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 [] -> []; _ -> [(),(),(),()]
    , \_ -> [(),(),(),(),()]
    ]
  , ...
  ]