map length (tiers :: [[ Nat->Nat->Nat ]])  =  [1,1,5,13,35,81,...]

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

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

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

tiers :: [Nat->Nat->Nat]  =
  [ [\_ _ -> 0]
  , [\_ _ -> 1]
  , [ \x _ -> case x of
              0 -> 1
              _ -> 0
    , \x _ -> case x of
              0 -> 0
              _ -> 1
    , \_ y -> case y of
              0 -> 1
              _ -> 0
    , \_ y -> case y of
              0 -> 0
              _ -> 1
    , \_ _ -> 2
    ]
  , [ \x y -> case (x,y) of
              (0,0) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (_,0) -> 0
              (0,_) -> 1
              _ -> 0
    , \x _ -> case x of
              0 -> 2
              _ -> 0
    , \x _ -> case x of
              1 -> 1
              _ -> 0
    , \x _ -> case x of
              1 -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 0
              _ -> 1
    , \x _ -> case x of
              0 -> 0
              _ -> 2
    , \_ y -> case y of
              0 -> 2
              _ -> 0
    , \_ y -> case y of
              1 -> 1
              _ -> 0
    , \_ y -> case y of
              1 -> 0
              _ -> 1
    , \_ y -> case y of
              0 -> 0
              _ -> 2
    , \_ _ -> 3
    ]
  , [ \x y -> case (x,y) of
              (0,0) -> 2
              _ -> 0
    , \x y -> case (x,y) of
              (0,1) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,0) -> 1
              (_,1) -> 0
              (1,_) -> 0
              (_,0) -> 0
              (0,_) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (_,0) -> 0
              (0,_) -> 2
              _ -> 0
    , \x _ -> case x of
              0 -> 3
              _ -> 0
    , \x y -> case (x,y) of
              (1,0) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 0
              (1,_) -> 1
              _ -> 0
    , \x _ -> case x of
              1 -> 2
              _ -> 0
    , \x _ -> case x of
              2 -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (_,0) -> 1
              (0,_) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,0) -> 0
              _ -> 1
    , \x _ -> case x of
              0 -> 2
              _ -> 1
    , \x _ -> case x of
              0 -> 0
              1 -> 0
              _ -> 1
    , \x _ -> case x of
              2 -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,_) -> 1
              (_,0) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,0) -> 1
              (0,_) -> 0
              (_,1) -> 0
              (1,_) -> 0
              (_,0) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 1
              (_,0) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (_,0) -> 0
              (1,_) -> 0
              _ -> 1
    , \x _ -> case x of
              0 -> 1
              _ -> 2
    , \x _ -> case x of
              1 -> 0
              _ -> 2
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 2
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 0
              (_,1) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,1) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 0
              _ -> 2
    , \x _ -> case x of
              0 -> 0
              _ -> 3
    , \_ y -> case y of
              0 -> 3
              _ -> 0
    , \_ y -> case y of
              1 -> 2
              _ -> 0
    , \_ y -> case y of
              2 -> 1
              _ -> 0
    , \_ y -> case y of
              0 -> 2
              _ -> 1
    , \_ y -> case y of
              0 -> 0
              1 -> 0
              _ -> 1
    , \_ y -> case y of
              2 -> 0
              _ -> 1
    , \_ y -> case y of
              0 -> 1
              _ -> 2
    , \_ y -> case y of
              1 -> 0
              _ -> 2
    , \_ y -> case y of
              0 -> 0
              _ -> 3
    , \_ _ -> 4
    ]
  , [ \x y -> case (x,y) of
              (0,0) -> 3
              _ -> 0
    , \x y -> case (x,y) of
              (0,1) -> 2
              _ -> 0
    , \x y -> case (x,y) of
              (0,2) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,0) -> 2
              (0,_) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (_,0) -> 0
              (_,1) -> 0
              (0,_) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,0) -> 1
              (0,1) -> 1
              (1,_) -> 0
              (_,0) -> 0
              (_,2) -> 0
              (0,_) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,0) -> 1
              (0,_) -> 2
              _ -> 0
    , \x y -> case (x,y) of
              (0,0) -> 2
              (_,1) -> 0
              (1,_) -> 0
              (_,0) -> 0
              (0,_) -> 2
              _ -> 0
    , \x y -> case (x,y) of
              (_,0) -> 0
              (0,_) -> 3
              _ -> 0
    , \x _ -> case x of
              0 -> 4
              _ -> 0
    , \x y -> case (x,y) of
              (1,0) -> 2
              _ -> 0
    , \x y -> case (x,y) of
              (1,1) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 0
              (1,0) -> 1
              (_,1) -> 0
              (2,_) -> 0
              (_,0) -> 0
              (1,_) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 0
              (1,_) -> 2
              _ -> 0
    , \x _ -> case x of
              1 -> 3
              _ -> 0
    , \x _ -> case x of
              0 -> 1
              1 -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (2,0) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 0
              (1,_) -> 0
              (2,_) -> 1
              _ -> 0
    , \x _ -> case x of
              2 -> 2
              _ -> 0
    , \x _ -> case x of
              3 -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,0) -> 2
              (0,_) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,0) -> 0
              (_,1) -> 1
              (1,_) -> 1
              (_,0) -> 1
              (0,_) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,1) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,0) -> 0
              (0,_) -> 2
              _ -> 1
    , \x _ -> case x of
              0 -> 3
              _ -> 1
    , \x y -> case (x,y) of
              (0,_) -> 1
              (_,0) -> 1
              (1,_) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (1,0) -> 0
              _ -> 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 y -> case (x,y) of
              (0,0) -> 0
              (0,_) -> 1
              (_,0) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 2
              (_,0) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (_,0) -> 1
              (1,_) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 0
              (1,_) -> 0
              (_,0) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,0) -> 1
              (0,1) -> 0
              (1,0) -> 1
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x y -> case (x,y) of
              (0,0) -> 1
              (0,_) -> 0
              (_,0) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,_) -> 2
              (_,0) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,0) -> 0
              (0,_) -> 1
              (_,1) -> 1
              (1,_) -> 1
              (_,0) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 0
              (1,_) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (_,0) -> 0
              (2,_) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,0) -> 1
              (0,_) -> 0
              _ -> 2
    , \x y -> case (x,y) of
              (0,0) -> 0
              (0,_) -> 1
              _ -> 2
    , \x _ -> case x of
              1 -> 1
              _ -> 2
    , \x _ -> case x of
              0 -> 0
              1 -> 0
              _ -> 2
    , \x _ -> case x of
              2 -> 0
              _ -> 2
    , \x y -> case (x,y) of
              (0,_) -> 1
              (_,0) -> 2
              _ -> 0
    , \x y -> case (x,y) of
              (0,0) -> 2
              (0,_) -> 0
              (_,1) -> 0
              (1,_) -> 0
              (_,0) -> 2
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 1
              (_,1) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (_,0) -> 0
              (0,1) -> 1
              (0,_) -> 0
              (_,2) -> 0
              (1,_) -> 0
              (_,1) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 1
              (_,0) -> 1
              (_,1) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (_,1) -> 0
              (1,_) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,_) -> 1
              (_,0) -> 0
              _ -> 2
    , \x y -> case (x,y) of
              (_,0) -> 0
              (1,_) -> 0
              _ -> 2
    , \x _ -> case x of
              0 -> 1
              _ -> 3
    , \x _ -> case x of
              1 -> 0
              _ -> 3
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 3
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 0
              (_,1) -> 2
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 0
              (_,1) -> 0
              (_,2) -> 1
              _ -> 0
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 2
              _ -> 1
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 0
              (_,1) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,2) -> 0
              _ -> 1
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 1
              _ -> 2
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,1) -> 0
              _ -> 2
    , \x y -> case (x,y) of
              (0,_) -> 0
              (_,0) -> 0
              _ -> 3
    , \x _ -> case x of
              0 -> 0
              _ -> 4
    , \_ y -> case y of
              0 -> 4
              _ -> 0
    , \_ y -> case y of
              1 -> 3
              _ -> 0
    , \_ y -> case y of
              0 -> 1
              1 -> 1
              _ -> 0
    , \_ y -> case y of
              2 -> 2
              _ -> 0
    , \_ y -> case y of
              3 -> 1
              _ -> 0
    , \_ y -> case y of
              0 -> 3
              _ -> 1
    , \_ y -> case y of
              1 -> 2
              _ -> 1
    , \_ y -> case y of
              0 -> 0
              2 -> 0
              _ -> 1
    , \_ y -> case y of
              3 -> 0
              _ -> 1
    , \_ y -> case y of
              1 -> 1
              _ -> 2
    , \_ y -> case y of
              0 -> 0
              1 -> 0
              _ -> 2
    , \_ y -> case y of
              2 -> 0
              _ -> 2
    , \_ y -> case y of
              0 -> 1
              _ -> 3
    , \_ y -> case y of
              1 -> 0
              _ -> 3
    , \_ y -> case y of
              0 -> 0
              _ -> 4
    , \_ _ -> 5
    ]
  , ...
  ]
