The rewrite relation of the following TRS is considered.
0(0(1(1(x1)))) | → | 2(2(1(3(x1)))) | (1) |
1(4(0(4(x1)))) | → | 1(2(3(1(x1)))) | (2) |
3(4(3(1(1(x1))))) | → | 3(4(0(3(1(x1))))) | (3) |
1(3(1(1(0(4(x1)))))) | → | 1(3(0(2(0(4(x1)))))) | (4) |
2(4(4(5(4(4(3(x1))))))) | → | 2(4(2(3(4(2(2(x1))))))) | (5) |
5(5(4(2(0(2(3(x1))))))) | → | 5(2(4(1(2(3(3(x1))))))) | (6) |
0(4(5(2(1(2(0(1(x1)))))))) | → | 0(1(5(4(2(5(0(0(x1)))))))) | (7) |
4(4(1(4(0(0(1(3(x1)))))))) | → | 4(1(2(3(4(2(5(3(x1)))))))) | (8) |
4(3(0(2(5(3(1(2(3(x1))))))))) | → | 4(1(1(0(0(0(5(3(x1)))))))) | (9) |
4(0(5(5(3(2(1(0(0(0(x1)))))))))) | → | 1(4(3(3(4(3(3(1(0(0(x1)))))))))) | (10) |
4(1(5(2(4(0(1(1(0(1(x1)))))))))) | → | 0(1(0(2(5(0(5(3(5(4(x1)))))))))) | (11) |
3(0(4(4(4(5(3(1(2(5(0(4(x1)))))))))))) | → | 5(3(3(0(3(5(1(0(0(1(0(x1))))))))))) | (12) |
4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) | → | 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) | (13) |
5(4(2(3(0(4(3(2(2(2(4(1(x1)))))))))))) | → | 5(1(0(2(4(4(4(5(1(4(1(x1))))))))))) | (14) |
3(0(0(2(1(1(3(1(5(0(5(1(0(5(x1)))))))))))))) | → | 5(1(0(1(2(2(1(3(3(1(0(2(5(x1))))))))))))) | (15) |
0(4(2(4(1(1(5(3(0(2(2(0(5(1(5(x1))))))))))))))) | → | 1(1(0(0(3(5(5(1(1(2(5(3(5(5(x1)))))))))))))) | (16) |
0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) | → | 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) | (17) |
2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) | → | 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) | (18) |
0(0(0(2(0(3(0(5(1(0(5(0(5(1(0(4(3(x1))))))))))))))))) | → | 0(0(1(4(5(0(0(2(0(0(1(1(3(2(5(3(x1)))))))))))))))) | (19) |
1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) | → | 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) | (20) |
2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) | → | 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) | (21) |
1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) | → | 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) | (22) |
2(4(2(1(5(5(0(1(0(4(2(2(2(3(4(1(0(4(x1)))))))))))))))))) | → | 2(1(3(2(1(2(2(5(1(1(3(5(4(4(5(5(5(x1))))))))))))))))) | (23) |
5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) | → | 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) | (24) |
0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) | → | 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) | (25) |
[5(x1)] | = |
x1 +
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[4(x1)] | = |
x1 +
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[3(x1)] | = |
x1 +
|
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[2(x1)] | = |
x1 +
|
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[1(x1)] | = |
x1 +
|
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[0(x1)] | = |
x1 +
|
4(3(0(2(5(3(1(2(3(x1))))))))) | → | 4(1(1(0(0(0(5(3(x1)))))))) | (9) |
3(0(4(4(4(5(3(1(2(5(0(4(x1)))))))))))) | → | 5(3(3(0(3(5(1(0(0(1(0(x1))))))))))) | (12) |
5(4(2(3(0(4(3(2(2(2(4(1(x1)))))))))))) | → | 5(1(0(2(4(4(4(5(1(4(1(x1))))))))))) | (14) |
3(0(0(2(1(1(3(1(5(0(5(1(0(5(x1)))))))))))))) | → | 5(1(0(1(2(2(1(3(3(1(0(2(5(x1))))))))))))) | (15) |
0(4(2(4(1(1(5(3(0(2(2(0(5(1(5(x1))))))))))))))) | → | 1(1(0(0(3(5(5(1(1(2(5(3(5(5(x1)))))))))))))) | (16) |
0(0(0(2(0(3(0(5(1(0(5(0(5(1(0(4(3(x1))))))))))))))))) | → | 0(0(1(4(5(0(0(2(0(0(1(1(3(2(5(3(x1)))))))))))))))) | (19) |
2(4(2(1(5(5(0(1(0(4(2(2(2(3(4(1(0(4(x1)))))))))))))))))) | → | 2(1(3(2(1(2(2(5(1(1(3(5(4(4(5(5(5(x1))))))))))))))))) | (23) |
{5(☐), 4(☐), 3(☐), 2(☐), 1(☐), 0(☐)}
We obtain the transformed TRSThere are 108 ruless (increase limit for explicit display).
As carrier we take the set {0,...,5}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 6):
[5(x1)] | = | 6x1 + 0 |
[4(x1)] | = | 6x1 + 1 |
[3(x1)] | = | 6x1 + 2 |
[2(x1)] | = | 6x1 + 3 |
[1(x1)] | = | 6x1 + 4 |
[0(x1)] | = | 6x1 + 5 |
There are 648 ruless (increase limit for explicit display).
[50(x1)] | = |
x1 +
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[51(x1)] | = |
x1 +
|
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[52(x1)] | = |
x1 +
|
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[53(x1)] | = |
x1 +
|
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[54(x1)] | = |
x1 +
|
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[55(x1)] | = |
x1 +
|
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[40(x1)] | = |
x1 +
|
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[41(x1)] | = |
x1 +
|
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[42(x1)] | = |
x1 +
|
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[43(x1)] | = |
x1 +
|
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[44(x1)] | = |
x1 +
|
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[45(x1)] | = |
x1 +
|
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[30(x1)] | = |
x1 +
|
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[31(x1)] | = |
x1 +
|
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[32(x1)] | = |
x1 +
|
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[33(x1)] | = |
x1 +
|
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[34(x1)] | = |
x1 +
|
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[35(x1)] | = |
x1 +
|
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[20(x1)] | = |
x1 +
|
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[21(x1)] | = |
x1 +
|
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[22(x1)] | = |
x1 +
|
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[23(x1)] | = |
x1 +
|
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[24(x1)] | = |
x1 +
|
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[25(x1)] | = |
x1 +
|
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[10(x1)] | = |
x1 +
|
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[11(x1)] | = |
x1 +
|
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[12(x1)] | = |
x1 +
|
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[13(x1)] | = |
x1 +
|
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[14(x1)] | = |
x1 +
|
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[15(x1)] | = |
x1 +
|
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[00(x1)] | = |
x1 +
|
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[01(x1)] | = |
x1 +
|
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[02(x1)] | = |
x1 +
|
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[03(x1)] | = |
x1 +
|
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[04(x1)] | = |
x1 +
|
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[05(x1)] | = |
x1 +
|
There are 648 ruless (increase limit for explicit display).
There are no rules in the TRS. Hence, it is terminating.