8.24/3.73	YES
10.13/4.32	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.13/4.32	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.13/4.32	
10.13/4.32	
10.13/4.32	H-Termination with start terms of the given HASKELL could be proven:
10.13/4.32	
10.13/4.32	(0) HASKELL
10.13/4.32	(1) BR [EQUIVALENT, 0 ms]
10.13/4.32	(2) HASKELL
10.13/4.32	(3) COR [EQUIVALENT, 0 ms]
10.13/4.32	(4) HASKELL
10.13/4.32	(5) Narrow [EQUIVALENT, 6 ms]
10.13/4.32	(6) YES
10.13/4.32	
10.13/4.32	
10.13/4.32	----------------------------------------
10.13/4.32	
10.13/4.32	(0)
10.13/4.32	Obligation:
10.13/4.32	mainModule Main 
10.13/4.32	module Main where {
10.13/4.32	import qualified Prelude;
10.13/4.32	data List a = Cons a (List a)  | Nil ;
10.13/4.32	
10.13/4.32	data MyBool = MyTrue  | MyFalse ;
10.13/4.32	
10.13/4.32	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.13/4.32	
10.13/4.32	data Main.Nat = Succ Main.Nat  | Zero ;
10.13/4.32	
10.13/4.32	data Ordering = LT  | EQ  | GT ;
10.13/4.32	
10.13/4.32	data Tup0 = Tup0 ;
10.13/4.32	
10.13/4.32	data Main.WHNF a = WHNF a ;
10.13/4.32	
10.13/4.32	compareMyInt :: MyInt  ->  MyInt  ->  Ordering;
10.13/4.32	compareMyInt = primCmpInt;
10.13/4.32	
10.13/4.32	dsEm :: (a  ->  b)  ->  a  ->  b;
10.13/4.32	dsEm f x = Main.seq x (f x);
10.13/4.32	
10.13/4.32	enforceWHNF :: Main.WHNF a  ->  b  ->  b;
10.13/4.32	enforceWHNF (Main.WHNF x) y = y;
10.13/4.32	
10.13/4.32	enumFromToMyInt :: MyInt  ->  MyInt  ->  List MyInt;
10.13/4.32	enumFromToMyInt = numericEnumFromTo;
10.13/4.32	
10.13/4.32	enumFromToTup0 :: Tup0  ->  Tup0  ->  List Tup0;
10.13/4.32	enumFromToTup0 x y = map toEnumTup0 (enumFromToMyInt (fromEnumTup0 x) (fromEnumTup0 y));
10.13/4.32	
10.13/4.32	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
10.13/4.32	esEsMyInt = primEqInt;
10.13/4.32	
10.13/4.32	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
10.13/4.32	esEsOrdering LT LT = MyTrue;
10.13/4.32	esEsOrdering LT EQ = MyFalse;
10.13/4.32	esEsOrdering LT GT = MyFalse;
10.13/4.32	esEsOrdering EQ LT = MyFalse;
10.13/4.32	esEsOrdering EQ EQ = MyTrue;
10.13/4.32	esEsOrdering EQ GT = MyFalse;
10.13/4.32	esEsOrdering GT LT = MyFalse;
10.13/4.32	esEsOrdering GT EQ = MyFalse;
10.13/4.32	esEsOrdering GT GT = MyTrue;
10.13/4.32	
10.13/4.32	flip :: (c  ->  a  ->  b)  ->  a  ->  c  ->  b;
10.13/4.32	flip f x y = f y x;
10.13/4.32	
10.13/4.32	fromEnumTup0 :: Tup0  ->  MyInt;
10.13/4.32	fromEnumTup0 Tup0 = Main.Pos Main.Zero;
10.13/4.32	
10.13/4.32	fromIntMyInt :: MyInt  ->  MyInt;
10.13/4.32	fromIntMyInt x = x;
10.13/4.32	
10.13/4.32	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
10.13/4.32	fsEsOrdering x y = not (esEsOrdering x y);
10.13/4.32	
10.13/4.32	ltEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
10.13/4.32	ltEsMyInt x y = fsEsOrdering (compareMyInt x y) GT;
10.13/4.32	
10.13/4.32	map :: (b  ->  a)  ->  List b  ->  List a;
10.13/4.32	map f Nil = Nil;
10.13/4.32	map f (Cons x xs) = Cons (f x) (map f xs);
10.13/4.32	
10.13/4.32	not :: MyBool  ->  MyBool;
10.13/4.32	not MyTrue = MyFalse;
10.13/4.32	not MyFalse = MyTrue;
10.13/4.32	
10.13/4.32	numericEnumFrom n = Cons n (dsEm numericEnumFrom (psMyInt n (fromIntMyInt (Main.Pos (Main.Succ Main.Zero)))));
10.13/4.32	
10.13/4.32	numericEnumFromTo n m = takeWhile (flip ltEsMyInt m) (numericEnumFrom n);
10.13/4.32	
10.13/4.32	otherwise :: MyBool;
10.13/4.32	otherwise = MyTrue;
10.13/4.32	
10.13/4.32	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
10.13/4.32	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
10.13/4.32	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
10.13/4.32	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
10.13/4.32	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
10.13/4.32	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
10.13/4.32	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
10.13/4.32	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
10.13/4.32	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
10.13/4.32	
10.13/4.32	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
10.13/4.32	primCmpNat Main.Zero Main.Zero = EQ;
10.13/4.32	primCmpNat Main.Zero (Main.Succ y) = LT;
10.13/4.32	primCmpNat (Main.Succ x) Main.Zero = GT;
10.13/4.32	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
10.13/4.32	
10.13/4.32	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
10.13/4.32	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
10.13/4.32	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
10.13/4.32	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.13/4.32	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.13/4.32	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.13/4.32	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.13/4.32	primEqInt vv vw = MyFalse;
10.13/4.32	
10.13/4.32	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
10.13/4.32	primEqNat Main.Zero Main.Zero = MyTrue;
10.13/4.32	primEqNat Main.Zero (Main.Succ y) = MyFalse;
10.13/4.32	primEqNat (Main.Succ x) Main.Zero = MyFalse;
10.13/4.32	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
10.13/4.32	
10.13/4.32	primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
10.13/4.32	primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
10.13/4.32	primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
10.13/4.32	primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
10.13/4.32	primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;
10.13/4.32	
10.13/4.32	primPlusInt :: MyInt  ->  MyInt  ->  MyInt;
10.13/4.32	primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y;
10.13/4.32	primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x;
10.13/4.32	primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y);
10.13/4.32	primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y);
10.13/4.32	
10.13/4.32	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
10.13/4.32	primPlusNat Main.Zero Main.Zero = Main.Zero;
10.13/4.32	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
10.13/4.32	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
10.13/4.32	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
10.13/4.32	
10.13/4.32	psMyInt :: MyInt  ->  MyInt  ->  MyInt;
10.13/4.32	psMyInt = primPlusInt;
10.13/4.32	
10.13/4.32	seq :: a  ->  b  ->  b;
10.13/4.32	seq x y = Main.enforceWHNF (Main.WHNF x) y;
10.13/4.32	
10.13/4.32	takeWhile :: (a  ->  MyBool)  ->  List a  ->  List a;
10.13/4.32	takeWhile p Nil = takeWhile3 p Nil;
10.13/4.32	takeWhile p (Cons x xs) = takeWhile2 p (Cons x xs);
10.13/4.32	
10.13/4.32	takeWhile0 p x xs MyTrue = Nil;
10.13/4.32	
10.13/4.32	takeWhile1 p x xs MyTrue = Cons x (takeWhile p xs);
10.13/4.32	takeWhile1 p x xs MyFalse = takeWhile0 p x xs otherwise;
10.13/4.32	
10.13/4.32	takeWhile2 p (Cons x xs) = takeWhile1 p x xs (p x);
10.13/4.32	
10.13/4.32	takeWhile3 p Nil = Nil;
10.13/4.32	takeWhile3 wu wv = takeWhile2 wu wv;
10.13/4.32	
10.13/4.32	toEnum0 MyTrue vx = Tup0;
10.13/4.32	
10.13/4.32	toEnum1 vx = toEnum0 (esEsMyInt vx (Main.Pos Main.Zero)) vx;
10.13/4.32	
10.13/4.32	toEnumTup0 :: MyInt  ->  Tup0;
10.13/4.32	toEnumTup0 vx = toEnum1 vx;
10.13/4.32	
10.13/4.32	}
10.13/4.32	
10.13/4.32	----------------------------------------
10.13/4.32	
10.13/4.32	(1) BR (EQUIVALENT)
10.13/4.32	Replaced joker patterns by fresh variables and removed binding patterns.
10.13/4.32	----------------------------------------
10.13/4.32	
10.13/4.32	(2)
10.13/4.32	Obligation:
10.13/4.32	mainModule Main 
10.13/4.32	module Main where {
10.13/4.32	import qualified Prelude;
10.13/4.32	data List a = Cons a (List a)  | Nil ;
10.13/4.32	
10.13/4.32	data MyBool = MyTrue  | MyFalse ;
10.13/4.32	
10.13/4.32	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.13/4.32	
10.13/4.32	data Main.Nat = Succ Main.Nat  | Zero ;
10.13/4.32	
10.13/4.32	data Ordering = LT  | EQ  | GT ;
10.13/4.32	
10.13/4.32	data Tup0 = Tup0 ;
10.13/4.32	
10.13/4.32	data Main.WHNF a = WHNF a ;
10.13/4.32	
10.13/4.32	compareMyInt :: MyInt  ->  MyInt  ->  Ordering;
10.13/4.32	compareMyInt = primCmpInt;
10.13/4.32	
10.13/4.32	dsEm :: (b  ->  a)  ->  b  ->  a;
10.13/4.32	dsEm f x = Main.seq x (f x);
10.13/4.32	
10.13/4.32	enforceWHNF :: Main.WHNF a  ->  b  ->  b;
10.13/4.32	enforceWHNF (Main.WHNF x) y = y;
10.13/4.32	
10.13/4.32	enumFromToMyInt :: MyInt  ->  MyInt  ->  List MyInt;
10.13/4.32	enumFromToMyInt = numericEnumFromTo;
10.13/4.32	
10.13/4.32	enumFromToTup0 :: Tup0  ->  Tup0  ->  List Tup0;
10.13/4.32	enumFromToTup0 x y = map toEnumTup0 (enumFromToMyInt (fromEnumTup0 x) (fromEnumTup0 y));
10.13/4.32	
10.13/4.32	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
10.13/4.32	esEsMyInt = primEqInt;
10.13/4.32	
10.13/4.32	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
10.13/4.32	esEsOrdering LT LT = MyTrue;
10.13/4.32	esEsOrdering LT EQ = MyFalse;
10.13/4.32	esEsOrdering LT GT = MyFalse;
10.13/4.32	esEsOrdering EQ LT = MyFalse;
10.13/4.32	esEsOrdering EQ EQ = MyTrue;
10.13/4.32	esEsOrdering EQ GT = MyFalse;
10.13/4.32	esEsOrdering GT LT = MyFalse;
10.13/4.32	esEsOrdering GT EQ = MyFalse;
10.13/4.32	esEsOrdering GT GT = MyTrue;
10.13/4.32	
10.13/4.32	flip :: (b  ->  a  ->  c)  ->  a  ->  b  ->  c;
10.13/4.32	flip f x y = f y x;
10.13/4.32	
10.13/4.32	fromEnumTup0 :: Tup0  ->  MyInt;
10.13/4.32	fromEnumTup0 Tup0 = Main.Pos Main.Zero;
10.13/4.32	
10.13/4.32	fromIntMyInt :: MyInt  ->  MyInt;
10.13/4.32	fromIntMyInt x = x;
10.13/4.32	
10.13/4.32	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
10.13/4.32	fsEsOrdering x y = not (esEsOrdering x y);
10.13/4.32	
10.13/4.32	ltEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
10.13/4.32	ltEsMyInt x y = fsEsOrdering (compareMyInt x y) GT;
10.13/4.32	
10.13/4.32	map :: (a  ->  b)  ->  List a  ->  List b;
10.13/4.32	map f Nil = Nil;
10.13/4.32	map f (Cons x xs) = Cons (f x) (map f xs);
10.13/4.32	
10.13/4.32	not :: MyBool  ->  MyBool;
10.39/4.32	not MyTrue = MyFalse;
10.39/4.32	not MyFalse = MyTrue;
10.39/4.32	
10.39/4.32	numericEnumFrom n = Cons n (dsEm numericEnumFrom (psMyInt n (fromIntMyInt (Main.Pos (Main.Succ Main.Zero)))));
10.39/4.32	
10.39/4.32	numericEnumFromTo n m = takeWhile (flip ltEsMyInt m) (numericEnumFrom n);
10.39/4.32	
10.39/4.32	otherwise :: MyBool;
10.39/4.32	otherwise = MyTrue;
10.39/4.32	
10.39/4.32	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
10.39/4.32	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
10.39/4.32	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
10.39/4.32	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
10.39/4.32	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
10.39/4.32	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
10.39/4.32	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
10.39/4.32	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
10.39/4.32	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
10.39/4.32	
10.39/4.32	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
10.39/4.32	primCmpNat Main.Zero Main.Zero = EQ;
10.39/4.32	primCmpNat Main.Zero (Main.Succ y) = LT;
10.39/4.32	primCmpNat (Main.Succ x) Main.Zero = GT;
10.39/4.32	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
10.39/4.32	
10.39/4.32	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
10.39/4.32	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
10.39/4.32	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
10.39/4.32	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.39/4.32	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.39/4.32	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.39/4.32	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.39/4.32	primEqInt vv vw = MyFalse;
10.39/4.32	
10.39/4.32	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
10.39/4.32	primEqNat Main.Zero Main.Zero = MyTrue;
10.39/4.32	primEqNat Main.Zero (Main.Succ y) = MyFalse;
10.39/4.32	primEqNat (Main.Succ x) Main.Zero = MyFalse;
10.39/4.32	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
10.39/4.32	
10.39/4.32	primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
10.39/4.32	primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
10.39/4.32	primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
10.39/4.32	primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
10.39/4.32	primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;
10.39/4.32	
10.39/4.32	primPlusInt :: MyInt  ->  MyInt  ->  MyInt;
10.39/4.32	primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y;
10.39/4.32	primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x;
10.39/4.32	primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y);
10.39/4.32	primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y);
10.39/4.32	
10.39/4.32	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
10.39/4.32	primPlusNat Main.Zero Main.Zero = Main.Zero;
10.39/4.32	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
10.39/4.32	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
10.39/4.32	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
10.39/4.32	
10.39/4.32	psMyInt :: MyInt  ->  MyInt  ->  MyInt;
10.39/4.32	psMyInt = primPlusInt;
10.39/4.32	
10.39/4.32	seq :: a  ->  b  ->  b;
10.39/4.32	seq x y = Main.enforceWHNF (Main.WHNF x) y;
10.39/4.32	
10.39/4.32	takeWhile :: (a  ->  MyBool)  ->  List a  ->  List a;
10.39/4.32	takeWhile p Nil = takeWhile3 p Nil;
10.39/4.32	takeWhile p (Cons x xs) = takeWhile2 p (Cons x xs);
10.39/4.32	
10.39/4.32	takeWhile0 p x xs MyTrue = Nil;
10.39/4.32	
10.39/4.32	takeWhile1 p x xs MyTrue = Cons x (takeWhile p xs);
10.39/4.32	takeWhile1 p x xs MyFalse = takeWhile0 p x xs otherwise;
10.39/4.32	
10.39/4.32	takeWhile2 p (Cons x xs) = takeWhile1 p x xs (p x);
10.39/4.32	
10.39/4.32	takeWhile3 p Nil = Nil;
10.39/4.32	takeWhile3 wu wv = takeWhile2 wu wv;
10.39/4.32	
10.39/4.32	toEnum0 MyTrue vx = Tup0;
10.39/4.32	
10.39/4.32	toEnum1 vx = toEnum0 (esEsMyInt vx (Main.Pos Main.Zero)) vx;
10.39/4.32	
10.39/4.32	toEnumTup0 :: MyInt  ->  Tup0;
10.39/4.32	toEnumTup0 vx = toEnum1 vx;
10.39/4.32	
10.39/4.32	}
10.39/4.32	
10.39/4.32	----------------------------------------
10.39/4.32	
10.39/4.32	(3) COR (EQUIVALENT)
10.39/4.32	Cond Reductions:
10.39/4.32	The following Function with conditions
10.39/4.32	"undefined |Falseundefined;
10.39/4.32	"
10.39/4.32	is transformed to
10.39/4.32	"undefined  = undefined1;
10.39/4.32	"
10.39/4.32	"undefined0 True = undefined;
10.39/4.32	"
10.39/4.32	"undefined1  = undefined0 False;
10.39/4.32	"
10.39/4.32	
10.39/4.32	----------------------------------------
10.39/4.32	
10.39/4.32	(4)
10.39/4.32	Obligation:
10.39/4.32	mainModule Main 
10.39/4.32	module Main where {
10.39/4.32	import qualified Prelude;
10.39/4.32	data List a = Cons a (List a)  | Nil ;
10.39/4.32	
10.39/4.32	data MyBool = MyTrue  | MyFalse ;
10.39/4.32	
10.39/4.32	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.39/4.32	
10.39/4.32	data Main.Nat = Succ Main.Nat  | Zero ;
10.39/4.32	
10.39/4.32	data Ordering = LT  | EQ  | GT ;
10.39/4.32	
10.39/4.32	data Tup0 = Tup0 ;
10.39/4.32	
10.39/4.32	data Main.WHNF a = WHNF a ;
10.39/4.32	
10.39/4.32	compareMyInt :: MyInt  ->  MyInt  ->  Ordering;
10.39/4.32	compareMyInt = primCmpInt;
10.39/4.32	
10.39/4.32	dsEm :: (a  ->  b)  ->  a  ->  b;
10.39/4.32	dsEm f x = Main.seq x (f x);
10.39/4.32	
10.39/4.32	enforceWHNF :: Main.WHNF a  ->  b  ->  b;
10.39/4.32	enforceWHNF (Main.WHNF x) y = y;
10.39/4.32	
10.39/4.32	enumFromToMyInt :: MyInt  ->  MyInt  ->  List MyInt;
10.39/4.32	enumFromToMyInt = numericEnumFromTo;
10.39/4.32	
10.39/4.32	enumFromToTup0 :: Tup0  ->  Tup0  ->  List Tup0;
10.39/4.32	enumFromToTup0 x y = map toEnumTup0 (enumFromToMyInt (fromEnumTup0 x) (fromEnumTup0 y));
10.39/4.32	
10.39/4.32	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
10.39/4.32	esEsMyInt = primEqInt;
10.39/4.32	
10.39/4.32	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
10.39/4.32	esEsOrdering LT LT = MyTrue;
10.39/4.32	esEsOrdering LT EQ = MyFalse;
10.39/4.32	esEsOrdering LT GT = MyFalse;
10.39/4.32	esEsOrdering EQ LT = MyFalse;
10.39/4.32	esEsOrdering EQ EQ = MyTrue;
10.39/4.32	esEsOrdering EQ GT = MyFalse;
10.39/4.32	esEsOrdering GT LT = MyFalse;
10.39/4.32	esEsOrdering GT EQ = MyFalse;
10.39/4.32	esEsOrdering GT GT = MyTrue;
10.39/4.32	
10.39/4.32	flip :: (b  ->  c  ->  a)  ->  c  ->  b  ->  a;
10.39/4.32	flip f x y = f y x;
10.39/4.32	
10.39/4.32	fromEnumTup0 :: Tup0  ->  MyInt;
10.39/4.32	fromEnumTup0 Tup0 = Main.Pos Main.Zero;
10.39/4.32	
10.39/4.32	fromIntMyInt :: MyInt  ->  MyInt;
10.39/4.32	fromIntMyInt x = x;
10.39/4.32	
10.39/4.32	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
10.39/4.32	fsEsOrdering x y = not (esEsOrdering x y);
10.39/4.32	
10.39/4.32	ltEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
10.39/4.32	ltEsMyInt x y = fsEsOrdering (compareMyInt x y) GT;
10.39/4.32	
10.39/4.32	map :: (a  ->  b)  ->  List a  ->  List b;
10.39/4.32	map f Nil = Nil;
10.39/4.32	map f (Cons x xs) = Cons (f x) (map f xs);
10.39/4.32	
10.39/4.32	not :: MyBool  ->  MyBool;
10.39/4.32	not MyTrue = MyFalse;
10.39/4.32	not MyFalse = MyTrue;
10.39/4.32	
10.39/4.32	numericEnumFrom n = Cons n (dsEm numericEnumFrom (psMyInt n (fromIntMyInt (Main.Pos (Main.Succ Main.Zero)))));
10.39/4.32	
10.39/4.32	numericEnumFromTo n m = takeWhile (flip ltEsMyInt m) (numericEnumFrom n);
10.39/4.32	
10.39/4.32	otherwise :: MyBool;
10.39/4.32	otherwise = MyTrue;
10.39/4.32	
10.39/4.32	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
10.39/4.32	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
10.39/4.32	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
10.39/4.32	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
10.39/4.32	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
10.39/4.32	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
10.39/4.32	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
10.39/4.32	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
10.39/4.32	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
10.39/4.32	
10.39/4.32	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
10.39/4.32	primCmpNat Main.Zero Main.Zero = EQ;
10.39/4.32	primCmpNat Main.Zero (Main.Succ y) = LT;
10.39/4.32	primCmpNat (Main.Succ x) Main.Zero = GT;
10.39/4.32	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
10.39/4.32	
10.39/4.32	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
10.39/4.32	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
10.39/4.32	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
10.39/4.32	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.39/4.32	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.39/4.32	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.39/4.32	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.39/4.32	primEqInt vv vw = MyFalse;
10.39/4.32	
10.39/4.32	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
10.39/4.32	primEqNat Main.Zero Main.Zero = MyTrue;
10.39/4.32	primEqNat Main.Zero (Main.Succ y) = MyFalse;
10.39/4.32	primEqNat (Main.Succ x) Main.Zero = MyFalse;
10.39/4.32	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
10.39/4.32	
10.39/4.32	primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
10.39/4.32	primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
10.39/4.32	primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
10.39/4.32	primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
10.39/4.32	primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;
10.39/4.32	
10.39/4.32	primPlusInt :: MyInt  ->  MyInt  ->  MyInt;
10.39/4.32	primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y;
10.39/4.32	primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x;
10.39/4.32	primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y);
10.39/4.32	primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y);
10.39/4.32	
10.39/4.32	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
10.39/4.32	primPlusNat Main.Zero Main.Zero = Main.Zero;
10.39/4.32	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
10.39/4.32	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
10.39/4.32	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
10.39/4.32	
10.39/4.32	psMyInt :: MyInt  ->  MyInt  ->  MyInt;
10.39/4.32	psMyInt = primPlusInt;
10.39/4.32	
10.39/4.32	seq :: b  ->  a  ->  a;
10.39/4.32	seq x y = Main.enforceWHNF (Main.WHNF x) y;
10.39/4.32	
10.39/4.32	takeWhile :: (a  ->  MyBool)  ->  List a  ->  List a;
10.39/4.32	takeWhile p Nil = takeWhile3 p Nil;
10.39/4.32	takeWhile p (Cons x xs) = takeWhile2 p (Cons x xs);
10.39/4.32	
10.39/4.32	takeWhile0 p x xs MyTrue = Nil;
10.39/4.32	
10.39/4.32	takeWhile1 p x xs MyTrue = Cons x (takeWhile p xs);
10.39/4.32	takeWhile1 p x xs MyFalse = takeWhile0 p x xs otherwise;
10.39/4.32	
10.39/4.32	takeWhile2 p (Cons x xs) = takeWhile1 p x xs (p x);
10.39/4.32	
10.39/4.32	takeWhile3 p Nil = Nil;
10.39/4.32	takeWhile3 wu wv = takeWhile2 wu wv;
10.39/4.32	
10.39/4.32	toEnum0 MyTrue vx = Tup0;
10.39/4.32	
10.39/4.32	toEnum1 vx = toEnum0 (esEsMyInt vx (Main.Pos Main.Zero)) vx;
10.39/4.32	
10.39/4.32	toEnumTup0 :: MyInt  ->  Tup0;
10.39/4.32	toEnumTup0 vx = toEnum1 vx;
10.39/4.32	
10.39/4.32	}
10.39/4.32	
10.39/4.32	----------------------------------------
10.39/4.32	
10.39/4.32	(5) Narrow (EQUIVALENT)
10.39/4.32	Haskell To QDPs
10.39/4.32	
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10.39/4.32	44[label="map toEnumTup0 (takeWhile1 (flip ltEsMyInt (Pos Zero)) (Pos (Succ Zero)) (dsEm numericEnumFrom (psMyInt (Pos (Succ Zero)) (fromIntMyInt (Pos (Succ Zero))))) (not (esEsOrdering (primCmpInt (Pos (Succ Zero)) (Pos Zero)) GT)))",fontsize=16,color="black",shape="box"];44 -> 45[label="",style="solid", color="black", weight=3];
10.39/4.32	45[label="map toEnumTup0 (takeWhile1 (flip ltEsMyInt (Pos Zero)) (Pos (Succ Zero)) (dsEm numericEnumFrom (psMyInt (Pos (Succ Zero)) (fromIntMyInt (Pos (Succ Zero))))) (not (esEsOrdering (primCmpNat (Succ Zero) Zero) GT)))",fontsize=16,color="black",shape="box"];45 -> 46[label="",style="solid", color="black", weight=3];
10.39/4.32	46[label="map toEnumTup0 (takeWhile1 (flip ltEsMyInt (Pos Zero)) (Pos (Succ Zero)) (dsEm numericEnumFrom (psMyInt (Pos (Succ Zero)) (fromIntMyInt (Pos (Succ Zero))))) (not (esEsOrdering GT GT)))",fontsize=16,color="black",shape="box"];46 -> 47[label="",style="solid", color="black", weight=3];
10.39/4.32	47[label="map toEnumTup0 (takeWhile1 (flip ltEsMyInt (Pos Zero)) (Pos (Succ Zero)) (dsEm numericEnumFrom (psMyInt (Pos (Succ Zero)) (fromIntMyInt (Pos (Succ Zero))))) (not MyTrue))",fontsize=16,color="black",shape="box"];47 -> 48[label="",style="solid", color="black", weight=3];
10.39/4.32	48[label="map toEnumTup0 (takeWhile1 (flip ltEsMyInt (Pos Zero)) (Pos (Succ Zero)) (dsEm numericEnumFrom (psMyInt (Pos (Succ Zero)) (fromIntMyInt (Pos (Succ Zero))))) MyFalse)",fontsize=16,color="black",shape="box"];48 -> 49[label="",style="solid", color="black", weight=3];
10.39/4.32	49[label="map toEnumTup0 (takeWhile0 (flip ltEsMyInt (Pos Zero)) (Pos (Succ Zero)) (dsEm numericEnumFrom (psMyInt (Pos (Succ Zero)) (fromIntMyInt (Pos (Succ Zero))))) otherwise)",fontsize=16,color="black",shape="box"];49 -> 50[label="",style="solid", color="black", weight=3];
10.39/4.32	50[label="map toEnumTup0 (takeWhile0 (flip ltEsMyInt (Pos Zero)) (Pos (Succ Zero)) (dsEm numericEnumFrom (psMyInt (Pos (Succ Zero)) (fromIntMyInt (Pos (Succ Zero))))) MyTrue)",fontsize=16,color="black",shape="box"];50 -> 51[label="",style="solid", color="black", weight=3];
10.39/4.32	51[label="map toEnumTup0 Nil",fontsize=16,color="black",shape="box"];51 -> 52[label="",style="solid", color="black", weight=3];
10.39/4.32	52[label="Nil",fontsize=16,color="green",shape="box"];}
10.39/4.32	
10.39/4.32	----------------------------------------
10.39/4.32	
10.39/4.32	(6)
10.39/4.32	YES
10.44/4.39	EOF