Fixed-parameter tractability for three ranks parameterized by agony and lifetime

Determine whether temporal agony with three ranks is fixed-parameter tractable when parameterized by the combined parameter α+τ, where α is the target temporal agony and τ is the lifetime of the temporal digraph.

Background

The paper leaves open not only fixed-parameter tractability with respect to α alone, but also the apparently more permissive combined parameter α+τ. The lifetime τ denotes the number of temporal layers, and the authors explicitly note that even this combined parameterization is unresolved.