We consider the TRS containing the following rules:
| f(a) | → | b | (1) |
| f(a) | → | f(c) | (2) |
| a | → | d | (3) |
| f(d) | → | b | (4) |
| f(c) | → | b | (5) |
| d | → | c | (6) |
The underlying signature is as follows:
{f/1, a/0, b/0, c/0, d/0}To prove that the TRS is (non-)confluent, we show (non-)confluence of the following modified system:
| a | → | d | (3) |
| f(c) | → | b | (5) |
| d | → | c | (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.