map length (tiers :: [[ Nat->Nat ]]) = [1,1,3,5,10,16,30,48,80,...] length (list :: [ Nat->Nat ]) = Infinity allUnique (list :: [ Nat->Nat ]) = True ratioRepetitions (list :: [ Nat->Nat ]) = 0 % 1 tiers :: [Nat->Nat] = [ [\_ -> 0] , [\_ -> 1] , [ \x -> case x of 0 -> 1 _ -> 0 , \x -> case x of 0 -> 0 _ -> 1 , \_ -> 2 ] , [ \x -> case x of 0 -> 2 _ -> 0 , \x -> case x of 1 -> 1 _ -> 0 , \x -> case x of 1 -> 0 _ -> 1 , \x -> case x of 0 -> 0 _ -> 2 , \_ -> 3 ] , [ \x -> case x of 0 -> 3 _ -> 0 , \x -> case x of 1 -> 2 _ -> 0 , \x -> case x of 2 -> 1 _ -> 0 , \x -> case x of 0 -> 2 _ -> 1 , \x -> case x of 0 -> 0 1 -> 0 _ -> 1 , \x -> case x of 2 -> 0 _ -> 1 , \x -> case x of 0 -> 1 _ -> 2 , \x -> case x of 1 -> 0 _ -> 2 , \x -> case x of 0 -> 0 _ -> 3 , \_ -> 4 ] , [ \x -> case x of 0 -> 4 _ -> 0 , \x -> case x of 1 -> 3 _ -> 0 , \x -> case x of 0 -> 1 1 -> 1 _ -> 0 , \x -> case x of 2 -> 2 _ -> 0 , \x -> case x of 3 -> 1 _ -> 0 , \x -> case x of 0 -> 3 _ -> 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 -> case x of 1 -> 1 _ -> 2 , \x -> case x of 0 -> 0 1 -> 0 _ -> 2 , \x -> case x of 2 -> 0 _ -> 2 , \x -> case x of 0 -> 1 _ -> 3 , \x -> case x of 1 -> 0 _ -> 3 , \x -> case x of 0 -> 0 _ -> 4 , \_ -> 5 ] , [ \x -> case x of 0 -> 5 _ -> 0 , \x -> case x of 1 -> 4 _ -> 0 , \x -> case x of 0 -> 1 1 -> 2 _ -> 0 , \x -> case x of 0 -> 2 1 -> 1 _ -> 0 , \x -> case x of 2 -> 3 _ -> 0 , \x -> case x of 0 -> 1 2 -> 1 _ -> 0 , \x -> case x of 3 -> 2 _ -> 0 , \x -> case x of 4 -> 1 _ -> 0 , \x -> case x of 0 -> 4 _ -> 1 , \x -> case x of 1 -> 3 _ -> 1 , \x -> case x of 0 -> 0 1 -> 2 _ -> 1 , \x -> case x of 0 -> 2 1 -> 0 _ -> 1 , \x -> case x of 2 -> 2 _ -> 1 , \x -> case x of 0 -> 0 3 -> 0 _ -> 1 , \x -> case x of 1 -> 0 2 -> 0 _ -> 1 , \x -> case x of 4 -> 0 _ -> 1 , \x -> case x of 0 -> 3 _ -> 2 , \x -> case x of 0 -> 0 1 -> 1 _ -> 2 , \x -> case x of 0 -> 1 1 -> 0 _ -> 2 , \x -> case x of 2 -> 1 _ -> 2 , \x -> case x of 0 -> 0 2 -> 0 _ -> 2 , \x -> case x of 3 -> 0 _ -> 2 , \x -> case x of 0 -> 2 _ -> 3 , \x -> case x of 1 -> 1 _ -> 3 , \x -> case x of 0 -> 0 1 -> 0 _ -> 3 , \x -> case x of 2 -> 0 _ -> 3 , \x -> case x of 0 -> 1 _ -> 4 , \x -> case x of 1 -> 0 _ -> 4 , \x -> case x of 0 -> 0 _ -> 5 , \_ -> 6 ] , [ \x -> case x of 0 -> 6 _ -> 0 , \x -> case x of 1 -> 5 _ -> 0 , \x -> case x of 0 -> 1 1 -> 3 _ -> 0 , \x -> case x of 0 -> 2 1 -> 2 _ -> 0 , \x -> case x of 0 -> 3 1 -> 1 _ -> 0 , \x -> case x of 2 -> 4 _ -> 0 , \x -> case x of 0 -> 1 2 -> 2 _ -> 0 , \x -> case x of 0 -> 2 2 -> 1 _ -> 0 , \x -> case x of 3 -> 3 _ -> 0 , \x -> case x of 0 -> 1 3 -> 1 _ -> 0 , \x -> case x of 1 -> 1 2 -> 1 _ -> 0 , \x -> case x of 4 -> 2 _ -> 0 , \x -> case x of 5 -> 1 _ -> 0 , \x -> case x of 0 -> 5 _ -> 1 , \x -> case x of 1 -> 4 _ -> 1 , \x -> case x of 0 -> 0 1 -> 3 _ -> 1 , \x -> case x of 0 -> 3 1 -> 0 _ -> 1 , \x -> case x of 2 -> 3 _ -> 1 , \x -> case x of 0 -> 0 2 -> 2 _ -> 1 , \x -> case x of 0 -> 2 2 -> 0 _ -> 1 , \x -> case x of 3 -> 2 _ -> 1 , \x -> case x of 0 -> 0 1 -> 0 2 -> 0 _ -> 1 , \x -> case x of 0 -> 0 4 -> 0 _ -> 1 , \x -> case x of 1 -> 0 3 -> 0 _ -> 1 , \x -> case x of 5 -> 0 _ -> 1 , \x -> case x of 0 -> 4 _ -> 2 , \x -> case x of 1 -> 3 _ -> 2 , \x -> case x of 0 -> 1 1 -> 1 _ -> 2 , \x -> case x of 0 -> 0 2 -> 1 _ -> 2 , \x -> case x of 0 -> 1 2 -> 0 _ -> 2 , \x -> case x of 3 -> 1 _ -> 2 , \x -> case x of 0 -> 0 3 -> 0 _ -> 2 , \x -> case x of 1 -> 0 2 -> 0 _ -> 2 , \x -> case x of 4 -> 0 _ -> 2 , \x -> case x of 1 -> 2 _ -> 3 , \x -> case x of 0 -> 0 1 -> 1 _ -> 3 , \x -> case x of 0 -> 1 1 -> 0 _ -> 3 , \x -> case x of 2 -> 1 _ -> 3 , \x -> case x of 0 -> 0 2 -> 0 _ -> 3 , \x -> case x of 3 -> 0 _ -> 3 , \x -> case x of 0 -> 2 _ -> 4 , \x -> case x of 1 -> 1 _ -> 4 , \x -> case x of 0 -> 0 1 -> 0 _ -> 4 , \x -> case x of 2 -> 0 _ -> 4 , \x -> case x of 0 -> 1 _ -> 5 , \x -> case x of 1 -> 0 _ -> 5 , \x -> case x of 0 -> 0 _ -> 6 , \_ -> 7 ] , [ \x -> case x of 0 -> 7 _ -> 0 , \x -> case x of 1 -> 6 _ -> 0 , \x -> case x of 0 -> 1 1 -> 4 _ -> 0 , \x -> case x of 0 -> 2 1 -> 3 _ -> 0 , \x -> case x of 0 -> 3 1 -> 2 _ -> 0 , \x -> case x of 0 -> 4 1 -> 1 _ -> 0 , \x -> case x of 2 -> 5 _ -> 0 , \x -> case x of 0 -> 1 2 -> 3 _ -> 0 , \x -> case x of 0 -> 2 2 -> 2 _ -> 0 , \x -> case x of 0 -> 3 2 -> 1 _ -> 0 , \x -> case x of 3 -> 4 _ -> 0 , \x -> case x of 0 -> 1 3 -> 2 _ -> 0 , \x -> case x of 0 -> 2 3 -> 1 _ -> 0 , \x -> case x of 1 -> 1 2 -> 2 _ -> 0 , \x -> case x of 1 -> 2 2 -> 1 _ -> 0 , \x -> case x of 4 -> 3 _ -> 0 , \x -> case x of 0 -> 1 4 -> 1 _ -> 0 , \x -> case x of 1 -> 1 3 -> 1 _ -> 0 , \x -> case x of 5 -> 2 _ -> 0 , \x -> case x of 6 -> 1 _ -> 0 , \x -> case x of 0 -> 6 _ -> 1 , \x -> case x of 1 -> 5 _ -> 1 , \x -> case x of 0 -> 0 1 -> 4 _ -> 1 , \x -> case x of 0 -> 2 1 -> 2 _ -> 1 , \x -> case x of 0 -> 4 1 -> 0 _ -> 1 , \x -> case x of 2 -> 4 _ -> 1 , \x -> case x of 0 -> 0 2 -> 3 _ -> 1 , \x -> case x of 0 -> 3 2 -> 0 _ -> 1 , \x -> case x of 3 -> 3 _ -> 1 , \x -> case x of 0 -> 0 3 -> 2 _ -> 1 , \x -> case x of 0 -> 2 3 -> 0 _ -> 1 , \x -> case x of 1 -> 0 2 -> 2 _ -> 1 , \x -> case x of 1 -> 2 2 -> 0 _ -> 1 , \x -> case x of 4 -> 2 _ -> 1 , \x -> case x of 0 -> 0 1 -> 0 3 -> 0 _ -> 1 , \x -> case x of 0 -> 0 5 -> 0 _ -> 1 , \x -> case x of 1 -> 0 4 -> 0 _ -> 1 , \x -> case x of 2 -> 0 3 -> 0 _ -> 1 , \x -> case x of 6 -> 0 _ -> 1 , \x -> case x of 0 -> 5 _ -> 2 , \x -> case x of 1 -> 4 _ -> 2 , \x -> case x of 0 -> 0 1 -> 3 _ -> 2 , \x -> case x of 0 -> 3 1 -> 0 _ -> 2 , \x -> case x of 2 -> 3 _ -> 2 , \x -> case x of 0 -> 1 2 -> 1 _ -> 2 , \x -> case x of 0 -> 0 3 -> 1 _ -> 2 , \x -> case x of 0 -> 1 3 -> 0 _ -> 2 , \x -> case x of 1 -> 0 2 -> 1 _ -> 2 , \x -> case x of 1 -> 1 2 -> 0 _ -> 2 , \x -> case x of 4 -> 1 _ -> 2 , \x -> case x of 0 -> 0 1 -> 0 2 -> 0 _ -> 2 , \x -> case x of 0 -> 0 4 -> 0 _ -> 2 , \x -> case x of 1 -> 0 3 -> 0 _ -> 2 , \x -> case x of 5 -> 0 _ -> 2 , \x -> case x of 0 -> 4 _ -> 3 , \x -> case x of 0 -> 0 1 -> 2 _ -> 3 , \x -> case x of 0 -> 1 1 -> 1 _ -> 3 , \x -> case x of 0 -> 2 1 -> 0 _ -> 3 , \x -> case x of 2 -> 2 _ -> 3 , \x -> case x of 0 -> 0 2 -> 1 _ -> 3 , \x -> case x of 0 -> 1 2 -> 0 _ -> 3 , \x -> case x of 3 -> 1 _ -> 3 , \x -> case x of 0 -> 0 3 -> 0 _ -> 3 , \x -> case x of 1 -> 0 2 -> 0 _ -> 3 , \x -> case x of 4 -> 0 _ -> 3 , \x -> case x of 0 -> 3 _ -> 4 , \x -> case x of 1 -> 2 _ -> 4 , \x -> case x of 0 -> 0 1 -> 1 _ -> 4 , \x -> case x of 0 -> 1 1 -> 0 _ -> 4 , \x -> case x of 2 -> 1 _ -> 4 , \x -> case x of 0 -> 0 2 -> 0 _ -> 4 , \x -> case x of 3 -> 0 _ -> 4 , \x -> case x of 0 -> 2 _ -> 5 , \x -> case x of 1 -> 1 _ -> 5 , \x -> case x of 0 -> 0 1 -> 0 _ -> 5 , \x -> case x of 2 -> 0 _ -> 5 , \x -> case x of 0 -> 1 _ -> 6 , \x -> case x of 1 -> 0 _ -> 6 , \x -> case x of 0 -> 0 _ -> 7 , \_ -> 8 ] , ... ]