  This is the third revision. We study bases of Pfaffian systems for
$A$-hypergeometric system. Gr\"obner deformations give bases. These bases also
give those for twisted cohomology groups. For hypergeometric system associated
to a class of order polytopes, these bases have a combinatorial description.
The size of the bases associated to a subclass of the order polytopes have the
growth rate of the polynomial order. Bases associated to two chain posets and
bouquets are studied.
