The rewrite relation of the following TRS is considered.
0(0(0(1(3(3(2(2(3(0(0(1(3(2(2(3(3(2(x1)))))))))))))))))) |
→ |
3(0(2(3(0(3(0(3(0(0(1(2(3(3(1(2(2(2(x1)))))))))))))))))) |
(1) |
0(0(0(2(2(3(0(0(1(0(0(0(1(0(3(1(2(2(x1)))))))))))))))))) |
→ |
0(0(0(3(2(0(1(3(0(2(1(0(0(1(2(0(0(2(x1)))))))))))))))))) |
(2) |
0(0(1(3(1(0(0(1(3(3(0(0(1(2(2(1(1(1(x1)))))))))))))))))) |
→ |
3(3(0(2(0(0(0(0(1(0(2(1(3(1(1(1(1(1(x1)))))))))))))))))) |
(3) |
0(0(2(0(1(1(3(0(2(3(2(2(0(2(3(3(1(2(x1)))))))))))))))))) |
→ |
0(0(3(2(1(0(0(3(1(3(0(3(2(2(1(2(2(2(x1)))))))))))))))))) |
(4) |
0(0(2(0(3(0(2(2(3(0(2(0(0(2(3(0(0(2(x1)))))))))))))))))) |
→ |
0(0(3(2(2(0(2(0(0(0(2(2(0(3(0(0(3(2(x1)))))))))))))))))) |
(5) |
0(0(2(0(3(3(2(3(1(3(1(0(2(1(3(0(2(0(x1)))))))))))))))))) |
→ |
0(0(1(1(3(0(3(3(1(2(0(2(3(0(2(2(0(3(x1)))))))))))))))))) |
(6) |
0(1(0(0(2(2(2(3(2(1(3(2(3(3(1(0(1(0(x1)))))))))))))))))) |
→ |
0(1(2(3(0(3(3(0(2(0(1(0(2(1(3(2(1(2(x1)))))))))))))))))) |
(7) |
0(1(0(2(2(1(2(1(3(1(1(2(0(1(2(0(1(0(x1)))))))))))))))))) |
→ |
2(0(0(3(1(2(2(1(2(0(1(0(1(2(1(1(1(0(x1)))))))))))))))))) |
(8) |
0(1(1(1(3(0(1(3(1(2(0(2(1(2(2(0(3(0(x1)))))))))))))))))) |
→ |
3(0(3(2(2(1(1(1(2(0(1(1(2(1(3(0(0(0(x1)))))))))))))))))) |
(9) |
0(1(2(2(3(1(3(3(1(3(2(2(3(3(0(2(0(2(x1)))))))))))))))))) |
→ |
0(1(2(3(0(3(3(3(3(2(2(1(2(0(2(3(1(2(x1)))))))))))))))))) |
(10) |
0(1(2(3(0(2(1(1(3(3(3(2(3(1(3(1(3(1(x1)))))))))))))))))) |
→ |
2(1(3(2(3(1(1(3(3(0(3(3(0(3(2(1(1(1(x1)))))))))))))))))) |
(11) |
0(1(2(3(3(3(1(3(3(3(2(3(1(2(0(1(3(1(x1)))))))))))))))))) |
→ |
2(3(0(3(3(3(1(1(3(0(3(1(3(2(3(1(2(1(x1)))))))))))))))))) |
(12) |
0(1(3(2(3(1(1(3(2(2(0(0(1(3(2(3(3(3(x1)))))))))))))))))) |
→ |
2(3(0(3(3(3(1(0(0(1(2(1(3(2(3(2(1(3(x1)))))))))))))))))) |
(13) |
0(2(0(1(0(0(0(1(0(3(0(2(3(3(3(3(0(3(x1)))))))))))))))))) |
→ |
0(3(0(0(0(3(3(2(0(1(1(0(2(3(0(0(3(3(x1)))))))))))))))))) |
(14) |
0(2(0(1(3(1(0(0(3(2(0(2(2(3(0(1(0(0(x1)))))))))))))))))) |
→ |
1(0(0(3(2(1(2(2(2(0(0(3(1(0(0(0(3(0(x1)))))))))))))))))) |
(15) |
0(2(1(0(2(0(3(0(1(0(2(0(2(0(1(2(0(3(x1)))))))))))))))))) |
→ |
0(2(1(2(0(2(1(2(0(3(0(0(3(2(1(0(0(0(x1)))))))))))))))))) |
(16) |
0(3(1(1(2(2(0(0(0(1(3(2(3(3(3(3(3(3(x1)))))))))))))))))) |
→ |
3(0(3(2(3(3(0(0(3(2(1(1(0(3(1(2(3(3(x1)))))))))))))))))) |
(17) |
0(3(1(2(1(0(2(1(3(0(3(2(3(2(3(0(1(2(x1)))))))))))))))))) |
→ |
3(0(2(3(0(3(1(2(1(2(3(0(3(1(0(2(1(2(x1)))))))))))))))))) |
(18) |
0(3(2(3(1(0(0(1(0(0(1(2(3(2(1(1(0(1(x1)))))))))))))))))) |
→ |
3(0(0(3(1(1(0(0(2(1(2(2(0(1(1(0(3(1(x1)))))))))))))))))) |
(19) |
0(3(3(2(3(1(3(2(0(0(2(1(3(1(3(2(3(3(x1)))))))))))))))))) |
→ |
3(2(2(3(2(0(1(2(1(3(1(3(0(3(0(3(3(3(x1)))))))))))))))))) |
(20) |
1(0(0(0(3(0(2(1(3(3(1(2(2(3(1(3(2(1(x1)))))))))))))))))) |
→ |
1(2(1(3(3(0(3(0(3(1(0(2(2(3(1(0(2(1(x1)))))))))))))))))) |
(21) |
1(0(2(0(0(0(1(2(3(0(1(2(2(2(1(2(2(0(x1)))))))))))))))))) |
→ |
1(2(2(0(0(1(1(0(0(2(2(2(2(1(2(0(0(3(x1)))))))))))))))))) |
(22) |
1(0(2(1(2(3(3(0(1(0(2(3(0(1(1(3(3(1(x1)))))))))))))))))) |
→ |
1(2(1(1(1(3(0(3(0(3(1(0(3(2(2(0(3(1(x1)))))))))))))))))) |
(23) |
1(1(0(0(0(2(0(1(0(1(1(0(3(2(1(0(0(2(x1)))))))))))))))))) |
→ |
1(1(2(1(1(0(0(2(3(0(0(0(0(1(1(0(0(2(x1)))))))))))))))))) |
(24) |
1(1(0(3(1(2(0(0(1(3(2(1(2(0(3(0(2(2(x1)))))))))))))))))) |
→ |
1(1(2(2(3(2(1(0(0(3(2(3(0(0(0(1(1(2(x1)))))))))))))))))) |
(25) |
1(2(2(0(3(1(3(0(0(1(3(3(0(3(2(3(1(2(x1)))))))))))))))))) |
→ |
1(0(2(3(3(3(3(0(2(0(3(1(0(3(1(2(1(2(x1)))))))))))))))))) |
(26) |
1(2(2(2(2(0(3(3(2(1(3(0(2(1(3(2(0(3(x1)))))))))))))))))) |
→ |
1(2(2(1(2(1(2(0(2(3(2(2(0(0(3(3(3(3(x1)))))))))))))))))) |
(27) |
1(2(3(0(1(0(3(1(2(3(1(1(1(1(3(2(3(0(x1)))))))))))))))))) |
→ |
1(1(2(1(1(3(0(3(3(2(1(2(0(3(1(1(3(0(x1)))))))))))))))))) |
(28) |
1(3(0(2(0(3(2(2(1(3(2(3(2(2(2(1(3(2(x1)))))))))))))))))) |
→ |
1(3(2(1(2(2(3(3(3(2(1(3(2(0(0(2(2(2(x1)))))))))))))))))) |
(29) |
1(3(1(3(1(1(1(2(1(3(0(1(2(1(3(1(1(0(x1)))))))))))))))))) |
→ |
1(0(1(1(1(3(3(2(3(0(1(2(1(1(1(1(1(3(x1)))))))))))))))))) |
(30) |
1(3(1(3(2(0(0(0(1(3(1(0(2(2(2(1(0(2(x1)))))))))))))))))) |
→ |
1(0(1(1(2(2(0(3(3(0(1(0(1(2(2(3(0(2(x1)))))))))))))))))) |
(31) |
1(3(2(2(0(3(1(1(3(1(3(0(2(1(2(2(0(3(x1)))))))))))))))))) |
→ |
1(1(2(1(0(1(2(3(3(0(3(0(3(2(2(1(2(3(x1)))))))))))))))))) |
(32) |
1(3(3(1(3(1(3(0(1(0(2(3(1(1(1(3(0(3(x1)))))))))))))))))) |
→ |
1(1(1(2(1(3(0(0(3(3(3(0(1(1(3(3(1(3(x1)))))))))))))))))) |
(33) |
2(0(0(0(1(1(3(1(1(1(2(2(2(2(2(0(1(3(x1)))))))))))))))))) |
→ |
2(0(1(2(0(0(3(2(2(1(1(1(1(2(2(1(3(0(x1)))))))))))))))))) |
(34) |
2(0(0(1(3(1(3(2(1(0(0(2(2(2(0(2(0(3(x1)))))))))))))))))) |
→ |
0(2(2(2(0(2(1(0(0(3(0(0(1(2(2(1(3(3(x1)))))))))))))))))) |
(35) |
2(0(1(0(1(2(2(2(2(3(3(1(1(1(1(2(1(2(x1)))))))))))))))))) |
→ |
0(2(2(1(1(1(2(1(0(3(3(2(2(1(1(2(1(2(x1)))))))))))))))))) |
(36) |
2(0(2(0(3(0(0(2(2(1(1(0(3(1(0(3(1(1(x1)))))))))))))))))) |
→ |
2(0(0(3(3(2(2(1(0(1(0(1(0(3(2(1(0(1(x1)))))))))))))))))) |
(37) |
2(0(2(2(3(1(0(3(2(3(0(3(2(0(0(2(0(2(x1)))))))))))))))))) |
→ |
2(0(0(2(3(0(3(3(0(3(2(0(1(2(2(2(0(2(x1)))))))))))))))))) |
(38) |
2(0(3(0(0(1(3(1(2(0(2(1(3(0(2(2(0(0(x1)))))))))))))))))) |
→ |
0(0(3(0(3(2(1(2(1(2(2(1(2(0(0(0(3(0(x1)))))))))))))))))) |
(39) |
2(0(3(1(0(3(2(1(0(2(3(1(0(2(2(1(1(1(x1)))))))))))))))))) |
→ |
2(1(2(2(2(0(1(1(0(0(3(3(1(3(0(2(1(1(x1)))))))))))))))))) |
(40) |
2(1(0(3(1(3(1(2(2(2(2(1(2(3(1(3(0(2(x1)))))))))))))))))) |
→ |
2(3(3(2(1(2(0(3(1(2(2(1(0(3(2(2(1(1(x1)))))))))))))))))) |
(41) |
2(1(2(1(3(0(2(2(3(2(3(1(1(1(3(3(0(2(x1)))))))))))))))))) |
→ |
2(1(2(1(3(2(1(2(3(2(3(3(0(0(3(1(2(1(x1)))))))))))))))))) |
(42) |
2(1(2(2(2(2(2(0(1(3(2(0(0(1(2(3(1(2(x1)))))))))))))))))) |
→ |
2(1(2(2(1(0(0(3(3(0(1(2(2(2(2(2(1(2(x1)))))))))))))))))) |
(43) |
2(1(2(3(1(3(2(0(2(2(3(3(3(2(3(1(3(3(x1)))))))))))))))))) |
→ |
2(3(3(2(2(1(3(2(3(2(1(0(3(3(1(2(3(3(x1)))))))))))))))))) |
(44) |
2(1(3(0(0(2(2(1(1(3(1(3(1(0(0(2(1(2(x1)))))))))))))))))) |
→ |
0(1(2(1(0(1(2(1(0(0(1(1(2(3(3(3(2(2(x1)))))))))))))))))) |
(45) |
2(2(0(0(3(0(1(3(1(0(2(2(2(3(0(1(2(0(x1)))))))))))))))))) |
→ |
0(2(0(3(2(3(2(1(0(2(0(2(1(0(1(0(2(3(x1)))))))))))))))))) |
(46) |
2(2(1(3(1(3(0(0(2(1(2(2(2(1(1(1(0(1(x1)))))))))))))))))) |
→ |
0(2(2(3(3(1(1(2(0(2(1(1(2(1(0(1(2(1(x1)))))))))))))))))) |
(47) |
2(2(1(3(3(0(0(2(1(3(0(1(2(2(2(2(3(3(x1)))))))))))))))))) |
→ |
2(0(2(2(0(2(1(0(3(2(2(1(1(3(2(3(3(3(x1)))))))))))))))))) |
(48) |
2(2(2(2(3(2(0(1(3(1(2(2(2(1(3(2(3(3(x1)))))))))))))))))) |
→ |
2(3(1(2(2(1(2(2(1(0(2(2(2(2(3(3(3(3(x1)))))))))))))))))) |
(49) |
2(2(2(3(0(1(3(2(1(3(3(2(1(2(2(1(2(3(x1)))))))))))))))))) |
→ |
2(2(2(1(1(2(3(2(3(2(2(0(3(1(2(1(3(3(x1)))))))))))))))))) |
(50) |
2(2(3(1(1(1(3(1(2(0(1(2(2(0(1(2(2(2(x1)))))))))))))))))) |
→ |
2(2(1(2(1(3(1(1(2(3(2(2(0(1(2(0(1(2(x1)))))))))))))))))) |
(51) |
2(2(3(2(2(3(1(0(2(3(1(1(1(0(0(1(0(2(x1)))))))))))))))))) |
→ |
0(2(1(1(2(2(0(3(3(0(1(1(2(2(1(0(3(2(x1)))))))))))))))))) |
(52) |
2(3(0(1(3(1(3(3(0(3(0(2(0(3(1(3(2(3(x1)))))))))))))))))) |
→ |
0(2(0(3(3(3(2(1(3(0(3(3(3(3(1(1(2(0(x1)))))))))))))))))) |
(53) |
2(3(2(3(1(2(0(1(3(0(1(3(2(1(0(2(3(3(x1)))))))))))))))))) |
→ |
0(3(1(0(2(2(1(2(2(1(3(3(3(1(0(2(3(3(x1)))))))))))))))))) |
(54) |
2(3(3(2(1(0(3(0(0(0(3(3(1(3(0(0(0(3(x1)))))))))))))))))) |
→ |
2(1(0(3(0(3(0(3(3(3(0(0(0(0(2(1(3(3(x1)))))))))))))))))) |
(55) |
3(0(0(0(2(0(3(2(0(2(2(2(0(0(1(3(0(2(x1)))))))))))))))))) |
→ |
0(0(2(1(2(3(0(3(2(0(2(0(0(3(0(2(0(2(x1)))))))))))))))))) |
(56) |
3(0(0(2(2(2(1(3(1(3(3(3(2(0(2(3(3(3(x1)))))))))))))))))) |
→ |
2(1(2(1(2(3(3(0(2(3(0(3(3(3(2(0(3(3(x1)))))))))))))))))) |
(57) |
3(0(0(3(1(3(0(2(0(2(0(0(1(0(3(2(3(2(x1)))))))))))))))))) |
→ |
0(0(3(2(3(3(0(0(0(3(2(0(1(2(3(1(0(2(x1)))))))))))))))))) |
(58) |
3(0(1(2(1(0(2(1(1(3(0(1(2(3(1(1(1(1(x1)))))))))))))))))) |
→ |
3(3(1(1(1(0(1(2(1(1(1(2(2(3(0(1(0(1(x1)))))))))))))))))) |
(59) |
3(0(2(2(0(1(2(0(0(2(0(2(2(2(3(1(0(2(x1)))))))))))))))))) |
→ |
0(2(1(2(2(3(0(0(3(2(2(1(2(0(2(0(0(2(x1)))))))))))))))))) |
(60) |
3(0(2(2(3(2(2(3(2(2(3(3(2(0(1(3(2(3(x1)))))))))))))))))) |
→ |
0(3(3(2(1(3(3(2(2(3(2(2(2(0(3(2(2(3(x1)))))))))))))))))) |
(61) |
3(0(3(2(2(0(2(0(0(0(1(3(2(3(3(0(3(0(x1)))))))))))))))))) |
→ |
3(0(2(0(1(2(2(0(3(0(2(0(3(0(3(3(3(0(x1)))))))))))))))))) |
(62) |
3(1(0(0(3(0(0(0(0(1(2(0(2(0(2(0(0(1(x1)))))))))))))))))) |
→ |
3(0(0(0(0(0(2(0(0(0(0(3(0(2(1(1(2(1(x1)))))))))))))))))) |
(63) |
3(1(1(1(3(1(3(3(3(2(3(0(0(2(3(1(3(1(x1)))))))))))))))))) |
→ |
3(3(1(2(2(3(0(1(0(3(3(3(1(1(1(3(3(1(x1)))))))))))))))))) |
(64) |
3(1(3(1(1(1(1(3(2(0(0(2(2(2(1(3(3(1(x1)))))))))))))))))) |
→ |
3(1(0(3(1(1(0(2(2(2(3(1(2(1(1(3(3(1(x1)))))))))))))))))) |
(65) |
3(1(3(2(1(1(3(1(2(2(1(3(2(3(1(0(3(1(x1)))))))))))))))))) |
→ |
3(1(3(3(1(2(0(1(1(2(2(1(3(3(2(3(1(1(x1)))))))))))))))))) |
(66) |
3(1(3(2(1(3(1(0(3(2(0(2(0(3(0(2(3(3(x1)))))))))))))))))) |
→ |
2(2(0(1(2(1(0(3(3(3(0(3(2(1(3(3(3(0(x1)))))))))))))))))) |
(67) |
3(2(0(0(0(2(3(3(1(1(0(1(3(2(3(3(0(0(x1)))))))))))))))))) |
→ |
3(0(2(1(2(3(3(0(3(1(0(1(2(3(3(0(0(0(x1)))))))))))))))))) |
(68) |
3(2(1(3(1(2(2(2(3(3(0(2(1(3(0(2(0(2(x1)))))))))))))))))) |
→ |
3(3(3(2(3(2(2(0(2(2(1(0(3(2(1(2(1(0(x1)))))))))))))))))) |
(69) |
3(2(2(1(2(2(3(1(1(2(0(1(3(1(2(2(1(1(x1)))))))))))))))))) |
→ |
3(1(1(1(2(2(1(3(2(3(2(2(1(1(2(0(2(1(x1)))))))))))))))))) |
(70) |
3(2(2(2(3(2(3(0(1(3(2(1(3(2(3(0(2(1(x1)))))))))))))))))) |
→ |
0(0(3(3(2(1(2(1(3(3(3(3(2(2(2(2(2(1(x1)))))))))))))))))) |
(71) |
3(2(3(0(2(2(2(2(0(0(0(1(1(1(3(0(2(3(x1)))))))))))))))))) |
→ |
3(0(2(3(2(0(3(1(2(0(2(1(0(3(2(1(2(0(x1)))))))))))))))))) |
(72) |
3(3(0(2(0(2(0(1(2(0(2(3(0(2(2(0(3(3(x1)))))))))))))))))) |
→ |
3(2(0(3(2(0(0(0(3(0(3(2(2(2(1(2(0(3(x1)))))))))))))))))) |
(73) |
3(3(0(2(3(0(1(3(3(3(1(2(1(3(2(2(0(3(x1)))))))))))))))))) |
→ |
2(3(1(1(0(1(2(0(3(3(3(2(3(2(3(3(0(3(x1)))))))))))))))))) |
(74) |
3(3(0(3(1(0(0(2(2(2(0(0(0(2(2(1(3(2(x1)))))))))))))))))) |
→ |
0(3(2(0(3(3(1(2(1(2(2(0(3(0(0(0(2(2(x1)))))))))))))))))) |
(75) |
3(3(2(0(0(1(0(2(3(3(0(3(1(3(3(1(3(3(x1)))))))))))))))))) |
→ |
0(0(3(3(1(1(0(2(2(3(1(3(3(0(3(3(3(3(x1)))))))))))))))))) |
(76) |
3(3(2(1(3(0(0(1(3(2(0(0(2(3(3(0(0(2(x1)))))))))))))))))) |
→ |
3(0(0(3(0(3(0(1(2(0(3(1(3(0(3(2(2(2(x1)))))))))))))))))) |
(77) |
3(3(2(1(3(2(0(2(0(0(3(1(3(0(2(0(2(2(x1)))))))))))))))))) |
→ |
2(0(1(3(2(2(2(1(2(3(3(0(3(0(0(0(3(2(x1)))))))))))))))))) |
(78) |
3(3(3(1(3(1(3(0(3(3(2(0(1(3(0(1(2(3(x1)))))))))))))))))) |
→ |
3(3(3(1(1(3(1(3(3(3(2(3(0(3(1(2(0(0(x1)))))))))))))))))) |
(79) |
3(3(3(2(3(0(2(2(3(1(2(3(0(3(3(2(2(2(x1)))))))))))))))))) |
→ |
3(0(3(2(2(2(0(3(3(3(2(2(3(2(1(3(3(2(x1)))))))))))))))))) |
(80) |
There are 320 ruless (increase limit for explicit display).
As carrier we take the set
{0,...,3}.
Symbols are labeled by the interpretation of their arguments using the interpretations
(modulo 4):
There are 1280 ruless (increase limit for explicit display).
There are 1280 ruless (increase limit for explicit display).
There are no rules in the TRS. Hence, it is terminating.