diff --git a/app/Main.hs b/app/Main.hs
index 20b1a2c..00c18ef 100644
--- a/app/Main.hs
+++ b/app/Main.hs
@@ -3,16 +3,18 @@ module Main where
 import DotParser
 import Mealy
 import MealyRefine
+import Partition
 
--- import Control.Monad.IO.Class (liftIO)
--- import Control.Monad.Trans.State.Strict
-import Control.Monad (forM_)
--- import Data.Map.Strict qualified as Map
+import Control.Monad.IO.Class (liftIO)
+import Control.Monad.Trans.State.Strict
+import Control.Monad (forM_, when, forever)
+import Data.Map.Strict qualified as Map
 import Data.Maybe (mapMaybe)
-import Data.Partition (isRefinementOf, numBlocks)
 -- import Data.Semigroup (Arg(..))
 -- import Data.Set qualified as Set
 -- import Data.List.Ordered (nubSort)
+import Data.List (minimumBy)
+import Data.Function (on)
 import System.Environment
 import Text.Megaparsec
 
@@ -70,6 +72,29 @@ main = do
     printPartition partition
     )
 
+  let totalSize = sum (fmap (numBlocks . snd) projections)
+
+  putStrLn $ "total size = " <> show totalSize
+
+  let score p1 p2 p3 = numBlocks p3 - numBlocks p2 - numBlocks p1
+      combine (o1, p1) (o2, p2) = let p3 = commonRefinement p1 p2 in ((o1, o2, p3), score p1 p2 p3)
+      allCombs projs = [combine op1 op2 | op1 <- projs, op2 <- projs, fst op1 < fst op2]
+      minComb projs = minimumBy (compare `on` snd) (allCombs projs)
+
+  _ <- flip execStateT (Map.fromList projections, totalSize) $ forever (do
+    (projmap, currentSize) <- get
+    liftIO . print . fmap numBlocks . Map.elems $ projmap
+    let ((o1, o2, p3), gain) = minComb (Map.assocs projmap)
+        o3 = o1 <> "x" <> o2
+        newSize = currentSize + gain
+        newProjmap = Map.insert o3 p3 . Map.delete o2 . Map.delete o1 $ projmap
+    liftIO $ putStrLn (show o3 <> " -> " <> show newSize)
+    put (newProjmap, newSize)
+    )
+
+  print "done"
+
+
   {-
 
   -- Check refinement relations for all pairs
diff --git a/mealy-decompose.cabal b/mealy-decompose.cabal
index 9b1b634..ede0889 100644
--- a/mealy-decompose.cabal
+++ b/mealy-decompose.cabal
@@ -14,7 +14,8 @@ common stuff
     containers,
     copar,
     data-ordlist,
-    megaparsec
+    megaparsec,
+    transformers
   default-language: GHC2021
   default-extensions:
     RecordWildCards
@@ -26,7 +27,8 @@ library
   exposed-modules:
     DotParser,
     Mealy,
-    MealyRefine
+    MealyRefine,
+    Partition
   build-depends:
     vector
 
@@ -35,8 +37,7 @@ executable mealy-decompose
   hs-source-dirs: app
   main-is: Main.hs
   build-depends:
-    mealy-decompose,
-    transformers
+    mealy-decompose
 
 test-suite mealy-decompose-test
   import: stuff
diff --git a/src/MealyRefine.hs b/src/MealyRefine.hs
index 2ff98bc..01f2142 100644
--- a/src/MealyRefine.hs
+++ b/src/MealyRefine.hs
@@ -1,6 +1,7 @@
 module MealyRefine where
 
 import Mealy
+import Partition (Partition)
 
 import Control.Monad.ST (runST)
 import Copar.Algorithm (refine)
@@ -9,7 +10,6 @@ import Copar.RefinementInterface (Label, F1)
 import Data.Bool (bool)
 import Data.CoalgebraEncoding (Encoding(..))
 import Data.Map.Strict qualified as Map
-import Data.Partition (Partition)
 import Data.Proxy (Proxy(..))
 import Data.Vector qualified
 import Data.Vector.Unboxed qualified
diff --git a/src/Partition.hs b/src/Partition.hs
new file mode 100644
index 0000000..58ead5d
--- /dev/null
+++ b/src/Partition.hs
@@ -0,0 +1,29 @@
+module Partition
+  ( module Partition
+  , module Data.Partition
+  ) where
+
+import Control.Monad.Trans.State.Strict (runState, get, put)
+import Data.Partition (Partition(..), isRefinementOf, numStates)
+import Data.Vector qualified as V
+import Data.Map.Strict qualified as Map
+import Unsafe.Coerce (unsafeCoerce)
+
+-- Returns the coarsest partition which is finer than either input
+-- i.e., the greatest lower bound
+commonRefinement :: Partition -> Partition -> Partition
+commonRefinement p1 p2 =
+  let n = numStates p1
+      sa1 = (stateAssignment p1 V.!)
+      sa2 = (stateAssignment p2 V.!)
+      blockAtIdx i = do
+        (m, b) <- get
+        let key = (sa1 i, sa2 i)
+        case Map.lookup key m of
+          Just b0 -> return b0
+          Nothing -> do
+            put (Map.insert key b m, succ b)
+            return b
+      (vect, (_, nextBlock)) = runState (V.generateM n blockAtIdx) (Map.empty, 0)
+  in Partition { numBlocks = unsafeCoerce nextBlock, stateAssignment = vect }
+