Certification Problem

Input (COPS 671)

We consider the TRS containing the following rules:

f(f(f(b))) b (1)
h(h(a,a),h(f(f(a)),h(c,b))) f(c) (2)

The underlying signature is as follows:

{f/1, b/0, h/2, a/0, c/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).