Certification Problem

Input (COPS 90)

We consider the TRS containing the following rules:

f(f(x)) → f(g(f(x))) (1)

The underlying signature is as follows:

{f/1, g/1}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2023)

1 Strongly closed

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