Certification Problem

Input (COPS 34)

We consider the TRS containing the following rules:

f(a,b) c (1)
a a' (2)
b b' (3)
c f(a',b) (4)
c f(a,b') (5)
c f(a,b) (6)

The underlying signature is as follows:

{f/2, a/0, b/0, c/0, a'/0, b'/0}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by csi @ CoCo 2021)

1 Strongly closed

Confluence is proven since the TRS is strongly closed. The joins can be performed using 7 step(s).