We consider the TRS containing the following rules:
| +(x,0) | → | x | (1) |
| +(s(x),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) |
| +(s(x),y) | → | s(+(y,x)) | (2) |
| +(x,0) | → | x | (1) |
| s(+(0,x33)) | → | s(x33) | (4) |
| +(0,x) | → | x | (5) |
| +(y,s(x)) | → | s(+(y,x)) | (6) |
| s(+(0,x)) | → | s(x) | (7) |
| +(y,s(x31)) | → | s(+(y,x31)) | (8) |
All redundant rules that were added or removed can be simulated in 2 steps .