#!/usr/bin/perl
use strict;
use warnings;

my (%seen, %signatures);
my @words = qw / ba ab aabb aaabbb xxyy xxxyyy baaab baba xxy xyz ABBA dcdccd cd/;

for my $word (@words) {
    chomp $word;   # not needed here, but may be useful when reading from a file or a DATA section
    my $word = lc $word; 
    next if $seen{$word}++;
    next if $word =~ /(.).*\1/;  # skip if the word has repeated letters
    my $signature = join "", sort split //, $word;
    push @{$signatures{$signature}}, $word;
}

for  my $word (@words) {
    chomp $word;
    my $word = lc $word;
    next unless $word =~ /(.).*\1/;;    # skip words already stored (having no duplicate letters)
    my %unique_letters = map { $_ => 1 } split //, $word;  # could use the uniqstr function of Lists::Util
    my $signature = join "", keys %unique_letters;
    push @{$signatures{$signature}}, $word if exists $signatures{$signature};
}

for my $key (keys %signatures) {
    if (scalar @{$signatures{$key}} > 1) {
        print "@{$signatures{$key}}\n"
    }
}

##</code><code>##

ba ab aabb aaabbb baaab baba abba
cd dcdccd