map length (tiers :: [[ Nat3->Nat3 ]])  =  [2,6,12,14,12,6,2]

length (list :: [ Nat3->Nat3 ])  =  Infinity

allUnique (list :: [ Nat3->Nat3 ])  =  False

ratioRepetitions (list :: [ Nat3->Nat3 ])  =  1 % 2

tiers :: [Nat3->Nat3]  =
  [ [ \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
    ]
  , [ \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
    ]
  , [ \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 2
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 1
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 0
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 0
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 0
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 2
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 1
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 0
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 0
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 0
    ]
  , [ \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 2
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 1
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 2
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 1
    , \x -> case x of
              0 -> 1
              1 -> 2
              2 -> 0
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 1
    , \x -> case x of
              0 -> 2
              1 -> 1
              2 -> 0
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 2
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 1
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 2
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 1
    , \x -> case x of
              0 -> 1
              1 -> 2
              2 -> 0
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 1
    , \x -> case x of
              0 -> 2
              1 -> 1
              2 -> 0
    ]
  , [ \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 2
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 2
    , \x -> case x of
              0 -> 1
              1 -> 2
              2 -> 1
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 2
    , \x -> case x of
              0 -> 2
              1 -> 1
              2 -> 1
    , \x -> case x of
              0 -> 2
              1 -> 2
              2 -> 0
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 2
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 2
    , \x -> case x of
              0 -> 1
              1 -> 2
              2 -> 1
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 2
    , \x -> case x of
              0 -> 2
              1 -> 1
              2 -> 1
    , \x -> case x of
              0 -> 2
              1 -> 2
              2 -> 0
    ]
  , [ \x -> case x of
              0 -> 1
              1 -> 2
              2 -> 2
    , \x -> case x of
              0 -> 2
              1 -> 1
              2 -> 2
    , \x -> case x of
              0 -> 2
              1 -> 2
              2 -> 1
    , \x -> case x of
              0 -> 1
              1 -> 2
              2 -> 2
    , \x -> case x of
              0 -> 2
              1 -> 1
              2 -> 2
    , \x -> case x of
              0 -> 2
              1 -> 2
              2 -> 1
    ]
  , [ \x -> case x of
              0 -> 2
              1 -> 2
              2 -> 2
    , \x -> case x of
              0 -> 2
              1 -> 2
              2 -> 2
    ]
  ]