Candidates for: foo :: Int -> Int pruning with 13/26 rules [3,2,4,3,12,7,27,25,58] direct candidates, 0 duplicates [3,6,15,34,61,111,174,344,529] pattern candidates, 0 duplicates rules: dec 1 == 0 x * y == x + y x * y == y + x x + 0 == x 0 + x == x dec (x + y) == x + dec y dec (x + y) == y + dec x dec (x + y) == dec x + y dec (x + y) == dec y + x 1 + dec x == x dec x + 1 == x (x + y) + z == x + (y + z) (x + y) + z == y + (x + z) equations: y + x == x + y y + dec x == x + dec y dec x + y == x + dec y dec y + x == dec x + y x + dec 0 == dec x dec 0 + x == dec x y + (x + z) == x + (y + z) z + (x + y) == x + (y + z) z + (y + x) == x + (y + z) y + dec (dec x) == x + dec (dec y) dec (dec x) + y == x + dec (dec y) x + dec (dec 0) == dec (dec x) dec (dec 0) + x == dec (dec x) direct candidates: foo x = x foo x = 0 foo x = 1 foo x = dec x foo x = dec 0 foo x = x + x foo x = x + 1 foo x = 1 + x foo x = 1 + 1 foo x = dec 0 + x foo x = x + dec x foo x = x + dec 0 foo x = x + (x + x) foo x = x + (x + 1) foo x = x + (1 + x) foo x = x + (1 + 1) foo x = 1 + (x + x) foo x = 1 + (x + 1) foo x = 1 + (1 + x) foo x = 1 + (1 + 1) foo x = dec x + dec x foo x = dec x + dec 0 foo x = dec 0 + dec x foo x = dec 0 + dec 0 foo x = x + (dec 0 + x) foo x = x + (x + dec x) foo x = x + (x + dec 0) foo x = 1 + (dec 0 + x) foo x = 1 + (x + dec x) foo x = 1 + (x + dec 0) foo x = dec 0 + (x + x) pattern candidates: foo x = x foo x = 0 foo x = 1 foo x = dec x foo x = dec 0 foo 0 = 0 foo x = x foo 0 = 0 foo x = 1 foo 0 = 1 foo x = x foo 0 = 1 foo x = 0 foo x = x + x foo x = x + 1 foo x = 1 + x foo x = 1 + 1 foo 0 = 0 foo x = dec x foo 0 = 0 foo x = dec 0 foo 0 = 1 foo x = dec x foo 0 = 1 foo x = dec 0 foo 0 = dec 0 foo x = x foo 0 = dec 0 foo x = 0 foo 0 = dec 0 foo x = 1 foo 1 = 0 foo x = x foo 1 = 0 foo x = 1 foo 1 = 1 foo x = x foo 1 = 1 foo x = 0 foo 0 = 0 foo x = foo (dec x) foo 0 = 1 foo x = foo (dec x) foo x = dec 0 + x foo x = x + dec x foo x = x + dec 0 foo 0 = 0 foo x = x + x foo 0 = 0 foo x = x + 1 foo 0 = 0 foo x = 1 + x foo 0 = 0 foo x = 1 + 1 foo 0 = 1 foo x = x + x foo 0 = 1 foo x = x + 1 foo 0 = 1 foo x = 1 + x foo 0 = 1 foo x = 1 + 1 foo 0 = dec 0 foo x = dec x foo 0 = 1 + 1 foo x = x foo 0 = 1 + 1 foo x = 0 foo 0 = 1 + 1 foo x = 1 foo 1 = 0 foo x = dec x foo 1 = 0 foo x = dec 0 foo 1 = 1 foo x = dec x foo 1 = 1 foo x = dec 0 foo 1 = dec 0 foo x = x foo 1 = dec 0 foo x = 0 foo 1 = dec 0 foo x = 1 foo 0 = 0 foo 1 = 0 foo x = x foo 0 = 0 foo 1 = 0 foo x = 1 foo 0 = 0 foo 1 = 1 foo x = x foo 0 = 0 foo 1 = 1 foo x = 0 foo 0 = 0 foo 1 = 1 foo x = 1 foo 0 = 1 foo 1 = 0 foo x = x foo 0 = 1 foo 1 = 0 foo x = 0 foo 0 = 1 foo 1 = 0 foo x = 1 foo 0 = 1 foo 1 = 1 foo x = x foo 0 = 1 foo 1 = 1 foo x = 0 foo 0 = 0 foo x = dec (foo (dec x)) foo 0 = 1 foo x = dec (foo (dec x)) foo 0 = dec 0 foo x = foo (dec x) foo 1 = 0 foo x = foo (dec x) foo 1 = 1 foo x = foo (dec x) foo x = x + (x + x) foo x = x + (x + 1) foo x = x + (1 + x) foo x = x + (1 + 1) foo x = 1 + (x + x) foo x = 1 + (x + 1) foo x = 1 + (1 + x) foo x = 1 + (1 + 1) foo x = dec x + dec x foo x = dec x + dec 0 foo x = dec 0 + dec x foo x = dec 0 + dec 0 foo 0 = 0 foo x = dec 0 + x foo 0 = 0 foo x = x + dec x foo 0 = 0 foo x = x + dec 0 foo 0 = 1 foo x = dec 0 + x foo 0 = 1 foo x = x + dec x foo 0 = 1 foo x = x + dec 0 foo 0 = dec 0 foo x = x + x foo 0 = dec 0 foo x = x + 1 foo 0 = dec 0 foo x = 1 + x foo 0 = dec 0 foo x = 1 + 1 foo 0 = 1 + 1 foo x = dec x foo 0 = 1 + 1 foo x = dec 0 foo 1 = 0 foo x = x + x foo 1 = 0 foo x = x + 1 foo 1 = 0 foo x = 1 + x foo 1 = 0 foo x = 1 + 1 foo 1 = 1 foo x = x + x foo 1 = 1 foo x = x + 1 foo 1 = 1 foo x = 1 + x foo 1 = 1 foo x = 1 + 1 foo 1 = dec 0 foo x = dec x foo 1 = 1 + 1 foo x = x foo 1 = 1 + 1 foo x = 0 foo 1 = 1 + 1 foo x = 1 foo 0 = 0 foo 1 = 0 foo x = dec x foo 0 = 0 foo 1 = 0 foo x = dec 0 foo 0 = 0 foo 1 = 1 foo x = dec x foo 0 = 0 foo 1 = 1 foo x = dec 0 foo 0 = 0 foo 1 = dec 0 foo x = x foo 0 = 0 foo 1 = dec 0 foo x = 0 foo 0 = 0 foo 1 = dec 0 foo x = 1 foo 0 = 1 foo 1 = 0 foo x = dec x foo 0 = 1 foo 1 = 0 foo x = dec 0 foo 0 = 1 foo 1 = 1 foo x = dec x foo 0 = 1 foo 1 = 1 foo x = dec 0 foo 0 = 1 foo 1 = dec 0 foo x = x foo 0 = 1 foo 1 = dec 0 foo x = 0 foo 0 = 1 foo 1 = dec 0 foo x = 1 foo 0 = dec 0 foo 1 = 0 foo x = x foo 0 = dec 0 foo 1 = 0 foo x = 0 foo 0 = dec 0 foo 1 = 0 foo x = 1 foo 0 = dec 0 foo 1 = 1 foo x = x foo 0 = dec 0 foo 1 = 1 foo x = 0 foo 0 = dec 0 foo 1 = 1 foo x = 1 foo 0 = 0 foo x = x + foo (dec x) foo 0 = 0 foo x = foo (dec x) + x foo 0 = 0 foo x = foo (dec x) + 1 foo 0 = 0 foo x = 1 + foo (dec x) foo 0 = 1 foo x = x + foo (dec x) foo 0 = 1 foo x = foo (dec x) + x foo 0 = 1 foo x = foo (dec x) + 1 foo 0 = 1 foo x = 1 + foo (dec x) foo 0 = dec 0 foo x = dec (foo (dec x)) foo 0 = 1 + 1 foo x = foo (dec x) foo 1 = 0 foo x = dec (foo (dec x)) foo 1 = 1 foo x = dec (foo (dec x)) foo 1 = dec 0 foo x = foo (dec x) foo 0 = 0 foo 1 = 0 foo x = foo (dec x) foo 0 = 0 foo 1 = 1 foo x = foo (dec x) foo 0 = 1 foo 1 = 0 foo x = foo (dec x) foo 0 = 1 foo 1 = 1 foo x = foo (dec x) foo x = x + (dec 0 + x) foo x = x + (x + dec x) foo x = x + (x + dec 0) foo x = 1 + (dec 0 + x) foo x = 1 + (x + dec x) foo x = 1 + (x + dec 0) foo x = dec 0 + (x + x) foo 0 = 0 foo x = x + (x + x) foo 0 = 0 foo x = x + (x + 1) foo 0 = 0 foo x = x + (1 + x) foo 0 = 0 foo x = x + (1 + 1) foo 0 = 0 foo x = 1 + (x + x) foo 0 = 0 foo x = 1 + (x + 1) foo 0 = 0 foo x = 1 + (1 + x) foo 0 = 0 foo x = 1 + (1 + 1) foo 0 = 0 foo x = dec x + dec x foo 0 = 0 foo x = dec x + dec 0 foo 0 = 0 foo x = dec 0 + dec x foo 0 = 0 foo x = dec 0 + dec 0 foo 0 = 1 foo x = x + (x + x) foo 0 = 1 foo x = x + (x + 1) foo 0 = 1 foo x = x + (1 + x) foo 0 = 1 foo x = x + (1 + 1) foo 0 = 1 foo x = 1 + (x + x) foo 0 = 1 foo x = 1 + (x + 1) foo 0 = 1 foo x = 1 + (1 + x) foo 0 = 1 foo x = 1 + (1 + 1) foo 0 = 1 foo x = dec x + dec x foo 0 = 1 foo x = dec x + dec 0 foo 0 = 1 foo x = dec 0 + dec x foo 0 = 1 foo x = dec 0 + dec 0 foo 0 = dec 0 foo x = dec 0 + x foo 0 = dec 0 foo x = x + dec x foo 0 = dec 0 foo x = x + dec 0 foo 0 = 1 + 1 foo x = x + x foo 0 = 1 + 1 foo x = x + 1 foo 0 = 1 + 1 foo x = 1 + x foo 0 = 1 + (1 + 1) foo x = x foo 0 = 1 + (1 + 1) foo x = 0 foo 0 = 1 + (1 + 1) foo x = 1 foo 0 = dec 0 + dec 0 foo x = x foo 0 = dec 0 + dec 0 foo x = 0 foo 0 = dec 0 + dec 0 foo x = 1 foo 1 = 0 foo x = dec 0 + x foo 1 = 0 foo x = x + dec x foo 1 = 0 foo x = x + dec 0 foo 1 = 1 foo x = dec 0 + x foo 1 = 1 foo x = x + dec x foo 1 = 1 foo x = x + dec 0 foo 1 = dec 0 foo x = x + x foo 1 = dec 0 foo x = x + 1 foo 1 = dec 0 foo x = 1 + x foo 1 = dec 0 foo x = 1 + 1 foo 1 = 1 + 1 foo x = dec x foo 1 = 1 + 1 foo x = dec 0 foo 0 = 0 foo 1 = 0 foo x = x + x foo 0 = 0 foo 1 = 0 foo x = x + 1 foo 0 = 0 foo 1 = 0 foo x = 1 + x foo 0 = 0 foo 1 = 0 foo x = 1 + 1 foo 0 = 0 foo 1 = 1 foo x = x + x foo 0 = 0 foo 1 = 1 foo x = x + 1 foo 0 = 0 foo 1 = 1 foo x = 1 + x foo 0 = 0 foo 1 = 1 foo x = 1 + 1 foo 0 = 0 foo 1 = dec 0 foo x = dec x foo 0 = 0 foo 1 = dec 0 foo x = dec 0 foo 0 = 0 foo 1 = 1 + 1 foo x = x foo 0 = 0 foo 1 = 1 + 1 foo x = 0 foo 0 = 0 foo 1 = 1 + 1 foo x = 1 foo 0 = 1 foo 1 = 0 foo x = x + x foo 0 = 1 foo 1 = 0 foo x = x + 1 foo 0 = 1 foo 1 = 0 foo x = 1 + x foo 0 = 1 foo 1 = 0 foo x = 1 + 1 foo 0 = 1 foo 1 = 1 foo x = x + x foo 0 = 1 foo 1 = 1 foo x = x + 1 foo 0 = 1 foo 1 = 1 foo x = 1 + x foo 0 = 1 foo 1 = 1 foo x = 1 + 1 foo 0 = 1 foo 1 = dec 0 foo x = dec x foo 0 = 1 foo 1 = dec 0 foo x = dec 0 foo 0 = 1 foo 1 = 1 + 1 foo x = x foo 0 = 1 foo 1 = 1 + 1 foo x = 0 foo 0 = 1 foo 1 = 1 + 1 foo x = 1 foo 0 = dec 0 foo 1 = 0 foo x = dec x foo 0 = dec 0 foo 1 = 0 foo x = dec 0 foo 0 = dec 0 foo 1 = 1 foo x = dec x foo 0 = dec 0 foo 1 = 1 foo x = dec 0 foo 0 = dec 0 foo 1 = dec 0 foo x = x foo 0 = dec 0 foo 1 = dec 0 foo x = 0 foo 0 = dec 0 foo 1 = dec 0 foo x = 1 foo 0 = 1 + 1 foo 1 = 0 foo x = x foo 0 = 1 + 1 foo 1 = 0 foo x = 0 foo 0 = 1 + 1 foo 1 = 0 foo x = 1 foo 0 = 1 + 1 foo 1 = 1 foo x = x foo 0 = 1 + 1 foo 1 = 1 foo x = 0 foo 0 = 1 + 1 foo 1 = 1 foo x = 1 Candidates for: ? :: Int -> Int -> Int pruning with 10/23 rules [3,3,4,10,17,26,54,93,162] direct candidates, 0 duplicates [3,11,39,88,245,596,1542,3881,9466] pattern candidates, 0 duplicates rules: x * y == x + y x * y == y + x x + 0 == x 0 + x == x dec (x + y) == x + dec y dec (x + y) == y + dec x dec (x + y) == dec x + y dec (x + y) == dec y + x (x + y) + z == x + (y + z) (x + y) + z == y + (x + z) equations: y + x == x + y y + dec x == x + dec y dec x + y == x + dec y dec y + x == dec x + y x + dec 0 == dec x dec 0 + x == dec x y + (x + z) == x + (y + z) z + (x + y) == x + (y + z) z + (y + x) == x + (y + z) y + dec (dec x) == x + dec (dec y) dec (dec x) + y == x + dec (dec y) x + dec (dec 0) == dec (dec x) dec (dec 0) + x == dec (dec x) direct candidates: x ? y = x x ? y = y x ? y = 0 x ? y = dec x x ? y = dec y x ? y = dec 0 x ? y = x + x x ? y = x + y x ? y = y + x x ? y = y + y x ? y = dec x + y x ? y = dec y + x x ? y = dec 0 + x x ? y = dec 0 + y x ? y = x + dec x x ? y = x + dec y x ? y = x + dec 0 x ? y = y + dec x x ? y = y + dec y x ? y = y + dec 0 x ? y = x + (x + x) x ? y = x + (x + y) x ? y = x + (y + x) x ? y = x + (y + y) x ? y = y + (x + x) x ? y = y + (x + y) x ? y = y + (y + x) x ? y = y + (y + y) x ? y = dec x + dec x x ? y = dec x + dec y x ? y = dec x + dec 0 x ? y = dec y + dec x x ? y = dec y + dec y x ? y = dec y + dec 0 x ? y = dec 0 + dec x x ? y = dec 0 + dec y x ? y = dec 0 + dec 0 x ? y = x + (dec x + y) x ? y = x + (dec y + x) x ? y = x + (dec 0 + x) x ? y = x + (dec 0 + y) x ? y = x + (x + dec x) x ? y = x + (x + dec y) x ? y = x + (x + dec 0) x ? y = x + (y + dec x) x ? y = x + (y + dec y) x ? y = x + (y + dec 0) x ? y = y + (dec x + y) x ? y = y + (dec y + x) x ? y = y + (dec 0 + x) x ? y = y + (dec 0 + y) x ? y = y + (x + dec x) x ? y = y + (x + dec y) x ? y = y + (x + dec 0) x ? y = y + (y + dec x) x ? y = y + (y + dec y) x ? y = y + (y + dec 0) x ? y = dec x + (y + y) x ? y = dec y + (x + x) x ? y = dec 0 + (x + x) x ? y = dec 0 + (x + y) x ? y = dec 0 + (y + x) x ? y = dec 0 + (y + y) pattern candidates: x ? y = x x ? y = y x ? y = 0 x ? y = dec x x ? y = dec y x ? y = dec 0 x ? 0 = x x ? y = y x ? 0 = x x ? y = 0 x ? 0 = 0 x ? y = x x ? 0 = 0 x ? y = y 0 ? x = x x ? y = y 0 ? x = x x ? y = 0 0 ? x = 0 x ? y = x 0 ? x = 0 x ? y = y x ? y = x + x x ? y = x + y x ? y = y + x x ? y = y + y x ? 0 = x x ? y = dec x x ? 0 = x x ? y = dec y x ? 0 = x x ? y = dec 0 x ? 0 = 0 x ? y = dec x x ? 0 = 0 x ? y = dec y x ? 0 = 0 x ? y = dec 0 x ? 0 = dec x x ? y = x x ? 0 = dec x x ? y = y x ? 0 = dec x x ? y = 0 x ? 0 = dec 0 x ? y = x x ? 0 = dec 0 x ? y = y x ? 0 = dec 0 x ? y = 0 0 ? x = x x ? y = dec x 0 ? x = x x ? y = dec y 0 ? x = x x ? y = dec 0 0 ? x = 0 x ? y = dec x 0 ? x = 0 x ? y = dec y 0 ? x = 0 x ? y = dec 0 0 ? x = dec x x ? y = x 0 ? x = dec x x ? y = y 0 ? x = dec x x ? y = 0 0 ? x = dec 0 x ? y = x 0 ? x = dec 0 x ? y = y 0 ? x = dec 0 x ? y = 0 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = x 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = y 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = 0 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = x 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = y 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = x 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = y x ? y = dec x + y x ? y = dec y + x x ? y = dec 0 + x x ? y = dec 0 + y x ? y = x + dec x x ? y = x + dec y x ? y = x + dec 0 x ? y = y + dec x x ? y = y + dec y x ? y = y + dec 0 x ? 0 = x x ? y = x + x x ? 0 = x x ? y = x + y x ? 0 = x x ? y = y + x x ? 0 = x x ? y = y + y x ? 0 = 0 x ? y = x + x x ? 0 = 0 x ? y = x + y x ? 0 = 0 x ? y = y + x x ? 0 = 0 x ? y = y + y x ? 0 = dec x x ? y = dec y x ? 0 = dec x x ? y = dec 0 x ? 0 = dec 0 x ? y = dec x x ? 0 = dec 0 x ? y = dec y x ? 0 = x + x x ? y = x x ? 0 = x + x x ? y = y x ? 0 = x + x x ? y = 0 0 ? x = x x ? y = x + x 0 ? x = x x ? y = x + y 0 ? x = x x ? y = y + x 0 ? x = x x ? y = y + y 0 ? x = 0 x ? y = x + x 0 ? x = 0 x ? y = x + y 0 ? x = 0 x ? y = y + x 0 ? x = 0 x ? y = y + y 0 ? x = dec x x ? y = dec y 0 ? x = dec x x ? y = dec 0 0 ? x = dec 0 x ? y = dec x 0 ? x = dec 0 x ? y = dec y 0 ? x = x + x x ? y = x 0 ? x = x + x x ? y = y 0 ? x = x + x x ? y = 0 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = dec x 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = dec y 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = dec 0 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = dec x 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = dec y 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = dec 0 0 ? 0 = 0 0 ? x = x x ? 0 = dec x x ? y = x 0 ? 0 = 0 0 ? x = x x ? 0 = dec x x ? y = y 0 ? 0 = 0 0 ? x = x x ? 0 = dec x x ? y = 0 0 ? 0 = 0 0 ? x = x x ? 0 = dec 0 x ? y = x 0 ? 0 = 0 0 ? x = x x ? 0 = dec 0 x ? y = y 0 ? 0 = 0 0 ? x = x x ? 0 = dec 0 x ? y = 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = dec 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = dec 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x x ? y = x 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x x ? y = y 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x x ? y = 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec 0 x ? y = x 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec 0 x ? y = y 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec 0 x ? y = 0 0 ? 0 = 0 0 ? x = dec x x ? 0 = x x ? y = x 0 ? 0 = 0 0 ? x = dec x x ? 0 = x x ? y = y 0 ? 0 = 0 0 ? x = dec x x ? 0 = x x ? y = 0 0 ? 0 = 0 0 ? x = dec x x ? 0 = 0 x ? y = x 0 ? 0 = 0 0 ? x = dec x x ? 0 = 0 x ? y = y 0 ? 0 = 0 0 ? x = dec x x ? 0 = 0 x ? y = 0 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = x x ? y = x 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = x x ? y = y 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = x x ? y = 0 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = 0 x ? y = x 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = 0 x ? y = y 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = 0 x ? y = 0 0 ? 0 = dec 0 0 ? x = x x ? 0 = x x ? y = x 0 ? 0 = dec 0 0 ? x = x x ? 0 = x x ? y = y 0 ? 0 = dec 0 0 ? x = x x ? 0 = x x ? y = 0 0 ? 0 = dec 0 0 ? x = x x ? 0 = 0 x ? y = x 0 ? 0 = dec 0 0 ? x = x x ? 0 = 0 x ? y = y 0 ? 0 = dec 0 0 ? x = x x ? 0 = 0 x ? y = 0 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = x x ? y = x 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = x x ? y = y 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = x x ? y = 0 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = 0 x ? y = x 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = 0 x ? y = y 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = 0 x ? y = 0 x ? 0 = x x ? y = x ? dec x x ? 0 = x x ? y = x ? dec y x ? 0 = x x ? y = y ? dec x x ? 0 = x x ? y = y ? dec y x ? 0 = x x ? y = 0 ? dec x x ? 0 = x x ? y = 0 ? dec y x ? 0 = x x ? y = dec x ? x x ? 0 = x x ? y = dec x ? y x ? 0 = x x ? y = dec x ? 0 x ? 0 = x x ? y = dec y ? x x ? 0 = x x ? y = dec y ? y x ? 0 = x x ? y = dec y ? 0 x ? 0 = 0 x ? y = x ? dec x x ? 0 = 0 x ? y = x ? dec y x ? 0 = 0 x ? y = y ? dec x x ? 0 = 0 x ? y = y ? dec y x ? 0 = 0 x ? y = 0 ? dec x x ? 0 = 0 x ? y = 0 ? dec y x ? 0 = 0 x ? y = dec x ? x x ? 0 = 0 x ? y = dec x ? y x ? 0 = 0 x ? y = dec x ? 0 x ? 0 = 0 x ? y = dec y ? x x ? 0 = 0 x ? y = dec y ? y x ? 0 = 0 x ? y = dec y ? 0 0 ? x = x x ? y = x ? dec x 0 ? x = x x ? y = x ? dec y 0 ? x = x x ? y = y ? dec x 0 ? x = x x ? y = y ? dec y 0 ? x = x x ? y = 0 ? dec x 0 ? x = x x ? y = 0 ? dec y 0 ? x = x x ? y = dec x ? x 0 ? x = x x ? y = dec x ? y 0 ? x = x x ? y = dec x ? 0 0 ? x = x x ? y = dec y ? x 0 ? x = x x ? y = dec y ? y 0 ? x = x x ? y = dec y ? 0 0 ? x = 0 x ? y = x ? dec x 0 ? x = 0 x ? y = x ? dec y 0 ? x = 0 x ? y = y ? dec x 0 ? x = 0 x ? y = y ? dec y 0 ? x = 0 x ? y = 0 ? dec x 0 ? x = 0 x ? y = 0 ? dec y 0 ? x = 0 x ? y = dec x ? x 0 ? x = 0 x ? y = dec x ? y 0 ? x = 0 x ? y = dec x ? 0 0 ? x = 0 x ? y = dec y ? x 0 ? x = 0 x ? y = dec y ? y 0 ? x = 0 x ? y = dec y ? 0 x ? y = x + (x + x) x ? y = x + (x + y) x ? y = x + (y + x) x ? y = x + (y + y) x ? y = y + (x + x) x ? y = y + (x + y) x ? y = y + (y + x) x ? y = y + (y + y) x ? y = dec x + dec x x ? y = dec x + dec y x ? y = dec x + dec 0 x ? y = dec y + dec x x ? y = dec y + dec y x ? y = dec y + dec 0 x ? y = dec 0 + dec x x ? y = dec 0 + dec y x ? y = dec 0 + dec 0 x ? 0 = x x ? y = dec x + y x ? 0 = x x ? y = dec y + x x ? 0 = x x ? y = dec 0 + x x ? 0 = x x ? y = dec 0 + y x ? 0 = x x ? y = x + dec x x ? 0 = x x ? y = x + dec y x ? 0 = x x ? y = x + dec 0 x ? 0 = x x ? y = y + dec x x ? 0 = x x ? y = y + dec y x ? 0 = x x ? y = y + dec 0 x ? 0 = 0 x ? y = dec x + y x ? 0 = 0 x ? y = dec y + x x ? 0 = 0 x ? y = dec 0 + x x ? 0 = 0 x ? y = dec 0 + y x ? 0 = 0 x ? y = x + dec x x ? 0 = 0 x ? y = x + dec y x ? 0 = 0 x ? y = x + dec 0 x ? 0 = 0 x ? y = y + dec x x ? 0 = 0 x ? y = y + dec y x ? 0 = 0 x ? y = y + dec 0 x ? 0 = dec x x ? y = x + x x ? 0 = dec x x ? y = x + y x ? 0 = dec x x ? y = y + x x ? 0 = dec x x ? y = y + y x ? 0 = dec 0 x ? y = x + x x ? 0 = dec 0 x ? y = x + y x ? 0 = dec 0 x ? y = y + x x ? 0 = dec 0 x ? y = y + y x ? 0 = x + x x ? y = dec x x ? 0 = x + x x ? y = dec y x ? 0 = x + x x ? y = dec 0 x ? 0 = dec 0 + x x ? y = x x ? 0 = dec 0 + x x ? y = y x ? 0 = dec 0 + x x ? y = 0 x ? 0 = x + dec x x ? y = x x ? 0 = x + dec x x ? y = y x ? 0 = x + dec x x ? y = 0 x ? 0 = x + dec 0 x ? y = x x ? 0 = x + dec 0 x ? y = y x ? 0 = x + dec 0 x ? y = 0 0 ? x = x x ? y = dec x + y 0 ? x = x x ? y = dec y + x 0 ? x = x x ? y = dec 0 + x 0 ? x = x x ? y = dec 0 + y 0 ? x = x x ? y = x + dec x 0 ? x = x x ? y = x + dec y 0 ? x = x x ? y = x + dec 0 0 ? x = x x ? y = y + dec x 0 ? x = x x ? y = y + dec y 0 ? x = x x ? y = y + dec 0 0 ? x = 0 x ? y = dec x + y 0 ? x = 0 x ? y = dec y + x 0 ? x = 0 x ? y = dec 0 + x 0 ? x = 0 x ? y = dec 0 + y 0 ? x = 0 x ? y = x + dec x 0 ? x = 0 x ? y = x + dec y 0 ? x = 0 x ? y = x + dec 0 0 ? x = 0 x ? y = y + dec x 0 ? x = 0 x ? y = y + dec y 0 ? x = 0 x ? y = y + dec 0 0 ? x = dec x x ? y = x + x 0 ? x = dec x x ? y = x + y 0 ? x = dec x x ? y = y + x 0 ? x = dec x x ? y = y + y 0 ? x = dec 0 x ? y = x + x 0 ? x = dec 0 x ? y = x + y 0 ? x = dec 0 x ? y = y + x 0 ? x = dec 0 x ? y = y + y 0 ? x = x + x x ? y = dec x 0 ? x = x + x x ? y = dec y 0 ? x = x + x x ? y = dec 0 0 ? x = dec 0 + x x ? y = x 0 ? x = dec 0 + x x ? y = y 0 ? x = dec 0 + x x ? y = 0 0 ? x = x + dec x x ? y = x 0 ? x = x + dec x x ? y = y 0 ? x = x + dec x x ? y = 0 0 ? x = x + dec 0 x ? y = x 0 ? x = x + dec 0 x ? y = y 0 ? x = x + dec 0 x ? y = 0 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = x + x 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = x + y 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = y + x 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = y + y 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = x + x 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = x + y 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = y + x 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = y + y 0 ? 0 = 0 0 ? x = x x ? 0 = dec x x ? y = dec x 0 ? 0 = 0 0 ? x = x x ? 0 = dec x x ? y = dec y 0 ? 0 = 0 0 ? x = x x ? 0 = dec x x ? y = dec 0 0 ? 0 = 0 0 ? x = x x ? 0 = dec 0 x ? y = dec x 0 ? 0 = 0 0 ? x = x x ? 0 = dec 0 x ? y = dec y 0 ? 0 = 0 0 ? x = x x ? 0 = dec 0 x ? y = dec 0 0 ? 0 = 0 0 ? x = x x ? 0 = x + x x ? y = x 0 ? 0 = 0 0 ? x = x x ? 0 = x + x x ? y = y 0 ? 0 = 0 0 ? x = x x ? 0 = x + x x ? y = 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = x + x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = x + y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = y + x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = y + y 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = x + x 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = x + y 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = y + x 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = y + y 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x x ? y = dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x x ? y = dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x x ? y = dec 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec 0 x ? y = dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec 0 x ? y = dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec 0 x ? y = dec 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = x + x x ? y = x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x + x x ? y = y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x + x x ? y = 0 0 ? 0 = 0 0 ? x = dec x x ? 0 = x x ? y = dec x 0 ? 0 = 0 0 ? x = dec x x ? 0 = x x ? y = dec y 0 ? 0 = 0 0 ? x = dec x x ? 0 = x x ? y = dec 0 0 ? 0 = 0 0 ? x = dec x x ? 0 = 0 x ? y = dec x 0 ? 0 = 0 0 ? x = dec x x ? 0 = 0 x ? y = dec y 0 ? 0 = 0 0 ? x = dec x x ? 0 = 0 x ? y = dec 0 0 ? 0 = 0 0 ? x = dec x x ? 0 = dec x x ? y = x 0 ? 0 = 0 0 ? x = dec x x ? 0 = dec x x ? y = y 0 ? 0 = 0 0 ? x = dec x x ? 0 = dec x x ? y = 0 0 ? 0 = 0 0 ? x = dec x x ? 0 = dec 0 x ? y = x 0 ? 0 = 0 0 ? x = dec x x ? 0 = dec 0 x ? y = y 0 ? 0 = 0 0 ? x = dec x x ? 0 = dec 0 x ? y = 0 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = x x ? y = dec x 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = x x ? y = dec y 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = x x ? y = dec 0 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = 0 x ? y = dec x 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = 0 x ? y = dec y 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = 0 x ? y = dec 0 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = dec x x ? y = x 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = dec x x ? y = y 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = dec x x ? y = 0 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = dec 0 x ? y = x 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = dec 0 x ? y = y 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = dec 0 x ? y = 0 0 ? 0 = 0 0 ? x = x + x x ? 0 = x x ? y = x 0 ? 0 = 0 0 ? x = x + x x ? 0 = x x ? y = y 0 ? 0 = 0 0 ? x = x + x x ? 0 = x x ? y = 0 0 ? 0 = 0 0 ? x = x + x x ? 0 = 0 x ? y = x 0 ? 0 = 0 0 ? x = x + x x ? 0 = 0 x ? y = y 0 ? 0 = 0 0 ? x = x + x x ? 0 = 0 x ? y = 0 0 ? 0 = dec 0 0 ? x = x x ? 0 = x x ? y = dec x 0 ? 0 = dec 0 0 ? x = x x ? 0 = x x ? y = dec y 0 ? 0 = dec 0 0 ? x = x x ? 0 = x x ? y = dec 0 0 ? 0 = dec 0 0 ? x = x x ? 0 = 0 x ? y = dec x 0 ? 0 = dec 0 0 ? x = x x ? 0 = 0 x ? y = dec y 0 ? 0 = dec 0 0 ? x = x x ? 0 = 0 x ? y = dec 0 0 ? 0 = dec 0 0 ? x = x x ? 0 = dec x x ? y = x 0 ? 0 = dec 0 0 ? x = x x ? 0 = dec x x ? y = y 0 ? 0 = dec 0 0 ? x = x x ? 0 = dec x x ? y = 0 0 ? 0 = dec 0 0 ? x = x x ? 0 = dec 0 x ? y = x 0 ? 0 = dec 0 0 ? x = x x ? 0 = dec 0 x ? y = y 0 ? 0 = dec 0 0 ? x = x x ? 0 = dec 0 x ? y = 0 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = x x ? y = dec x 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = x x ? y = dec y 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = x x ? y = dec 0 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = 0 x ? y = dec x 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = 0 x ? y = dec y 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = 0 x ? y = dec 0 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = dec x x ? y = x 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = dec x x ? y = y 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = dec x x ? y = 0 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = dec 0 x ? y = x 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = dec 0 x ? y = y 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = dec 0 x ? y = 0 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = x x ? y = x 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = x x ? y = y 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = x x ? y = 0 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = 0 x ? y = x 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = 0 x ? y = y 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = 0 x ? y = 0 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = x x ? y = x 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = x x ? y = y 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = x x ? y = 0 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = 0 x ? y = x 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = 0 x ? y = y 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = 0 x ? y = 0 x ? 0 = x x ? y = dec x ? dec x x ? 0 = x x ? y = dec x ? dec y x ? 0 = x x ? y = dec x ? dec 0 x ? 0 = x x ? y = dec y ? dec x x ? 0 = x x ? y = dec y ? dec y x ? 0 = x x ? y = dec y ? dec 0 x ? 0 = x x ? y = dec 0 ? dec x x ? 0 = x x ? y = dec 0 ? dec y x ? 0 = 0 x ? y = dec x ? dec x x ? 0 = 0 x ? y = dec x ? dec y x ? 0 = 0 x ? y = dec x ? dec 0 x ? 0 = 0 x ? y = dec y ? dec x x ? 0 = 0 x ? y = dec y ? dec y x ? 0 = 0 x ? y = dec y ? dec 0 x ? 0 = 0 x ? y = dec 0 ? dec x x ? 0 = 0 x ? y = dec 0 ? dec y 0 ? x = x x ? y = dec x ? dec x 0 ? x = x x ? y = dec x ? dec y 0 ? x = x x ? y = dec x ? dec 0 0 ? x = x x ? y = dec y ? dec x 0 ? x = x x ? y = dec y ? dec y 0 ? x = x x ? y = dec y ? dec 0 0 ? x = x x ? y = dec 0 ? dec x 0 ? x = x x ? y = dec 0 ? dec y 0 ? x = 0 x ? y = dec x ? dec x 0 ? x = 0 x ? y = dec x ? dec y 0 ? x = 0 x ? y = dec x ? dec 0 0 ? x = 0 x ? y = dec y ? dec x 0 ? x = 0 x ? y = dec y ? dec y 0 ? x = 0 x ? y = dec y ? dec 0 0 ? x = 0 x ? y = dec 0 ? dec x 0 ? x = 0 x ? y = dec 0 ? dec y x ? 0 = x x ? y = dec (x ? dec x) x ? 0 = x x ? y = dec (x ? dec y) x ? 0 = x x ? y = dec (y ? dec x) x ? 0 = x x ? y = dec (y ? dec y) x ? 0 = x x ? y = dec (0 ? dec x) x ? 0 = x x ? y = dec (0 ? dec y) x ? 0 = x x ? y = dec (dec x ? x) x ? 0 = x x ? y = dec (dec x ? y) x ? 0 = x x ? y = dec (dec x ? 0) x ? 0 = x x ? y = dec (dec y ? x) x ? 0 = x x ? y = dec (dec y ? y) x ? 0 = x x ? y = dec (dec y ? 0) x ? 0 = 0 x ? y = dec (x ? dec x) x ? 0 = 0 x ? y = dec (x ? dec y) x ? 0 = 0 x ? y = dec (y ? dec x) x ? 0 = 0 x ? y = dec (y ? dec y) x ? 0 = 0 x ? y = dec (0 ? dec x) x ? 0 = 0 x ? y = dec (0 ? dec y) x ? 0 = 0 x ? y = dec (dec x ? x) x ? 0 = 0 x ? y = dec (dec x ? y) x ? 0 = 0 x ? y = dec (dec x ? 0) x ? 0 = 0 x ? y = dec (dec y ? x) x ? 0 = 0 x ? y = dec (dec y ? y) x ? 0 = 0 x ? y = dec (dec y ? 0) x ? 0 = dec x x ? y = x ? dec x x ? 0 = dec x x ? y = x ? dec y x ? 0 = dec x x ? y = y ? dec x x ? 0 = dec x x ? y = y ? dec y x ? 0 = dec x x ? y = 0 ? dec x x ? 0 = dec x x ? y = 0 ? dec y x ? 0 = dec x x ? y = dec x ? x x ? 0 = dec x x ? y = dec x ? y x ? 0 = dec x x ? y = dec x ? 0 x ? 0 = dec x x ? y = dec y ? x x ? 0 = dec x x ? y = dec y ? y x ? 0 = dec x x ? y = dec y ? 0 x ? 0 = dec 0 x ? y = x ? dec x x ? 0 = dec 0 x ? y = x ? dec y x ? 0 = dec 0 x ? y = y ? dec x x ? 0 = dec 0 x ? y = y ? dec y x ? 0 = dec 0 x ? y = 0 ? dec x x ? 0 = dec 0 x ? y = 0 ? dec y x ? 0 = dec 0 x ? y = dec x ? x x ? 0 = dec 0 x ? y = dec x ? y x ? 0 = dec 0 x ? y = dec x ? 0 x ? 0 = dec 0 x ? y = dec y ? x x ? 0 = dec 0 x ? y = dec y ? y x ? 0 = dec 0 x ? y = dec y ? 0 0 ? x = x x ? y = dec (x ? dec x) 0 ? x = x x ? y = dec (x ? dec y) 0 ? x = x x ? y = dec (y ? dec x) 0 ? x = x x ? y = dec (y ? dec y) 0 ? x = x x ? y = dec (0 ? dec x) 0 ? x = x x ? y = dec (0 ? dec y) 0 ? x = x x ? y = dec (dec x ? x) 0 ? x = x x ? y = dec (dec x ? y) 0 ? x = x x ? y = dec (dec x ? 0) 0 ? x = x x ? y = dec (dec y ? x) 0 ? x = x x ? y = dec (dec y ? y) 0 ? x = x x ? y = dec (dec y ? 0) 0 ? x = 0 x ? y = dec (x ? dec x) 0 ? x = 0 x ? y = dec (x ? dec y) 0 ? x = 0 x ? y = dec (y ? dec x) 0 ? x = 0 x ? y = dec (y ? dec y) 0 ? x = 0 x ? y = dec (0 ? dec x) 0 ? x = 0 x ? y = dec (0 ? dec y) 0 ? x = 0 x ? y = dec (dec x ? x) 0 ? x = 0 x ? y = dec (dec x ? y) 0 ? x = 0 x ? y = dec (dec x ? 0) 0 ? x = 0 x ? y = dec (dec y ? x) 0 ? x = 0 x ? y = dec (dec y ? y) 0 ? x = 0 x ? y = dec (dec y ? 0) 0 ? x = dec x x ? y = x ? dec x 0 ? x = dec x x ? y = x ? dec y 0 ? x = dec x x ? y = y ? dec x 0 ? x = dec x x ? y = y ? dec y 0 ? x = dec x x ? y = 0 ? dec x 0 ? x = dec x x ? y = 0 ? dec y 0 ? x = dec x x ? y = dec x ? x 0 ? x = dec x x ? y = dec x ? y 0 ? x = dec x x ? y = dec x ? 0 0 ? x = dec x x ? y = dec y ? x 0 ? x = dec x x ? y = dec y ? y 0 ? x = dec x x ? y = dec y ? 0 0 ? x = dec 0 x ? y = x ? dec x 0 ? x = dec 0 x ? y = x ? dec y 0 ? x = dec 0 x ? y = y ? dec x 0 ? x = dec 0 x ? y = y ? dec y 0 ? x = dec 0 x ? y = 0 ? dec x 0 ? x = dec 0 x ? y = 0 ? dec y 0 ? x = dec 0 x ? y = dec x ? x 0 ? x = dec 0 x ? y = dec x ? y 0 ? x = dec 0 x ? y = dec x ? 0 0 ? x = dec 0 x ? y = dec y ? x 0 ? x = dec 0 x ? y = dec y ? y 0 ? x = dec 0 x ? y = dec y ? 0 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = x ? dec x 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = x ? dec y 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = y ? dec x 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = y ? dec y 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = 0 ? dec x 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = 0 ? dec y 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = dec x ? x 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = dec x ? y 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = dec x ? 0 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = dec y ? x 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = dec y ? y 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = dec y ? 0 0 ? 0 = 0 0 ? x = x x ? 0 = dec x ? x x ? y = x 0 ? 0 = 0 0 ? x = x x ? 0 = dec x ? 0 x ? y = x 0 ? 0 = 0 0 ? x = x x ? 0 = dec x ? x x ? y = y 0 ? 0 = 0 0 ? x = x x ? 0 = dec x ? 0 x ? y = y 0 ? 0 = 0 0 ? x = x x ? 0 = dec x ? x x ? y = 0 0 ? 0 = 0 0 ? x = x x ? 0 = dec x ? 0 x ? y = 0 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = x ? dec x 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = x ? dec y 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = y ? dec x 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = y ? dec y 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = 0 ? dec x 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = 0 ? dec y 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = dec x ? x 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = dec x ? y 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = dec x ? 0 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = dec y ? x 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = dec y ? y 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = dec y ? 0 0 ? 0 = 0 0 ? x = x ? dec x x ? 0 = x x ? y = x 0 ? 0 = 0 0 ? x = 0 ? dec x x ? 0 = x x ? y = x 0 ? 0 = 0 0 ? x = x ? dec x x ? 0 = x x ? y = y 0 ? 0 = 0 0 ? x = 0 ? dec x x ? 0 = x x ? y = y 0 ? 0 = 0 0 ? x = x ? dec x x ? 0 = x x ? y = 0 0 ? 0 = 0 0 ? x = 0 ? dec x x ? 0 = x x ? y = 0 0 ? 0 = 0 0 ? x = x ? dec x x ? 0 = 0 x ? y = x 0 ? 0 = 0 0 ? x = 0 ? dec x x ? 0 = 0 x ? y = x 0 ? 0 = 0 0 ? x = x ? dec x x ? 0 = 0 x ? y = y 0 ? 0 = 0 0 ? x = 0 ? dec x x ? 0 = 0 x ? y = y 0 ? 0 = 0 0 ? x = x ? dec x x ? 0 = 0 x ? y = 0 0 ? 0 = 0 0 ? x = 0 ? dec x x ? 0 = 0 x ? y = 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = x ? dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = x ? dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = y ? dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = y ? dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = 0 ? dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = 0 ? dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = dec x ? x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = dec x ? y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = dec x ? 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = dec y ? x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = dec y ? y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = dec y ? 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x ? x x ? y = x 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x ? 0 x ? y = x 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x ? x x ? y = y 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x ? 0 x ? y = y 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x ? x x ? y = 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x ? 0 x ? y = 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = x ? dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = x ? dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = y ? dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = y ? dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = 0 ? dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = 0 ? dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = dec x ? x 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = dec x ? y 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = dec x ? 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = dec y ? x 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = dec y ? y 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = dec y ? 0 x ? y = x + (dec x + y) x ? y = x + (dec y + x) x ? y = x + (dec 0 + x) x ? y = x + (dec 0 + y) x ? y = x + (x + dec x) x ? y = x + (x + dec y) x ? y = x + (x + dec 0) x ? y = x + (y + dec x) x ? y = x + (y + dec y) x ? y = x + (y + dec 0) x ? y = y + (dec x + y) x ? y = y + (dec y + x) x ? y = y + (dec 0 + x) x ? y = y + (dec 0 + y) x ? y = y + (x + dec x) x ? y = y + (x + dec y) x ? y = y + (x + dec 0) x ? y = y + (y + dec x) x ? y = y + (y + dec y) x ? y = y + (y + dec 0) x ? y = dec x + (y + y) x ? y = dec y + (x + x) x ? y = dec 0 + (x + x) x ? y = dec 0 + (x + y) x ? y = dec 0 + (y + x) x ? y = dec 0 + (y + y) x ? 0 = x x ? y = x + (x + x) x ? 0 = x x ? y = x + (x + y) x ? 0 = x x ? y = x + (y + x) x ? 0 = x x ? y = x + (y + y) x ? 0 = x x ? y = y + (x + x) x ? 0 = x x ? y = y + (x + y) x ? 0 = x x ? y = y + (y + x) x ? 0 = x x ? y = y + (y + y) x ? 0 = x x ? y = dec x + dec x x ? 0 = x x ? y = dec x + dec y x ? 0 = x x ? y = dec x + dec 0 x ? 0 = x x ? y = dec y + dec x x ? 0 = x x ? y = dec y + dec y x ? 0 = x x ? y = dec y + dec 0 x ? 0 = x x ? y = dec 0 + dec x x ? 0 = x x ? y = dec 0 + dec y x ? 0 = x x ? y = dec 0 + dec 0 x ? 0 = 0 x ? y = x + (x + x) x ? 0 = 0 x ? y = x + (x + y) x ? 0 = 0 x ? y = x + (y + x) x ? 0 = 0 x ? y = x + (y + y) x ? 0 = 0 x ? y = y + (x + x) x ? 0 = 0 x ? y = y + (x + y) x ? 0 = 0 x ? y = y + (y + x) x ? 0 = 0 x ? y = y + (y + y) x ? 0 = 0 x ? y = dec x + dec x x ? 0 = 0 x ? y = dec x + dec y x ? 0 = 0 x ? y = dec x + dec 0 x ? 0 = 0 x ? y = dec y + dec x x ? 0 = 0 x ? y = dec y + dec y x ? 0 = 0 x ? y = dec y + dec 0 x ? 0 = 0 x ? y = dec 0 + dec x x ? 0 = 0 x ? y = dec 0 + dec y x ? 0 = 0 x ? y = dec 0 + dec 0 x ? 0 = dec x x ? y = dec x + y x ? 0 = dec x x ? y = dec y + x x ? 0 = dec x x ? y = dec 0 + x x ? 0 = dec x x ? y = dec 0 + y x ? 0 = dec x x ? y = x + dec x x ? 0 = dec x x ? y = x + dec y x ? 0 = dec x x ? y = x + dec 0 x ? 0 = dec x x ? y = y + dec x x ? 0 = dec x x ? y = y + dec y x ? 0 = dec x x ? y = y + dec 0 x ? 0 = dec 0 x ? y = dec x + y x ? 0 = dec 0 x ? y = dec y + x x ? 0 = dec 0 x ? y = dec 0 + x x ? 0 = dec 0 x ? y = dec 0 + y x ? 0 = dec 0 x ? y = x + dec x x ? 0 = dec 0 x ? y = x + dec y x ? 0 = dec 0 x ? y = x + dec 0 x ? 0 = dec 0 x ? y = y + dec x x ? 0 = dec 0 x ? y = y + dec y x ? 0 = dec 0 x ? y = y + dec 0 x ? 0 = x + x x ? y = x + y x ? 0 = x + x x ? y = y + x x ? 0 = x + x x ? y = y + y x ? 0 = dec 0 + x x ? y = dec x x ? 0 = dec 0 + x x ? y = dec y x ? 0 = dec 0 + x x ? y = dec 0 x ? 0 = x + dec x x ? y = dec x x ? 0 = x + dec x x ? y = dec y x ? 0 = x + dec x x ? y = dec 0 x ? 0 = x + dec 0 x ? y = dec x x ? 0 = x + dec 0 x ? y = dec y x ? 0 = x + dec 0 x ? y = dec 0 x ? 0 = x + (x + x) x ? y = x x ? 0 = x + (x + x) x ? y = y x ? 0 = x + (x + x) x ? y = 0 x ? 0 = dec x + dec x x ? y = x x ? 0 = dec x + dec x x ? y = y x ? 0 = dec x + dec x x ? y = 0 x ? 0 = dec x + dec 0 x ? y = x x ? 0 = dec x + dec 0 x ? y = y x ? 0 = dec x + dec 0 x ? y = 0 x ? 0 = dec 0 + dec x x ? y = x x ? 0 = dec 0 + dec x x ? y = y x ? 0 = dec 0 + dec x x ? y = 0 x ? 0 = dec 0 + dec 0 x ? y = x x ? 0 = dec 0 + dec 0 x ? y = y x ? 0 = dec 0 + dec 0 x ? y = 0 0 ? x = x x ? y = x + (x + x) 0 ? x = x x ? y = x + (x + y) 0 ? x = x x ? y = x + (y + x) 0 ? x = x x ? y = x + (y + y) 0 ? x = x x ? y = y + (x + x) 0 ? x = x x ? y = y + (x + y) 0 ? x = x x ? y = y + (y + x) 0 ? x = x x ? y = y + (y + y) 0 ? x = x x ? y = dec x + dec x 0 ? x = x x ? y = dec x + dec y 0 ? x = x x ? y = dec x + dec 0 0 ? x = x x ? y = dec y + dec x 0 ? x = x x ? y = dec y + dec y 0 ? x = x x ? y = dec y + dec 0 0 ? x = x x ? y = dec 0 + dec x 0 ? x = x x ? y = dec 0 + dec y 0 ? x = x x ? y = dec 0 + dec 0 0 ? x = 0 x ? y = x + (x + x) 0 ? x = 0 x ? y = x + (x + y) 0 ? x = 0 x ? y = x + (y + x) 0 ? x = 0 x ? y = x + (y + y) 0 ? x = 0 x ? y = y + (x + x) 0 ? x = 0 x ? y = y + (x + y) 0 ? x = 0 x ? y = y + (y + x) 0 ? x = 0 x ? y = y + (y + y) 0 ? x = 0 x ? y = dec x + dec x 0 ? x = 0 x ? y = dec x + dec y 0 ? x = 0 x ? y = dec x + dec 0 0 ? x = 0 x ? y = dec y + dec x 0 ? x = 0 x ? y = dec y + dec y 0 ? x = 0 x ? y = dec y + dec 0 0 ? x = 0 x ? y = dec 0 + dec x 0 ? x = 0 x ? y = dec 0 + dec y 0 ? x = 0 x ? y = dec 0 + dec 0 0 ? x = dec x x ? y = dec x + y 0 ? x = dec x x ? y = dec y + x 0 ? x = dec x x ? y = dec 0 + x 0 ? x = dec x x ? y = dec 0 + y 0 ? x = dec x x ? y = x + dec x 0 ? x = dec x x ? y = x + dec y 0 ? x = dec x x ? y = x + dec 0 0 ? x = dec x x ? y = y + dec x 0 ? x = dec x x ? y = y + dec y 0 ? x = dec x x ? y = y + dec 0 0 ? x = dec 0 x ? y = dec x + y 0 ? x = dec 0 x ? y = dec y + x 0 ? x = dec 0 x ? y = dec 0 + x 0 ? x = dec 0 x ? y = dec 0 + y 0 ? x = dec 0 x ? y = x + dec x 0 ? x = dec 0 x ? y = x + dec y 0 ? x = dec 0 x ? y = x + dec 0 0 ? x = dec 0 x ? y = y + dec x 0 ? x = dec 0 x ? y = y + dec y 0 ? x = dec 0 x ? y = y + dec 0 0 ? x = x + x x ? y = x + y 0 ? x = x + x x ? y = y + x 0 ? x = x + x x ? y = y + y 0 ? x = dec 0 + x x ? y = dec x 0 ? x = dec 0 + x x ? y = dec y 0 ? x = dec 0 + x x ? y = dec 0 0 ? x = x + dec x x ? y = dec x 0 ? x = x + dec x x ? y = dec y 0 ? x = x + dec x x ? y = dec 0 0 ? x = x + dec 0 x ? y = dec x 0 ? x = x + dec 0 x ? y = dec y 0 ? x = x + dec 0 x ? y = dec 0 0 ? x = x + (x + x) x ? y = x 0 ? x = x + (x + x) x ? y = y 0 ? x = x + (x + x) x ? y = 0 0 ? x = dec x + dec x x ? y = x 0 ? x = dec x + dec x x ? y = y 0 ? x = dec x + dec x x ? y = 0 0 ? x = dec x + dec 0 x ? y = x 0 ? x = dec x + dec 0 x ? y = y 0 ? x = dec x + dec 0 x ? y = 0 0 ? x = dec 0 + dec x x ? y = x 0 ? x = dec 0 + dec x x ? y = y 0 ? x = dec 0 + dec x x ? y = 0 0 ? x = dec 0 + dec 0 x ? y = x 0 ? x = dec 0 + dec 0 x ? y = y 0 ? x = dec 0 + dec 0 x ? y = 0 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = dec x + y 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = dec y + x 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = dec 0 + x 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = dec 0 + y 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = x + dec x 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = x + dec y 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = x + dec 0 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = y + dec x 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = y + dec y 0 ? 0 = 0 0 ? x = x x ? 0 = x x ? y = y + dec 0 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = dec x + y 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = dec y + x 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = dec 0 + x 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = dec 0 + y 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = x + dec x 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = x + dec y 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = x + dec 0 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = y + dec x 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = y + dec y 0 ? 0 = 0 0 ? x = x x ? 0 = 0 x ? y = y + dec 0 0 ? 0 = 0 0 ? x = x x ? 0 = dec x x ? y = x + x 0 ? 0 = 0 0 ? x = x x ? 0 = dec x x ? y = x + y 0 ? 0 = 0 0 ? x = x x ? 0 = dec x x ? y = y + x 0 ? 0 = 0 0 ? x = x x ? 0 = dec x x ? y = y + y 0 ? 0 = 0 0 ? x = x x ? 0 = dec 0 x ? y = x + x 0 ? 0 = 0 0 ? x = x x ? 0 = dec 0 x ? y = x + y 0 ? 0 = 0 0 ? x = x x ? 0 = dec 0 x ? y = y + x 0 ? 0 = 0 0 ? x = x x ? 0 = dec 0 x ? y = y + y 0 ? 0 = 0 0 ? x = x x ? 0 = x + x x ? y = dec x 0 ? 0 = 0 0 ? x = x x ? 0 = x + x x ? y = dec y 0 ? 0 = 0 0 ? x = x x ? 0 = x + x x ? y = dec 0 0 ? 0 = 0 0 ? x = x x ? 0 = dec 0 + x x ? y = x 0 ? 0 = 0 0 ? x = x x ? 0 = dec 0 + x x ? y = y 0 ? 0 = 0 0 ? x = x x ? 0 = dec 0 + x x ? y = 0 0 ? 0 = 0 0 ? x = x x ? 0 = x + dec x x ? y = x 0 ? 0 = 0 0 ? x = x x ? 0 = x + dec x x ? y = y 0 ? 0 = 0 0 ? x = x x ? 0 = x + dec x x ? y = 0 0 ? 0 = 0 0 ? x = x x ? 0 = x + dec 0 x ? y = x 0 ? 0 = 0 0 ? x = x x ? 0 = x + dec 0 x ? y = y 0 ? 0 = 0 0 ? x = x x ? 0 = x + dec 0 x ? y = 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = dec x + y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = dec y + x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = dec 0 + x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = dec 0 + y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = x + dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = x + dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = x + dec 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = y + dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = y + dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x x ? y = y + dec 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = dec x + y 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = dec y + x 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = dec 0 + x 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = dec 0 + y 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = x + dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = x + dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = x + dec 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = y + dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = y + dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = 0 x ? y = y + dec 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x x ? y = x + x 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x x ? y = x + y 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x x ? y = y + x 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec x x ? y = y + y 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec 0 x ? y = x + x 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec 0 x ? y = x + y 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec 0 x ? y = y + x 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec 0 x ? y = y + y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x + x x ? y = dec x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x + x x ? y = dec y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x + x x ? y = dec 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec 0 + x x ? y = x 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec 0 + x x ? y = y 0 ? 0 = 0 0 ? x = 0 x ? 0 = dec 0 + x x ? y = 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = x + dec x x ? y = x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x + dec x x ? y = y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x + dec x x ? y = 0 0 ? 0 = 0 0 ? x = 0 x ? 0 = x + dec 0 x ? y = x 0 ? 0 = 0 0 ? x = 0 x ? 0 = x + dec 0 x ? y = y 0 ? 0 = 0 0 ? x = 0 x ? 0 = x + dec 0 x ? y = 0 0 ? 0 = 0 0 ? x = dec x x ? 0 = x x ? y = x + x 0 ? 0 = 0 0 ? x = dec x x ? 0 = x x ? y = x + y 0 ? 0 = 0 0 ? x = dec x x ? 0 = x x ? y = y + x 0 ? 0 = 0 0 ? x = dec x x ? 0 = x x ? y = y + y 0 ? 0 = 0 0 ? x = dec x x ? 0 = 0 x ? y = x + x 0 ? 0 = 0 0 ? x = dec x x ? 0 = 0 x ? y = x + y 0 ? 0 = 0 0 ? x = dec x x ? 0 = 0 x ? y = y + x 0 ? 0 = 0 0 ? x = dec x x ? 0 = 0 x ? y = y + y 0 ? 0 = 0 0 ? x = dec x x ? 0 = dec x x ? y = dec x 0 ? 0 = 0 0 ? x = dec x x ? 0 = dec x x ? y = dec y 0 ? 0 = 0 0 ? x = dec x x ? 0 = dec x x ? y = dec 0 0 ? 0 = 0 0 ? x = dec x x ? 0 = dec 0 x ? y = dec x 0 ? 0 = 0 0 ? x = dec x x ? 0 = dec 0 x ? y = dec y 0 ? 0 = 0 0 ? x = dec x x ? 0 = dec 0 x ? y = dec 0 0 ? 0 = 0 0 ? x = dec x x ? 0 = x + x x ? y = x 0 ? 0 = 0 0 ? x = dec x x ? 0 = x + x x ? y = y 0 ? 0 = 0 0 ? x = dec x x ? 0 = x + x x ? y = 0 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = x x ? y = x + x 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = x x ? y = x + y 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = x x ? y = y + x 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = x x ? y = y + y 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = 0 x ? y = x + x 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = 0 x ? y = x + y 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = 0 x ? y = y + x 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = 0 x ? y = y + y 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = dec x x ? y = dec x 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = dec x x ? y = dec y 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = dec x x ? y = dec 0 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = dec 0 x ? y = dec x 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = dec 0 x ? y = dec y 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = dec 0 x ? y = dec 0 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = x + x x ? y = x 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = x + x x ? y = y 0 ? 0 = 0 0 ? x = dec 0 x ? 0 = x + x x ? y = 0 0 ? 0 = 0 0 ? x = x + x x ? 0 = x x ? y = dec x 0 ? 0 = 0 0 ? x = x + x x ? 0 = x x ? y = dec y 0 ? 0 = 0 0 ? x = x + x x ? 0 = x x ? y = dec 0 0 ? 0 = 0 0 ? x = x + x x ? 0 = 0 x ? y = dec x 0 ? 0 = 0 0 ? x = x + x x ? 0 = 0 x ? y = dec y 0 ? 0 = 0 0 ? x = x + x x ? 0 = 0 x ? y = dec 0 0 ? 0 = 0 0 ? x = x + x x ? 0 = dec x x ? y = x 0 ? 0 = 0 0 ? x = x + x x ? 0 = dec x x ? y = y 0 ? 0 = 0 0 ? x = x + x x ? 0 = dec x x ? y = 0 0 ? 0 = 0 0 ? x = x + x x ? 0 = dec 0 x ? y = x 0 ? 0 = 0 0 ? x = x + x x ? 0 = dec 0 x ? y = y 0 ? 0 = 0 0 ? x = x + x x ? 0 = dec 0 x ? y = 0 0 ? 0 = 0 0 ? x = dec 0 + x x ? 0 = x x ? y = x 0 ? 0 = 0 0 ? x = dec 0 + x x ? 0 = x x ? y = y 0 ? 0 = 0 0 ? x = dec 0 + x x ? 0 = x x ? y = 0 0 ? 0 = 0 0 ? x = dec 0 + x x ? 0 = 0 x ? y = x 0 ? 0 = 0 0 ? x = dec 0 + x x ? 0 = 0 x ? y = y 0 ? 0 = 0 0 ? x = dec 0 + x x ? 0 = 0 x ? y = 0 0 ? 0 = 0 0 ? x = x + dec x x ? 0 = x x ? y = x 0 ? 0 = 0 0 ? x = x + dec x x ? 0 = x x ? y = y 0 ? 0 = 0 0 ? x = x + dec x x ? 0 = x x ? y = 0 0 ? 0 = 0 0 ? x = x + dec x x ? 0 = 0 x ? y = x 0 ? 0 = 0 0 ? x = x + dec x x ? 0 = 0 x ? y = y 0 ? 0 = 0 0 ? x = x + dec x x ? 0 = 0 x ? y = 0 0 ? 0 = 0 0 ? x = x + dec 0 x ? 0 = x x ? y = x 0 ? 0 = 0 0 ? x = x + dec 0 x ? 0 = x x ? y = y 0 ? 0 = 0 0 ? x = x + dec 0 x ? 0 = x x ? y = 0 0 ? 0 = 0 0 ? x = x + dec 0 x ? 0 = 0 x ? y = x 0 ? 0 = 0 0 ? x = x + dec 0 x ? 0 = 0 x ? y = y 0 ? 0 = 0 0 ? x = x + dec 0 x ? 0 = 0 x ? y = 0 0 ? 0 = dec 0 0 ? x = x x ? 0 = x x ? y = x + x 0 ? 0 = dec 0 0 ? x = x x ? 0 = x x ? y = x + y 0 ? 0 = dec 0 0 ? x = x x ? 0 = x x ? y = y + x 0 ? 0 = dec 0 0 ? x = x x ? 0 = x x ? y = y + y 0 ? 0 = dec 0 0 ? x = x x ? 0 = 0 x ? y = x + x 0 ? 0 = dec 0 0 ? x = x x ? 0 = 0 x ? y = x + y 0 ? 0 = dec 0 0 ? x = x x ? 0 = 0 x ? y = y + x 0 ? 0 = dec 0 0 ? x = x x ? 0 = 0 x ? y = y + y 0 ? 0 = dec 0 0 ? x = x x ? 0 = dec x x ? y = dec x 0 ? 0 = dec 0 0 ? x = x x ? 0 = dec x x ? y = dec y 0 ? 0 = dec 0 0 ? x = x x ? 0 = dec x x ? y = dec 0 0 ? 0 = dec 0 0 ? x = x x ? 0 = dec 0 x ? y = dec x 0 ? 0 = dec 0 0 ? x = x x ? 0 = dec 0 x ? y = dec y 0 ? 0 = dec 0 0 ? x = x x ? 0 = dec 0 x ? y = dec 0 0 ? 0 = dec 0 0 ? x = x x ? 0 = x + x x ? y = x 0 ? 0 = dec 0 0 ? x = x x ? 0 = x + x x ? y = y 0 ? 0 = dec 0 0 ? x = x x ? 0 = x + x x ? y = 0 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = x x ? y = x + x 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = x x ? y = x + y 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = x x ? y = y + x 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = x x ? y = y + y 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = 0 x ? y = x + x 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = 0 x ? y = x + y 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = 0 x ? y = y + x 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = 0 x ? y = y + y 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = dec x x ? y = dec x 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = dec x x ? y = dec y 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = dec x x ? y = dec 0 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = dec 0 x ? y = dec x 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = dec 0 x ? y = dec y 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = dec 0 x ? y = dec 0 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = x + x x ? y = x 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = x + x x ? y = y 0 ? 0 = dec 0 0 ? x = 0 x ? 0 = x + x x ? y = 0 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = x x ? y = dec x 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = x x ? y = dec y 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = x x ? y = dec 0 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = 0 x ? y = dec x 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = 0 x ? y = dec y 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = 0 x ? y = dec 0 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = dec x x ? y = x 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = dec x x ? y = y 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = dec x x ? y = 0 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = dec 0 x ? y = x 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = dec 0 x ? y = y 0 ? 0 = dec 0 0 ? x = dec x x ? 0 = dec 0 x ? y = 0 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = x x ? y = dec x 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = x x ? y = dec y 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = x x ? y = dec 0 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = 0 x ? y = dec x 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = 0 x ? y = dec y 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = 0 x ? y = dec 0 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = dec x x ? y = x 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = dec x x ? y = y 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = dec x x ? y = 0 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = dec 0 x ? y = x 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = dec 0 x ? y = y 0 ? 0 = dec 0 0 ? x = dec 0 x ? 0 = dec 0 x ? y = 0 0 ? 0 = dec 0 0 ? x = x + x x ? 0 = x x ? y = x 0 ? 0 = dec 0 0 ? x = x + x x ? 0 = x x ? y = y 0 ? 0 = dec 0 0 ? x = x + x x ? 0 = x x ? y = 0 0 ? 0 = dec 0 0 ? x = x + x x ? 0 = 0 x ? y = x 0 ? 0 = dec 0 0 ? x = x + x x ? 0 = 0 x ? y = y 0 ? 0 = dec 0 0 ? x = x + x x ? 0 = 0 x ? y = 0 Candidates for: goo :: [Int] -> [Int] pruning with 4/4 rules [2,0,1,0,1,0,1,0,1] direct candidates, 0 duplicates [2,1,2,3,4,7,10,17,26] pattern candidates, 0 duplicates rules: xs ++ [] == xs [] ++ xs == xs (xs ++ ys) ++ zs == xs ++ (ys ++ zs) (x:xs) ++ ys == x:(xs ++ ys) direct candidates: goo xs = xs goo xs = [] goo xs = xs ++ xs goo xs = xs ++ (xs ++ xs) pattern candidates: goo xs = xs goo xs = [] goo [] = [] goo (x:xs) = xs goo [] = [] goo (x:xs) = goo xs goo xs = xs ++ xs goo [] = [] goo (x:xs) = x:xs goo [] = [] goo (x:xs) = [x] goo [] = [] goo (x:xs) = xs ++ xs goo [] = [] goo (x:xs) = x:goo xs goo [] = [] goo (x:xs) = xs ++ goo xs goo [] = [] goo (x:xs) = goo xs ++ xs goo xs = xs ++ (xs ++ xs) goo [] = [] goo (x:xs) = goo xs ++ goo xs goo [] = [] goo (x:xs) = x:x:xs goo [] = [] goo (x:xs) = [x,x] goo [] = [] goo (x:xs) = x:(xs ++ xs) goo [] = [] goo (x:xs) = xs ++ (x:xs) goo [] = [] goo (x:xs) = xs ++ [x] goo [] = [] goo (x:xs) = xs ++ (xs ++ xs) Candidates for: ?? :: [Int] -> [Int] -> [Int] pruning with 4/4 rules [3,0,4,0,8,0,16,0,32] direct candidates, 0 duplicates [3,8,15,66,152,362,1400,2084,11820] pattern candidates, 0 duplicates rules: xs ++ [] == xs [] ++ xs == xs (xs ++ ys) ++ zs == xs ++ (ys ++ zs) (x:xs) ++ ys == x:(xs ++ ys) direct candidates: xs ?? ys = xs xs ?? ys = ys xs ?? ys = [] xs ?? ys = xs ++ xs xs ?? ys = xs ++ ys xs ?? ys = ys ++ xs xs ?? ys = ys ++ ys xs ?? ys = xs ++ (xs ++ xs) xs ?? ys = xs ++ (xs ++ ys) xs ?? ys = xs ++ (ys ++ xs) xs ?? ys = xs ++ (ys ++ ys) xs ?? ys = ys ++ (xs ++ xs) xs ?? ys = ys ++ (xs ++ ys) xs ?? ys = ys ++ (ys ++ xs) xs ?? ys = ys ++ (ys ++ ys) pattern candidates: xs ?? ys = xs xs ?? ys = ys xs ?? ys = [] xs ?? [] = xs xs ?? (x:ys) = ys xs ?? [] = xs xs ?? (x:ys) = [] xs ?? [] = [] xs ?? (x:ys) = xs xs ?? [] = [] xs ?? (x:ys) = ys [] ?? xs = xs (x:xs) ?? ys = ys [] ?? xs = xs (x:xs) ?? ys = [] [] ?? xs = [] (x:xs) ?? ys = xs [] ?? xs = [] (x:xs) ?? ys = ys xs ?? ys = xs ++ xs xs ?? ys = xs ++ ys xs ?? ys = ys ++ xs xs ?? ys = ys ++ ys [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = [] (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = [] (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = [] (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = [] (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = [] (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = ys xs ?? [] = xs xs ?? (x:ys) = xs ?? xs xs ?? [] = xs xs ?? (x:ys) = xs ?? ys xs ?? [] = xs xs ?? (x:ys) = xs ?? [] xs ?? [] = xs xs ?? (x:ys) = ys ?? xs xs ?? [] = xs xs ?? (x:ys) = ys ?? ys xs ?? [] = xs xs ?? (x:ys) = ys ?? [] xs ?? [] = xs xs ?? (x:ys) = [] ?? xs xs ?? [] = xs xs ?? (x:ys) = [] ?? ys xs ?? [] = [] xs ?? (x:ys) = xs ?? xs xs ?? [] = [] xs ?? (x:ys) = xs ?? ys xs ?? [] = [] xs ?? (x:ys) = xs ?? [] xs ?? [] = [] xs ?? (x:ys) = ys ?? xs xs ?? [] = [] xs ?? (x:ys) = ys ?? ys xs ?? [] = [] xs ?? (x:ys) = ys ?? [] xs ?? [] = [] xs ?? (x:ys) = [] ?? xs xs ?? [] = [] xs ?? (x:ys) = [] ?? ys [] ?? xs = xs (x:xs) ?? ys = xs ?? xs [] ?? xs = xs (x:xs) ?? ys = xs ?? ys [] ?? xs = xs (x:xs) ?? ys = xs ?? [] [] ?? xs = xs (x:xs) ?? ys = ys ?? xs [] ?? xs = xs (x:xs) ?? ys = ys ?? ys [] ?? xs = xs (x:xs) ?? ys = ys ?? [] [] ?? xs = xs (x:xs) ?? ys = [] ?? xs [] ?? xs = xs (x:xs) ?? ys = [] ?? ys [] ?? xs = [] (x:xs) ?? ys = xs ?? xs [] ?? xs = [] (x:xs) ?? ys = xs ?? ys [] ?? xs = [] (x:xs) ?? ys = xs ?? [] [] ?? xs = [] (x:xs) ?? ys = ys ?? xs [] ?? xs = [] (x:xs) ?? ys = ys ?? ys [] ?? xs = [] (x:xs) ?? ys = ys ?? [] [] ?? xs = [] (x:xs) ?? ys = [] ?? xs [] ?? xs = [] (x:xs) ?? ys = [] ?? ys xs ?? [] = xs xs ?? (x:ys) = x:xs xs ?? [] = xs xs ?? (x:ys) = x:ys xs ?? [] = xs xs ?? (x:ys) = [x] xs ?? [] = xs xs ?? (x:ys) = xs ++ xs xs ?? [] = xs xs ?? (x:ys) = xs ++ ys xs ?? [] = xs xs ?? (x:ys) = ys ++ xs xs ?? [] = xs xs ?? (x:ys) = ys ++ ys xs ?? [] = [] xs ?? (x:ys) = x:xs xs ?? [] = [] xs ?? (x:ys) = x:ys xs ?? [] = [] xs ?? (x:ys) = [x] xs ?? [] = [] xs ?? (x:ys) = xs ++ xs xs ?? [] = [] xs ?? (x:ys) = xs ++ ys xs ?? [] = [] xs ?? (x:ys) = ys ++ xs xs ?? [] = [] xs ?? (x:ys) = ys ++ ys xs ?? [] = xs ++ xs xs ?? (x:ys) = xs xs ?? [] = xs ++ xs xs ?? (x:ys) = ys xs ?? [] = xs ++ xs xs ?? (x:ys) = [] [] ?? xs = xs (x:xs) ?? ys = x:xs [] ?? xs = xs (x:xs) ?? ys = x:ys [] ?? xs = xs (x:xs) ?? ys = [x] [] ?? xs = xs (x:xs) ?? ys = xs ++ xs [] ?? xs = xs (x:xs) ?? ys = xs ++ ys [] ?? xs = xs (x:xs) ?? ys = ys ++ xs [] ?? xs = xs (x:xs) ?? ys = ys ++ ys [] ?? xs = [] (x:xs) ?? ys = x:xs [] ?? xs = [] (x:xs) ?? ys = x:ys [] ?? xs = [] (x:xs) ?? ys = [x] [] ?? xs = [] (x:xs) ?? ys = xs ++ xs [] ?? xs = [] (x:xs) ?? ys = xs ++ ys [] ?? xs = [] (x:xs) ?? ys = ys ++ xs [] ?? xs = [] (x:xs) ?? ys = ys ++ ys [] ?? xs = xs ++ xs (x:xs) ?? ys = xs [] ?? xs = xs ++ xs (x:xs) ?? ys = ys [] ?? xs = xs ++ xs (x:xs) ?? ys = [] [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = xs ?? xs [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = xs ?? ys [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = xs ?? [] [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = ys ?? xs [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = ys ?? ys [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = ys ?? [] [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = [] ?? xs [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = [] ?? ys [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs ?? xs (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs ?? [] (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] ?? xs (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs ?? xs (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs ?? [] (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] ?? xs (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs ?? xs (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = xs ?? [] (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] ?? xs (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = xs ?? xs [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = xs ?? ys [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = xs ?? [] [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = ys ?? xs [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = ys ?? ys [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = ys ?? [] [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = [] ?? xs [] ?? [] = [] [] ?? (x:xs) = xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = [] ?? ys [] ?? [] = [] [] ?? (x:xs) = xs ?? xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = xs ?? [] (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = [] ?? xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = xs ?? xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = xs ?? [] (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = ys [] ?? 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(x:xs) = [] (x:xs) ?? [] = x:xs (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = [] (x:xs) ?? [] = x:xs (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = [] (x:xs) ?? [] = x:xs (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = [] (x:xs) ?? [] = [x] (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = [] (x:xs) ?? [] = [x] (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = [] (x:xs) ?? [] = [x] (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = [] (x:xs) ?? [] = xs ++ xs (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = [] (x:xs) ?? [] = xs ++ xs (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = [] (x:xs) ?? [] = xs ++ xs (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = x:xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = x:xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = x:xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = x:xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = x:xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = x:xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = [x] (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = [x] (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = [x] (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = [x] (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = [x] (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = [x] (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = xs ++ xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = xs ++ xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = xs ++ xs (x:xs) ?? [] = xs (x:xs) ?? (y:ys) = [] [] ?? [] = [] [] ?? (x:xs) = xs ++ xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = xs [] ?? [] = [] [] ?? (x:xs) = xs ++ xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = ys [] ?? [] = [] [] ?? (x:xs) = xs ++ xs (x:xs) ?? [] = [] (x:xs) ?? (y:ys) = [] xs ?? [] = xs xs ?? (x:ys) = (x:xs) ?? xs xs ?? [] = xs xs ?? (x:ys) = (x:xs) ?? ys xs ?? [] = xs xs ?? (x:ys) = (x:xs) ?? [] xs ?? [] = xs xs ?? (x:ys) = (x:ys) ?? xs xs ?? [] = xs xs ?? (x:ys) = (x:ys) ?? ys xs ?? [] = xs xs ?? (x:ys) = (x:ys) ?? [] xs ?? [] = xs xs ?? (x:ys) = [x] ?? xs xs ?? [] = xs xs ?? (x:ys) = [x] ?? ys xs ?? [] = xs xs ?? (x:ys) = [x] ?? [] xs ?? [] = xs xs ?? (x:ys) = (xs ++ xs) ?? xs xs ?? [] = xs xs ?? (x:ys) = (xs ++ xs) ?? ys xs ?? [] = xs xs ?? (x:ys) = (xs ++ xs) ?? [] xs ?? [] = xs xs ?? (x:ys) = (xs ++ ys) ?? xs xs ?? [] = xs xs ?? (x:ys) = (xs ++ ys) ?? ys xs ?? [] = xs xs ?? (x:ys) = (xs ++ ys) ?? [] xs ?? [] = xs xs ?? (x:ys) = (ys ++ xs) ?? xs xs ?? [] = xs xs ?? (x:ys) = (ys ++ xs) ?? ys xs ?? [] = xs xs ?? (x:ys) = (ys ++ xs) ?? [] xs ?? [] = xs xs ?? (x:ys) = (ys ++ ys) ?? xs xs ?? [] = xs xs ?? (x:ys) = (ys ++ ys) ?? ys xs ?? [] = xs xs ?? (x:ys) = (ys ++ ys) ?? [] xs ?? [] = [] xs ?? (x:ys) = (x:xs) ?? xs xs ?? [] = [] xs ?? (x:ys) = (x:xs) ?? ys xs ?? [] = [] xs ?? (x:ys) = (x:xs) ?? [] xs ?? [] = [] xs ?? (x:ys) = (x:ys) ?? xs xs ?? [] = [] xs ?? (x:ys) = (x:ys) ?? ys xs ?? [] = [] xs ?? (x:ys) = (x:ys) ?? [] xs ?? [] = [] xs ?? (x:ys) = [x] ?? xs xs ?? [] = [] xs ?? (x:ys) = [x] ?? ys xs ?? [] = [] xs ?? (x:ys) = [x] ?? [] xs ?? [] = [] xs ?? (x:ys) = (xs ++ xs) ?? xs xs ?? [] = [] xs ?? (x:ys) = (xs ++ xs) ?? ys xs ?? [] = [] xs ?? (x:ys) = (xs ++ xs) ?? [] xs ?? [] = [] xs ?? (x:ys) = (xs ++ ys) ?? xs xs ?? [] = [] xs ?? (x:ys) = (xs ++ ys) ?? ys xs ?? [] = [] xs ?? (x:ys) = (xs ++ ys) ?? [] xs ?? [] = [] xs ?? (x:ys) = (ys ++ xs) ?? xs xs ?? [] = [] xs ?? (x:ys) = (ys ++ xs) ?? ys xs ?? [] = [] xs ?? (x:ys) = (ys ++ xs) ?? [] xs ?? [] = [] xs ?? (x:ys) = (ys ++ ys) ?? xs xs ?? [] = [] xs ?? (x:ys) = (ys ++ ys) ?? ys xs ?? [] = [] xs ?? (x:ys) = (ys ++ ys) ?? [] [] ?? xs = xs (x:xs) ?? ys = xs ?? (x:xs) [] ?? xs = xs (x:xs) ?? ys = xs ?? (x:ys) [] ?? xs = xs (x:xs) ?? ys = xs ?? [x] [] ?? xs = xs (x:xs) ?? ys = xs ?? (xs ++ xs) [] ?? xs = xs (x:xs) ?? ys = xs ?? (xs ++ ys) [] ?? xs = xs (x:xs) ?? ys = xs ?? (ys ++ xs) [] ?? xs = xs (x:xs) ?? ys = xs ?? (ys ++ ys) [] ?? xs = xs (x:xs) ?? ys = ys ?? (x:xs) [] ?? xs = xs (x:xs) ?? ys = ys ?? (x:ys) [] ?? xs = xs (x:xs) ?? ys = ys ?? [x] [] ?? xs = xs (x:xs) ?? ys = ys ?? (xs ++ xs) [] ?? xs = xs (x:xs) ?? ys = ys ?? (xs ++ ys) [] ?? xs = xs (x:xs) ?? ys = ys ?? (ys ++ xs) [] ?? xs = xs (x:xs) ?? ys = ys ?? (ys ++ ys) [] ?? xs = xs (x:xs) ?? ys = [] ?? (x:xs) [] ?? xs = xs (x:xs) ?? ys = [] ?? (x:ys) [] ?? xs = xs (x:xs) ?? ys = [] ?? [x] [] ?? xs = xs (x:xs) ?? ys = [] ?? (xs ++ xs) [] ?? xs = xs (x:xs) ?? ys = [] ?? (xs ++ ys) [] ?? xs = xs (x:xs) ?? ys = [] ?? (ys ++ xs) [] ?? xs = xs (x:xs) ?? ys = [] ?? (ys ++ ys) [] ?? xs = [] (x:xs) ?? ys = xs ?? (x:xs) [] ?? xs = [] (x:xs) ?? ys = xs ?? (x:ys) [] ?? xs = [] (x:xs) ?? ys = xs ?? [x] [] ?? xs = [] (x:xs) ?? ys = xs ?? (xs ++ xs) [] ?? xs = [] (x:xs) ?? ys = xs ?? (xs ++ ys) [] ?? xs = [] (x:xs) ?? ys = xs ?? (ys ++ xs) [] ?? xs = [] (x:xs) ?? ys = xs ?? (ys ++ ys) [] ?? xs = [] (x:xs) ?? ys = ys ?? (x:xs) [] ?? xs = [] (x:xs) ?? ys = ys ?? (x:ys) [] ?? xs = [] (x:xs) ?? ys = ys ?? [x] [] ?? xs = [] (x:xs) ?? ys = ys ?? (xs ++ xs) [] ?? xs = [] (x:xs) ?? ys = ys ?? (xs ++ ys) [] ?? xs = [] (x:xs) ?? ys = ys ?? (ys ++ xs) [] ?? xs = [] (x:xs) ?? ys = ys ?? (ys ++ ys) [] ?? xs = [] (x:xs) ?? ys = [] ?? (x:xs) [] ?? xs = [] (x:xs) ?? ys = [] ?? (x:ys) [] ?? xs = [] (x:xs) ?? ys = [] ?? [x] [] ?? xs = [] (x:xs) ?? ys = [] ?? (xs ++ xs) [] ?? xs = [] (x:xs) ?? ys = [] ?? (xs ++ ys) [] ?? xs = [] (x:xs) ?? ys = [] ?? (ys ++ xs) [] ?? xs = [] (x:xs) ?? ys = [] ?? (ys ++ ys) xs ?? [] = xs xs ?? (x:ys) = x:xs ?? xs xs ?? [] = xs xs ?? (x:ys) = x:xs ?? ys xs ?? [] = xs xs ?? (x:ys) = x:xs ?? [] xs ?? [] = xs xs ?? (x:ys) = x:ys ?? xs xs ?? [] = xs xs ?? (x:ys) = x:ys ?? ys xs ?? [] = xs xs ?? (x:ys) = x:ys ?? [] xs ?? [] = xs xs ?? (x:ys) = [x,] ?? xs xs ?? [] = xs xs ?? (x:ys) = [x,] ?? ys xs ?? [] = xs xs ?? (x:ys) = xs ++ xs ?? xs xs ?? [] = xs xs ?? (x:ys) = xs ++ xs ?? ys xs ?? [] = xs xs ?? (x:ys) = xs ++ xs ?? [] xs ?? [] = xs xs ?? (x:ys) = xs ++ ys ?? xs xs ?? [] = xs xs ?? (x:ys) = xs ++ ys ?? ys xs ?? [] = xs xs ?? (x:ys) = xs ++ ys ?? [] xs ?? [] = xs xs ?? (x:ys) = xs ++ [] ?? xs xs ?? [] = xs xs ?? (x:ys) = xs ++ [] ?? ys xs ?? [] = xs xs ?? (x:ys) = ys ++ xs ?? xs xs ?? [] = xs xs ?? (x:ys) = ys ++ xs ?? ys xs ?? [] = xs xs ?? (x:ys) = ys ++ xs ?? [] xs ?? [] = xs xs ?? (x:ys) = ys ++ ys ?? xs xs ?? [] = xs xs ?? (x:ys) = ys ++ ys ?? ys xs ?? [] = xs xs ?? (x:ys) = ys ++ ys ?? [] xs ?? [] = xs xs ?? (x:ys) = ys ++ [] ?? xs xs ?? [] = xs xs ?? (x:ys) = ys ++ [] ?? ys xs ?? [] = xs xs ?? (x:ys) = xs ?? xs ++ xs xs ?? [] = xs xs ?? (x:ys) = xs ?? ys ++ xs xs ?? [] = xs xs ?? (x:ys) = xs ?? [] ++ xs xs ?? [] = xs xs ?? (x:ys) = ys ?? xs ++ xs xs ?? [] = xs xs ?? (x:ys) = ys ?? ys ++ xs xs ?? [] = xs xs ?? (x:ys) = ys ?? [] ++ xs xs ?? [] = xs xs ?? (x:ys) = [] ?? xs ++ xs xs ?? [] = xs xs ?? (x:ys) = [] ?? ys ++ xs xs ?? [] = xs xs ?? (x:ys) = xs ?? xs ++ ys xs ?? [] = xs xs ?? (x:ys) = xs ?? ys ++ ys xs ?? [] = xs xs ?? (x:ys) = xs ?? [] ++ ys xs ?? [] = xs xs ?? (x:ys) = ys ?? xs ++ ys xs ?? [] = xs xs ?? (x:ys) = ys ?? ys ++ ys xs ?? [] = xs xs ?? (x:ys) = ys ?? [] ++ ys xs ?? [] = xs xs ?? (x:ys) = [] ?? xs ++ ys xs ?? [] = xs xs ?? (x:ys) = [] ?? ys ++ ys xs ?? [] = [] xs ?? (x:ys) = x:xs ?? xs xs ?? [] = [] xs ?? (x:ys) = x:xs ?? ys xs ?? [] = [] xs ?? (x:ys) = x:xs ?? [] xs ?? [] = [] xs ?? (x:ys) = x:ys ?? xs xs ?? [] = [] xs ?? (x:ys) = x:ys ?? ys xs ?? [] = [] xs ?? (x:ys) = x:ys ?? [] xs ?? [] = [] xs ?? (x:ys) = [x,] ?? xs xs ?? [] = [] xs ?? (x:ys) = [x,] ?? ys xs ?? [] = [] xs ?? (x:ys) = xs ++ xs ?? xs xs ?? [] = [] xs ?? (x:ys) = xs ++ xs ?? ys xs ?? [] = [] xs ?? (x:ys) = xs ++ xs ?? [] xs ?? [] = [] xs ?? (x:ys) = xs ++ ys ?? xs xs ?? [] = [] xs ?? (x:ys) = xs ++ ys ?? ys xs ?? [] = [] xs ?? (x:ys) = xs ++ ys ?? [] xs ?? [] = [] xs ?? (x:ys) = xs ++ [] ?? xs xs ?? [] = [] xs ?? (x:ys) = xs ++ [] ?? ys xs ?? [] = [] xs ?? (x:ys) = ys ++ xs ?? xs xs ?? [] = [] xs ?? (x:ys) = ys ++ xs ?? ys xs ?? [] = [] xs ?? (x:ys) = ys ++ xs ?? [] xs ?? [] = [] xs ?? (x:ys) = ys ++ ys ?? xs xs ?? [] = [] xs ?? (x:ys) = ys ++ ys ?? ys xs ?? [] = [] xs ?? (x:ys) = ys ++ ys ?? [] xs ?? [] = [] xs ?? (x:ys) = ys ++ [] ?? xs xs ?? [] = [] xs ?? (x:ys) = ys ++ [] ?? ys xs ?? [] = [] xs ?? (x:ys) = xs ?? xs ++ xs xs ?? [] = [] xs ?? (x:ys) = xs ?? ys ++ xs xs ?? [] = [] xs ?? (x:ys) = xs ?? [] ++ xs xs ?? [] = [] xs ?? (x:ys) = ys ?? xs ++ xs xs ?? [] = [] xs ?? (x:ys) = ys ?? ys ++ xs xs ?? [] = [] xs ?? (x:ys) = ys ?? [] ++ xs xs ?? [] = [] xs ?? (x:ys) = [] ?? xs ++ xs xs ?? [] = [] xs ?? (x:ys) = [] ?? ys ++ xs xs ?? [] = [] xs ?? (x:ys) = xs ?? xs ++ ys xs ?? [] = [] xs ?? (x:ys) = xs ?? ys ++ ys xs ?? [] = [] xs ?? (x:ys) = xs ?? [] ++ ys xs ?? [] = [] xs ?? (x:ys) = ys ?? xs ++ ys xs ?? [] = [] xs ?? (x:ys) = ys ?? ys ++ ys xs ?? [] = [] xs ?? (x:ys) = ys ?? [] ++ ys xs ?? [] = [] xs ?? (x:ys) = [] ?? xs ++ ys xs ?? [] = [] xs ?? (x:ys) = [] ?? ys ++ ys xs ?? [] = xs ++ xs xs ?? (x:ys) = xs ?? xs xs ?? [] = xs ++ xs xs ?? (x:ys) = xs ?? ys xs ?? [] = xs ++ xs xs ?? (x:ys) = xs ?? [] xs ?? [] = xs ++ xs xs ?? (x:ys) = ys ?? xs xs ?? [] = xs ++ xs xs ?? (x:ys) = ys ?? ys xs ?? [] = xs ++ xs xs ?? (x:ys) = ys ?? [] xs ?? [] = xs ++ xs xs ?? (x:ys) = [] ?? xs xs ?? [] = xs ++ xs xs ?? (x:ys) = [] ?? ys [] ?? xs = xs (x:xs) ?? ys = x:xs ?? xs [] ?? xs = xs (x:xs) ?? ys = x:xs ?? ys [] ?? xs = xs (x:xs) ?? ys = x:xs ?? [] [] ?? xs = xs (x:xs) ?? ys = x:ys ?? xs [] ?? xs = xs (x:xs) ?? ys = x:ys ?? ys [] ?? xs = xs (x:xs) ?? ys = x:ys ?? [] [] ?? xs = xs (x:xs) ?? ys = [x,] ?? xs [] ?? xs = xs (x:xs) ?? ys = [x,] ?? ys [] ?? xs = xs (x:xs) ?? ys = xs ++ xs ?? xs [] ?? xs = xs (x:xs) ?? ys = xs ++ xs ?? ys [] ?? xs = xs (x:xs) ?? ys = xs ++ xs ?? [] [] ?? xs = xs (x:xs) ?? ys = xs ++ ys ?? xs [] ?? xs = xs (x:xs) ?? ys = xs ++ ys ?? ys [] ?? xs = xs (x:xs) ?? ys = xs ++ ys ?? [] [] ?? xs = xs (x:xs) ?? ys = xs ++ [] ?? xs [] ?? xs = xs (x:xs) ?? ys = xs ++ [] ?? ys [] ?? xs = xs (x:xs) ?? ys = ys ++ xs ?? xs [] ?? xs = xs (x:xs) ?? ys = ys ++ xs ?? ys [] ?? xs = xs (x:xs) ?? ys = ys ++ xs ?? [] [] ?? xs = xs (x:xs) ?? ys = ys ++ ys ?? xs [] ?? xs = xs (x:xs) ?? ys = ys ++ ys ?? ys [] ?? xs = xs (x:xs) ?? ys = ys ++ ys ?? [] [] ?? xs = xs (x:xs) ?? ys = ys ++ [] ?? xs [] ?? xs = xs (x:xs) ?? ys = ys ++ [] ?? ys [] ?? xs = xs (x:xs) ?? ys = xs ?? xs ++ xs [] ?? xs = xs (x:xs) ?? ys = xs ?? ys ++ xs [] ?? xs = xs (x:xs) ?? ys = xs ?? [] ++ xs [] ?? xs = xs (x:xs) ?? ys = ys ?? xs ++ xs [] ?? xs = xs (x:xs) ?? ys = ys ?? ys ++ xs [] ?? xs = xs (x:xs) ?? ys = ys ?? [] ++ xs [] ?? xs = xs (x:xs) ?? ys = [] ?? xs ++ xs [] ?? xs = xs (x:xs) ?? ys = [] ?? ys ++ xs [] ?? xs = xs (x:xs) ?? ys = xs ?? xs ++ ys [] ?? xs = xs (x:xs) ?? ys = xs ?? ys ++ ys [] ?? xs = xs (x:xs) ?? ys = xs ?? [] ++ ys [] ?? xs = xs (x:xs) ?? ys = ys ?? xs ++ ys [] ?? xs = xs (x:xs) ?? ys = ys ?? ys ++ ys [] ?? xs = xs (x:xs) ?? ys = ys ?? [] ++ ys [] ?? xs = xs (x:xs) ?? ys = [] ?? xs ++ ys [] ?? xs = xs (x:xs) ?? ys = [] ?? ys ++ ys [] ?? xs = [] (x:xs) ?? ys = x:xs ?? xs [] ?? xs = [] (x:xs) ?? ys = x:xs ?? ys [] ?? xs = [] (x:xs) ?? ys = x:xs ?? [] [] ?? xs = [] (x:xs) ?? ys = x:ys ?? xs [] ?? xs = [] (x:xs) ?? ys = x:ys ?? ys [] ?? xs = [] (x:xs) ?? ys = x:ys ?? [] [] ?? xs = [] (x:xs) ?? ys = [x,] ?? xs [] ?? xs = [] (x:xs) ?? ys = [x,] ?? ys [] ?? xs = [] (x:xs) ?? ys = xs ++ xs ?? xs [] ?? xs = [] (x:xs) ?? ys = xs ++ xs ?? ys [] ?? xs = [] (x:xs) ?? ys = xs ++ xs ?? [] [] ?? xs = [] (x:xs) ?? ys = xs ++ ys ?? xs [] ?? xs = [] (x:xs) ?? ys = xs ++ ys ?? ys [] ?? xs = [] (x:xs) ?? ys = xs ++ ys ?? [] [] ?? xs = [] (x:xs) ?? ys = xs ++ [] ?? xs [] ?? xs = [] (x:xs) ?? ys = xs ++ [] ?? ys [] ?? xs = [] (x:xs) ?? ys = ys ++ xs ?? xs [] ?? xs = [] (x:xs) ?? ys = ys ++ xs ?? ys [] ?? xs = [] (x:xs) ?? ys = ys ++ xs ?? [] [] ?? xs = [] (x:xs) ?? ys = ys ++ ys ?? xs [] ?? xs = [] (x:xs) ?? ys = ys ++ ys ?? ys [] ?? xs = [] (x:xs) ?? ys = ys ++ ys ?? [] [] ?? xs = [] (x:xs) ?? ys = ys ++ [] ?? xs [] ?? xs = [] (x:xs) ?? ys = ys ++ [] ?? ys [] ?? xs = [] (x:xs) ?? ys = xs ?? xs ++ xs [] ?? xs = [] (x:xs) ?? ys = xs ?? ys ++ xs [] ?? xs = [] (x:xs) ?? ys = xs ?? [] ++ xs [] ?? xs = [] (x:xs) ?? ys = ys ?? xs ++ xs [] ?? xs = [] (x:xs) ?? ys = ys ?? ys ++ xs [] ?? xs = [] (x:xs) ?? ys = ys ?? [] ++ xs [] ?? xs = [] (x:xs) ?? ys = [] ?? xs ++ xs [] ?? xs = [] (x:xs) ?? ys = [] ?? ys ++ xs [] ?? xs = [] (x:xs) ?? ys = xs ?? xs ++ ys [] ?? xs = [] (x:xs) ?? ys = xs ?? ys ++ ys [] ?? xs = [] (x:xs) ?? ys = xs ?? [] ++ ys [] ?? xs = [] (x:xs) ?? ys = ys ?? xs ++ ys [] ?? xs = [] (x:xs) ?? ys = ys ?? ys ++ ys [] ?? xs = [] (x:xs) ?? ys = ys ?? [] ++ ys [] ?? xs = [] (x:xs) ?? ys = [] ?? xs ++ ys [] ?? xs = [] (x:xs) ?? ys = [] ?? ys ++ ys [] ?? xs = xs ++ xs (x:xs) ?? ys = xs ?? xs [] ?? xs = xs ++ xs (x:xs) ?? ys = xs ?? ys [] ?? xs = xs ++ xs (x:xs) ?? ys = xs ?? [] [] ?? xs = xs ++ xs (x:xs) ?? ys = ys ?? xs [] ?? xs = xs ++ xs (x:xs) ?? ys = ys ?? ys [] ?? xs = xs ++ xs (x:xs) ?? ys = ys ?? [] [] ?? xs = xs ++ xs (x:xs) ?? ys = [] ?? xs [] ?? xs = xs ++ xs (x:xs) ?? ys = [] ?? ys xs ?? [] = xs xs ?? (x:ys) = x:x:xs xs ?? [] = xs xs ?? (x:ys) = x:x:ys xs ?? [] = xs xs ?? (x:ys) = [x,x] xs ?? [] = xs xs ?? (x:ys) = x:(xs ++ xs) xs ?? [] = xs xs ?? (x:ys) = x:(xs ++ ys) xs ?? [] = xs xs ?? (x:ys) = x:(ys ++ xs) xs ?? [] = xs xs ?? (x:ys) = x:(ys ++ ys) xs ?? [] = xs xs ?? (x:ys) = xs ++ (x:xs) xs ?? [] = xs xs ?? (x:ys) = xs ++ (x:ys) xs ?? [] = xs xs ?? (x:ys) = xs ++ [x] xs ?? [] = xs xs ?? (x:ys) = xs ++ (xs ++ xs) xs ?? [] = xs xs ?? (x:ys) = xs ++ (xs ++ ys) xs ?? [] = xs xs ?? (x:ys) = xs ++ (ys ++ xs) xs ?? [] = xs xs ?? (x:ys) = xs ++ (ys ++ ys) xs ?? [] = xs xs ?? (x:ys) = ys ++ (x:xs) xs ?? [] = xs xs ?? (x:ys) = ys ++ (x:ys) xs ?? [] = xs xs ?? (x:ys) = ys ++ [x] xs ?? [] = xs xs ?? (x:ys) = ys ++ (xs ++ xs) xs ?? [] = xs xs ?? (x:ys) = ys ++ (xs ++ ys) xs ?? [] = xs xs ?? (x:ys) = ys ++ (ys ++ xs) xs ?? [] = xs xs ?? (x:ys) = ys ++ (ys ++ ys) xs ?? [] = [] xs ?? (x:ys) = x:x:xs xs ?? [] = [] xs ?? (x:ys) = x:x:ys xs ?? [] = [] xs ?? (x:ys) = [x,x] xs ?? [] = [] xs ?? (x:ys) = x:(xs ++ xs) xs ?? [] = [] xs ?? (x:ys) = x:(xs ++ ys) xs ?? [] = [] xs ?? (x:ys) = x:(ys ++ xs) xs ?? [] = [] xs ?? (x:ys) = x:(ys ++ ys) xs ?? [] = [] xs ?? (x:ys) = xs ++ (x:xs) xs ?? [] = [] xs ?? (x:ys) = xs ++ (x:ys) xs ?? [] = [] xs ?? (x:ys) = xs ++ [x] xs ?? [] = [] xs ?? (x:ys) = xs ++ (xs ++ xs) xs ?? [] = [] xs ?? (x:ys) = xs ++ (xs ++ ys) xs ?? [] = [] xs ?? (x:ys) = xs ++ (ys ++ xs) xs ?? [] = [] xs ?? (x:ys) = xs ++ (ys ++ ys) xs ?? [] = [] xs ?? (x:ys) = ys ++ (x:xs) xs ?? [] = [] xs ?? (x:ys) = ys ++ (x:ys) xs ?? [] = [] xs ?? (x:ys) = ys ++ [x] xs ?? [] = [] xs ?? (x:ys) = ys ++ (xs ++ xs) xs ?? [] = [] xs ?? (x:ys) = ys ++ (xs ++ ys) xs ?? [] = [] xs ?? (x:ys) = ys ++ (ys ++ xs) xs ?? [] = [] xs ?? (x:ys) = ys ++ (ys ++ ys) xs ?? [] = xs ++ xs xs ?? (x:ys) = x:xs xs ?? [] = xs ++ xs xs ?? (x:ys) = x:ys xs ?? [] = xs ++ xs xs ?? (x:ys) = [x] xs ?? [] = xs ++ xs xs ?? (x:ys) = xs ++ ys xs ?? [] = xs ++ xs xs ?? (x:ys) = ys ++ xs xs ?? [] = xs ++ xs xs ?? (x:ys) = ys ++ ys xs ?? [] = xs ++ (xs ++ xs) xs ?? (x:ys) = xs xs ?? [] = xs ++ (xs ++ xs) xs ?? (x:ys) = ys xs ?? [] = xs ++ (xs ++ xs) xs ?? (x:ys) = [] [] ?? xs = xs (x:xs) ?? ys = x:x:xs [] ?? xs = xs (x:xs) ?? ys = x:x:ys [] ?? xs = xs (x:xs) ?? ys = [x,x] [] ?? xs = xs (x:xs) ?? ys = x:(xs ++ xs) [] ?? xs = xs (x:xs) ?? ys = x:(xs ++ ys) [] ?? xs = xs (x:xs) ?? ys = x:(ys ++ xs) [] ?? xs = xs (x:xs) ?? ys = x:(ys ++ ys) [] ?? xs = xs (x:xs) ?? ys = xs ++ (x:xs) [] ?? xs = xs (x:xs) ?? ys = xs ++ (x:ys) [] ?? xs = xs (x:xs) ?? ys = xs ++ [x] [] ?? xs = xs (x:xs) ?? ys = xs ++ (xs ++ xs) [] ?? xs = xs (x:xs) ?? ys = xs ++ (xs ++ ys) [] ?? xs = xs (x:xs) ?? ys = xs ++ (ys ++ xs) [] ?? xs = xs (x:xs) ?? ys = xs ++ (ys ++ ys) [] ?? xs = xs (x:xs) ?? ys = ys ++ (x:xs) [] ?? xs = xs (x:xs) ?? ys = ys ++ (x:ys) [] ?? xs = xs (x:xs) ?? ys = ys ++ [x] [] ?? xs = xs (x:xs) ?? ys = ys ++ (xs ++ xs) [] ?? xs = xs (x:xs) ?? ys = ys ++ (xs ++ ys) [] ?? xs = xs (x:xs) ?? ys = ys ++ (ys ++ xs) [] ?? xs = xs (x:xs) ?? ys = ys ++ (ys ++ ys) [] ?? xs = [] (x:xs) ?? ys = x:x:xs [] ?? xs = [] (x:xs) ?? ys = x:x:ys [] ?? xs = [] (x:xs) ?? ys = [x,x] [] ?? xs = [] (x:xs) ?? ys = x:(xs ++ xs) [] ?? xs = [] (x:xs) ?? ys = x:(xs ++ ys) [] ?? xs = [] (x:xs) ?? ys = x:(ys ++ xs) [] ?? xs = [] (x:xs) ?? ys = x:(ys ++ ys) [] ?? xs = [] (x:xs) ?? ys = xs ++ (x:xs) [] ?? xs = [] (x:xs) ?? ys = xs ++ (x:ys) [] ?? xs = [] (x:xs) ?? ys = xs ++ [x] [] ?? xs = [] (x:xs) ?? ys = xs ++ (xs ++ xs) [] ?? xs = [] (x:xs) ?? ys = xs ++ (xs ++ ys) [] ?? xs = [] (x:xs) ?? ys = xs ++ (ys ++ xs) [] ?? xs = [] (x:xs) ?? ys = xs ++ (ys ++ ys) [] ?? xs = [] (x:xs) ?? ys = ys ++ (x:xs) [] ?? xs = [] (x:xs) ?? ys = ys ++ (x:ys) [] ?? xs = [] (x:xs) ?? ys = ys ++ [x] [] ?? xs = [] (x:xs) ?? ys = ys ++ (xs ++ xs) [] ?? xs = [] (x:xs) ?? ys = ys ++ (xs ++ ys) [] ?? xs = [] (x:xs) ?? ys = ys ++ (ys ++ xs) [] ?? xs = [] (x:xs) ?? ys = ys ++ (ys ++ ys) [] ?? xs = xs ++ xs (x:xs) ?? ys = x:xs [] ?? xs = xs ++ xs (x:xs) ?? ys = x:ys [] ?? xs = xs ++ xs (x:xs) ?? ys = [x] [] ?? xs = xs ++ xs (x:xs) ?? ys = xs ++ ys [] ?? xs = xs ++ xs (x:xs) ?? ys = ys ++ xs [] ?? xs = xs ++ xs (x:xs) ?? ys = ys ++ ys [] ?? xs = xs ++ (xs ++ xs) (x:xs) ?? ys = xs [] ?? xs = xs ++ (xs ++ xs) (x:xs) ?? ys = ys [] ?? xs = xs ++ (xs ++ xs) (x:xs) ?? ys = [] Candidates for: ton :: Bool -> Bool pruning with 39/49 rules [3,1,0,0,0,0,0,0,0] direct candidates, 0 duplicates [3,3,0,0,0,0,0,0,0] pattern candidates, 0 duplicates rules: not False == True not True == False p && p == p p || p == p not (not p) == p p && False == False p && True == p False && p == False True && p == p p || False == p p || True == True False || p == p True || p == True not (p && q) == not p || not q not (p && q) == not q || not p not (p || q) == not p && not q not (p || q) == not q && not p p && not p == False not p && p == False p || not p == True not p || p == True (p && q) && r == p && (q && r) (p && q) && r == q && (p && r) (p || q) || r == p || (q || r) (p || q) || r == q || (p || r) p && (p && q) == p && q p && (q && p) == p && q p && (q && p) == q && p p || (p || q) == p || q p || (q || p) == p || q p || (q || p) == q || p p && (p || q) == p p && (q || p) == p (p || q) && p == p (p || q) && q == q p || p && q == p p || q && p == p p && q || p == p p && q || q == q equations: q && p == p && q q || p == p || q q && (p && r) == p && (q && r) r && (p && q) == p && (q && r) r && (q && p) == p && (q && r) q || (p || r) == p || (q || r) r || (p || q) == p || (q || r) r || (q || p) == p || (q || r) (r || q) && p == p && (q || r) r && q || p == p || q && r direct candidates: ton p = p ton p = False ton p = True ton p = not p pattern candidates: ton p = p ton p = False ton p = True ton p = not p ton False = False ton True = True ton False = True ton True = False Candidates for: &| :: Bool -> Bool -> Bool pruning with 39/49 rules [4,2,4,8,4,32,36,112,264] direct candidates, 0 duplicates [4,14,30,8,4,32,36,112,264] pattern candidates, 0 duplicates rules: not False == True not True == False p && p == p p || p == p not (not p) == p p && False == False p && True == p False && p == False True && p == p p || False == p p || True == True False || p == p True || p == True not (p && q) == not p || not q not (p && q) == not q || not p not (p || q) == not p && not q not (p || q) == not q && not p p && not p == False not p && p == False p || not p == True not p || p == True (p && q) && r == p && (q && r) (p && q) && r == q && (p && r) (p || q) || r == p || (q || r) (p || q) || r == q || (p || r) p && (p && q) == p && q p && (q && p) == p && q p && (q && p) == q && p p || (p || q) == p || q p || (q || p) == p || q p || (q || p) == q || p p && (p || q) == p p && (q || p) == p (p || q) && p == p (p || q) && q == q p || p && q == p p || q && p == p p && q || p == p p && q || q == q equations: q && p == p && q q || p == p || q q && (p && r) == p && (q && r) r && (p && q) == p && (q && r) r && (q && p) == p && (q && r) q || (p || r) == p || (q || r) r || (p || q) == p || (q || r) r || (q || p) == p || (q || r) (r || q) && p == p && (q || r) r && q || p == p || q && r direct candidates: p &| q = p p &| q = q p &| q = False p &| q = True p &| q = not p p &| q = not q p &| q = p && q p &| q = q && p p &| q = p || q p &| q = q || p p &| q = not p && q p &| q = not q && p p &| q = not p || q p &| q = not q || p p &| q = p && not q p &| q = q && not p p &| q = p || not q p &| q = q || not p p &| q = not p && not q p &| q = not q && not p p &| q = not p || not q p &| q = not q || not p p &| q = p && (not p && q) p &| q = p && (not p || q) p &| q = p && (q && not p) p &| q = p && (q || not p) p &| q = q && (not q && p) p &| q = q && (not q || p) p &| q = q && (p && not q) p &| q = q && (p || not q) p &| q = p || not p && q p &| q = p || (not p || q) p &| q = p || q && not p p &| q = p || (q || not p) p &| q = q || not q && p p &| q = q || (not q || p) p &| q = q || p && not q p &| q = q || (p || not q) p &| q = not p && (p || q) p &| q = not p && (q || p) p &| q = not q && (p || q) p &| q = not q && (q || p) p &| q = not p || p && q p &| q = not p || q && p p &| q = not q || p && q p &| q = not q || q && p p &| q = (p || q) && not p p &| q = (p || q) && not q p &| q = (q || p) && not p p &| q = (q || p) && not q p &| q = p && q || not p p &| q = p && q || not q p &| q = q && p || not p p &| q = q && p || not q pattern candidates: p &| q = p p &| q = q p &| q = False p &| q = True p &| q = not p p &| q = not q p &| False = p p &| True = False p &| False = p p &| True = True p &| False = False p &| True = p p &| False = False p &| True = True p &| False = True p &| True = p p &| False = True p &| True = False False &| p = p True &| p = False False &| p = p True &| p = True False &| p = False True &| p = p False &| p = False True &| p = True False &| p = True True &| p = p False &| p = True True &| p = False p &| q = p && q p &| q = q && p p &| q = p || q p &| q = q || p p &| False = p p &| True = not p p &| False = False p &| True = not p p &| False = True p &| True = not p p &| False = not p p &| True = p p &| False = not p p &| True = False p &| False = not p p &| True = True False &| p = p True &| p = not p False &| p = False True &| p = not p False &| p = True True &| p = not p False &| p = not p True &| p = p False &| p = not p True &| p = False False &| p = not p True &| p = True False &| False = False False &| True = False True &| False = False True &| True = True False &| False = False False &| True = False True &| False = True True &| True = False False &| False = False False &| True = False True &| False = True True &| True = True False &| False = False False &| True = True True &| False = False True &| True = False False &| False = False False &| True = True True &| False = False True &| True = True False &| False = False False &| True = True True &| False = True True &| True = False False &| False = False False &| True = True True &| False = True True &| True = True False &| False = True False &| True = False True &| False = False True &| True = False False &| False = True False &| True = False True &| False = False True &| True = True False &| False = True False &| True = False True &| False = True True &| True = False False &| False = True False &| True = False True &| False = True True &| True = True False &| False = True False &| True = True True &| False = False True &| True = False False &| False = True False &| True = True True &| False = False True &| True = True False &| False = True False &| True = True True &| False = True True &| True = False p &| q = not p && q p &| q = not q && p p &| q = not p || q p &| q = not q || p p &| q = p && not q p &| q = q && not p p &| q = p || not q p &| q = q || not p p &| q = not p && not q p &| q = not q && not p p &| q = not p || not q p &| q = not q || not p p &| q = p && (not p && q) p &| q = p && (not p || q) p &| q = p && (q && not p) p &| q = p && (q || not p) p &| q = q && (not q && p) p &| q = q && (not q || p) p &| q = q && (p && not q) p &| q = q && (p || not q) p &| q = p || not p && q p &| q = p || (not p || q) p &| q = p || q && not p p &| q = p || (q || not p) p &| q = q || not q && p p &| q = q || (not q || p) p &| q = q || p && not q p &| q = q || (p || not q) p &| q = not p && (p || q) p &| q = not p && (q || p) p &| q = not q && (p || q) p &| q = not q && (q || p) p &| q = not p || p && q p &| q = not p || q && p p &| q = not q || p && q p &| q = not q || q && p p &| q = (p || q) && not p p &| q = (p || q) && not q p &| q = (q || p) && not p p &| q = (q || p) && not q p &| q = p && q || not p p &| q = p && q || not q p &| q = q && p || not p p &| q = q && p || not q