  An affine model of computation is defined as a subset of iterated
immediate-snapshot runs, capturing a wide variety of shared-memory systems,
such as wait-freedom, t-resilience, k-concurrency, and fair shared-memory
adversaries. The question of whether a given task is solvable in a given affine
model is, in general, undecidable. In this paper, we focus on affine models
defined for a system of two processes. We show that the task computability of
2-process affine models is decidable and presents a complete hierarchy of the
five equivalence classes of 2-process affine models.
