code-conjure 0.4.2 → 0.4.4

raw patch · 66 files changed

+12642/−7826 lines, 66 filesdep ~expressdep ~speculatePVP: major bump suggested

API removals or changes: PVP suggests a major version bump

Dependency ranges changed: express, speculate

API changes (from Hackage documentation)

Files

• .gitignore +2/−0
• Makefile +2/−0
• README.md +9/−8
• TODO.md +10/−8
• bench/candidates.hs +1/−1
• bench/candidates.out +9723/−7483
• bench/gps.hs +601/−0
• bench/gps.out +334/−14
• bench/gps2.hs +797/−0
• bench/gps2.out +349/−0
• bench/ill-hit.out +6/−6
• bench/lowtests.out +1/−1
• bench/p12.out +4/−4
• bench/runtime/zero/bench/candidates.runtime +1/−1
• bench/runtime/zero/bench/gps.runtime +1/−1
• bench/runtime/zero/bench/gps2.runtime +1/−0
• bench/runtime/zero/bench/lowtests.runtime +1/−1
• bench/runtime/zero/bench/p12.runtime +1/−1
• bench/runtime/zero/bench/take-drop.runtime +1/−1
• bench/runtime/zero/bench/terpret.runtime +1/−0
• bench/runtime/zero/eg/bools.runtime +1/−1
• bench/runtime/zero/eg/count.runtime +1/−1
• bench/runtime/zero/eg/dupos.runtime +1/−1
• bench/runtime/zero/eg/factorial.runtime +1/−1
• bench/runtime/zero/eg/fib01.runtime +1/−1
• bench/runtime/zero/eg/fibonacci.runtime +1/−1
• bench/runtime/zero/eg/ints.runtime +1/−1
• bench/runtime/zero/eg/list.runtime +1/−1
• bench/runtime/zero/eg/pow.runtime +1/−1
• bench/runtime/zero/eg/setelem.runtime +1/−1
• bench/runtime/zero/eg/sort.runtime +1/−1
• bench/runtime/zero/eg/tree.runtime +1/−1
• bench/runtime/zero/versions +2/−2
• bench/take-drop.hs +13/−10
• bench/take-drop.out +20/−18
• bench/terpret.hs +249/−0
• bench/terpret.out +156/−0
• changelog.md +12/−0
• code-conjure.cabal +4/−4
• eg/arith.out +3/−3
• eg/bools.out +2/−2
• eg/count.out +5/−5
• eg/dupos.out +2/−2
• eg/factorial.hs +13/−63
• eg/factorial.out +17/−16
• eg/fib01.hs +6/−0
• eg/fib01.out +1/−1
• eg/fibonacci.hs +5/−16
• eg/fibonacci.out +15/−14
• eg/gcd.hs +1/−1
• eg/gcd.out +3/−3
• eg/ints.hs +26/−8
• eg/ints.out +23/−23
• eg/pow.hs +3/−6
• eg/pow.out +12/−11
• eg/replicate.hs +2/−1
• eg/replicate.out +6/−5
• eg/setelem.out +6/−6
• eg/tapps.out +4/−4
• eg/tree.out +4/−4
• mk/depend.mk +26/−0
• src/Conjure.hs +2/−0
• src/Conjure/Conjurable.hs +36/−1
• src/Conjure/Engine.hs +63/−53
• stack.yaml +2/−2
• test/conjurable.hs +40/−0

@@ -56,7 +56,9 @@ bench/p30 bench/candidates bench/gps+bench/gps2 bench/lowtests+bench/terpret proto/u-conjure test/expr test/conjurable

@@ -33,6 +33,8 @@   bench/p12 \   bench/p30 \   bench/gps \+  bench/gps2 \+  bench/terpret \   proto/u-conjure  TESTS = \

@@ -94,7 +94,7 @@ 	               , pr (1::Int) 	               , prim "+" ((+) :: Int -> Int -> Int) 	               , prim "*" ((*) :: Int -> Int -> Int)-	               , prim "dec" (subtract 1 :: Int -> Int)+	               , prim "-" ((-) :: Int -> Int -> Int) 	               ]  running@@ -105,15 +105,16 @@  	factorial :: Int -> Int 	-- testing 4 combinations of argument values-	-- pruning with 22/42 rules+	-- pruning with 27/65 rules 	-- looking through 3 candidates of size 1-	-- looking through 6 candidates of size 2-	-- looking through 16 candidates of size 3-	-- looking through 39 candidates of size 4-	-- looking through 78 candidates of size 5-	-- looking through 166 candidates of size 6+	-- looking through 4 candidates of size 2+	-- looking through 13 candidates of size 3+	-- looking through 34 candidates of size 4+	-- looking through 75 candidates of size 5+	-- looking through 183 candidates of size 6+	-- looking through 577 candidates of size 7 	factorial 0  =  1-	factorial x  =  x * factorial (dec x)+	factorial x  =  x * factorial (x - 1)  in less than a second. 

@@ -3,25 +3,27 @@  A non-exhaustive list of things TO DO for Conjure. -* pretty-print top-level ifs?+* consider not breaking in some cases (increased crossproduct of patterns) -* carry on implementing all GPS benches while taking notes on the paper+* reduce the number of `deconstructions` considered: -* consider memoizing `recs ep` in `candidateDefnsC`-  and a sub function with `vs` arguments.+	1. place a `traceShowId` in `deconstructions :: [Expr]`+	2. run the GCD example -* remove `requireDescent=False` requirement from `gcd`-  (add and use `isDeconstruction`)-  this would also eliminate the requirement of providing `dec`+		[_ `mod` y :: Int,x `mod` _ :: Int,_ `mod` x :: Int,y `mod` _ :: Int,0 `mod` _ :: Int,0 `mod` _ :: Int] -* consider not breaking in some cases (increased crossproduct of patterns)+	3. there's no need to go variable by variable.  Just generating expressions+	   with a _single hole_ should be enough.  + ### for later  * allow specifying properties that need to be true  * allow recursion under any lazy functions (discover them by testing!)++* pretty-print top-level ifs?  * exclude magic numbers?  e.g.: `1+1`? 

@@ -38,7 +38,7 @@     , pr (1 :: Int)     , prim "+" ((+) :: Int -> Int -> Int)     , prim "*" ((+) :: Int -> Int -> Int)-    , prim "dec" (subtract 1 :: Int -> Int)+    , prim "-" ((-) :: Int -> Int -> Int)     ]    printCandidates 9 6 "?" (undefined :: Int -> Int -> Int)

@@ -1,7487 +1,9727 @@ 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+  pruning with 15/35 rules+  [3,0,7,0,20,0,75,0,297] direct candidates, 0 duplicates+  [3,4,12,32,54,139,287,691,1713] pattern candidates, 0 duplicates++rules:+x * y == x + y+x * y == y + x+x - x == 0+x + 0 == x+0 + x == x+x - 0 == x+(x + y) + z == x + (y + z)+(x + y) + z == y + (x + z)+x - (y - z) == z + (x - y)+(x - y) - z == x - (y + z)+(x - y) - z == x - (z + y)+(x + y) - z == x + (y - z)+(x + y) - z == y + (x - z)+x + (y - x) == y+(x - y) + y == x+equations:+y + x == x + y+y + (x + z) == x + (y + z)+z + (x + y) == x + (y + z)+z + (y + x) == x + (y + z)+y + (x - z) == x + (y - z)+(x - z) + y == x + (y - z)+(z - y) + x == (x - y) + z+y - (x + y) == 0 - x+y - (y + x) == 0 - x+z - (y + z) == x - (x + y)+z - (y + z) == x - (y + x)+z - (z + y) == x - (x + y)+z - (z + y) == x - (y + x)+x + (0 - y) == x - y+(0 - y) + x == x - y+x - (x + 1) == 0 - 1+x - (1 + x) == 0 - 1+y - (y + 1) == x - (x + 1)+y - (y + 1) == x - (1 + x)+y - (1 + y) == x - (1 + x)++direct candidates:++foo x  =  x++foo x  =  0++foo x  =  1++foo x  =  x + x++foo x  =  x + 1++foo x  =  1 + x++foo x  =  1 + 1++foo x  =  x - 1++foo x  =  0 - x++foo x  =  0 - 1++foo x  =  (0 - 1) + x++foo x  =  x + (x + x)++foo x  =  x + (x + 1)++foo x  =  x + (1 + x)++foo x  =  x + (1 + 1)++foo x  =  x + (x - 1)++foo x  =  x + (0 - 1)++foo x  =  1 + (x + x)++foo x  =  1 + (x + 1)++foo x  =  1 + (1 + x)++foo x  =  1 + (1 + 1)++foo x  =  1 + (0 - x)++foo x  =  x - (x + x)++foo x  =  x - (x + 1)++foo x  =  x - (1 + x)++foo x  =  x - (1 + 1)++foo x  =  0 - (x + x)++foo x  =  0 - (x + 1)++foo x  =  0 - (1 + x)++foo x  =  0 - (1 + 1)+++pattern candidates:++foo x  =  x++foo x  =  0++foo x  =  1++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 x  =  x - 1++foo x  =  0 - x++foo x  =  0 - 1++foo x  =  1 - x++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  =  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  =  0+foo x  =  x - 1++foo 0  =  0+foo x  =  0 - x++foo 0  =  0+foo x  =  0 - 1++foo 0  =  0+foo x  =  1 - x++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  =  1+foo x  =  x - 1++foo 0  =  1+foo x  =  0 - x++foo 0  =  1+foo x  =  0 - 1++foo 0  =  1+foo x  =  1 - x++foo 0  =  1 + 1+foo x  =  x++foo 0  =  1 + 1+foo x  =  0++foo 0  =  1 + 1+foo x  =  1++foo 0  =  0 - 1+foo x  =  x++foo 0  =  0 - 1+foo x  =  0++foo 0  =  0 - 1+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  =  foo (x - 1)++foo 0  =  0+foo x  =  foo (1 - x)++foo 0  =  1+foo x  =  foo (x - 1)++foo 0  =  1+foo x  =  foo (1 - x)++foo x  =  (x - 1) + x++foo x  =  (0 - x) + 1++foo x  =  (0 - 1) + x++foo x  =  (1 - x) + 1++foo x  =  x + (x + x)++foo x  =  x + (x + 1)++foo x  =  x + (1 + x)++foo x  =  x + (1 + 1)++foo x  =  x + (x - 1)++foo x  =  x + (0 - 1)++foo x  =  1 + (x + x)++foo x  =  1 + (x + 1)++foo x  =  1 + (1 + x)++foo x  =  1 + (1 + 1)++foo x  =  1 + (0 - x)++foo x  =  1 + (1 - x)++foo x  =  x - (x + x)++foo x  =  x - (x + 1)++foo x  =  x - (1 + x)++foo x  =  x - (1 + 1)++foo x  =  0 - (x + x)++foo x  =  0 - (x + 1)++foo x  =  0 - (1 + x)++foo x  =  0 - (1 + 1)++foo x  =  1 - (x + x)++foo x  =  1 - (x + 1)++foo x  =  1 - (1 + x)++foo x  =  1 - (1 + 1)++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  =  0+foo x  =  x - 1++foo 1  =  0+foo x  =  0 - x++foo 1  =  0+foo x  =  0 - 1++foo 1  =  0+foo x  =  1 - x++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  =  1+foo x  =  x - 1++foo 1  =  1+foo x  =  0 - x++foo 1  =  1+foo x  =  0 - 1++foo 1  =  1+foo x  =  1 - x++foo 1  =  1 + 1+foo x  =  x++foo 1  =  1 + 1+foo x  =  0++foo 1  =  1 + 1+foo x  =  1++foo 1  =  0 - 1+foo x  =  x++foo 1  =  0 - 1+foo x  =  0++foo 1  =  0 - 1+foo x  =  1++foo 1  =  0+foo x  =  foo (x - 1)++foo 1  =  0+foo x  =  foo (1 - x)++foo 1  =  1+foo x  =  foo (x - 1)++foo 1  =  1+foo x  =  foo (1 - x)++foo 0  =  0+foo x  =  (x - 1) + x++foo 0  =  0+foo x  =  (0 - x) + 1++foo 0  =  0+foo x  =  (0 - 1) + x++foo 0  =  0+foo x  =  (1 - x) + 1++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  =  x + (x - 1)++foo 0  =  0+foo x  =  x + (0 - 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  =  1 + (0 - x)++foo 0  =  0+foo x  =  1 + (1 - 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  =  0 - (x + x)++foo 0  =  0+foo x  =  0 - (x + 1)++foo 0  =  0+foo x  =  0 - (1 + x)++foo 0  =  0+foo x  =  0 - (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  =  1+foo x  =  (x - 1) + x++foo 0  =  1+foo x  =  (0 - x) + 1++foo 0  =  1+foo x  =  (0 - 1) + x++foo 0  =  1+foo x  =  (1 - x) + 1++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  =  x + (x - 1)++foo 0  =  1+foo x  =  x + (0 - 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  =  1 + (0 - x)++foo 0  =  1+foo x  =  1 + (1 - x)++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  =  0 - (x + x)++foo 0  =  1+foo x  =  0 - (x + 1)++foo 0  =  1+foo x  =  0 - (1 + x)++foo 0  =  1+foo x  =  0 - (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 + 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+foo x  =  x - 1++foo 0  =  1 + 1+foo x  =  0 - x++foo 0  =  1 + 1+foo x  =  0 - 1++foo 0  =  1 + 1+foo x  =  1 - x++foo 0  =  0 - 1+foo x  =  x + x++foo 0  =  0 - 1+foo x  =  x + 1++foo 0  =  0 - 1+foo x  =  1 + x++foo 0  =  0 - 1+foo x  =  1 + 1++foo 0  =  0 - 1+foo x  =  x - 1++foo 0  =  0 - 1+foo x  =  0 - x++foo 0  =  0 - 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  =  0 - (1 + 1)+foo x  =  x++foo 0  =  0 - (1 + 1)+foo x  =  0++foo 0  =  0 - (1 + 1)+foo x  =  1++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  =  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  =  0+foo x  =  x - 1++foo 0  =  0+foo 1  =  0+foo x  =  0 - x++foo 0  =  0+foo 1  =  0+foo x  =  0 - 1++foo 0  =  0+foo 1  =  0+foo x  =  1 - x++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  =  1+foo x  =  x - 1++foo 0  =  0+foo 1  =  1+foo x  =  0 - x++foo 0  =  0+foo 1  =  1+foo x  =  0 - 1++foo 0  =  0+foo 1  =  1+foo x  =  1 - x++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  =  0+foo 1  =  0 - 1+foo x  =  x++foo 0  =  0+foo 1  =  0 - 1+foo x  =  0++foo 0  =  0+foo 1  =  0 - 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  =  0+foo x  =  x - 1++foo 0  =  1+foo 1  =  0+foo x  =  0 - x++foo 0  =  1+foo 1  =  0+foo x  =  0 - 1++foo 0  =  1+foo 1  =  0+foo x  =  1 - x++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  =  1+foo x  =  x - 1++foo 0  =  1+foo 1  =  1+foo x  =  0 - x++foo 0  =  1+foo 1  =  1+foo x  =  0 - 1++foo 0  =  1+foo 1  =  1+foo x  =  1 - x++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  =  1+foo 1  =  0 - 1+foo x  =  x++foo 0  =  1+foo 1  =  0 - 1+foo x  =  0++foo 0  =  1+foo 1  =  0 - 1+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++foo 0  =  0 - 1+foo 1  =  0+foo x  =  x++foo 0  =  0 - 1+foo 1  =  0+foo x  =  0++foo 0  =  0 - 1+foo 1  =  0+foo x  =  1++foo 0  =  0 - 1+foo 1  =  1+foo x  =  x++foo 0  =  0 - 1+foo 1  =  1+foo x  =  0++foo 0  =  0 - 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+  [3,11,42,117,346,955,2714,7510,20754] 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 ? y  =  dec (dec x)++x ? y  =  dec (dec y)++x ? y  =  dec (dec 0)++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 + x++x ? y  =  dec x + y++x ? y  =  dec y + x++x ? y  =  dec y + y++x ? y  =  dec 0 + x++x ? y  =  dec 0 + y++x ? y  =  dec (dec (dec x))++x ? y  =  dec (dec (dec y))++x ? y  =  dec (dec (dec 0))++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  =  x+x ? y  =  dec (dec x)++x ? 0  =  x+x ? y  =  dec (dec y)++x ? 0  =  x+x ? y  =  dec (dec 0)++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  =  0+x ? y  =  dec (dec x)++x ? 0  =  0+x ? y  =  dec (dec y)++x ? 0  =  0+x ? y  =  dec (dec 0)++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++x ? 0  =  dec (dec x)+x ? y  =  x++x ? 0  =  dec (dec x)+x ? y  =  y++x ? 0  =  dec (dec x)+x ? y  =  0++x ? 0  =  dec (dec 0)+x ? y  =  x++x ? 0  =  dec (dec 0)+x ? y  =  y++x ? 0  =  dec (dec 0)+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  =  x+x ? y  =  dec (dec x)++0 ? x  =  x+x ? y  =  dec (dec y)++0 ? x  =  x+x ? y  =  dec (dec 0)++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  =  0+x ? y  =  dec (dec x)++0 ? x  =  0+x ? y  =  dec (dec y)++0 ? x  =  0+x ? y  =  dec (dec 0)++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 ? x  =  dec (dec x)+x ? y  =  x++0 ? x  =  dec (dec x)+x ? y  =  y++0 ? x  =  dec (dec x)+x ? y  =  0++0 ? x  =  dec (dec 0)+x ? y  =  x++0 ? x  =  dec (dec 0)+x ? y  =  y++0 ? x  =  dec (dec 0)+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 y++x ? 0  =  x+x ? y  =  y ? dec y++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  =  0+x ? y  =  x ? dec y++x ? 0  =  0+x ? y  =  y ? dec y++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++0 ? x  =  x+x ? y  =  x ? dec y++0 ? x  =  x+x ? y  =  y ? dec y++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  =  0+x ? y  =  x ? dec y++0 ? x  =  0+x ? y  =  y ? dec y++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++x ? y  =  dec (dec x) + x++x ? y  =  dec (dec x) + y++x ? y  =  dec (dec y) + x++x ? y  =  dec (dec y) + y++x ? y  =  dec (dec 0) + x++x ? y  =  dec (dec 0) + y++x ? y  =  dec (dec (dec (dec x)))++x ? y  =  dec (dec (dec (dec y)))++x ? y  =  dec (dec (dec (dec 0)))++x ? y  =  x + (x + x)++x ? y  =  x + (x + y)++x ? y  =  x + (y + x)++x ? y  =  x + (y + y)++x ? y  =  x + dec (dec x)++x ? y  =  x + dec (dec y)++x ? y  =  x + dec (dec 0)++x ? y  =  y + (x + x)++x ? y  =  y + (x + y)++x ? y  =  y + (y + x)++x ? y  =  y + (y + y)++x ? y  =  y + dec (dec x)++x ? y  =  y + dec (dec y)++x ? y  =  y + dec (dec 0)++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 + x++x ? 0  =  x+x ? y  =  dec x + y++x ? 0  =  x+x ? y  =  dec y + x++x ? 0  =  x+x ? y  =  dec y + y++x ? 0  =  x+x ? y  =  dec 0 + x++x ? 0  =  x+x ? y  =  dec 0 + y++x ? 0  =  x+x ? y  =  dec (dec (dec x))++x ? 0  =  x+x ? y  =  dec (dec (dec y))++x ? 0  =  x+x ? y  =  dec (dec (dec 0))++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 + x++x ? 0  =  0+x ? y  =  dec x + y++x ? 0  =  0+x ? y  =  dec y + x++x ? 0  =  0+x ? y  =  dec y + y++x ? 0  =  0+x ? y  =  dec 0 + x++x ? 0  =  0+x ? y  =  dec 0 + y++x ? 0  =  0+x ? y  =  dec (dec (dec x))++x ? 0  =  0+x ? y  =  dec (dec (dec y))++x ? 0  =  0+x ? y  =  dec (dec (dec 0))++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 x+x ? y  =  dec (dec x)++x ? 0  =  dec x+x ? y  =  dec (dec y)++x ? 0  =  dec x+x ? y  =  dec (dec 0)++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  =  dec 0+x ? y  =  dec (dec x)++x ? 0  =  dec 0+x ? y  =  dec (dec y)++x ? 0  =  dec 0+x ? y  =  dec (dec 0)++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 (dec x)+x ? y  =  dec x++x ? 0  =  dec (dec x)+x ? y  =  dec y++x ? 0  =  dec (dec x)+x ? y  =  dec 0++x ? 0  =  dec (dec 0)+x ? y  =  dec x++x ? 0  =  dec (dec 0)+x ? y  =  dec y++x ? 0  =  dec (dec 0)+x ? y  =  dec 0++x ? 0  =  dec x + x+x ? y  =  x++x ? 0  =  dec x + x+x ? y  =  y++x ? 0  =  dec x + x+x ? y  =  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  =  dec (dec (dec x))+x ? y  =  x++x ? 0  =  dec (dec (dec x))+x ? y  =  y++x ? 0  =  dec (dec (dec x))+x ? y  =  0++x ? 0  =  dec (dec (dec 0))+x ? y  =  x++x ? 0  =  dec (dec (dec 0))+x ? y  =  y++x ? 0  =  dec (dec (dec 0))+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 + x++0 ? x  =  x+x ? y  =  dec x + y++0 ? x  =  x+x ? y  =  dec y + x++0 ? x  =  x+x ? y  =  dec y + y++0 ? x  =  x+x ? y  =  dec 0 + x++0 ? x  =  x+x ? y  =  dec 0 + y++0 ? x  =  x+x ? y  =  dec (dec (dec x))++0 ? x  =  x+x ? y  =  dec (dec (dec y))++0 ? x  =  x+x ? y  =  dec (dec (dec 0))++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 + x++0 ? x  =  0+x ? y  =  dec x + y++0 ? x  =  0+x ? y  =  dec y + x++0 ? x  =  0+x ? y  =  dec y + y++0 ? x  =  0+x ? y  =  dec 0 + x++0 ? x  =  0+x ? y  =  dec 0 + y++0 ? x  =  0+x ? y  =  dec (dec (dec x))++0 ? x  =  0+x ? y  =  dec (dec (dec y))++0 ? x  =  0+x ? y  =  dec (dec (dec 0))++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 x+x ? y  =  dec (dec x)++0 ? x  =  dec x+x ? y  =  dec (dec y)++0 ? x  =  dec x+x ? y  =  dec (dec 0)++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  =  dec 0+x ? y  =  dec (dec x)++0 ? x  =  dec 0+x ? y  =  dec (dec y)++0 ? x  =  dec 0+x ? y  =  dec (dec 0)++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 (dec x)+x ? y  =  dec x++0 ? x  =  dec (dec x)+x ? y  =  dec y++0 ? x  =  dec (dec x)+x ? y  =  dec 0++0 ? x  =  dec (dec 0)+x ? y  =  dec x++0 ? x  =  dec (dec 0)+x ? y  =  dec y++0 ? x  =  dec (dec 0)+x ? y  =  dec 0++0 ? x  =  dec x + x+x ? y  =  x++0 ? x  =  dec x + x+x ? y  =  y++0 ? x  =  dec x + x+x ? y  =  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  =  dec (dec (dec x))+x ? y  =  x++0 ? x  =  dec (dec (dec x))+x ? y  =  y++0 ? x  =  dec (dec (dec x))+x ? y  =  0++0 ? x  =  dec (dec (dec 0))+x ? y  =  x++0 ? x  =  dec (dec (dec 0))+x ? y  =  y++0 ? x  =  dec (dec (dec 0))+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  =  x+x ? y  =  dec (dec x)++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  x+x ? y  =  dec (dec y)++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  x+x ? y  =  dec (dec 0)++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  =  0+x ? y  =  dec (dec x)++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  0+x ? y  =  dec (dec y)++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  0+x ? y  =  dec (dec 0)++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  =  x+x ? 0  =  dec (dec x)+x ? y  =  x++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec x)+x ? y  =  y++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec x)+x ? y  =  0++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec 0)+x ? y  =  x++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec 0)+x ? y  =  y++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec 0)+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  =  x+x ? y  =  dec (dec x)++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  x+x ? y  =  dec (dec y)++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  x+x ? y  =  dec (dec 0)++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  =  0+x ? y  =  dec (dec x)++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  0+x ? y  =  dec (dec y)++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  0+x ? y  =  dec (dec 0)++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  =  0+x ? 0  =  dec (dec x)+x ? y  =  x++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec x)+x ? y  =  y++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec x)+x ? y  =  0++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec 0)+x ? y  =  x++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec 0)+x ? y  =  y++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec 0)+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  =  0+0 ? x  =  dec (dec x)+x ? 0  =  x+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  x+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  x+x ? y  =  0++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  0+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  0+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  0+x ? y  =  0++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  x+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  x+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  x+x ? y  =  0++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  0+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  0+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec (dec 0)+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++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  x+x ? y  =  x++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  x+x ? y  =  y++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  x+x ? y  =  0++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  0+x ? y  =  x++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  0+x ? y  =  y++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  0+x ? y  =  0++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  x+x ? y  =  x++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  x+x ? y  =  y++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  x+x ? y  =  0++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  0+x ? y  =  x++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  0+x ? y  =  y++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  0+x ? y  =  0++x ? 0  =  x+x ? y  =  x ? dec (dec y)++x ? 0  =  x+x ? y  =  y ? dec (dec y)++x ? 0  =  x+x ? y  =  0 ? dec (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 x ? dec 0++x ? 0  =  x+x ? y  =  dec y ? dec y++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  =  0+x ? y  =  x ? dec (dec y)++x ? 0  =  0+x ? y  =  y ? dec (dec y)++x ? 0  =  0+x ? y  =  0 ? dec (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 y++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++0 ? x  =  x+x ? y  =  x ? dec (dec y)++0 ? x  =  x+x ? y  =  y ? dec (dec y)++0 ? x  =  x+x ? y  =  0 ? dec (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 y++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  =  0+x ? y  =  x ? dec (dec y)++0 ? x  =  0+x ? y  =  y ? dec (dec y)++0 ? x  =  0+x ? y  =  0 ? dec (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 y++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++x ? 0  =  x+x ? y  =  dec (x ? dec y)++x ? 0  =  x+x ? y  =  dec (y ? dec y)++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  =  0+x ? y  =  dec (x ? dec y)++x ? 0  =  0+x ? y  =  dec (y ? dec y)++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  =  dec x+x ? y  =  x ? dec y++x ? 0  =  dec x+x ? y  =  y ? dec y++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 0+x ? y  =  x ? dec y++x ? 0  =  dec 0+x ? y  =  y ? dec y++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++0 ? x  =  x+x ? y  =  dec (x ? dec y)++0 ? x  =  x+x ? y  =  dec (y ? dec y)++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  =  0+x ? y  =  dec (x ? dec y)++0 ? x  =  0+x ? y  =  dec (y ? dec y)++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  =  dec x+x ? y  =  x ? dec y++0 ? x  =  dec x+x ? y  =  y ? dec y++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 0+x ? y  =  x ? dec y++0 ? x  =  dec 0+x ? y  =  y ? dec y++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 ? 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 y++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  =  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 y++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 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 ? 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 y++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 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  =  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 y++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 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++x ? y  =  dec (dec (dec x)) + x++x ? y  =  dec (dec (dec x)) + y++x ? y  =  dec (dec (dec y)) + x++x ? y  =  dec (dec (dec y)) + y++x ? y  =  dec (dec (dec 0)) + x++x ? y  =  dec (dec (dec 0)) + y++x ? y  =  dec (dec (dec (dec (dec x))))++x ? y  =  dec (dec (dec (dec (dec y))))++x ? y  =  dec (dec (dec (dec (dec 0))))++x ? y  =  x + (dec x + x)++x ? y  =  x + (dec x + y)++x ? y  =  x + (dec y + x)++x ? y  =  x + (dec y + y)++x ? y  =  x + (dec 0 + x)++x ? y  =  x + (dec 0 + y)++x ? y  =  x + dec (dec (dec x))++x ? y  =  x + dec (dec (dec y))++x ? y  =  x + dec (dec (dec 0))++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 + x)++x ? y  =  y + (dec x + y)++x ? y  =  y + (dec y + x)++x ? y  =  y + (dec y + y)++x ? y  =  y + (dec 0 + x)++x ? y  =  y + (dec 0 + y)++x ? y  =  y + dec (dec (dec x))++x ? y  =  y + dec (dec (dec y))++x ? y  =  y + dec (dec (dec 0))++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 + (x + x)++x ? y  =  dec x + (x + y)++x ? y  =  dec x + (y + x)++x ? y  =  dec x + (y + y)++x ? y  =  dec x + dec (dec x)++x ? y  =  dec x + dec (dec y)++x ? y  =  dec x + dec (dec 0)++x ? y  =  dec y + (x + x)++x ? y  =  dec y + (x + y)++x ? y  =  dec y + (y + x)++x ? y  =  dec y + (y + y)++x ? y  =  dec y + dec (dec x)++x ? y  =  dec y + dec (dec y)++x ? y  =  dec y + dec (dec 0)++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 ? y  =  dec 0 + dec (dec x)++x ? y  =  dec 0 + dec (dec y)++x ? y  =  dec 0 + dec (dec 0)++x ? y  =  dec (dec x) + dec x++x ? y  =  dec (dec x) + dec y++x ? y  =  dec (dec x) + dec 0++x ? y  =  dec (dec y) + dec x++x ? y  =  dec (dec y) + dec y++x ? y  =  dec (dec y) + dec 0++x ? y  =  dec (dec 0) + dec x++x ? y  =  dec (dec 0) + dec y++x ? y  =  dec (dec 0) + dec 0++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 y) + x++x ? 0  =  x+x ? y  =  dec (dec y) + y++x ? 0  =  x+x ? y  =  dec (dec 0) + x++x ? 0  =  x+x ? y  =  dec (dec 0) + y++x ? 0  =  x+x ? y  =  dec (dec (dec (dec x)))++x ? 0  =  x+x ? y  =  dec (dec (dec (dec y)))++x ? 0  =  x+x ? y  =  dec (dec (dec (dec 0)))++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  =  x + dec (dec x)++x ? 0  =  x+x ? y  =  x + dec (dec y)++x ? 0  =  x+x ? y  =  x + dec (dec 0)++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  =  y + dec (dec x)++x ? 0  =  x+x ? y  =  y + dec (dec y)++x ? 0  =  x+x ? y  =  y + dec (dec 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  =  x+x ? y  =  dec 0 + dec 0++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 y) + x++x ? 0  =  0+x ? y  =  dec (dec y) + y++x ? 0  =  0+x ? y  =  dec (dec 0) + x++x ? 0  =  0+x ? y  =  dec (dec 0) + y++x ? 0  =  0+x ? y  =  dec (dec (dec (dec x)))++x ? 0  =  0+x ? y  =  dec (dec (dec (dec y)))++x ? 0  =  0+x ? y  =  dec (dec (dec (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  =  x + dec (dec x)++x ? 0  =  0+x ? y  =  x + dec (dec y)++x ? 0  =  0+x ? y  =  x + dec (dec 0)++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  =  y + dec (dec x)++x ? 0  =  0+x ? y  =  y + dec (dec y)++x ? 0  =  0+x ? y  =  y + dec (dec 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 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 + x++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 y + y++x ? 0  =  dec x+x ? y  =  dec 0 + x++x ? 0  =  dec x+x ? y  =  dec 0 + y++x ? 0  =  dec x+x ? y  =  dec (dec (dec x))++x ? 0  =  dec x+x ? y  =  dec (dec (dec y))++x ? 0  =  dec x+x ? y  =  dec (dec (dec 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  =  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 + x++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 y + y++x ? 0  =  dec 0+x ? y  =  dec 0 + x++x ? 0  =  dec 0+x ? y  =  dec 0 + y++x ? 0  =  dec 0+x ? y  =  dec (dec (dec x))++x ? 0  =  dec 0+x ? y  =  dec (dec (dec y))++x ? 0  =  dec 0+x ? y  =  dec (dec (dec 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  =  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  =  x + x+x ? y  =  dec (dec x)++x ? 0  =  x + x+x ? y  =  dec (dec y)++x ? 0  =  x + x+x ? y  =  dec (dec 0)++x ? 0  =  dec (dec x)+x ? y  =  x + x++x ? 0  =  dec (dec x)+x ? y  =  x + y++x ? 0  =  dec (dec x)+x ? y  =  y + x++x ? 0  =  dec (dec x)+x ? y  =  y + y++x ? 0  =  dec (dec x)+x ? y  =  dec (dec y)++x ? 0  =  dec (dec x)+x ? y  =  dec (dec 0)++x ? 0  =  dec (dec 0)+x ? y  =  x + x++x ? 0  =  dec (dec 0)+x ? y  =  x + y++x ? 0  =  dec (dec 0)+x ? y  =  y + x++x ? 0  =  dec (dec 0)+x ? y  =  y + y++x ? 0  =  dec (dec 0)+x ? y  =  dec (dec x)++x ? 0  =  dec (dec 0)+x ? y  =  dec (dec y)++x ? 0  =  dec x + x+x ? y  =  dec x++x ? 0  =  dec x + x+x ? y  =  dec y++x ? 0  =  dec x + x+x ? y  =  dec 0++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  =  dec (dec (dec x))+x ? y  =  dec x++x ? 0  =  dec (dec (dec x))+x ? y  =  dec y++x ? 0  =  dec (dec (dec x))+x ? y  =  dec 0++x ? 0  =  dec (dec (dec 0))+x ? y  =  dec x++x ? 0  =  dec (dec (dec 0))+x ? y  =  dec y++x ? 0  =  dec (dec (dec 0))+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  =  dec (dec x) + x+x ? y  =  x++x ? 0  =  dec (dec x) + x+x ? y  =  y++x ? 0  =  dec (dec x) + x+x ? y  =  0++x ? 0  =  dec (dec 0) + x+x ? y  =  x++x ? 0  =  dec (dec 0) + x+x ? y  =  y++x ? 0  =  dec (dec 0) + x+x ? y  =  0++x ? 0  =  dec (dec (dec (dec x)))+x ? y  =  x++x ? 0  =  dec (dec (dec (dec x)))+x ? y  =  y++x ? 0  =  dec (dec (dec (dec x)))+x ? y  =  0++x ? 0  =  dec (dec (dec (dec 0)))+x ? y  =  x++x ? 0  =  dec (dec (dec (dec 0)))+x ? y  =  y++x ? 0  =  dec (dec (dec (dec 0)))+x ? y  =  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  =  x + dec (dec x)+x ? y  =  x++x ? 0  =  x + dec (dec x)+x ? y  =  y++x ? 0  =  x + dec (dec x)+x ? y  =  0++x ? 0  =  x + dec (dec 0)+x ? y  =  x++x ? 0  =  x + dec (dec 0)+x ? y  =  y++x ? 0  =  x + dec (dec 0)+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  =  dec (dec x) + x++0 ? x  =  x+x ? y  =  dec (dec x) + y++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 0) + x++0 ? x  =  x+x ? y  =  dec (dec 0) + y++0 ? x  =  x+x ? y  =  dec (dec (dec (dec x)))++0 ? x  =  x+x ? y  =  dec (dec (dec (dec y)))++0 ? x  =  x+x ? y  =  dec (dec (dec (dec 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  =  x + dec (dec x)++0 ? x  =  x+x ? y  =  x + dec (dec y)++0 ? x  =  x+x ? y  =  x + dec (dec 0)++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  =  y + dec (dec x)++0 ? x  =  x+x ? y  =  y + dec (dec y)++0 ? x  =  x+x ? y  =  y + dec (dec 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 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  =  dec (dec x) + x++0 ? x  =  0+x ? y  =  dec (dec x) + y++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 0) + x++0 ? x  =  0+x ? y  =  dec (dec 0) + y++0 ? x  =  0+x ? y  =  dec (dec (dec (dec x)))++0 ? x  =  0+x ? y  =  dec (dec (dec (dec y)))++0 ? x  =  0+x ? y  =  dec (dec (dec (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  =  x + dec (dec x)++0 ? x  =  0+x ? y  =  x + dec (dec y)++0 ? x  =  0+x ? y  =  x + dec (dec 0)++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  =  y + dec (dec x)++0 ? x  =  0+x ? y  =  y + dec (dec y)++0 ? x  =  0+x ? y  =  y + dec (dec 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 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 + x++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 y + y++0 ? x  =  dec x+x ? y  =  dec 0 + x++0 ? x  =  dec x+x ? y  =  dec 0 + y++0 ? x  =  dec x+x ? y  =  dec (dec (dec x))++0 ? x  =  dec x+x ? y  =  dec (dec (dec y))++0 ? x  =  dec x+x ? y  =  dec (dec (dec 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  =  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 + x++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 y + y++0 ? x  =  dec 0+x ? y  =  dec 0 + x++0 ? x  =  dec 0+x ? y  =  dec 0 + y++0 ? x  =  dec 0+x ? y  =  dec (dec (dec x))++0 ? x  =  dec 0+x ? y  =  dec (dec (dec y))++0 ? x  =  dec 0+x ? y  =  dec (dec (dec 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  =  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  =  x + x+x ? y  =  dec (dec x)++0 ? x  =  x + x+x ? y  =  dec (dec y)++0 ? x  =  x + x+x ? y  =  dec (dec 0)++0 ? x  =  dec (dec x)+x ? y  =  x + x++0 ? x  =  dec (dec x)+x ? y  =  x + y++0 ? x  =  dec (dec x)+x ? y  =  y + x++0 ? x  =  dec (dec x)+x ? y  =  y + y++0 ? x  =  dec (dec x)+x ? y  =  dec (dec y)++0 ? x  =  dec (dec x)+x ? y  =  dec (dec 0)++0 ? x  =  dec (dec 0)+x ? y  =  x + x++0 ? x  =  dec (dec 0)+x ? y  =  x + y++0 ? x  =  dec (dec 0)+x ? y  =  y + x++0 ? x  =  dec (dec 0)+x ? y  =  y + y++0 ? x  =  dec (dec 0)+x ? y  =  dec (dec x)++0 ? x  =  dec (dec 0)+x ? y  =  dec (dec y)++0 ? x  =  dec x + x+x ? y  =  dec x++0 ? x  =  dec x + x+x ? y  =  dec y++0 ? x  =  dec x + x+x ? y  =  dec 0++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  =  dec (dec (dec x))+x ? y  =  dec x++0 ? x  =  dec (dec (dec x))+x ? y  =  dec y++0 ? x  =  dec (dec (dec x))+x ? y  =  dec 0++0 ? x  =  dec (dec (dec 0))+x ? y  =  dec x++0 ? x  =  dec (dec (dec 0))+x ? y  =  dec y++0 ? x  =  dec (dec (dec 0))+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  =  dec (dec x) + x+x ? y  =  x++0 ? x  =  dec (dec x) + x+x ? y  =  y++0 ? x  =  dec (dec x) + x+x ? y  =  0++0 ? x  =  dec (dec 0) + x+x ? y  =  x++0 ? x  =  dec (dec 0) + x+x ? y  =  y++0 ? x  =  dec (dec 0) + x+x ? y  =  0++0 ? x  =  dec (dec (dec (dec x)))+x ? y  =  x++0 ? x  =  dec (dec (dec (dec x)))+x ? y  =  y++0 ? x  =  dec (dec (dec (dec x)))+x ? y  =  0++0 ? x  =  dec (dec (dec (dec 0)))+x ? y  =  x++0 ? x  =  dec (dec (dec (dec 0)))+x ? y  =  y++0 ? x  =  dec (dec (dec (dec 0)))+x ? y  =  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  =  x + dec (dec x)+x ? y  =  x++0 ? x  =  x + dec (dec x)+x ? y  =  y++0 ? x  =  x + dec (dec x)+x ? y  =  0++0 ? x  =  x + dec (dec 0)+x ? y  =  x++0 ? x  =  x + dec (dec 0)+x ? y  =  y++0 ? x  =  x + dec (dec 0)+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 + 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 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 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  =  dec (dec (dec x))++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  x+x ? y  =  dec (dec (dec y))++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  x+x ? y  =  dec (dec (dec 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  =  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 + 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 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 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  =  dec (dec (dec x))++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  0+x ? y  =  dec (dec (dec y))++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  0+x ? y  =  dec (dec (dec 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  =  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 x+x ? y  =  dec (dec x)++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec x+x ? y  =  dec (dec y)++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec x+x ? y  =  dec (dec 0)++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  =  dec 0+x ? y  =  dec (dec x)++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec 0+x ? y  =  dec (dec y)++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec 0+x ? y  =  dec (dec 0)++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 (dec x)+x ? y  =  dec x++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec x)+x ? y  =  dec y++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec x)+x ? y  =  dec 0++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec 0)+x ? y  =  dec x++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec 0)+x ? y  =  dec y++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec 0)+x ? y  =  dec 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 + x+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 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  =  dec (dec (dec x))+x ? y  =  x++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec (dec x))+x ? y  =  y++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec (dec x))+x ? y  =  0++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec (dec 0))+x ? y  =  x++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec (dec 0))+x ? y  =  y++0 ? 0  =  0+0 ? x  =  x+x ? 0  =  dec (dec (dec 0))+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 + 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 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 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  =  dec (dec (dec x))++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  x+x ? y  =  dec (dec (dec y))++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  x+x ? y  =  dec (dec (dec 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  =  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 + 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 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 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  =  dec (dec (dec x))++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  0+x ? y  =  dec (dec (dec y))++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  0+x ? y  =  dec (dec (dec 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  =  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 x+x ? y  =  dec (dec x)++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec x+x ? y  =  dec (dec y)++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec x+x ? y  =  dec (dec 0)++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  =  dec 0+x ? y  =  dec (dec x)++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec 0+x ? y  =  dec (dec y)++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec 0+x ? y  =  dec (dec 0)++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 (dec x)+x ? y  =  dec x++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec x)+x ? y  =  dec y++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec x)+x ? y  =  dec 0++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec 0)+x ? y  =  dec x++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec 0)+x ? y  =  dec y++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec 0)+x ? y  =  dec 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 + x+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 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  =  dec (dec (dec x))+x ? y  =  x++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec (dec x))+x ? y  =  y++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec (dec x))+x ? y  =  0++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec (dec 0))+x ? y  =  x++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec (dec 0))+x ? y  =  y++0 ? 0  =  0+0 ? x  =  0+x ? 0  =  dec (dec (dec 0))+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  =  x+x ? y  =  dec (dec x)++0 ? 0  =  0+0 ? x  =  dec x+x ? 0  =  x+x ? y  =  dec (dec y)++0 ? 0  =  0+0 ? x  =  dec x+x ? 0  =  x+x ? y  =  dec (dec 0)++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  =  0+x ? y  =  dec (dec x)++0 ? 0  =  0+0 ? x  =  dec x+x ? 0  =  0+x ? y  =  dec (dec y)++0 ? 0  =  0+0 ? x  =  dec x+x ? 0  =  0+x ? y  =  dec (dec 0)++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 x+x ? 0  =  dec (dec x)+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec x+x ? 0  =  dec (dec x)+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec x+x ? 0  =  dec (dec x)+x ? y  =  0++0 ? 0  =  0+0 ? x  =  dec x+x ? 0  =  dec (dec 0)+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec x+x ? 0  =  dec (dec 0)+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec x+x ? 0  =  dec (dec 0)+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  =  x+x ? y  =  dec (dec x)++0 ? 0  =  0+0 ? x  =  dec 0+x ? 0  =  x+x ? y  =  dec (dec y)++0 ? 0  =  0+0 ? x  =  dec 0+x ? 0  =  x+x ? y  =  dec (dec 0)++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  =  0+x ? y  =  dec (dec x)++0 ? 0  =  0+0 ? x  =  dec 0+x ? 0  =  0+x ? y  =  dec (dec y)++0 ? 0  =  0+0 ? x  =  dec 0+x ? 0  =  0+x ? y  =  dec (dec 0)++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  =  dec 0+x ? 0  =  dec (dec x)+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec 0+x ? 0  =  dec (dec x)+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec 0+x ? 0  =  dec (dec x)+x ? y  =  0++0 ? 0  =  0+0 ? x  =  dec 0+x ? 0  =  dec (dec 0)+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec 0+x ? 0  =  dec (dec 0)+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec 0+x ? 0  =  dec (dec 0)+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 (dec x)+x ? 0  =  x+x ? y  =  dec x++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  x+x ? y  =  dec y++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  x+x ? y  =  dec 0++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  0+x ? y  =  dec x++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  0+x ? y  =  dec y++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  0+x ? y  =  dec 0++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  dec x+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  dec x+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  dec x+x ? y  =  0++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  dec 0+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  dec 0+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec (dec x)+x ? 0  =  dec 0+x ? y  =  0++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  x+x ? y  =  dec x++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  x+x ? y  =  dec y++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  x+x ? y  =  dec 0++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  0+x ? y  =  dec x++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  0+x ? y  =  dec y++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  0+x ? y  =  dec 0++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  dec x+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  dec x+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  dec x+x ? y  =  0++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  dec 0+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  dec 0+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec (dec 0)+x ? 0  =  dec 0+x ? y  =  0++0 ? 0  =  0+0 ? x  =  dec x + x+x ? 0  =  x+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec x + x+x ? 0  =  x+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec x + x+x ? 0  =  x+x ? y  =  0++0 ? 0  =  0+0 ? x  =  dec x + x+x ? 0  =  0+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec x + x+x ? 0  =  0+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec x + x+x ? 0  =  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  =  dec (dec (dec x))+x ? 0  =  x+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec (dec (dec x))+x ? 0  =  x+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec (dec (dec x))+x ? 0  =  x+x ? y  =  0++0 ? 0  =  0+0 ? x  =  dec (dec (dec x))+x ? 0  =  0+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec (dec (dec x))+x ? 0  =  0+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec (dec (dec x))+x ? 0  =  0+x ? y  =  0++0 ? 0  =  0+0 ? x  =  dec (dec (dec 0))+x ? 0  =  x+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec (dec (dec 0))+x ? 0  =  x+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec (dec (dec 0))+x ? 0  =  x+x ? y  =  0++0 ? 0  =  0+0 ? x  =  dec (dec (dec 0))+x ? 0  =  0+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec (dec (dec 0))+x ? 0  =  0+x ? y  =  y++0 ? 0  =  0+0 ? x  =  dec (dec (dec 0))+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  =  x+x ? y  =  dec (dec x)++0 ? 0  =  dec 0+0 ? x  =  x+x ? 0  =  x+x ? y  =  dec (dec y)++0 ? 0  =  dec 0+0 ? x  =  x+x ? 0  =  x+x ? y  =  dec (dec 0)++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  =  0+x ? y  =  dec (dec x)++0 ? 0  =  dec 0+0 ? x  =  x+x ? 0  =  0+x ? y  =  dec (dec y)++0 ? 0  =  dec 0+0 ? x  =  x+x ? 0  =  0+x ? y  =  dec (dec 0)++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  =  x+x ? 0  =  dec (dec x)+x ? y  =  x++0 ? 0  =  dec 0+0 ? x  =  x+x ? 0  =  dec (dec x)+x ? y  =  y++0 ? 0  =  dec 0+0 ? x  =  x+x ? 0  =  dec (dec x)+x ? y  =  0++0 ? 0  =  dec 0+0 ? x  =  x+x ? 0  =  dec (dec 0)+x ? y  =  x++0 ? 0  =  dec 0+0 ? x  =  x+x ? 0  =  dec (dec 0)+x ? y  =  y++0 ? 0  =  dec 0+0 ? x  =  x+x ? 0  =  dec (dec 0)+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  =  x+x ? y  =  dec (dec x)++0 ? 0  =  dec 0+0 ? x  =  0+x ? 0  =  x+x ? y  =  dec (dec y)++0 ? 0  =  dec 0+0 ? x  =  0+x ? 0  =  x+x ? y  =  dec (dec 0)++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  =  0+x ? y  =  dec (dec x)++0 ? 0  =  dec 0+0 ? x  =  0+x ? 0  =  0+x ? y  =  dec (dec y)++0 ? 0  =  dec 0+0 ? x  =  0+x ? 0  =  0+x ? y  =  dec (dec 0)++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  =  0+x ? 0  =  dec (dec x)+x ? y  =  x++0 ? 0  =  dec 0+0 ? x  =  0+x ? 0  =  dec (dec x)+x ? y  =  y++0 ? 0  =  dec 0+0 ? x  =  0+x ? 0  =  dec (dec x)+x ? y  =  0++0 ? 0  =  dec 0+0 ? x  =  0+x ? 0  =  dec (dec 0)+x ? y  =  x++0 ? 0  =  dec 0+0 ? x  =  0+x ? 0  =  dec (dec 0)+x ? y  =  y++0 ? 0  =  dec 0+0 ? x  =  0+x ? 0  =  dec (dec 0)+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++0 ? 0  =  dec 0+0 ? x  =  dec (dec x)+x ? 0  =  x+x ? y  =  x++0 ? 0  =  dec 0+0 ? x  =  dec (dec x)+x ? 0  =  x+x ? y  =  y++0 ? 0  =  dec 0+0 ? x  =  dec (dec x)+x ? 0  =  x+x ? y  =  0++0 ? 0  =  dec 0+0 ? x  =  dec (dec x)+x ? 0  =  0+x ? y  =  x++0 ? 0  =  dec 0+0 ? x  =  dec (dec x)+x ? 0  =  0+x ? y  =  y++0 ? 0  =  dec 0+0 ? x  =  dec (dec x)+x ? 0  =  0+x ? y  =  0++0 ? 0  =  dec 0+0 ? x  =  dec (dec 0)+x ? 0  =  x+x ? y  =  x++0 ? 0  =  dec 0+0 ? x  =  dec (dec 0)+x ? 0  =  x+x ? y  =  y++0 ? 0  =  dec 0+0 ? x  =  dec (dec 0)+x ? 0  =  x+x ? y  =  0++0 ? 0  =  dec 0+0 ? x  =  dec (dec 0)+x ? 0  =  0+x ? y  =  x++0 ? 0  =  dec 0+0 ? x  =  dec (dec 0)+x ? 0  =  0+x ? y  =  y++0 ? 0  =  dec 0+0 ? x  =  dec (dec 0)+x ? 0  =  0+x ? y  =  0++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  x+x ? y  =  dec x++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  x+x ? y  =  dec y++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  x+x ? y  =  dec 0++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  0+x ? y  =  dec x++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  0+x ? y  =  dec y++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  0+x ? y  =  dec 0++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  dec x+x ? y  =  x++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  dec x+x ? y  =  y++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  dec x+x ? y  =  0++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  dec 0+x ? y  =  x++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  dec 0+x ? y  =  y++0 ? 0  =  dec (dec 0)+0 ? x  =  x+x ? 0  =  dec 0+x ? y  =  0++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  x+x ? y  =  dec x++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  x+x ? y  =  dec y++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  x+x ? y  =  dec 0++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  0+x ? y  =  dec x++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  0+x ? y  =  dec y++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  0+x ? y  =  dec 0++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  dec x+x ? y  =  x++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  dec x+x ? y  =  y++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  dec x+x ? y  =  0++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  dec 0+x ? y  =  x++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  dec 0+x ? y  =  y++0 ? 0  =  dec (dec 0)+0 ? x  =  0+x ? 0  =  dec 0+x ? y  =  0++0 ? 0  =  dec (dec 0)+0 ? x  =  dec x+x ? 0  =  x+x ? y  =  x++0 ? 0  =  dec (dec 0)+0 ? x  =  dec x+x ? 0  =  x+x ? y  =  y++0 ? 0  =  dec (dec 0)+0 ? x  =  dec x+x ? 0  =  x+x ? y  =  0++0 ? 0  =  dec (dec 0)+0 ? x  =  dec x+x ? 0  =  0+x ? y  =  x++0 ? 0  =  dec (dec 0)+0 ? x  =  dec x+x ? 0  =  0+x ? y  =  y++0 ? 0  =  dec (dec 0)+0 ? x  =  dec x+x ? 0  =  0+x ? y  =  0++0 ? 0  =  dec (dec 0)+0 ? x  =  dec 0+x ? 0  =  x+x ? y  =  x++0 ? 0  =  dec (dec 0)+0 ? x  =  dec 0+x ? 0  =  x+x ? y  =  y++0 ? 0  =  dec (dec 0)+0 ? x  =  dec 0+x ? 0  =  x+x ? y  =  0++0 ? 0  =  dec (dec 0)+0 ? x  =  dec 0+x ? 0  =  0+x ? y  =  x++0 ? 0  =  dec (dec 0)+0 ? x  =  dec 0+x ? 0  =  0+x ? y  =  y++0 ? 0  =  dec (dec 0)+0 ? x  =  dec 0+x ? 0  =  0+x ? y  =  0++0 ? 0  =  dec (dec (dec 0))+0 ? x  =  x+x ? 0  =  x+x ? y  =  x++0 ? 0  =  dec (dec (dec 0))+0 ? x  =  x+x ? 0  =  x+x ? y  =  y++0 ? 0  =  dec (dec (dec 0))+0 ? x  =  x+x ? 0  =  x+x ? y  =  0++0 ? 0  =  dec (dec (dec 0))+0 ? x  =  x+x ? 0  =  0+x ? y  =  x++0 ? 0  =  dec (dec (dec 0))+0 ? x  =  x+x ? 0  =  0+x ? y  =  y++0 ? 0  =  dec (dec (dec 0))+0 ? x  =  x+x ? 0  =  0+x ? y  =  0++0 ? 0  =  dec (dec (dec 0))+0 ? x  =  0+x ? 0  =  x+x ? y  =  x++0 ? 0  =  dec (dec (dec 0))+0 ? x  =  0+x ? 0  =  x+x ? y  =  y++0 ? 0  =  dec (dec (dec 0))+0 ? x  =  0+x ? 0  =  x+x ? y  =  0++0 ? 0  =  dec (dec (dec 0))+0 ? x  =  0+x ? 0  =  0+x ? y  =  x++0 ? 0  =  dec (dec (dec 0))+0 ? x  =  0+x ? 0  =  0+x ? y  =  y++0 ? 0  =  dec (dec (dec 0))+0 ? x  =  0+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+  [3,1,0,2,6,14,38,68,140] 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++ton p  =  p && ton p++ton p  =  p || ton p++ton p  =  p && ton (not p)++ton p  =  p || ton (not p)++ton p  =  p && not (ton p)++ton p  =  not p && ton p++ton p  =  p || not (ton p)++ton p  =  not p || ton p++ton p  =  p && not (ton (not p))++ton p  =  not p && ton (not p)++ton p  =  p || not (ton (not p))++ton p  =  not p || ton (not p)++ton p  =  p && (p && ton p)++ton p  =  p && (ton p && p)++ton p  =  p && (p || ton p)++ton p  =  p && (ton p || p)++ton p  =  not p && not (ton p)++ton p  =  p || p && ton p++ton p  =  p || ton p && p++ton p  =  p || (p || ton p)++ton p  =  p || (ton p || p)++ton p  =  not p || not (ton 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+  [4,2,4,8,32,128,468,1576,4924] direct candidates, 0 duplicates+  [4,14,30,8,4,48,60,280,592] 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 && p &| p++p &| q  =  p && p &| q++p &| q  =  p && p &| False++p &| q  =  p && p &| True++p &| q  =  p && q &| q++p &| q  =  p && False &| q++p &| q  =  p && True &| q++p &| q  =  q && p &| p++p &| q  =  q && p &| q++p &| q  =  q && p &| False++p &| q  =  q && p &| True++p &| q  =  q && q &| q++p &| q  =  q && False &| q++p &| q  =  q && True &| q++p &| q  =  p || p &| p++p &| q  =  p || p &| q++p &| q  =  p || p &| False++p &| q  =  p || p &| True++p &| q  =  p || q &| q++p &| q  =  p || False &| q++p &| q  =  p || True &| q++p &| q  =  q || p &| p++p &| q  =  q || p &| q++p &| q  =  q || p &| False++p &| q  =  q || p &| True++p &| q  =  q || q &| q++p &| q  =  q || False &| q++p &| q  =  q || True &| 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  =  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++p &| q  =  p && p &| not p++p &| q  =  p && p &| not q++p &| q  =  p && q &| not q++p &| q  =  p && False &| not q++p &| q  =  p && True &| not q++p &| q  =  p && not p &| p++p &| q  =  p && not p &| q++p &| q  =  p && not p &| False++p &| q  =  p && not p &| True++p &| q  =  p && not q &| q++p &| q  =  q && p &| not p++p &| q  =  q && p &| not q++p &| q  =  q && q &| not q++p &| q  =  q && False &| not q++p &| q  =  q && True &| not q++p &| q  =  q && not p &| p++p &| q  =  q && not p &| q++p &| q  =  q && not p &| False++p &| q  =  q && not p &| True++p &| q  =  q && not q &| q++p &| q  =  p || p &| not p++p &| q  =  p || p &| not q++p &| q  =  p || q &| not q++p &| q  =  p || False &| not q++p &| q  =  p || True &| not q++p &| q  =  p || not p &| p++p &| q  =  p || not p &| q++p &| q  =  p || not p &| False++p &| q  =  p || not p &| True++p &| q  =  p || not q &| q++p &| q  =  q || p &| not p++p &| q  =  q || p &| not q++p &| q  =  q || q &| not q++p &| q  =  q || False &| not q++p &| q  =  q || True &| not q++p &| q  =  q || not p &| p++p &| q  =  q || not p &| q++p &| q  =  q || not p &| False++p &| q  =  q || not p &| True++p &| q  =  q || not q &| q++p &| q  =  p && not (p &| p)++p &| q  =  p && not (p &| q)++p &| q  =  p && not (p &| False)++p &| q  =  p && not (p &| True)++p &| q  =  p && not (q &| q)++p &| q  =  p && not (False &| q)++p &| q  =  p && not (True &| q)++p &| q  =  q && not (p &| p)++p &| q  =  q && not (p &| q)++p &| q  =  q && not (p &| False)++p &| q  =  q && not (p &| True)++p &| q  =  q && not (q &| q)++p &| q  =  q && not (False &| q)++p &| q  =  q && not (True &| q)++p &| q  =  not p && p &| p++p &| q  =  not p && p &| q++p &| q  =  not p && p &| False++p &| q  =  not p && p &| True++p &| q  =  not p && q &| q++p &| q  =  not p && False &| q++p &| q  =  not p && True &| q++p &| q  =  not q && p &| p++p &| q  =  not q && p &| q++p &| q  =  not q && p &| False++p &| q  =  not q && p &| True++p &| q  =  not q && q &| q++p &| q  =  not q && False &| q++p &| q  =  not q && True &| q++p &| q  =  p || not (p &| p)++p &| q  =  p || not (p &| q)++p &| q  =  p || not (p &| False)++p &| q  =  p || not (p &| True)++p &| q  =  p || not (q &| q)++p &| q  =  p || not (False &| q)++p &| q  =  p || not (True &| q)++p &| q  =  q || not (p &| p)++p &| q  =  q || not (p &| q)++p &| q  =  q || not (p &| False)++p &| q  =  q || not (p &| True)++p &| q  =  q || not (q &| q)++p &| q  =  q || not (False &| q)++p &| q  =  q || not (True &| q)++p &| q  =  not p || p &| p++p &| q  =  not p || p &| q++p &| q  =  not p || p &| False++p &| q  =  not p || p &| True++p &| q  =  not p || q &| q++p &| q  =  not p || False &| q++p &| q  =  not p || True &| q++p &| q  =  not q || p &| p++p &| q  =  not q || p &| q++p &| q  =  not q || p &| False++p &| q  =  not q || p &| True++p &| q  =  not q || q &| q++p &| q  =  not q || False &| q++p &| q  =  not q || True &| 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  =  (not p || q) && p++p &| q  =  (not q || p) && q++p &| q  =  (p || not q) && q++p &| q  =  (q || not p) && p++p &| q  =  not p && q || p++p &| q  =  not q && p || q++p &| q  =  p && not q || q++p &| q  =  q && not p || 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 p && (p || q)++p &| q  =  not p && (q || p)++p &| q  =  not q && (p && q)++p &| q  =  not q && (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 p || (p || q)++p &| q  =  not p || (q || p)++p &| q  =  not q || p && q++p &| q  =  not q || q && p++p &| q  =  not q || (p || q)++p &| q  =  not q || (q || p)  p &| q  =  (p || q) && not p