id p = p p && p = p p || p = p p && q = q && p p || q = q || p not (not p) = p p && True = p True && p = p p && False = False False && p = False p || True = True True || p = True p || False = p False || p = p p && not p = False p || not p = True not p && p = False not p || p = True (p && q) && r = p && (q && r) (p || q) || r = p || (q || r) not (p && q) = not p || not q not (p || q) = not p && not q not False = True not True = False not (not p && not q) = p || q not (not p || not q) = p && q p && not (p && q) = p && not q id x = x abs (abs x) = abs x x + 0 = x 0 + x = x x * 1 = x 1 * x = x x * 0 = 0 0 * x = 0 x + y = y + x x * y = y * x (x + y) + z = x + (y + z) (x * y) * z = x * (y * z) (x + x) * y = x * (y + y) x * (y + 1) = x + x * y (x + 1) * y = x + x * y x * (y + z) = x * y + x * z (x + y) * z = x * z + y * z negate (negate x) = x x + negate x = 0 negate x + x = 0 abs (negate x) = abs x 2 * x = x + x x * 2 = x + x 3 * x = x + (x + x) x * 3 = x + (x + x) 4 * x = x + (x + (x + x)) x * 4 = x + (x + (x + x)) abs (x * x) = x * x abs x * abs y = abs (x * y) abs x * abs x = abs (x + x) abs (abs x + abs y) = abs x + abs y abs (x + x) * y = abs x * y + abs x * y abs x * signum x = x signum x * abs x = x id xs = xs head (x:xs) = x tail (x:xs) = xs xs ++ [] = xs [] ++ xs = xs [x] ++ xs = x:xs (x:xs) ++ ys = x:(xs ++ ys) (xs ++ ys) ++ zs = xs ++ (ys ++ zs) elem x (sort xs) = elem x xs elem x (insert y xs) = elem x (y:xs) sort (sort xs) = sort xs insert x [] = [x] sort (xs ++ ys) = sort (ys ++ xs) sort (insert x xs) = insert x (sort xs) sort (x:xs) = insert x (sort xs) sort (xs ++ sort ys) = sort (xs ++ ys) sort (sort xs ++ ys) = sort (xs ++ ys) insert x (insert y xs) = insert y (insert x xs) insert x (x:xs) = x:x:xs insert x [y] = insert y [x] length (x:xs) = length (y:xs) length (xs ++ ys) = length (ys ++ xs) length (x:y:xs) = length (z:x':xs) length (x:(xs ++ ys)) = length (y:(ys ++ xs)) length (xs ++ (ys ++ zs)) = length (xs ++ (zs ++ ys)) not (odd x) = even x not (even x) = odd x x == x = True x /= x = False p == p = True p /= p = False f (g x) = (f . g) x map id xs = xs map (f . g) xs = map f (map g xs) f . id = f id . f = f (f . g) . h = f . (g . h) not . not = id (id x :: Int,[(x :: Int,_ :: Int)],x :: Int) (id x :: Int,[(x :: Int,x :: Int)],x :: Int) (id x :: Int,[(x :: Int,0 :: Int)],x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,_ :: Int)],y + x :: Int) (id x :: Int,[(x :: Int,y :: Int)],x :: Int) (id x :: Int,[(x :: Int,1 :: Int)],x :: Int) (f (g x) :: Int,[(x :: Int,x :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,0 :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id _ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,(_ +) :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (id x :: Int,[(x :: Int,head _ :: Int)],x :: Int) (id x :: Int,[(x :: Int,ord _ :: Int)],x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,negate :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,abs :: Int -> Int)],(f . g) x :: Int) (x + y :: Int,[(y :: Int,x :: Int),(x :: Int,_ :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,0 :: Int),(x :: Int,_ :: Int)],y + x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,(_ +) :: Int -> Int)],(f . g) x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,x :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,0 :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,id _ :: Int)],y + x :: Int) (x * y :: Int,[(y :: Int,_ :: Int),(x :: Int,_ :: Int)],y * x :: Int) (head (x:xs) :: Int,[(xs :: [Int],_ :: [Int]),(x :: Int,_ :: Int)],x :: Int) (not False :: Bool,[],True :: Bool) (not True :: Bool,[],False :: Bool) (not (not p) :: Bool,[(p :: Bool,_ :: Bool)],p :: Bool) (p || p :: Bool,[(p :: Bool,_ :: Bool)],p :: Bool) (id x :: Int,[(x :: Int,z :: Int)],x :: Int) (id x :: Int,[(x :: Int,-1 :: Int)],x :: Int) (f (g x) :: Int,[(x :: Int,y :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,1 :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id x :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id 0 :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,negate _ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,abs _ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ + _ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,head _ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,ord _ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,x :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,0 :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id _ :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,x :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,0 :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id _ :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,x :: Int),(g :: Int -> Int,(_ +) :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,0 :: Int),(g :: Int -> Int,(_ +) :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id _ :: Int),(g :: Int -> Int,(_ +) :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,(x +) :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,(0 +) :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,(id _ +) :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,(_ *) :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,f :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (id x :: Int,[(x :: Int,head xs :: Int)],x :: Int) (id x :: Int,[(x :: Int,head [] :: Int)],x :: Int) (id x :: Int,[(x :: Int,head (_:_) :: Int)],x :: Int) (id x :: Int,[(x :: Int,ord c :: Int)],x :: Int) (id x :: Int,[(x :: Int,ord 'a' :: Int)],x :: Int) (f (g x) :: Int,[(x :: Int,x :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,negate :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,0 :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,negate :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id _ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,negate :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,negate :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,negate :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,(_ +) :: Int -> Int),(f :: Int -> Int,negate :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,x :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,abs :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,0 :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,abs :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id _ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,abs :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,abs :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,abs :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,(_ +) :: Int -> Int),(f :: Int -> Int,abs :: Int -> Int)],(f . g) x :: Int) (x + y :: Int,[(y :: Int,y :: Int),(x :: Int,_ :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,1 :: Int),(x :: Int,_ :: Int)],y + x :: Int) (f (g x) :: Int,[(x :: Int,x :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,(_ +) :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,0 :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,(_ +) :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id _ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,(_ +) :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,(_ +) :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,(_ +) :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,(_ +) :: Int -> Int),(f :: Int -> Int,(_ +) :: Int -> Int)],(f . g) x :: Int) (x + y :: Int,[(y :: Int,head _ :: Int),(x :: Int,_ :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,ord _ :: Int),(x :: Int,_ :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,x :: Int),(x :: Int,x :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,0 :: Int),(x :: Int,x :: Int)],y + x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,(x +) :: Int -> Int)],(f . g) x :: Int) (x + y :: Int,[(y :: Int,x :: Int),(x :: Int,0 :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,0 :: Int),(x :: Int,0 :: Int)],y + x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,(0 +) :: Int -> Int)],(f . g) x :: Int) (x + y :: Int,[(y :: Int,x :: Int),(x :: Int,id _ :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,0 :: Int),(x :: Int,id _ :: Int)],y + x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,(id _ +) :: Int -> Int)],(f . g) x :: Int) (x * y :: Int,[(y :: Int,x :: Int),(x :: Int,_ :: Int)],y * x :: Int) (x * y :: Int,[(y :: Int,0 :: Int),(x :: Int,_ :: Int)],y * x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,(_ *) :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,f :: Int -> Int)],(f . g) x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,y :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,1 :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,id x :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,id 0 :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,id (id _) :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,negate _ :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,abs _ :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,_ + _ :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,head _ :: Int)],y + x :: Int) (x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,ord _ :: Int)],y + x :: Int) (x * y :: Int,[(y :: Int,_ :: Int),(x :: Int,x :: Int)],y * x :: Int) (x * y :: Int,[(y :: Int,_ :: Int),(x :: Int,0 :: Int)],y * x :: Int) (x * y :: Int,[(y :: Int,_ :: Int),(x :: Int,id _ :: Int)],y * x :: Int) (head (x:xs) :: Int,[(xs :: [Int],xs :: [Int]),(x :: Int,_ :: Int)],x :: Int) (head (x:xs) :: Int,[(xs :: [Int],[] :: [Int]),(x :: Int,_ :: Int)],x :: Int) (head (x:xs) :: Int,[(xs :: [Int],_:_ :: [Int]),(x :: Int,_ :: Int)],x :: Int) (head (x:xs) :: Int,[(xs :: [Int],_ :: [Int]),(x :: Int,x :: Int)],x :: Int) (head (x:xs) :: Int,[(xs :: [Int],_ :: [Int]),(x :: Int,0 :: Int)],x :: Int) (head (x:xs) :: Int,[(xs :: [Int],_ :: [Int]),(x :: Int,id _ :: Int)],x :: Int) (not (not p) :: Bool,[(p :: Bool,p :: Bool)],p :: Bool) (not (not p) :: Bool,[(p :: Bool,False :: Bool)],p :: Bool) (not (not p) :: Bool,[(p :: Bool,True :: Bool)],p :: Bool) (not (not p) :: Bool,[(p :: Bool,not _ :: Bool)],p :: Bool) (not (p || q) :: Bool,[(q :: Bool,_ :: Bool),(p :: Bool,_ :: Bool)],not p && not q :: Bool) (p || q :: Bool,[(q :: Bool,p :: Bool),(p :: Bool,_ :: Bool)],q || p :: Bool) (p || q :: Bool,[(q :: Bool,False :: Bool),(p :: Bool,_ :: Bool)],q || p :: Bool) (p || q :: Bool,[(q :: Bool,True :: Bool),(p :: Bool,_ :: Bool)],q || p :: Bool) (p || q :: Bool,[(q :: Bool,not _ :: Bool),(p :: Bool,_ :: Bool)],q || p :: Bool) (p || q :: Bool,[(q :: Bool,_ :: Bool),(p :: Bool,p :: Bool)],q || p :: Bool) (p || q :: Bool,[(q :: Bool,_ :: Bool),(p :: Bool,False :: Bool)],q || p :: Bool) (p || q :: Bool,[(q :: Bool,_ :: Bool),(p :: Bool,True :: Bool)],q || p :: Bool) (p || q :: Bool,[(q :: Bool,_ :: Bool),(p :: Bool,not _ :: Bool)],q || p :: Bool) (p && p :: Bool,[(p :: Bool,_ :: Bool)],p :: Bool) (x == x :: Bool,[(x :: Int,_ :: Int)],True :: Bool) (p == p :: Bool,[(p :: Bool,_ :: Bool)],True :: Bool) (tail (x:xs) :: [Int],[(xs :: [Int],_ :: [Int]),(x :: Int,_ :: Int)],xs :: [Int]) (xs ++ [] :: [Int],[(xs :: [Int],_ :: [Int])],xs :: [Int]) ([] ++ xs :: [Int],[(xs :: [Int],_ :: [Int])],xs :: [Int]) ((x:xs) ++ ys :: [Int],[(ys :: [Int],_ :: [Int]),(xs :: [Int],_ :: [Int]),(x :: Int,_ :: Int)],x:(xs ++ ys) :: [Int]) (id x :: Int,[(x :: Int,x' :: Int)],x :: Int) (id x :: Int,[(x :: Int,2 :: Int)],x :: Int) (f (g x) :: Int,[(x :: Int,z :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,-1 :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id y :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id 1 :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id x) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id 0) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id (id _)) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (negate _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (abs _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (_ + _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (head _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (ord _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,negate x :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,negate 0 :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,negate (id _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,abs x :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,abs 0 :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,abs (id _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> 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Bool,not p :: Bool)],q || p :: Bool) (p || q :: Bool,[(q :: Bool,_ :: Bool),(p :: Bool,not False :: Bool)],q || p :: Bool) (p || q :: Bool,[(q :: Bool,_ :: Bool),(p :: Bool,not True :: Bool)],q || p :: Bool) (p || q :: Bool,[(q :: Bool,_ :: Bool),(p :: Bool,not (not _) :: Bool)],q || p :: Bool) (p || q :: Bool,[(q :: Bool,_ :: Bool),(p :: Bool,_ || _ :: Bool)],q || p :: Bool) (p && q :: Bool,[(q :: Bool,_ :: Bool),(p :: Bool,p :: Bool)],q && p :: Bool) (p && q :: Bool,[(q :: Bool,_ :: Bool),(p :: Bool,False :: Bool)],q && p :: Bool) (p && q :: Bool,[(q :: Bool,_ :: Bool),(p :: Bool,True :: Bool)],q && p :: Bool) (p && q :: Bool,[(q :: Bool,_ :: Bool),(p :: Bool,not _ :: Bool)],q && p :: Bool) (tail (x:xs) :: [Int],[(xs :: [Int],xs :: [Int]),(x :: Int,_ :: Int)],xs :: [Int]) (tail (x:xs) :: [Int],[(xs :: [Int],[] :: [Int]),(x :: Int,_ :: Int)],xs :: [Int]) (tail (x:xs) :: [Int],[(xs :: [Int],_:_ :: [Int]),(x :: Int,_ :: Int)],xs :: [Int]) (tail (x:xs) :: [Int],[(xs :: [Int],_ :: [Int]),(x :: Int,x :: Int)],xs :: [Int]) (tail (x:xs) :: [Int],[(xs :: [Int],_ :: [Int]),(x :: Int,0 :: Int)],xs :: [Int]) (tail (x:xs) :: [Int],[(xs :: [Int],_ :: [Int]),(x :: Int,id _ :: Int)],xs :: [Int]) (xs ++ [] :: [Int],[(xs :: [Int],xs :: [Int])],xs :: [Int]) ([] ++ xs :: [Int],[(xs :: [Int],xs :: [Int])],xs :: [Int]) (xs ++ [] :: [Int],[(xs :: [Int],[] :: [Int])],xs :: [Int]) ([] ++ xs :: [Int],[(xs :: [Int],_:_ :: [Int])],xs :: [Int]) ((x:xs) ++ ys :: [Int],[(ys :: [Int],xs :: [Int]),(xs :: [Int],_ :: [Int]),(x :: Int,_ :: Int)],x:(xs ++ ys) :: [Int]) (xs ++ [] :: [Int],[(xs :: [Int],_:_ :: [Int])],xs :: [Int]) ((x:xs) ++ ys :: [Int],[(ys :: [Int],_:_ :: [Int]),(xs :: [Int],_ :: [Int]),(x :: Int,_ :: Int)],x:(xs ++ ys) :: [Int]) ((x:xs) ++ ys :: [Int],[(ys :: [Int],_ :: [Int]),(xs :: [Int],xs :: [Int]),(x :: Int,_ :: Int)],x:(xs ++ ys) :: [Int]) ((x:xs) ++ ys :: [Int],[(ys :: [Int],_ :: [Int]),(xs :: [Int],[] :: [Int]),(x :: Int,_ :: Int)],x:(xs ++ ys) :: [Int]) ((x:xs) ++ ys :: [Int],[(ys :: [Int],_ :: [Int]),(xs :: [Int],_:_ :: [Int]),(x :: Int,_ :: Int)],x:(xs ++ ys) :: [Int]) ((x:xs) ++ ys :: [Int],[(ys :: [Int],_ :: [Int]),(xs :: [Int],_ :: [Int]),(x :: Int,x :: Int)],x:(xs ++ ys) :: [Int]) ((x:xs) ++ ys :: [Int],[(ys :: [Int],_ :: [Int]),(xs :: [Int],_ :: [Int]),(x :: Int,0 :: Int)],x:(xs ++ ys) :: [Int]) ((x:xs) ++ ys :: [Int],[(ys :: [Int],_ :: [Int]),(xs :: [Int],_ :: [Int]),(x :: Int,id _ :: Int)],x:(xs ++ ys) :: [Int]) ((xs ++ ys) ++ zs :: [Int],[(zs :: [Int],_ :: [Int]),(ys :: [Int],_ :: [Int]),(xs :: [Int],_ :: [Int])],xs ++ (ys ++ zs) :: [Int]) (sort (x:xs) :: [Int],[(xs :: [Int],_ :: [Int]),(x :: Int,_ :: Int)],insert x (sort xs) :: [Int]) (insert x [] :: [Int],[(x :: Int,_ :: Int)],[x] :: [Int]) (insert x (x:xs) :: [Int],[(xs :: [Int],_ :: [Int]),(x :: Int,_ :: Int)],x:x:xs :: [Int]) (id x :: Int,[(x :: Int,y' :: Int)],x :: Int) (id x :: Int,[(x :: Int,-2 :: Int)],x :: Int) (f (g x) :: Int,[(x :: Int,x' :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,2 :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id z :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (-1) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id y) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id 1) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id (id x)) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id (id 0)) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id (id (id _))) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id (negate _)) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id (abs _)) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id (_ + _)) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id (head _)) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id (ord _)) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (negate x) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (negate 0) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (negate (id _)) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (abs x) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (abs 0) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (abs (id _)) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (_ + x) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (_ + 0) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (_ + id _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (x + _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (0 + _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id _ + _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (_ * _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (f _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (head xs) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (head []) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (head (_:_)) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (ord c) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (ord 'a') :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,negate y :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,negate 1 :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,negate (id x) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,negate (id 0) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x 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:: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id _ * _ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,g _ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,head ys :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,head [0] :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,head (_:xs) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,head [_] :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,head (_:_:_) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> 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Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,ord 'a' :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,z :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,-1 :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id y :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id 1 :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id x) :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id 0) :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) (f (g x) :: Int,[(x :: Int,id (id (id _)) :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int) True