Certification Problem

Input (COPS 46)

We consider the TRS containing the following rules:

F(x,x) A (1)
F(x,G(x)) B (2)
C G(C) (3)

The underlying signature is as follows:

{F/2, A/0, G/1, B/0, C/0}

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by csi @ CoCo 2020)

1 Non-Joinable Fork

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

t0 = F(C,C)
F(C,G(C))
B
= t2

t0 = F(C,C)
A
= t1

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