  In this paper, we apply quantitative operator K-theory to develop an
algorithm for computing K-theory for the class of filtered C *-algebras with
asymptotic finite nuclear decomposition. As a consequence, we prove the
K{\"u}nneth formula for C *-algebras in this class. Our main technical tool is
a quantitative Mayer-Vietoris sequence for K-theory of filtered C *-algebras.
