Certification Problem

Input (COPS 664)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by csi @ CoCo 2022)

1 Non-Joinable Fork

The system is not confluent due to the following forking derivations.

t0 = f(f(f(c)))
f(f(f(a)))
= t1

t0 = f(f(f(c)))
b
f(h(c,b))
f(h(a,b))
= t3

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