Certification Problem

Input (COPS 698)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

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 = c
a
= t1

t0 = c
b
= t1

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