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