A good answer might be:

  boolean equals( String strA, String strB )
  {
    if       ( strA.length() == 0 && strB.length() == 0 )
      return true;
      
    else if  ( strA.length() == 0 && strB.length() != 0 )
      return false;
      
    else if  ( strA.length() != 0 && strB.length() == 0 )
      return false;
      
    else if  ( strA.charAt(0) != strB.charAt(0) )
      return false;
      
    else
      return equals( strA.substring(1), strB.substring(1) );
  }

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