map length (tiers :: [[ [Nat]->[Nat] ]])  =  [1,1,4,10,29,75,...]

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

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

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

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