length($a) lt 2 should be length($a) < 2. You are converting the returned length to a string and doing a lexical (not a numerical) compare.

$a = "abcdefghij";
length($a) lt 2  ==>  "10" lt "2"  ==>  true
$a = "0$a";
length($a) lt 2  ==>  "11" lt "2"  ==>  true
...
$a = "0$a";
length($a) lt 2  ==>  "20" lt "2"  ==>  false
[download]

If length($a) starts in [0..1], the final length($a) will be 2.
If length($a) starts in [2..9], $a won't change.
If length($a) starts in [10..19], the final length($a) will be 20.
If length($a) starts in [20..99], $a won't change.
If length($a) starts in [100..199], the final length($a) will be 200.
If length($a) starts in [200..999], $a won't change.
If length($a) starts in [1000..1999], the final length($a) will be 2000.
If length($a) starts in [2000..9999], $a won't change.
If length($a) starts in [10000..19999], the final length($a) will be 20000.
etc.

This could cause thrashing with very long strings (which localtime doesn't return), but I don't see this ever creating an infinite loop.

Try using

my $min = (localtime)[1];
$min = sprintf('%02d', $min);
[download]

• $a (and $b) are reserved for sort. List::Util and List::MoreUtils also use these variables. They're somewhat magical and should be avoided.
• A nearby declared lexical will avoid the possibility of the variable used being tied or other special.
• Using sprintf will change the code to something quite different, possibly avoiding a compiler bug.

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