Let S =  be a given vector of n real numbers. The
rank of a real z with respect to S is defined as the number of elements s_i in
S such that s_i is less than or equal to z. We consider the following decision
problem: determine whether the odd-numbered elements s_1, s_3, s_5, ... are
precisely the elements of S whose rank with respect to S is odd. We prove a
bound of Theta(n log n) on the number of operations required to solve this
problem in the algebraic computation tree model.Comment: 3 page