The rewrite relation of the following TRS is considered.
5(5(x1)) | → | 1(1(2(3(3(2(3(0(4(4(x1)))))))))) | (1) |
0(5(5(x1))) | → | 1(0(1(3(3(0(1(2(4(4(x1)))))))))) | (2) |
5(2(5(x1))) | → | 4(3(0(3(4(4(1(4(3(5(x1)))))))))) | (3) |
0(2(2(4(x1)))) | → | 1(1(3(0(1(2(2(2(1(4(x1)))))))))) | (4) |
0(5(5(1(x1)))) | → | 2(2(3(2(4(1(1(3(3(2(x1)))))))))) | (5) |
0(5(5(4(x1)))) | → | 1(0(4(4(5(2(4(4(4(1(x1)))))))))) | (6) |
1(5(4(0(x1)))) | → | 0(4(4(2(3(3(0(3(3(2(x1)))))))))) | (7) |
5(4(0(0(x1)))) | → | 0(4(3(0(4(3(3(5(0(0(x1)))))))))) | (8) |
5(5(3(4(x1)))) | → | 1(3(2(3(3(0(0(3(2(4(x1)))))))))) | (9) |
0(5(0(2(1(x1))))) | → | 1(2(1(2(2(3(0(1(2(0(x1)))))))))) | (10) |
2(2(5(3(5(x1))))) | → | 0(1(1(5(3(0(3(3(1(4(x1)))))))))) | (11) |
2(4(0(5(0(x1))))) | → | 1(1(2(4(4(1(2(2(5(0(x1)))))))))) | (12) |
2(4(0(5(4(x1))))) | → | 2(4(3(1(4(4(0(5(4(4(x1)))))))))) | (13) |
3(5(3(4(0(x1))))) | → | 3(0(3(3(5(2(3(3(4(0(x1)))))))))) | (14) |
0(0(5(1(1(5(x1)))))) | → | 3(1(0(3(3(0(3(2(1(5(x1)))))))))) | (15) |
0(5(5(0(5(5(x1)))))) | → | 2(0(2(2(1(1(0(4(0(5(x1)))))))))) | (16) |
0(5(5(1(1(2(x1)))))) | → | 2(4(3(1(2(1(2(0(4(2(x1)))))))))) | (17) |
1(5(4(0(5(5(x1)))))) | → | 3(0(3(0(4(5(1(5(1(5(x1)))))))))) | (18) |
1(5(5(5(0(5(x1)))))) | → | 0(2(0(3(2(0(3(2(4(5(x1)))))))))) | (19) |
2(2(0(2(3(4(x1)))))) | → | 3(3(2(3(2(1(2(3(2(4(x1)))))))))) | (20) |
2(5(4(0(2(5(x1)))))) | → | 3(2(0(4(0(2(3(0(4(5(x1)))))))))) | (21) |
3(4(2(5(0(0(x1)))))) | → | 0(4(0(0(3(0(3(3(0(0(x1)))))))))) | (22) |
4(0(0(0(4(0(x1)))))) | → | 1(4(3(2(4(3(5(0(2(0(x1)))))))))) | (23) |
4(0(0(5(3(4(x1)))))) | → | 4(0(3(1(1(1(0(0(0(4(x1)))))))))) | (24) |
4(0(5(2(4(0(x1)))))) | → | 2(1(3(3(0(4(2(2(0(0(x1)))))))))) | (25) |
4(0(5(2(5(0(x1)))))) | → | 3(2(1(2(3(5(0(4(1(1(x1)))))))))) | (26) |
4(3(0(2(5(0(x1)))))) | → | 4(1(3(4(1(1(0(1(5(0(x1)))))))))) | (27) |
5(1(4(0(5(2(x1)))))) | → | 5(4(5(1(5(1(2(0(3(3(x1)))))))))) | (28) |
5(1(5(0(2(5(x1)))))) | → | 5(2(2(5(3(1(4(1(4(4(x1)))))))))) | (29) |
5(2(5(2(5(2(x1)))))) | → | 1(1(4(4(5(4(0(4(4(2(x1)))))))))) | (30) |
5(3(5(5(3(2(x1)))))) | → | 3(0(4(5(4(1(5(0(3(2(x1)))))))))) | (31) |
5(5(1(2(5(2(x1)))))) | → | 5(1(3(4(4(0(3(2(4(1(x1)))))))))) | (32) |
5(5(3(4(5(1(x1)))))) | → | 2(1(2(0(3(3(1(0(0(5(x1)))))))))) | (33) |
0(5(3(2(5(1(0(x1))))))) | → | 3(3(0(1(3(4(5(1(4(0(x1)))))))))) | (34) |
2(2(5(3(4(0(1(x1))))))) | → | 2(1(2(2(4(0(2(0(1(3(x1)))))))))) | (35) |
2(3(2(5(1(0(5(x1))))))) | → | 2(0(3(3(3(1(0(5(4(5(x1)))))))))) | (36) |
2(4(1(0(5(5(5(x1))))))) | → | 3(3(3(2(2(1(4(4(5(5(x1)))))))))) | (37) |
2(4(3(1(5(5(3(x1))))))) | → | 0(1(0(4(2(2(2(0(0(3(x1)))))))))) | (38) |
4(0(2(4(5(2(5(x1))))))) | → | 2(0(2(0(4(4(1(3(5(5(x1)))))))))) | (39) |
4(0(5(2(4(2(5(x1))))))) | → | 4(4(4(2(4(2(0(2(1(5(x1)))))))))) | (40) |
4(1(2(4(5(1(4(x1))))))) | → | 4(4(3(3(4(0(4(4(5(4(x1)))))))))) | (41) |
5(1(1(5(2(0(0(x1))))))) | → | 2(3(0(1(1(1(2(3(1(0(x1)))))))))) | (42) |
5(2(2(5(3(0(2(x1))))))) | → | 1(4(2(1(0(2(3(2(4(4(x1)))))))))) | (43) |
5(3(4(0(1(5(3(x1))))))) | → | 4(4(4(2(3(0(4(3(5(3(x1)))))))))) | (44) |
5(4(2(3(1(5(0(x1))))))) | → | 1(2(2(3(3(0(0(2(4(1(x1)))))))))) | (45) |
{5(☐), 4(☐), 3(☐), 2(☐), 1(☐), 0(☐)}
We obtain the transformed TRSThere are 270 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 1620 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 1584 ruless (increase limit for explicit display).
53#(21(45(00(51(40(x1)))))) | → | 53#(21(42(34(11(41(45(00(51(41(40(x1))))))))))) | (1936) |
53#(21(45(00(51(41(x1)))))) | → | 53#(21(42(34(11(41(45(00(51(41(41(x1))))))))))) | (1937) |
53#(21(45(00(51(42(x1)))))) | → | 53#(21(42(34(11(41(45(00(51(41(42(x1))))))))))) | (1938) |
53#(21(45(00(51(43(x1)))))) | → | 53#(21(42(34(11(41(45(00(51(41(43(x1))))))))))) | (1939) |
53#(21(45(00(51(44(x1)))))) | → | 53#(21(42(34(11(41(45(00(51(41(44(x1))))))))))) | (1940) |
53#(21(45(00(51(45(x1)))))) | → | 53#(21(42(34(11(41(45(00(51(41(45(x1))))))))))) | (1941) |
43#(21(45(00(51(40(x1)))))) | → | 43#(21(42(34(11(41(45(00(51(41(40(x1))))))))))) | (1942) |
43#(21(45(00(51(41(x1)))))) | → | 43#(21(42(34(11(41(45(00(51(41(41(x1))))))))))) | (1943) |
43#(21(45(00(51(42(x1)))))) | → | 43#(21(42(34(11(41(45(00(51(41(42(x1))))))))))) | (1944) |
43#(21(45(00(51(43(x1)))))) | → | 43#(21(42(34(11(41(45(00(51(41(43(x1))))))))))) | (1945) |
43#(21(45(00(51(44(x1)))))) | → | 43#(21(42(34(11(41(45(00(51(41(44(x1))))))))))) | (1946) |
43#(21(45(00(51(45(x1)))))) | → | 43#(21(42(34(11(41(45(00(51(41(45(x1))))))))))) | (1947) |
33#(21(45(00(51(40(x1)))))) | → | 33#(21(42(34(11(41(45(00(51(41(40(x1))))))))))) | (1948) |
33#(21(45(00(51(41(x1)))))) | → | 33#(21(42(34(11(41(45(00(51(41(41(x1))))))))))) | (1949) |
33#(21(45(00(51(42(x1)))))) | → | 33#(21(42(34(11(41(45(00(51(41(42(x1))))))))))) | (1950) |
33#(21(45(00(51(43(x1)))))) | → | 33#(21(42(34(11(41(45(00(51(41(43(x1))))))))))) | (1951) |
33#(21(45(00(51(44(x1)))))) | → | 33#(21(42(34(11(41(45(00(51(41(44(x1))))))))))) | (1952) |
33#(21(45(00(51(45(x1)))))) | → | 33#(21(42(34(11(41(45(00(51(41(45(x1))))))))))) | (1953) |
23#(21(45(00(51(40(x1)))))) | → | 23#(21(42(34(11(41(45(00(51(41(40(x1))))))))))) | (1954) |
23#(21(45(00(51(41(x1)))))) | → | 23#(21(42(34(11(41(45(00(51(41(41(x1))))))))))) | (1955) |
23#(21(45(00(51(42(x1)))))) | → | 23#(21(42(34(11(41(45(00(51(41(42(x1))))))))))) | (1956) |
23#(21(45(00(51(43(x1)))))) | → | 23#(21(42(34(11(41(45(00(51(41(43(x1))))))))))) | (1957) |
23#(21(45(00(51(44(x1)))))) | → | 23#(21(42(34(11(41(45(00(51(41(44(x1))))))))))) | (1958) |
23#(21(45(00(51(45(x1)))))) | → | 23#(21(42(34(11(41(45(00(51(41(45(x1))))))))))) | (1959) |
13#(21(45(00(51(40(x1)))))) | → | 13#(21(42(34(11(41(45(00(51(41(40(x1))))))))))) | (1960) |
13#(21(45(00(51(41(x1)))))) | → | 13#(21(42(34(11(41(45(00(51(41(41(x1))))))))))) | (1961) |
13#(21(45(00(51(42(x1)))))) | → | 13#(21(42(34(11(41(45(00(51(41(42(x1))))))))))) | (1962) |
13#(21(45(00(51(43(x1)))))) | → | 13#(21(42(34(11(41(45(00(51(41(43(x1))))))))))) | (1963) |
13#(21(45(00(51(44(x1)))))) | → | 13#(21(42(34(11(41(45(00(51(41(44(x1))))))))))) | (1964) |
13#(21(45(00(51(45(x1)))))) | → | 13#(21(42(34(11(41(45(00(51(41(45(x1))))))))))) | (1965) |
03#(21(45(00(51(40(x1)))))) | → | 03#(21(42(34(11(41(45(00(51(41(40(x1))))))))))) | (1966) |
03#(21(45(00(51(41(x1)))))) | → | 03#(21(42(34(11(41(45(00(51(41(41(x1))))))))))) | (1967) |
03#(21(45(00(51(42(x1)))))) | → | 03#(21(42(34(11(41(45(00(51(41(42(x1))))))))))) | (1968) |
03#(21(45(00(51(43(x1)))))) | → | 03#(21(42(34(11(41(45(00(51(41(43(x1))))))))))) | (1969) |
03#(21(45(00(51(44(x1)))))) | → | 03#(21(42(34(11(41(45(00(51(41(44(x1))))))))))) | (1970) |
03#(21(45(00(51(45(x1)))))) | → | 03#(21(42(34(11(41(45(00(51(41(45(x1))))))))))) | (1971) |
The dependency pairs are split into 0 components.