Certification Problem

Input (COPS 704)

We consider the TRS containing the following rules:

a f(a) (1)
h(c,a) b (2)

The underlying signature is as follows:

{a/0, f/1, h/2, c/0, b/0}

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by ACP @ CoCo 2020)

1 Non-Joinable Fork

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

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

t0 = h(c,a)
b
= t1

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