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 |