Update After sleeping over it I've greatly simplified the algoritm, now I think it's elegant. You have to decide yourself if this algorithm is nicer than the rather elegant recursive solution.

sub demangle {
    my $r = shift;
    my %illegal;
    @illegal{%$r} = ();

    my @chains;

    LOOP:
    while (my($k,$v) = each %$r) {
        for my $c (@chains) {
            if ($c->[-1] eq $k) {   # append to end of chain
                push @$c, $v;
                next LOOP;
            };
            if ($c->[0] eq $v) {    # prepend to start of chain
                unshift @$c, $k;
                next LOOP;
            }
        }
        push @chains, [$k, $v];     # create new chain
    }

    # fix circular replacements
    for my $c (@chains) {
        if ($c->[0] eq $c->[-1]) {  # we have a circle
            my $new_key;
            do {
                $new_key = join '', map { ('a'..'z')[rand 26] } 1..8;
            } while exists $illegal{$new_key};
            $illegal{$new_key}++;

            unshift @$c, $new_key;
            push @$c, $new_key;
        }
    }

    my @order;

    while (@chains) {
        push @order, { map { $_->[-2] => pop @$_ } @chains };
        @chains = grep @$_ > 1, @chains;
    }

    return @order;
}
[download]

-- Hofmator