A very short and neat recursive solution:

use Data::Dumper;

use strict;
use warnings;

sub move {
   my ($parn, $chld, $result, $index, $ordr, $chain, $len) = @_;
   if ($index > $#{$chld}) {
      $result->{$chain} = $len;
      return;
   } else {
      move($parn, $chld, $result, $index + 1, $parn->{$chld->[$index]}
+, "$chain,$chld->[$index]", $len + 1) if ($parn->{$chld->[$index]} > 
+$ordr);
      move($parn, $chld, $result, $index + 1, $ordr, $chain, $len);
   }
}

my $a = [1,2,3,8,4,5,6];
my $index = 0;
my %a = map {$_=>$index ++} @{$a};
my $b = [2,1,4,3,5];
my $result = {};

move(\%a, $b, $result, 0, -1, "", 0);
print Dumper($result);
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