Blackbox computation of $A_infty$-algebras

Kadeishvilis 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.