The rewrite relation of the following TRS is considered.
| f(0,1,x) | → | f(x,x,x) | (1) |
| f(x,y,z) | → | 2 | (2) |
| 0 | → | 2 | (3) |
| 1 | → | 2 | (4) |
| f#(0,1,x) | → | f#(x,x,x) | (5) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
| f#(0,1,x) | → | f#(x,x,x) | (5) |
| 3 | ≥ | 1 | |
| 3 | ≥ | 2 | |
| 3 | ≥ | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.