Certification Problem

Input (COPS 511)

We consider the TRS containing the following rules:

b a (1)
b c (2)
c c (3)
d c (4)
d e (5)
f(x,a) A (6)
f(x,e) A (7)
f(x,A) A (8)
f(c,x) A (9)

The underlying signature is as follows:

{b/0, a/0, c/0, d/0, e/0, f/2, A/0}

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by ACP @ CoCo 2023)

1 Non-Joinable Fork

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

t0 = b
a
= t1

t0 = b
c
= t1

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