Your suspicions are correct. The + is a special character in regexps. You need to escape it. Here are two methods of doing it programatically:

if ($a =~ m/\Q$b\E/i)
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$b = quotemeta($b);
if ($a =~ m/$b/i)
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References: perlre and quotemeta

Update: It's much faster to use string functions when dealing which constant strings. Case-insensitivity is obtained by converting both strings to a common case using lc or uc.

if (lc($a) eq lc($b))
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