Certification Problem

Input (COPS 103)

We consider the TRS containing the following rules:

f(f(x,y),z) f(x,f(y,z)) (1)
f(x,y) f(y,x) (2)

The underlying signature is as follows:

{f/2}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by csi @ CoCo 2020)

1 Strongly closed

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