We consider the TRS containing the following rules:
| f(x1,g(x2)) | → | f(x1,g(x1)) | (1) |
| f(g(y1),y2) | → | f(g(y1),g(y1)) | (2) |
| g(a) | → | g(b) | (3) |
| b | → | a | (4) |
The underlying signature is as follows:
{f/2, g/1, a/0, b/0}To prove that the TRS is (non-)confluent, we show (non-)confluence of the following modified system:
| b | → | a | (4) |
| g(a) | → | g(b) | (3) |
| f(g(y1),y2) | → | f(g(y1),g(y1)) | (2) |
| f(x1,g(x2)) | → | f(x1,g(x1)) | (1) |
| g(a) | → | g(a) | (5) |
| f(g(y1),y2) | → | f(g(y1),g(g(y1))) | (6) |
All redundant rules that were added or removed can be simulated in 2 steps .