Can one determine in finite time whether a point is $S$-integral

Question

Let $x$ be a $\mathbf{Q}$-rational point of $\mathbf{P}^1-\{0,1,\infty\}$.

Let $S$ be a finite set of primes. How do I check in finite time whether $x$ is $S$-integral or not?

I know how to do this in "infinite time". I just check that $v(x) \geq 0$ for all $v\not \in S$.