Certification Problem

Input (COPS 684)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

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 = b
f(c)
= t1

t0 = b
c
= t1

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