Walking Up The Tree In Tsql Or Stored Procedure

Well I have a two tables lets say they look like as follows:

Table A
CompanyID
Location

TableB
CompanyID
CompanyName
Date


The CompanyID column has values that look like this:

AAA OR
AAA.BBB OR
AAA.BBB.CCC OR
AAA.BBB.CCC.DDD OR
AAA.BBB.CCC.DDD.EEE OR
AAA.BBB.CCC.DDD.EEE.FFF

each line representing the level of the company.


we can see that CompanyID column exists in both tables. and I would like to find out the CompanyName from table B for each companyID that exists in Table A.


but the tricky part is that for a specific CompanyID in tableA I might not have a exact match.
e.g. in A lets say I have AAA.BBB.CCC.DDD.EEE for CompanyID but in table B i might not have AAA.BBB.CCC.DDD.EEE but instead have AAA.BBB or AAA.BBB.CCC or AAA.

so I have to walk up the tree or these levels to look for a match an get the companyName. the match logic is as such.

If in table A companyID = AAA.BBB.CCC.DDD.EEE then look for same value in B if NOT FOUND then
remove the last level from the companyID value from Table A. so new value of CompanyID = AAA.BBB.CCC.DDD
Now look for this new value AAA.BBB.CCC.DDD in table B. IF NOT FOUND then

remove another level from ComapnyID in table A so new companyID = AAA.BBB.CCC and look for
AAA.BBB.CCC in table B. just going up the tree by chopping off a level till I find a match.

now the question is how to do this in TSQL.... can someone help?

So what I really want to do is to look for a match between A and B based on companyID.