bool is_less_than (const std::string& t, const std::string& s)
{
  bool same = true;
  string::const_iterator p1 = t.begin ();
  string::const_iterator p2 = s.begin ();

  while (p1 != t.end () && p2 != s.end ())
  {
    if (std::tolower (*p2) < std::tolower (*p1))
      return false;
    if (same && (std::tolower (*p2) != std::tolower (*p1)))
      same = false;

    *p1++;
    *p2++;
  }

  if (same && (t.length() >= s.length ()))
    return false;
  else
    return true;
}

int main()
{
  string q = "queue";
  string c = "cancel";
  cout << is_less_than(q,c) << endl;
  cout << is_less_than(c,q) << endl;
}

false
false