content: {-# LANGUAGE DeriveDataTypeable,FlexibleInstances #-}
  module Test where
  
  import HipSpec
  import Prelude(Eq, Ord, return, div, (-))
  
  data Bool = True | False deriving (Eq, Typeable, Ord)
  
  instance Names Bool where
    names _ = ["var0_0", "var0_1", "var0_2"]
  
  instance Arbitrary Bool where
    arbitrary = sized arb
      where
        arb 0 = frequency
          [
            (1, do
              return True
            ),
            (1, do
              return False
            )
          ]
        arb n = frequency
          [
            (1, do
              return True
            ),
            (1, do
              return False
            )
          ]
  
  instance Partial Bool where
    unlifted True = return True
    unlifted False = return False
  
  
  data Nat = Zero | Succ Nat deriving (Eq, Typeable, Ord)
  
  instance Names Nat where
    names _ = ["var0_0", "var0_1", "var0_2"]
  
  instance Arbitrary Nat where
    arbitrary = sized arb
      where
        arb 0 = frequency
          [
            (1, do
              return Zero
            )
          ]
        arb n = frequency
          [
            (1, do
              return Zero
            ),
            (n, do
              let n' = n - 1
              x0 <- arb n'
              return (Succ x0)
            )
          ]
  
  instance Partial Nat where
    unlifted Zero = return Zero
    unlifted (Succ x0) = do
      x0' <- lifted x0
      return (Succ x0')
  
  
  data List = Elt Nat | Cons Nat List deriving (Eq, Typeable, Ord)
  
  instance Names List where
    names _ = ["var0_0", "var0_1", "var0_2"]
  
  instance Arbitrary List where
    arbitrary = sized arb
      where
        arb 0 = frequency
          [
            (1, do
              x0 <- arbitrary
              return (Elt x0)
            )
          ]
        arb n = frequency
          [
            (1, do
              x0 <- arbitrary
              return (Elt x0)
            ),
            (n, do
              let n' = n - 1
              x0 <- arbitrary
              x1 <- arb n'
              return (Cons x0 x1)
            )
          ]
  
  instance Partial List where
    unlifted (Elt x0) = do
      x0' <- lifted x0
      return (Elt x0')
    unlifted (Cons x0 x1) = do
      x0' <- lifted x0
      x1' <- lifted x1
      return (Cons x0' x1')
  
  
  data CList = Single Nat | Concat CList CList deriving (Eq, Typeable, Ord)
  
  instance Names CList where
    names _ = ["var0_0", "var0_1", "var0_2"]
  
  instance Arbitrary CList where
    arbitrary = sized arb
      where
        arb 0 = frequency
          [
            (1, do
              x0 <- arbitrary
              return (Single x0)
            )
          ]
        arb n = frequency
          [
            (1, do
              x0 <- arbitrary
              return (Single x0)
            ),
            (n, do
              let n' = n `div` 2
              x0 <- arb n'
              x1 <- arb n'
              return (Concat x0 x1)
            )
          ]
  
  instance Partial CList where
    unlifted (Single x0) = do
      x0' <- lifted x0
      return (Single x0')
    unlifted (Concat x0 x1) = do
      x0' <- lifted x0
      x1' <- lifted x1
      return (Concat x0' x1')
  
  
  gq :: Nat -> Nat -> Bool
  gq Zero x = False
  gq (Succ x) Zero = True
  gq (Succ x) (Succ y) = (gq x y)
  
  ite2 :: Bool -> Nat -> Nat -> Nat
  ite2 True x y = x
  ite2 False x y = y
  
  max :: Nat -> Nat -> Nat
  max tv0 tv1 = (ite2 (gq tv0 tv1) tv0 tv1)
  
  tf1 :: List -> Nat
  tf1 (Elt tv5) = tv5
  tf1 (Cons tv6 tv7) = (max tv6 (tf0 tv7))
  
  tf0 :: List -> Nat
  tf0 tv3 = (tf1 tv3)
  
  spec :: List -> Nat
  spec tv2 = (tf0 tv2)
  
  tf3 :: List -> List -> List
  tf3 tv13 (Elt tv14) = (Cons tv14 tv13)
  tf3 tv13 (Cons tv15 tv16) = (Cons tv15 (tf2 tv16 tv13))
  
  tf2 :: List -> List -> List
  tf2 tv10 tv11 = (tf3 tv11 tv10)
  
  cat :: List -> List -> List
  cat tv8 tv9 = (tf2 tv8 tv9)
  
  tf5 :: CList -> List
  tf5 (Single tv20) = (Elt tv20)
  tf5 (Concat tv21 tv22) = (cat (tf4 tv21) (tf4 tv22))
  
  tf4 :: CList -> List
  tf4 tv18 = (tf5 tv18)
  
  repr :: CList -> List
  repr tv17 = (tf4 tv17)
  
  main :: CList -> Nat
  main tv23 = (spec (repr tv23))
  
  tf7 :: CList -> Nat
  tf7 (Single tv27) = tv27
  tf7 (Concat tv28 tv29) = (max (tf6 tv29) (tf6 tv28))
  
  tf6 :: CList -> Nat
  tf6 tv25 = (tf7 tv25)
  
  reprNew :: CList -> Nat
  reprNew tv24 = (tf6 tv24)
  
  mainNew :: CList -> Nat
  mainNew tv30 = (reprNew tv30)
  
  optimize inp0 = (main inp0)=:=(mainNew inp0)
  