Certification Problem

Input (COPS 696)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

{h/2, a/0, c/0, b/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(c,c)
h(a,c)
h(a,a)
= t2

t0 = h(c,c)
h(a,c)
b
= t2

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