The rewrite relation of the following TRS is considered.
5(2(5(3(0(x1))))) |
→ |
5(1(0(0(1(3(0(4(5(1(2(x1))))))))))) |
(15) |
5(1(3(5(4(3(x1)))))) |
→ |
5(2(1(4(1(4(0(3(0(1(1(x1))))))))))) |
(16) |
5(5(1(3(5(0(x1)))))) |
→ |
5(5(1(4(3(0(4(4(5(2(1(x1))))))))))) |
(17) |
5(5(4(4(2(5(x1)))))) |
→ |
5(4(3(1(1(1(1(5(3(3(5(x1))))))))))) |
(18) |
5(2(2(5(0(5(4(x1))))))) |
→ |
5(2(1(4(1(3(3(2(2(5(4(x1))))))))))) |
(19) |
5(3(0(5(5(4(3(x1))))))) |
→ |
5(3(3(0(3(2(3(5(5(1(0(x1))))))))))) |
(20) |
5(3(5(4(3(5(2(x1))))))) |
→ |
5(2(0(5(2(0(5(2(2(3(2(x1))))))))))) |
(21) |
5(4(4(2(5(5(0(x1))))))) |
→ |
5(4(4(0(0(3(3(3(2(2(3(x1))))))))))) |
(22) |
5(4(5(3(5(5(0(x1))))))) |
→ |
5(4(2(2(3(0(2(4(1(1(5(x1))))))))))) |
(23) |
5(5(4(5(1(1(2(x1))))))) |
→ |
5(5(4(0(3(3(3(3(2(5(5(x1))))))))))) |
(24) |
5(5(5(5(5(5(3(x1))))))) |
→ |
5(5(5(0(1(4(0(0(5(0(1(x1))))))))))) |
(25) |
5(3(5(0(0(5(4(3(x1)))))))) |
→ |
5(0(1(2(1(1(5(5(2(1(0(x1))))))))))) |
(26) |
5(3(5(4(2(5(2(3(x1)))))))) |
→ |
5(4(0(4(0(0(2(2(3(4(4(x1))))))))))) |
(27) |
5(3(5(4(5(1(4(0(x1)))))))) |
→ |
5(1(1(1(0(0(3(3(1(2(5(x1))))))))))) |
(28) |
4(2(5(3(0(x1))))) |
→ |
4(1(0(0(1(3(0(4(5(1(2(x1))))))))))) |
(29) |
4(1(3(5(4(3(x1)))))) |
→ |
4(2(1(4(1(4(0(3(0(1(1(x1))))))))))) |
(30) |
4(5(1(3(5(0(x1)))))) |
→ |
4(5(1(4(3(0(4(4(5(2(1(x1))))))))))) |
(31) |
4(5(4(4(2(5(x1)))))) |
→ |
4(4(3(1(1(1(1(5(3(3(5(x1))))))))))) |
(32) |
4(2(2(5(0(5(4(x1))))))) |
→ |
4(2(1(4(1(3(3(2(2(5(4(x1))))))))))) |
(33) |
4(3(0(5(5(4(3(x1))))))) |
→ |
4(3(3(0(3(2(3(5(5(1(0(x1))))))))))) |
(34) |
4(3(5(4(3(5(2(x1))))))) |
→ |
4(2(0(5(2(0(5(2(2(3(2(x1))))))))))) |
(35) |
4(4(4(2(5(5(0(x1))))))) |
→ |
4(4(4(0(0(3(3(3(2(2(3(x1))))))))))) |
(36) |
4(4(5(3(5(5(0(x1))))))) |
→ |
4(4(2(2(3(0(2(4(1(1(5(x1))))))))))) |
(37) |
4(5(4(5(1(1(2(x1))))))) |
→ |
4(5(4(0(3(3(3(3(2(5(5(x1))))))))))) |
(38) |
4(5(5(5(5(5(3(x1))))))) |
→ |
4(5(5(0(1(4(0(0(5(0(1(x1))))))))))) |
(39) |
4(3(5(0(0(5(4(3(x1)))))))) |
→ |
4(0(1(2(1(1(5(5(2(1(0(x1))))))))))) |
(40) |
4(3(5(4(2(5(2(3(x1)))))))) |
→ |
4(4(0(4(0(0(2(2(3(4(4(x1))))))))))) |
(41) |
4(3(5(4(5(1(4(0(x1)))))))) |
→ |
4(1(1(1(0(0(3(3(1(2(5(x1))))))))))) |
(42) |
3(2(5(3(0(x1))))) |
→ |
3(1(0(0(1(3(0(4(5(1(2(x1))))))))))) |
(43) |
3(1(3(5(4(3(x1)))))) |
→ |
3(2(1(4(1(4(0(3(0(1(1(x1))))))))))) |
(44) |
3(5(1(3(5(0(x1)))))) |
→ |
3(5(1(4(3(0(4(4(5(2(1(x1))))))))))) |
(45) |
3(5(4(4(2(5(x1)))))) |
→ |
3(4(3(1(1(1(1(5(3(3(5(x1))))))))))) |
(46) |
3(2(2(5(0(5(4(x1))))))) |
→ |
3(2(1(4(1(3(3(2(2(5(4(x1))))))))))) |
(47) |
3(3(0(5(5(4(3(x1))))))) |
→ |
3(3(3(0(3(2(3(5(5(1(0(x1))))))))))) |
(48) |
3(3(5(4(3(5(2(x1))))))) |
→ |
3(2(0(5(2(0(5(2(2(3(2(x1))))))))))) |
(49) |
3(4(4(2(5(5(0(x1))))))) |
→ |
3(4(4(0(0(3(3(3(2(2(3(x1))))))))))) |
(50) |
3(4(5(3(5(5(0(x1))))))) |
→ |
3(4(2(2(3(0(2(4(1(1(5(x1))))))))))) |
(51) |
3(5(4(5(1(1(2(x1))))))) |
→ |
3(5(4(0(3(3(3(3(2(5(5(x1))))))))))) |
(52) |
3(5(5(5(5(5(3(x1))))))) |
→ |
3(5(5(0(1(4(0(0(5(0(1(x1))))))))))) |
(53) |
3(3(5(0(0(5(4(3(x1)))))))) |
→ |
3(0(1(2(1(1(5(5(2(1(0(x1))))))))))) |
(54) |
3(3(5(4(2(5(2(3(x1)))))))) |
→ |
3(4(0(4(0(0(2(2(3(4(4(x1))))))))))) |
(55) |
3(3(5(4(5(1(4(0(x1)))))))) |
→ |
3(1(1(1(0(0(3(3(1(2(5(x1))))))))))) |
(56) |
2(2(5(3(0(x1))))) |
→ |
2(1(0(0(1(3(0(4(5(1(2(x1))))))))))) |
(57) |
2(1(3(5(4(3(x1)))))) |
→ |
2(2(1(4(1(4(0(3(0(1(1(x1))))))))))) |
(58) |
2(5(1(3(5(0(x1)))))) |
→ |
2(5(1(4(3(0(4(4(5(2(1(x1))))))))))) |
(59) |
2(5(4(4(2(5(x1)))))) |
→ |
2(4(3(1(1(1(1(5(3(3(5(x1))))))))))) |
(60) |
2(2(2(5(0(5(4(x1))))))) |
→ |
2(2(1(4(1(3(3(2(2(5(4(x1))))))))))) |
(61) |
2(3(0(5(5(4(3(x1))))))) |
→ |
2(3(3(0(3(2(3(5(5(1(0(x1))))))))))) |
(62) |
2(3(5(4(3(5(2(x1))))))) |
→ |
2(2(0(5(2(0(5(2(2(3(2(x1))))))))))) |
(63) |
2(4(4(2(5(5(0(x1))))))) |
→ |
2(4(4(0(0(3(3(3(2(2(3(x1))))))))))) |
(64) |
2(4(5(3(5(5(0(x1))))))) |
→ |
2(4(2(2(3(0(2(4(1(1(5(x1))))))))))) |
(65) |
2(5(4(5(1(1(2(x1))))))) |
→ |
2(5(4(0(3(3(3(3(2(5(5(x1))))))))))) |
(66) |
2(5(5(5(5(5(3(x1))))))) |
→ |
2(5(5(0(1(4(0(0(5(0(1(x1))))))))))) |
(67) |
2(3(5(0(0(5(4(3(x1)))))))) |
→ |
2(0(1(2(1(1(5(5(2(1(0(x1))))))))))) |
(68) |
2(3(5(4(2(5(2(3(x1)))))))) |
→ |
2(4(0(4(0(0(2(2(3(4(4(x1))))))))))) |
(69) |
2(3(5(4(5(1(4(0(x1)))))))) |
→ |
2(1(1(1(0(0(3(3(1(2(5(x1))))))))))) |
(70) |
1(2(5(3(0(x1))))) |
→ |
1(1(0(0(1(3(0(4(5(1(2(x1))))))))))) |
(71) |
1(1(3(5(4(3(x1)))))) |
→ |
1(2(1(4(1(4(0(3(0(1(1(x1))))))))))) |
(72) |
1(5(1(3(5(0(x1)))))) |
→ |
1(5(1(4(3(0(4(4(5(2(1(x1))))))))))) |
(73) |
1(5(4(4(2(5(x1)))))) |
→ |
1(4(3(1(1(1(1(5(3(3(5(x1))))))))))) |
(74) |
1(2(2(5(0(5(4(x1))))))) |
→ |
1(2(1(4(1(3(3(2(2(5(4(x1))))))))))) |
(75) |
1(3(0(5(5(4(3(x1))))))) |
→ |
1(3(3(0(3(2(3(5(5(1(0(x1))))))))))) |
(76) |
1(3(5(4(3(5(2(x1))))))) |
→ |
1(2(0(5(2(0(5(2(2(3(2(x1))))))))))) |
(77) |
1(4(4(2(5(5(0(x1))))))) |
→ |
1(4(4(0(0(3(3(3(2(2(3(x1))))))))))) |
(78) |
1(4(5(3(5(5(0(x1))))))) |
→ |
1(4(2(2(3(0(2(4(1(1(5(x1))))))))))) |
(79) |
1(5(4(5(1(1(2(x1))))))) |
→ |
1(5(4(0(3(3(3(3(2(5(5(x1))))))))))) |
(80) |
1(5(5(5(5(5(3(x1))))))) |
→ |
1(5(5(0(1(4(0(0(5(0(1(x1))))))))))) |
(81) |
1(3(5(0(0(5(4(3(x1)))))))) |
→ |
1(0(1(2(1(1(5(5(2(1(0(x1))))))))))) |
(82) |
1(3(5(4(2(5(2(3(x1)))))))) |
→ |
1(4(0(4(0(0(2(2(3(4(4(x1))))))))))) |
(83) |
1(3(5(4(5(1(4(0(x1)))))))) |
→ |
1(1(1(1(0(0(3(3(1(2(5(x1))))))))))) |
(84) |
0(2(5(3(0(x1))))) |
→ |
0(1(0(0(1(3(0(4(5(1(2(x1))))))))))) |
(85) |
0(1(3(5(4(3(x1)))))) |
→ |
0(2(1(4(1(4(0(3(0(1(1(x1))))))))))) |
(86) |
0(5(1(3(5(0(x1)))))) |
→ |
0(5(1(4(3(0(4(4(5(2(1(x1))))))))))) |
(87) |
0(5(4(4(2(5(x1)))))) |
→ |
0(4(3(1(1(1(1(5(3(3(5(x1))))))))))) |
(88) |
0(2(2(5(0(5(4(x1))))))) |
→ |
0(2(1(4(1(3(3(2(2(5(4(x1))))))))))) |
(89) |
0(3(0(5(5(4(3(x1))))))) |
→ |
0(3(3(0(3(2(3(5(5(1(0(x1))))))))))) |
(90) |
0(3(5(4(3(5(2(x1))))))) |
→ |
0(2(0(5(2(0(5(2(2(3(2(x1))))))))))) |
(91) |
0(4(4(2(5(5(0(x1))))))) |
→ |
0(4(4(0(0(3(3(3(2(2(3(x1))))))))))) |
(92) |
0(4(5(3(5(5(0(x1))))))) |
→ |
0(4(2(2(3(0(2(4(1(1(5(x1))))))))))) |
(93) |
0(5(4(5(1(1(2(x1))))))) |
→ |
0(5(4(0(3(3(3(3(2(5(5(x1))))))))))) |
(94) |
0(5(5(5(5(5(3(x1))))))) |
→ |
0(5(5(0(1(4(0(0(5(0(1(x1))))))))))) |
(95) |
0(3(5(0(0(5(4(3(x1)))))))) |
→ |
0(0(1(2(1(1(5(5(2(1(0(x1))))))))))) |
(96) |
0(3(5(4(2(5(2(3(x1)))))))) |
→ |
0(4(0(4(0(0(2(2(3(4(4(x1))))))))))) |
(97) |
0(3(5(4(5(1(4(0(x1)))))))) |
→ |
0(1(1(1(0(0(3(3(1(2(5(x1))))))))))) |
(98) |
As carrier we take the set
{0,...,5}.
Symbols are labeled by the interpretation of their arguments using the interpretations
(modulo 6):
There are 504 ruless (increase limit for explicit display).
There are 504 ruless (increase limit for explicit display).
There are no rules in the TRS. Hence, it is terminating.