The rewrite relation of the following TRS is considered.
0(0(0(0(0(1(2(2(1(0(3(2(3(x1))))))))))))) |
→ |
1(1(2(2(3(0(2(2(0(1(2(0(2(2(1(3(2(x1))))))))))))))))) |
(1) |
0(0(2(3(2(1(0(2(1(2(0(3(0(x1))))))))))))) |
→ |
3(2(2(2(2(3(3(3(2(2(3(0(2(2(2(0(0(x1))))))))))))))))) |
(2) |
0(1(0(2(1(0(3(2(0(3(0(2(0(x1))))))))))))) |
→ |
0(3(3(2(2(3(2(2(2(0(1(0(2(0(3(2(0(x1))))))))))))))))) |
(3) |
0(1(2(2(0(2(2(3(0(1(1(1(3(x1))))))))))))) |
→ |
0(2(2(2(1(3(1(2(3(0(2(0(0(2(2(1(1(x1))))))))))))))))) |
(4) |
0(3(0(2(0(0(2(1(2(3(1(3(2(x1))))))))))))) |
→ |
1(0(2(2(1(1(3(0(2(0(0(0(2(2(0(3(2(x1))))))))))))))))) |
(5) |
1(2(2(1(0(0(1(0(3(2(1(2(3(x1))))))))))))) |
→ |
1(2(2(1(3(3(0(2(2(0(2(2(2(0(0(2(1(x1))))))))))))))))) |
(6) |
1(3(0(1(1(1(2(3(1(3(0(2(2(x1))))))))))))) |
→ |
0(2(0(2(2(0(1(1(2(2(2(3(2(0(2(2(1(x1))))))))))))))))) |
(7) |
1(3(3(1(0(1(3(2(2(2(0(0(3(x1))))))))))))) |
→ |
0(2(1(2(2(0(0(0(2(2(2(0(1(2(2(0(1(x1))))))))))))))))) |
(8) |
1(3(3(2(2(0(1(1(1(1(2(0(3(x1))))))))))))) |
→ |
1(2(2(2(3(2(0(2(1(1(2(2(1(3(1(2(1(x1))))))))))))))))) |
(9) |
1(3(3(3(2(2(3(1(2(2(3(3(1(x1))))))))))))) |
→ |
2(1(2(1(2(3(0(2(2(0(0(2(2(2(1(3(1(x1))))))))))))))))) |
(10) |
2(0(0(1(2(0(3(2(3(2(2(3(2(x1))))))))))))) |
→ |
2(0(2(3(0(2(2(1(3(2(2(0(0(0(2(0(2(x1))))))))))))))))) |
(11) |
2(0(0(2(3(2(3(2(1(0(3(2(1(x1))))))))))))) |
→ |
2(0(0(0(0(0(2(2(2(2(1(3(2(2(3(2(1(x1))))))))))))))))) |
(12) |
2(0(1(0(2(2(0(3(0(0(3(3(0(x1))))))))))))) |
→ |
2(0(2(0(2(3(1(1(2(3(1(2(2(2(0(2(0(x1))))))))))))))))) |
(13) |
2(0(1(1(1(3(2(0(0(0(1(0(1(x1))))))))))))) |
→ |
2(1(2(2(2(2(2(0(2(3(2(0(2(1(0(0(0(x1))))))))))))))))) |
(14) |
2(0(3(3(1(0(3(1(2(2(2(2(1(x1))))))))))))) |
→ |
2(2(3(1(0(1(2(2(3(2(2(0(0(1(1(2(2(x1))))))))))))))))) |
(15) |
2(1(0(3(3(0(0(3(1(1(2(3(2(x1))))))))))))) |
→ |
2(1(1(3(1(0(0(2(2(2(1(3(1(1(3(1(2(x1))))))))))))))))) |
(16) |
2(1(1(2(1(1(1(1(1(2(0(3(0(x1))))))))))))) |
→ |
2(1(1(1(0(0(2(0(2(2(0(1(3(2(0(1(0(x1))))))))))))))))) |
(17) |
2(1(1(2(2(3(0(0(3(3(1(3(2(x1))))))))))))) |
→ |
2(1(3(1(0(2(0(3(2(3(2(2(3(2(0(2(2(x1))))))))))))))))) |
(18) |
2(1(1(3(2(3(3(1(0(0(1(2(0(x1))))))))))))) |
→ |
2(3(3(1(2(2(2(1(1(2(2(1(0(3(2(2(3(x1))))))))))))))))) |
(19) |
2(1(1(3(3(0(1(0(0(0(2(1(3(x1))))))))))))) |
→ |
2(0(2(2(1(3(0(2(1(2(3(2(0(0(2(3(0(x1))))))))))))))))) |
(20) |
2(1(2(3(1(2(3(3(2(3(3(1(1(x1))))))))))))) |
→ |
2(2(3(0(0(2(2(1(2(0(1(0(2(0(3(1(2(x1))))))))))))))))) |
(21) |
2(2(0(2(3(2(3(3(1(1(1(3(3(x1))))))))))))) |
→ |
2(2(2(2(2(3(3(3(1(1(3(2(3(2(2(2(2(x1))))))))))))))))) |
(22) |
2(2(1(0(2(3(3(3(0(1(1(1(1(x1))))))))))))) |
→ |
2(0(2(3(1(2(0(2(2(3(2(2(3(2(2(2(2(x1))))))))))))))))) |
(23) |
2(2(1(1(2(0(1(1(0(3(3(0(1(x1))))))))))))) |
→ |
0(2(2(1(0(0(0(1(2(2(0(2(3(1(2(2(0(x1))))))))))))))))) |
(24) |
2(2(1(1(3(1(3(2(0(1(0(0(1(x1))))))))))))) |
→ |
0(0(0(2(2(1(3(0(3(0(0(2(2(3(0(1(1(x1))))))))))))))))) |
(25) |
2(3(0(0(1(2(1(2(3(0(2(1(1(x1))))))))))))) |
→ |
2(2(2(0(1(3(3(0(3(2(0(2(2(0(0(2(2(x1))))))))))))))))) |
(26) |
2(3(2(0(0(0(0(0(3(1(0(2(3(x1))))))))))))) |
→ |
2(3(0(0(2(2(2(1(1(1(3(2(1(3(1(3(2(x1))))))))))))))))) |
(27) |
3(0(1(2(2(3(3(2(2(2(0(1(3(x1))))))))))))) |
→ |
3(1(2(2(0(2(2(0(2(2(1(3(0(0(2(2(1(x1))))))))))))))))) |
(28) |
3(1(2(1(2(3(0(2(1(2(1(2(3(x1))))))))))))) |
→ |
0(0(2(2(2(3(1(0(1(3(2(2(0(1(2(2(2(x1))))))))))))))))) |
(29) |
3(2(0(3(2(0(2(3(1(0(3(2(3(x1))))))))))))) |
→ |
2(1(1(1(3(2(2(0(0(2(3(2(1(2(2(1(3(x1))))))))))))))))) |
(30) |
There are 120 ruless (increase limit for explicit display).
There are 480 ruless (increase limit for explicit display).
As carrier we take the set
{0,...,15}.
Symbols are labeled by the interpretation of their arguments using the interpretations
(modulo 16):
There are 7680 ruless (increase limit for explicit display).
There are 7680 ruless (increase limit for explicit display).
There are no rules in the TRS. Hence, it is terminating.