Given two strings, write a method that finds the longest common sub sequence

public String findLongestCommonSequence(String s1, String s2) {
String result = "";
for (int length = s1.length(); length > 0; length--) {
    int startIndex = 0;
    while (startIndex + length <= s1.length()) {
        String current = s1.substring(startIndex, startIndex + length);
        if (s2.contains(current)) {
            result = current;
            break;
        }
        startIndex++;
    }
    if (result.length() != 0) {
        break;
    }
}
return result;
}