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