  Coverability in Petri nets finds applications in verification of safety
properties of reactive systems. We study coverability in the equivalent model:
Vector Addition Systems with States (VASS).
  A k-VASS can be seen as k counters and a finite automaton whose transitions
are labelled with k integers. Counter values are updated by adding the
respective transition labels. A configuration in this system consists of a
state and k counter values. Importantly, the counters are never allowed to take
negative values. The coverability problem asks whether one can traverse the
k-VASS from the initial configuration to a configuration with at least the
counter values of the target.
  In a well-established line of work on k-VASS, coverability in 2-VASS is
already PSPACE-hard when the integer updates are encoded in binary. This lower
bound limits the practicality of applications, so it is natural to focus on
restrictions. In this paper we initiate the study of 2-VASS with one unary
counter. Here, one counter receives binary encoded updates and the other
receives unary encoded updates. Our main result is that coverability in 2-VASS
with one unary counter is in NP. This improves upon the inherited
state-of-the-art PSPACE upper bound. Our main technical contribution is that
one only needs to consider runs in a certain compressed linear form.
