YES
by ttt2 (version ttt2 1.15)
The rewrite relation of the following TRS is considered.
| a(b(x0)) | → | d(x0) |
| b(a(x0)) | → | a(b(x0)) |
| d(c(x0)) | → | f(a(b(b(c(x0))))) |
| d(f(x0)) | → | f(a(b(x0))) |
| a(f(x0)) | → | a(x0) |
final states:
{11, 10, 5, 3, 1}
transitions:
| 23 | → | 4 |
| 23 | → | 3 |
| 23 | → | 25 |
| 25 | → | 4 |
| 25 | → | 3 |
| 10 | → | 3 |
| 10 | → | 1 |
| 10 | → | 13 |
| 3 | → | 4 |
| 3 | → | 24 |
| 9 | → | 22 |
| 5 | → | 3 |
| 5 | → | 1 |
| 5 | → | 13 |
| 1 | → | 11 |
| 13 | → | 3 |
| 2 | → | 12 |
| 7 | → | 18 |
| 19 | → | 9 |
| f0(3) | → | 10 |
| f0(9) | → | 5 |
| c0(2) | → | 6 |
| b0(7) | → | 8 |
| b0(6) | → | 7 |
| b0(2) | → | 4 |
| d1(18) | → | 19 |
| d1(12) | → | 13 |
| a1(24) | → | 25 |
| a1(22) | → | 23 |
| d0(2) | → | 1 |
| a0(2) | → | 11 |
| a0(4) | → | 3 |
| a0(8) | → | 9 |
| f50 | → | 2 |