  De Vrijer has presented a proof of the finite developments theorem which, in
addition to showing that all developments are finite, gives an effective
reduction strategy computing longest developments as well as a simple formula
computing their length.
  We show that by applying a rather simple and intuitive principle of duality
to de Vrijer's approach one arrives at a proof that some developments are
finite which in addition yields an effective reduction strategy computing
shortest developments as well as a simple formula computing their length. The
duality fails for general beta-reduction.
  Our results simplify previous work by Khasidashvili.
