Certification Problem

Input (COPS 253)

We consider the TRS containing the following rules:

c f(c) (1)
c f(h(a)) (2)
f(x) h(f(x)) (3)

The underlying signature is as follows:

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

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by ACP @ CoCo 2023)

1 Non-Joinable Fork

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

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

t0 = c
f(c)
= t1

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