Certification Problem

Input (COPS 40)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

{f/1, a/0, b/0, c/0, d/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 3 step(s).