Certification Problem

Input (COPS 711)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by csi @ CoCo 2021)

1 Non-Joinable Fork

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

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

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

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