Certification Problem

Input (COPS 712)

We consider the TRS containing the following rules:

c a (1)
f(c) f(h(b,c)) (2)
a c (3)
c h(f(c),h(b,h(h(b,c),a))) (4)
c b (5)

The underlying signature is as follows:

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

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

t0 = f(c)
f(b)
= t1

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