my@wordsInOrder;
while (<>) {
    foreach ("$_" =~ m/\w+/g) {
        push @wordsInOrder, lc($_);
    }
}
[download]

Wow!   You are copying $_ to a string before binding it to a match and then iterating over a list in a loop when you could just use the list directly:

my@wordsInOrder;
while (<>) {
    push @wordsInOrder, lc() =~ m/\w+/g;
}
[download]