  Chu has recently shown that the Abel lemma on summations by parts can serve
as the underlying relation for Bailey's ${}_6\psi_6$ bilateral summation
formula. In other words, the Abel lemma spells out the telescoping nature of
the ${}_6\psi_6$ sum. We present a systematic approach to compute Abel pairs
for bilateral and unilateral basic hypergeometric summation formulas by using
the $q$-Gosper algorithm. It is demonstrated that Abel pairs can be derived
from Gosper pairs. This approach applies to many classical summation formulas.
