#!/usr/bin/perl

use strict;
use warnings;


my $alphabet = uc('ADEFGMSTV');


my $N = length($alphabet);
my $L = $N - 1;

my @ltr_lkup = $alphabet =~ /./g;
my %idx_lkup = map { substr($alphabet, $_, 1) => $_ } 0..$L;


sub tupple { return join '', @ltr_lkup[ sort { $a <=> $b } @_ ]; }


sub find {
    my ($counts) = @_;

    my %solutions;


    local *try_straight_tupple = sub {
        my ($counts, $i, $solution) = @_;

        my $instances = $counts->[$i];

        if ($instances == 0) {
            process($counts, $i+1, $solution);
            return;
        }

        return
            if $i+3 > $L
            || $counts->[$i+1] < $instances
            || $counts->[$i+2] < $instances
            || $counts->[$i+3] < $instances;

        my @counts   = @$counts;
        my @solution = ( @$solution, tupple( $i+0 .. $i+3 ) );

        $counts[$i+$_] -= $instances for 0..3;

        process(\@counts, $i+1, \@solution);
    };


    local *try_quad_tupple = sub {
        my ($counts, $i, $solution) = @_;

        try_straight_tupple($counts, $i, $solution);

        if ($counts->[$i] < 4) {
            return;
        }

        my @counts   = @$counts;
        my @solution = ( @$solution, tupple( ($i) x 4 ) );

        while ($counts[$i] >= 4) {
            $counts[$i] -= 4;
            try_straight_tupple(\@counts, $i, \@solution);
        }
    };


    local *process = sub {
        my ($counts, $i, $solution) = @_;

        if (!grep $_, @$counts) {
            ++$solutions{ join(';', @$solution) };
            return;
        }

        if ($i > $L) {
            return;
        }

        try_quad_tupple($counts, $i, $solution);
    };


    try_quad_tupple($counts, 0, []);

    return [ sort keys %solutions ];
}


{
    my ($input) = @ARGV
        or die("usage: $0 string\n");

    $input = uc($input);

    my @counts;
    while ($input =~ /(.)/g) {
        defined($idx_lkup{$1})
            or die("'$1' not in alphabet\n");

        ++$counts[ $idx_lkup{$1} ];
    }

    $counts[$_] ||= 0 for 0..$L;  # Avoid warnings.

    my $solutions = find(\@counts);
    die "No solution\n" if !@$solutions;
    print("$_\n") for @$solutions;
}
[download]

$ perl all.pl AAAAADDDDDEFFGMMSSTVVVVV
AAAA;ADEF;DDDD;FGMS;MSTV;VVVV

perl all.pl AADDDEEEEFFFFGGMMMMMMMMMMSTV
ADEF;DEFG;EFGM;MMMM;MSTV

$ perl all.pl AAAADDDDEEEEFFFFGGGG
AAAA;DDDD;EEEE;FFFF;GGGG
AAAA;DEFG
ADEF;GGGG
[download]

I think this can be optimised for strings with a lot of repetition, but I haven't found out how yet.

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