Affine Chabauty II

We present an algorithm for determining the set of $S$-integral points on an affine curve based on the Affine Chabauty method developed in the first part of this series. We achieve this by constructing explicit logarithmic differentials whose integrals take on prescribed values on $S$-integral points. Along the way, we prove a $p$-adic residue theorem for Coleman integrals of log differentials.