Certification Problem

Input (COPS 38)

We consider the TRS containing the following rules:

b a (1)
b c (2)
c b (3)
c d (4)

The underlying signature is as follows:

{b/0, a/0, c/0, d/0}

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by ACP @ CoCo 2020)

1 Non-Joinable Fork

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

t0 = c
b
a
= t2

t0 = c
d
= t1

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