Certification Problem

Input (COPS 678)

We consider the TRS containing the following rules:

b a (1)
b c (2)
b h(h(c,a),f(f(b))) (3)
a f(a) (4)
b h(a,a) (5)

The underlying signature is as follows:

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

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by ACP @ CoCo 2023)

1 Non-Joinable Fork

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

t0 = b
a
= t1

t0 = b
c
= t1

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