brian_d_foy gave you pretty much the answer you need, but he didn't mention some of the foibles in your code that make it clear Perl is not your first language. :)

Perl is pretty good at handling lists of things, to the extent that there is a special version of the for loop to itterate over lists. Your nested loops could be rewritten as:

for my $line (@lines){
  for my $line2 (@lines2){
    next if $line !~ /$line2/;
    print $line;
    print "\nyes $line2 exists\n\n";
  }
}
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One side effect of that is to remove $a and $b - which actually are special variables in Perl because they are used as the two arguments passed into a sort block.