Sequencia de chars comum em 2 strings

public static String MaxSeq(String a, String b){
       String maxs = "";
       String aux = "";
       int i,j;
       j = a.length();
       for(i=0; i<a.length();i++){
         for(j=a.length();j>=i;j--){ 
            aux = a.substring(i,j);
            if (b.indexOf(aux) >= 0){
                if (aux.length() > maxs.length()){
                    maxs = aux;
                }
            }
         }
       }
       return maxs;
    }

public static String MaxSeq2(String a,String b,String maxs){
       String aux = "";
       String cad = "";
       int i;
    
       for(i=0;i<a.length();i++){
         aux = a.substring(i,a.length()-1);
         if (b.indexOf(aux) >= 0){
            if(aux.length() > cad.length()){
              cad = aux;
            } 
            if (cad.length() > maxs.length()){
                maxs = cad;
            }
            
         }
       }
       
       if (a.length() > 1){
          maxs = MaxSeq2( a.substring(1,a.length()-1), b, maxs);
       }    
       return maxs;
    }