Let $K$ be a finite extension of $\mathbb{Q}_p$, and let $A$ be an affinoid $K$-algebra, i.e. $A$ is isomorphic to a quotient of the Tate algebra $K\left<T_1,\dotsc,T_n\right>$ for some $n$.  Let $A^{\circ}$ be the subring of power-bounded elements.  Is there a general algorithm for computing $A^{\circ}$, or at least identifying whether a subring consisting of power-bounded elements contains all of $A^{\circ}$?

If the general case is too difficult, I'm willing to assume that $A$ is reduced and one-dimensional.