What degree is this palindrome?
Perl, 53 bytes
52 bytes of code + 1 byte for -p.
$\++while s/^((.+).?)(??{reverse$2})$/$1/||s/^.$//}{

To run it :
perl -pE '$\++while s/^((.+).?)(??{reverse$2})$/$1/||s/^.$//}{' &lt;&lt;&lt; &quot;zzzzz&quot;