  The origin semantics for transducers was proposed in 2014, and led to various
characterizations and decidability results that are in contrast with the
classical semantics. In this paper we add a further decidability result for
characterizing transducers that are close to one-way transducers in the origin
semantics. We show that it is decidable whether a non-deterministic two-way
word transducer can be resynchronized by a bounded, regular resynchronizer into
an origin-equivalent one-way transducer. The result is in contrast with the
usual semantics, where it is undecidable to know if a non-deterministic two-way
transducer is equivalent to some one-way transducer.
