Main{{
     public static void main(String s[]) throws Exception{
         Main m = Main.parse(new FileInputStream(s[0]));
         System.out.println("  Start: "+str(m.term));
         System.out.println(" Simple: "+str(simplify(m.term)));
     }

     static Term simplify(Term t){
        return new Traversal(new Bc(){
           class Zero extends Term{}
           class One extends Term{}
           Term combine(Num t, int i){
               switch(i){
               case 0: return new Zero();
               case 1: return new One();
               default: return t; 
               }
           }
           Term combine(Mul t, One l, Term r){ return r; }
           Term combine(Mul t, Term l, One r){ return l; }
           Term combine(Mul t, Zero l, Term r){ return l; }
           Term combine(Mul t, Term l, Zero r){ return r; }
           Term combine(Add t, Zero l, Term r){ return r; }
           Term combine(Add t, Term l, Zero r){ return l; }
        }).<Term>traverse(t);
     }

     static String str(Term t){
        return new Traversal(new ID(){
           String combine(Num t, int n){ return ""+n; }
           String combine(Var t, Ident id){ return ""+id; }
           String combine(Mul t, String l, String r){ return infix(l,"*",r); }
           String combine(Add t, String l, String r){ return infix(l,"+",r); }
           String infix(String l, String op, String r)
            { return "("+l+" "+op+" "+r+")"; }
        }, EdgeControl.builtIns(Ident.class)).traverse(t);
     }
  }}