YES
by ttt2 (version ttt2 1.15)
The rewrite relation of the following TRS is considered.
| a(b(a(a(x0)))) | → | c(b(a(b(a(x0))))) | 
| a(c(b(x0))) | → | a(a(b(c(b(a(x0)))))) | 
| a(a(b(a(x0)))) | → | a(b(a(b(c(x0))))) | 
| b(c(a(x0))) | → | a(b(c(b(a(a(x0)))))) | 
final states:
{7, 1}
transitions:
| 18 | → | 9 | 
| 31 | → | 15 | 
| 1 | → | 9 | 
| 1 | → | 8 | 
| 4 | → | 13 | 
| 12 | → | 25 | 
| 7 | → | 4 | 
| c1(13) | → | 14 | 
| c1(28) | → | 29 | 
| b1(14) | → | 15 | 
| b1(29) | → | 30 | 
| b1(27) | → | 28 | 
| b1(16) | → | 17 | 
| f30 | → | 2 | 
| a0(8) | → | 9 | 
| a0(2) | → | 8 | 
| a0(12) | → | 7 | 
| a0(6) | → | 1 | 
| a0(4) | → | 5 | 
| c0(10) | → | 11 | 
| c0(2) | → | 3 | 
| a1(30) | → | 31 | 
| a1(25) | → | 26 | 
| a1(26) | → | 27 | 
| a1(17) | → | 18 | 
| a1(15) | → | 16 | 
| b0(5) | → | 6 | 
| b0(9) | → | 10 | 
| b0(11) | → | 12 | 
| b0(3) | → | 4 |