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For every fixed-point expression e of alternation-depth r,we construct a new fixed-point expression e' of alternation-depth 2 and size ${\cal O}(r\cdot|e|)$ 
. Expression e' is equivalent to e whenever operators are distributive and the underlyingcomplete lattice has a co-continuous least upper bound. We alternation-depth but also w.r.t. the increase in size of theresulting expression.
