  This work aims at further investigations on the work of Giambruno and Restivo
to find the rank of the intersection of two finitely generated submonoids of a
free monoid. In this connection, we obtain the rank of a finitely generated
submonoid of a free monoid that is accepted by semi-flower automaton with two
bpi's. Further, when the product automaton of two deterministic semi-flower
automata with a unique bpi is semi-flower with two bpi's, we obtain a
sufficient condition on the product automaton in order to satisfy the Hanna
Neumann property.
