map length (tiers :: [[ Bag Nat ]])  =  [1,1,2,3,5,7,11,15,22,30,42,56,...]

length (list :: [ Bag Nat ])  =  Infinity

allUnique (list :: [ Bag Nat ])  =  True

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

tiers :: [Bag Nat]  =
  [ [Bag []]
  , [Bag [0]]
  , [ Bag [0,0]
    , Bag [1]
    ]
  , [ Bag [0,0,0]
    , Bag [0,1]
    , Bag [2]
    ]
  , [ Bag [0,0,0,0]
    , Bag [0,0,1]
    , Bag [0,2]
    , Bag [1,1]
    , Bag [3]
    ]
  , [ Bag [0,0,0,0,0]
    , Bag [0,0,0,1]
    , Bag [0,0,2]
    , Bag [0,1,1]
    , Bag [0,3]
    , Bag [1,2]
    , Bag [4]
    ]
  , [ Bag [0,0,0,0,0,0]
    , Bag [0,0,0,0,1]
    , Bag [0,0,0,2]
    , Bag [0,0,1,1]
    , Bag [0,0,3]
    , Bag [0,1,2]
    , Bag [0,4]
    , Bag [1,1,1]
    , Bag [1,3]
    , Bag [2,2]
    , Bag [5]
    ]
  , [ Bag [0,0,0,0,0,0,0]
    , Bag [0,0,0,0,0,1]
    , Bag [0,0,0,0,2]
    , Bag [0,0,0,1,1]
    , Bag [0,0,0,3]
    , Bag [0,0,1,2]
    , Bag [0,0,4]
    , Bag [0,1,1,1]
    , Bag [0,1,3]
    , Bag [0,2,2]
    , Bag [0,5]
    , Bag [1,1,2]
    , Bag [1,4]
    , Bag [2,3]
    , Bag [6]
    ]
  , [ Bag [0,0,0,0,0,0,0,0]
    , Bag [0,0,0,0,0,0,1]
    , Bag [0,0,0,0,0,2]
    , Bag [0,0,0,0,1,1]
    , Bag [0,0,0,0,3]
    , Bag [0,0,0,1,2]
    , Bag [0,0,0,4]
    , Bag [0,0,1,1,1]
    , Bag [0,0,1,3]
    , Bag [0,0,2,2]
    , Bag [0,0,5]
    , Bag [0,1,1,2]
    , Bag [0,1,4]
    , Bag [0,2,3]
    , Bag [0,6]
    , Bag [1,1,1,1]
    , Bag [1,1,3]
    , Bag [1,2,2]
    , Bag [1,5]
    , Bag [2,4]
    , Bag [3,3]
    , Bag [7]
    ]
  , [ Bag [0,0,0,0,0,0,0,0,0]
    , Bag [0,0,0,0,0,0,0,1]
    , Bag [0,0,0,0,0,0,2]
    , Bag [0,0,0,0,0,1,1]
    , Bag [0,0,0,0,0,3]
    , Bag [0,0,0,0,1,2]
    , Bag [0,0,0,0,4]
    , Bag [0,0,0,1,1,1]
    , Bag [0,0,0,1,3]
    , Bag [0,0,0,2,2]
    , Bag [0,0,0,5]
    , Bag [0,0,1,1,2]
    , Bag [0,0,1,4]
    , Bag [0,0,2,3]
    , Bag [0,0,6]
    , Bag [0,1,1,1,1]
    , Bag [0,1,1,3]
    , Bag [0,1,2,2]
    , Bag [0,1,5]
    , Bag [0,2,4]
    , Bag [0,3,3]
    , Bag [0,7]
    , Bag [1,1,1,2]
    , Bag [1,1,4]
    , Bag [1,2,3]
    , Bag [1,6]
    , Bag [2,2,2]
    , Bag [2,5]
    , Bag [3,4]
    , Bag [8]
    ]
  , [ Bag [0,0,0,0,0,0,0,0,0,0]
    , Bag [0,0,0,0,0,0,0,0,1]
    , Bag [0,0,0,0,0,0,0,2]
    , Bag [0,0,0,0,0,0,1,1]
    , Bag [0,0,0,0,0,0,3]
    , Bag [0,0,0,0,0,1,2]
    , Bag [0,0,0,0,0,4]
    , Bag [0,0,0,0,1,1,1]
    , Bag [0,0,0,0,1,3]
    , Bag [0,0,0,0,2,2]
    , Bag [0,0,0,0,5]
    , Bag [0,0,0,1,1,2]
    , Bag [0,0,0,1,4]
    , Bag [0,0,0,2,3]
    , Bag [0,0,0,6]
    , Bag [0,0,1,1,1,1]
    , Bag [0,0,1,1,3]
    , Bag [0,0,1,2,2]
    , Bag [0,0,1,5]
    , Bag [0,0,2,4]
    , Bag [0,0,3,3]
    , Bag [0,0,7]
    , Bag [0,1,1,1,2]
    , Bag [0,1,1,4]
    , Bag [0,1,2,3]
    , Bag [0,1,6]
    , Bag [0,2,2,2]
    , Bag [0,2,5]
    , Bag [0,3,4]
    , Bag [0,8]
    , Bag [1,1,1,1,1]
    , Bag [1,1,1,3]
    , Bag [1,1,2,2]
    , Bag [1,1,5]
    , Bag [1,2,4]
    , Bag [1,3,3]
    , Bag [1,7]
    , Bag [2,2,3]
    , Bag [2,6]
    , Bag [3,5]
    , Bag [4,4]
    , Bag [9]
    ]
  , [ Bag [0,0,0,0,0,0,0,0,0,0,0]
    , Bag [0,0,0,0,0,0,0,0,0,1]
    , Bag [0,0,0,0,0,0,0,0,2]
    , Bag [0,0,0,0,0,0,0,1,1]
    , Bag [0,0,0,0,0,0,0,3]
    , Bag [0,0,0,0,0,0,1,2]
    , Bag [0,0,0,0,0,0,4]
    , Bag [0,0,0,0,0,1,1,1]
    , Bag [0,0,0,0,0,1,3]
    , Bag [0,0,0,0,0,2,2]
    , Bag [0,0,0,0,0,5]
    , Bag [0,0,0,0,1,1,2]
    , Bag [0,0,0,0,1,4]
    , Bag [0,0,0,0,2,3]
    , Bag [0,0,0,0,6]
    , Bag [0,0,0,1,1,1,1]
    , Bag [0,0,0,1,1,3]
    , Bag [0,0,0,1,2,2]
    , Bag [0,0,0,1,5]
    , Bag [0,0,0,2,4]
    , Bag [0,0,0,3,3]
    , Bag [0,0,0,7]
    , Bag [0,0,1,1,1,2]
    , Bag [0,0,1,1,4]
    , Bag [0,0,1,2,3]
    , Bag [0,0,1,6]
    , Bag [0,0,2,2,2]
    , Bag [0,0,2,5]
    , Bag [0,0,3,4]
    , Bag [0,0,8]
    , Bag [0,1,1,1,1,1]
    , Bag [0,1,1,1,3]
    , Bag [0,1,1,2,2]
    , Bag [0,1,1,5]
    , Bag [0,1,2,4]
    , Bag [0,1,3,3]
    , Bag [0,1,7]
    , Bag [0,2,2,3]
    , Bag [0,2,6]
    , Bag [0,3,5]
    , Bag [0,4,4]
    , Bag [0,9]
    , Bag [1,1,1,1,2]
    , Bag [1,1,1,4]
    , Bag [1,1,2,3]
    , Bag [1,1,6]
    , Bag [1,2,2,2]
    , Bag [1,2,5]
    , Bag [1,3,4]
    , Bag [1,8]
    , Bag [2,2,4]
    , Bag [2,3,3]
    , Bag [2,7]
    , Bag [3,6]
    , Bag [4,5]
    , Bag [10]
    ]
  , ...
  ]