tiers-4cases-Nat-Nat.out

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
    ]
  , ...
  ]