Java (a?)^na^n

package main;

import java.util.regex.Matcher;
import java.util.regex.Pattern;

public class Main {
    public static void main(String[] args) {
        String regex = "";
        String haystack = "";
        for( int i = 1; i < 30; i++ ){
            regex = "a?" + regex + "a";
            haystack = "a" + haystack;
            long start = System.nanoTime();
            Pattern pattern = Pattern.compile( regex );
            Matcher matcher = pattern.matcher( haystack );
            if( matcher.find() ){
                long end = System.nanoTime();
                System.err.println("i = " + i + " found in " + (end - start) + " nanoseconds.");
            }
        }
    }
}