Certification Problem

Input (COPS 674)

We consider the TRS containing the following rules:

b f(f(b)) (1)
c b (2)
f(f(c)) a (3)

The underlying signature is as follows:

{b/0, f/1, c/0, a/0}

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by ACP @ CoCo 2022)

1 Non-Joinable Fork

The system is not confluent due to the following forking derivations.

t0 = f(f(c))
f(f(b))
= t1

t0 = f(f(c))
a
= t1

The two resulting terms cannot be joined for the following reason: