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 24 candidates of size 2
-- looking through 75 candidates of size 3
-- looking through 234 candidates of size 4
-- tested 337 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 17 candidates of size 3
-- looking through 62 candidates of size 4
-- looking through 266 candidates of size 5
-- looking through 1154 candidates of size 6
-- tested 1503 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 8 candidates of size 4
-- looking through 6 candidates of size 5
-- looking through 46 candidates of size 6
-- looking through 26 candidates of size 7
-- looking through 400 candidates of size 8
-- looking through 134 candidates of size 9
-- looking through 3914 candidates of size 10
-- tested 1552 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 82 candidates of size 6
-- looking through 428 candidates of size 7
-- looking through 887 candidates of size 8
-- looking through 4354 candidates of size 9
-- looking through 9260 candidates of size 10
-- looking through 43875 candidates of size 11
-- tested 32327 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

gps8 :: 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

gps9 :: 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

gps10 :: [Int] -> Int
-- testing 7 combinations of argument values
-- pruning with 67/100 rules
-- looking through 4 candidates of size 1
-- looking through 16 candidates of size 2
-- looking through 4 candidates of size 3
-- looking through 68 candidates of size 4
-- looking through 80 candidates of size 5
-- looking through 1084 candidates of size 6
-- looking through 1556 candidates of size 7
-- looking through 20600 candidates of size 8
-- looking through 35632 candidates of size 9
-- tested 29542 candidates
gps10 []  =  0
gps10 (x:xs)  =  gps10 xs + (x `div` 3 - 2)

gcd :: Int -> Int -> Int
-- testing 11 combinations of argument values
-- pruning with 0/0 rules
-- looking through 3 candidates of size 1
-- looking through 5 candidates of size 2
-- looking through 11 candidates of size 3
-- looking through 50 candidates of size 4
-- looking through 98 candidates of size 5
-- looking through 359 candidates of size 6
-- tested 171 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 3 candidates of size 5
-- tested 9 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 32 candidates of size 3
-- looking through 86 candidates of size 4
-- looking through 412 candidates of size 5
-- looking through 1072 candidates of size 6
-- tested 1612 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 4 candidates of size 2
-- looking through 22 candidates of size 3
-- looking through 118 candidates of size 4
-- looking through 318 candidates of size 5
-- looking through 1936 candidates of size 6
-- tested 2401 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 14 candidates of size 5
-- looking through 13 candidates of size 6
-- looking through 94 candidates of size 7
-- looking through 104 candidates of size 8
-- looking through 856 candidates of size 9
-- looking through 929 candidates of size 10
-- looking through 8914 candidates of size 11
-- looking through 9686 candidates of size 12
-- tested 20616 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 9 candidates of size 2
-- looking through 31 candidates of size 3
-- looking through 36 candidates of size 4
-- looking through 187 candidates of size 5
-- looking through 627 candidates of size 6
-- looking through 944 candidates of size 7
-- looking through 863 candidates of size 8
-- looking through 951 candidates of size 9
-- looking through 3902 candidates of size 10
-- looking through 6758 candidates of size 11
-- looking through 3276 candidates of size 12
-- tested 17587 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 49 candidates of size 3
-- looking through 211 candidates of size 4
-- looking through 1063 candidates of size 5
-- looking through 4717 candidates of size 6
-- tested 6051 candidates
cannot conjure