Certification Problem

Input (COPS 740)

We consider the TRS containing the following rules:

f(a,f(x,a)) f(a,f(f(a,a),a)) (1)

The underlying signature is as follows:

{f/2, a/0}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2022)

1 Strongly closed

Confluence is proven since the TRS is strongly closed. The joins can be performed using 0 step(s).