Certification Problem

Input (COPS 679)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

{f/1, a/0, c/0, b/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 = b
a
= t1

t0 = b
c
= t1

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