Certification Problem

Input (COPS 702)

We consider the TRS containing the following rules:

h(b,a) a (1)
a c (2)
h(c,c) a (3)
f(b) c (4)

The underlying signature is as follows:

{h/2, b/0, a/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 = h(b,a)
h(b,c)
= t1

t0 = h(b,a)
a
= t1

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