  Solvable vertex models in statistical mechanics give rise to soliton cellular
automata at q=0 in a ferromagnetic regime. By means of the crystal base theory
we study a class of such automata associated with non-exceptional quantum
affine algebras U'_q(\hat{\geh}_n). Let B_l be the crystal of the
U'_q(\hat{\geh}_n)-module corresponding to the l-fold symmetric fusion of the
vector representation. For any crystal of the form B = B_{l_1} \otimes ...
\otimes B_{l_N}, we prove that the combinatorial R matrix B_M \otimes B
\xrightarrow{\sim} B \otimes B_M is factorized into a product of Weyl group
operators in a certain domain if M is sufficiently large. It implies the
factorization of certain transfer matrix at q=0, hence the time evolution in
the associated cellular automata. The result generalizes the ball-moving
algorithm in the box-ball systems.
