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