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 ACP @ CoCo 2021)

1 Non-Joinable Fork

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

t0 = f(c)
f(a)
c
a
= t3

t0 = f(c)
f(a)
c
b
= t3

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