A direct method based on a finite set of path formulas which describe
the input-output relations of a given program can be used to verify programs
containing no overlapping loops. One major difficulty in verifying programs
with overlapping loops using the above method is that too many path formulas
(possibly infinite) needed to be considered. In this paper, we circumvent
the above difficulty by applying the concept of modularity. The idea is to
divide a program with overlapping loops into several small modules so that each
module contains no overlapping loop. This can always be achieved if the
program is in structured form. Then the path formulas will be derived for
each module. By combining the path formulas for the modules, one can further
obtain the path formulas for the given program and then use them to verify
the program
