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 |