11.76/4.99 YES 14.24/5.67 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 14.24/5.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.24/5.67 14.24/5.67 14.24/5.67 H-Termination with start terms of the given HASKELL could be proven: 14.24/5.67 14.24/5.67 (0) HASKELL 14.24/5.67 (1) BR [EQUIVALENT, 0 ms] 14.24/5.67 (2) HASKELL 14.24/5.67 (3) COR [EQUIVALENT, 0 ms] 14.24/5.67 (4) HASKELL 14.24/5.67 (5) Narrow [SOUND, 0 ms] 14.24/5.67 (6) QDP 14.24/5.67 (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] 14.24/5.67 (8) YES 14.24/5.67 14.24/5.67 14.24/5.67 ---------------------------------------- 14.24/5.67 14.24/5.67 (0) 14.24/5.67 Obligation: 14.24/5.67 mainModule Main 14.24/5.67 module Main where { 14.24/5.67 import qualified Prelude; 14.24/5.67 data Main.Char = Char MyInt ; 14.24/5.67 14.24/5.67 data List a = Cons a (List a) | Nil ; 14.24/5.67 14.24/5.67 data MyBool = MyTrue | MyFalse ; 14.24/5.67 14.24/5.67 data MyInt = Pos Main.Nat | Neg Main.Nat ; 14.24/5.67 14.24/5.67 data Main.Nat = Succ Main.Nat | Zero ; 14.24/5.67 14.24/5.67 data Ordering = LT | EQ | GT ; 14.24/5.67 14.24/5.67 compareMyInt :: MyInt -> MyInt -> Ordering; 14.24/5.67 compareMyInt = primCmpInt; 14.24/5.67 14.24/5.67 esEsOrdering :: Ordering -> Ordering -> MyBool; 14.24/5.67 esEsOrdering LT LT = MyTrue; 14.24/5.67 esEsOrdering LT EQ = MyFalse; 14.24/5.67 esEsOrdering LT GT = MyFalse; 14.24/5.67 esEsOrdering EQ LT = MyFalse; 14.24/5.67 esEsOrdering EQ EQ = MyTrue; 14.24/5.67 esEsOrdering EQ GT = MyFalse; 14.24/5.67 esEsOrdering GT LT = MyFalse; 14.24/5.67 esEsOrdering GT EQ = MyFalse; 14.24/5.67 esEsOrdering GT GT = MyTrue; 14.24/5.67 14.24/5.67 gtMyInt :: MyInt -> MyInt -> MyBool; 14.24/5.67 gtMyInt x y = esEsOrdering (compareMyInt x y) GT; 14.24/5.67 14.24/5.67 primCmpInt :: MyInt -> MyInt -> Ordering; 14.24/5.67 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 14.24/5.67 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 14.24/5.67 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 14.24/5.67 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 14.24/5.67 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 14.24/5.67 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 14.24/5.67 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 14.24/5.67 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 14.24/5.67 14.24/5.67 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 14.24/5.67 primCmpNat Main.Zero Main.Zero = EQ; 14.24/5.67 primCmpNat Main.Zero (Main.Succ y) = LT; 14.24/5.67 primCmpNat (Main.Succ x) Main.Zero = GT; 14.24/5.67 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 14.24/5.67 14.24/5.67 psPs :: List a -> List a -> List a; 14.24/5.67 psPs Nil ys = ys; 14.24/5.67 psPs (Cons x xs) ys = Cons x (psPs xs ys); 14.24/5.67 14.24/5.67 pt :: (c -> b) -> (a -> c) -> a -> b; 14.24/5.67 pt f g x = f (g x); 14.24/5.67 14.24/5.67 showChar :: Main.Char -> List Main.Char -> List Main.Char; 14.24/5.67 showChar = Cons; 14.24/5.67 14.24/5.67 showParen :: MyBool -> (List Main.Char -> List Main.Char) -> List Main.Char -> List Main.Char; 14.24/5.67 showParen b p = showParen0 p b; 14.24/5.67 14.24/5.67 showParen0 p MyTrue = pt (showChar (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))) (pt p (showChar (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))); 14.24/5.67 showParen0 p MyFalse = p; 14.24/5.67 14.24/5.67 showString :: List Main.Char -> List Main.Char -> List Main.Char; 14.24/5.67 showString = psPs; 14.24/5.67 14.24/5.67 showsPrecOrdering :: MyInt -> Ordering -> List Main.Char -> List Main.Char; 14.24/5.67 showsPrecOrdering d LT = showParen (gtMyInt d (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))) (showString (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))) Nil)))); 14.24/5.67 showsPrecOrdering d EQ = showParen (gtMyInt d (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))) (showString (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))) Nil)))); 14.24/5.67 showsPrecOrdering d GT = showParen (gtMyInt d (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))) (showString (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))) Nil)))); 14.24/5.67 14.24/5.67 } 14.24/5.67 14.24/5.67 ---------------------------------------- 14.24/5.67 14.24/5.67 (1) BR (EQUIVALENT) 14.24/5.67 Replaced joker patterns by fresh variables and removed binding patterns. 14.24/5.67 ---------------------------------------- 14.24/5.67 14.24/5.67 (2) 14.24/5.67 Obligation: 14.24/5.67 mainModule Main 14.24/5.67 module Main where { 14.24/5.67 import qualified Prelude; 14.24/5.67 data Main.Char = Char MyInt ; 14.24/5.67 14.24/5.67 data List a = Cons a (List a) | Nil ; 14.24/5.67 14.24/5.67 data MyBool = MyTrue | MyFalse ; 14.24/5.67 14.24/5.67 data MyInt = Pos Main.Nat | Neg Main.Nat ; 14.24/5.67 14.24/5.67 data Main.Nat = Succ Main.Nat | Zero ; 14.24/5.67 14.24/5.67 data Ordering = LT | EQ | GT ; 14.24/5.67 14.24/5.67 compareMyInt :: MyInt -> MyInt -> Ordering; 14.24/5.67 compareMyInt = primCmpInt; 14.24/5.67 14.24/5.67 esEsOrdering :: Ordering -> Ordering -> MyBool; 14.24/5.67 esEsOrdering LT LT = MyTrue; 14.24/5.67 esEsOrdering LT EQ = MyFalse; 14.24/5.67 esEsOrdering LT GT = MyFalse; 14.24/5.67 esEsOrdering EQ LT = MyFalse; 14.24/5.67 esEsOrdering EQ EQ = MyTrue; 14.24/5.67 esEsOrdering EQ GT = MyFalse; 14.24/5.67 esEsOrdering GT LT = MyFalse; 14.24/5.67 esEsOrdering GT EQ = MyFalse; 14.24/5.67 esEsOrdering GT GT = MyTrue; 14.24/5.67 14.24/5.67 gtMyInt :: MyInt -> MyInt -> MyBool; 14.24/5.67 gtMyInt x y = esEsOrdering (compareMyInt x y) GT; 14.24/5.67 14.24/5.67 primCmpInt :: MyInt -> MyInt -> Ordering; 14.24/5.67 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 14.24/5.67 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 14.24/5.67 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 14.24/5.67 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 14.24/5.67 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 14.24/5.67 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 14.24/5.67 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 14.24/5.67 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 14.24/5.67 14.24/5.67 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 14.24/5.67 primCmpNat Main.Zero Main.Zero = EQ; 14.24/5.67 primCmpNat Main.Zero (Main.Succ y) = LT; 14.24/5.67 primCmpNat (Main.Succ x) Main.Zero = GT; 14.24/5.67 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 14.24/5.67 14.24/5.67 psPs :: List a -> List a -> List a; 14.24/5.67 psPs Nil ys = ys; 14.24/5.67 psPs (Cons x xs) ys = Cons x (psPs xs ys); 14.24/5.67 14.24/5.67 pt :: (c -> a) -> (b -> c) -> b -> a; 14.24/5.67 pt f g x = f (g x); 14.24/5.67 14.24/5.67 showChar :: Main.Char -> List Main.Char -> List Main.Char; 14.24/5.67 showChar = Cons; 14.24/5.67 14.24/5.67 showParen :: MyBool -> (List Main.Char -> List Main.Char) -> List Main.Char -> List Main.Char; 14.24/5.67 showParen b p = showParen0 p b; 14.24/5.67 14.24/5.67 showParen0 p MyTrue = pt (showChar (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))) (pt p (showChar (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))); 14.24/5.67 showParen0 p MyFalse = p; 14.24/5.67 14.24/5.67 showString :: List Main.Char -> List Main.Char -> List Main.Char; 14.24/5.67 showString = psPs; 14.24/5.67 14.24/5.67 showsPrecOrdering :: MyInt -> Ordering -> List Main.Char -> List Main.Char; 14.24/5.67 showsPrecOrdering d LT = showParen (gtMyInt d (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))) (showString (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))) Nil)))); 14.24/5.67 showsPrecOrdering d EQ = showParen (gtMyInt d (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))) (showString (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))) Nil)))); 14.24/5.67 showsPrecOrdering d GT = showParen (gtMyInt d (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))) (showString (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))) Nil)))); 14.24/5.67 14.24/5.67 } 14.24/5.67 14.24/5.67 ---------------------------------------- 14.24/5.67 14.24/5.67 (3) COR (EQUIVALENT) 14.24/5.67 Cond Reductions: 14.24/5.67 The following Function with conditions 14.24/5.67 "undefined |Falseundefined; 14.24/5.67 " 14.24/5.67 is transformed to 14.24/5.67 "undefined = undefined1; 14.24/5.67 " 14.24/5.67 "undefined0 True = undefined; 14.24/5.67 " 14.24/5.67 "undefined1 = undefined0 False; 14.24/5.67 " 14.24/5.67 14.24/5.67 ---------------------------------------- 14.24/5.67 14.24/5.67 (4) 14.24/5.67 Obligation: 14.24/5.67 mainModule Main 14.24/5.67 module Main where { 14.24/5.67 import qualified Prelude; 14.24/5.67 data Main.Char = Char MyInt ; 14.24/5.67 14.24/5.67 data List a = Cons a (List a) | Nil ; 14.24/5.67 14.24/5.67 data MyBool = MyTrue | MyFalse ; 14.24/5.67 14.24/5.67 data MyInt = Pos Main.Nat | Neg Main.Nat ; 14.24/5.67 14.24/5.67 data Main.Nat = Succ Main.Nat | Zero ; 14.24/5.67 14.24/5.67 data Ordering = LT | EQ | GT ; 14.24/5.67 14.24/5.67 compareMyInt :: MyInt -> MyInt -> Ordering; 14.24/5.67 compareMyInt = primCmpInt; 14.24/5.67 14.24/5.67 esEsOrdering :: Ordering -> Ordering -> MyBool; 14.24/5.67 esEsOrdering LT LT = MyTrue; 14.24/5.67 esEsOrdering LT EQ = MyFalse; 14.24/5.67 esEsOrdering LT GT = MyFalse; 14.24/5.67 esEsOrdering EQ LT = MyFalse; 14.24/5.67 esEsOrdering EQ EQ = MyTrue; 14.24/5.67 esEsOrdering EQ GT = MyFalse; 14.24/5.67 esEsOrdering GT LT = MyFalse; 14.24/5.67 esEsOrdering GT EQ = MyFalse; 14.24/5.67 esEsOrdering GT GT = MyTrue; 14.24/5.67 14.24/5.67 gtMyInt :: MyInt -> MyInt -> MyBool; 14.24/5.67 gtMyInt x y = esEsOrdering (compareMyInt x y) GT; 14.24/5.67 14.24/5.67 primCmpInt :: MyInt -> MyInt -> Ordering; 14.24/5.67 primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ; 14.24/5.67 primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ; 14.24/5.67 primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ; 14.24/5.67 primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ; 14.24/5.67 primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y; 14.24/5.67 primCmpInt (Main.Pos x) (Main.Neg y) = GT; 14.24/5.67 primCmpInt (Main.Neg x) (Main.Pos y) = LT; 14.24/5.67 primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x; 14.24/5.67 14.24/5.67 primCmpNat :: Main.Nat -> Main.Nat -> Ordering; 14.24/5.67 primCmpNat Main.Zero Main.Zero = EQ; 14.24/5.67 primCmpNat Main.Zero (Main.Succ y) = LT; 14.24/5.67 primCmpNat (Main.Succ x) Main.Zero = GT; 14.24/5.67 primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y; 14.24/5.67 14.24/5.67 psPs :: List a -> List a -> List a; 14.24/5.67 psPs Nil ys = ys; 14.24/5.67 psPs (Cons x xs) ys = Cons x (psPs xs ys); 14.24/5.67 14.24/5.67 pt :: (a -> b) -> (c -> a) -> c -> b; 14.24/5.67 pt f g x = f (g x); 14.24/5.67 14.24/5.67 showChar :: Main.Char -> List Main.Char -> List Main.Char; 14.24/5.67 showChar = Cons; 14.24/5.67 14.24/5.67 showParen :: MyBool -> (List Main.Char -> List Main.Char) -> List Main.Char -> List Main.Char; 14.24/5.67 showParen b p = showParen0 p b; 14.24/5.67 14.24/5.67 showParen0 p MyTrue = pt (showChar (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))) (pt p (showChar (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))); 14.24/5.67 showParen0 p MyFalse = p; 14.24/5.67 14.24/5.67 showString :: List Main.Char -> List Main.Char -> List Main.Char; 14.24/5.67 showString = psPs; 14.24/5.67 14.24/5.67 showsPrecOrdering :: MyInt -> Ordering -> List Main.Char -> List Main.Char; 14.24/5.67 showsPrecOrdering d LT = showParen (gtMyInt d (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))) (showString (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))) Nil)))); 14.24/5.67 showsPrecOrdering d EQ = showParen (gtMyInt d (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))) (showString (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))) Nil)))); 14.24/5.67 showsPrecOrdering d GT = showParen (gtMyInt d (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))) (showString (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))) Nil)))); 14.24/5.67 14.24/5.67 } 14.24/5.67 14.24/5.67 ---------------------------------------- 14.24/5.67 14.24/5.67 (5) Narrow (SOUND) 14.24/5.67 Haskell To QDPs 14.24/5.67 14.24/5.67 digraph dp_graph { 14.24/5.67 node [outthreshold=100, inthreshold=100];1[label="showsPrecOrdering",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 14.24/5.67 3[label="showsPrecOrdering vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 14.24/5.67 4[label="showsPrecOrdering vx3 vx4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 14.24/5.67 5[label="showsPrecOrdering vx3 vx4 vx5",fontsize=16,color="burlywood",shape="triangle"];160[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];5 -> 160[label="",style="solid", color="burlywood", weight=9]; 14.24/5.67 160 -> 6[label="",style="solid", color="burlywood", weight=3]; 14.24/5.67 161[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];5 -> 161[label="",style="solid", color="burlywood", weight=9]; 14.24/5.67 161 -> 7[label="",style="solid", color="burlywood", weight=3]; 14.24/5.67 162[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];5 -> 162[label="",style="solid", color="burlywood", weight=9]; 14.24/5.67 162 -> 8[label="",style="solid", color="burlywood", weight=3]; 14.24/5.67 6[label="showsPrecOrdering vx3 LT vx5",fontsize=16,color="black",shape="box"];6 -> 9[label="",style="solid", color="black", weight=3]; 14.24/5.67 7[label="showsPrecOrdering vx3 EQ vx5",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3]; 14.24/5.67 8[label="showsPrecOrdering vx3 GT vx5",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3]; 14.24/5.67 9 -> 67[label="",style="dashed", color="red", weight=0]; 14.24/5.67 9[label="showParen (gtMyInt vx3 (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) (showString (Cons (Char (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Char (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Cons (Char (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))) Nil)))) vx5",fontsize=16,color="magenta"];9 -> 68[label="",style="dashed", color="magenta", weight=3]; 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14.24/5.67 111[label="showParen0 (showString (Cons (Char (Pos (Succ vx32))) (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil)))) (esEsOrdering (primCmpNat (Succ vx30000) (Succ vx310)) GT) vx35",fontsize=16,color="black",shape="box"];111 -> 116[label="",style="solid", color="black", weight=3]; 14.24/5.67 112[label="showParen0 (showString (Cons (Char (Pos (Succ vx32))) (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil)))) (esEsOrdering (primCmpNat (Succ vx30000) Zero) GT) vx35",fontsize=16,color="black",shape="box"];112 -> 117[label="",style="solid", color="black", weight=3]; 14.24/5.67 113[label="showParen0 (showString (Cons (Char (Pos (Succ vx32))) (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil)))) (esEsOrdering (primCmpNat Zero (Succ vx310)) GT) vx35",fontsize=16,color="black",shape="box"];113 -> 118[label="",style="solid", color="black", weight=3]; 14.24/5.67 114[label="showParen0 (showString (Cons (Char (Pos (Succ vx32))) (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil)))) (esEsOrdering (primCmpNat Zero Zero) GT) vx35",fontsize=16,color="black",shape="box"];114 -> 119[label="",style="solid", color="black", weight=3]; 14.24/5.67 115[label="psPs (Cons (Char (Pos (Succ vx32))) (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil))) vx35",fontsize=16,color="black",shape="box"];115 -> 120[label="",style="solid", color="black", weight=3]; 14.24/5.67 116 -> 105[label="",style="dashed", color="red", weight=0]; 14.24/5.67 116[label="showParen0 (showString (Cons (Char (Pos (Succ vx32))) (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil)))) (esEsOrdering (primCmpNat vx30000 vx310) GT) vx35",fontsize=16,color="magenta"];116 -> 121[label="",style="dashed", color="magenta", weight=3]; 14.24/5.67 116 -> 122[label="",style="dashed", color="magenta", weight=3]; 14.24/5.67 117[label="showParen0 (showString (Cons (Char (Pos (Succ vx32))) (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil)))) (esEsOrdering GT GT) vx35",fontsize=16,color="black",shape="box"];117 -> 123[label="",style="solid", color="black", weight=3]; 14.24/5.67 118 -> 103[label="",style="dashed", color="red", weight=0]; 14.24/5.67 118[label="showParen0 (showString (Cons (Char (Pos (Succ vx32))) (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil)))) (esEsOrdering LT GT) vx35",fontsize=16,color="magenta"];119[label="showParen0 (showString (Cons (Char (Pos (Succ vx32))) (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil)))) (esEsOrdering EQ GT) vx35",fontsize=16,color="black",shape="box"];119 -> 124[label="",style="solid", color="black", weight=3]; 14.24/5.67 120[label="Cons (Char (Pos (Succ vx32))) (psPs (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil)) vx35)",fontsize=16,color="green",shape="box"];120 -> 125[label="",style="dashed", color="green", weight=3]; 14.24/5.67 121[label="vx310",fontsize=16,color="green",shape="box"];122[label="vx30000",fontsize=16,color="green",shape="box"];123[label="showParen0 (showString (Cons (Char (Pos (Succ vx32))) (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil)))) MyTrue vx35",fontsize=16,color="black",shape="box"];123 -> 126[label="",style="solid", color="black", weight=3]; 14.24/5.67 124 -> 107[label="",style="dashed", color="red", weight=0]; 14.24/5.67 124[label="showParen0 (showString (Cons (Char (Pos (Succ vx32))) (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil)))) MyFalse vx35",fontsize=16,color="magenta"];125[label="psPs (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil)) vx35",fontsize=16,color="black",shape="box"];125 -> 127[label="",style="solid", color="black", weight=3]; 14.24/5.67 126 -> 135[label="",style="dashed", color="red", weight=0]; 14.24/5.67 126[label="pt (showChar (Char (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))) (pt (showString (Cons (Char (Pos (Succ vx32))) (Cons (Char (Pos (Succ vx33))) (Cons (Char (Pos (Succ vx34))) Nil)))) (showChar (Char (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))) vx35",fontsize=16,color="magenta"];126 -> 136[label="",style="dashed", color="magenta", weight=3]; 14.24/5.67 126 -> 137[label="",style="dashed", color="magenta", weight=3]; 14.24/5.67 126 -> 138[label="",style="dashed", color="magenta", weight=3]; 14.24/5.67 126 -> 139[label="",style="dashed", color="magenta", weight=3]; 14.24/5.67 126 -> 140[label="",style="dashed", color="magenta", weight=3]; 14.24/5.67 126 -> 141[label="",style="dashed", color="magenta", weight=3]; 14.24/5.67 127[label="Cons (Char (Pos (Succ vx33))) (psPs (Cons (Char (Pos (Succ vx34))) Nil) vx35)",fontsize=16,color="green",shape="box"];127 -> 134[label="",style="dashed", color="green", weight=3]; 14.24/5.67 136[label="vx34",fontsize=16,color="green",shape="box"];137[label="vx33",fontsize=16,color="green",shape="box"];138[label="vx32",fontsize=16,color="green",shape="box"];139[label="vx35",fontsize=16,color="green",shape="box"];140[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];141[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];135[label="pt (showChar (Char (Pos (Succ vx43)))) (pt (showString (Cons (Char (Pos (Succ vx44))) (Cons (Char (Pos (Succ vx45))) (Cons (Char (Pos (Succ vx46))) Nil)))) (showChar (Char (Pos (Succ vx47))))) vx48",fontsize=16,color="black",shape="triangle"];135 -> 148[label="",style="solid", color="black", weight=3]; 14.24/5.67 134[label="psPs (Cons (Char (Pos (Succ vx34))) Nil) vx35",fontsize=16,color="black",shape="box"];134 -> 149[label="",style="solid", color="black", weight=3]; 14.24/5.67 148[label="showChar (Char (Pos (Succ vx43))) (pt (showString (Cons (Char (Pos (Succ vx44))) (Cons (Char (Pos (Succ vx45))) (Cons (Char (Pos (Succ vx46))) Nil)))) (showChar (Char (Pos (Succ vx47)))) vx48)",fontsize=16,color="black",shape="box"];148 -> 150[label="",style="solid", color="black", weight=3]; 14.24/5.67 149[label="Cons (Char (Pos (Succ vx34))) (psPs Nil vx35)",fontsize=16,color="green",shape="box"];149 -> 151[label="",style="dashed", color="green", weight=3]; 14.24/5.67 150[label="Cons (Char (Pos (Succ vx43))) (pt (showString (Cons (Char (Pos (Succ vx44))) (Cons (Char (Pos (Succ vx45))) (Cons (Char (Pos (Succ vx46))) Nil)))) (showChar (Char (Pos (Succ vx47)))) vx48)",fontsize=16,color="green",shape="box"];150 -> 152[label="",style="dashed", color="green", weight=3]; 14.24/5.67 151[label="psPs Nil vx35",fontsize=16,color="black",shape="box"];151 -> 153[label="",style="solid", color="black", weight=3]; 14.24/5.67 152[label="pt (showString (Cons (Char (Pos (Succ vx44))) (Cons (Char (Pos (Succ vx45))) (Cons (Char (Pos (Succ vx46))) Nil)))) (showChar (Char (Pos (Succ vx47)))) vx48",fontsize=16,color="black",shape="box"];152 -> 154[label="",style="solid", color="black", weight=3]; 14.24/5.67 153[label="vx35",fontsize=16,color="green",shape="box"];154 -> 110[label="",style="dashed", color="red", weight=0]; 14.24/5.67 154[label="showString (Cons (Char (Pos (Succ vx44))) (Cons (Char (Pos (Succ vx45))) (Cons (Char (Pos (Succ vx46))) Nil))) (showChar (Char (Pos (Succ vx47))) vx48)",fontsize=16,color="magenta"];154 -> 155[label="",style="dashed", color="magenta", weight=3]; 14.24/5.67 154 -> 156[label="",style="dashed", color="magenta", weight=3]; 14.24/5.67 154 -> 157[label="",style="dashed", color="magenta", weight=3]; 14.24/5.67 154 -> 158[label="",style="dashed", color="magenta", weight=3]; 14.24/5.67 155[label="vx44",fontsize=16,color="green",shape="box"];156[label="showChar (Char (Pos (Succ vx47))) vx48",fontsize=16,color="black",shape="box"];156 -> 159[label="",style="solid", color="black", weight=3]; 14.24/5.67 157[label="vx45",fontsize=16,color="green",shape="box"];158[label="vx46",fontsize=16,color="green",shape="box"];159[label="Cons (Char (Pos (Succ vx47))) vx48",fontsize=16,color="green",shape="box"];} 14.24/5.67 14.24/5.67 ---------------------------------------- 14.24/5.67 14.24/5.67 (6) 14.24/5.67 Obligation: 14.24/5.67 Q DP problem: 14.24/5.67 The TRS P consists of the following rules: 14.24/5.67 14.24/5.67 new_showParen0(vx32, vx33, vx34, Main.Succ(vx30000), Main.Succ(vx310), vx35) -> new_showParen0(vx32, vx33, vx34, vx30000, vx310, vx35) 14.24/5.67 14.24/5.67 R is empty. 14.24/5.67 Q is empty. 14.24/5.67 We have to consider all minimal (P,Q,R)-chains. 14.24/5.67 ---------------------------------------- 14.24/5.67 14.24/5.67 (7) QDPSizeChangeProof (EQUIVALENT) 14.24/5.67 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 14.24/5.67 14.24/5.67 From the DPs we obtained the following set of size-change graphs: 14.24/5.67 *new_showParen0(vx32, vx33, vx34, Main.Succ(vx30000), Main.Succ(vx310), vx35) -> new_showParen0(vx32, vx33, vx34, vx30000, vx310, vx35) 14.24/5.67 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 > 5, 6 >= 6 14.24/5.67 14.24/5.67 14.24/5.67 ---------------------------------------- 14.24/5.67 14.24/5.67 (8) 14.24/5.67 YES 14.35/9.14 EOF