Certification Problem

Input (COPS 677)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by ACP @ CoCo 2022)

1 Non-Joinable Fork

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

t0 = b
h(b,c)
h(c,c)
h(a,c)
h(a,a)
= t4

t0 = b
c
a
= t2

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