map length (tiers :: [[ Map Nat Nat ]]) = [1,1,2,4,7,12,20,33,53,84,131,202,...] length (list :: [ Map Nat Nat ]) = Infinity allUnique (list :: [ Map Nat Nat ]) = True ratioRepetitions (list :: [ Map Nat Nat ]) = 0 % 1 tiers :: [Map Nat Nat] = [ [Map []] , [Map [(0,0)]] , [ Map [(0,1)] , Map [(1,0)] ] , [ Map [(0,2)] , Map [(1,1)] , Map [(0,0),(1,0)] , Map [(2,0)] ] , [ Map [(0,3)] , Map [(1,2)] , Map [(0,0),(1,1)] , Map [(0,1),(1,0)] , Map [(2,1)] , Map [(0,0),(2,0)] , Map [(3,0)] ] , [ Map [(0,4)] , Map [(1,3)] , Map [(0,0),(1,2)] , Map [(0,1),(1,1)] , Map [(0,2),(1,0)] , Map [(2,2)] , Map [(0,0),(2,1)] , Map [(0,1),(2,0)] , Map [(3,1)] , Map [(0,0),(3,0)] , Map [(1,0),(2,0)] , Map [(4,0)] ] , [ Map [(0,5)] , Map [(1,4)] , Map [(0,0),(1,3)] , Map [(0,1),(1,2)] , Map [(0,2),(1,1)] , Map [(0,3),(1,0)] , Map [(2,3)] , Map [(0,0),(2,2)] , Map [(0,1),(2,1)] , Map [(0,2),(2,0)] , Map [(3,2)] , Map [(0,0),(3,1)] , Map [(0,1),(3,0)] , Map [(1,0),(2,1)] , Map [(1,1),(2,0)] , Map [(4,1)] , Map [(0,0),(1,0),(2,0)] , Map [(0,0),(4,0)] , Map [(1,0),(3,0)] , Map [(5,0)] ] , [ Map [(0,6)] , Map [(1,5)] , Map [(0,0),(1,4)] , Map [(0,1),(1,3)] , Map [(0,2),(1,2)] , Map [(0,3),(1,1)] , Map [(0,4),(1,0)] , Map [(2,4)] , Map [(0,0),(2,3)] , Map [(0,1),(2,2)] , Map [(0,2),(2,1)] , Map [(0,3),(2,0)] , Map [(3,3)] , Map [(0,0),(3,2)] , Map [(0,1),(3,1)] , Map [(0,2),(3,0)] , Map [(1,0),(2,2)] , Map [(1,1),(2,1)] , Map [(1,2),(2,0)] , Map [(4,2)] , Map [(0,0),(1,0),(2,1)] , Map [(0,0),(1,1),(2,0)] , Map [(0,1),(1,0),(2,0)] , Map [(0,0),(4,1)] , Map [(0,1),(4,0)] , Map [(1,0),(3,1)] , Map [(1,1),(3,0)] , Map [(5,1)] , Map [(0,0),(1,0),(3,0)] , Map [(0,0),(5,0)] , Map [(1,0),(4,0)] , Map [(2,0),(3,0)] , Map [(6,0)] ] , [ Map [(0,7)] , Map [(1,6)] , Map [(0,0),(1,5)] , Map [(0,1),(1,4)] , Map [(0,2),(1,3)] , Map [(0,3),(1,2)] , Map [(0,4),(1,1)] , Map [(0,5),(1,0)] , Map [(2,5)] , Map [(0,0),(2,4)] , Map [(0,1),(2,3)] , Map [(0,2),(2,2)] , Map [(0,3),(2,1)] , Map [(0,4),(2,0)] , Map [(3,4)] , Map [(0,0),(3,3)] , Map [(0,1),(3,2)] , Map [(0,2),(3,1)] , Map [(0,3),(3,0)] , Map [(1,0),(2,3)] , Map [(1,1),(2,2)] , Map [(1,2),(2,1)] , Map [(1,3),(2,0)] , Map [(4,3)] , Map [(0,0),(1,0),(2,2)] , Map [(0,0),(1,1),(2,1)] , Map [(0,0),(1,2),(2,0)] , Map [(0,1),(1,0),(2,1)] , Map [(0,1),(1,1),(2,0)] , Map [(0,2),(1,0),(2,0)] , Map [(0,0),(4,2)] , Map [(0,1),(4,1)] , Map [(0,2),(4,0)] , Map [(1,0),(3,2)] , Map [(1,1),(3,1)] , Map [(1,2),(3,0)] , Map [(5,2)] , Map [(0,0),(1,0),(3,1)] , Map [(0,0),(1,1),(3,0)] , Map [(0,1),(1,0),(3,0)] , Map [(0,0),(5,1)] , Map [(0,1),(5,0)] , Map [(1,0),(4,1)] , Map [(1,1),(4,0)] , Map [(2,0),(3,1)] , Map [(2,1),(3,0)] , Map [(6,1)] , Map [(0,0),(1,0),(4,0)] , Map [(0,0),(2,0),(3,0)] , Map [(0,0),(6,0)] , Map [(1,0),(5,0)] , Map [(2,0),(4,0)] , Map [(7,0)] ] , [ Map [(0,8)] , Map [(1,7)] , Map [(0,0),(1,6)] , Map [(0,1),(1,5)] , Map [(0,2),(1,4)] , Map [(0,3),(1,3)] , Map [(0,4),(1,2)] , Map [(0,5),(1,1)] , Map [(0,6),(1,0)] , Map [(2,6)] , Map [(0,0),(2,5)] , Map [(0,1),(2,4)] , Map [(0,2),(2,3)] , Map [(0,3),(2,2)] , Map [(0,4),(2,1)] , Map [(0,5),(2,0)] , Map [(3,5)] , Map [(0,0),(3,4)] , Map [(0,1),(3,3)] , Map [(0,2),(3,2)] , Map [(0,3),(3,1)] , Map [(0,4),(3,0)] , Map [(1,0),(2,4)] , Map [(1,1),(2,3)] , Map [(1,2),(2,2)] , Map [(1,3),(2,1)] , Map [(1,4),(2,0)] , Map [(4,4)] , Map [(0,0),(1,0),(2,3)] , Map [(0,0),(1,1),(2,2)] , Map [(0,0),(1,2),(2,1)] , Map [(0,0),(1,3),(2,0)] , Map [(0,1),(1,0),(2,2)] , Map [(0,1),(1,1),(2,1)] , Map [(0,1),(1,2),(2,0)] , Map [(0,2),(1,0),(2,1)] , Map [(0,2),(1,1),(2,0)] , Map [(0,3),(1,0),(2,0)] , Map [(0,0),(4,3)] , Map [(0,1),(4,2)] , Map [(0,2),(4,1)] , Map [(0,3),(4,0)] , Map [(1,0),(3,3)] , Map [(1,1),(3,2)] , Map [(1,2),(3,1)] , Map [(1,3),(3,0)] , Map [(5,3)] , Map [(0,0),(1,0),(3,2)] , Map [(0,0),(1,1),(3,1)] , Map [(0,0),(1,2),(3,0)] , Map [(0,1),(1,0),(3,1)] , Map [(0,1),(1,1),(3,0)] , Map [(0,2),(1,0),(3,0)] , Map [(0,0),(5,2)] , Map [(0,1),(5,1)] , Map [(0,2),(5,0)] , Map [(1,0),(4,2)] , Map [(1,1),(4,1)] , Map [(1,2),(4,0)] , Map [(2,0),(3,2)] , Map [(2,1),(3,1)] , Map [(2,2),(3,0)] , Map [(6,2)] , Map [(0,0),(1,0),(4,1)] , Map [(0,0),(1,1),(4,0)] , Map [(0,1),(1,0),(4,0)] , Map [(0,0),(2,0),(3,1)] , Map [(0,0),(2,1),(3,0)] , Map [(0,1),(2,0),(3,0)] , Map [(0,0),(6,1)] , Map [(0,1),(6,0)] , Map [(1,0),(5,1)] , Map [(1,1),(5,0)] , Map [(2,0),(4,1)] , Map [(2,1),(4,0)] , Map [(7,1)] , Map [(0,0),(1,0),(5,0)] , Map [(0,0),(2,0),(4,0)] , Map [(0,0),(7,0)] , Map [(1,0),(2,0),(3,0)] , Map [(1,0),(6,0)] , Map [(2,0),(5,0)] , Map [(3,0),(4,0)] , Map [(8,0)] ] , [ Map [(0,9)] , Map [(1,8)] , Map [(0,0),(1,7)] , Map [(0,1),(1,6)] , Map [(0,2),(1,5)] , Map [(0,3),(1,4)] , Map [(0,4),(1,3)] , Map [(0,5),(1,2)] , Map [(0,6),(1,1)] , Map [(0,7),(1,0)] , Map [(2,7)] , Map [(0,0),(2,6)] , Map [(0,1),(2,5)] , Map [(0,2),(2,4)] , Map [(0,3),(2,3)] , Map [(0,4),(2,2)] , Map [(0,5),(2,1)] , Map [(0,6),(2,0)] , Map [(3,6)] , Map [(0,0),(3,5)] , Map [(0,1),(3,4)] , Map [(0,2),(3,3)] , Map [(0,3),(3,2)] , Map [(0,4),(3,1)] , Map [(0,5),(3,0)] , Map [(1,0),(2,5)] , Map [(1,1),(2,4)] , Map [(1,2),(2,3)] , Map [(1,3),(2,2)] , Map [(1,4),(2,1)] , Map [(1,5),(2,0)] , Map [(4,5)] , Map [(0,0),(1,0),(2,4)] , Map [(0,0),(1,1),(2,3)] , Map [(0,0),(1,2),(2,2)] , Map [(0,0),(1,3),(2,1)] , Map [(0,0),(1,4),(2,0)] , Map [(0,1),(1,0),(2,3)] , Map [(0,1),(1,1),(2,2)] , Map [(0,1),(1,2),(2,1)] , Map [(0,1),(1,3),(2,0)] , Map [(0,2),(1,0),(2,2)] , Map [(0,2),(1,1),(2,1)] , Map [(0,2),(1,2),(2,0)] , Map [(0,3),(1,0),(2,1)] , Map [(0,3),(1,1),(2,0)] , Map [(0,4),(1,0),(2,0)] , Map [(0,0),(4,4)] , Map [(0,1),(4,3)] , Map [(0,2),(4,2)] , Map [(0,3),(4,1)] , Map [(0,4),(4,0)] , Map [(1,0),(3,4)] , Map [(1,1),(3,3)] , Map [(1,2),(3,2)] , Map [(1,3),(3,1)] , Map [(1,4),(3,0)] , Map [(5,4)] , Map [(0,0),(1,0),(3,3)] , Map [(0,0),(1,1),(3,2)] , Map [(0,0),(1,2),(3,1)] , Map [(0,0),(1,3),(3,0)] , Map [(0,1),(1,0),(3,2)] , Map [(0,1),(1,1),(3,1)] , Map [(0,1),(1,2),(3,0)] , Map [(0,2),(1,0),(3,1)] , Map [(0,2),(1,1),(3,0)] , Map [(0,3),(1,0),(3,0)] , Map [(0,0),(5,3)] , Map [(0,1),(5,2)] , Map [(0,2),(5,1)] , Map [(0,3),(5,0)] , Map [(1,0),(4,3)] , Map [(1,1),(4,2)] , Map [(1,2),(4,1)] , Map [(1,3),(4,0)] , Map [(2,0),(3,3)] , Map [(2,1),(3,2)] , Map [(2,2),(3,1)] , Map [(2,3),(3,0)] , Map [(6,3)] , Map [(0,0),(1,0),(4,2)] , Map [(0,0),(1,1),(4,1)] , Map [(0,0),(1,2),(4,0)] , Map [(0,1),(1,0),(4,1)] , Map [(0,1),(1,1),(4,0)] , Map [(0,2),(1,0),(4,0)] , Map [(0,0),(2,0),(3,2)] , Map [(0,0),(2,1),(3,1)] , Map [(0,0),(2,2),(3,0)] , Map [(0,1),(2,0),(3,1)] , Map [(0,1),(2,1),(3,0)] , Map [(0,2),(2,0),(3,0)] , Map [(0,0),(6,2)] , Map [(0,1),(6,1)] , Map [(0,2),(6,0)] , Map [(1,0),(5,2)] , Map [(1,1),(5,1)] , Map [(1,2),(5,0)] , Map [(2,0),(4,2)] , Map [(2,1),(4,1)] , Map [(2,2),(4,0)] , Map [(7,2)] , Map [(0,0),(1,0),(5,1)] , Map [(0,0),(1,1),(5,0)] , Map [(0,1),(1,0),(5,0)] , Map [(0,0),(2,0),(4,1)] , Map [(0,0),(2,1),(4,0)] , Map [(0,1),(2,0),(4,0)] , Map [(0,0),(7,1)] , Map [(0,1),(7,0)] , Map [(1,0),(2,0),(3,1)] , Map [(1,0),(2,1),(3,0)] , Map [(1,1),(2,0),(3,0)] , Map [(1,0),(6,1)] , Map [(1,1),(6,0)] , Map [(2,0),(5,1)] , Map [(2,1),(5,0)] , Map [(3,0),(4,1)] , Map [(3,1),(4,0)] , Map [(8,1)] , Map [(0,0),(1,0),(2,0),(3,0)] , Map [(0,0),(1,0),(6,0)] , Map [(0,0),(2,0),(5,0)] , Map [(0,0),(3,0),(4,0)] , Map [(0,0),(8,0)] , Map [(1,0),(2,0),(4,0)] , Map [(1,0),(7,0)] , Map [(2,0),(6,0)] , Map [(3,0),(5,0)] , Map [(9,0)] ] , [ Map [(0,10)] , Map [(1,9)] , Map [(0,0),(1,8)] , Map [(0,1),(1,7)] , Map [(0,2),(1,6)] , Map [(0,3),(1,5)] , Map [(0,4),(1,4)] , Map [(0,5),(1,3)] , Map [(0,6),(1,2)] , Map [(0,7),(1,1)] , Map [(0,8),(1,0)] , Map [(2,8)] , Map [(0,0),(2,7)] , Map [(0,1),(2,6)] , Map [(0,2),(2,5)] , Map [(0,3),(2,4)] , Map [(0,4),(2,3)] , Map [(0,5),(2,2)] , Map [(0,6),(2,1)] , Map [(0,7),(2,0)] , Map [(3,7)] , Map [(0,0),(3,6)] , Map [(0,1),(3,5)] , Map [(0,2),(3,4)] , Map [(0,3),(3,3)] , Map [(0,4),(3,2)] , Map [(0,5),(3,1)] , Map [(0,6),(3,0)] , Map [(1,0),(2,6)] , Map [(1,1),(2,5)] , Map [(1,2),(2,4)] , Map [(1,3),(2,3)] , Map [(1,4),(2,2)] , Map [(1,5),(2,1)] , Map [(1,6),(2,0)] , Map [(4,6)] , Map [(0,0),(1,0),(2,5)] , Map [(0,0),(1,1),(2,4)] , Map [(0,0),(1,2),(2,3)] , Map [(0,0),(1,3),(2,2)] , Map [(0,0),(1,4),(2,1)] , Map [(0,0),(1,5),(2,0)] , Map [(0,1),(1,0),(2,4)] , Map [(0,1),(1,1),(2,3)] , Map [(0,1),(1,2),(2,2)] , Map [(0,1),(1,3),(2,1)] , Map [(0,1),(1,4),(2,0)] , Map [(0,2),(1,0),(2,3)] , Map [(0,2),(1,1),(2,2)] , Map [(0,2),(1,2),(2,1)] , Map [(0,2),(1,3),(2,0)] , Map [(0,3),(1,0),(2,2)] , Map [(0,3),(1,1),(2,1)] , Map [(0,3),(1,2),(2,0)] , Map [(0,4),(1,0),(2,1)] , Map [(0,4),(1,1),(2,0)] , Map [(0,5),(1,0),(2,0)] , Map [(0,0),(4,5)] , Map [(0,1),(4,4)] , Map [(0,2),(4,3)] , Map [(0,3),(4,2)] , Map [(0,4),(4,1)] , Map [(0,5),(4,0)] , Map [(1,0),(3,5)] , Map [(1,1),(3,4)] , Map [(1,2),(3,3)] , Map [(1,3),(3,2)] , Map [(1,4),(3,1)] , Map [(1,5),(3,0)] , Map [(5,5)] , Map [(0,0),(1,0),(3,4)] , Map [(0,0),(1,1),(3,3)] , Map [(0,0),(1,2),(3,2)] , Map [(0,0),(1,3),(3,1)] , Map [(0,0),(1,4),(3,0)] , Map [(0,1),(1,0),(3,3)] , Map [(0,1),(1,1),(3,2)] , Map [(0,1),(1,2),(3,1)] , Map [(0,1),(1,3),(3,0)] , Map [(0,2),(1,0),(3,2)] , Map [(0,2),(1,1),(3,1)] , Map [(0,2),(1,2),(3,0)] , Map [(0,3),(1,0),(3,1)] , Map [(0,3),(1,1),(3,0)] , Map [(0,4),(1,0),(3,0)] , Map [(0,0),(5,4)] , Map [(0,1),(5,3)] , Map [(0,2),(5,2)] , Map [(0,3),(5,1)] , Map [(0,4),(5,0)] , Map [(1,0),(4,4)] , Map [(1,1),(4,3)] , Map [(1,2),(4,2)] , Map [(1,3),(4,1)] , Map [(1,4),(4,0)] , Map [(2,0),(3,4)] , Map [(2,1),(3,3)] , Map [(2,2),(3,2)] , Map [(2,3),(3,1)] , Map [(2,4),(3,0)] , Map [(6,4)] , Map [(0,0),(1,0),(4,3)] , Map [(0,0),(1,1),(4,2)] , Map [(0,0),(1,2),(4,1)] , Map [(0,0),(1,3),(4,0)] , Map [(0,1),(1,0),(4,2)] , Map [(0,1),(1,1),(4,1)] , Map [(0,1),(1,2),(4,0)] , Map [(0,2),(1,0),(4,1)] , Map [(0,2),(1,1),(4,0)] , Map [(0,3),(1,0),(4,0)] , Map [(0,0),(2,0),(3,3)] , Map [(0,0),(2,1),(3,2)] , Map [(0,0),(2,2),(3,1)] , Map [(0,0),(2,3),(3,0)] , Map [(0,1),(2,0),(3,2)] , Map [(0,1),(2,1),(3,1)] , Map [(0,1),(2,2),(3,0)] , Map [(0,2),(2,0),(3,1)] , Map [(0,2),(2,1),(3,0)] , Map [(0,3),(2,0),(3,0)] , Map [(0,0),(6,3)] , Map [(0,1),(6,2)] , Map [(0,2),(6,1)] , Map [(0,3),(6,0)] , Map [(1,0),(5,3)] , Map [(1,1),(5,2)] , Map [(1,2),(5,1)] , Map [(1,3),(5,0)] , Map [(2,0),(4,3)] , Map [(2,1),(4,2)] , Map [(2,2),(4,1)] , Map [(2,3),(4,0)] , Map [(7,3)] , Map [(0,0),(1,0),(5,2)] , Map [(0,0),(1,1),(5,1)] , Map [(0,0),(1,2),(5,0)] , Map [(0,1),(1,0),(5,1)] , Map [(0,1),(1,1),(5,0)] , Map [(0,2),(1,0),(5,0)] , Map [(0,0),(2,0),(4,2)] , Map [(0,0),(2,1),(4,1)] , Map [(0,0),(2,2),(4,0)] , Map [(0,1),(2,0),(4,1)] , Map [(0,1),(2,1),(4,0)] , Map [(0,2),(2,0),(4,0)] , Map [(0,0),(7,2)] , Map [(0,1),(7,1)] , Map [(0,2),(7,0)] , Map [(1,0),(2,0),(3,2)] , Map [(1,0),(2,1),(3,1)] , Map [(1,0),(2,2),(3,0)] , Map [(1,1),(2,0),(3,1)] , Map [(1,1),(2,1),(3,0)] , Map [(1,2),(2,0),(3,0)] , Map [(1,0),(6,2)] , Map [(1,1),(6,1)] , Map [(1,2),(6,0)] , Map [(2,0),(5,2)] , Map [(2,1),(5,1)] , Map [(2,2),(5,0)] , Map [(3,0),(4,2)] , Map [(3,1),(4,1)] , Map [(3,2),(4,0)] , Map [(8,2)] , Map [(0,0),(1,0),(2,0),(3,1)] , Map [(0,0),(1,0),(2,1),(3,0)] , Map [(0,0),(1,1),(2,0),(3,0)] , Map [(0,1),(1,0),(2,0),(3,0)] , Map [(0,0),(1,0),(6,1)] , Map [(0,0),(1,1),(6,0)] , Map [(0,1),(1,0),(6,0)] , Map [(0,0),(2,0),(5,1)] , Map [(0,0),(2,1),(5,0)] , Map [(0,1),(2,0),(5,0)] , Map [(0,0),(3,0),(4,1)] , Map [(0,0),(3,1),(4,0)] , Map [(0,1),(3,0),(4,0)] , Map [(0,0),(8,1)] , Map [(0,1),(8,0)] , Map [(1,0),(2,0),(4,1)] , Map [(1,0),(2,1),(4,0)] , Map [(1,1),(2,0),(4,0)] , Map [(1,0),(7,1)] , Map [(1,1),(7,0)] , Map [(2,0),(6,1)] , Map [(2,1),(6,0)] , Map [(3,0),(5,1)] , Map [(3,1),(5,0)] , Map [(9,1)] , Map [(0,0),(1,0),(2,0),(4,0)] , Map [(0,0),(1,0),(7,0)] , Map [(0,0),(2,0),(6,0)] , Map [(0,0),(3,0),(5,0)] , Map [(0,0),(9,0)] , Map [(1,0),(2,0),(5,0)] , Map [(1,0),(3,0),(4,0)] , Map [(1,0),(8,0)] , Map [(2,0),(7,0)] , Map [(3,0),(6,0)] , Map [(4,0),(5,0)] , Map [(10,0)] ] , ... ]