  We present a new algorithm to compute minimal telescopers for rational
functions in two discrete variables. As with recent reduction-based approaches,
our algorithm has the important feature that the computation of a telescoper is
independent of its certificate. In addition, our algorithm uses a compact
representation of the certificate, which allows it to be easily manipulated and
analyzed without knowing the precise expanded form. This representation hides
potential expression swell until the final (and optional) expansion, which can
be accomplished in time polynomial in the size of the expanded certificate. A
complexity analysis, along with a Maple implementation, indicates that our
algorithm has better theoretical and practical performance than the
reduction-based approach in the rational case.
