Certification Problem

Input (COPS 660)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

t0 = c
f(b)
= t1

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