The rewrite relation of the following TRS is considered.
| a(x1) | → | x1 | (1) |
| a(a(x1)) | → | a(b(a(b(c(a(x1)))))) | (2) |
| c(b(x1)) | → | a(x1) | (3) |
| a#(a(x1)) | → | a#(b(a(b(c(a(x1)))))) | (4) |
| a#(a(x1)) | → | a#(b(c(a(x1)))) | (5) |
| a#(a(x1)) | → | c#(a(x1)) | (6) |
| c#(b(x1)) | → | a#(x1) | (7) |
The dependency pairs are split into 1 component.
| a#(a(x1)) | → | c#(a(x1)) | (6) |
| c#(b(x1)) | → | a#(x1) | (7) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
| c#(b(x1)) | → | a#(x1) | (7) |
| 1 | > | 1 | |
| a#(a(x1)) | → | c#(a(x1)) | (6) |
| 1 | ≥ | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.