diff --git a/src/AbstractLStar.hs b/src/AbstractLStar.hs
index 653b83f..12df888 100644
--- a/src/AbstractLStar.hs
+++ b/src/AbstractLStar.hs
@@ -32,8 +32,8 @@ makeCompleteWith tests teacher state0 = go tests state0
             Succes -> go ts state
             -- Otherwise we add the changes
             Failed newRows newColumns ->
-                let state2 = addRows teacher newRows state in
-                let state3 = addColumns teacher newColumns state2 in
+                let state2 = simplify $ addRows teacher newRows state in
+                let state3 = simplify $ addColumns teacher newColumns state2 in
                 -- restart the whole business
                 makeCompleteWith tests teacher state3
 
diff --git a/src/Angluin.hs b/src/Angluin.hs
index de15d08..0e107a3 100644
--- a/src/Angluin.hs
+++ b/src/Angluin.hs
@@ -36,8 +36,8 @@ consistencyTestDirect State{..} = case solve (isEmpty defect) of
 
 -- Given a C&C table, constructs an automaton. The states are given by 2^E (not
 -- necessarily equivariant functions)
-constructHypothesis :: NominalType i => State i -> Automaton (BRow i) i
-constructHypothesis State{..} = automaton q a d i f
+constructHypothesis :: LearnableAlphabet i => State i -> Automaton (BRow i) i
+constructHypothesis State{..} = simplify $ automaton q a d i f
     where
         q = map (row t) ss
         a = aa
diff --git a/src/ObservationTable.hs b/src/ObservationTable.hs
index 4e5844b..517da0f 100644
--- a/src/ObservationTable.hs
+++ b/src/ObservationTable.hs
@@ -88,6 +88,11 @@ instance NominalType i => Conditional (State i) where
         toTup State{..} = (t,ss,ssa,ee,aa)
         fromTup (t,ss,ssa,ee,aa) = State{..}
 
+instance (Ord i, Contextual i) => Contextual (State i) where
+    when f s = fromTup (when f (toTup s)) where
+        toTup State{..} = (t,ss,ssa,ee,aa)
+        fromTup (t,ss,ssa,ee,aa) = State{..}
+
 -- Precondition: the set together with the current rows is prefix closed
 addRows :: LearnableAlphabet i => Teacher i -> Set [i] -> State i -> State i
 addRows teacher ds0 state@State{..} =