s(0))), s(s(s(0))))
mult14_in_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U36_gaa(T111, T113, mult166_in_ga(T111, T113))
U36_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult14_out_gaa(s(s(T111)), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult14_in_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U37_gaa(T114, T116, mult190_in_ga(T114, T116))
U37_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult14_out_gaa(s(T114), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult14_in_gaa(T117, s(s(s(0))), s(s(s(s(T120))))) → U38_gaa(T117, T120, mult190_in_ga(T117, T120))
U38_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult14_out_gaa(T117, s(s(s(0))), s(s(s(s(T120)))))
mult14_in_gaa(0, s(s(s(s(0)))), s(s(s(s(0))))) → mult14_out_gaa(0, s(s(s(s(0)))), s(s(s(s(0)))))
mult14_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult14_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult14_in_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U39_gaa(T145, T147, mult229_in_ga(T145, T147))
U39_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult14_out_gaa(s(s(T145)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult14_in_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U40_gaa(T148, T150, mult261_in_ga(T148, T150))
U40_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult14_out_gaa(s(T148), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult14_in_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U41_gaa(T151, T154, mult261_in_ga(T151, T154))
U41_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult14_out_gaa(T151, s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult14_in_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult14_out_gaa(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult14_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult14_in_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U42_gaa(T182, T184, mult300_in_ga(T182, T184))
U42_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult14_out_gaa(s(s(T182)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult14_in_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U43_gaa(T185, T187, mult340_in_ga(T185, T187))
U43_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult14_out_gaa(s(T185), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult14_in_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U44_gaa(T188, T191, mult340_in_ga(T188, T191))
U44_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult14_out_gaa(T188, s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult14_in_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult14_out_gaa(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult14_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult14_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult14_in_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U45_gaa(T222, T224, mult379_in_ga(T222, T224))
U45_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult14_out_gaa(s(s(T222)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult14_in_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U46_gaa(T225, T227, mult427_in_ga(T225, T227))
U46_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult14_out_gaa(s(T225), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult14_in_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U47_gaa(T228, T231, mult427_in_ga(T228, T231))
U47_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult14_out_gaa(T228, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult14_in_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult14_out_gaa(0, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult14_in_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U48_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U49_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(0, T8, 0) → mult3_out_gaa(0, T8, 0)
mult3_in_gaa(s(0), 0, 0) → mult3_out_gaa(s(0), 0, 0)
mult3_in_gaa(s(s(0)), 0, 0) → mult3_out_gaa(s(s(0)), 0, 0)
mult3_in_gaa(s(s(s(T27))), 0, T29) → U51_gaa(T27, T29, mult25_in_ga(T27, T29))
U51_gaa(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gaa(s(s(s(T27))), 0, T29)
mult3_in_gaa(s(s(T30)), 0, s(T32)) → U52_gaa(T30, T32, mult25_in_ga(T30, T32))
U52_gaa(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gaa(s(s(T30)), 0, s(T32))
mult3_in_gaa(s(T33), 0, s(T36)) → U53_gaa(T33, T36, mult25_in_ga(T33, T36))
U53_gaa(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gaa(s(T33), 0, s(T36))
mult3_in_gaa(s(0), s(0), s(0)) → mult3_out_gaa(s(0), s(0), s(0))
mult3_in_gaa(s(s(0)), s(0), s(s(0))) → mult3_out_gaa(s(s(0)), s(0), s(s(0)))
mult3_in_gaa(s(s(s(T52))), s(0), s(s(T54))) → U54_gaa(T52, T54, mult64_in_ga(T52, T54))
U54_gaa(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gaa(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gaa(s(s(T55)), s(0), s(s(s(T57)))) → U55_gaa(T55, T57, mult72_in_ga(T55, T57))
U55_gaa(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gaa(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gaa(s(T58), s(0), s(s(T61))) → U56_gaa(T58, T61, mult72_in_ga(T58, T61))
U56_gaa(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gaa(s(T58), s(0), s(s(T61)))
mult3_in_gaa(s(0), s(s(0)), s(s(0))) → mult3_out_gaa(s(0), s(s(0)), s(s(0)))
mult3_in_gaa(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gaa(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gaa(T80, T82, mult111_in_ga(T80, T82))
U57_gaa(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gaa(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gaa(T83, T85, mult127_in_ga(T83, T85))
U58_gaa(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gaa(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gaa(s(T86), s(s(0)), s(s(s(T89)))) → U59_gaa(T86, T89, mult127_in_ga(T86, T89))
U59_gaa(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gaa(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gaa(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gaa(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gaa(T111, T113, mult166_in_ga(T111, T113))
U60_gaa(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gaa(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gaa(T114, T116, mult190_in_ga(T114, T116))
U61_gaa(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gaa(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gaa(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gaa(T117, T120, mult190_in_ga(T117, T120))
U62_gaa(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gaa(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gaa(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gaa(T145, T147, mult229_in_ga(T145, T147))
U63_gaa(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gaa(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gaa(T148, T150, mult261_in_ga(T148, T150))
U64_gaa(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gaa(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gaa(T151, T154, mult261_in_ga(T151, T154))
U65_gaa(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gaa(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gaa(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gaa(T182, T184, mult300_in_ga(T182, T184))
U66_gaa(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gaa(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gaa(T185, T187, mult340_in_ga(T185, T187))
U67_gaa(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gaa(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gaa(T188, T191, mult340_in_ga(T188, T191))
U68_gaa(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gaa(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gaa(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gaa(T222, T224, mult379_in_ga(T222, T224))
U69_gaa(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gaa(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gaa(T225, T227, mult427_in_ga(T225, T227))
U70_gaa(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gaa(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gaa(T228, T231, mult427_in_ga(T228, T231))
U71_gaa(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gaa(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gaa(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gaa(T238, T241, mult14_in_gaa(T238, s(T239), T241))
mult14_in_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U50_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(0, T234, 0, 0) → mult456_out_gaaa(0, T234, 0, 0)
mult456_in_gaaa(s(T238), T239, 0, T241) → U76_gaaa(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaaa(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaaa(s(T238), T239, 0, T241)
mult456_in_gaaa(T242, T243, 0, s(T246)) → U77_gaaa(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gaa(T242, T246, mult3_in_gaa(T242, s(T243), T246))
mult3_in_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gaa(T242, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
mult456_in_gaaa(T242, T243, s(T247), s(T246)) → U78_gaaa(T242, T243, T247, T246, mult456_in_gaaa(T242, T243, T247, T246))
U78_gaaa(T242, T243, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult456_out_gaaa(T242, T243, s(T247), s(T246))
U74_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gaa(T248, T249, s(T251)) → U75_gaa(T248, T249, T251, mult3_in_gaa(T248, T249, T251))
U75_gaa(T248, T249, T251, mult3_out_gaa(T248, T249, T251)) → mult3_out_gaa(T248, T249, s(T251))
U73_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gaa(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U77_gaaa(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaaa(T242, T243, 0, s(T246))
U50_gaa(T242, T247, T246, mult456_out_gaaa(T242, T243, T247, T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
U72_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gaa(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U49_gaa(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult14_out_gaa(T242, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
U48_gaa(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult14_out_gaa(s(T238), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
U100_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → times1_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U101_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U101_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U102_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
mult456_in_gaga(0, T234, 0, 0) → mult456_out_gaga(0, T234, 0, 0)
mult456_in_gaga(s(T238), T239, 0, T241) → U76_gaga(T238, T239, T241, mult14_in_gaa(T238, s(T239), T241))
U76_gaga(T238, T239, T241, mult14_out_gaa(T238, s(T239), T241)) → mult456_out_gaga(s(T238), T239, 0, T241)
mult456_in_gaga(T242, T243, 0, s(T246)) → U77_gaga(T242, T243, T246, mult3_in_gaa(T242, s(T243), T246))
U77_gaga(T242, T243, T246, mult3_out_gaa(T242, s(T243), T246)) → mult456_out_gaga(T242, T243, 0, s(T246))
mult456_in_gaga(T242, T243, s(T247), s(T246)) → U78_gaga(T242, T243, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U78_gaga(T242, T243, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult456_out_gaga(T242, T243, s(T247), s(T246))
U102_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → times1_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
times1_in_gga(T248, T249, s(T251)) → U103_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
mult3_in_gga(0, T8, 0) → mult3_out_gga(0, T8, 0)
mult3_in_gga(s(0), 0, 0) → mult3_out_gga(s(0), 0, 0)
mult3_in_gga(s(s(0)), 0, 0) → mult3_out_gga(s(s(0)), 0, 0)
mult3_in_gga(s(s(s(T27))), 0, T29) → U51_gga(T27, T29, mult25_in_ga(T27, T29))
U51_gga(T27, T29, mult25_out_ga(T27, T29)) → mult3_out_gga(s(s(s(T27))), 0, T29)
mult3_in_gga(s(s(T30)), 0, s(T32)) → U52_gga(T30, T32, mult25_in_ga(T30, T32))
U52_gga(T30, T32, mult25_out_ga(T30, T32)) → mult3_out_gga(s(s(T30)), 0, s(T32))
mult3_in_gga(s(T33), 0, s(T36)) → U53_gga(T33, T36, mult25_in_ga(T33, T36))
U53_gga(T33, T36, mult25_out_ga(T33, T36)) → mult3_out_gga(s(T33), 0, s(T36))
mult3_in_gga(s(0), s(0), s(0)) → mult3_out_gga(s(0), s(0), s(0))
mult3_in_gga(s(s(0)), s(0), s(s(0))) → mult3_out_gga(s(s(0)), s(0), s(s(0)))
mult3_in_gga(s(s(s(T52))), s(0), s(s(T54))) → U54_gga(T52, T54, mult64_in_ga(T52, T54))
U54_gga(T52, T54, mult64_out_ga(T52, T54)) → mult3_out_gga(s(s(s(T52))), s(0), s(s(T54)))
mult3_in_gga(s(s(T55)), s(0), s(s(s(T57)))) → U55_gga(T55, T57, mult72_in_ga(T55, T57))
U55_gga(T55, T57, mult72_out_ga(T55, T57)) → mult3_out_gga(s(s(T55)), s(0), s(s(s(T57))))
mult3_in_gga(s(T58), s(0), s(s(T61))) → U56_gga(T58, T61, mult72_in_ga(T58, T61))
U56_gga(T58, T61, mult72_out_ga(T58, T61)) → mult3_out_gga(s(T58), s(0), s(s(T61)))
mult3_in_gga(s(0), s(s(0)), s(s(0))) → mult3_out_gga(s(0), s(s(0)), s(s(0)))
mult3_in_gga(s(s(0)), s(s(0)), s(s(s(s(0))))) → mult3_out_gga(s(s(0)), s(s(0)), s(s(s(s(0)))))
mult3_in_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82))))) → U57_gga(T80, T82, mult111_in_ga(T80, T82))
U57_gga(T80, T82, mult111_out_ga(T80, T82)) → mult3_out_gga(s(s(s(T80))), s(s(0)), s(s(s(s(T82)))))
mult3_in_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85)))))) → U58_gga(T83, T85, mult127_in_ga(T83, T85))
U58_gga(T83, T85, mult127_out_ga(T83, T85)) → mult3_out_gga(s(s(T83)), s(s(0)), s(s(s(s(s(T85))))))
mult3_in_gga(s(T86), s(s(0)), s(s(s(T89)))) → U59_gga(T86, T89, mult127_in_ga(T86, T89))
U59_gga(T86, T89, mult127_out_ga(T86, T89)) → mult3_out_gga(s(T86), s(s(0)), s(s(s(T89))))
mult3_in_gga(s(0), s(s(s(0))), s(s(s(0)))) → mult3_out_gga(s(0), s(s(s(0))), s(s(s(0))))
mult3_in_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113))))))) → U60_gga(T111, T113, mult166_in_ga(T111, T113))
U60_gga(T111, T113, mult166_out_ga(T111, T113)) → mult3_out_gga(s(s(s(T111))), s(s(s(0))), s(s(s(s(s(s(T113)))))))
mult3_in_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116)))))))) → U61_gga(T114, T116, mult190_in_ga(T114, T116))
U61_gga(T114, T116, mult190_out_ga(T114, T116)) → mult3_out_gga(s(s(T114)), s(s(s(0))), s(s(s(s(s(s(s(T116))))))))
mult3_in_gga(s(T117), s(s(s(0))), s(s(s(s(T120))))) → U62_gga(T117, T120, mult190_in_ga(T117, T120))
U62_gga(T117, T120, mult190_out_ga(T117, T120)) → mult3_out_gga(s(T117), s(s(s(0))), s(s(s(s(T120)))))
mult3_in_gga(s(0), s(s(s(s(0)))), s(s(s(s(0))))) → mult3_out_gga(s(0), s(s(s(s(0)))), s(s(s(s(0)))))
mult3_in_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(0)))))))))
mult3_in_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147))))))))) → U63_gga(T145, T147, mult229_in_ga(T145, T147))
U63_gga(T145, T147, mult229_out_ga(T145, T147)) → mult3_out_gga(s(s(s(T145))), s(s(s(s(0)))), s(s(s(s(s(s(s(s(T147)))))))))
mult3_in_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150)))))))))) → U64_gga(T148, T150, mult261_in_ga(T148, T150))
U64_gga(T148, T150, mult261_out_ga(T148, T150)) → mult3_out_gga(s(s(T148)), s(s(s(s(0)))), s(s(s(s(s(s(s(s(s(T150))))))))))
mult3_in_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154)))))) → U65_gga(T151, T154, mult261_in_ga(T151, T154))
U65_gga(T151, T154, mult261_out_ga(T151, T154)) → mult3_out_gga(s(T151), s(s(s(s(0)))), s(s(s(s(s(T154))))))
mult3_in_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0)))))) → mult3_out_gga(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(0)))))))))))
mult3_in_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184))))))))))) → U66_gga(T182, T184, mult300_in_ga(T182, T184))
U66_gga(T182, T184, mult300_out_ga(T182, T184)) → mult3_out_gga(s(s(s(T182))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(T184)))))))))))
mult3_in_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187)))))))))))) → U67_gga(T185, T187, mult340_in_ga(T185, T187))
U67_gga(T185, T187, mult340_out_ga(T185, T187)) → mult3_out_gga(s(s(T185)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(s(s(s(s(T187))))))))))))
mult3_in_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191))))))) → U68_gga(T188, T191, mult340_in_ga(T188, T191))
U68_gga(T188, T191, mult340_out_ga(T188, T191)) → mult3_out_gga(s(T188), s(s(s(s(s(0))))), s(s(s(s(s(s(T191)))))))
mult3_in_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))))
mult3_in_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) → mult3_out_gga(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))
mult3_in_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224))))))))))))) → U69_gga(T222, T224, mult379_in_ga(T222, T224))
U69_gga(T222, T224, mult379_out_ga(T222, T224)) → mult3_out_gga(s(s(s(T222))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(T224)))))))))))))
mult3_in_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227)))))))))))))) → U70_gga(T225, T227, mult427_in_ga(T225, T227))
U70_gga(T225, T227, mult427_out_ga(T225, T227)) → mult3_out_gga(s(s(T225)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(s(s(s(s(s(s(T227))))))))))))))
mult3_in_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231)))))))) → U71_gga(T228, T231, mult427_in_ga(T228, T231))
U71_gga(T228, T231, mult427_out_ga(T228, T231)) → mult3_out_gga(s(T228), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T231))))))))
mult3_in_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0)))))))) → mult3_out_gga(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))))
mult3_in_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241)))))))) → U72_gga(T238, T241, mult14_in_gaa(T238, s(T239), T241))
U72_gga(T238, T241, mult14_out_gaa(T238, s(T239), T241)) → mult3_out_gga(s(s(T238)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(T241))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246))))))))) → U73_gga(T242, T246, mult3_in_gaa(T242, s(T243), T246))
U73_gga(T242, T246, mult3_out_gaa(T242, s(T243), T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246))))))))) → U74_gga(T242, T247, T246, mult456_in_gaga(T242, T243, T247, T246))
U74_gga(T242, T247, T246, mult456_out_gaga(T242, T243, T247, T246)) → mult3_out_gga(s(T242), s(s(s(s(s(s(s(s(T247)))))))), s(s(s(s(s(s(s(s(T246)))))))))
mult3_in_gga(T248, T249, s(T251)) → U75_gga(T248, T249, T251, mult3_in_gga(T248, T249, T251))
U75_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → mult3_out_gga(T248, T249, s(T251))
U103_gga(T248, T249, T251, mult3_out_gga(T248, T249, T251)) → times1_out_gga(T248, T249, s(T251))

The argument filtering Pi contains the following mapping:
times1_in_gga(x1, x2, x3)  =  times1_in_gga(x1, x2)
0  =  0
times1_out_gga(x1, x2, x3)  =  times1_out_gga(x1, x2, x3)
s(x1)  =  s(x1)
U79_gga(x1, x2, x3)  =  U79_gga(x1, x3)
mult25_in_ga(x1, x2)  =  mult25_in_ga(x1)
mult25_out_ga(x1, x2)  =  mult25_out_ga(x1, x2)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U80_gga(x1, x2, x3)  =  U80_gga(x1, x3)
U81_gga(x1, x2, x3)  =  U81_gga(x1, x3)
U82_gga(x1, x2, x3)  =  U82_gga(x1, x3)
mult64_in_ga(x1, x2)  =  mult64_in_ga(x1)
mult64_out_ga(x1, x2)  =  mult64_out_ga(x1, x2)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
mult72_in_ga(x1, x2)  =  mult72_in_ga(x1)
mult72_out_ga(x1, x2)  =  mult72_out_ga(x1, x2)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
U83_gga(x1, x2, x3)  =  U83_gga(x1, x3)
U84_gga(x1, x2, x3)  =  U84_gga(x1, x3)
U85_gga(x1, x2, x3)  =  U85_gga(x1, x3)
mult111_in_ga(x1, x2)  =  mult111_in_ga(x1)
mult111_out_ga(x1, x2)  =  mult111_out_ga(x1, x2)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
mult127_in_ga(x1, x2)  =  mult127_in_ga(x1)
mult127_out_ga(x1, x2)  =  mult127_out_ga(x1, x2)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U86_gga(x1, x2, x3)  =  U86_gga(x1, x3)
U87_gga(x1, x2, x3)  =  U87_gga(x1, x3)
U88_gga(x1, x2, x3)  =  U88_gga(x1, x3)
mult166_in_ga(x1, x2)  =  mult166_in_ga(x1)
mult166_out_ga(x1, x2)  =  mult166_out_ga(x1, x2)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
mult190_in_ga(x1, x2)  =  mult190_in_ga(x1)
mult190_out_ga(x1, x2)  =  mult190_out_ga(x1, x2)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
U89_gga(x1, x2, x3)  =  U89_gga(x1, x3)
U90_gga(x1, x2, x3)  =  U90_gga(x1, x3)
U91_gga(x1, x2, x3)  =  U91_gga(x1, x3)
mult229_in_ga(x1, x2)  =  mult229_in_ga(x1)
mult229_out_ga(x1, x2)  =  mult229_out_ga(x1, x2)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
mult261_in_ga(x1, x2)  =  mult261_in_ga(x1)
mult261_out_ga(x1, x2)  =  mult261_out_ga(x1, x2)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
U92_gga(x1, x2, x3)  =  U92_gga(x1, x3)
U93_gga(x1, x2, x3)  =  U93_gga(x1, x3)
U94_gga(x1, x2, x3)  =  U94_gga(x1, x3)
mult300_in_ga(x1, x2)  =  mult300_in_ga(x1)
mult300_out_ga(x1, x2)  =  mult300_out_ga(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
mult340_in_ga(x1, x2)  =  mult340_in_ga(x1)
mult340_out_ga(x1, x2)  =  mult340_out_ga(x1, x2)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U95_gga(x1, x2, x3)  =  U95_gga(x1, x3)
U96_gga(x1, x2, x3)  =  U96_gga(x1, x3)
U97_gga(x1, x2, x3)  =  U97_gga(x1, x3)
mult379_in_ga(x1, x2)  =  mult379_in_ga(x1)
mult379_out_ga(x1, x2)  =  mult379_out_ga(x1, x2)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
mult427_in_ga(x1, x2)  =  mult427_in_ga(x1)
mult427_out_ga(x1, x2)  =  mult427_out_ga(x1, x2)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U98_gga(x1, x2, x3)  =  U98_gga(x1, x3)
U99_gga(x1, x2, x3)  =  U99_gga(x1, x3)
U100_gga(x1, x2, x3)  =  U100_gga(x1, x3)
mult14_in_gaa(x1, x2, x3)  =  mult14_in_gaa(x1)
mult14_out_gaa(x1, x2, x3)  =  mult14_out_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3)  =  U27_gaa(x1, x3)
U28_gaa(x1, x2, x3)  =  U28_gaa(x1, x3)
U29_gaa(x1, x2, x3)  =  U29_gaa(x1, x3)
U30_gaa(x1, x2, x3)  =  U30_gaa(x1, x3)
U31_gaa(x1, x2, x3)  =  U31_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x3)
U33_gaa(x1, x2, x3)  =  U33_gaa(x1, x3)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x3)
U35_gaa(x1, x2, x3)  =  U35_gaa(x1, x3)
U36_gaa(x1, x2, x3)  =  U36_gaa(x1, x3)
U37_gaa(x1, x2, x3)  =  U37_gaa(x1, x3)
U38_gaa(x1, x2, x3)  =  U38_gaa(x1, x3)
U39_gaa(x1, x2, x3)  =  U39_gaa(x1, x3)
U40_gaa(x1, x2, x3)  =  U40_gaa(x1, x3)
U41_gaa(x1, x2, x3)  =  U41_gaa(x1, x3)
U42_gaa(x1, x2, x3)  =  U42_gaa(x1, x3)
U43_gaa(x1, x2, x3)  =  U43_gaa(x1, x3)
U44_gaa(x1, x2, x3)  =  U44_gaa(x1, x3)
U45_gaa(x1, x2, x3)  =  U45_gaa(x1, x3)
U46_gaa(x1, x2, x3)  =  U46_gaa(x1, x3)
U47_gaa(x1, x2, x3)  =  U47_gaa(x1, x3)
U48_gaa(x1, x2, x3)  =  U48_gaa(x1, x3)
U49_gaa(x1, x2, x3)  =  U49_gaa(x1, x3)
mult3_in_gaa(x1, x2, x3)  =  mult3_in_gaa(x1)
mult3_out_gaa(x1, x2, x3)  =  mult3_out_gaa(x1, x3)
U51_gaa(x1, x2, x3)  =  U51_gaa(x1, x3)
U52_gaa(x1, x2, x3)  =  U52_gaa(x1, x3)
U53_gaa(x1, x2, x3)  =  U53_gaa(x1, x3)
U54_gaa(x1, x2, x3)  =  U54_gaa(x1, x3)
U55_gaa(x1, x2, x3)  =  U55_gaa(x1, x3)
U56_gaa(x1, x2, x3)  =  U56_gaa(x1, x3)
U57_gaa(x1, x2, x3)  =  U57_gaa(x1, x3)
U58_gaa(x1, x2, x3)  =  U58_gaa(x1, x3)
U59_gaa(x1, x2, x3)  =  U59_gaa(x1, x3)
U60_gaa(x1, x2, x3)  =  U60_gaa(x1, x3)
U61_gaa(x1, x2, x3)  =  U61_gaa(x1, x3)
U62_gaa(x1, x2, x3)  =  U62_gaa(x1, x3)
U63_gaa(x1, x2, x3)  =  U63_gaa(x1, x3)
U64_gaa(x1, x2, x3)  =  U64_gaa(x1, x3)
U65_gaa(x1, x2, x3)  =  U65_gaa(x1, x3)
U66_gaa(x1, x2, x3)  =  U66_gaa(x1, x3)
U67_gaa(x1, x2, x3)  =  U67_gaa(x1, x3)
U68_gaa(x1, x2, x3)  =  U68_gaa(x1, x3)
U69_gaa(x1, x2, x3)  =  U69_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x3)
U71_gaa(x1, x2, x3)  =  U71_gaa(x1, x3)
U72_gaa(x1, x2, x3)  =  U72_gaa(x1, x3)
U50_gaa(x1, x2, x3, x4)  =  U50_gaa(x1, x4)
mult456_in_gaaa(x1, x2, x3, x4)  =  mult456_in_gaaa(x1)
mult456_out_gaaa(x1, x2, x3, x4)  =  mult456_out_gaaa(x1, x3, x4)
U76_gaaa(x1, x2, x3, x4)  =  U76_gaaa(x1, x4)
U77_gaaa(x1, x2, x3, x4)  =  U77_gaaa(x1, x4)
U73_gaa(x1, x2, x3)  =  U73_gaa(x1, x3)
U74_gaa(x1, x2, x3, x4)  =  U74_gaa(x1, x4)
U78_gaaa(x1, x2, x3, x4, x5)  =  U78_gaaa(x1, x5)
U75_gaa(x1, x2, x3, x4)  =  U75_gaa(x1, x4)
U101_gga(x1, x2, x3)  =  U101_gga(x1, x3)
U102_gga(x1, x2, x3, x4)  =  U102_gga(x1, x2, x4)
mult456_in_gaga(x1, x2, x3, x4)  =  mult456_in_gaga(x1, x3)
mult456_out_gaga(x1, x2, x3, x4)  =  mult456_out_gaga(x1, x3, x4)
U76_gaga(x1, x2, x3, x4)  =  U76_gaga(x1, x4)
U77_gaga(x1, x2, x3, x4)  =  U77_gaga(x1, x4)
U78_gaga(x1, x2, x3, x4, x5)  =  U78_gaga(x1, x3, x5)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
mult3_in_gga(x1, x2, x3)  =  mult3_in_gga(x1, x2)
mult3_out_gga(x1, x2, x3)  =  mult3_out_gga(x1, x2, x3)
U51_gga(x1, x2, x3)  =  U51_gga(x1, x3)
U52_gga(x1, x2, x3)  =  U52_gga(x1, x3)
U53_gga(x1, x2, x3)  =  U53_gga(x1, x3)
U54_gga(x1, x2, x3)  =  U54_gga(x1, x3)
U55_gga(x1, x2, x3)  =  U55_gga(x1, x3)
U56_gga(x1, x2, x3)  =  U56_gga(x1, x3)
U57_gga(x1, x2, x3)  =  U57_gga(x1, x3)
U58_gga(x1, x2, x3)  =  U58_gga(x1, x3)
U59_gga(x1, x2, x3)  =  U59_gga(x1, x3)
U60_gga(x1, x2, x3)  =  U60_gga(x1, x3)
U61_gga(x1, x2, x3)  =  U61_gga(x1, x3)
U62_gga(x1, x2, x3)  =  U62_gga(x1, x3)
U63_gga(x1, x2, x3)  =  U63_gga(x1, x3)
U64_gga(x1, x2, x3)  =  U64_gga(x1, x3)
U65_gga(x1, x2, x3)  =  U65_gga(x1, x3)
U66_gga(x1, x2, x3)  =  U66_gga(x1, x3)
U67_gga(x1, x2, x3)  =  U67_gga(x1, x3)
U68_gga(x1, x2, x3)  =  U68_gga(x1, x3)
U69_gga(x1, x2, x3)  =  U69_gga(x1, x3)
U70_gga(x1, x2, x3)  =  U70_gga(x1, x3)
U71_gga(x1, x2, x3)  =  U71_gga(x1, x3)
U72_gga(x1, x2, x3)  =  U72_gga(x1, x3)
U73_gga(x1, x2, x3)  =  U73_gga(x1, x3)
U74_gga(x1, x2, x3, x4)  =  U74_gga(x1, x2, x4)
U75_gga(x1, x2, x3, x4)  =  U75_gga(x1, x2, x4)
MULT3_IN_GGA(x1, x2, x3)  =  MULT3_IN_GGA(x1, x2)

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

(193) UsableRulesProof (EQUIVALENT transformation)

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

(194) Obligation:

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

MULT3_IN_GGA(T248, T249, s(T251)) → MULT3_IN_GGA(T248, T249, T251)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
MULT3_IN_GGA(x1, x2, x3)  =  MULT3_IN_GGA(x1, x2)

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

(195) PiDPToQDPProof (SOUND transformation)

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

(196) Obligation:

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

MULT3_IN_GGA(T248, T249) → MULT3_IN_GGA(T248, T249)

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

(197) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = MULT3_IN_GGA(T248, T249) evaluates to t =MULT3_IN_GGA(T248, T249)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from MULT3_IN_GGA(T248, T249) to MULT3_IN_GGA(T248, T249).

(198) FALSE