Repeated hypermoves in minimal optimal sequences

Determine whether a minimal finite optimal hypermove sequence for a finite water-transport instance can average over the same set of barrels more than once.

Background

Theorem finitemacro establishes that, when simultaneous averaging operations (hypermoves) are allowed, the supremum water level at the target vertex is attained by a finite sequence of hypermoves. The paper leaves unresolved whether a sequence that is minimal in the number of hypermoves may repeat an identical averaging operation. Resolving this question would determine whether the number of hypermoves required by a minimal optimal strategy admits a universal bound depending only on the number of vertices; the paper notes that ruling out repetitions would yield a bound of 2^{|V|}.