  The paper presents an elaborated and simplified version of the structural
result for branching bisimilarity on normed BPA (Basic Process Algebra)
processes that was the crux of a conference paper by Czerwinski and Jancar
(arxiv 7/2014 and LiCS 2015). That paper focused on the computational
complexity, and a NEXPTIME-upper bound has been derived; the authors built on
the ideas by Fu (ICALP 2013), and strengthened his decidability result. Later
He and Huang announced the EXPTIME-completeness of this problem (arxiv 1/2015,
and LiCS 2015), giving a technical proof for the EXPTIME membership. He and
Huang indirectly acknowledge the decomposition ideas by Czerwinski and Jancar
on which they also built, but it is difficult to separate their starting point
from their new ideas. One aim here is to present the previous decomposition
result of Czerwinski and Jancar in a technically new framework, noting that
branching bisimulation equivalence on normed BPA processes corresponds to a
rational monoid (in the sense of [Sakarovitch, 1987]); in particular it is
shown that the mentioned equivalence can be decided by normal-form computing
deterministic finite transducers. Another aim is to provide a complete
description, including an informal overview, that should also make clear how
Fu's ideas were used, and to give all proofs in a form that should be readable
and easily verifiable.
