  A generalized method of alternating resolvents was introduced by Boikanyo and
Moro{\c s}anu as a way to approximate common zeros of two maximal monotone
operators. In this paper we analyse the strong convergence of this algorithm
under two different sets of conditions. As a consequence we obtain effective
rates of metastability (in the sense of Terence Tao) and quasi-rates of
asymptotic regularity. Furthermore, we bypass the need for sequential weak
compactness in the original proofs. Our quantitative results are obtained using
proof-theoretical techniques in the context of the proof mining program.
