Order-independent termination of the reversible-realization heuristic

Let a kinetic differential equation be represented by a polynomial vector field, and consider the heuristic that repeatedly pairs monomial reactant vectors with reaction vectors to construct a reversible realization. Order-independent termination conjecture. If there exists a reversible realization, then this process terminates, independently of the order of the actions, and necessarily produces one of the reversible realizations, although the realization may depend on the order of the steps. The claim concerns whether this heuristic always succeeds when a reversible realization exists; no resolution is given in the source.