{-# htermination (floorRatio :: Ratio MyInt  ->  MyInt) #-} 
import qualified Prelude 
data MyBool = MyTrue | MyFalse 
data List a = Cons a (List a) | Nil 
data Tup2 a b = Tup2 a b ;

data Double = Double MyInt MyInt ;

data Float = Float MyInt MyInt ;

data Integer = Integer MyInt ;

data MyInt = Pos Nat  | Neg Nat ;

data Nat = Succ Nat  | Zero ;

data Ordering = LT  | EQ  | GT ;

data Ratio a = CnPc a a;

floorN0 xv (Tup2 n vw) = n;

fromIntMyInt :: MyInt  ->  MyInt
fromIntMyInt x = x;

properFractionQ1 xw xx (Tup2 q vx) = q;

stop :: MyBool  ->  a;
stop MyFalse = stop MyFalse;

error :: a;
error = stop MyTrue;

primMinusNatS :: Nat  ->  Nat  ->  Nat;
primMinusNatS (Succ x) (Succ y) = primMinusNatS x y;
primMinusNatS Zero (Succ y) = Zero;
primMinusNatS x Zero = x;

primDivNatS0 x y MyTrue = Succ (primDivNatS (primMinusNatS x y) (Succ y));
primDivNatS0 x y MyFalse = Zero;

primGEqNatS :: Nat  ->  Nat  ->  MyBool;
primGEqNatS (Succ x) Zero = MyTrue;
primGEqNatS (Succ x) (Succ y) = primGEqNatS x y;
primGEqNatS Zero (Succ x) = MyFalse;
primGEqNatS Zero Zero = MyTrue;

primDivNatS :: Nat  ->  Nat  ->  Nat;
primDivNatS Zero Zero = error;
primDivNatS (Succ x) Zero = error;
primDivNatS (Succ x) (Succ y) = primDivNatS0 x y (primGEqNatS x y);
primDivNatS Zero (Succ x) = Zero;

primQuotInt :: MyInt  ->  MyInt  ->  MyInt;
primQuotInt (Pos x) (Pos (Succ y)) = Pos (primDivNatS x (Succ y));
primQuotInt (Pos x) (Neg (Succ y)) = Neg (primDivNatS x (Succ y));
primQuotInt (Neg x) (Pos (Succ y)) = Neg (primDivNatS x (Succ y));
primQuotInt (Neg x) (Neg (Succ y)) = Pos (primDivNatS x (Succ y));
primQuotInt wx wy = error;

primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Succ y)) (Succ (Succ y));
primModNatS0 x y MyFalse = Succ x;

primModNatS :: Nat  ->  Nat  ->  Nat;
primModNatS Zero Zero = error;
primModNatS Zero (Succ x) = Zero;
primModNatS (Succ x) Zero = error;
primModNatS (Succ x) (Succ Zero) = Zero;
primModNatS (Succ x) (Succ (Succ y)) = primModNatS0 x y (primGEqNatS x (Succ y));

primRemInt :: MyInt  ->  MyInt  ->  MyInt;
primRemInt (Pos x) (Pos (Succ y)) = Pos (primModNatS x (Succ y));
primRemInt (Pos x) (Neg (Succ y)) = Pos (primModNatS x (Succ y));
primRemInt (Neg x) (Pos (Succ y)) = Neg (primModNatS x (Succ y));
primRemInt (Neg x) (Neg (Succ y)) = Neg (primModNatS x (Succ y));
primRemInt vz wu = error;

primQrmInt :: MyInt  ->  MyInt  ->  Tup2 MyInt MyInt;
primQrmInt x y = Tup2 (primQuotInt x y) (primRemInt x y);

quotRemMyInt :: MyInt  ->  MyInt  ->  Tup2 MyInt MyInt
quotRemMyInt = primQrmInt;

properFractionVu30 xw xx = quotRemMyInt xw xx;

properFractionQ xw xx = properFractionQ1 xw xx (properFractionVu30 xw xx);

properFractionR1 xw xx (Tup2 vy r) = r;

properFractionR xw xx = properFractionR1 xw xx (properFractionVu30 xw xx);

properFractionRatio :: Ratio MyInt  ->  Tup2 MyInt (Ratio MyInt)
properFractionRatio (CnPc x y) = Tup2 (fromIntMyInt (properFractionQ x y)) (CnPc (properFractionR x y) y);

floorVu9 xv = properFractionRatio xv;

floorN xv = floorN0 xv (floorVu9 xv);

primMinusNat :: Nat  ->  Nat  ->  MyInt;
primMinusNat Zero Zero = Pos Zero;
primMinusNat Zero (Succ y) = Neg (Succ y);
primMinusNat (Succ x) Zero = Pos (Succ x);
primMinusNat (Succ x) (Succ y) = primMinusNat x y;

primPlusNat :: Nat  ->  Nat  ->  Nat;
primPlusNat Zero Zero = Zero;
primPlusNat Zero (Succ y) = Succ y;
primPlusNat (Succ x) Zero = Succ x;
primPlusNat (Succ x) (Succ y) = Succ (Succ (primPlusNat x y));

primMinusInt :: MyInt  ->  MyInt  ->  MyInt;
primMinusInt (Pos x) (Neg y) = Pos (primPlusNat x y);
primMinusInt (Neg x) (Pos y) = Neg (primPlusNat x y);
primMinusInt (Neg x) (Neg y) = primMinusNat y x;
primMinusInt (Pos x) (Pos y) = primMinusNat x y;

msMyInt :: MyInt  ->  MyInt  ->  MyInt
msMyInt = primMinusInt;

floorFloor0 xv MyTrue = msMyInt (floorN xv) (fromIntMyInt (Pos (Succ Zero)));
floorFloor0 xv MyFalse = floorN xv;

floorR0 xv (Tup2 vv r) = r;

floorR xv = floorR0 xv (floorVu9 xv);

intToRatio x = CnPc (fromIntMyInt x) (fromIntMyInt (Pos (Succ Zero)));

fromIntRatio :: MyInt  ->  Ratio MyInt
fromIntRatio = intToRatio;

primCmpNat :: Nat  ->  Nat  ->  Ordering;
primCmpNat Zero Zero = EQ;
primCmpNat Zero (Succ y) = LT;
primCmpNat (Succ x) Zero = GT;
primCmpNat (Succ x) (Succ y) = primCmpNat x y;

primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
primCmpInt (Pos Zero) (Pos Zero) = EQ;
primCmpInt (Pos Zero) (Neg Zero) = EQ;
primCmpInt (Neg Zero) (Pos Zero) = EQ;
primCmpInt (Neg Zero) (Neg Zero) = EQ;
primCmpInt (Pos x) (Pos y) = primCmpNat x y;
primCmpInt (Pos x) (Neg y) = GT;
primCmpInt (Neg x) (Pos y) = LT;
primCmpInt (Neg x) (Neg y) = primCmpNat y x;

compareMyInt :: MyInt  ->  MyInt  ->  Ordering
compareMyInt = primCmpInt;

primMulNat :: Nat  ->  Nat  ->  Nat;
primMulNat Zero Zero = Zero;
primMulNat Zero (Succ y) = Zero;
primMulNat (Succ x) Zero = Zero;
primMulNat (Succ x) (Succ y) = primPlusNat (primMulNat x (Succ y)) (Succ y);

primMulInt :: MyInt  ->  MyInt  ->  MyInt;
primMulInt (Pos x) (Pos y) = Pos (primMulNat x y);
primMulInt (Pos x) (Neg y) = Neg (primMulNat x y);
primMulInt (Neg x) (Pos y) = Neg (primMulNat x y);
primMulInt (Neg x) (Neg y) = Pos (primMulNat x y);

srMyInt :: MyInt  ->  MyInt  ->  MyInt
srMyInt = primMulInt;

compareRatio :: Ratio MyInt  ->  Ratio MyInt  ->  Ordering
compareRatio (CnPc x y) (CnPc x' y') = compareMyInt (srMyInt x y') (srMyInt x' y);

esEsOrdering :: Ordering  ->  Ordering  ->  MyBool
esEsOrdering LT LT = MyTrue;
esEsOrdering LT EQ = MyFalse;
esEsOrdering LT GT = MyFalse;
esEsOrdering EQ LT = MyFalse;
esEsOrdering EQ EQ = MyTrue;
esEsOrdering EQ GT = MyFalse;
esEsOrdering GT LT = MyFalse;
esEsOrdering GT EQ = MyFalse;
esEsOrdering GT GT = MyTrue;

ltRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool
ltRatio x y = esEsOrdering (compareRatio x y) LT;

floorRatio :: Ratio MyInt  ->  MyInt
floorRatio x = floorFloor0 x (ltRatio (floorR x) (fromIntRatio (Pos Zero)));