Certification Problem

Input (COPS 669)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by csi @ CoCo 2023)

1 Non-Joinable Fork

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

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

t0 = f(a)
b
= t1

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