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) |
There 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):
There are 1620 ruless (increase limit for explicit display).
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.