map length (tiers :: [[ (Nat,Nat) ]])  =  [1,2,3,4,5,6,7,8,9,10,11,12,...]

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

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

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

tiers :: [(Nat,Nat)]  =
  [ [(0,0)]
  , [ (0,1)
    , (1,0)
    ]
  , [ (0,2)
    , (1,1)
    , (2,0)
    ]
  , [ (0,3)
    , (1,2)
    , (2,1)
    , (3,0)
    ]
  , [ (0,4)
    , (1,3)
    , (2,2)
    , (3,1)
    , (4,0)
    ]
  , [ (0,5)
    , (1,4)
    , (2,3)
    , (3,2)
    , (4,1)
    , (5,0)
    ]
  , [ (0,6)
    , (1,5)
    , (2,4)
    , (3,3)
    , (4,2)
    , (5,1)
    , (6,0)
    ]
  , [ (0,7)
    , (1,6)
    , (2,5)
    , (3,4)
    , (4,3)
    , (5,2)
    , (6,1)
    , (7,0)
    ]
  , [ (0,8)
    , (1,7)
    , (2,6)
    , (3,5)
    , (4,4)
    , (5,3)
    , (6,2)
    , (7,1)
    , (8,0)
    ]
  , [ (0,9)
    , (1,8)
    , (2,7)
    , (3,6)
    , (4,5)
    , (5,4)
    , (6,3)
    , (7,2)
    , (8,1)
    , (9,0)
    ]
  , [ (0,10)
    , (1,9)
    , (2,8)
    , (3,7)
    , (4,6)
    , (5,5)
    , (6,4)
    , (7,3)
    , (8,2)
    , (9,1)
    , (10,0)
    ]
  , [ (0,11)
    , (1,10)
    , (2,9)
    , (3,8)
    , (4,7)
    , (5,6)
    , (6,5)
    , (7,4)
    , (8,3)
    , (9,2)
    , (10,1)
    , (11,0)
    ]
  , ...
  ]