How to write a recursive query which does not add already visited values?

Question

Let's suppose that any given client can have multiple boxes. Each box can contain multiple items as well as multiple boxes (sub-boxes).

BoxA -> Item1, Item2, BoxB, BoxC

Unfortunately, due to the business rules, it's possible to create a circular cycle.

BoxA -> Item1, BoxB, BoxC  
BoxB -> BoxA, BoxD

As you can see, BoxA contains BoxB, and BoxB contains BoxA.

The problem I'm attempting to solve is to get all the sub-boxes for a given list of boxes in a client.
So if I was looking for the sub-boxes for BoxA (from the previous example), I would get the following: BoxB, BoxC, BoxA, BoxD.

This is what I have so far:

WITH box_info AS (
    -- This is typically a bit more complicated, that's why I have it in a seperate WITH clause
    SELECT sub_box_id
    FROM client_box
    WHERE box_id = 1
),
all_sub_boxes(sub_box_id) AS (
    SELECT sub_box_id
    FROM box_info
    WHERE sub_box_id IS NOT NULL

    UNION ALL

    SELECT cb.sub_box_id
    FROM client_box cb, all_sub_boxes asb
    WHERE cb.box_id = asb.sub_box_id AND cb.sub_box_id IS NOT NULL
    -- AND cb.sub_box_id NOT IN (SELECT sub_box_id FROM all_sub_boxes)
)
SELECT sub_box_id FROM all_sub_boxes;

However, since it's possible to get stuck in a recursive loop, the "all_sub_boxes" WITH clause will fail. The commented out line is what I would intuitively put in since it prevents already visited sub-boxes from getting added to the recursive list, but it seems that we can't reference "all_sub_boxes" from within.

So essentially, I need a way to not include already included sub-boxes in the recursive query.
Perhaps I could create a temp table? But I don't even know if it's possible to insert into a table during a recursive query. And additionally, what is the cost each time this query is run if we do create a temp table every time?

I'm trying to write this query so that it could be used across different commercial DBs, so if I can avoid non-standard sql, that would be great. But I understand that if it's not possible, then it is what it is.

Edit

For the sake of clarity, here's how the client_box table might look:

+--------+---------+------------+
| BOX_ID | ITEM_ID | SUB_BOX_ID |
+--------+---------+------------+
| BoxA   | Item1   | (null)     |
| BoxA   | (null)  | BoxB       |
| BoxA   | (null)  | BoxC       |
| BoxB   | (null)  | BoxA       |
| BoxB   | (null)  | BoxD       |
+--------+---------+------------+

Answer 1

You were on the right track, and you seem to just need a little help dealing with cycles. See the CYCLE clause right at the end of the recursive CTE definition (even though the CYCLE clause comes AFTER the closing parenthesis for the recursive CTE, it is still part of it):

with
-- Begin simulated data.
  client_box ( box_id, item_id, sub_box_id ) as (
    select 'BoxA', 'Item1', null   from dual union all
    select 'BoxA', null   , 'BoxB' from dual union all
    select 'BoxA', null   , 'BoxC' from dual union all
    select 'BoxB', null   , 'BoxA' from dual union all
    select 'BoxB', null   , 'BoxD' from dual
  ),
-- End of simulated data (for testing only, not part of the solution).
-- SQL query consists of the keyword WITH (above) and the lines below.
-- Use your actual table and column names.
-- Use whatever mechanism works for you in the ANCHOR branch of r (below).
  r ( box_id ) as (
    select  'BoxA' from dual   --  Modify this for inputs
    union all
    select  c.sub_box_id
      from  client_box c join r on c.box_id = r.box_id
      where c.sub_box_id is not null
  )
  cycle box_id set cycle to 1 default 0
select box_id
from   r
where  cycle = 0
;

BOX_ID
------
BoxA
BoxB
BoxC
BoxD