  In this paper we investigate the intrinsic sequential time complexity of
universal elimination procedures for arbitrary continuous data structures
encoding input and output objects of elimination theory (i.e. polynomial
equation systems) and admitting the representation of certain limit objects.
  Our main result is the following: let be given such a data structure and
together with this data structure a universal elimination algorithm, say P,
solving arbitrary parametric polynomial equation systems. Suppose that the
algorithm P avoids "unnecessary" branchings and that P admits the efficient
computation of certain natural limit objects (as e.g. the Zariski closure of a
given constructible algebraic set or the parametric greatest common divisor of
two given algebraic families of univariate polynomials). Then P cannot be a
polynomial time algorithm.
  The paper contains different variants of this result and discusses their
practical implications.
