Certification Problem

Input (COPS 71)

We consider the TRS containing the following rules:

F(x,y) c(y) (1)
G(x) x (2)
f(x) g(x) (3)
g(x) c(x) (4)

The underlying signature is as follows:

{F/2, c/1, G/1, f/1, g/1}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2022)

1 Strongly closed

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