map length (tiers :: [[ [()]->[()] ]])  =  [1,1,3,5,10,16,...]

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

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

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

tiers :: [[()]->[()]]  =
  [ [\_ -> []]
  , [\_ -> [()]]
  , [ \x -> case x of
            [] -> [()]
            _ -> []
    , \x -> case x of
            [] -> []
            _ -> [()]
    , \_ -> [(),()]
    ]
  , [ \x -> case x of
            [] -> [(),()]
            _ -> []
    , \x -> case x of
            [()] -> [()]
            _ -> []
    , \x -> case x of
            [()] -> []
            _ -> [()]
    , \x -> case x of
            [] -> []
            _ -> [(),()]
    , \_ -> [(),(),()]
    ]
  , [ \x -> case x of
            [] -> [(),(),()]
            _ -> []
    , \x -> case x of
            [()] -> [(),()]
            _ -> []
    , \x -> case x of
            [(),()] -> [()]
            _ -> []
    , \x -> case x of
            [] -> [(),()]
            _ -> [()]
    , \x -> case x of
            [] -> []
            [()] -> []
            _ -> [()]
    , \x -> case x of
            [(),()] -> []
            _ -> [()]
    , \x -> case x of
            [] -> [()]
            _ -> [(),()]
    , \x -> case x of
            [()] -> []
            _ -> [(),()]
    , \x -> case x of
            [] -> []
            _ -> [(),(),()]
    , \_ -> [(),(),(),()]
    ]
  , [ \x -> case x of
            [] -> [(),(),(),()]
            _ -> []
    , \x -> case x of
            [()] -> [(),(),()]
            _ -> []
    , \x -> case x of
            [] -> [()]
            [()] -> [()]
            _ -> []
    , \x -> case x of
            [(),()] -> [(),()]
            _ -> []
    , \x -> case x of
            [(),(),()] -> [()]
            _ -> []
    , \x -> case x of
            [] -> [(),(),()]
            _ -> [()]
    , \x -> case x of
            [()] -> [(),()]
            _ -> [()]
    , \x -> case x of
            [] -> []
            [(),()] -> []
            _ -> [()]
    , \x -> case x of
            [(),(),()] -> []
            _ -> [()]
    , \x -> case x of
            [()] -> [()]
            _ -> [(),()]
    , \x -> case x of
            [] -> []
            [()] -> []
            _ -> [(),()]
    , \x -> case x of
            [(),()] -> []
            _ -> [(),()]
    , \x -> case x of
            [] -> [()]
            _ -> [(),(),()]
    , \x -> case x of
            [()] -> []
            _ -> [(),(),()]
    , \x -> case x of
            [] -> []
            _ -> [(),(),(),()]
    , \_ -> [(),(),(),(),()]
    ]
  , ...
  ]