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We give an upper bound of n((n−1)!−(n−3)!) for the possible largest size of a subsemigroup of the full transformational semigroup over n elements consisting only of nonpermutational transformations. As an application we gain the same upper bound for the syntactic complexity of (generalized) definite languages as well.doi:10.14232/actacyb.22.3.2016.9 fatcat:xrfbkivuuzgqjan7miaelavjn4