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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.arXiv:1402.7289v1 fatcat:kb6jyj656zguzn5tl5clplmham