Certification Problem

Input (COPS 691)

We consider the TRS containing the following rules:

h(a,a) f(c) (1)
a a (2)
a a (2)
b h(c,a) (3)

The underlying signature is as follows:

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