Is "banana" the shortest overlap word?
Solution 1:
In the FreeBSD operating system /usr/share/dict/words list, the following words of 6 letters or fewer match the pattern:
ajaja
alala
anana
arara
ululu
Bororo
Carara
Macaca
amamau
ananas
ararao
auhuhu
banana
batata
marara
rococo
venene
I believe the word list is based on (but not identical to) the 1934 Webster's New International Dictionary, Second Edition.
I generated the list with:
egrep '(.)(.)\1\2\1' /usr/share/dict/words | awk '{ print length, $0 }' | sort -n | cut -d" " -f2-