Let $R$ be a Noetherian local ring with maximal ideal $I$.

Suppose we have a morphism of smooth $R$-algebras $f : A\to B$ such that its reduction modulo $I^n$

$$f_n : A/I^n \to B/I^n$$

is an isomorphism for all $n\ge 1$. What can we say about $f$? Is $f$ smooth?