Certification Problem

Input (COPS 687)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

{b/0, f/1, h/2, a/0, c/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 = h(a,c)
h(a,a)
= t1

t0 = h(a,c)
b
= t1

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