We consider the TRS containing the following rules:
| g(a,y) | → | y | (1) |
| f(x,a) | → | f(x,g(x,b)) | (2) |
| g(h(x),y) | → | g(x,h(y)) | (3) |
The underlying signature is as follows:
{g/2, a/0, f/2, b/0, h/1}To prove that the TRS is (non-)confluent, we show (non-)confluence of the following modified system:
| g(h(x),y) | → | g(x,h(y)) | (3) |
| f(x,a) | → | f(x,g(x,b)) | (2) |
| g(a,y) | → | y | (1) |
All redundant rules that were added or removed can be simulated in 2 steps .
Confluence is proven using the following terminating critical-pair-closing-system R:
There are no rules.
There are no rules in the TRS. Hence, it is terminating.