Certification Problem

Input (COPS 225)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by csi @ CoCo 2020)

1 Non-Joinable Fork

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

t0 = f(a)
f(a')
= t1

t0 = f(a)
b
= t1

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