We consider the TRS containing the following rules:
| a(x) | → | x | (1) |
| a(a(x)) | → | b(c(x)) | (2) |
| b(x) | → | x | (3) |
| c(x) | → | x | (4) |
| c(b(x)) | → | b(a(c(x))) | (5) |
The underlying signature is as follows:
{a/1, b/1, c/1}To prove that the TRS is (non-)confluent, we show (non-)confluence of the following modified system:
| a(x) | → | x | (1) |
| b(x) | → | x | (3) |
| c(x) | → | x | (4) |
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.