diff --git a/checks/ArrayUsageCheck.hs b/checks/ArrayUsageCheck.hs
index 7ef466f..2fdf7e2 100644
--- a/checks/ArrayUsageCheck.hs
+++ b/checks/ArrayUsageCheck.hs
@@ -16,7 +16,7 @@ You should have received a copy of the GNU General Public License along
 with this program.  If not, see <http://www.gnu.org/licenses/>.
 -}
 
-module ArrayUsageCheck (BackgroundKnowledge(..), BK, checkArrayUsage, FlattenedExp(..), makeEquations, makeExpSet, ModuloCase(..), onlyConst, showFlattenedExp, VarMap) where
+module ArrayUsageCheck (BackgroundKnowledge(..), BK, checkArrayUsage, FlattenedExp(..), makeEquations, makeExpSet, ModuloCase(..), onlyConst, showFlattenedExp, VarMap, canonicalise, fmapFlattenedExp) where
 
 import Control.Monad.Error
 import Control.Monad.State
@@ -235,6 +235,14 @@ onlyConst [] = Just 0
 onlyConst ((Const n):es) = liftM2 (+) (return n) $ onlyConst es
 onlyConst _ = Nothing
 
+fmapFlattenedExp :: (A.Expression -> A.Expression) -> FlattenedExp -> FlattenedExp
+fmapFlattenedExp f x@(Const _) = x
+fmapFlattenedExp f (Scale n (e, i)) = Scale n (f e, i)
+fmapFlattenedExp f (Modulo n top bottom)
+  = Modulo n (Set.map (fmapFlattenedExp f) top) (Set.map (fmapFlattenedExp f) bottom)
+fmapFlattenedExp f (Divide n top bottom)
+  = Divide n (Set.map (fmapFlattenedExp f) top) (Set.map (fmapFlattenedExp f) bottom)
+
 -- | A data type representing an array access.  Each triple is (index, extra-equalities, extra-inequalities).
 -- A Single item can be paired with every other access.
 -- Each item of a Group cannot be paired with each other, but can be paired with each other access.
@@ -468,7 +476,21 @@ makeEquations accesses bound
         var = A.Variable m varName
 
 -- Note that in all these functions, the divisor should always be positive!
-  
+
+canonicalise :: A.Expression -> A.Expression
+canonicalise e@(A.Dyadic m op _ _) | op == A.Add || op == A.Mul
+  = foldl1 (A.Dyadic m op) $ sort $ gatherTerms op e
+  where
+    gatherTerms :: A.DyadicOp -> A.Expression -> [A.Expression]
+    gatherTerms op (A.Dyadic _ op' lhs rhs) | op == op'
+      = gatherTerms op lhs ++ gatherTerms op rhs
+    gatherTerms _ e = [canonicalise e]
+canonicalise (A.Dyadic m op lhs rhs)
+  = A.Dyadic m op (canonicalise lhs) (canonicalise rhs)
+canonicalise (A.Monadic m op rhs)
+  = A.Monadic m op (canonicalise rhs)
+canonicalise e = e
+
 flatten :: A.Expression -> Either String [FlattenedExp]
 flatten (A.Literal _ _ (A.IntLiteral _ n)) = return [Const (read n)]
 flatten e@(A.Dyadic m op lhs rhs)
@@ -480,7 +502,7 @@ flatten e@(A.Dyadic m op lhs rhs)
                        case onlyConst rhs' of
                          Just _ -> liftM2L (Divide 1) (flatten lhs) (return rhs')
                          -- Can't deal with variable divisors, leave expression as-is:
-                         Nothing -> return [Scale 1 (e,0)]
+                         Nothing -> return [Scale 1 (canonicalise e,0)]
   where
 --    liftM2L :: (Ord a, Ord b, Monad m) => (Set.Set a -> Set.Set b -> c) -> m [a] -> m [b] -> m [c]
     liftM2L f x y = liftM singleton $ liftM2 f (x >>= makeExpSet) (y >>= makeExpSet)
@@ -499,12 +521,11 @@ flatten e@(A.Dyadic m op lhs rhs)
         mult lhs rhs
           = do lhs' <- backToEq lhs
                rhs' <- backToEq rhs
-               let (onLeft, onRight) = if lhs' <= rhs' then (lhs', rhs') else (rhs', lhs')
-               return $ (Scale 1 (A.Dyadic emptyMeta A.Mul onLeft onRight, 0))
+               return $ (Scale 1 (canonicalise $ A.Dyadic emptyMeta A.Mul lhs' rhs', 0))
     
         backScale :: Integer -> A.Expression -> A.Expression
         backScale 1 = id
-        backScale n = A.Dyadic emptyMeta A.Mul (makeConstant emptyMeta (fromInteger n))
+        backScale n = canonicalise . A.Dyadic emptyMeta A.Mul (makeConstant emptyMeta (fromInteger n))
     
         backToEq :: FlattenedExp -> Either String A.Expression
         backToEq (Const c) = return $ makeConstant emptyMeta (fromInteger c)
@@ -540,7 +561,7 @@ flatten e@(A.Dyadic m op lhs rhs)
     -- | Combines (adds) two flattened expressions.
     combine :: [FlattenedExp] -> [FlattenedExp] -> [FlattenedExp]
     combine = (++)
-flatten e = return [Scale 1 (e,0)]
+flatten e = return [Scale 1 (canonicalise e,0)]
 
 -- | The "square" refers to making all equations the length of the longest
 -- one, and the pair refers to pairing each in a list of array accesses (e.g. 
diff --git a/checks/ArrayUsageCheckTest.hs b/checks/ArrayUsageCheckTest.hs
index 4f21451..af38a00 100644
--- a/checks/ArrayUsageCheckTest.hs
+++ b/checks/ArrayUsageCheckTest.hs
@@ -869,8 +869,11 @@ testIndexes = TestList
 
 generateMapping :: TestMonad m r => String -> VarMap -> VarMap -> m [(CoeffIndex,CoeffIndex)]
 generateMapping msg m0 m1
-  = do testEqual ("Keys in variable mapping " ++ msg) (Map.keys m0) (Map.keys m1)
-       return $ Map.elems $ zipMap mergeMaybe m0 m1
+  = do testEqual ("Keys in variable mapping " ++ msg) (Map.keys m0') (Map.keys m1')
+       return $ Map.elems $ zipMap mergeMaybe m0' m1'
+  where
+    m0' = Map.mapKeys (fmapFlattenedExp canonicalise) m0
+    m1' = Map.mapKeys (fmapFlattenedExp canonicalise) m1
 
 -- | Given a forward mapping list, translates equations across
 translateEquations :: forall m r. TestMonad m r =>