12 years of peace since the end of the war, not the events of CONQUEST which came before (1992).
The war occurred in 1993 AD.
2010 AD: The World War III "officially" ends, leaving in North-America ravaged soils and few thousand of survivors behind (Apes and Humans).
2022 AD: BATTLE FOR THE PLANET OF THE APES.
Actually, Conquest was set in 1991.
You're telling me that the Kolp of Battle was thirty years older than he was in Conquest. Sorry, but I don't buy it. First of all, he didn't look that much older.
Second, living in the radioactive ruins like he did, would almost certainly shorten his life expectancy.
Finally, if thirty years had passed from Conquest to Battle, I would expect Caesar to have grandchildren. The first duty of a king is to start making heirs to the throne. Cornelius II being only twelve years old lends support to an early 2000s date for Battle.