diff --git a/lib/Frenetic_NetKAT_Equivalence.ml b/lib/Frenetic_NetKAT_Equivalence.ml
index c3c9bdcb1..d8bb069d3 100644
--- a/lib/Frenetic_NetKAT_Equivalence.ml
+++ b/lib/Frenetic_NetKAT_Equivalence.ml
@@ -1,6 +1,6 @@
 open Core.Std
 
-module A = Frenetic_NetKAT_Compiler.Automaton
+module Automaton = Frenetic_NetKAT_Compiler.Automaton
 module FDD = Frenetic_NetKAT_Compiler.FDD
 
 type state = FDD.t * FDD.t
@@ -11,12 +11,20 @@ module type UPTO = sig
 end
 
 module Upto_Sym () : UPTO = struct
-  (* FIXME: avoid polymorphic hash/max/min *)
+  (* FIXME: avoid polymorphic hash/max/min/equality *)
   let cache = Hash_set.Poly.create ()
-  let equiv s1 s2 = Hash_set.mem cache (min s1 s2, max s1 s2)
+  let equiv s1 s2 = (s1 = s2) || Hash_set.mem cache (min s1 s2, max s1 s2)
   let add_equiv s1 s2 = Hash_set.add cache (min s1 s2, max s1 s2)
 end
 
+module Upto_Trans () : UPTO = struct
+  (* FIXME: avoid polymorphic hash/max/min/equality *)
+  let cache = Hashtbl.Poly.create ()
+  let find = Hashtbl.find_or_add cache ~default:Union_find.create
+  let equiv s1 s2 = (s1 = s2) || Union_find.same_class (find s1) (find s2)
+  let add_equiv s1 s2 = Union_find.union (find s1) (find s2)
+end
+
 module Make_Naive(Upto : UPTO) = struct
 
   module SymPkt = struct
@@ -41,7 +49,7 @@ module Make_Naive(Upto : UPTO) = struct
 
 
 
-  let equiv ?(pk=SymPkt.all) (a1 : A.t) (a2 : A.t) =
+  let equiv ?(pk=SymPkt.all) (a1 : Automaton.t) (a2 : Automaton.t) =
     
     let rec eq_states pk (s1 : int) (s2 : int) =
       let mask = SymPkt.to_alist pk in