Certification Problem

Input (COPS 721)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

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 = b
h(b,a)
= t1

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

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