The usual technique for testing "foundness" is to use a hash. Consider:

use strict;
use warnings;

my @a = ('a','r','z','x');
my $match = join '|', @a;
my $mystring = 'areqrtyzx';
my %found;

$found{$_}++ for grep /$match/, split '', $mystring;

print "No match" unless @a == keys %found;
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which also notices how many times each searched for item is found, although that may not be important depending on your application.