map length (tiers :: [[ Nat->Nat ]])  =  [1,1,3,5,10,16,30,48,80,...]

length (list :: [ Nat->Nat ])  =  Infinity

allUnique (list :: [ Nat->Nat ])  =  True

ratioRepetitions (list :: [ Nat->Nat ])  =  0 % 1

tiers :: [Nat->Nat]  =
  [ [\_ -> 0]
  , [\_ -> 1]
  , [ \x -> case x of
            0 -> 1
            _ -> 0
    , \x -> case x of
            0 -> 0
            _ -> 1
    , \_ -> 2
    ]
  , [ \x -> case x of
            0 -> 2
            _ -> 0
    , \x -> case x of
            1 -> 1
            _ -> 0
    , \x -> case x of
            1 -> 0
            _ -> 1
    , \x -> case x of
            0 -> 0
            _ -> 2
    , \_ -> 3
    ]
  , [ \x -> case x of
            0 -> 3
            _ -> 0
    , \x -> case x of
            1 -> 2
            _ -> 0
    , \x -> case x of
            2 -> 1
            _ -> 0
    , \x -> case x of
            0 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 0
            1 -> 0
            _ -> 1
    , \x -> case x of
            2 -> 0
            _ -> 1
    , \x -> case x of
            0 -> 1
            _ -> 2
    , \x -> case x of
            1 -> 0
            _ -> 2
    , \x -> case x of
            0 -> 0
            _ -> 3
    , \_ -> 4
    ]
  , [ \x -> case x of
            0 -> 4
            _ -> 0
    , \x -> case x of
            1 -> 3
            _ -> 0
    , \x -> case x of
            0 -> 1
            1 -> 1
            _ -> 0
    , \x -> case x of
            2 -> 2
            _ -> 0
    , \x -> case x of
            3 -> 1
            _ -> 0
    , \x -> case x of
            0 -> 3
            _ -> 1
    , \x -> case x of
            1 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 0
            2 -> 0
            _ -> 1
    , \x -> case x of
            3 -> 0
            _ -> 1
    , \x -> case x of
            1 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 0
            1 -> 0
            _ -> 2
    , \x -> case x of
            2 -> 0
            _ -> 2
    , \x -> case x of
            0 -> 1
            _ -> 3
    , \x -> case x of
            1 -> 0
            _ -> 3
    , \x -> case x of
            0 -> 0
            _ -> 4
    , \_ -> 5
    ]
  , [ \x -> case x of
            0 -> 5
            _ -> 0
    , \x -> case x of
            1 -> 4
            _ -> 0
    , \x -> case x of
            0 -> 1
            1 -> 2
            _ -> 0
    , \x -> case x of
            0 -> 2
            1 -> 1
            _ -> 0
    , \x -> case x of
            2 -> 3
            _ -> 0
    , \x -> case x of
            0 -> 1
            2 -> 1
            _ -> 0
    , \x -> case x of
            3 -> 2
            _ -> 0
    , \x -> case x of
            4 -> 1
            _ -> 0
    , \x -> case x of
            0 -> 4
            _ -> 1
    , \x -> case x of
            1 -> 3
            _ -> 1
    , \x -> case x of
            0 -> 0
            1 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 2
            1 -> 0
            _ -> 1
    , \x -> case x of
            2 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 0
            3 -> 0
            _ -> 1
    , \x -> case x of
            1 -> 0
            2 -> 0
            _ -> 1
    , \x -> case x of
            4 -> 0
            _ -> 1
    , \x -> case x of
            0 -> 3
            _ -> 2
    , \x -> case x of
            0 -> 0
            1 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 1
            1 -> 0
            _ -> 2
    , \x -> case x of
            2 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 0
            2 -> 0
            _ -> 2
    , \x -> case x of
            3 -> 0
            _ -> 2
    , \x -> case x of
            0 -> 2
            _ -> 3
    , \x -> case x of
            1 -> 1
            _ -> 3
    , \x -> case x of
            0 -> 0
            1 -> 0
            _ -> 3
    , \x -> case x of
            2 -> 0
            _ -> 3
    , \x -> case x of
            0 -> 1
            _ -> 4
    , \x -> case x of
            1 -> 0
            _ -> 4
    , \x -> case x of
            0 -> 0
            _ -> 5
    , \_ -> 6
    ]
  , [ \x -> case x of
            0 -> 6
            _ -> 0
    , \x -> case x of
            1 -> 5
            _ -> 0
    , \x -> case x of
            0 -> 1
            1 -> 3
            _ -> 0
    , \x -> case x of
            0 -> 2
            1 -> 2
            _ -> 0
    , \x -> case x of
            0 -> 3
            1 -> 1
            _ -> 0
    , \x -> case x of
            2 -> 4
            _ -> 0
    , \x -> case x of
            0 -> 1
            2 -> 2
            _ -> 0
    , \x -> case x of
            0 -> 2
            2 -> 1
            _ -> 0
    , \x -> case x of
            3 -> 3
            _ -> 0
    , \x -> case x of
            0 -> 1
            3 -> 1
            _ -> 0
    , \x -> case x of
            1 -> 1
            2 -> 1
            _ -> 0
    , \x -> case x of
            4 -> 2
            _ -> 0
    , \x -> case x of
            5 -> 1
            _ -> 0
    , \x -> case x of
            0 -> 5
            _ -> 1
    , \x -> case x of
            1 -> 4
            _ -> 1
    , \x -> case x of
            0 -> 0
            1 -> 3
            _ -> 1
    , \x -> case x of
            0 -> 3
            1 -> 0
            _ -> 1
    , \x -> case x of
            2 -> 3
            _ -> 1
    , \x -> case x of
            0 -> 0
            2 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 2
            2 -> 0
            _ -> 1
    , \x -> case x of
            3 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 0
            1 -> 0
            2 -> 0
            _ -> 1
    , \x -> case x of
            0 -> 0
            4 -> 0
            _ -> 1
    , \x -> case x of
            1 -> 0
            3 -> 0
            _ -> 1
    , \x -> case x of
            5 -> 0
            _ -> 1
    , \x -> case x of
            0 -> 4
            _ -> 2
    , \x -> case x of
            1 -> 3
            _ -> 2
    , \x -> case x of
            0 -> 1
            1 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 0
            2 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 1
            2 -> 0
            _ -> 2
    , \x -> case x of
            3 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 0
            3 -> 0
            _ -> 2
    , \x -> case x of
            1 -> 0
            2 -> 0
            _ -> 2
    , \x -> case x of
            4 -> 0
            _ -> 2
    , \x -> case x of
            1 -> 2
            _ -> 3
    , \x -> case x of
            0 -> 0
            1 -> 1
            _ -> 3
    , \x -> case x of
            0 -> 1
            1 -> 0
            _ -> 3
    , \x -> case x of
            2 -> 1
            _ -> 3
    , \x -> case x of
            0 -> 0
            2 -> 0
            _ -> 3
    , \x -> case x of
            3 -> 0
            _ -> 3
    , \x -> case x of
            0 -> 2
            _ -> 4
    , \x -> case x of
            1 -> 1
            _ -> 4
    , \x -> case x of
            0 -> 0
            1 -> 0
            _ -> 4
    , \x -> case x of
            2 -> 0
            _ -> 4
    , \x -> case x of
            0 -> 1
            _ -> 5
    , \x -> case x of
            1 -> 0
            _ -> 5
    , \x -> case x of
            0 -> 0
            _ -> 6
    , \_ -> 7
    ]
  , [ \x -> case x of
            0 -> 7
            _ -> 0
    , \x -> case x of
            1 -> 6
            _ -> 0
    , \x -> case x of
            0 -> 1
            1 -> 4
            _ -> 0
    , \x -> case x of
            0 -> 2
            1 -> 3
            _ -> 0
    , \x -> case x of
            0 -> 3
            1 -> 2
            _ -> 0
    , \x -> case x of
            0 -> 4
            1 -> 1
            _ -> 0
    , \x -> case x of
            2 -> 5
            _ -> 0
    , \x -> case x of
            0 -> 1
            2 -> 3
            _ -> 0
    , \x -> case x of
            0 -> 2
            2 -> 2
            _ -> 0
    , \x -> case x of
            0 -> 3
            2 -> 1
            _ -> 0
    , \x -> case x of
            3 -> 4
            _ -> 0
    , \x -> case x of
            0 -> 1
            3 -> 2
            _ -> 0
    , \x -> case x of
            0 -> 2
            3 -> 1
            _ -> 0
    , \x -> case x of
            1 -> 1
            2 -> 2
            _ -> 0
    , \x -> case x of
            1 -> 2
            2 -> 1
            _ -> 0
    , \x -> case x of
            4 -> 3
            _ -> 0
    , \x -> case x of
            0 -> 1
            4 -> 1
            _ -> 0
    , \x -> case x of
            1 -> 1
            3 -> 1
            _ -> 0
    , \x -> case x of
            5 -> 2
            _ -> 0
    , \x -> case x of
            6 -> 1
            _ -> 0
    , \x -> case x of
            0 -> 6
            _ -> 1
    , \x -> case x of
            1 -> 5
            _ -> 1
    , \x -> case x of
            0 -> 0
            1 -> 4
            _ -> 1
    , \x -> case x of
            0 -> 2
            1 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 4
            1 -> 0
            _ -> 1
    , \x -> case x of
            2 -> 4
            _ -> 1
    , \x -> case x of
            0 -> 0
            2 -> 3
            _ -> 1
    , \x -> case x of
            0 -> 3
            2 -> 0
            _ -> 1
    , \x -> case x of
            3 -> 3
            _ -> 1
    , \x -> case x of
            0 -> 0
            3 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 2
            3 -> 0
            _ -> 1
    , \x -> case x of
            1 -> 0
            2 -> 2
            _ -> 1
    , \x -> case x of
            1 -> 2
            2 -> 0
            _ -> 1
    , \x -> case x of
            4 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 0
            1 -> 0
            3 -> 0
            _ -> 1
    , \x -> case x of
            0 -> 0
            5 -> 0
            _ -> 1
    , \x -> case x of
            1 -> 0
            4 -> 0
            _ -> 1
    , \x -> case x of
            2 -> 0
            3 -> 0
            _ -> 1
    , \x -> case x of
            6 -> 0
            _ -> 1
    , \x -> case x of
            0 -> 5
            _ -> 2
    , \x -> case x of
            1 -> 4
            _ -> 2
    , \x -> case x of
            0 -> 0
            1 -> 3
            _ -> 2
    , \x -> case x of
            0 -> 3
            1 -> 0
            _ -> 2
    , \x -> case x of
            2 -> 3
            _ -> 2
    , \x -> case x of
            0 -> 1
            2 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 0
            3 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 1
            3 -> 0
            _ -> 2
    , \x -> case x of
            1 -> 0
            2 -> 1
            _ -> 2
    , \x -> case x of
            1 -> 1
            2 -> 0
            _ -> 2
    , \x -> case x of
            4 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 0
            1 -> 0
            2 -> 0
            _ -> 2
    , \x -> case x of
            0 -> 0
            4 -> 0
            _ -> 2
    , \x -> case x of
            1 -> 0
            3 -> 0
            _ -> 2
    , \x -> case x of
            5 -> 0
            _ -> 2
    , \x -> case x of
            0 -> 4
            _ -> 3
    , \x -> case x of
            0 -> 0
            1 -> 2
            _ -> 3
    , \x -> case x of
            0 -> 1
            1 -> 1
            _ -> 3
    , \x -> case x of
            0 -> 2
            1 -> 0
            _ -> 3
    , \x -> case x of
            2 -> 2
            _ -> 3
    , \x -> case x of
            0 -> 0
            2 -> 1
            _ -> 3
    , \x -> case x of
            0 -> 1
            2 -> 0
            _ -> 3
    , \x -> case x of
            3 -> 1
            _ -> 3
    , \x -> case x of
            0 -> 0
            3 -> 0
            _ -> 3
    , \x -> case x of
            1 -> 0
            2 -> 0
            _ -> 3
    , \x -> case x of
            4 -> 0
            _ -> 3
    , \x -> case x of
            0 -> 3
            _ -> 4
    , \x -> case x of
            1 -> 2
            _ -> 4
    , \x -> case x of
            0 -> 0
            1 -> 1
            _ -> 4
    , \x -> case x of
            0 -> 1
            1 -> 0
            _ -> 4
    , \x -> case x of
            2 -> 1
            _ -> 4
    , \x -> case x of
            0 -> 0
            2 -> 0
            _ -> 4
    , \x -> case x of
            3 -> 0
            _ -> 4
    , \x -> case x of
            0 -> 2
            _ -> 5
    , \x -> case x of
            1 -> 1
            _ -> 5
    , \x -> case x of
            0 -> 0
            1 -> 0
            _ -> 5
    , \x -> case x of
            2 -> 0
            _ -> 5
    , \x -> case x of
            0 -> 1
            _ -> 6
    , \x -> case x of
            1 -> 0
            _ -> 6
    , \x -> case x of
            0 -> 0
            _ -> 7
    , \_ -> 8
    ]
  , ...
  ]
