sub traverse {
    my $t = shift;
    my $d = shift || 0;

    foreach my $k (sort keys %$t) {
        print '  ' x $depth, "$k\n";
        traverse( $t->{$k}, $depth + 1 );
    }
}

sub rebuild {
    my $sub;
    $sub = sub {
        my ($t) = @_;

        my $r = {};
        while (my ($k, $v) = keys %$t) {
            while (keys %$v == 1)
            {
                my $k1 = (keys %$v)[0];
                $k .= " $k1";
                $v = $v->{$k1};
            }

            $r->{$k} = $sub->($v);
        }

        $r;
    };

    $sub->{$_[0]};
}

traverse( $old_tree );
my $rebuilt = rebuild( $old_tree );
traverse( $rebuilt );