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A model for searching algorithms is developed which includes most tree-like searching structures such as lists, binary trees, AVL trees and 2, 3-trees. It is shown that no searching algorithm employing a data structure that is uniquely represented (up to isomorphism) can provide search, insert and delete functions all operating faster than c√n time for every n key tree. The c√n bound is shown to be achievable for uniquely represented data structures.