  For any simple complex algebraic group, we define upper/lower half-decorated
geometric crystals and show that their tropicalization will be upper/lower
normal Kashiwara's crystals. In particular, we show that the tropicalization of
the half-decorated geometric crystal on the big Bruhat
cell(=$B^-_{w_0}:=B^-\cap U\bar w_0 U$) is isomorphic to the crystal
$B(\infty)$ of the nilpotent subalgebra of quantum group $U_q^-(\mathfrak g)$.
As an application, we shall show that any cellular crystal associated with a
reduced word is connected in the sense of a crystal graph.
