map length (tiers :: [[ [Nat]->[Nat] ]])  =  [1,2,6,21,...]

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

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

ratioRepetitions (list :: [ [Nat]->[Nat] ])  =  2 % 5

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