  A linear constraint loop is specified by a system of linear
  inequalities that define the relation between the values of the
  program variables before and after a single execution of the loop
  body. In this paper we consider the problem of determining whether
  such a loop terminates, i.e., whether all maximal executions are
  finite, regardless of how the loop is initialised and how the
  non-determinism in the loop body is resolved. We focus on the
  variant of the termination problem in which the loop variables range
  over $\mathbb{R}$. Our main result is that the termination problem
  is decidable over the reals in dimension~2. A more abstract
  formulation of our main result is that it is decidable whether a
  binary relation on $\mathbb{R}^2$ that is given as a conjunction of
  linear constraints is well-founded.
