YES
by ttt2 (version ttt2 1.15)
The rewrite relation of the following TRS is considered.
| a(a(b(a(a(b(a(x0))))))) | → | a(b(a(a(b(a(a(a(b(x0))))))))) | 
| a(b(a(a(b(a(a(x0))))))) | → | b(a(a(a(b(a(a(b(a(x0))))))))) | 
final states:
{1}
transitions:
| 33 | → | 119 | 
| 128 | → | 82 | 
| 98 | → | 85 | 
| 1 | → | 8 | 
| 1 | → | 5 | 
| 1 | → | 3 | 
| 1 | → | 32 | 
| 1 | → | 52 | 
| 40 | → | 27 | 
| 8 | → | 21 | 
| 60 | → | 24 | 
| 38 | → | 80 | 
| 36 | → | 89 | 
| 88 | → | 10 | 
| 4 | → | 51 | 
| 7 | → | 31 | 
| 30 | → | 9 | 
| 30 | → | 22 | 
| 30 | → | 6 | 
| a2(124) | → | 125 | 
| a2(126) | → | 127 | 
| a2(91) | → | 92 | 
| a2(125) | → | 126 | 
| a2(95) | → | 96 | 
| a2(92) | → | 93 | 
| a2(121) | → | 122 | 
| a2(96) | → | 97 | 
| a2(94) | → | 95 | 
| a2(119) | → | 120 | 
| a2(122) | → | 123 | 
| a2(89) | → | 90 | 
| b0(3) | → | 4 | 
| b0(6) | → | 7 | 
| b0(10) | → | 1 | 
| a0(5) | → | 6 | 
| a0(7) | → | 8 | 
| a0(9) | → | 10 | 
| a0(8) | → | 9 | 
| a0(2) | → | 3 | 
| a0(4) | → | 5 | 
| f20 | → | 2 | 
| a1(28) | → | 29 | 
| a1(37) | → | 38 | 
| a1(51) | → | 52 | 
| a1(23) | → | 24 | 
| a1(24) | → | 25 | 
| a1(26) | → | 27 | 
| a1(54) | → | 55 | 
| a1(58) | → | 59 | 
| a1(86) | → | 87 | 
| a1(57) | → | 58 | 
| a1(38) | → | 39 | 
| a1(82) | → | 83 | 
| a1(81) | → | 82 | 
| a1(53) | → | 54 | 
| a1(84) | → | 85 | 
| a1(85) | → | 86 | 
| a1(31) | → | 32 | 
| a1(34) | → | 35 | 
| a1(27) | → | 28 | 
| a1(33) | → | 34 | 
| a1(56) | → | 57 | 
| a1(36) | → | 37 | 
| a1(21) | → | 22 | 
| b2(123) | → | 124 | 
| b2(90) | → | 91 | 
| b2(93) | → | 94 | 
| b2(127) | → | 128 | 
| b2(120) | → | 121 | 
| b2(97) | → | 98 | 
| b1(22) | → | 23 | 
| b1(29) | → | 30 | 
| b1(80) | → | 81 | 
| b1(55) | → | 56 | 
| b1(87) | → | 88 | 
| b1(35) | → | 36 | 
| b1(59) | → | 60 | 
| b1(32) | → | 33 | 
| b1(52) | → | 53 | 
| b1(39) | → | 40 | 
| b1(83) | → | 84 | 
| b1(25) | → | 26 |