Certification Problem

Input (COPS 72)

We consider the TRS containing the following rules:

F(c(x)) G(x) (1)
G(x) F(x) (2)
c(x) x (3)

The underlying signature is as follows:

{F/1, c/1, G/1}

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 2 step(s).