code-conjure-0.4.2: bench/candidates.out

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

[] ?? []  =  []
[] ?? (x:xs)  =  [] ?? xs
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  ys

[] ?? []  =  []
[] ?? (x:xs)  =  xs ?? xs
(x: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 ?? 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)  =  xs ?? 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)  =  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
(x:xs) ?? (y:ys)  =  xs ?? xs

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  xs ?? ys

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  xs ?? []

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  ys ?? xs

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  ys ?? ys

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  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 ?? 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

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs ?? 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

[] ?? []  =  []
[] ?? (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

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)

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  x:xs

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  x:ys

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  [x]

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  y:xs

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  y:ys

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  [y]

[] ?? []  =  []
[] ?? (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)  =  ys ++ xs

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  ys ++ ys

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  x:xs

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  x:ys

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  [x]

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  y:xs

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  y:ys

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  [y]

[] ?? []  =  []
[] ?? (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)  =  ys ++ xs

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  ys ++ ys

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  x:xs
(x:xs) ?? (y:ys)  =  xs

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  x:xs
(x:xs) ?? (y:ys)  =  ys

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  x:xs
(x:xs) ?? (y:ys)  =  []

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  [x]
(x:xs) ?? (y:ys)  =  xs

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  [x]
(x:xs) ?? (y:ys)  =  ys

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  [x]
(x:xs) ?? (y:ys)  =  []

[] ?? []  =  []
[] ?? (x:xs)  =  xs
(x:xs) ?? []  =  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 ++ xs
(x:xs) ?? (y:ys)  =  []

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  x:xs

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  x:ys

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  [x]

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  y:xs

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  y:ys

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  [y]

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  xs ++ xs

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  xs ++ ys

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  ys ++ xs

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  xs
(x:xs) ?? (y:ys)  =  ys ++ ys

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  x:xs

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  x:ys

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  [x]

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  y:xs

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  y:ys

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  [y]

[] ?? []  =  []
[] ?? (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)  =  ys ++ xs

[] ?? []  =  []
[] ?? (x:xs)  =  []
(x:xs) ?? []  =  []
(x:xs) ?? (y:ys)  =  ys ++ 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: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