Crap! This almost does it, but I have to run to work. Maybe this will give you some ideas?

#!/usr/local/bin/perl -wl
use strict;
use Test::More qw'no_plan';                                           
+                                                                   

my %strings = (
    XAA     => 'XAA',
    YXAA    => 'YXAA',
    YXAAXAA => 'YXAA',
    XAAXAA  => 'XAAAA',
    VXAAXAA => 'VAAAA',
    AA      => 'AA',
    YAA     => 'YAA',
    YXX     => 'YX',
);                                                                    
+                                          

while (my ($orig_string, $result) = each %strings) {
    my $string = $orig_string;
    $string = scalar reverse $string;
    # last or directly before a Y
    $string =~ s/X(?!Y|\Z)//g;
    $string = scalar reverse $string;
    is($string, $result, "$orig_string => $result");
}
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