gps1 :: [Int] -> Maybe Int
-- testing 4 combinations of argument values
-- pruning with 11/21 rules
-- looking through 0 candidates of size 1
-- looking through 0 candidates of size 2
-- looking through 0 candidates of size 3
-- looking through 1 candidates of size 4
-- looking through 0 candidates of size 5
-- looking through 0 candidates of size 6
-- looking through 1 candidates of size 7
-- looking through 0 candidates of size 8
-- looking through 1 candidates of size 9
-- looking through 2 candidates of size 10
-- tested 5 candidates
gps1 xs  =  findIndex (0 >) (map (foldr (+) 0) (tail (inits xs)))

gps1 :: [Int] -> Maybe Int
-- testing 4 combinations of argument values
-- pruning with 11/21 rules
-- looking through 0 candidates of size 1
-- looking through 0 candidates of size 2
-- looking through 0 candidates of size 3
-- looking through 1 candidates of size 4
-- looking through 1 candidates of size 5
-- looking through 0 candidates of size 6
-- looking through 1 candidates of size 7
-- looking through 4 candidates of size 8
-- tested 6 candidates
gps1 xs  =  findIndex (0 >) (map sum (tail (inits xs)))

gps1 :: Int -> [Int] -> Int
-- testing 6 combinations of argument values
-- pruning with 8/9 rules
-- looking through 4 candidates of size 1
-- looking through 25 candidates of size 2
-- looking through 237 candidates of size 3
-- looking through 433 candidates of size 4
-- tested 699 candidates
cannot conjure

gps2 :: Double -> Double -> Int -> Double
-- testing 5 combinations of argument values
-- pruning with 2/6 rules
-- looking through 2 candidates of size 1
-- looking through 2 candidates of size 2
-- looking through 18 candidates of size 3
-- looking through 70 candidates of size 4
-- looking through 316 candidates of size 5
-- looking through 1440 candidates of size 6
-- tested 1848 candidates
cannot conjure

gps3 :: [Char] -> Int
-- pruning with 0/0 rules
-- looking through 0 candidates of size 1
-- looking through 0 candidates of size 2
-- tested 0 candidates
cannot conjure

gps4 :: [Char] -> [Char]
-- pruning with 13/20 rules
-- looking through 2 candidates of size 1
-- looking through 3 candidates of size 2
-- looking through 9 candidates of size 3
-- looking through 22 candidates of size 4
-- looking through 54 candidates of size 5
-- looking through 124 candidates of size 6
-- tested 214 candidates
cannot conjure

gps5 :: Int -> [Int]
-- testing 6 combinations of argument values
-- pruning with 0/0 rules
-- looking through 0 candidates of size 1
-- tested 0 candidates
cannot conjure

tell :: [Int] -> Int -> [Int]
-- pruning with 0/0 rules
-- looking through 2 candidates of size 1
-- looking through 1 candidates of size 2
-- looking through 2 candidates of size 3
-- looking through 10 candidates of size 4
-- looking through 6 candidates of size 5
-- looking through 60 candidates of size 6
-- looking through 26 candidates of size 7
-- looking through 538 candidates of size 8
-- looking through 134 candidates of size 9
-- looking through 5296 candidates of size 10
-- tested 2698 candidates
tell [] x  =  []
tell (x:xs) y  =  y `div` x:tell xs (y `mod` x)

gps5 :: Int -> [Int]
-- testing 6 combinations of argument values
-- pruning with 0/0 rules
-- looking through 1 candidates of size 1
-- looking through 0 candidates of size 2
-- looking through 1 candidates of size 3
-- tested 2 candidates
gps5 x  =  tell [25,10,5,1] x

gps5 :: Int -> [Int]
-- testing 6 combinations of argument values
-- pruning with 12/12 rules
-- looking through 1 candidates of size 1
-- looking through 0 candidates of size 2
-- looking through 5 candidates of size 3
-- looking through 9 candidates of size 4
-- looking through 45 candidates of size 5
-- looking through 92 candidates of size 6
-- looking through 438 candidates of size 7
-- looking through 944 candidates of size 8
-- looking through 4413 candidates of size 9
-- looking through 9649 candidates of size 10
-- looking through 44336 candidates of size 11
-- tested 32852 candidates
gps5 x  =  tell [25,10,5,1] x

gps6 :: [Int] -> Int
-- testing 360 combinations of argument values
-- pruning with 0/0 rules
-- looking through 0 candidates of size 1
-- looking through 1 candidates of size 2
-- looking through 1 candidates of size 3
-- tested 2 candidates
cannot conjure

gps7 :: Integer -> Integer -> Ratio Integer
-- testing 6 combinations of argument values
-- pruning with 0/0 rules
-- looking through 0 candidates of size 1
-- tested 0 candidates
cannot conjure

gps :: Int -> [Int] -> (Int,Int)
-- testing 3 combinations of argument values
-- pruning with 0/0 rules
-- looking through 0 candidates of size 1
-- looking through 0 candidates of size 2
-- tested 0 candidates
cannot conjure

gps :: Int -> [Char]
-- testing 7 combinations of argument values
-- pruning with 0/0 rules
-- looking through 0 candidates of size 1
-- tested 0 candidates
cannot conjure

gps :: Int -> [Char]
-- testing 7 combinations of argument values
-- pruning with 0/0 rules
-- looking through 0 candidates of size 1
-- tested 0 candidates
cannot conjure

gcd :: Int -> Int -> Int
-- testing 11 combinations of argument values
-- pruning with 0/0 rules
-- looking through 3 candidates of size 1
-- looking through 7 candidates of size 2
-- looking through 18 candidates of size 3
-- looking through 60 candidates of size 4
-- looking through 150 candidates of size 5
-- looking through 469 candidates of size 6
-- tested 243 candidates
gcd x 0  =  x
gcd x y  =  gcd y (x `mod` y)

gps12 :: [Char] -> [Char] -> [Int]
-- testing 5 combinations of argument values
-- pruning with 1/2 rules
-- looking through 0 candidates of size 1
-- looking through 0 candidates of size 2
-- looking through 0 candidates of size 3
-- looking through 0 candidates of size 4
-- looking through 4 candidates of size 5
-- tested 3 candidates
gps12 cs ds  =  findIndices (ds `isPrefixOf`) (tails cs)

gps13_leaders :: [Int] -> [Int]
-- testing 4 combinations of argument values
-- pruning with 5/5 rules
-- looking through 2 candidates of size 1
-- looking through 1 candidates of size 2
-- looking through 1 candidates of size 3
-- looking through 2 candidates of size 4
-- looking through 1 candidates of size 5
-- looking through 2 candidates of size 6
-- looking through 1 candidates of size 7
-- looking through 4 candidates of size 8
-- looking through 7 candidates of size 9
-- looking through 21 candidates of size 10
-- looking through 34 candidates of size 11
-- looking through 67 candidates of size 12
-- tested 83 candidates
gps13_leaders []  =  []
gps13_leaders (x:xs)  =  if all (x >) xs then x:gps13_leaders xs else gps13_leaders xs

gps14_luhn :: [Int] -> Int
-- pruning with 0/0 rules
-- looking through 0 candidates of size 1
-- looking through 0 candidates of size 2
-- tested 0 candidates
cannot conjure

gps15_mastermind :: () -> ()
-- pruning with 0/1 rules
-- looking through 1 candidates of size 1
-- tested 1 candidates
gps15_mastermind u  =  u

gps16_middle :: [Char] -> [Char]
-- testing 7 combinations of argument values
-- pruning with 10/11 rules
-- looking through 2 candidates of size 1
-- looking through 3 candidates of size 2
-- looking through 7 candidates of size 3
-- looking through 12 candidates of size 4
-- looking through 21 candidates of size 5
-- looking through 34 candidates of size 6
-- looking through 61 candidates of size 7
-- looking through 126 candidates of size 8
-- looking through 307 candidates of size 9
-- looking through 824 candidates of size 10
-- looking through 2282 candidates of size 11
-- looking through 6293 candidates of size 12
-- tested 3977 candidates
gps16_middle ""  =  ""
gps16_middle (c:cs)  =  if length cs <= 1 then c:cs else gps16_middle (init cs)

gps17_pds :: [Int] -> Int
-- testing 5 combinations of argument values
-- pruning with 29/40 rules
-- looking through 1 candidates of size 1
-- looking through 2 candidates of size 2
-- looking through 2 candidates of size 3
-- looking through 1 candidates of size 4
-- looking through 5 candidates of size 5
-- tested 11 candidates
cannot conjure

gps18_price :: [Double] -> [Double] -> Double
-- testing 4 combinations of argument values
-- pruning with 26/35 rules
-- looking through 2 candidates of size 1
-- looking through 8 candidates of size 2
-- looking through 64 candidates of size 3
-- looking through 72 candidates of size 4
-- looking through 1193 candidates of size 5
-- looking through 714 candidates of size 6
-- tested 2053 candidates
cannot conjure

gps19_snowday :: Int -> Double -> Double -> Double -> Double
-- testing 7 combinations of argument values
-- pruning with 6/19 rules
-- looking through 3 candidates of size 1
-- looking through 0 candidates of size 2
-- looking through 24 candidates of size 3
-- looking through 150 candidates of size 4
-- looking through 546 candidates of size 5
-- looking through 3540 candidates of size 6
-- tested 4263 candidates
cannot conjure

gps20 :: [Char] -> Bool
-- pruning with 0/0 rules
-- looking through 0 candidates of size 1
-- looking through 0 candidates of size 2
-- tested 0 candidates
cannot conjure

spin :: [Char] -> [Char]
-- pruning with 6/6 rules
-- reasoning produced 1 incorrect properties, please re-run with more tests for faster results
-- looking through 1 candidates of size 1
-- looking through 1 candidates of size 2
-- looking through 0 candidates of size 3
-- looking through 0 candidates of size 4
-- looking through 0 candidates of size 5
-- looking through 0 candidates of size 6
-- looking through 0 candidates of size 7
-- looking through 4 candidates of size 8
-- tested 3 candidates
spin cs  =  if length cs >= 5 then reverse cs else cs

gps21_spinwords :: [Char] -> [Char]
-- pruning with 16/16 rules
-- reasoning produced 2 incorrect properties, please re-run with more tests for faster results
-- looking through 1 candidates of size 1
-- looking through 2 candidates of size 2
-- looking through 2 candidates of size 3
-- looking through 3 candidates of size 4
-- looking through 5 candidates of size 5
-- tested 12 candidates
gps21_spinwords cs  =  unwords (map spin (words cs))

digits :: Int -> [Int]
-- testing 5 combinations of argument values
-- pruning with 7/7 rules
-- looking through 1 candidates of size 1
-- looking through 0 candidates of size 2
-- looking through 2 candidates of size 3
-- looking through 3 candidates of size 4
-- looking through 17 candidates of size 5
-- looking through 14 candidates of size 6
-- looking through 103 candidates of size 7
-- looking through 104 candidates of size 8
-- looking through 901 candidates of size 9
-- looking through 935 candidates of size 10
-- looking through 9226 candidates of size 11
-- looking through 9686 candidates of size 12
-- tested 20992 candidates
cannot conjure

gps22 :: Int -> [Char]
-- pruning with 0/0 rules
-- looking through 0 candidates of size 1
-- tested 0 candidates
cannot conjure

gps23 :: [Char] -> [Char] -> [Char] -> [Char]
-- pruning with 0/0 rules
-- looking through 3 candidates of size 1
-- looking through 5 candidates of size 2
-- looking through 9 candidates of size 3
-- looking through 0 candidates of size 4
-- looking through 162 candidates of size 5
-- looking through 612 candidates of size 6
-- looking through 0 candidates of size 7
-- looking through 0 candidates of size 8
-- looking through 3168 candidates of size 9
-- looking through 0 candidates of size 10
-- looking through 0 candidates of size 11
-- looking through 5184 candidates of size 12
-- tested 9143 candidates
cannot conjure

gps24 :: [Char] -> Twitter
-- pruning with 4/8 rules
-- reasoning produced 4 incorrect properties, please re-run with more tests for faster results
-- looking through 2 candidates of size 1
-- looking through 3 candidates of size 2
-- looking through 8 candidates of size 3
-- looking through 7 candidates of size 4
-- looking through 4 candidates of size 5
-- looking through 5 candidates of size 6
-- looking through 10 candidates of size 7
-- looking through 48 candidates of size 8
-- looking through 138 candidates of size 9
-- looking through 232 candidates of size 10
-- looking through 322 candidates of size 11
-- looking through 483 candidates of size 12
-- tested 936 candidates
gps24 ""  =  Empty
gps24 (c:cs)  =  if 140 > length cs then Tweet (length (c:cs)) else TooMany

gps25 :: [Double] -> [Double] -> Double
-- testing 6 combinations of argument values
-- pruning with 31/59 rules
-- looking through 2 candidates of size 1
-- looking through 9 candidates of size 2
-- looking through 81 candidates of size 3
-- looking through 312 candidates of size 4
-- looking through 2249 candidates of size 5
-- looking through 9419 candidates of size 6
-- tested 12072 candidates
cannot conjure