Shell code to judge the year based on date, month, and week

Three time variables are known:
time1="Fri Aug 23 11:35:21"
time2="Mon Sep 2 16:18:09"
time3="Tue Sep 3 16:06:33"
It is known that these three times can be determined to occur in 2011-2013. How to quickly determine which year it was?

Hope output:
time1="2013/8/23 11:35:21"
time2="2013/9/2 16:18:09"
time3="2013/9/3 16:06:33"

#!/bin/bash
time1="Fri Aug 23 11:35:21"
time2="Mon Sep 2 16:18:09"
time3="Tue Sep 3 16:06:33"
time4="Sun Dec 2 16:06:34"
for((i=1;i<=4;i++)); do
  for((j=2011;j<=2013;j++)); do
    str=$(eval echo \$time$i)
    WEEK_DAY=$(date -d "${str:0:10} $j ${str:10}" "+%a")
    if [ "${str:0:3}" == $WEEK_DAY ]; then
      echo time$i=\"$(date -d "${str:0:10} $j ${str:10}" "+%Y/%m/%d %T")\"
      # break
    fi
  done
done