map length (tiers :: [[ Int->Int->Int ]]) = [1,1,5,13,35,81,...] length (list :: [ Int->Int->Int ]) = Infinity allUnique (list :: [ Int->Int->Int ]) = True ratioRepetitions (list :: [ Int->Int->Int ]) = 0 % 1 tiers :: [Int->Int->Int] = [ [\_ _ -> 0] , [\_ _ -> 1] , [ \x _ -> case x of 0 -> 1; _ -> 0 , \x _ -> case x of 0 -> 0; _ -> 1 , \_ y -> case y of 0 -> 1; _ -> 0 , \_ y -> case y of 0 -> 0; _ -> 1 , \_ _ -> -1 ] , [ \x y -> case (x,y) of (0,0) -> 1; _ -> 0 , \x y -> case (x,y) of (_,0) -> 0; (0,_) -> 1; _ -> 0 , \x _ -> case x of 0 -> -1; _ -> 0 , \x _ -> case x of 1 -> 1; _ -> 0 , \x _ -> case x of 1 -> 0; _ -> 1 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> 1; _ -> 0 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> 0; _ -> 1 , \x _ -> case x of 0 -> 0; _ -> -1 , \_ y -> case y of 0 -> -1; _ -> 0 , \_ y -> case y of 1 -> 1; _ -> 0 , \_ y -> case y of 1 -> 0; _ -> 1 , \_ y -> case y of 0 -> 0; _ -> -1 , \_ _ -> 2 ] , [ \x y -> case (x,y) of (0,0) -> -1; _ -> 0 , \x y -> case (x,y) of (0,1) -> 1; _ -> 0 , \x y -> case (x,y) of (0,0) -> 1; (0,1) -> 0; (1,0) -> 0; (0,-1) -> 1; ... , \x y -> case (x,y) of (_,0) -> 0; (0,_) -> -1; _ -> 0 , \x _ -> case x of 0 -> 2; _ -> 0 , \x y -> case (x,y) of (1,0) -> 1; _ -> 0 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> 0; (1,_) -> 1; _ -> 0 , \x _ -> case x of 1 -> -1; _ -> 0 , \x _ -> case x of -1 -> 1; _ -> 0 , \x y -> case (x,y) of (_,0) -> 1; (0,_) -> 0; _ -> 1 , \x y -> case (x,y) of (0,0) -> 0; _ -> 1 , \x _ -> case x of 0 -> -1; _ -> 1 , \x _ -> case x of 0 -> 0; 1 -> 0; _ -> 1 , \x _ -> case x of -1 -> 0; _ -> 1 , \x y -> case (x,y) of (0,_) -> 1; (_,0) -> 1; _ -> 0 , \x y -> case (x,y) of (0,0) -> 1; (0,1) -> 0; (1,0) -> 0; (0,-1) -> 0; ... , \x y -> case (x,y) of (0,_) -> 1; (_,0) -> 0; _ -> 1 , \x y -> case (x,y) of (_,0) -> 0; (0,_) -> 1; (1,_) -> 0; _ -> 1 , \x _ -> case x of 0 -> 1; _ -> -1 , \x _ -> case x of 1 -> 0; _ -> -1 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> -1; _ -> 0 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> 0; (_,1) -> 1; _ -> 0 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> 1; (_,1) -> 0; _ -> 1 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> 0; _ -> -1 , \x _ -> case x of 0 -> 0; _ -> 2 , \_ y -> case y of 0 -> 2; _ -> 0 , \_ y -> case y of 1 -> -1; _ -> 0 , \_ y -> case y of -1 -> 1; _ -> 0 , \_ y -> case y of 0 -> -1; _ -> 1 , \_ y -> case y of 0 -> 0; 1 -> 0; _ -> 1 , \_ y -> case y of -1 -> 0; _ -> 1 , \_ y -> case y of 0 -> 1; _ -> -1 , \_ y -> case y of 1 -> 0; _ -> -1 , \_ y -> case y of 0 -> 0; _ -> 2 , \_ _ -> -2 ] , [ \x y -> case (x,y) of (0,0) -> 2; _ -> 0 , \x y -> case (x,y) of (0,1) -> -1; _ -> 0 , \x y -> case (x,y) of (0,-1) -> 1; _ -> 0 , \x y -> case (x,y) of (0,0) -> -1; (0,_) -> 1; _ -> 0 , \x y -> case (x,y) of (_,0) -> 0; (_,1) -> 0; (0,_) -> 1; _ -> 0 , \x y -> case (x,y) of (0,0) -> 1; (0,1) -> 1; (1,0) -> 0; (0,-1) -> 0; ... , \x y -> case (x,y) of (0,0) -> 1; (0,_) -> -1; _ -> 0 , \x y -> case (x,y) of (0,0) -> -1; (0,1) -> 0; (1,0) -> 0; (0,-1) -> -1; ... , \x y -> case (x,y) of (_,0) -> 0; (0,_) -> 2; _ -> 0 , \x _ -> case x of 0 -> -2; _ -> 0 , \x y -> case (x,y) of (1,0) -> -1; _ -> 0 , \x y -> case (x,y) of (1,1) -> 1; _ -> 0 , \x y -> case (x,y) of (0,0) -> 0; (0,1) -> 0; (1,0) -> 1; (0,-1) -> 0; ... , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> 0; (1,_) -> -1; _ -> 0 , \x _ -> case x of 1 -> 2; _ -> 0 , \x _ -> case x of 0 -> 1; 1 -> 1; _ -> 0 , \x y -> case (x,y) of (-1,0) -> 1; _ -> 0 , \x y -> case (x,y) of (-1,1) -> 1; (-1,-1) -> 1; _ -> 0 , \x _ -> case x of -1 -> -1; _ -> 0 , \x _ -> case x of 2 -> 1; _ -> 0 , \x y -> case (x,y) of (0,0) -> -1; (0,_) -> 0; _ -> 1 , \x y -> case (x,y) of (0,0) -> 0; (0,1) -> 1; (1,0) -> 1; (0,-1) -> 0; ... , \x y -> case (x,y) of (0,1) -> 0; _ -> 1 , \x y -> case (x,y) of (0,0) -> 0; (0,_) -> -1; _ -> 1 , \x _ -> case x of 0 -> 2; _ -> 1 , \x y -> case (x,y) of (0,_) -> 1; (_,0) -> 1; (1,_) -> 0; _ -> 1 , \x y -> case (x,y) of (1,0) -> 0; _ -> 1 , \x _ -> case x of 1 -> -1; _ -> 1 , \x _ -> case x of 0 -> 0; 1 -> 1; -1 -> 0; _ -> 1 , \x _ -> case x of 2 -> 0; _ -> 1 , \x y -> case (x,y) of (0,0) -> 0; (0,_) -> 1; (_,0) -> 1; _ -> 0 , \x y -> case (x,y) of (0,_) -> -1; (_,0) -> 1; _ -> 0 , \x y -> case (x,y) of (_,0) -> 1; (0,_) -> 0; (1,_) -> 1; _ -> 0 , \x y -> case (x,y) of (0,_) -> 0; (1,_) -> 0; (_,0) -> 1; _ -> 0 , \x y -> case (x,y) of (0,0) -> 1; (0,1) -> 0; (1,0) -> 1; (0,-1) -> 0; ... , \x y -> case (x,y) of (0,0) -> 1; (0,_) -> 0; (_,0) -> 0; _ -> 1 , \x y -> case (x,y) of (0,_) -> -1; (_,0) -> 0; _ -> 1 , \x y -> case (x,y) of (0,0) -> 0; (0,1) -> 1; (1,0) -> 1; (0,-1) -> 1; ... , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> 0; (1,_) -> 0; _ -> 1 , \x y -> case (x,y) of (_,0) -> 0; (-1,_) -> 0; _ -> 1 , \x y -> case (x,y) of (0,0) -> 1; (0,_) -> 0; _ -> -1 , \x y -> case (x,y) of (0,0) -> 0; (0,_) -> 1; _ -> -1 , \x _ -> case x of 1 -> 1; _ -> -1 , \x _ -> case x of 0 -> 0; 1 -> 0; _ -> -1 , \x _ -> case x of -1 -> 0; _ -> -1 , \x y -> case (x,y) of (0,_) -> 1; (_,0) -> -1; _ -> 0 , \x y -> case (x,y) of (0,0) -> -1; (0,1) -> 0; (1,0) -> 0; (0,-1) -> 0; ... , \x y -> case (x,y) of (0,_) -> 1; (_,0) -> 0; (_,1) -> 1; _ -> 0 , \x y -> case (x,y) of (0,1) -> 1; (-1,1) -> 1; (2,1) -> 1; _ -> 0 , \x y -> case (x,y) of (0,_) -> 1; (_,0) -> 1; (_,1) -> 0; _ -> 1 , \x y -> case (x,y) of (_,1) -> 0; (1,_) -> 0; _ -> 1 , \x y -> case (x,y) of (0,_) -> 1; (_,0) -> 0; _ -> -1 , \x y -> case (x,y) of (_,0) -> 0; (0,_) -> -1; (1,_) -> 0; _ -> -1 , \x _ -> case x of 0 -> 1; _ -> 2 , \x _ -> case x of 1 -> 0; _ -> 2 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> 2; _ -> 0 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> 0; (_,1) -> -1; _ -> 0 , \x y -> case (x,y) of (1,-1) -> 1; (-1,-1) -> 1; _ -> 0 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> -1; _ -> 1 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> 0; (_,1) -> 0; _ -> 1 , \x y -> case (x,y) of (0,_) -> 0; (_,-1) -> 0; _ -> 1 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> 1; _ -> -1 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> -1; (_,1) -> 0; _ -> -1 , \x y -> case (x,y) of (0,_) -> 0; (_,0) -> 0; _ -> 2 , \x _ -> case x of 0 -> 0; _ -> -2 , \_ y -> case y of 0 -> -2; _ -> 0 , \_ y -> case y of 1 -> 2; _ -> 0 , \_ y -> case y of 0 -> 1; 1 -> 1; _ -> 0 , \_ y -> case y of -1 -> -1; _ -> 0 , \_ y -> case y of 2 -> 1; _ -> 0 , \_ y -> case y of 0 -> 2; _ -> 1 , \_ y -> case y of 1 -> -1; _ -> 1 , \_ y -> case y of 0 -> 0; -1 -> 0; _ -> 1 , \_ y -> case y of 2 -> 0; _ -> 1 , \_ y -> case y of 1 -> 1; _ -> -1 , \_ y -> case y of 0 -> 0; 1 -> 0; _ -> -1 , \_ y -> case y of -1 -> 0; _ -> -1 , \_ y -> case y of 0 -> 1; _ -> 2 , \_ y -> case y of 1 -> 0; _ -> 2 , \_ y -> case y of 0 -> 0; _ -> -2 , \_ _ -> 3 ] , ... ]