We consider the TRS containing the following rules:
| f(a,a,b,b) | → | f(c,c,c,c) | (1) |
| a | → | b | (2) |
| a | → | c | (3) |
| b | → | a | (4) |
| b | → | c | (5) |
The underlying signature is as follows:
{f/4, a/0, b/0, c/0}To prove that the TRS is (non-)confluent, we show (non-)confluence of the following modified system:
| b | → | c | (5) |
| b | → | a | (4) |
| a | → | c | (3) |
| a | → | b | (2) |
| f(a,a,b,b) | → | f(c,c,c,c) | (1) |
| b | → | b | (6) |
| a | → | a | (7) |
All redundant rules that were added or removed can be simulated in 2 steps .