We consider the TRS containing the following rules:
| +(x,0) | → | x | (1) |
| +(x,s(y)) | → | s(+(y,x)) | (2) |
| +(x,y) | → | +(y,x) | (3) |
The underlying signature is as follows:
{+/2, 0/0, s/1}To prove that the TRS is (non-)confluent, we show (non-)confluence of the following modified system:
| +(x,y) | → | +(y,x) | (3) |
| +(x,s(y)) | → | s(+(y,x)) | (2) |
| +(x,0) | → | x | (1) |
| +(0,x) | → | x | (4) |
| +(s(y),x) | → | s(+(y,x)) | (5) |
| +(s(x32),x) | → | s(+(x32,x)) | (6) |
All redundant rules that were added or removed can be simulated in 2 steps .