These are the processing dates on the USCIS website:
Adjustment of Status for Asylees
By law, only 10,000 asylees can adjust status to Lawful Permanent Resident per year; however, the Service is receiving between 25,405– 43,881 applications per year. As a result, as of January 10, 2005, approximately 186,170 asylee adjustment applications were pending. We anticipate that we will process pending applications according to the following schedule:
Date Received (Mail Date)---------Timeframe to be Processed
Feb. 18, 1996 - May. 30, 2000-----Oct. 1, 2004 - Sep. 30, 2005
May. 31, 2000 - Apr. 12, 2001-----Oct. 1, 2005 - Sep. 30, 2006
Apr. 13, 2001 - Mar. 7, 2002-------Oct. 1, 2006 - Sep. 30, 2007
Mar. 8, 2002 - Jun. 20, 2002-------Oct. 1, 2007 - Sep. 30, 2008
Jun. 21, 2002 - Sep. 30, 2002------Oct. 1, 2008 - Sep. 30, 2009
Oct. 1, 2002 - Feb. 6, 2003--------Oct. 1, 2009 - Sep. 30, 2010
Feb. 7, 2003 - May. 23, 2003-------Oct. 1, 2010 - Sep. 30, 2011
May. 24, 2003 - Sep. 26, 2003------Oct. 1, 2011 - Sep. 30, 2012
Sep. 27, 2003 - Feb. 25, 2004-------Oct. 1, 2012 - Sep. 30, 2013
Feb. 26, 2004 - Jun. 21, 2004--------Oct. 1, 2013 - Sep. 30, 2014
Jun. 22, 2004 - Nov. 8, 2004---------Oct. I, 2014 - Sep. 30, 2015
Nov. 9, 2004 - Jan. 10, 2005----------Oct. 1, 2015 - Sep. 30, 2016
We emphasize that these dates are APPROXIMATIONS; unforeseen occurrences may delay processing.
http://uscis.gov/graphics/fieldoffices/nebraska/asyleeadj.htm