The rewrite relation of the following TRS is considered.
| f(x,a(b(c(y)))) | → | f(b(c(a(b(x)))),y) | (1) |
| f(a(x),y) | → | f(x,a(y)) | (2) |
| f(b(x),y) | → | f(x,b(y)) | (3) |
| f(c(x),y) | → | f(x,c(y)) | (4) |
final states:
{0, 1}
transitions:
| a0(0) | → | 0 |
| b0(0) | → | 0 |
| c0(0) | → | 0 |
| f0(0,0) | → | 1 |
| b1(0) | → | 5 |
| a1(5) | → | 4 |
| c1(4) | → | 3 |
| b1(3) | → | 2 |
| f1(2,0) | → | 1 |
| a1(0) | → | 6 |
| f1(0,6) | → | 1 |
| b1(0) | → | 7 |
| f1(0,7) | → | 1 |
| c1(0) | → | 8 |
| f1(0,8) | → | 1 |
| b1(2) | → | 5 |
| a1(6) | → | 6 |
| a1(7) | → | 6 |
| a1(8) | → | 6 |
| b1(6) | → | 7 |
| b1(7) | → | 7 |
| b1(8) | → | 7 |
| b2(0) | → | 9 |
| f2(3,9) | → | 1 |
| c1(6) | → | 8 |
| c1(7) | → | 8 |
| c1(8) | → | 8 |
| b2(0) | → | 13 |
| a2(13) | → | 12 |
| c2(12) | → | 11 |
| b2(11) | → | 10 |
| f2(10,0) | → | 1 |
| f2(10,6) | → | 1 |
| f2(10,7) | → | 1 |
| f2(10,8) | → | 1 |
| c2(9) | → | 14 |
| f2(4,14) | → | 1 |
| b1(10) | → | 5 |
| b2(10) | → | 13 |
| a2(14) | → | 15 |
| f2(5,15) | → | 1 |
| b3(0) | → | 16 |
| f3(11,16) | → | 1 |
| b3(6) | → | 16 |
| b3(7) | → | 16 |
| b3(8) | → | 16 |
| b2(15) | → | 9 |
| f2(0,9) | → | 1 |
| f2(2,9) | → | 1 |
| f2(10,9) | → | 1 |
| c3(16) | → | 17 |
| f3(12,17) | → | 1 |
| a1(9) | → | 6 |
| b1(9) | → | 7 |
| b2(9) | → | 9 |
| b3(9) | → | 16 |
| c1(9) | → | 8 |
| a3(17) | → | 18 |
| f3(13,18) | → | 1 |
| b3(18) | → | 16 |
| f3(0,16) | → | 1 |
| f3(10,16) | → | 1 |
| a1(16) | → | 6 |
| b1(16) | → | 7 |
| b3(16) | → | 16 |
| c1(16) | → | 8 |
| f2(10,16) | → | 1 |