2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231304Kadeishvili's proof of the minimality theorem induces an algorithm for the inductive computation of an $A_\infty$-algebra structure on the homology of a dg-algebra. In this paper, we prove that for one class of dg-algebras, the resulting computation will generate a complete $A_\infty$-algebra structure after a finite amount of computational work.11 pages, accepted to the Georgian Journal of Mathematics: Kadeishvili Festschrift issue, tweaked bibliographyRings and AlgebrasAlgebraic Topology17A42, 17-04text