Certification Problem

Input (COPS 656)

We consider the TRS containing the following rules:

a → f(c) (1)
c → c (2)

The underlying signature is as follows:

{a/0, f/1, c/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 0 step(s).