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 Unit = Null deriving (Eq, Typeable, Ord)
  
  instance Names Unit where
    names _ = ["var0_0", "var0_1", "var0_2"]
  
  instance Arbitrary Unit where
    arbitrary = sized arb
      where
        arb 0 = frequency
          [
            (1, do
              return Null
            )
          ]
        arb n = frequency
          [
            (1, do
              return Null
            )
          ]
  
  instance Partial Unit where
    unlifted Null = return Null
  
  
  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 CList = Cnil Unit | 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 (Cnil x0)
            ),
            (1, do
              x0 <- arbitrary
              return (Single x0)
            )
          ]
        arb n = frequency
          [
            (1, do
              x0 <- arbitrary
              return (Cnil x0)
            ),
            (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 (Cnil x0) = do
      x0' <- lifted x0
      return (Cnil x0')
    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')
  
  
  data List = Nil Unit | 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 (Nil x0)
            )
          ]
        arb n = frequency
          [
            (1, do
              x0 <- arbitrary
              return (Nil x0)
            ),
            (n, do
              let n' = n - 1
              x0 <- arbitrary
              x1 <- arb n'
              return (Cons x0 x1)
            )
          ]
  
  instance Partial List where
    unlifted (Nil x0) = do
      x0' <- lifted x0
      return (Nil x0')
    unlifted (Cons x0 x1) = do
      x0' <- lifted x0
      x1' <- lifted x1
      return (Cons x0' x1')
  
  
  gq :: Nat -> Nat -> Bool
  gq Zero x = False
  gq (Succ x) Zero = True
  gq (Succ x) (Succ y) = (gq x y)
  
  and :: Bool -> Bool -> Bool
  and False x = False
  and x False = False
  and True True = True
  
  tf1 :: CList -> Bool
  tf1 (Cnil tv3) = True
  tf1 (Single tv4) = (gq tv4 Zero)
  tf1 (Concat tv5 tv6) = (and (tf0 tv5) (tf0 tv6))
  
  tf0 :: CList -> Bool
  tf0 tv1 = (tf1 tv1)
  
  allpos :: CList -> Bool
  allpos tv0 = (tf0 tv0)
  
  tf3 :: List -> List -> List
  tf3 tv11 (Cons tv13 tv14) = (Cons tv13 (tf2 tv14 tv11))
  tf3 tv11 (Nil tv15) = tv11
  
  tf2 :: List -> List -> List
  tf2 tv9 tv10 = (tf3 tv10 tv9)
  
  cat :: List -> List -> List
  cat tv7 tv8 = (tf2 tv7 tv8)
  
  tf5 :: CList -> List
  tf5 (Cnil tv19) = (Nil Null)
  tf5 (Single tv20) = (Cons tv20 (Nil Null))
  tf5 (Concat tv21 tv22) = (cat (tf4 tv21) (tf4 tv22))
  
  tf4 :: CList -> List
  tf4 tv17 = (tf5 tv17)
  
  repr :: CList -> List
  repr tv16 = (tf4 tv16)
  
  lq :: Nat -> Nat -> Bool
  lq Zero (Succ x) = True
  lq x Zero = False
  lq (Succ x) (Succ y) = (lq x y)
  
  ite2 :: Bool -> Nat -> Nat -> Nat
  ite2 True x y = x
  ite2 False x y = y
  
  max :: Nat -> Nat
  max tv23 = (ite2 (lq tv23 Zero) Zero tv23)
  
  plus :: Nat -> Nat -> Nat
  plus Zero x = x
  plus (Succ x) y = (Succ (plus x y))
  
  tf7 :: List -> Nat
  tf7 (Nil tv28) = Zero
  tf7 (Cons tv29 tv30) = (max (plus (tf6 tv30) tv29))
  
  tf6 :: List -> Nat
  tf6 tv26 = (tf7 tv26)
  
  spec :: List -> Nat
  spec tv25 = (tf6 tv25)
  
  tf9 :: CList -> CList
  tf9 (Cnil tv34) = (Cnil Null)
  tf9 (Single tv35) = (Single tv35)
  tf9 (Concat tv36 tv37) = (Concat (tf8 tv36) (tf8 tv37))
  
  tf8 :: CList -> CList
  tf8 tv32 = (tf9 tv32)
  
  target :: CList -> CList
  target tv31 = (tf8 tv31)
  
  main :: CList -> Nat
  main tv38 = (ite2 (allpos tv38) (spec (repr (target tv38))) Zero)
  
  tf11 :: CList -> Nat
  tf11 (Cnil tv42) = Zero
  tf11 (Single tv43) = tv43
  tf11 (Concat tv44 tv45) = (plus (tf10 tv45) (tf10 tv44))
  
  tf10 :: CList -> Nat
  tf10 tv40 = (tf11 tv40)
  
  targetNew :: CList -> Nat
  targetNew tv39 = (tf10 tv39)
  
  mainNew :: CList -> Nat
  mainNew tv46 = (ite2 (allpos tv46) (targetNew tv46) Zero)
  
  optimize inp0 = (main inp0)=:=(mainNew inp0)
  