Certification Problem

Input (COPS 150)

We consider the TRS containing the following rules:

f(0,0) → f(0,1) (1)
f(1,0) → f(0,0) (2)
f(x,y) → f(y,x) (3)

The underlying signature is as follows:

{f/2, 0/0, 1/0}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2021)

1 Strongly closed

Confluence is proven since the TRS is strongly closed. The joins can be performed using 2 step(s).