We study and present our findings on two closely related problems on xpath rewriting using views when both the view and the query are tree patterns involving /,// and []. First, given view V and query Q, is it possible for Q to have an equivalent rewriting using V which is the union of two or more tree patterns, but not an equivalent rewriting which is a single pattern? This problem is of both theoretical and practical importance because, if the answer is no, then, to answer a query completely using the views, we should use more efficient methods, such as the PTIME algorithm of [12], to find the equivalent rewriting, rather than try to find the union of all contained rewritings and test its equivalence to Q. Second, given a set V of views, we want to know under what conditions a subset V′ of the views are redundant in the sense that for any query Q, the contained rewritings of Q using the views in V′ are contained in those using the views in V − V′ . Solving this problem can...