Certification Problem

Input (COPS 673)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by csi @ CoCo 2022)

1 Non-Joinable Fork

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

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

t0 = h(b,b)
a
= t1

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