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