Is strong sequentiality decidable for arbitrary rewrite systems?

The source page states the original problem together with its recorded qualifications and progress updates as follows.

Strong sequentiality is a property of rewrite systems introduced in [Comon, 1995] (see [Comon, 1995]), which ensures the existence of optimal reduction strategies. Is strong sequentiality decidable for arbitrary rewrite systems? What is the complexity of strong sequentiality in the linear case? in the orthogonal case? Decidability results for particular rewrite systems are given in [Comon, 1995], among others.