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