Certification Problem

Input (COPS 717)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

{a/0, c/0, f/1, h/2, b/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 = f(f(a))
f(f(c))
= t1

t0 = f(f(a))
b
= t1

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