FWIW: you might be able to use Bitwise String Operators to your benefit. (with different sub-strings of $A and counting the ` afterwards with tr )

But I have problems to match documentation with the behavior of 5.32

  DB<32> p "$A $B"
abbaba babbaaaa
  DB<33> no feature 'bitwise'; print 'abbaba' & 'babbaaaa'
``b``a
  DB<34> no feature 'bitwise'; print $A & $B
0
  DB<35> no feature 'bitwise'; print "$A" & "$B"
``b``a
  DB<36> print "$A" & "$B"
0
  DB<37>
[download]

looks like feature bitwise is now default w/o being explicitly explained in perlop