## if there are no common words between the sentences, exit early
        next unless first{ exists $ua->{ $_ } } keys %{ $ub };

        ## fragment both sentences, discarding one-word fragments
        ## and sorting them by number of words, longest first.
        @aFragments = sort{ @$b <=> @$a } grep{ @$_ > 1 } 
             @{ fragmentSentence( $sa, $ub ) };
        @bFragments = sort{ @$b <=> @$a } grep{ @$_ > 1 } 
             @{ fragmentSentence( $sb, $ua ) };

        ## Exit early if either sentence has no remaining fragments
        next unless @aFragments and @bFragments;
        my @best;

        ## For each A fragment
        for my $aFrag ( @aFragments ) {
            ## early exit if this fragment is shorter than the best so far
            next if @$aFrag <= @best;

            ## for each B fragment
            for my $bFrag ( @bFragments ) {
                ## Ditto early exit
                next if @$bFrag <= @best;

                ## Finally, perform the LCS algorithm
                my @lcws = lcws( $aFrag, $bFrag );

                ## And save if its the longest yet seen
                @best = @lcws if @lcws > @best
            }
        }
        ## Skip if we didn't find one
        next unless @best;
         
        ## Output the sentence numbers and the best LCWS we found.
        printf "( %4d / %4d )=>[ %s ]\n", $ai, $bi, join( ' ', @best );