Here are two SQL queries that will tell you the date of the last document in each Application Group. This does not mean the Application Groups are idle (ie, nobody accessing them), just what the maximum date value is:
db2 "select substr(ag.name,1,25) as Application_Group,date(TIMESTAMP('1970-01-01-00.00.00.000000') + int(max(seg.stop_date)/86400) days ) as Max_Date_In_Database from arsag as ag,arsseg as seg where ag.agid=seg.agid and seg.stop_date > 36525 group by substr(ag.name,1,25) order by Max_Date_In Database"
db2 "select substr(ag.name,1,25) as Application_Group,date(TIMESTAMP('1970-01-01-00.00.00.000000') + int(max(seg.stop_date)) days ) as Max_Date_In_Database from arsag as ag,arsseg as seg where ag.agid=seg.agid and seg.stop_date < 36525 group by substr(ag.name,1,25) order by Max_Date_In Database"
Bonus points if you can tell me why two queries are necessary ("You suck at SQL!" won't get you any bonus points!).
This is really just a 'second best' answer to your original question, because parsing through the System Log to get exactly the data you're looking for is very difficult.
Good luck!