For a two-phase problem, the
second phase of the algorithm
derives the data-flow input to each procedure and its subregions.
This phase of the analysis is performed top-down over the call graph
and from outermost to innermost loops within each procedure body.
For a procedure, the analysis derives the set of calling contexts
contributed by calls to the procedure.
Instead of performing a meet operation over all of the calling contexts,
the analysis partitions these contexts into equivalence classes
under the 
relation
according to their data-flow information before meeting only the
contexts within each equivalence class.
The number of partitions
is reduced by first using a 
to eliminate from the data-flow
values information not relevant to the called procedure.
(We describe an example of this
filtering in Section 4.)
Each partition defines a data-flow input value 
, the
meet of the calling contexts in that partition. For each partition,
the analysis applies the transfer functions to this data-flow value to
propagate information from outermost to innermost to yield the input
to inner regions.
For a region R representing a procedure call, the analysis adds
to the corresponding call graph edge the calling context 
.
It is important to note that our analysis does not actually generate
cloned procedure bodies, but merely replicates their data-flow information
for the purposes of analysis.