On the order of the recurrence produced by the method of creative telescoping

We present an algorithm which computes a non-trivial lower bound for the order of the minimal telescoper for a given hypergeometric term. The combination of this algorithm and techniques from indefinite summation leads to an efficiency improvement in Zeilberger's algorithm. We also describe a Maple implementation, and conduct experiments which show the improvement that it makes in the construction of the telescopers.