/a/
[download]

does not contain a quantifier, but there are an infinite amount of strings it will match. And if you only want to consider anchored strings:

    my $q1;
       $q1 = qr /a(??{$q1})?/;
    my $q2 = qr /^$q1$/;
[download]

matches all strings containing nothing but a's. But it doesn't use any of the quantifiers you mentioned.

Also,

    /^(?!)*$/
[download]

contains a * quantifier, but it doesn't actually match any string. Perhaps you want to discount lookahead. Then I give you:

    /^(|)*$/
[download]

It'll give a warning, but all it matches is the empty string. But it does have a * quantifier.

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