Certification Problem

Input (COPS 718)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

{h/2, c/0, b/0, f/1, a/0}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2020)

1 Strongly closed

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