The rewrite relation of the following TRS is considered.
| dec(Cons(Nil,Nil)) | → | Nil | (1) |
| dec(Cons(Nil,Cons(x,xs))) | → | dec(Cons(x,xs)) | (2) |
| dec(Cons(Cons(x,xs),Nil)) | → | dec(Nil) | (3) |
| dec(Cons(Cons(x',xs'),Cons(x,xs))) | → | dec(Cons(x,xs)) | (4) |
| isNilNil(Cons(Nil,Nil)) | → | True | (5) |
| isNilNil(Cons(Nil,Cons(x,xs))) | → | False | (6) |
| isNilNil(Cons(Cons(x,xs),Nil)) | → | False | (7) |
| isNilNil(Cons(Cons(x',xs'),Cons(x,xs))) | → | False | (8) |
| nestdec(Nil) | → | Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Nil))))))))))))))))) | (9) |
| nestdec(Cons(x,xs)) | → | nestdec(dec(Cons(x,xs))) | (10) |
| number17(n) | → | Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Cons(Nil,Nil))))))))))))))))) | (11) |
| goal(x) | → | nestdec(x) | (12) |
final states:
{0, 1, 2, 3, 4, 5}
transitions:
| Cons0(0,0) | → | 0 |
| Nil0 | → | 0 |
| True0 | → | 0 |
| False0 | → | 0 |
| dec0(0) | → | 1 |
| isNilNil0(0) | → | 2 |
| nestdec0(0) | → | 3 |
| number170(0) | → | 4 |
| goal0(0) | → | 5 |
| Nil1 | → | 1 |
| Cons1(0,0) | → | 6 |
| dec1(6) | → | 1 |
| Nil1 | → | 7 |
| dec1(7) | → | 1 |
| True1 | → | 2 |
| False1 | → | 2 |
| Nil1 | → | 8 |
| Nil1 | → | 11 |
| Cons1(8,11) | → | 10 |
| Cons1(8,10) | → | 9 |
| Cons1(8,9) | → | 9 |
| Cons1(8,9) | → | 3 |
| dec1(6) | → | 12 |
| nestdec1(12) | → | 3 |
| Cons1(8,9) | → | 4 |
| nestdec1(0) | → | 5 |
| Nil1 | → | 12 |
| dec1(7) | → | 12 |
| Cons1(8,9) | → | 5 |
| nestdec1(12) | → | 5 |
| Nil2 | → | 13 |
| Nil2 | → | 16 |
| Cons2(13,16) | → | 15 |
| Cons2(13,15) | → | 14 |
| Cons2(13,14) | → | 14 |
| Cons2(13,14) | → | 3 |
| Cons2(13,14) | → | 5 |