Certification Problem

Input (COPS 21)

We consider the TRS containing the following rules:

b a (1)
b c (2)
c h(b) (3)
c d (4)
a h(a) (5)
d h(d) (6)

The underlying signature is as follows:

{b/0, a/0, c/0, h/1, d/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 = b
a
h(a)
= t2

t0 = b
c
d
= t2

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