second :: [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
second xs  =  head (tail xs)

third :: [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
-- looking through 1 candidates of size 4
third xs  =  head (tail (tail xs))

sum :: [Int] -> Int
-- testing 360 combinations of argument values
-- pruning with 14/25 rules
-- looking through 2 candidates of size 1
-- looking through 4 candidates of size 2
-- looking through 3 candidates of size 3
-- looking through 13 candidates of size 4
-- looking through 14 candidates of size 5
sum []  =  0
sum (x:xs)  =  x + sum xs

product :: [Int] -> Int
-- testing 360 combinations of argument values
-- pruning with 14/25 rules
-- looking through 2 candidates of size 1
-- looking through 4 candidates of size 2
-- looking through 3 candidates of size 3
-- looking through 13 candidates of size 4
-- looking through 14 candidates of size 5
product []  =  1
product (x:xs)  =  x * product xs

sum :: [Int] -> Int
-- testing 360 combinations of argument values
-- pruning with 15/26 rules
-- looking through 2 candidates of size 1
-- looking through 4 candidates of size 2
-- looking through 3 candidates of size 3
-- looking through 16 candidates of size 4
sum xs  =  foldr (+) 0 xs

product :: [Int] -> Int
-- testing 360 combinations of argument values
-- pruning with 15/26 rules
-- looking through 2 candidates of size 1
-- looking through 4 candidates of size 2
-- looking through 3 candidates of size 3
-- looking through 16 candidates of size 4
product xs  =  foldr (*) 1 xs