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 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 List = Cons Nat List | Nil Unit 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
          [
            (n, do
              let n' = n - 1
              x0 <- arbitrary
              x1 <- arb n'
              return (Cons x0 x1)
            ),
            (1, do
              x0 <- arbitrary
              return (Nil x0)
            )
          ]
  
  instance Partial List where
    unlifted (Cons x0 x1) = do
      x0' <- lifted x0
      x1' <- lifted x1
      return (Cons x0' x1')
    unlifted (Nil x0) = do
      x0' <- lifted x0
      return (Nil x0')
  
  
  tf1 :: List -> List -> List
  tf1 tv4 (Nil tv5) = tv4
  tf1 tv4 (Cons tv6 tv7) = (Cons tv6 (tf0 tv7))
  
  tf0 :: List -> List
  tf0 tv2 = (tf1 tv2 tv2)
  
  tf2 :: List -> Nat
  tf2 tv9 = (mis (tf0 tv9))
  
  singlepass :: List -> Nat
  singlepass tv1 = (tf2 tv1)
  
  lq :: Nat -> Nat -> Bool
  lq Zero (Succ x) = True
  lq x Zero = False
  lq (Succ x) (Succ y) = (lq x y)
  
  ite1 :: Bool -> Nat -> Nat -> Nat
  ite1 True x y = x
  ite1 False x y = y
  
  max :: Nat -> Nat -> Nat
  max tv10 tv11 = (ite1 (lq tv10 tv11) tv11 tv10)
  
  plus :: Nat -> Nat -> Nat
  plus Zero x = x
  plus (Succ x) y = (Succ (plus x y))
  
  tf4 :: Nat -> Nat -> List -> Nat
  tf4 tv17 tv18 (Nil tv19) = (max tv18 tv17)
  tf4 tv17 tv18 (Cons tv20 tv21) = (tf3 (plus tv20 tv17) (max tv18 tv17) tv21)
  
  tf3 :: Nat -> Nat -> List -> Nat
  tf3 tv13 tv14 tv15 = (tf4 tv14 tv13 tv15)
  
  mis :: List -> Nat
  mis tv12 = (tf3 Zero Zero tv12)
  
  main :: List -> Nat
  main tv22 = (singlepass tv22)
  
  data Tuple2 = MakeTuple2 Nat Nat deriving (Eq, Typeable, Ord)
  
  instance Names Tuple2 where
    names _ = ["var0_0", "var0_1", "var0_2"]
  
  instance Arbitrary Tuple2 where
    arbitrary = sized arb
      where
        arb 0 = frequency
          [
            (1, do
              x0 <- arbitrary
              x1 <- arbitrary
              return (MakeTuple2 x0 x1)
            )
          ]
        arb n = frequency
          [
            (1, do
              x0 <- arbitrary
              x1 <- arbitrary
              return (MakeTuple2 x0 x1)
            )
          ]
  
  instance Partial Tuple2 where
    unlifted (MakeTuple2 x0 x1) = do
      x0' <- lifted x0
      x1' <- lifted x1
      return (MakeTuple2 x0' x1')
  
  
  fst2 :: Tuple2 -> Nat
  fst2 (MakeTuple2 x0 x1) = x0
  
  snd2 :: Tuple2 -> Nat
  snd2 (MakeTuple2 x0 x1) = x1
  
  tf6 :: List -> Tuple2
  tf6 (Nil tv27) = (MakeTuple2 Zero Zero)
  tf6 (Cons tv28 tv29) = (MakeTuple2 (ite1 (lq (fst2 (tf5 tv29)) (plus tv28 (snd2 (tf5 tv29)))) (plus tv28 (snd2 (tf5 tv29))) (fst2 (tf5 tv29))) (fst2 (tf5 tv29)))
  
  tf5 :: List -> Tuple2
  tf5 tv25 = (tf6 tv25)
  
  tf7 :: List -> Nat
  tf7 tv30 = (fst2 (tf5 tv30))
  
  singlepassNew :: List -> Nat
  singlepassNew tv24 = (tf7 tv24)
  
  mainNew :: List -> Nat
  mainNew tv31 = (singlepassNew tv31)
  
  optimize inp0 = (main inp0)=:=(mainNew inp0)
  