map length (tiers :: [[ (Nat,Nat)->Nat ]])  =  [1,1,3,7,17,35,...]

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 (0,0) -> 1; _ -> 0
    , \x -> case x of (0,0) -> 0; _ -> 1
    , \_ -> 2
    ]
  , [ \x -> case x of (0,0) -> 2; _ -> 0
    , \x -> case x of (0,1) -> 1; _ -> 0
    , \x -> case x of (1,0) -> 1; _ -> 0
    , \x -> case x of (0,1) -> 0; _ -> 1
    , \x -> case x of (1,0) -> 0; _ -> 1
    , \x -> case x of (0,0) -> 0; _ -> 2
    , \_ -> 3
    ]
  , [ \x -> case x of (0,0) -> 3; _ -> 0
    , \x -> case x of (0,1) -> 2; _ -> 0
    , \x -> case x of (1,0) -> 2; _ -> 0
    , \x -> case x of (0,2) -> 1; _ -> 0
    , \x -> case x of (1,1) -> 1; _ -> 0
    , \x -> case x of (2,0) -> 1; _ -> 0
    , \x -> case x of (0,0) -> 2; _ -> 1
    , \x -> case x of (0,0) -> 0; (0,1) -> 0; _ -> 1
    , \x -> case x of (0,0) -> 0; (1,0) -> 0; _ -> 1
    , \x -> case x of (0,2) -> 0; _ -> 1
    , \x -> case x of (1,1) -> 0; _ -> 1
    , \x -> case x of (2,0) -> 0; _ -> 1
    , \x -> case x of (0,0) -> 1; _ -> 2
    , \x -> case x of (0,1) -> 0; _ -> 2
    , \x -> case x of (1,0) -> 0; _ -> 2
    , \x -> case x of (0,0) -> 0; _ -> 3
    , \_ -> 4
    ]
  , [ \x -> case x of (0,0) -> 4; _ -> 0
    , \x -> case x of (0,1) -> 3; _ -> 0
    , \x -> case x of (1,0) -> 3; _ -> 0
    , \x -> case x of (0,0) -> 1; (0,1) -> 1; _ -> 0
    , \x -> case x of (0,0) -> 1; (1,0) -> 1; _ -> 0
    , \x -> case x of (0,2) -> 2; _ -> 0
    , \x -> case x of (1,1) -> 2; _ -> 0
    , \x -> case x of (2,0) -> 2; _ -> 0
    , \x -> case x of (0,3) -> 1; _ -> 0
    , \x -> case x of (1,2) -> 1; _ -> 0
    , \x -> case x of (2,1) -> 1; _ -> 0
    , \x -> case x of (3,0) -> 1; _ -> 0
    , \x -> case x of (0,0) -> 3; _ -> 1
    , \x -> case x of (0,1) -> 2; _ -> 1
    , \x -> case x of (1,0) -> 2; _ -> 1
    , \x -> case x of (0,0) -> 0; (0,2) -> 0; _ -> 1
    , \x -> case x of (0,0) -> 0; (1,1) -> 0; _ -> 1
    , \x -> case x of (0,0) -> 0; (2,0) -> 0; _ -> 1
    , \x -> case x of (0,1) -> 0; (1,0) -> 0; _ -> 1
    , \x -> case x of (0,3) -> 0; _ -> 1
    , \x -> case x of (1,2) -> 0; _ -> 1
    , \x -> case x of (2,1) -> 0; _ -> 1
    , \x -> case x of (3,0) -> 0; _ -> 1
    , \x -> case x of (0,1) -> 1; _ -> 2
    , \x -> case x of (1,0) -> 1; _ -> 2
    , \x -> case x of (0,0) -> 0; (0,1) -> 0; _ -> 2
    , \x -> case x of (0,0) -> 0; (1,0) -> 0; _ -> 2
    , \x -> case x of (0,2) -> 0; _ -> 2
    , \x -> case x of (1,1) -> 0; _ -> 2
    , \x -> case x of (2,0) -> 0; _ -> 2
    , \x -> case x of (0,0) -> 1; _ -> 3
    , \x -> case x of (0,1) -> 0; _ -> 3
    , \x -> case x of (1,0) -> 0; _ -> 3
    , \x -> case x of (0,0) -> 0; _ -> 4
    , \_ -> 5
    ]
  , ...
  ]