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