code-conjure 0.4.0 → 0.4.2

raw patch · 84 files changed

+9338/−2660 lines, 84 filesPVP: major bump suggested

API removals or changes: PVP suggests a major version bump

API changes (from Hackage documentation)

Files

• .gitignore +6/−0
• Makefile +10/−4
• README.md +22/−22
• TODO.md +11/−4
• bench/candidates.hs +22/−16
• bench/candidates.out +7246/−1703
• bench/gps.hs +337/−0
• bench/gps.out +156/−0
• bench/ill-hit.out +18/−30
• bench/longshot.hs +1/−114
• bench/longshot.out +0/−77
• bench/lowtests.hs +86/−0
• bench/lowtests.out +81/−0
• bench/p12.out +7/−6
• bench/runtime/zero/bench/candidates.runtime +1/−1
• bench/runtime/zero/bench/gps.runtime +1/−0
• bench/runtime/zero/bench/ill-hit.runtime +1/−1
• bench/runtime/zero/bench/longshot.runtime +1/−1
• bench/runtime/zero/bench/lowtests.runtime +1/−0
• bench/runtime/zero/bench/p12.runtime +1/−1
• bench/runtime/zero/bench/take-drop.runtime +1/−1
• bench/runtime/zero/eg/arith.runtime +1/−1
• bench/runtime/zero/eg/bools.runtime +1/−1
• bench/runtime/zero/eg/count.runtime +1/−1
• bench/runtime/zero/eg/dupos.runtime +1/−0
• bench/runtime/zero/eg/factorial.runtime +1/−1
• bench/runtime/zero/eg/fib01.runtime +1/−0
• 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/−0
• bench/runtime/zero/eg/replicate.runtime +1/−1
• bench/runtime/zero/eg/setelem.runtime +1/−1
• bench/runtime/zero/eg/sort.runtime +1/−0
• bench/runtime/zero/eg/subset.runtime +1/−1
• bench/runtime/zero/eg/tapps.runtime +1/−1
• bench/runtime/zero/eg/tree.runtime +1/−1
• bench/runtime/zero/versions +2/−2
• bench/self.out +12/−12
• bench/take-drop.hs +7/−6
• bench/take-drop.out +27/−34
• changelog.md +13/−0
• code-conjure.cabal +2/−2
• eg/arith.out +12/−12
• eg/bools.out +18/−25
• eg/count.out +11/−15
• eg/dupos.hs +77/−0
• eg/dupos.out +43/−0
• eg/factorial.hs +0/−3
• eg/factorial.out +14/−17
• eg/fib01.hs +31/−0
• eg/fib01.out +25/−0
• eg/fibonacci.hs +15/−26
• eg/fibonacci.out +15/−32
• eg/gcd.hs +0/−1
• eg/gcd.out +8/−11
• eg/ints.out +29/−37
• eg/list.hs +0/−19
• eg/list.out +49/−88
• eg/pow.hs +42/−0
• eg/pow.out +24/−0
• eg/replicate.hs +3/−4
• eg/replicate.out +17/−24
• eg/setelem.out +20/−28
• eg/sort.hs +82/−0
• eg/sort.out +57/−0
• eg/spec.out +13/−21
• eg/subset.hs +6/−4
• eg/subset.out +11/−14
• eg/tapps.out +15/−19
• eg/tree.hs +9/−16
• eg/tree.out +66/−72
• mk/depend.mk +78/−0
• src/Conjure.hs +4/−2
• src/Conjure/Conjurable.hs +103/−14
• src/Conjure/Defn.hs +42/−31
• src/Conjure/Engine.hs +80/−66
• src/Conjure/Expr.hs +25/−0
• src/Conjure/Prim.hs +10/−4
• src/Conjure/Utils.hs +28/−0
• test/Test/ListableExpr.hs +0/−2
• test/conjurable.hs +45/−0
• test/defn.hs +84/−4
• test/expr.hs +38/−0

@@ -32,15 +32,19 @@ eg/arith eg/bools eg/count+eg/dupos eg/factorial eg/fibonacci+eg/fib01 eg/ints eg/gcd eg/list+eg/pow eg/tapps eg/tree eg/replicate eg/setelem+eg/sort eg/subset eg/spec bench/self@@ -51,6 +55,8 @@ bench/p12 bench/p30 bench/candidates+bench/gps+bench/lowtests proto/u-conjure test/expr test/conjurable

@@ -8,14 +8,18 @@ EG = \   eg/arith \   eg/count \+  eg/dupos \   eg/factorial \   eg/fibonacci \+  eg/fib01 \   eg/ints \   eg/bools \   eg/gcd \   eg/list \+  eg/pow \   eg/replicate \   eg/setelem \+  eg/sort \   eg/subset \   eg/spec \   eg/tapps \@@ -23,10 +27,12 @@   bench/candidates \   bench/ill-hit \   bench/longshot \+  bench/lowtests \   bench/self \   bench/take-drop \   bench/p12 \   bench/p30 \+  bench/gps \   proto/u-conjure  TESTS = \@@ -39,10 +45,10 @@  all-all: all $(EG) $(TESTS) -test: $(patsubst %,%.run,$(TESTS)) diff-test test-sdist+test: $(TESTS) $(patsubst %,%.run,$(TESTS)) diff-test test-sdist  .PHONY: bench-bench: $(patsubst %,%.bench,$(EG))+bench: $(EG) $(patsubst %,%.bench,$(EG)) 	@mkdir -p bench/runtime/$$HOSTNAME 	./bench/versions | tee bench/runtime/$$HOSTNAME/versions @@ -55,9 +61,9 @@ 	python3 -c 'print("%.1f" % float(input()))' | \ 	tee bench/runtime/$$HOSTNAME/$<.runtime -diff-test: $(patsubst %,%.diff-test,$(EG))+diff-test: $(EG) $(patsubst %,%.diff-test,$(EG)) -out: $(patsubst %,%.out,$(EG))+out: $(EG) $(patsubst %,%.out,$(EG))  test-sdist: 	./test/sdist

@@ -37,8 +37,12 @@ Conjuring functions ------------------- -Given+You first need to import the library with: +	import Conjure++Then, given+ 	square :: Int -> Int 	square 0  =  0 	square 1  =  1@@ -61,9 +65,10 @@  	square :: Int -> Int 	-- testing 3 combinations of argument values+	-- pruning with 14/25 rules 	-- looking through 3 candidates of size 1-	-- looking through 3 candidates of size 2-	-- looking through 5 candidates of size 3+	-- looking through 4 candidates of size 2+	-- looking through 9 candidates of size 3 	square x  =  x * x  in less than a second.@@ -77,12 +82,10 @@ Given  	factorial :: Int -> Int-	factorial 0  =  1 	factorial 1  =  1 	factorial 2  =  2 	factorial 3  =  6 	factorial 4  =  24-	factorial 5  =  120  and @@ -92,7 +95,6 @@ 	               , prim "+" ((+) :: Int -> Int -> Int) 	               , prim "*" ((*) :: Int -> Int -> Int) 	               , prim "dec" (subtract 1 :: Int -> Int)-	               , prim "==" ((==) :: Int -> Int -> Bool) 	               ]  running@@ -102,28 +104,26 @@ yields  	factorial :: Int -> Int-	-- testing 6 combinations of argument values+	-- testing 4 combinations of argument values+	-- pruning with 22/42 rules 	-- looking through 3 candidates of size 1-	-- looking through 5 candidates of size 2-	-- looking through 8 candidates of size 3-	-- looking through 26 candidates of size 4-	-- looking through 59 candidates of size 5-	-- looking through 167 candidates of size 6-	-- looking through 581 candidates of size 7-	-- looking through 1654 candidates of size 8-	-- looking through 5754 candidates of size 9-	-- looking through 17797 candidates of size 10-	factorial n  =  if n == 0 then 1 else n * factorial (dec n)+	-- 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+	factorial 0  =  1+	factorial x  =  x * factorial (dec x) -in about 3 seconds.+in less than a second. -See the `eg/factorial.hs` example.+It is also possible to generate -It is also possible to generate:+	factorial x  =  foldr (*) 1 [1..x] -    factorial n  =  if n == 0 then 1 else n * factorial (n - 1)+by including `enumFromTo` and `foldr` in the background. -in about 90s by including `(-) :: Int -> Int -> Int` in the primitives.+See the `eg/factorial.hs` example.   Related work

@@ -3,14 +3,21 @@  A non-exhaustive list of things TO DO for Conjure. -* add switch for case candidates?+* pretty-print top-level ifs? -* improve pruning of generated case candidates+* carry on implementing all GPS benches while taking notes on the paper +* consider memoizing `recs ep` in `candidateDefnsC`+  and a sub function with `vs` arguments. -### for later+* remove `requireDescent=False` requirement from `gcd`+  (add and use `isDeconstruction`)+  this would also eliminate the requirement of providing `dec` -* add machinery to reify `Int -> Int` from the `(Expr,Expr)` definition+* consider not breaking in some cases (increased crossproduct of patterns)+++### for later  * allow specifying properties that need to be true 

@@ -7,54 +7,60 @@ import Conjure.Defn import Data.Express.Fixtures -printCandidates :: Conjurable f => Int -> String -> f -> [Prim] -> IO ()-printCandidates n nm f ps  =  do+printCandidates :: Conjurable f => Int -> Int -> String -> f -> [Prim] -> IO ()+printCandidates m n nm f ps  =  do   putStrLn $ "Candidates for: " ++ nm ++ " :: " ++ show (typeOf f)   putStrLn $ "  pruning with " ++ show nRules ++ "/" ++ show nREs ++ " rules"-  putStrLn $ "  " ++ show (map length cs1) ++ " direct candidates"-  putStrLn $ "  " ++ show (map length csC) ++ " pattern candidates"+  putStrLn $ "  " ++ show (map length css1) ++ " direct candidates, " ++ show nd1 ++ " duplicates"+  putStrLn $ "  " ++ show (map length cssC) ++ " pattern candidates, " ++ show ndC ++ " duplicates"   putStrLn ""   printThy thy   putStrLn $ "direct candidates:\n"-  putStrLn $ unlines $ map showDefn $ concat $ cs1+  putStrLn $ unlines $ map showDefn $ concat $ take n $ css1   putStrLn $ "pattern candidates:\n"-  putStrLn $ unlines $ map showDefn $ concat $ csC+  putStrLn $ unlines $ map showDefn $ concat $ take n $ cssC   where-  cs1  =  take n cs1'-  csC  =  take n csC'-  (cs1', thy)  =  candidateDefns1 args nm f ps-  (csC', _)    =  candidateDefnsC args nm f ps+  nd1  =  length cs1 - length (nubSort cs1)+  ndC  =  length csC - length (nubSort csC)+  cs1  =  concat css1+  csC  =  concat cssC+  css1  =  take m css1'+  cssC  =  take m cssC'+  (css1', thy)  =  candidateDefns1 args nm f ps+  (cssC', _)    =  candidateDefnsC args nm f ps   nRules  =  length (rules thy)   nREs  =  length (equations thy) + nRules  main :: IO () main  =  do-  printCandidates 6 "foo" (undefined :: Int -> Int)+  printCandidates 9 6 "foo" (undefined :: Int -> Int)     [ pr (0 :: Int)     , pr (1 :: Int)     , prim "+" ((+) :: Int -> Int -> Int)     , prim "*" ((+) :: Int -> Int -> Int)+    , prim "dec" (subtract 1 :: Int -> Int)     ] -  printCandidates 4 "?" (undefined :: Int -> Int -> Int)+  printCandidates 9 6 "?" (undefined :: Int -> Int -> Int)     [ pr (0 :: Int)     , prim "+" ((+) :: Int -> Int -> Int)     , prim "*" ((+) :: Int -> Int -> Int)+    , prim "dec" (subtract 1 :: Int -> Int)     ] -  printCandidates 6 "goo" (undefined :: [Int] -> [Int])+  printCandidates 9 6 "goo" (undefined :: [Int] -> [Int])     [ pr ([] :: [Int])     , prim ":" ((:) :: Int -> [Int] -> [Int])     , prim "++" ((++) :: [Int] -> [Int] -> [Int])     ] -  printCandidates 4 "??" (undefined :: [Int] -> [Int] -> [Int])+  printCandidates 9 6 "??" (undefined :: [Int] -> [Int] -> [Int])     [ pr ([] :: [Int])     , prim ":" ((:) :: Int -> [Int] -> [Int])     , prim "++" ((++) :: [Int] -> [Int] -> [Int])     ] -  printCandidates 6 "ton" (undefined :: Bool -> Bool)+  printCandidates 9 6 "ton" (undefined :: Bool -> Bool)     [ pr False     , pr True     , prim "&&" (&&)@@ -62,7 +68,7 @@     , prim "not" not     ] -  printCandidates 6 "&|" (undefined :: Bool -> Bool -> Bool)+  printCandidates 9 6 "&|" (undefined :: Bool -> Bool -> Bool)     [ pr False     , pr True     , prim "&&" (&&)

@@ -1,1707 +1,7250 @@ Candidates for: foo :: Int -> Int-  pruning with 6/10 rules-  [3,0,4,0,8,0] direct candidates-  [3,4,8,21,39,70] pattern candidates--rules:-x * y == x + y-x * y == y + x-x + 0 == x-0 + x == x-(x + y) + z == x + (y + z)-(x + y) + z == y + (x + z)-equations:-y + x == x + y-y + (x + z) == x + (y + z)-z + (x + y) == x + (y + z)-z + (y + x) == x + (y + z)--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 + (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)---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 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  =  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 + 1-foo x  =  x--foo 0  =  1 + 1-foo x  =  0--foo 0  =  1 + 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 + x)--foo 0  =  0-foo x  =  foo (x + 1)--foo 0  =  0-foo x  =  foo (x + 1)--foo 0  =  0-foo x  =  foo (1 + x)--foo 0  =  0-foo x  =  foo (1 + x)--foo 0  =  0-foo x  =  foo (x + x)--foo 0  =  0-foo x  =  foo (x + 1)--foo 0  =  0-foo x  =  foo (x + 1)--foo 0  =  0-foo x  =  foo (1 + x)--foo 0  =  0-foo x  =  foo (1 + x)--foo 0  =  1-foo x  =  foo (x + x)--foo 0  =  1-foo x  =  foo (x + 1)--foo 0  =  1-foo x  =  foo (x + 1)--foo 0  =  1-foo x  =  foo (1 + x)--foo 0  =  1-foo x  =  foo (1 + x)--foo 0  =  1-foo x  =  foo (x + x)--foo 0  =  1-foo x  =  foo (x + 1)--foo 0  =  1-foo x  =  foo (x + 1)--foo 0  =  1-foo x  =  foo (1 + x)--foo 0  =  1-foo x  =  foo (1 + 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 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  =  1 + 1-foo x  =  x--foo 1  =  1 + 1-foo x  =  0--foo 1  =  1 + 1-foo x  =  1--foo 1  =  0-foo x  =  foo (x + x)--foo 1  =  0-foo x  =  foo (x + 1)--foo 1  =  0-foo x  =  foo (x + 1)--foo 1  =  0-foo x  =  foo (1 + x)--foo 1  =  0-foo x  =  foo (1 + x)--foo 1  =  0-foo x  =  foo (x + x)--foo 1  =  0-foo x  =  foo (x + 1)--foo 1  =  0-foo x  =  foo (x + 1)--foo 1  =  0-foo x  =  foo (1 + x)--foo 1  =  0-foo x  =  foo (1 + x)--foo 1  =  1-foo x  =  foo (x + x)--foo 1  =  1-foo x  =  foo (x + 1)--foo 1  =  1-foo x  =  foo (x + 1)--foo 1  =  1-foo x  =  foo (1 + x)--foo 1  =  1-foo x  =  foo (1 + x)--foo 1  =  1-foo x  =  foo (x + x)--foo 1  =  1-foo x  =  foo (x + 1)--foo 1  =  1-foo x  =  foo (x + 1)--foo 1  =  1-foo x  =  foo (1 + x)--foo 1  =  1-foo x  =  foo (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  =  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 + (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 + 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  =  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  =  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  =  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 + 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 6/10 rules-  [3,0,4,0] direct candidates-  [3,8,15,84] pattern candidates--rules:-x * y == x + y-x * y == y + x-x + 0 == x-0 + x == x-(x + y) + z == x + (y + z)-(x + y) + z == y + (x + z)-equations:-y + x == x + y-y + (x + z) == x + (y + z)-z + (x + y) == x + (y + z)-z + (y + x) == x + (y + z)--direct candidates:--x ? y  =  x--x ? y  =  y--x ? y  =  0--x ? y  =  x + x--x ? y  =  x + y--x ? y  =  y + x--x ? y  =  y + y---pattern candidates:--x ? y  =  x--x ? y  =  y--x ? y  =  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--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 ? 0  =  x-x ? y  =  x ? x--x ? 0  =  x-x ? y  =  x ? 0--x ? 0  =  x-x ? y  =  x ? 0--x ? 0  =  x-x ? y  =  y ? x--x ? 0  =  x-x ? y  =  y ? y--x ? 0  =  x-x ? y  =  y ? 0--x ? 0  =  x-x ? y  =  y ? 0--x ? 0  =  x-x ? y  =  0 ? x--x ? 0  =  x-x ? y  =  0 ? y--x ? 0  =  x-x ? y  =  0 ? x--x ? 0  =  x-x ? y  =  0 ? y--x ? 0  =  x ? x-x ? y  =  x--x ? 0  =  0 ? x-x ? y  =  x--x ? 0  =  0 ? x-x ? y  =  x--x ? 0  =  x ? x-x ? y  =  y--x ? 0  =  0 ? x-x ? y  =  y--x ? 0  =  0 ? x-x ? y  =  y--x ? 0  =  x ? x-x ? y  =  0--x ? 0  =  0 ? x-x ? y  =  0--x ? 0  =  0 ? x-x ? y  =  0--x ? 0  =  0-x ? y  =  x ? x--x ? 0  =  0-x ? y  =  x ? 0--x ? 0  =  0-x ? y  =  x ? 0--x ? 0  =  0-x ? y  =  y ? x--x ? 0  =  0-x ? y  =  y ? y--x ? 0  =  0-x ? y  =  y ? 0--x ? 0  =  0-x ? y  =  y ? 0--x ? 0  =  0-x ? y  =  0 ? x--x ? 0  =  0-x ? y  =  0 ? y--x ? 0  =  0-x ? y  =  0 ? x--x ? 0  =  0-x ? y  =  0 ? y--0 ? x  =  x-x ? y  =  x ? x--0 ? x  =  x-x ? y  =  x ? 0--0 ? x  =  x-x ? y  =  x ? 0--0 ? x  =  x-x ? y  =  y ? x--0 ? x  =  x-x ? y  =  y ? y--0 ? x  =  x-x ? y  =  y ? 0--0 ? x  =  x-x ? y  =  y ? 0--0 ? x  =  x-x ? y  =  0 ? x--0 ? x  =  x-x ? y  =  0 ? y--0 ? x  =  x-x ? y  =  0 ? x--0 ? x  =  x-x ? y  =  0 ? y--0 ? x  =  x ? x-x ? y  =  x--0 ? x  =  x ? 0-x ? y  =  x--0 ? x  =  x ? 0-x ? y  =  x--0 ? x  =  x ? x-x ? y  =  y--0 ? x  =  x ? 0-x ? y  =  y--0 ? x  =  x ? 0-x ? y  =  y--0 ? x  =  x ? x-x ? y  =  0--0 ? x  =  x ? 0-x ? y  =  0--0 ? x  =  x ? 0-x ? y  =  0--0 ? x  =  0-x ? y  =  x ? x--0 ? x  =  0-x ? y  =  x ? 0--0 ? x  =  0-x ? y  =  x ? 0--0 ? x  =  0-x ? y  =  y ? x--0 ? x  =  0-x ? y  =  y ? y--0 ? x  =  0-x ? y  =  y ? 0--0 ? x  =  0-x ? y  =  y ? 0--0 ? x  =  0-x ? y  =  0 ? x--0 ? x  =  0-x ? y  =  0 ? y--0 ? x  =  0-x ? y  =  0 ? x--0 ? x  =  0-x ? y  =  0 ? y--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  =  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  =  x + x-x ? y  =  x--0 ? x  =  x + x-x ? y  =  y--0 ? x  =  x + x-x ? y  =  0---Candidates for: goo :: [Int] -> [Int]-  pruning with 4/4 rules-  [2,0,1,0,1,0] direct candidates-  [2,1,2,3,10,7] pattern candidates--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)  =  goo [x]--goo []  =  []-goo (x:xs)  =  goo [x]--goo []  =  []-goo (x:xs)  =  goo [x]--goo []  =  []-goo (x:xs)  =  goo [x]--goo []  =  []-goo (x:xs)  =  goo (xs ++ xs)--goo []  =  []-goo (x:xs)  =  goo (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] direct candidates-  [3,8,15,82] pattern candidates--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---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)  =  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)  =  ys ?? []--xs ?? []  =  xs-xs ?? (x:ys)  =  [] ?? xs--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)  =  xs ?? []--xs ?? []  =  []-xs ?? (x:ys)  =  ys ?? xs--xs ?? []  =  []-xs ?? (x:ys)  =  ys ?? ys--xs ?? []  =  []-xs ?? (x:ys)  =  ys ?? []--xs ?? []  =  []-xs ?? (x:ys)  =  ys ?? []--xs ?? []  =  []-xs ?? (x:ys)  =  [] ?? xs--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  =  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  =  ys ?? []--[] ?? xs  =  xs-(x:xs) ?? ys  =  [] ?? xs--[] ?? 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  =  xs ?? []--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ?? xs--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ?? ys--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ?? []--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ?? []--[] ?? xs  =  []-(x:xs) ?? ys  =  [] ?? xs--[] ?? 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  =  []---Candidates for: ton :: Bool -> Bool-  pruning with 39/49 rules-  [3,1,0,0,2,4] direct candidates-  [3,3,0,0,0,0] pattern candidates--rules:-not False == True-not True == False-p && p == p-p || p == p-not (not p) == p-p && False == False-p && True == p-False && p == False-True && p == p-p || False == p-p || True == True-False || p == p-True || p == True-not (p && q) == not p || not q-not (p && q) == not q || not p-not (p || q) == not p && not q-not (p || q) == not q && not p-p && not p == False-not p && p == False-p || not p == True-not p || p == True-(p && q) && r == p && (q && r)-(p && q) && r == q && (p && r)-(p || q) || r == p || (q || r)-(p || q) || r == q || (p || r)-p && (p && q) == p && q-p && (q && p) == p && q-p && (q && p) == q && p-p || (p || q) == p || q-p || (q || p) == p || q-p || (q || p) == q || p-p && (p || q) == p-p && (q || p) == p-(p || q) && p == p-(p || q) && q == q-p || p && q == p-p || q && p == p-p && q || p == p-p && q || q == q-equations:-q && p == p && q-q || p == p || q-q && (p && r) == p && (q && r)-r && (p && q) == p && (q && r)-r && (q && p) == p && (q && r)-q || (p || r) == p || (q || r)-r || (p || q) == p || (q || r)-r || (q || p) == p || (q || r)-(r || q) && p == p && (q || r)-r && q || p == p || q && r--direct candidates:--ton p  =  p--ton p  =  False--ton p  =  True--ton p  =  not p--ton p  =  p && ton (not p)--ton p  =  p || ton (not 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)---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-  [4,2,4,8,4,72] direct candidates-  [4,14,30,8,4,32] pattern candidates--rules:-not False == True-not True == False-p && p == p-p || p == p-not (not p) == p-p && False == False-p && True == p-False && p == False-True && p == p-p || False == p-p || True == True-False || p == p-True || p == True-not (p && q) == not p || not q-not (p && q) == not q || not p-not (p || q) == not p && not q-not (p || q) == not q && not p-p && not p == False-not p && p == False-p || not p == True-not p || p == True-(p && q) && r == p && (q && r)-(p && q) && r == q && (p && r)-(p || q) || r == p || (q || r)-(p || q) || r == q || (p || r)-p && (p && q) == p && q-p && (q && p) == p && q-p && (q && p) == q && p-p || (p || q) == p || q-p || (q || p) == p || q-p || (q || p) == q || p-p && (p || q) == p-p && (q || p) == p-(p || q) && p == p-(p || q) && q == q-p || p && q == p-p || q && p == p-p && q || p == p-p && q || q == q-equations:-q && p == p && q-q || p == p || q-q && (p && r) == p && (q && r)-r && (p && q) == p && (q && r)-r && (q && p) == p && (q && r)-q || (p || r) == p || (q || r)-r || (p || q) == p || (q || r)-r || (q || p) == p || (q || r)-(r || q) && p == p && (q || r)-r && q || p == p || q && r--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--p &| q  =  p && p &| not q--p &| q  =  p && q &| not p--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 &| p--p &| q  =  q && p &| not q--p &| q  =  q && q &| not p--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 &| p--p &| q  =  p || p &| not q--p &| q  =  p || q &| not p--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 &| p--p &| q  =  q || p &| not q--p &| q  =  q || q &| not p--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 &| p+  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: