Certification Problem

Input (COPS 693)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

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).