The rewrite relation of the following TRS is considered.
| a(a(x1)) | → | b(c(x1)) | (1) |
| b(b(x1)) | → | c(d(x1)) | (2) |
| c(c(x1)) | → | d(d(d(x1))) | (3) |
| d(c(x1)) | → | b(f(x1)) | (4) |
| d(d(d(x1))) | → | a(c(x1)) | (5) |
| f(f(x1)) | → | f(b(x1)) | (6) |
| b#(b(x1)) | → | d#(x1) | (7) |
| d#(d(d(x1))) | → | c#(x1) | (8) |
| d#(c(x1)) | → | f#(x1) | (9) |
| c#(c(x1)) | → | d#(x1) | (10) |
| a#(a(x1)) | → | c#(x1) | (11) |
| d#(c(x1)) | → | b#(f(x1)) | (12) |
| c#(c(x1)) | → | d#(d(d(x1))) | (13) |
| a#(a(x1)) | → | b#(c(x1)) | (14) |
| d#(d(d(x1))) | → | a#(c(x1)) | (15) |
| f#(f(x1)) | → | f#(b(x1)) | (16) |
| b#(b(x1)) | → | c#(d(x1)) | (17) |
| c#(c(x1)) | → | d#(d(x1)) | (18) |
| f#(f(x1)) | → | b#(x1) | (19) |
The dependency pairs are split into 1 component.
| f#(f(x1)) | → | b#(x1) | (19) |
| d#(c(x1)) | → | b#(f(x1)) | (12) |
| c#(c(x1)) | → | d#(d(x1)) | (18) |
| b#(b(x1)) | → | c#(d(x1)) | (17) |
| f#(f(x1)) | → | f#(b(x1)) | (16) |
| a#(a(x1)) | → | c#(x1) | (11) |
| c#(c(x1)) | → | d#(x1) | (10) |
| d#(c(x1)) | → | f#(x1) | (9) |
| d#(d(d(x1))) | → | c#(x1) | (8) |
| d#(d(d(x1))) | → | a#(c(x1)) | (15) |
| a#(a(x1)) | → | b#(c(x1)) | (14) |
| c#(c(x1)) | → | d#(d(d(x1))) | (13) |
| b#(b(x1)) | → | d#(x1) | (7) |
| [a(x1)] | = | x1 + 40 |
| [d(x1)] | = | x1 + 28 |
| [b(x1)] | = | x1 + 36 |
| [c(x1)] | = | x1 + 44 |
| [f(x1)] | = | x1 + 36 |
| [d#(x1)] | = | x1 + 0 |
| [f#(x1)] | = | x1 + 43 |
| [c#(x1)] | = | x1 + 13 |
| [a#(x1)] | = | x1 + 11 |
| [b#(x1)] | = | x1 + 6 |
| d(c(x1)) | → | b(f(x1)) | (4) |
| a(a(x1)) | → | b(c(x1)) | (1) |
| c(c(x1)) | → | d(d(d(x1))) | (3) |
| d(d(d(x1))) | → | a(c(x1)) | (5) |
| f(f(x1)) | → | f(b(x1)) | (6) |
| b(b(x1)) | → | c(d(x1)) | (2) |
| f#(f(x1)) | → | b#(x1) | (19) |
| d#(c(x1)) | → | b#(f(x1)) | (12) |
| c#(c(x1)) | → | d#(d(x1)) | (18) |
| b#(b(x1)) | → | c#(d(x1)) | (17) |
| a#(a(x1)) | → | c#(x1) | (11) |
| c#(c(x1)) | → | d#(x1) | (10) |
| d#(c(x1)) | → | f#(x1) | (9) |
| d#(d(d(x1))) | → | c#(x1) | (8) |
| d#(d(d(x1))) | → | a#(c(x1)) | (15) |
| a#(a(x1)) | → | b#(c(x1)) | (14) |
| c#(c(x1)) | → | d#(d(d(x1))) | (13) |
| b#(b(x1)) | → | d#(x1) | (7) |
The dependency pairs are split into 1 component.
| f#(f(x1)) | → | f#(b(x1)) | (16) |
| [a(x1)] | = | 1 |
| [d(x1)] | = | 1 |
| [b(x1)] | = | 1 |
| [c(x1)] | = | 1 |
| [f(x1)] | = | 2 |
| [d#(x1)] | = | x1 + 0 |
| [f#(x1)] | = | x1 + 43 |
| [c#(x1)] | = | x1 + 13 |
| [a#(x1)] | = | x1 + 11 |
| [b#(x1)] | = | x1 + 6 |
| d(c(x1)) | → | b(f(x1)) | (4) |
| a(a(x1)) | → | b(c(x1)) | (1) |
| c(c(x1)) | → | d(d(d(x1))) | (3) |
| d(d(d(x1))) | → | a(c(x1)) | (5) |
| f(f(x1)) | → | f(b(x1)) | (6) |
| b(b(x1)) | → | c(d(x1)) | (2) |
| f#(f(x1)) | → | f#(b(x1)) | (16) |
The dependency pairs are split into 0 components.