Demonstration of incorrect (Enum x, Enum y) => Enum (x, y) instance

Enum.hs

-- See http://stackoverflow.com/questions/9967790/instance-in-haskell

instance (Enum x, Enum y) => Enum (x, y) where
  fromEnum (x,y) =
    k^2 + 2*j + if permuted then 1 else 0
      where
        k = max (fromEnum x) (fromEnum y)
        j = min (fromEnum x) (fromEnum y)
        permuted = (fromEnum y) > (fromEnum x)
  toEnum n =
    let k = floor . sqrt $ fromIntegral n
        (j, permdAdd) = (n-k) `divMod` 2
        permute (x,y) | permdAdd>0  = (toEnum y, toEnum x)
                      | otherwise   = (toEnum x, toEnum y)
    in permute (k, j)

data A = A1 | A2 deriving (Show, Enum)
data B = B1 | B2 | B3 deriving (Show, Enum)

main = do
  print [(A1,A1)..(A2,A2)]
  print [(B1,B1)..(B3,B3)]
  print [(A1,B1)..(A2,B3)]
  print [(B1,A1)..(B3,A2)]

-- Program crashes, as expected, since creating such an instance is impossible.