@a_a = (\a_4, \a_3);
@a_b = (\@a_2, \a_a);
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You did not use references to your a_4, a_3 and a_a arrays. You probably meant to do this:

         |      |       
         V      V
@a_a = (\@a_4, \@a_3);
@a_b = (\@a_2, \@a_a);
                ^
                |
[download]

You would have had a clue something was wrong had you use strict and warnings.