factTD :: Int -> Int 
d :: Int -> Int -> Int 
factTD(x) -> d(x, 1)
d(x, a) -> a            | x<=0
d(x, a) -> d(x-1, a*x)  | x>0

factRU :: Int -> Int 
U :: Int -> Int -> Int 
factRU(x) -> U(1, x)
U(i, x) -> x | i>x-1
U(i, x) -> i*U(i+1, x) | i<=x-1

taildown :: (Int -> Int -> Int) -> Int -> Int -> Int -> Int
taildown(F, x, i, a) -> a                             | i < x
taildown(F, x, i, a) -> taildown(F, x, i - 1, F(a,i)) | i ≥ x

recup :: (Int -> Int -> Int) -> Int -> Int -> Int -> Int
recup(F, i, y, a) -> a                                | i > y
recup(F, i, y, a) -> F(recup(F, i + 1, y, a), i)      | i ≤ y

helper :: Int -> Int -> Int
helper(x, y) -> y*x