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diff --git a/ata.mli b/ata.mli
index e446c8a..362bfa8 100644
--- a/ata.mli
+++ b/ata.mli
@@ -1,79 +1,72 @@
-(* module Ptset : sig
-  include Set.S with type elt = int
-  val from_list : elt list -> t
- end
-*)
-
 type state = int
 val mk_state : unit -> state
 
-type predicate = [ `Left of (Tree.Binary.t -> bool) | `Right of (Tree.Binary.t -> bool) |
-		       `True
-		 ]
-
-
-val eval_pred : Tree.Binary.t -> predicate -> bool
-
 type formula_expr =
     False
   | True
   | Or of formula * formula
   | And of formula * formula
-  | Atom of ([ `Left | `Right ] * bool * state)
-and formula = { fid : int; pos : formula_expr; neg : formula; st : Ptset.t*Ptset.t; size: int;}
+  | Atom of ([ `Left | `Right | `LLeft | `RRight ] * bool * state)
+and formula = { fid : int; fkey : int; pos : formula_expr; neg : formula; st : (Ptset.t*Ptset.t*Ptset.t)*(Ptset.t*Ptset.t*Ptset.t); size: int;}
 val true_ : formula
 val false_ : formula
-val atom_ : [`Left | `Right ] -> bool -> state -> formula
+val atom_ : [`Left | `Right | `LLeft | `RRight ] -> bool -> state -> formula
 val and_ : formula -> formula -> formula
 val or_ : formula -> formula -> formula
 val not_ : formula -> formula 
-val equal_form : formula -> formula -> bool
+(*val equal_form : formula -> formula -> bool *)
 val pr_frm : Format.formatter -> formula -> unit
 
 
 module HTagSet : Hashtbl.S with type key = Ptset.t*Tag.t
 
-type t = {
+
+type 'a t = { 
   id : int;
   mutable states : Ptset.t;
   init : Ptset.t;
   mutable final : Ptset.t;
   universal : Ptset.t;
-  phi : (state,(TagSet.t*(bool*formula*predicate)) list) Hashtbl.t;
-  delta : (state*Tag.t, (bool*formula*predicate)) Hashtbl.t;
-(*  delta : (state,(bool*formula*predicate) TagMap.t) Hashtbl.t; *)
-  sigma : (bool*formula*(predicate list*predicate list)*bool) HTagSet.t;
-
+  starstate : Ptset.t option;
+  (* Transitions of the Alternating automaton *)
+  phi : (state,(TagSet.t*(bool*formula*bool)) list) Hashtbl.t;
+  sigma : (int,('a t -> Tree.t -> Tree.t -> Ptset.t*'a)) Hashtbl.t;
 }
-val dump : Format.formatter -> t -> unit
+
+val dump : Format.formatter -> 'a t -> unit
     
 module Transitions : sig
-type t = state*TagSet.t*bool*formula*predicate
+type t = state*TagSet.t*bool*formula*bool
 (* Doing this avoid the parenthesis *)
 val ( ?< ) : state -> state 
-val ( >< ) : state -> TagSet.t*bool -> state*(TagSet.t*bool*predicate)
-val ( ><@ ) : state -> TagSet.t*bool*predicate -> state*(TagSet.t*bool*predicate)
-val ( >=> ) : state*(TagSet.t*bool*predicate) -> formula -> t
+val ( >< ) : state -> TagSet.t*bool -> state*(TagSet.t*bool*bool)
+val ( ><@ ) : state -> TagSet.t*bool -> state*(TagSet.t*bool*bool)
+val ( >=> ) : state*(TagSet.t*bool*bool) -> formula -> t
 val ( +| ) : formula -> formula -> formula
 val ( *& ) : formula -> formula -> formula
-val ( ** ) : [`Left | `Right ] -> state -> formula
+val ( ** ) : [`Left | `Right | `LLeft | `RRight ] -> state -> formula
 
 end
 type transition = Transitions.t
-val equal_trans : transition -> transition -> bool
+val equal_trans : transition -> transition -> bool 
 
-module TS : sig
-  type t
-  val empty : t
-  val cons : Tree.Binary.t -> t -> t
-  val append : Tree.Binary.t -> t -> t
-  val concat : t -> t -> t
-  val to_list_rev : t -> Tree.Binary.t list
-  val length  : t -> int
-  val iter : (Tree.Binary.t -> unit) -> t -> unit
-end
 
-module BottomUpNew : 
-sig
-  val run : t -> Tree.Binary.t -> TS.t
-end
+  module type ResultSet = 
+  sig
+    type t
+    val empty : t
+    val cons : Tree.t -> t -> t
+    val concat : t -> t -> t
+    val iter : (Tree.t -> unit) -> t -> unit
+    val fold : (Tree.t -> 'a -> 'a) -> t -> 'a -> 'a
+    val map : (Tree.t -> Tree.t) -> t -> t
+    val length : t -> int
+  end
+
+  module IdSet : ResultSet
+
+  val top_down_count : 'a t -> Tree.t -> int
+  val top_down : 'a t -> Tree.t -> IdSet.t
+
+  type jump_kind = [ `TAG of Tag.t | `CONTAINS of string | `NOTHING ]
+  val bottom_up_count : 'a t -> Tree.t -> jump_kind -> int