We investigate combinatorial auctions from a practical perspective. The auctioneer gathers information according to a dynamical protocol termed ask price procedure. We demonstrate a method for elucidating whether a procedure gathers sufficient information for deriving a VCG mechanism. We calculate representative valuation functions in a history-contingent manner, and show that it is necessary and sufficient to examine whether efficient allocations with and without any buyer associated with the profile of representative valuation functions were revealed. This method is tractable, and can be applied to general procedures with connectedness. The representative valuation functions could be the sufficient statistics for privacy preservation.