  The Douglas-Rachford splitting algorithm was originally proposed in 1956 to
solve a system of linear equations arising from the discretization of a partial
differential equation. In 1979, Lions and Mercier brought forward a very
powerful extension of this method suitable to solve optimization problems.
  In this paper, we revisit the original affine setting. We provide a powerful
convergence result for finding a zero of the sum of two maximally monotone
affine relations. As a by product of our analysis, we obtain results concerning
the convergence of iterates of affine nonexpansive mappings as well as
Attouch-Th\'era duality. Numerous examples are presented.
