We consider the TRS containing the following rules:
| +(0,y) | → | y | (1) |
| +(s(0),y) | → | s(y) | (2) |
| +(s(s(x)),y) | → | s(s(+(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:
| +(s(s(x)),y) | → | s(s(+(y,x))) | (3) |
| +(s(0),y) | → | s(y) | (2) |
| +(0,y) | → | y | (1) |
All redundant rules that were added or removed can be simulated in 2 steps .
Confluence is proven using the following terminating critical-pair-closing-system R:
There are no rules.
There are no rules in the TRS. Hence, it is terminating.