Custom taxonomy not registering to permalinks

Hello,
I’m having a hellofa time getting the permalinks to reflect the rewrite rules and include the custom taxonomy names and hierarchy in my permalink URL’s.

Here’s what I have for the code registering the taxonomy:

add_action( 'init', 'build_taxonomies', 0 );
function build_taxonomies() {
	register_taxonomy("adspecialtiescats", array("adspecialties"), array("hierarchical" => true, "label" => "Ad Spec Categories", "singular_label" => "Ad Spec Category", "query_var" => true,  "rewrite" => array( "slug" => "adspecialties", "with_front" => false )));
}

This is showing in the permalinks:
/adspecialties/post-name

and what I want it to do is show if “drinkware” is selected as the main category and “mugs” is selected as a subcategory:
/drinkware/mugs/post-name