remove old directories according to directory name

in my bash script I create directory each month for backup as the follwoing:

DAY=$(date -d "$D" '+%d')
MONTH=$(date -d "$D" '+%m')
YEAR=$(date -d "$D" '+%Y')


mkdir -p /var/app/backup/$DAY$MONTH$YEAR

for example I get

 01012000
 01022000
 01032000
 .
 .
 .
 01012014
 01022014
 01032014
 01042014
 .
 .
 .
 .

after years , we want to remove the directories that old then half year

for example - the directories from 01012000 until 01062000 should be removed at 1/1/2015

what is the best approach ( from bash script ) in order to remove the directories that old then half year regarding that we have the date in the directory name