  Milner (1984) defined a process semantics for regular expressions. He
formulated a sound proof system for bisimilarity of process interpretations of
regular expressions, and asked whether this system is complete.
  We report conceptually on a proof that shows that Milner's system is
complete, by motivating, illustrating, and describing all of its main steps. We
substantially refine the completeness proof by Grabmayer and Fokkink (2020) for
the restriction of Milner's system to `1-free' regular expressions. As a
crucial complication we recognize that process graphs with empty-step
transitions that satisfy the layered loop-existence/elimination property LLEE
are not closed under bisimulation collapse (unlike process graphs with LLEE
that only have proper-step transitions). We circumnavigate this obstacle by
defining a LLEE-preserving `crystallization procedure' for such process graphs.
By that we obtain `near-collapsed' process graphs with LLEE whose strongly
connected components are either collapsed or of `twin-crystal' shape. Such
near-collapsed process graphs guarantee provable solutions for bisimulation
collapses of process interpretations of regular expressions.
