[An overflow post] Longest valid subsequence

Given a string s, and a function isValid(String str), write a function to check the longest subsequence in s that is valid. For example, a subsequence in "whreat" can be "rat", "eat", "what" or "wheat". Please don't speculate the implementation of isValid(String str) function. 

I was asked this question yesterday. It bothered some much that the person who asked me this question and I could not agree on the solution. Plus I had a rough day&night last night, so I decide to break my rule to write this overflow post (256).

At first I thought it should be a DP problem, however, since we cannot assume anything about the isValid function, we can not break down the problem to smaller problem, i.e., "wh" is true will not indicate "what" is also true. So the only bloody brutal solution I can think of is backtracking.

public class LongestValidSubSequence {
 private static boolean isValid(String str){
  if(str.equals("what") || str.equals("wheat") || str.equals("eat") || str.equals("rat"))
   return true;
  return false;
 }
 static String max = "";
 public static String longestValidSubsequence(String str){
  getSubsequence(str, new StringBuilder(), 0);
  return max;
 }
 
 private static void getSubsequence(String str, StringBuilder sb, int start){
  if(isValid(sb.toString())){
   String tmp = sb.toString();
   if(max.length() < tmp.length()){
    max = tmp;
   }
  }
  for(int i = start; i < str.length(); i++){
   sb.append(str.charAt(i));
   getSubsequence(str, sb, i + 1);
   sb.deleteCharAt(sb.length() - 1);
  }
 }
 public static void main(String[] args) {
  String s = "whreat";
  System.out.println(longestValidSubsequence(s));

 }

}