Decidability in dimensions two through five

Determine whether the existence of polyhedral inductive invariants suitable for proving that a control location is unreachable is decidable for linear-arithmetic programs with between two and five numerical variables, inclusive.

Background

The paper proves that deciding whether a linear-arithmetic program admits polyhedral inductive invariants sufficient to establish unreachability is undecidable for programs with six numerical variables, including deterministic programs with closed transition guards. It also notes that the problem is decidable in dimension one because one-dimensional polyhedra correspond to intervals, and that an encoding using seven numerical variables can reduce the number of control locations to one, apart from the bad state. The unresolved dimensional range is therefore dimensions two through five, inclusive.