Insertion propagation problem is a class of view update problem in relational databases [1]. Given a source database D, a monotone relational algebraic query Q, and the view V generated by the query Q(D), insertion propagation problem is to find a set Delta D of tuples whose insertion into D will add the given tuples Delta V into the view V via Q without producing side-effect on view. In this paper, we consider the fd-restricted version insertion propagation problem 'fd-vsef-ip', in which we aim to find the Delta D not only view side-effect free but also without introducing inconsistency with respect to the predefined functional dependencies. We study both data and combined complexity of fd-vsef-ip under both single and group insertion. Interestingly, the problem ranges from PTime to Sigma(P)(2)-complete, for queries in different classes in either complexity aspect. We show that the fd-restricted version will be harder to get the optimal solution, contrary to its counterpart under deletion. Our study of this fd-restricted version insertion propagation problem generalize the computational issues involved in data lineage - the process by which databases updated through view insertion under fd.