Certification Problem

Input (COPS 43)

We consider the TRS containing the following rules:

F(x) A (1)
F(x) G(F(x)) (2)
G(F(x)) F(H(x)) (3)
G(F(x)) B (4)

The underlying signature is as follows:

{F/1, A/0, G/1, H/1, B/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(F(x17))
F(A)
G(F(A))
B
= t3

t0 = F(F(x17))
A
= t1

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