code-conjure-0.5.6: bench/redundants.out
Redundant candidates for: foo :: Int -> Int
pruning with 15/35 rules
[3,4,12,32,54] candidates
68/105 unique candidates
37/105 redundant candidates
rules:
x * y == x + y
x * y == y + x
x - x == 0
x + 0 == x
0 + x == x
x - 0 == x
(x + y) + z == x + (y + z)
(x + y) + z == y + (x + z)
x - (y - z) == z + (x - y)
(x - y) - z == x - (y + z)
(x - y) - z == x - (z + y)
(x + y) - z == x + (y - z)
(x + y) - z == y + (x - z)
x + (y - x) == y
(x - y) + y == x
equations:
y + x == x + y
y + (x + z) == x + (y + z)
z + (x + y) == x + (y + z)
z + (y + x) == x + (y + z)
y + (x - z) == x + (y - z)
(x - z) + y == x + (y - z)
(z - y) + x == (x - y) + z
y - (x + y) == 0 - x
y - (y + x) == 0 - x
z - (y + z) == x - (x + y)
z - (y + z) == x - (y + x)
z - (z + y) == x - (x + y)
z - (z + y) == x - (y + x)
x + (0 - y) == x - y
(0 - y) + x == x - y
x - (x + 1) == 0 - 1
x - (1 + x) == 0 - 1
y - (y + 1) == x - (x + 1)
y - (y + 1) == x - (1 + x)
y - (1 + y) == x - (1 + x)
class of 4 equivalent candidates:
foo x = x
foo 0 = 0
foo x = x
foo 1 = 1
foo x = x
foo 0 = 0
foo 1 = 1
foo x = x
class of 2 equivalent candidates:
foo 0 = 0
foo x = 1
foo 0 = 0
foo 1 = 1
foo x = 1
class of 2 equivalent candidates:
foo 0 = 1
foo x = x
foo 0 = 1
foo 1 = 1
foo x = x
class of 2 equivalent candidates:
foo 0 = 1
foo x = 0
foo 0 = 1
foo 1 = 0
foo x = 0
class of 2 equivalent candidates:
foo x = x + x
foo 0 = 0
foo x = x + x
class of 4 equivalent candidates:
foo x = x + 1
foo x = 1 + x
foo 0 = 1
foo x = x + 1
foo 0 = 1
foo x = 1 + x
class of 4 equivalent candidates:
foo x = x - 1
foo x = (0 - 1) + x
foo x = x + (0 - 1)
foo 1 = 0
foo x = x - 1
class of 5 equivalent candidates:
foo x = 0 - x
foo 0 = 0
foo x = 0 - x
foo x = x - (x + x)
foo x = 1 - (x + 1)
foo x = 1 - (1 + x)
class of 4 equivalent candidates:
foo x = 0 - 1
foo x = x - (x + 1)
foo x = x - (1 + x)
foo x = 1 - (1 + 1)
class of 5 equivalent candidates:
foo x = 1 - x
foo 0 = 1
foo x = 1 - x
foo x = (0 - x) + 1
foo x = 1 + (0 - x)
foo 1 = 0
foo x = 1 - x
class of 2 equivalent candidates:
foo 1 = 0
foo x = x
foo 0 = 0
foo 1 = 0
foo x = x
class of 2 equivalent candidates:
foo 1 = 0
foo x = 1
foo 0 = 1
foo 1 = 0
foo x = 1
class of 2 equivalent candidates:
foo 1 = 1
foo x = 0
foo 0 = 0
foo 1 = 1
foo x = 0
class of 2 equivalent candidates:
foo 0 = 0
foo x = x + 1
foo 0 = 0
foo x = 1 + x
class of 2 equivalent candidates:
foo x = (x - 1) + x
foo x = x + (x - 1)
class of 2 equivalent candidates:
foo x = (1 - x) + 1
foo x = 1 + (1 - x)
class of 3 equivalent candidates:
foo x = x + (x + 1)
foo x = x + (1 + x)
foo x = 1 + (x + x)
class of 3 equivalent candidates:
foo x = x + (1 + 1)
foo x = 1 + (x + 1)
foo x = 1 + (1 + x)
class of 2 equivalent candidates:
foo x = 0 - (x + 1)
foo x = 0 - (1 + x)
class of 2 equivalent candidates:
foo 1 = 0
foo x = x + 1
foo 1 = 0
foo x = 1 + x
class of 2 equivalent candidates:
foo 1 = 1
foo x = x + 1
foo 1 = 1
foo x = 1 + x
Redundant candidates for: ? :: Int -> Int -> Int
pruning with 10/23 rules
[3,10,40,116,338] candidates
363/507 unique candidates
144/507 redundant candidates
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)
class of 2 equivalent candidates:
x ? y = x
0 ? x = 0
x ? y = x
class of 2 equivalent candidates:
x ? y = y
x ? 0 = 0
x ? y = y
class of 3 equivalent candidates:
x ? y = 0
x ? 0 = 0
x ? y = dec x ? 0
0 ? x = 0
x ? y = 0 ? dec y
class of 4 equivalent candidates:
x ? y = dec x
x ? y = dec 0 + x
x ? y = x + dec 0
0 ? x = dec 0
x ? y = dec x
class of 4 equivalent candidates:
x ? y = dec y
x ? y = dec 0 + y
x ? y = y + dec 0
x ? 0 = dec 0
x ? y = dec y
class of 2 equivalent candidates:
x ? 0 = x
x ? y = y
0 ? 0 = 0
0 ? x = x
x ? 0 = x
x ? y = y
class of 2 equivalent candidates:
x ? 0 = x
x ? y = 0
0 ? 0 = 0
0 ? x = 0
x ? 0 = x
x ? y = 0
class of 2 equivalent candidates:
x ? 0 = 0
x ? y = x
0 ? 0 = 0
0 ? x = 0
x ? 0 = 0
x ? y = x
class of 2 equivalent candidates:
0 ? x = x
x ? y = 0
0 ? 0 = 0
0 ? x = x
x ? 0 = 0
x ? y = 0
class of 2 equivalent candidates:
0 ? x = 0
x ? y = y
0 ? 0 = 0
0 ? x = 0
x ? 0 = 0
x ? y = y
class of 2 equivalent candidates:
x ? y = x + x
0 ? x = 0
x ? y = x + x
class of 8 equivalent candidates:
x ? y = x + y
x ? y = y + x
x ? 0 = x
x ? y = x + y
x ? 0 = x
x ? y = y + x
0 ? x = x
x ? y = x + y
0 ? x = x
x ? y = y + 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
class of 2 equivalent candidates:
x ? y = y + y
x ? 0 = 0
x ? y = y + y
class of 5 equivalent candidates:
x ? y = dec (dec x)
x ? y = dec (dec 0) + x
x ? y = x + dec (dec 0)
x ? y = dec x + dec 0
x ? y = dec 0 + dec x
class of 5 equivalent candidates:
x ? y = dec (dec y)
x ? y = dec (dec 0) + y
x ? y = y + dec (dec 0)
x ? y = dec y + dec 0
x ? y = dec 0 + dec y
class of 2 equivalent candidates:
x ? y = dec (dec 0)
x ? y = dec 0 + dec 0
class of 5 equivalent candidates:
x ? 0 = x
x ? y = dec x
x ? 0 = x
x ? y = dec x ? 0
x ? 0 = x
x ? y = dec 0 + x
x ? 0 = x
x ? y = x + dec 0
0 ? 0 = 0
0 ? x = dec 0
x ? 0 = x
x ? y = dec x
class of 4 equivalent candidates:
x ? 0 = x
x ? y = dec y
x ? 0 = x
x ? y = dec 0 + y
x ? 0 = x
x ? y = y + dec 0
0 ? 0 = 0
0 ? x = dec x
x ? 0 = x
x ? y = dec y
class of 2 equivalent candidates:
x ? 0 = x
x ? y = dec 0
0 ? 0 = 0
0 ? x = dec 0
x ? 0 = x
x ? y = dec 0
class of 4 equivalent candidates:
x ? 0 = 0
x ? y = dec x
x ? 0 = 0
x ? y = dec 0 + x
x ? 0 = 0
x ? y = x + dec 0
0 ? 0 = 0
0 ? x = dec 0
x ? 0 = 0
x ? y = dec x
class of 3 equivalent candidates:
x ? 0 = 0
x ? y = dec y
x ? 0 = 0
x ? y = dec 0 + y
x ? 0 = 0
x ? y = y + dec 0
class of 4 equivalent candidates:
x ? 0 = dec x
x ? y = x
x ? 0 = dec 0 + x
x ? y = x
x ? 0 = x + dec 0
x ? y = x
0 ? 0 = dec 0
0 ? x = 0
x ? 0 = dec x
x ? y = x
class of 4 equivalent candidates:
x ? 0 = dec x
x ? y = y
x ? 0 = dec 0 + x
x ? y = y
x ? 0 = x + dec 0
x ? y = y
0 ? 0 = dec 0
0 ? x = x
x ? 0 = dec x
x ? y = y
class of 4 equivalent candidates:
x ? 0 = dec x
x ? y = 0
x ? 0 = dec 0 + x
x ? y = 0
x ? 0 = x + dec 0
x ? y = 0
0 ? 0 = dec 0
0 ? x = 0
x ? 0 = dec x
x ? y = 0
class of 2 equivalent candidates:
x ? 0 = dec 0
x ? y = x
0 ? 0 = dec 0
0 ? x = 0
x ? 0 = dec 0
x ? y = x
class of 4 equivalent candidates:
0 ? x = x
x ? y = dec x
0 ? x = x
x ? y = dec 0 + x
0 ? x = x
x ? y = x + dec 0
0 ? 0 = 0
0 ? x = x
x ? 0 = dec x
x ? y = dec x
class of 5 equivalent candidates:
0 ? x = x
x ? y = dec y
0 ? x = x
x ? y = 0 ? dec y
0 ? x = x
x ? y = dec 0 + y
0 ? x = x
x ? y = y + dec 0
0 ? 0 = 0
0 ? x = x
x ? 0 = dec 0
x ? y = dec y
class of 2 equivalent candidates:
0 ? x = x
x ? y = dec 0
0 ? 0 = 0
0 ? x = x
x ? 0 = dec 0
x ? y = dec 0
class of 3 equivalent candidates:
0 ? x = 0
x ? y = dec x
0 ? x = 0
x ? y = dec 0 + x
0 ? x = 0
x ? y = x + dec 0
class of 4 equivalent candidates:
0 ? x = 0
x ? y = dec y
0 ? x = 0
x ? y = dec 0 + y
0 ? x = 0
x ? y = y + dec 0
0 ? 0 = 0
0 ? x = 0
x ? 0 = dec 0
x ? y = dec y
class of 4 equivalent candidates:
0 ? x = dec x
x ? y = x
0 ? x = dec 0 + x
x ? y = x
0 ? x = x + dec 0
x ? y = x
0 ? 0 = dec 0
0 ? x = dec x
x ? 0 = x
x ? y = x
class of 4 equivalent candidates:
0 ? x = dec x
x ? y = y
0 ? x = dec 0 + x
x ? y = y
0 ? x = x + dec 0
x ? y = y
0 ? 0 = dec 0
0 ? x = dec x
x ? 0 = 0
x ? y = y
class of 4 equivalent candidates:
0 ? x = dec x
x ? y = 0
0 ? x = dec 0 + x
x ? y = 0
0 ? x = x + dec 0
x ? y = 0
0 ? 0 = dec 0
0 ? x = dec x
x ? 0 = 0
x ? y = 0
class of 2 equivalent candidates:
0 ? x = dec 0
x ? y = y
0 ? 0 = dec 0
0 ? x = dec 0
x ? 0 = 0
x ? y = y
class of 2 equivalent candidates:
x ? y = dec x + x
x ? y = x + dec x
class of 4 equivalent candidates:
x ? y = dec x + y
x ? y = dec y + x
x ? y = x + dec y
x ? y = y + dec x
class of 2 equivalent candidates:
x ? y = dec y + y
x ? y = y + dec y
class of 2 equivalent candidates:
x ? 0 = x
x ? y = x + x
0 ? 0 = 0
0 ? x = 0
x ? 0 = x
x ? y = x + x
class of 2 equivalent candidates:
x ? 0 = 0
x ? y = x + x
0 ? 0 = 0
0 ? x = 0
x ? 0 = 0
x ? y = x + x
class of 4 equivalent candidates:
x ? 0 = 0
x ? y = x + y
x ? 0 = 0
x ? y = y + 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
class of 2 equivalent candidates:
x ? 0 = x + x
x ? y = x
0 ? 0 = 0
0 ? x = 0
x ? 0 = x + x
x ? y = x
class of 2 equivalent candidates:
x ? 0 = x + x
x ? y = y
0 ? 0 = 0
0 ? x = x
x ? 0 = x + x
x ? y = y
class of 2 equivalent candidates:
x ? 0 = x + x
x ? y = 0
0 ? 0 = 0
0 ? x = 0
x ? 0 = x + x
x ? y = 0
class of 2 equivalent candidates:
0 ? x = x
x ? y = y + y
0 ? 0 = 0
0 ? x = x
x ? 0 = 0
x ? y = y + y
class of 4 equivalent candidates:
0 ? x = 0
x ? y = x + y
0 ? x = 0
x ? y = y + 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
class of 2 equivalent candidates:
0 ? x = 0
x ? y = y + y
0 ? 0 = 0
0 ? x = 0
x ? 0 = 0
x ? y = y + y
class of 2 equivalent candidates:
0 ? x = x + x
x ? y = x
0 ? 0 = 0
0 ? x = x + x
x ? 0 = x
x ? y = x
class of 2 equivalent candidates:
0 ? x = x + x
x ? y = y
0 ? 0 = 0
0 ? x = x + x
x ? 0 = 0
x ? y = y
class of 2 equivalent candidates:
0 ? x = x + x
x ? y = 0
0 ? 0 = 0
0 ? x = x + x
x ? 0 = 0
x ? y = 0
class of 3 equivalent candidates:
x ? y = dec (dec x) + x
x ? y = x + dec (dec x)
x ? y = dec x + dec x
class of 6 equivalent candidates:
x ? y = dec (dec x) + y
x ? y = dec (dec y) + x
x ? y = x + dec (dec y)
x ? y = y + dec (dec x)
x ? y = dec x + dec y
x ? y = dec y + dec x
class of 3 equivalent candidates:
x ? y = dec (dec y) + y
x ? y = y + dec (dec y)
x ? y = dec y + dec y
class of 3 equivalent candidates:
x ? y = x + (x + y)
x ? y = x + (y + x)
x ? y = y + (x + x)
class of 3 equivalent candidates:
x ? y = x + (y + y)
x ? y = y + (x + y)
x ? y = y + (y + x)
class of 2 equivalent candidates:
x ? 0 = x
x ? y = dec x + x
x ? 0 = x
x ? y = x + dec x
class of 4 equivalent candidates:
x ? 0 = x
x ? y = dec x + y
x ? 0 = x
x ? y = dec y + x
x ? 0 = x
x ? y = x + dec y
x ? 0 = x
x ? y = y + dec x
class of 2 equivalent candidates:
x ? 0 = x
x ? y = dec y + y
x ? 0 = x
x ? y = y + dec y
class of 2 equivalent candidates:
x ? 0 = 0
x ? y = dec x + x
x ? 0 = 0
x ? y = x + dec x
class of 4 equivalent candidates:
x ? 0 = 0
x ? y = dec x + y
x ? 0 = 0
x ? y = dec y + x
x ? 0 = 0
x ? y = x + dec y
x ? 0 = 0
x ? y = y + dec x
class of 2 equivalent candidates:
x ? 0 = 0
x ? y = dec y + y
x ? 0 = 0
x ? y = y + dec y
class of 2 equivalent candidates:
x ? 0 = dec x
x ? y = x + y
x ? 0 = dec x
x ? y = y + x
class of 2 equivalent candidates:
x ? 0 = dec 0
x ? y = x + y
x ? 0 = dec 0
x ? y = y + x
class of 2 equivalent candidates:
x ? 0 = dec x + x
x ? y = x
x ? 0 = x + dec x
x ? y = x
class of 2 equivalent candidates:
x ? 0 = dec x + x
x ? y = y
x ? 0 = x + dec x
x ? y = y
class of 2 equivalent candidates:
x ? 0 = dec x + x
x ? y = 0
x ? 0 = x + dec x
x ? y = 0
class of 2 equivalent candidates:
0 ? x = x
x ? y = dec x + x
0 ? x = x
x ? y = x + dec x
class of 4 equivalent candidates:
0 ? x = x
x ? y = dec x + y
0 ? x = x
x ? y = dec y + x
0 ? x = x
x ? y = x + dec y
0 ? x = x
x ? y = y + dec x
class of 2 equivalent candidates:
0 ? x = x
x ? y = dec y + y
0 ? x = x
x ? y = y + dec y
class of 2 equivalent candidates:
0 ? x = 0
x ? y = dec x + x
0 ? x = 0
x ? y = x + dec x
class of 4 equivalent candidates:
0 ? x = 0
x ? y = dec x + y
0 ? x = 0
x ? y = dec y + x
0 ? x = 0
x ? y = x + dec y
0 ? x = 0
x ? y = y + dec x
class of 2 equivalent candidates:
0 ? x = 0
x ? y = dec y + y
0 ? x = 0
x ? y = y + dec y
class of 2 equivalent candidates:
0 ? x = dec x
x ? y = x + y
0 ? x = dec x
x ? y = y + x
class of 2 equivalent candidates:
0 ? x = dec 0
x ? y = x + y
0 ? x = dec 0
x ? y = y + x
class of 2 equivalent candidates:
0 ? x = dec x + x
x ? y = x
0 ? x = x + dec x
x ? y = x
class of 2 equivalent candidates:
0 ? x = dec x + x
x ? y = y
0 ? x = x + dec x
x ? y = y
class of 2 equivalent candidates:
0 ? x = dec x + x
x ? y = 0
0 ? x = x + dec x
x ? y = 0
class of 2 equivalent candidates:
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
Redundant candidates for: goo :: [Int] -> [Int]
pruning with 4/4 rules
[2,1,2,3,4] candidates
9/12 unique candidates
3/12 redundant candidates
rules:
xs ++ [] == xs
[] ++ xs == xs
(xs ++ ys) ++ zs == xs ++ (ys ++ zs)
(x:xs) ++ ys == x:(xs ++ ys)
class of 3 equivalent candidates:
goo xs = xs
goo [] = []
goo (x:xs) = x:xs
goo [] = []
goo (x:xs) = x:goo xs
class of 2 equivalent candidates:
goo xs = []
goo [] = []
goo (x:xs) = goo xs
Redundant candidates for: ?? :: [Int] -> [Int] -> [Int]
pruning with 4/4 rules
[3,7,13,66,152] candidates
161/241 unique candidates
80/241 redundant candidates
rules:
xs ++ [] == xs
[] ++ xs == xs
(xs ++ ys) ++ zs == xs ++ (ys ++ zs)
(x:xs) ++ ys == x:(xs ++ ys)
class of 4 equivalent candidates:
xs ?? ys = xs
xs ?? [] = xs
xs ?? (x:ys) = xs ?? ys
xs ?? [] = xs
xs ?? (x:ys) = xs ?? []
[] ?? xs = []
(x:xs) ?? ys = x:xs
class of 4 equivalent candidates:
xs ?? ys = ys
[] ?? xs = xs
(x:xs) ?? ys = xs ?? ys
[] ?? xs = xs
(x:xs) ?? ys = [] ?? ys
xs ?? [] = []
xs ?? (x:ys) = x:ys
class of 29 equivalent candidates:
xs ?? ys = []
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 = []
(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 ?? []
[] ?? xs = []
(x:xs) ?? ys = [] ?? xs
[] ?? xs = []
(x:xs) ?? ys = [] ?? ys
[] ?? [] = []
[] ?? (x:xs) = xs ?? xs
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = []
[] ?? [] = []
[] ?? (x:xs) = xs ?? []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = []
[] ?? [] = []
[] ?? (x:xs) = [] ?? xs
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = []
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = xs ?? xs
(x:xs) ?? (y:ys) = []
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = xs ?? []
(x:xs) ?? (y:ys) = []
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = [] ?? xs
(x:xs) ?? (y:ys) = []
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = xs ?? xs
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = xs ?? ys
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = xs ?? []
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = ys ?? xs
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = ys ?? ys
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = ys ?? []
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = [] ?? xs
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = [] ?? ys
class of 3 equivalent candidates:
xs ?? [] = xs
xs ?? (x:ys) = ys
xs ?? [] = xs
xs ?? (x:ys) = ys ?? []
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = x:xs
(x:xs) ?? (y:ys) = ys
class of 5 equivalent candidates:
xs ?? [] = xs
xs ?? (x:ys) = []
xs ?? [] = xs
xs ?? (x:ys) = ys ?? ys
xs ?? [] = xs
xs ?? (x:ys) = [] ?? xs
xs ?? [] = xs
xs ?? (x:ys) = [] ?? ys
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = x:xs
(x:xs) ?? (y:ys) = []
class of 2 equivalent candidates:
xs ?? [] = []
xs ?? (x:ys) = xs
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = x:xs
class of 2 equivalent candidates:
xs ?? [] = []
xs ?? (x:ys) = ys
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = xs ?? []
(x:xs) ?? (y:ys) = ys
class of 5 equivalent candidates:
[] ?? xs = xs
(x:xs) ?? ys = []
[] ?? xs = xs
(x:xs) ?? ys = xs ?? xs
[] ?? xs = xs
(x:xs) ?? ys = xs ?? []
[] ?? xs = xs
(x:xs) ?? ys = ys ?? []
[] ?? [] = []
[] ?? (x:xs) = x:xs
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = []
class of 2 equivalent candidates:
[] ?? xs = []
(x:xs) ?? ys = xs
[] ?? [] = []
[] ?? (x:xs) = [] ?? xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = xs
class of 2 equivalent candidates:
[] ?? xs = []
(x:xs) ?? ys = ys
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = y:ys
class of 3 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = []
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = xs ?? xs
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = ys ?? ys
class of 2 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = xs
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = xs ?? []
(x:xs) ?? (y:ys) = xs
class of 7 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = []
(x:xs) ?? (y: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) ?? [] = []
(x:xs) ?? (y:ys) = xs ?? xs
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = xs ?? []
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = ys ?? ys
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = ys ?? []
class of 2 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = ys
[] ?? [] = []
[] ?? (x:xs) = [] ?? xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = ys
class of 7 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = []
[] ?? [] = []
[] ?? (x:xs) = xs ?? xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = []
[] ?? [] = []
[] ?? (x:xs) = [] ?? xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = []
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = xs ?? xs
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = ys ?? ys
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = [] ?? xs
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = [] ?? ys
class of 5 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = xs
[] ?? [] = []
[] ?? (x:xs) = xs ?? []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = xs
[] ?? [] = []
[] ?? (x:xs) = [] ?? xs
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = xs
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = xs ?? []
(x:xs) ?? (y:ys) = xs
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = [] ?? xs
(x:xs) ?? (y:ys) = xs
class of 5 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = ys
[] ?? [] = []
[] ?? (x:xs) = xs ?? []
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = ys
[] ?? [] = []
[] ?? (x:xs) = [] ?? xs
(x:xs) ?? [] = []
(x:xs) ?? (y:ys) = ys
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = xs ?? []
(x:xs) ?? (y:ys) = ys
[] ?? [] = []
[] ?? (x:xs) = []
(x:xs) ?? [] = [] ?? xs
(x:xs) ?? (y:ys) = ys
class of 2 equivalent candidates:
[] ?? xs = xs
(x:xs) ?? ys = [] ?? xs
[] ?? [] = []
[] ?? (x:xs) = x:xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = xs
class of 2 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = xs ?? ys
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = ys ?? xs
class of 2 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = xs ?? []
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = [] ?? xs
class of 2 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = ys ?? []
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = [] ?? ys
class of 2 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = xs ?? xs
(x:xs) ?? (y:ys) = xs
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = [] ?? xs
(x:xs) ?? (y:ys) = xs
class of 2 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = xs ?? xs
(x:xs) ?? (y:ys) = ys
[] ?? [] = []
[] ?? (x:xs) = xs
(x:xs) ?? [] = [] ?? xs
(x:xs) ?? (y:ys) = ys
class of 2 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = xs ?? xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = xs
[] ?? [] = []
[] ?? (x:xs) = xs ?? []
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = xs
class of 2 equivalent candidates:
[] ?? [] = []
[] ?? (x:xs) = xs ?? xs
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = ys
[] ?? [] = []
[] ?? (x:xs) = xs ?? []
(x:xs) ?? [] = xs
(x:xs) ?? (y:ys) = ys
Redundant candidates for: ton :: Bool -> Bool
pruning with 39/49 rules
[3,3,0,0,0] candidates
4/6 unique candidates
2/6 redundant candidates
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
class of 2 equivalent candidates:
ton p = p
ton False = False
ton True = True
class of 2 equivalent candidates:
ton p = not p
ton False = True
ton True = False
Redundant candidates for: &| :: Bool -> Bool -> Bool
pruning with 39/49 rules
[4,14,26,8,4] candidates
16/56 unique candidates
40/56 redundant candidates
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
class of 2 equivalent candidates:
p &| q = p
False &| p = False
True &| p = True
class of 2 equivalent candidates:
p &| q = q
p &| False = False
p &| True = True
class of 2 equivalent candidates:
p &| q = not p
False &| p = True
True &| p = False
class of 2 equivalent candidates:
p &| q = not q
p &| False = True
p &| True = False
class of 5 equivalent candidates:
p &| False = p
p &| True = False
False &| p = False
True &| p = not p
False &| False = False
False &| True = False
True &| False = True
True &| True = False
p &| q = not q && p
p &| q = p && not q
class of 5 equivalent candidates:
p &| False = p
p &| True = True
False &| p = p
True &| p = True
p &| q = p || q
p &| q = q || p
False &| False = False
False &| True = True
True &| False = True
True &| True = True
class of 5 equivalent candidates:
p &| False = False
p &| True = p
False &| p = False
True &| p = p
p &| q = p && q
p &| q = q && p
False &| False = False
False &| True = False
True &| False = False
True &| True = True
class of 5 equivalent candidates:
p &| False = True
p &| True = p
False &| p = not p
True &| p = True
False &| False = True
False &| True = False
True &| False = True
True &| True = True
p &| q = not q || p
p &| q = p || not q
class of 5 equivalent candidates:
False &| p = p
True &| p = False
p &| False = False
p &| True = not p
False &| False = False
False &| True = True
True &| False = False
True &| True = False
p &| q = not p && q
p &| q = q && not p
class of 5 equivalent candidates:
False &| p = True
True &| p = p
p &| False = not p
p &| True = True
False &| False = True
False &| True = True
True &| False = False
True &| True = True
p &| q = not p || q
p &| q = q || not p
class of 3 equivalent candidates:
p &| False = p
p &| True = not p
False &| p = p
True &| p = not p
False &| False = False
False &| True = True
True &| False = True
True &| True = False
class of 5 equivalent candidates:
p &| False = True
p &| True = not p
False &| p = True
True &| p = not p
False &| False = True
False &| True = True
True &| False = True
True &| True = False
p &| q = not p || not q
p &| q = not q || not p
class of 3 equivalent candidates:
p &| False = not p
p &| True = p
False &| p = not p
True &| p = p
False &| False = True
False &| True = False
True &| False = False
True &| True = True
class of 5 equivalent candidates:
p &| False = not p
p &| True = False
False &| p = not p
True &| p = False
False &| False = True
False &| True = False
True &| False = False
True &| True = False
p &| q = not p && not q
p &| q = not q && not p