Certification Problem

Input (COPS 662)

We consider the TRS containing the following rules:

f(b) c (1)
c c (2)
f(c) b (3)
a b (4)

The underlying signature is as follows:

{f/1, b/0, c/0, a/0}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2021)

1 Strongly closed

Confluence is proven since the TRS is strongly closed. The joins can be performed using 2 step(s).