Certification Problem

Input (COPS 665)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by csi @ CoCo 2021)

1 Non-Joinable Fork

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

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

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

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