  The Abramov-Petkovsek reduction computes an additive decomposition of a
hypergeometric term, which extends the functionality of the Gosper algorithm
for indefinite hypergeometric summation. We modify the Abramov-Petkovsek
reduction so as to decompose a hypergeometric term as the sum of a summable
term and a non-summable one. The outputs of the Abramov-Petkovsek reduction and
our modified version share the same required properties. The modified reduction
does not solve any auxiliary linear difference equation explicitly. It is also
more efficient than the original reduction according to computational
experiments. Based on this reduction, we design a new algorithm to compute
minimal telescopers for bivariate hypergeometric terms. The new algorithm can
avoid the costly computation of certificates.
