A basis is a set A of nonnegative integers such that every sufficiently large integer n can be represented in the form n = a + a i with a , ai e A . If A is a basis, but no proper subset of A is a basis, then A is a minimal basis . A nonbasis is a set of nonnegative integers that is not a basis, and a nonbasis A is maximal if every proper superset of A is a basis . In this paper, minimal bases ...