YES 9.809000000000001
H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ LR
mainModule FiniteMap
|
| ((eltsFM_LE :: (Ord b, Ord a) => FiniteMap (Either b a) c -> Either b a -> [c]) :: (Ord b, Ord a) => FiniteMap (Either b a) c -> Either b a -> [c]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord a => FiniteMap a b -> a -> [b]
| eltsFM_LE | fm fr | = | foldFM_LE (\key elt rest ->elt : rest) [] fr fm |
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM (\key elt rest ->(key,elt) : rest) [] fm |
|
| | foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Lambda Reductions:
The following Lambda expression
\keyeltrest→(key,elt) : rest
is transformed to
| fmToList0 | key elt rest | = (key,elt) : rest |
The following Lambda expression
\keyeltrest→elt : rest
is transformed to
| eltsFM_LE0 | key elt rest | = elt : rest |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
mainModule FiniteMap
|
| ((eltsFM_LE :: (Ord c, Ord b) => FiniteMap (Either c b) a -> Either c b -> [a]) :: (Ord c, Ord b) => FiniteMap (Either c b) a -> Either c b -> [a]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord a => FiniteMap a b -> a -> [b]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Case Reductions:
The following Case expression
| case | compare x y of |
| | EQ | → o |
| | LT | → LT |
| | GT | → GT |
is transformed to
| primCompAux0 | o EQ | = o |
| primCompAux0 | o LT | = LT |
| primCompAux0 | o GT | = GT |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
mainModule FiniteMap
|
| ((eltsFM_LE :: (Ord b, Ord c) => FiniteMap (Either b c) a -> Either b c -> [a]) :: (Ord c, Ord b) => FiniteMap (Either b c) a -> Either b c -> [a]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord b => FiniteMap b a -> b -> [a]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (b -> c -> a -> a) -> a -> FiniteMap b c -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
If Reductions:
The following If expression
if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero
is transformed to
| primDivNatS0 | x y True | = Succ (primDivNatS (primMinusNatS x y) (Succ y)) |
| primDivNatS0 | x y False | = Zero |
The following If expression
if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x
is transformed to
| primModNatS0 | x y True | = primModNatS (primMinusNatS x y) (Succ y) |
| primModNatS0 | x y False | = Succ x |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
mainModule FiniteMap
|
| ((eltsFM_LE :: (Ord a, Ord c) => FiniteMap (Either a c) b -> Either a c -> [b]) :: (Ord a, Ord c) => FiniteMap (Either a c) b -> Either a c -> [b]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord b => FiniteMap b a -> b -> [a]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (b -> a -> c -> c) -> c -> FiniteMap b a -> c
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule FiniteMap
|
| ((eltsFM_LE :: (Ord b, Ord a) => FiniteMap (Either b a) c -> Either b a -> [c]) :: (Ord b, Ord a) => FiniteMap (Either b a) c -> Either b a -> [c]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord b => FiniteMap b a -> b -> [a]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (b -> c -> a -> a) -> a -> FiniteMap b c -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Cond Reductions:
The following Function with conditions
| foldFM_LE | k z fr EmptyFM | = z |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) |
| | | key <= fr |
| = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | |
|
is transformed to
| foldFM_LE | k z fr EmptyFM | = foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = foldFM_LE k z fr fm_l |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
| foldFM_LE3 | k z fr EmptyFM | = z |
| foldFM_LE3 | vvu vvv vvw vvx | = foldFM_LE2 vvu vvv vvw vvx |
The following Function with conditions
| compare | x y |
| | | x == y | |
| | | x <= y | |
| | | otherwise | |
|
is transformed to
| compare | x y | = compare3 x y |
| compare2 | x y True | = EQ |
| compare2 | x y False | = compare1 x y (x <= y) |
| compare1 | x y True | = LT |
| compare1 | x y False | = compare0 x y otherwise |
| compare3 | x y | = compare2 x y (x == y) |
The following Function with conditions
| gcd' | x 0 | = x |
| gcd' | x y | = gcd' y (x `rem` y) |
is transformed to
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
| gcd'0 | x y | = gcd' y (x `rem` y) |
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
The following Function with conditions
| gcd | 0 0 | = error [] |
| gcd | x y | =
| gcd' (abs x) (abs y) |
| where |
| gcd' | x 0 | = x |
| gcd' | x y | = gcd' y (x `rem` y) |
|
|
is transformed to
| gcd | vwy vwz | = gcd3 vwy vwz |
| gcd | x y | = gcd0 x y |
| gcd0 | x y | =
| gcd' (abs x) (abs y) |
| where |
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
|
|
| gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
|
|
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
|
|
| gcd1 | True vwy vwz | = error [] |
| gcd1 | vxu vxv vxw | = gcd0 vxv vxw |
| gcd2 | True vwy vwz | = gcd1 (vwz == 0) vwy vwz |
| gcd2 | vxx vxy vxz | = gcd0 vxy vxz |
| gcd3 | vwy vwz | = gcd2 (vwy == 0) vwy vwz |
| gcd3 | vyu vyv | = gcd0 vyu vyv |
The following Function with conditions
is transformed to
| absReal1 | x True | = x |
| absReal1 | x False | = absReal0 x otherwise |
| absReal0 | x True | = `negate` x |
| absReal2 | x | = absReal1 x (x >= 0) |
The following Function with conditions
is transformed to
| undefined0 | True | = undefined |
| undefined1 | | = undefined0 False |
The following Function with conditions
| reduce | x y |
| | | y == 0 | |
| | | otherwise |
| = | x `quot` d :% (y `quot` d) |
|
|
| where | |
|
is transformed to
| reduce2 | x y | =
| reduce1 x y (y == 0) |
| where | |
|
| reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
| reduce1 | x y True | = error [] |
| reduce1 | x y False | = reduce0 x y otherwise |
|
|
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
mainModule FiniteMap
|
| ((eltsFM_LE :: (Ord b, Ord a) => FiniteMap (Either b a) c -> Either b a -> [c]) :: (Ord b, Ord a) => FiniteMap (Either b a) c -> Either b a -> [c]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord a => FiniteMap a b -> a -> [b]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (a -> b -> c -> c) -> c -> FiniteMap a b -> c
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Let/Where Reductions:
The bindings of the following Let/Where expression
| reduce1 x y (y == 0) |
| where | |
|
| reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
| reduce1 | x y True | = error [] |
| reduce1 | x y False | = reduce0 x y otherwise |
|
are unpacked to the following functions on top level
| reduce2Reduce0 | vyw vyx x y True | = x `quot` reduce2D vyw vyx :% (y `quot` reduce2D vyw vyx) |
| reduce2Reduce1 | vyw vyx x y True | = error [] |
| reduce2Reduce1 | vyw vyx x y False | = reduce2Reduce0 vyw vyx x y otherwise |
| reduce2D | vyw vyx | = gcd vyw vyx |
The bindings of the following Let/Where expression
| gcd' (abs x) (abs y) |
| where |
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
|
|
| gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
|
|
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
|
are unpacked to the following functions on top level
| gcd0Gcd' | x vvy | = gcd0Gcd'2 x vvy |
| gcd0Gcd' | x y | = gcd0Gcd'0 x y |
| gcd0Gcd'1 | True x vvy | = x |
| gcd0Gcd'1 | vvz vwu vwv | = gcd0Gcd'0 vwu vwv |
| gcd0Gcd'2 | x vvy | = gcd0Gcd'1 (vvy == 0) x vvy |
| gcd0Gcd'2 | vww vwx | = gcd0Gcd'0 vww vwx |
| gcd0Gcd'0 | x y | = gcd0Gcd' y (x `rem` y) |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
mainModule FiniteMap
|
| ((eltsFM_LE :: (Ord a, Ord c) => FiniteMap (Either a c) b -> Either a c -> [b]) :: (Ord a, Ord c) => FiniteMap (Either a c) b -> Either a c -> [b]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord a => FiniteMap a b -> a -> [b]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
mainModule FiniteMap
|
| (eltsFM_LE :: (Ord b, Ord c) => FiniteMap (Either c b) a -> Either c b -> [a]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord a => FiniteMap a b -> a -> [b]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord b => (b -> c -> a -> a) -> a -> b -> FiniteMap b c -> a
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | Pos Zero |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Haskell To QDPs
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primCmpNat(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat(vyy30000, vyy4000)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primCmpNat(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat(vyy30000, vyy4000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(vyy10300), Succ(vyy400000)) → new_primPlusNat(vyy10300, vyy400000)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primPlusNat(Succ(vyy10300), Succ(vyy400000)) → new_primPlusNat(vyy10300, vyy400000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primMulNat(Succ(vyy300000), Succ(vyy40000)) → new_primMulNat(vyy300000, Succ(vyy40000))
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primMulNat(Succ(vyy300000), Succ(vyy40000)) → new_primMulNat(vyy300000, Succ(vyy40000))
The graph contains the following edges 1 > 1, 2 >= 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), h, ba) → new_foldFM(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, h, ba), vyy4733, h, ba)
new_foldFM(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), h, ba) → new_foldFM(vyy470, vyy471, vyy102, vyy4734, h, ba)
The TRS R consists of the following rules:
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, h, ba) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), h, ba) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, h, ba), vyy4733, h, ba)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), h, ba) → new_foldFM(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, h, ba), vyy4733, h, ba)
The graph contains the following edges 4 > 1, 4 > 2, 4 > 4, 5 >= 5, 6 >= 6
- new_foldFM(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), h, ba) → new_foldFM(vyy470, vyy471, vyy102, vyy4734, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5, 6 >= 6
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM1(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), h, ba) → new_foldFM1(vyy474, h, ba)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM1(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), h, ba) → new_foldFM1(vyy474, h, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primEqNat(Succ(vyy4700), Succ(vyy4800)) → new_primEqNat(vyy4700, vyy4800)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primEqNat(Succ(vyy4700), Succ(vyy4800)) → new_primEqNat(vyy4700, vyy4800)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy470, vyy480, bde, bdf)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(ty_[], bcd)) → new_esEs(vyy470, vyy480, bcd)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy470, vyy480, bfe, bff, bfg)
new_esEs1(Just(vyy470), Just(vyy480), app(app(app(ty_@3, hc), hd), he)) → new_esEs0(vyy470, vyy480, hc, hd, he)
new_esEs2(vyy47, vyy48, bae, baf) → new_esEs(new_fmToList(vyy47, bae, baf), new_fmToList(vyy48, bae, baf), app(app(ty_@2, bae), baf))
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy470, vyy480, bfh)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy470, vyy480, bdc, bdd)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_@2, gh), ha), ce, ec) → new_esEs4(vyy470, vyy480, gh, ha)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(ty_[], cf)) → new_esEs(vyy472, vyy482, cf)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs0(vyy470, vyy480, bce, bcf, bcg)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy470, vyy480, bbg, bbh)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_Either, baa), bab)) → new_esEs3(vyy470, vyy480, baa, bab)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy471, vyy481, bea, beb, bec)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_FiniteMap, bf), bg)) → new_esEs2(vyy470, vyy480, bf, bg)
new_esEs1(Just(vyy470), Just(vyy480), app(ty_[], hb)) → new_esEs(vyy470, vyy480, hb)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy471, vyy481, beg, beh)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, bh), ca)) → new_esEs3(vyy470, vyy480, bh, ca)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(ty_[], eb), ec) → new_esEs(vyy471, vyy481, eb)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_FiniteMap, bee), bef)) → new_esEs2(vyy471, vyy481, bee, bef)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, bbe), bbf), bah) → new_esEs2(vyy470, vyy480, bbe, bbf)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy470, vyy480, bca, bcb)
new_esEs1(Just(vyy470), Just(vyy480), app(ty_Maybe, hf)) → new_esEs1(vyy470, vyy480, hf)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_@2, cb), cc)) → new_esEs4(vyy470, vyy480, cb, cc)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, hg), hh)) → new_esEs2(vyy470, vyy480, hg, hh)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy471, vyy481, bfa, bfb)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_FiniteMap, bda), bdb)) → new_esEs2(vyy470, vyy480, bda, bdb)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(ty_Maybe, eg), ec) → new_esEs1(vyy471, vyy481, eg)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_FiniteMap, eh), fa), ec) → new_esEs2(vyy471, vyy481, eh, fa)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_@2, bac), bad)) → new_esEs4(vyy470, vyy480, bac, bad)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_Either, df), dg)) → new_esEs3(vyy472, vyy482, df, dg)
new_esEs3(Left(vyy470), Left(vyy480), app(ty_Maybe, bbd), bah) → new_esEs1(vyy470, vyy480, bbd)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_@2, fd), ff), ec) → new_esEs4(vyy471, vyy481, fd, ff)
new_esEs3(Left(vyy470), Left(vyy480), app(ty_[], bag), bah) → new_esEs(vyy470, vyy480, bag)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(app(ty_@3, ed), ee), ef), ec) → new_esEs0(vyy471, vyy481, ed, ee, ef)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(ty_[], bdh)) → new_esEs(vyy471, vyy481, bdh)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy471, vyy481, bed)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_FiniteMap, bga), bgb), bfd) → new_esEs2(vyy470, vyy480, bga, bgb)
new_esEs3(Left(vyy470), Left(vyy480), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(vyy470, vyy480, bba, bbb, bbc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_[], fg), ce, ec) → new_esEs(vyy470, vyy480, fg)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_FiniteMap, gd), ge), ce, ec) → new_esEs2(vyy470, vyy480, gd, ge)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), h) → new_esEs(vyy471, vyy481, h)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy472, vyy482, cg, da, db)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(ty_Maybe, dc)) → new_esEs1(vyy472, vyy482, dc)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_[], bfc), bfd) → new_esEs(vyy470, vyy480, bfc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy472, vyy482, dd, de)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(ty_Maybe, bch)) → new_esEs1(vyy470, vyy480, bch)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_Either, gf), gg), ce, ec) → new_esEs3(vyy470, vyy480, gf, gg)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy470, vyy480, bgc, bgd)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy470, vyy480, bb, bc, bd)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_Maybe, gc), ce, ec) → new_esEs1(vyy470, vyy480, gc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_Either, fb), fc), ec) → new_esEs3(vyy471, vyy481, fb, fc)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_[], ba)) → new_esEs(vyy470, vyy480, ba)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_@2, dh), ea)) → new_esEs4(vyy472, vyy482, dh, ea)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(app(ty_@3, fh), ga), gb), ce, ec) → new_esEs0(vyy470, vyy480, fh, ga, gb)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, be)) → new_esEs1(vyy470, vyy480, be)
The TRS R consists of the following rules:
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, bae, baf) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), bae, baf) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, bae, baf), vyy4733, bae, baf)
new_fmToList(vyy47, bae, baf) → new_foldFM2(vyy47, bae, baf)
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), bae, baf) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, bae, baf), vyy473, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs2(vyy47, vyy48, bae, baf) → new_esEs(new_fmToList(vyy47, bae, baf), new_fmToList(vyy48, bae, baf), app(app(ty_@2, bae), baf)) at position [0] we obtained the following new rules:
new_esEs2(vyy47, vyy48, bae, baf) → new_esEs(new_foldFM2(vyy47, bae, baf), new_fmToList(vyy48, bae, baf), app(app(ty_@2, bae), baf))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy470, vyy480, bde, bdf)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(ty_[], bcd)) → new_esEs(vyy470, vyy480, bcd)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy470, vyy480, bfe, bff, bfg)
new_esEs1(Just(vyy470), Just(vyy480), app(app(app(ty_@3, hc), hd), he)) → new_esEs0(vyy470, vyy480, hc, hd, he)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy470, vyy480, bdc, bdd)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy470, vyy480, bfh)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_@2, gh), ha), ce, ec) → new_esEs4(vyy470, vyy480, gh, ha)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(ty_[], cf)) → new_esEs(vyy472, vyy482, cf)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs0(vyy470, vyy480, bce, bcf, bcg)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy470, vyy480, bbg, bbh)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy471, vyy481, bea, beb, bec)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_Either, baa), bab)) → new_esEs3(vyy470, vyy480, baa, bab)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_FiniteMap, bf), bg)) → new_esEs2(vyy470, vyy480, bf, bg)
new_esEs1(Just(vyy470), Just(vyy480), app(ty_[], hb)) → new_esEs(vyy470, vyy480, hb)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy471, vyy481, beg, beh)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, bh), ca)) → new_esEs3(vyy470, vyy480, bh, ca)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(ty_[], eb), ec) → new_esEs(vyy471, vyy481, eb)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, bbe), bbf), bah) → new_esEs2(vyy470, vyy480, bbe, bbf)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_FiniteMap, bee), bef)) → new_esEs2(vyy471, vyy481, bee, bef)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy470, vyy480, bca, bcb)
new_esEs1(Just(vyy470), Just(vyy480), app(ty_Maybe, hf)) → new_esEs1(vyy470, vyy480, hf)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_@2, cb), cc)) → new_esEs4(vyy470, vyy480, cb, cc)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, hg), hh)) → new_esEs2(vyy470, vyy480, hg, hh)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy471, vyy481, bfa, bfb)
new_esEs2(vyy47, vyy48, bae, baf) → new_esEs(new_foldFM2(vyy47, bae, baf), new_fmToList(vyy48, bae, baf), app(app(ty_@2, bae), baf))
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_FiniteMap, bda), bdb)) → new_esEs2(vyy470, vyy480, bda, bdb)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(ty_Maybe, eg), ec) → new_esEs1(vyy471, vyy481, eg)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_@2, bac), bad)) → new_esEs4(vyy470, vyy480, bac, bad)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_FiniteMap, eh), fa), ec) → new_esEs2(vyy471, vyy481, eh, fa)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_Either, df), dg)) → new_esEs3(vyy472, vyy482, df, dg)
new_esEs3(Left(vyy470), Left(vyy480), app(ty_Maybe, bbd), bah) → new_esEs1(vyy470, vyy480, bbd)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_@2, fd), ff), ec) → new_esEs4(vyy471, vyy481, fd, ff)
new_esEs3(Left(vyy470), Left(vyy480), app(ty_[], bag), bah) → new_esEs(vyy470, vyy480, bag)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(app(ty_@3, ed), ee), ef), ec) → new_esEs0(vyy471, vyy481, ed, ee, ef)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(ty_[], bdh)) → new_esEs(vyy471, vyy481, bdh)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy471, vyy481, bed)
new_esEs3(Left(vyy470), Left(vyy480), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(vyy470, vyy480, bba, bbb, bbc)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_FiniteMap, bga), bgb), bfd) → new_esEs2(vyy470, vyy480, bga, bgb)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_[], fg), ce, ec) → new_esEs(vyy470, vyy480, fg)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), h) → new_esEs(vyy471, vyy481, h)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_FiniteMap, gd), ge), ce, ec) → new_esEs2(vyy470, vyy480, gd, ge)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(ty_Maybe, dc)) → new_esEs1(vyy472, vyy482, dc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy472, vyy482, cg, da, db)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy472, vyy482, dd, de)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_[], bfc), bfd) → new_esEs(vyy470, vyy480, bfc)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(ty_Maybe, bch)) → new_esEs1(vyy470, vyy480, bch)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_Either, gf), gg), ce, ec) → new_esEs3(vyy470, vyy480, gf, gg)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy470, vyy480, bgc, bgd)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy470, vyy480, bb, bc, bd)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_Maybe, gc), ce, ec) → new_esEs1(vyy470, vyy480, gc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_Either, fb), fc), ec) → new_esEs3(vyy471, vyy481, fb, fc)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_[], ba)) → new_esEs(vyy470, vyy480, ba)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(app(ty_@3, fh), ga), gb), ce, ec) → new_esEs0(vyy470, vyy480, fh, ga, gb)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_@2, dh), ea)) → new_esEs4(vyy472, vyy482, dh, ea)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, be)) → new_esEs1(vyy470, vyy480, be)
The TRS R consists of the following rules:
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, bae, baf) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), bae, baf) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, bae, baf), vyy4733, bae, baf)
new_fmToList(vyy47, bae, baf) → new_foldFM2(vyy47, bae, baf)
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), bae, baf) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, bae, baf), vyy473, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs2(vyy47, vyy48, bae, baf) → new_esEs(new_foldFM2(vyy47, bae, baf), new_fmToList(vyy48, bae, baf), app(app(ty_@2, bae), baf)) at position [1] we obtained the following new rules:
new_esEs2(vyy47, vyy48, bae, baf) → new_esEs(new_foldFM2(vyy47, bae, baf), new_foldFM2(vyy48, bae, baf), app(app(ty_@2, bae), baf))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy470, vyy480, bde, bdf)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(ty_[], bcd)) → new_esEs(vyy470, vyy480, bcd)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy470, vyy480, bfe, bff, bfg)
new_esEs1(Just(vyy470), Just(vyy480), app(app(app(ty_@3, hc), hd), he)) → new_esEs0(vyy470, vyy480, hc, hd, he)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy470, vyy480, bfh)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy470, vyy480, bdc, bdd)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_@2, gh), ha), ce, ec) → new_esEs4(vyy470, vyy480, gh, ha)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(ty_[], cf)) → new_esEs(vyy472, vyy482, cf)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs0(vyy470, vyy480, bce, bcf, bcg)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy470, vyy480, bbg, bbh)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_Either, baa), bab)) → new_esEs3(vyy470, vyy480, baa, bab)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy471, vyy481, bea, beb, bec)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_FiniteMap, bf), bg)) → new_esEs2(vyy470, vyy480, bf, bg)
new_esEs1(Just(vyy470), Just(vyy480), app(ty_[], hb)) → new_esEs(vyy470, vyy480, hb)
new_esEs2(vyy47, vyy48, bae, baf) → new_esEs(new_foldFM2(vyy47, bae, baf), new_foldFM2(vyy48, bae, baf), app(app(ty_@2, bae), baf))
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy471, vyy481, beg, beh)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, bh), ca)) → new_esEs3(vyy470, vyy480, bh, ca)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(ty_[], eb), ec) → new_esEs(vyy471, vyy481, eb)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_FiniteMap, bee), bef)) → new_esEs2(vyy471, vyy481, bee, bef)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, bbe), bbf), bah) → new_esEs2(vyy470, vyy480, bbe, bbf)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy470, vyy480, bca, bcb)
new_esEs1(Just(vyy470), Just(vyy480), app(ty_Maybe, hf)) → new_esEs1(vyy470, vyy480, hf)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_@2, cb), cc)) → new_esEs4(vyy470, vyy480, cb, cc)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, hg), hh)) → new_esEs2(vyy470, vyy480, hg, hh)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy471, vyy481, bfa, bfb)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_FiniteMap, bda), bdb)) → new_esEs2(vyy470, vyy480, bda, bdb)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(ty_Maybe, eg), ec) → new_esEs1(vyy471, vyy481, eg)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_FiniteMap, eh), fa), ec) → new_esEs2(vyy471, vyy481, eh, fa)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_@2, bac), bad)) → new_esEs4(vyy470, vyy480, bac, bad)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_Either, df), dg)) → new_esEs3(vyy472, vyy482, df, dg)
new_esEs3(Left(vyy470), Left(vyy480), app(ty_Maybe, bbd), bah) → new_esEs1(vyy470, vyy480, bbd)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_@2, fd), ff), ec) → new_esEs4(vyy471, vyy481, fd, ff)
new_esEs3(Left(vyy470), Left(vyy480), app(ty_[], bag), bah) → new_esEs(vyy470, vyy480, bag)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(app(ty_@3, ed), ee), ef), ec) → new_esEs0(vyy471, vyy481, ed, ee, ef)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(ty_[], bdh)) → new_esEs(vyy471, vyy481, bdh)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy471, vyy481, bed)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_FiniteMap, bga), bgb), bfd) → new_esEs2(vyy470, vyy480, bga, bgb)
new_esEs3(Left(vyy470), Left(vyy480), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(vyy470, vyy480, bba, bbb, bbc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_[], fg), ce, ec) → new_esEs(vyy470, vyy480, fg)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_FiniteMap, gd), ge), ce, ec) → new_esEs2(vyy470, vyy480, gd, ge)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), h) → new_esEs(vyy471, vyy481, h)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy472, vyy482, cg, da, db)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(ty_Maybe, dc)) → new_esEs1(vyy472, vyy482, dc)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_[], bfc), bfd) → new_esEs(vyy470, vyy480, bfc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy472, vyy482, dd, de)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(ty_Maybe, bch)) → new_esEs1(vyy470, vyy480, bch)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_Either, gf), gg), ce, ec) → new_esEs3(vyy470, vyy480, gf, gg)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy470, vyy480, bgc, bgd)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy470, vyy480, bb, bc, bd)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_Maybe, gc), ce, ec) → new_esEs1(vyy470, vyy480, gc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_Either, fb), fc), ec) → new_esEs3(vyy471, vyy481, fb, fc)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_[], ba)) → new_esEs(vyy470, vyy480, ba)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_@2, dh), ea)) → new_esEs4(vyy472, vyy482, dh, ea)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(app(ty_@3, fh), ga), gb), ce, ec) → new_esEs0(vyy470, vyy480, fh, ga, gb)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, be)) → new_esEs1(vyy470, vyy480, be)
The TRS R consists of the following rules:
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, bae, baf) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), bae, baf) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, bae, baf), vyy4733, bae, baf)
new_fmToList(vyy47, bae, baf) → new_foldFM2(vyy47, bae, baf)
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), bae, baf) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, bae, baf), vyy473, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy470, vyy480, bde, bdf)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(ty_[], bcd)) → new_esEs(vyy470, vyy480, bcd)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy470, vyy480, bfe, bff, bfg)
new_esEs1(Just(vyy470), Just(vyy480), app(app(app(ty_@3, hc), hd), he)) → new_esEs0(vyy470, vyy480, hc, hd, he)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy470, vyy480, bfh)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy470, vyy480, bdc, bdd)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_@2, gh), ha), ce, ec) → new_esEs4(vyy470, vyy480, gh, ha)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(ty_[], cf)) → new_esEs(vyy472, vyy482, cf)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs0(vyy470, vyy480, bce, bcf, bcg)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy470, vyy480, bbg, bbh)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_Either, baa), bab)) → new_esEs3(vyy470, vyy480, baa, bab)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy471, vyy481, bea, beb, bec)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_FiniteMap, bf), bg)) → new_esEs2(vyy470, vyy480, bf, bg)
new_esEs1(Just(vyy470), Just(vyy480), app(ty_[], hb)) → new_esEs(vyy470, vyy480, hb)
new_esEs2(vyy47, vyy48, bae, baf) → new_esEs(new_foldFM2(vyy47, bae, baf), new_foldFM2(vyy48, bae, baf), app(app(ty_@2, bae), baf))
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy471, vyy481, beg, beh)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, bh), ca)) → new_esEs3(vyy470, vyy480, bh, ca)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(ty_[], eb), ec) → new_esEs(vyy471, vyy481, eb)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_FiniteMap, bee), bef)) → new_esEs2(vyy471, vyy481, bee, bef)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, bbe), bbf), bah) → new_esEs2(vyy470, vyy480, bbe, bbf)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy470, vyy480, bca, bcb)
new_esEs1(Just(vyy470), Just(vyy480), app(ty_Maybe, hf)) → new_esEs1(vyy470, vyy480, hf)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_@2, cb), cc)) → new_esEs4(vyy470, vyy480, cb, cc)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, hg), hh)) → new_esEs2(vyy470, vyy480, hg, hh)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy471, vyy481, bfa, bfb)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_FiniteMap, bda), bdb)) → new_esEs2(vyy470, vyy480, bda, bdb)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(ty_Maybe, eg), ec) → new_esEs1(vyy471, vyy481, eg)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_FiniteMap, eh), fa), ec) → new_esEs2(vyy471, vyy481, eh, fa)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_@2, bac), bad)) → new_esEs4(vyy470, vyy480, bac, bad)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_Either, df), dg)) → new_esEs3(vyy472, vyy482, df, dg)
new_esEs3(Left(vyy470), Left(vyy480), app(ty_Maybe, bbd), bah) → new_esEs1(vyy470, vyy480, bbd)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_@2, fd), ff), ec) → new_esEs4(vyy471, vyy481, fd, ff)
new_esEs3(Left(vyy470), Left(vyy480), app(ty_[], bag), bah) → new_esEs(vyy470, vyy480, bag)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(app(ty_@3, ed), ee), ef), ec) → new_esEs0(vyy471, vyy481, ed, ee, ef)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(ty_[], bdh)) → new_esEs(vyy471, vyy481, bdh)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy471, vyy481, bed)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_FiniteMap, bga), bgb), bfd) → new_esEs2(vyy470, vyy480, bga, bgb)
new_esEs3(Left(vyy470), Left(vyy480), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(vyy470, vyy480, bba, bbb, bbc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_[], fg), ce, ec) → new_esEs(vyy470, vyy480, fg)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_FiniteMap, gd), ge), ce, ec) → new_esEs2(vyy470, vyy480, gd, ge)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), h) → new_esEs(vyy471, vyy481, h)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy472, vyy482, cg, da, db)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(ty_Maybe, dc)) → new_esEs1(vyy472, vyy482, dc)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_[], bfc), bfd) → new_esEs(vyy470, vyy480, bfc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy472, vyy482, dd, de)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(ty_Maybe, bch)) → new_esEs1(vyy470, vyy480, bch)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_Either, gf), gg), ce, ec) → new_esEs3(vyy470, vyy480, gf, gg)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy470, vyy480, bgc, bgd)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy470, vyy480, bb, bc, bd)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_Maybe, gc), ce, ec) → new_esEs1(vyy470, vyy480, gc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_Either, fb), fc), ec) → new_esEs3(vyy471, vyy481, fb, fc)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_[], ba)) → new_esEs(vyy470, vyy480, ba)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_@2, dh), ea)) → new_esEs4(vyy472, vyy482, dh, ea)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(app(ty_@3, fh), ga), gb), ce, ec) → new_esEs0(vyy470, vyy480, fh, ga, gb)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, be)) → new_esEs1(vyy470, vyy480, be)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), bae, baf) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, bae, baf), vyy473, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, bae, baf) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), bae, baf) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, bae, baf), vyy4733, bae, baf)
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_fmToList(x0, x1, x2)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy470, vyy480, bde, bdf)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(ty_[], bcd)) → new_esEs(vyy470, vyy480, bcd)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy470, vyy480, bfe, bff, bfg)
new_esEs1(Just(vyy470), Just(vyy480), app(app(app(ty_@3, hc), hd), he)) → new_esEs0(vyy470, vyy480, hc, hd, he)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy470, vyy480, bfh)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy470, vyy480, bdc, bdd)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_@2, gh), ha), ce, ec) → new_esEs4(vyy470, vyy480, gh, ha)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(ty_[], cf)) → new_esEs(vyy472, vyy482, cf)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs0(vyy470, vyy480, bce, bcf, bcg)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy470, vyy480, bbg, bbh)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_Either, baa), bab)) → new_esEs3(vyy470, vyy480, baa, bab)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy471, vyy481, bea, beb, bec)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_FiniteMap, bf), bg)) → new_esEs2(vyy470, vyy480, bf, bg)
new_esEs1(Just(vyy470), Just(vyy480), app(ty_[], hb)) → new_esEs(vyy470, vyy480, hb)
new_esEs2(vyy47, vyy48, bae, baf) → new_esEs(new_foldFM2(vyy47, bae, baf), new_foldFM2(vyy48, bae, baf), app(app(ty_@2, bae), baf))
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy471, vyy481, beg, beh)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, bh), ca)) → new_esEs3(vyy470, vyy480, bh, ca)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(ty_[], eb), ec) → new_esEs(vyy471, vyy481, eb)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, bbe), bbf), bah) → new_esEs2(vyy470, vyy480, bbe, bbf)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_FiniteMap, bee), bef)) → new_esEs2(vyy471, vyy481, bee, bef)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy470, vyy480, bca, bcb)
new_esEs1(Just(vyy470), Just(vyy480), app(ty_Maybe, hf)) → new_esEs1(vyy470, vyy480, hf)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_@2, cb), cc)) → new_esEs4(vyy470, vyy480, cb, cc)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, hg), hh)) → new_esEs2(vyy470, vyy480, hg, hh)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy471, vyy481, bfa, bfb)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_FiniteMap, bda), bdb)) → new_esEs2(vyy470, vyy480, bda, bdb)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(ty_Maybe, eg), ec) → new_esEs1(vyy471, vyy481, eg)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_FiniteMap, eh), fa), ec) → new_esEs2(vyy471, vyy481, eh, fa)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_@2, bac), bad)) → new_esEs4(vyy470, vyy480, bac, bad)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_Either, df), dg)) → new_esEs3(vyy472, vyy482, df, dg)
new_esEs3(Left(vyy470), Left(vyy480), app(ty_Maybe, bbd), bah) → new_esEs1(vyy470, vyy480, bbd)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_@2, fd), ff), ec) → new_esEs4(vyy471, vyy481, fd, ff)
new_esEs3(Left(vyy470), Left(vyy480), app(ty_[], bag), bah) → new_esEs(vyy470, vyy480, bag)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(app(ty_@3, ed), ee), ef), ec) → new_esEs0(vyy471, vyy481, ed, ee, ef)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(ty_[], bdh)) → new_esEs(vyy471, vyy481, bdh)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy471, vyy481, bed)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_FiniteMap, bga), bgb), bfd) → new_esEs2(vyy470, vyy480, bga, bgb)
new_esEs3(Left(vyy470), Left(vyy480), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(vyy470, vyy480, bba, bbb, bbc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_[], fg), ce, ec) → new_esEs(vyy470, vyy480, fg)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_FiniteMap, gd), ge), ce, ec) → new_esEs2(vyy470, vyy480, gd, ge)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), h) → new_esEs(vyy471, vyy481, h)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy472, vyy482, cg, da, db)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(ty_Maybe, dc)) → new_esEs1(vyy472, vyy482, dc)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_[], bfc), bfd) → new_esEs(vyy470, vyy480, bfc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy472, vyy482, dd, de)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(ty_Maybe, bch)) → new_esEs1(vyy470, vyy480, bch)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_Either, gf), gg), ce, ec) → new_esEs3(vyy470, vyy480, gf, gg)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy470, vyy480, bgc, bgd)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy470, vyy480, bb, bc, bd)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_Maybe, gc), ce, ec) → new_esEs1(vyy470, vyy480, gc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_Either, fb), fc), ec) → new_esEs3(vyy471, vyy481, fb, fc)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_[], ba)) → new_esEs(vyy470, vyy480, ba)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(app(ty_@3, fh), ga), gb), ce, ec) → new_esEs0(vyy470, vyy480, fh, ga, gb)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_@2, dh), ea)) → new_esEs4(vyy472, vyy482, dh, ea)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, be)) → new_esEs1(vyy470, vyy480, be)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), bae, baf) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, bae, baf), vyy473, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, bae, baf) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), bae, baf) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, bae, baf), vyy4733, bae, baf)
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].
The following pairs can be oriented strictly and are deleted.
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy470, vyy480, bde, bdf)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(ty_[], bcd)) → new_esEs(vyy470, vyy480, bcd)
new_esEs1(Just(vyy470), Just(vyy480), app(app(app(ty_@3, hc), hd), he)) → new_esEs0(vyy470, vyy480, hc, hd, he)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy470, vyy480, bdc, bdd)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_@2, gh), ha), ce, ec) → new_esEs4(vyy470, vyy480, gh, ha)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(ty_[], cf)) → new_esEs(vyy472, vyy482, cf)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs0(vyy470, vyy480, bce, bcf, bcg)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy470, vyy480, bbg, bbh)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_Either, baa), bab)) → new_esEs3(vyy470, vyy480, baa, bab)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_FiniteMap, bf), bg)) → new_esEs2(vyy470, vyy480, bf, bg)
new_esEs1(Just(vyy470), Just(vyy480), app(ty_[], hb)) → new_esEs(vyy470, vyy480, hb)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(ty_[], eb), ec) → new_esEs(vyy471, vyy481, eb)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, bbe), bbf), bah) → new_esEs2(vyy470, vyy480, bbe, bbf)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_FiniteMap, bee), bef)) → new_esEs2(vyy471, vyy481, bee, bef)
new_esEs3(Left(vyy470), Left(vyy480), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy470, vyy480, bca, bcb)
new_esEs1(Just(vyy470), Just(vyy480), app(ty_Maybe, hf)) → new_esEs1(vyy470, vyy480, hf)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, hg), hh)) → new_esEs2(vyy470, vyy480, hg, hh)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(app(ty_FiniteMap, bda), bdb)) → new_esEs2(vyy470, vyy480, bda, bdb)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(ty_Maybe, eg), ec) → new_esEs1(vyy471, vyy481, eg)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_FiniteMap, eh), fa), ec) → new_esEs2(vyy471, vyy481, eh, fa)
new_esEs1(Just(vyy470), Just(vyy480), app(app(ty_@2, bac), bad)) → new_esEs4(vyy470, vyy480, bac, bad)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_Either, df), dg)) → new_esEs3(vyy472, vyy482, df, dg)
new_esEs3(Left(vyy470), Left(vyy480), app(ty_Maybe, bbd), bah) → new_esEs1(vyy470, vyy480, bbd)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_@2, fd), ff), ec) → new_esEs4(vyy471, vyy481, fd, ff)
new_esEs3(Left(vyy470), Left(vyy480), app(ty_[], bag), bah) → new_esEs(vyy470, vyy480, bag)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(app(ty_@3, ed), ee), ef), ec) → new_esEs0(vyy471, vyy481, ed, ee, ef)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(ty_[], bdh)) → new_esEs(vyy471, vyy481, bdh)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_FiniteMap, bga), bgb), bfd) → new_esEs2(vyy470, vyy480, bga, bgb)
new_esEs3(Left(vyy470), Left(vyy480), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(vyy470, vyy480, bba, bbb, bbc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_[], fg), ce, ec) → new_esEs(vyy470, vyy480, fg)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_FiniteMap, gd), ge), ce, ec) → new_esEs2(vyy470, vyy480, gd, ge)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy472, vyy482, cg, da, db)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(ty_Maybe, dc)) → new_esEs1(vyy472, vyy482, dc)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_[], bfc), bfd) → new_esEs(vyy470, vyy480, bfc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy472, vyy482, dd, de)
new_esEs3(Right(vyy470), Right(vyy480), bcc, app(ty_Maybe, bch)) → new_esEs1(vyy470, vyy480, bch)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_Either, gf), gg), ce, ec) → new_esEs3(vyy470, vyy480, gf, gg)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_Maybe, gc), ce, ec) → new_esEs1(vyy470, vyy480, gc)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, app(app(ty_Either, fb), fc), ec) → new_esEs3(vyy471, vyy481, fb, fc)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_[], ba)) → new_esEs(vyy470, vyy480, ba)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(app(ty_@3, fh), ga), gb), ce, ec) → new_esEs0(vyy470, vyy480, fh, ga, gb)
new_esEs0(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cd, ce, app(app(ty_@2, dh), ea)) → new_esEs4(vyy472, vyy482, dh, ea)
The remaining pairs can at least be oriented weakly.
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy470, vyy480, bfe, bff, bfg)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy470, vyy480, bfh)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy471, vyy481, bea, beb, bec)
new_esEs2(vyy47, vyy48, bae, baf) → new_esEs(new_foldFM2(vyy47, bae, baf), new_foldFM2(vyy48, bae, baf), app(app(ty_@2, bae), baf))
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy471, vyy481, beg, beh)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, bh), ca)) → new_esEs3(vyy470, vyy480, bh, ca)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_@2, cb), cc)) → new_esEs4(vyy470, vyy480, cb, cc)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy471, vyy481, bfa, bfb)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy471, vyy481, bed)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), h) → new_esEs(vyy471, vyy481, h)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy470, vyy480, bgc, bgd)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy470, vyy480, bb, bc, bd)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, be)) → new_esEs1(vyy470, vyy480, be)
Used ordering: Polynomial interpretation [25]:
POL(:(x1, x2)) = 0
POL(@2(x1, x2)) = 0
POL(@3(x1, x2, x3)) = 0
POL(Branch(x1, x2, x3, x4, x5)) = 0
POL(EmptyFM) = 0
POL(Just(x1)) = 0
POL(Left(x1)) = 0
POL(Right(x1)) = 0
POL([]) = 0
POL(app(x1, x2)) = x1 + x2
POL(new_esEs(x1, x2, x3)) = x3
POL(new_esEs0(x1, x2, x3, x4, x5)) = 1 + x3 + x4 + x5
POL(new_esEs1(x1, x2, x3)) = 1 + x3
POL(new_esEs2(x1, x2, x3, x4)) = x3 + x4
POL(new_esEs3(x1, x2, x3, x4)) = 1 + x3 + x4
POL(new_esEs4(x1, x2, x3, x4)) = x3 + x4
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = 0
POL(new_foldFM2(x1, x2, x3)) = 0
POL(ty_@2) = 0
POL(ty_@3) = 1
POL(ty_Either) = 1
POL(ty_FiniteMap) = 1
POL(ty_Maybe) = 1
POL(ty_[]) = 1
The following usable rules [17] were oriented:
none
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(vyy47, vyy48, bae, baf) → new_esEs(new_foldFM2(vyy47, bae, baf), new_foldFM2(vyy48, bae, baf), app(app(ty_@2, bae), baf))
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy471, vyy481, beg, beh)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), h) → new_esEs(vyy471, vyy481, h)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, bh), ca)) → new_esEs3(vyy470, vyy480, bh, ca)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy470, vyy480, bfe, bff, bfg)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy470, vyy480, bgc, bgd)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy470, vyy480, bb, bc, bd)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy470, vyy480, bfh)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_@2, cb), cc)) → new_esEs4(vyy470, vyy480, cb, cc)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy471, vyy481, bfa, bfb)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy471, vyy481, bea, beb, bec)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy471, vyy481, bed)
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, be)) → new_esEs1(vyy470, vyy480, be)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), bae, baf) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, bae, baf), vyy473, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, bae, baf) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), bae, baf) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, bae, baf), vyy4733, bae, baf)
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs with 11 less nodes.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy471, vyy481, bfa, bfb)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy470, vyy480, bge, bgf)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), bae, baf) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, bae, baf), vyy473, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, bae, baf) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), bae, baf) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, bae, baf), vyy4733, bae, baf)
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy471, vyy481, bfa, bfb)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy470, vyy480, bge, bgf)
R is empty.
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy471, vyy481, bfa, bfb)
new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy470, vyy480, bge, bgf)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy471, vyy481, bfa, bfb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs4(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy470, vyy480, bge, bgf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), h) → new_esEs(vyy471, vyy481, h)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), bae, baf) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, bae, baf), vyy473, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, bae, baf) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), bae, baf) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, bae, baf), vyy4733, bae, baf)
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), h) → new_esEs(vyy471, vyy481, h)
R is empty.
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), h) → new_esEs(vyy471, vyy481, h)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_esEs(:(vyy470, vyy471), :(vyy480, vyy481), h) → new_esEs(vyy471, vyy481, h)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, cb, app(app(ty_Either, fg), fh)) → new_ltEs3(vyy3002, vyy402, fg, fh)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_primCompAux(vyy3000, vyy400, new_compare4(vyy3001, vyy401, bae), bae)
new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), hc, app(app(ty_@2, hh), baa)) → new_ltEs1(vyy3001, vyy401, hh, baa)
new_ltEs3(Left(vyy3000), Left(vyy400), app(app(ty_Either, bcg), bch), bbh) → new_ltEs3(vyy3000, vyy400, bcg, bch)
new_compare22(vyy3000, vyy400, False, dc, dd) → new_ltEs3(vyy3000, vyy400, dc, dd)
new_ltEs3(Right(vyy3000), Right(vyy400), bda, app(ty_[], bdh)) → new_ltEs2(vyy3000, vyy400, bdh)
new_ltEs(Just(vyy3000), Just(vyy400), app(ty_[], bf)) → new_ltEs2(vyy3000, vyy400, bf)
new_primCompAux(vyy3000, vyy400, vyy84, app(app(app(ty_@3, bag), bah), bba)) → new_compare1(vyy3000, vyy400, bag, bah, bba)
new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_Maybe, ga), gb) → new_lt(vyy3000, vyy400, ga)
new_primCompAux(vyy3000, vyy400, vyy84, app(app(ty_@2, bbb), bbc)) → new_compare3(vyy3000, vyy400, bbb, bbc)
new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), hc, app(app(app(ty_@3, he), hf), hg)) → new_ltEs0(vyy3001, vyy401, he, hf, hg)
new_ltEs3(Left(vyy3000), Left(vyy400), app(ty_Maybe, bbg), bbh) → new_ltEs(vyy3000, vyy400, bbg)
new_ltEs3(Right(vyy3000), Right(vyy400), bda, app(app(app(ty_@3, bdc), bdd), bde)) → new_ltEs0(vyy3000, vyy400, bdc, bdd, bde)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(app(ty_@3, cd), ce), cf), cb, cc) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, cd, ce, cf), cd, ce, cf)
new_lt3(vyy3000, vyy400, dc, dd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, dc, dd), dc, dd)
new_ltEs(Just(vyy3000), Just(vyy400), app(app(ty_Either, bg), bh)) → new_ltEs3(vyy3000, vyy400, bg, bh)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, app(ty_[], ed), cc) → new_lt2(vyy3001, vyy401, ed)
new_primCompAux(vyy3000, vyy400, vyy84, app(ty_[], bbd)) → new_compare(vyy3000, vyy400, bbd)
new_ltEs(Just(vyy3000), Just(vyy400), app(ty_Maybe, h)) → new_ltEs(vyy3000, vyy400, h)
new_lt(vyy3000, vyy400, ca) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, ca), ca)
new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), hc, app(ty_[], bab)) → new_ltEs2(vyy3001, vyy401, bab)
new_compare3(vyy3000, vyy400, cg, da) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, cg, da), cg, da)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_Maybe, ca), cb, cc) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, ca), ca)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_[], db), cb, cc) → new_compare(vyy3000, vyy400, db)
new_ltEs3(Left(vyy3000), Left(vyy400), app(ty_[], bcf), bbh) → new_ltEs2(vyy3000, vyy400, bcf)
new_primCompAux(vyy3000, vyy400, vyy84, app(app(ty_Either, bbe), bbf)) → new_compare5(vyy3000, vyy400, bbe, bbf)
new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), hc, app(ty_Maybe, hd)) → new_ltEs(vyy3001, vyy401, hd)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, app(app(app(ty_@3, dg), dh), ea), cc) → new_lt0(vyy3001, vyy401, dg, dh, ea)
new_compare1(vyy3000, vyy400, cd, ce, cf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, cd, ce, cf), cd, ce, cf)
new_compare21(vyy3000, vyy400, False, cg, da) → new_ltEs1(vyy3000, vyy400, cg, da)
new_ltEs3(Right(vyy3000), Right(vyy400), bda, app(app(ty_Either, bea), beb)) → new_ltEs3(vyy3000, vyy400, bea, beb)
new_ltEs(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ba), bb), bc)) → new_ltEs0(vyy3000, vyy400, ba, bb, bc)
new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_Either, ha), hb), gb) → new_lt3(vyy3000, vyy400, ha, hb)
new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_@2, gf), gg), gb) → new_lt1(vyy3000, vyy400, gf, gg)
new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_[], gh), gb) → new_lt2(vyy3000, vyy400, gh)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, cb, app(app(app(ty_@3, eh), fa), fb)) → new_ltEs0(vyy3002, vyy402, eh, fa, fb)
new_ltEs(Just(vyy3000), Just(vyy400), app(app(ty_@2, bd), be)) → new_ltEs1(vyy3000, vyy400, bd, be)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, app(app(ty_@2, eb), ec), cc) → new_lt1(vyy3001, vyy401, eb, ec)
new_compare2(vyy3000, vyy400, False, ca) → new_ltEs(vyy3000, vyy400, ca)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, cb, app(ty_[], ff)) → new_ltEs2(vyy3002, vyy402, ff)
new_ltEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_compare(vyy3001, vyy401, bae)
new_ltEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_primCompAux(vyy3000, vyy400, new_compare4(vyy3001, vyy401, bae), bae)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_compare(vyy3001, vyy401, bae)
new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(app(ty_@3, gc), gd), ge), gb) → new_lt0(vyy3000, vyy400, gc, gd, ge)
new_compare0(vyy3000, vyy400, ca) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, ca), ca)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, cb, app(app(ty_@2, fc), fd)) → new_ltEs1(vyy3002, vyy402, fc, fd)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, cb, app(ty_Maybe, eg)) → new_ltEs(vyy3002, vyy402, eg)
new_lt2(vyy3000, vyy400, db) → new_compare(vyy3000, vyy400, db)
new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), hc, app(app(ty_Either, bac), bad)) → new_ltEs3(vyy3001, vyy401, bac, bad)
new_ltEs3(Right(vyy3000), Right(vyy400), bda, app(app(ty_@2, bdf), bdg)) → new_ltEs1(vyy3000, vyy400, bdf, bdg)
new_ltEs3(Right(vyy3000), Right(vyy400), bda, app(ty_Maybe, bdb)) → new_ltEs(vyy3000, vyy400, bdb)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_Either, dc), dd), cb, cc) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, dc, dd), dc, dd)
new_compare5(vyy3000, vyy400, dc, dd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, dc, dd), dc, dd)
new_lt0(vyy3000, vyy400, cd, ce, cf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, cd, ce, cf), cd, ce, cf)
new_compare20(vyy3000, vyy400, False, cd, ce, cf) → new_ltEs0(vyy3000, vyy400, cd, ce, cf)
new_lt1(vyy3000, vyy400, cg, da) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, cg, da), cg, da)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, app(app(ty_Either, ee), ef), cc) → new_lt3(vyy3001, vyy401, ee, ef)
new_ltEs3(Left(vyy3000), Left(vyy400), app(app(ty_@2, bcd), bce), bbh) → new_ltEs1(vyy3000, vyy400, bcd, bce)
new_ltEs3(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bca), bcb), bcc), bbh) → new_ltEs0(vyy3000, vyy400, bca, bcb, bcc)
new_primCompAux(vyy3000, vyy400, vyy84, app(ty_Maybe, baf)) → new_compare0(vyy3000, vyy400, baf)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, app(ty_Maybe, df), cc) → new_lt(vyy3001, vyy401, df)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_@2, cg), da), cb, cc) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, cg, da), cg, da)
The TRS R consists of the following rules:
new_esEs28(vyy471, vyy481, app(ty_[], dbg)) → new_esEs13(vyy471, vyy481, dbg)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_@0, bbh) → new_ltEs9(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, app(ty_Ratio, cfh)) → new_ltEs16(vyy3001, vyy401, cfh)
new_ltEs18(vyy3002, vyy402, ty_@0) → new_ltEs9(vyy3002, vyy402)
new_ltEs10(False, True) → True
new_compare17(vyy3000, vyy400, ca) → new_compare23(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, ca), ca)
new_esEs13([], [], bhc) → True
new_compare10(vyy3000, vyy400, True, dc, dd) → LT
new_esEs11(Integer(vyy470), Integer(vyy480)) → new_primEqInt(vyy470, vyy480)
new_ltEs5(EQ, GT) → True
new_esEs28(vyy471, vyy481, ty_Integer) → new_esEs11(vyy471, vyy481)
new_esEs26(vyy470, vyy480, ty_Integer) → new_esEs11(vyy470, vyy480)
new_ltEs6(Nothing, Just(vyy400), bfh) → True
new_ltEs19(vyy3001, vyy401, ty_Double) → new_ltEs11(vyy3001, vyy401)
new_compare31(vyy3000, vyy400, app(app(app(ty_@3, bag), bah), bba)) → new_compare9(vyy3000, vyy400, bag, bah, bba)
new_esEs27(vyy47, vyy48, ty_Bool) → new_esEs17(vyy47, vyy48)
new_esEs23(vyy470, vyy480, ty_Float) → new_esEs19(vyy470, vyy480)
new_primMulNat0(Zero, Zero) → Zero
new_lt10(vyy3001, vyy401, app(app(ty_@2, eb), ec)) → new_lt12(vyy3001, vyy401, eb, ec)
new_lt20(vyy3000, vyy400, ty_Float) → new_lt4(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, app(ty_Ratio, dbf)) → new_compare18(vyy3000, vyy400, dbf)
new_esEs5(Just(vyy470), Just(vyy480), app(ty_Ratio, bfe)) → new_esEs16(vyy470, vyy480, bfe)
new_compare13(vyy3000, vyy400, False, cd, ce, cf) → GT
new_esEs5(Just(vyy470), Just(vyy480), ty_@0) → new_esEs12(vyy470, vyy480)
new_esEs8(Right(vyy470), Right(vyy480), cgb, app(app(ty_FiniteMap, dag), dah)) → new_esEs15(vyy470, vyy480, dag, dah)
new_esEs9(LT) → True
new_lt20(vyy3000, vyy400, ty_Int) → new_lt18(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, ty_Bool) → new_esEs17(vyy471, vyy481)
new_esEs27(vyy47, vyy48, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs15(vyy47, vyy48, bgc, bgd)
new_lt9(vyy3000, vyy400, app(ty_Ratio, bgf)) → new_lt19(vyy3000, vyy400, bgf)
new_not(GT) → False
new_esEs8(Right(vyy470), Right(vyy480), cgb, ty_@0) → new_esEs12(vyy470, vyy480)
new_lt9(vyy3000, vyy400, ty_Ordering) → new_lt8(vyy3000, vyy400)
new_esEs29(vyy470, vyy480, app(app(ty_Either, deb), dec)) → new_esEs8(vyy470, vyy480, deb, dec)
new_esEs8(Left(vyy470), Left(vyy480), ty_Integer, cgc) → new_esEs11(vyy470, vyy480)
new_esEs17(True, True) → True
new_lt17(vyy3000, vyy400, dc, dd) → new_esEs9(new_compare27(vyy3000, vyy400, dc, dd))
new_lt10(vyy3001, vyy401, ty_Ordering) → new_lt8(vyy3001, vyy401)
new_esEs8(Right(vyy470), Right(vyy480), cgb, app(ty_Ratio, dbc)) → new_esEs16(vyy470, vyy480, dbc)
new_ltEs15(vyy300, vyy40) → new_not(new_compare7(vyy300, vyy40))
new_esEs23(vyy470, vyy480, app(app(ty_FiniteMap, caa), cab)) → new_esEs15(vyy470, vyy480, caa, cab)
new_compare27(vyy3000, vyy400, dc, dd) → new_compare211(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, dc, dd), dc, dd)
new_ltEs11(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_esEs8(Right(vyy470), Right(vyy480), cgb, ty_Bool) → new_esEs17(vyy470, vyy480)
new_lt9(vyy3000, vyy400, app(app(app(ty_@3, cd), ce), cf)) → new_lt6(vyy3000, vyy400, cd, ce, cf)
new_esEs5(Just(vyy470), Just(vyy480), app(ty_Maybe, beh)) → new_esEs5(vyy470, vyy480, beh)
new_ltEs5(EQ, LT) → False
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt16(vyy3000, vyy400)
new_esEs12(@0, @0) → True
new_esEs28(vyy471, vyy481, ty_@0) → new_esEs12(vyy471, vyy481)
new_ltEs18(vyy3002, vyy402, ty_Bool) → new_ltEs10(vyy3002, vyy402)
new_ltEs10(False, False) → True
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, bgc, bgd) → :(@2(vyy470, vyy471), vyy102)
new_lt8(vyy3000, vyy400) → new_esEs9(new_compare19(vyy3000, vyy400))
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs10(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt14(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, ty_Integer) → new_compare28(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, app(app(ty_@2, hh), baa)) → new_ltEs8(vyy3001, vyy401, hh, baa)
new_esEs25(vyy471, vyy481, app(app(ty_@2, cea), ceb)) → new_esEs7(vyy471, vyy481, cea, ceb)
new_ltEs18(vyy3002, vyy402, app(app(app(ty_@3, eh), fa), fb)) → new_ltEs7(vyy3002, vyy402, eh, fa, fb)
new_compare31(vyy3000, vyy400, app(app(ty_Either, bbe), bbf)) → new_compare27(vyy3000, vyy400, bbe, bbf)
new_ltEs14(Right(vyy3000), Right(vyy400), bda, ty_Char) → new_ltEs12(vyy3000, vyy400)
new_compare29(@0, @0) → EQ
new_compare31(vyy3000, vyy400, ty_@0) → new_compare29(vyy3000, vyy400)
new_esEs26(vyy470, vyy480, app(app(ty_FiniteMap, ceh), cfa)) → new_esEs15(vyy470, vyy480, ceh, cfa)
new_esEs23(vyy470, vyy480, app(app(ty_Either, cac), cad)) → new_esEs8(vyy470, vyy480, cac, cad)
new_compare15(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs26(vyy470, vyy480, app(app(ty_Either, cfb), cfc)) → new_esEs8(vyy470, vyy480, cfb, cfc)
new_ltEs14(Right(vyy3000), Right(vyy400), bda, app(ty_[], bdh)) → new_ltEs4(vyy3000, vyy400, bdh)
new_compare8(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare7(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs6(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), cah, cba, cbb) → new_asAs(new_esEs26(vyy470, vyy480, cah), new_asAs(new_esEs25(vyy471, vyy481, cba), new_esEs24(vyy472, vyy482, cbb)))
new_esEs28(vyy471, vyy481, app(app(ty_FiniteMap, dcd), dce)) → new_esEs15(vyy471, vyy481, dcd, dce)
new_lt9(vyy3000, vyy400, ty_Double) → new_lt5(vyy3000, vyy400)
new_esEs14(EQ, EQ) → True
new_ltEs18(vyy3002, vyy402, app(app(ty_Either, fg), fh)) → new_ltEs14(vyy3002, vyy402, fg, fh)
new_esEs27(vyy47, vyy48, ty_Float) → new_esEs19(vyy47, vyy48)
new_esEs28(vyy471, vyy481, app(ty_Ratio, dch)) → new_esEs16(vyy471, vyy481, dch)
new_ltEs14(Left(vyy3000), Left(vyy400), app(ty_Ratio, bha), bbh) → new_ltEs16(vyy3000, vyy400, bha)
new_esEs25(vyy471, vyy481, app(app(ty_FiniteMap, cdd), cde)) → new_esEs15(vyy471, vyy481, cdd, cde)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_lt7(vyy3000, vyy400) → new_esEs9(new_compare15(vyy3000, vyy400))
new_ltEs6(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ba), bb), bc)) → new_ltEs7(vyy3000, vyy400, ba, bb, bc)
new_compare14(vyy3000, vyy400, False) → GT
new_esEs25(vyy471, vyy481, ty_@0) → new_esEs12(vyy471, vyy481)
new_compare6(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare7(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs28(vyy471, vyy481, ty_Float) → new_esEs19(vyy471, vyy481)
new_esEs29(vyy470, vyy480, ty_Char) → new_esEs10(vyy470, vyy480)
new_esEs29(vyy470, vyy480, app(app(ty_@2, dee), def)) → new_esEs7(vyy470, vyy480, dee, def)
new_compare18(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare7(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs8(Right(vyy470), Right(vyy480), cgb, app(app(ty_@2, dbd), dbe)) → new_esEs7(vyy470, vyy480, dbd, dbe)
new_ltEs14(Right(vyy3000), Right(vyy400), bda, app(ty_Ratio, bhb)) → new_ltEs16(vyy3000, vyy400, bhb)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Int, bbh) → new_ltEs15(vyy3000, vyy400)
new_lt10(vyy3001, vyy401, ty_Integer) → new_lt16(vyy3001, vyy401)
new_primEqNat0(Zero, Zero) → True
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Ordering, bbh) → new_ltEs5(vyy3000, vyy400)
new_esEs23(vyy470, vyy480, ty_Ordering) → new_esEs14(vyy470, vyy480)
new_ltEs14(Right(vyy3000), Right(vyy400), bda, ty_Ordering) → new_ltEs5(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, True) → LT
new_ltEs14(Right(vyy3000), Right(vyy400), bda, app(app(ty_@2, bdf), bdg)) → new_ltEs8(vyy3000, vyy400, bdf, bdg)
new_ltEs19(vyy3001, vyy401, app(ty_[], bab)) → new_ltEs4(vyy3001, vyy401, bab)
new_lt9(vyy3000, vyy400, app(app(ty_Either, dc), dd)) → new_lt17(vyy3000, vyy400, dc, dd)
new_esEs8(Right(vyy470), Right(vyy480), cgb, ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs29(vyy470, vyy480, app(ty_[], ddc)) → new_esEs13(vyy470, vyy480, ddc)
new_esEs24(vyy472, vyy482, ty_Char) → new_esEs10(vyy472, vyy482)
new_esEs17(False, False) → True
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_compare12(vyy3000, vyy400, False, ca) → GT
new_sr(vyy3000, vyy400) → new_primMulInt(vyy3000, vyy400)
new_esEs24(vyy472, vyy482, ty_Bool) → new_esEs17(vyy472, vyy482)
new_esEs8(Right(vyy470), Right(vyy480), cgb, app(ty_Maybe, daf)) → new_esEs5(vyy470, vyy480, daf)
new_compare7(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_esEs8(Left(vyy470), Left(vyy480), ty_Float, cgc) → new_esEs19(vyy470, vyy480)
new_esEs24(vyy472, vyy482, app(app(ty_@2, cce), ccf)) → new_esEs7(vyy472, vyy482, cce, ccf)
new_esEs14(LT, GT) → False
new_esEs14(GT, LT) → False
new_esEs18(Double(vyy470, vyy471), Double(vyy480, vyy481)) → new_esEs20(new_sr(vyy470, vyy480), new_sr(vyy471, vyy481))
new_lt20(vyy3000, vyy400, app(ty_Maybe, ga)) → new_lt11(vyy3000, vyy400, ga)
new_primPlusNat0(Succ(vyy1030), vyy40000) → Succ(Succ(new_primPlusNat1(vyy1030, vyy40000)))
new_compare4([], [], bae) → EQ
new_esEs27(vyy47, vyy48, ty_Char) → new_esEs10(vyy47, vyy48)
new_lt10(vyy3001, vyy401, ty_Double) → new_lt5(vyy3001, vyy401)
new_esEs5(Just(vyy470), Just(vyy480), app(app(ty_Either, bfc), bfd)) → new_esEs8(vyy470, vyy480, bfc, bfd)
new_esEs26(vyy470, vyy480, app(app(app(ty_@3, ced), cee), cef)) → new_esEs6(vyy470, vyy480, ced, cee, cef)
new_ltEs5(LT, LT) → True
new_esEs8(Right(vyy470), Right(vyy480), cgb, ty_Float) → new_esEs19(vyy470, vyy480)
new_lt20(vyy3000, vyy400, app(app(ty_Either, ha), hb)) → new_lt17(vyy3000, vyy400, ha, hb)
new_compare211(vyy3000, vyy400, False, dc, dd) → new_compare10(vyy3000, vyy400, new_ltEs14(vyy3000, vyy400, dc, dd), dc, dd)
new_esEs8(Left(vyy470), Left(vyy480), ty_Int, cgc) → new_esEs20(vyy470, vyy480)
new_esEs21(vyy471, vyy481, ty_Int) → new_esEs20(vyy471, vyy481)
new_primEqInt(Neg(Succ(vyy4700)), Neg(Succ(vyy4800))) → new_primEqNat0(vyy4700, vyy4800)
new_ltEs8(@2(vyy3000, vyy3001), @2(vyy400, vyy401), hc, gb) → new_pePe(new_lt20(vyy3000, vyy400, hc), vyy3000, vyy400, new_ltEs19(vyy3001, vyy401, gb), hc)
new_compare25(vyy3000, vyy400, True) → EQ
new_compare23(vyy3000, vyy400, False, ca) → new_compare12(vyy3000, vyy400, new_ltEs6(vyy3000, vyy400, ca), ca)
new_compare26(vyy3000, vyy400, False, cd, ce, cf) → new_compare13(vyy3000, vyy400, new_ltEs7(vyy3000, vyy400, cd, ce, cf), cd, ce, cf)
new_esEs9(GT) → False
new_esEs26(vyy470, vyy480, app(ty_[], cec)) → new_esEs13(vyy470, vyy480, cec)
new_esEs13(:(vyy470, vyy471), :(vyy480, vyy481), bhc) → new_asAs(new_esEs23(vyy470, vyy480, bhc), new_esEs13(vyy471, vyy481, bhc))
new_compare25(vyy3000, vyy400, False) → new_compare110(vyy3000, vyy400, new_ltEs10(vyy3000, vyy400))
new_primPlusNat1(Succ(vyy10300), Zero) → Succ(vyy10300)
new_primPlusNat1(Zero, Succ(vyy400000)) → Succ(vyy400000)
new_compare31(vyy3000, vyy400, ty_Ordering) → new_compare19(vyy3000, vyy400)
new_esEs9(EQ) → False
new_ltEs14(Right(vyy3000), Left(vyy400), bda, bbh) → False
new_esEs8(Left(vyy470), Right(vyy480), cgb, cgc) → False
new_esEs8(Right(vyy470), Left(vyy480), cgb, cgc) → False
new_esEs8(Right(vyy470), Right(vyy480), cgb, app(app(ty_Either, dba), dbb)) → new_esEs8(vyy470, vyy480, dba, dbb)
new_lt9(vyy3000, vyy400, app(app(ty_@2, cg), da)) → new_lt12(vyy3000, vyy400, cg, da)
new_lt10(vyy3001, vyy401, app(ty_Ratio, bgg)) → new_lt19(vyy3001, vyy401, bgg)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy472, vyy482, app(app(app(ty_@3, cbd), cbe), cbf)) → new_esEs6(vyy472, vyy482, cbd, cbe, cbf)
new_ltEs14(Right(vyy3000), Right(vyy400), bda, ty_Int) → new_ltEs15(vyy3000, vyy400)
new_esEs5(Just(vyy470), Just(vyy480), app(ty_[], bed)) → new_esEs13(vyy470, vyy480, bed)
new_lt9(vyy3000, vyy400, ty_Bool) → new_lt14(vyy3000, vyy400)
new_esEs21(vyy471, vyy481, ty_Integer) → new_esEs11(vyy471, vyy481)
new_lt13(vyy3000, vyy400) → new_esEs9(new_compare29(vyy3000, vyy400))
new_primEqInt(Neg(Zero), Neg(Succ(vyy4800))) → False
new_primEqInt(Neg(Succ(vyy4700)), Neg(Zero)) → False
new_ltEs19(vyy3001, vyy401, ty_Char) → new_ltEs12(vyy3001, vyy401)
new_lt9(vyy3000, vyy400, ty_Char) → new_lt7(vyy3000, vyy400)
new_esEs19(Float(vyy470, vyy471), Float(vyy480, vyy481)) → new_esEs20(new_sr(vyy470, vyy480), new_sr(vyy471, vyy481))
new_lt10(vyy3001, vyy401, ty_Char) → new_lt7(vyy3001, vyy401)
new_esEs27(vyy47, vyy48, app(app(ty_Either, cgb), cgc)) → new_esEs8(vyy47, vyy48, cgb, cgc)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt8(vyy3000, vyy400)
new_lt9(vyy3000, vyy400, ty_Integer) → new_lt16(vyy3000, vyy400)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), bgc, bgd) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, bgc, bgd), vyy4733, bgc, bgd)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs9(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs11(vyy3000, vyy400)
new_esEs24(vyy472, vyy482, ty_Int) → new_esEs20(vyy472, vyy482)
new_esEs28(vyy471, vyy481, app(app(ty_@2, dda), ddb)) → new_esEs7(vyy471, vyy481, dda, ddb)
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, gc), gd), ge)) → new_lt6(vyy3000, vyy400, gc, gd, ge)
new_ltEs18(vyy3002, vyy402, app(ty_Ratio, bgh)) → new_ltEs16(vyy3002, vyy402, bgh)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs5(EQ, EQ) → True
new_sizeFM(EmptyFM, bgc, bgd) → Pos(Zero)
new_ltEs18(vyy3002, vyy402, ty_Integer) → new_ltEs13(vyy3002, vyy402)
new_esEs29(vyy470, vyy480, ty_Ordering) → new_esEs14(vyy470, vyy480)
new_esEs22(vyy470, vyy480, ty_Int) → new_esEs20(vyy470, vyy480)
new_primEqInt(Pos(Succ(vyy4700)), Pos(Succ(vyy4800))) → new_primEqNat0(vyy4700, vyy4800)
new_ltEs19(vyy3001, vyy401, app(app(app(ty_@3, he), hf), hg)) → new_ltEs7(vyy3001, vyy401, he, hf, hg)
new_compare10(vyy3000, vyy400, False, dc, dd) → GT
new_esEs24(vyy472, vyy482, app(app(ty_Either, ccb), ccc)) → new_esEs8(vyy472, vyy482, ccb, ccc)
new_ltEs14(Right(vyy3000), Right(vyy400), bda, ty_@0) → new_ltEs9(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, app(ty_Maybe, cdc)) → new_esEs5(vyy471, vyy481, cdc)
new_esEs24(vyy472, vyy482, app(ty_Ratio, ccd)) → new_esEs16(vyy472, vyy482, ccd)
new_esEs29(vyy470, vyy480, app(ty_Maybe, ddg)) → new_esEs5(vyy470, vyy480, ddg)
new_esEs8(Left(vyy470), Left(vyy480), app(app(app(ty_@3, cgg), cgh), cha), cgc) → new_esEs6(vyy470, vyy480, cgg, cgh, cha)
new_esEs5(Just(vyy470), Just(vyy480), ty_Char) → new_esEs10(vyy470, vyy480)
new_esEs25(vyy471, vyy481, ty_Char) → new_esEs10(vyy471, vyy481)
new_primEqNat0(Succ(vyy4700), Succ(vyy4800)) → new_primEqNat0(vyy4700, vyy4800)
new_esEs27(vyy47, vyy48, ty_@0) → new_esEs12(vyy47, vyy48)
new_esEs23(vyy470, vyy480, ty_Integer) → new_esEs11(vyy470, vyy480)
new_esEs26(vyy470, vyy480, ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs26(vyy470, vyy480, ty_@0) → new_esEs12(vyy470, vyy480)
new_esEs8(Left(vyy470), Left(vyy480), app(ty_Maybe, chb), cgc) → new_esEs5(vyy470, vyy480, chb)
new_esEs29(vyy470, vyy480, ty_@0) → new_esEs12(vyy470, vyy480)
new_primCompAux00(vyy88, LT) → LT
new_esEs15(vyy47, vyy48, bgc, bgd) → new_asAs(new_esEs20(new_sizeFM(vyy47, bgc, bgd), new_sizeFM(vyy48, bgc, bgd)), new_esEs13(new_fmToList(vyy47, bgc, bgd), new_fmToList(vyy48, bgc, bgd), app(app(ty_@2, bgc), bgd)))
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_lt15(vyy3000, vyy400, db) → new_esEs9(new_compare4(vyy3000, vyy400, db))
new_lt10(vyy3001, vyy401, app(app(app(ty_@3, dg), dh), ea)) → new_lt6(vyy3001, vyy401, dg, dh, ea)
new_esEs8(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, chc), chd), cgc) → new_esEs15(vyy470, vyy480, chc, chd)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs12(vyy3000, vyy400)
new_ltEs17(vyy300, vyy40) → new_not(new_compare6(vyy300, vyy40))
new_ltEs18(vyy3002, vyy402, ty_Double) → new_ltEs11(vyy3002, vyy402)
new_lt10(vyy3001, vyy401, app(app(ty_Either, ee), ef)) → new_lt17(vyy3001, vyy401, ee, ef)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4800))) → False
new_primEqInt(Pos(Succ(vyy4700)), Pos(Zero)) → False
new_ltEs19(vyy3001, vyy401, app(ty_Maybe, hd)) → new_ltEs6(vyy3001, vyy401, hd)
new_compare28(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_ltEs6(Just(vyy3000), Nothing, bfh) → False
new_esEs8(Left(vyy470), Left(vyy480), ty_Double, cgc) → new_esEs18(vyy470, vyy480)
new_ltEs5(GT, LT) → False
new_ltEs19(vyy3001, vyy401, ty_Float) → new_ltEs17(vyy3001, vyy401)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_esEs29(vyy470, vyy480, ty_Double) → new_esEs18(vyy470, vyy480)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_lt10(vyy3001, vyy401, ty_@0) → new_lt13(vyy3001, vyy401)
new_ltEs14(Left(vyy3000), Left(vyy400), app(ty_[], bcf), bbh) → new_ltEs4(vyy3000, vyy400, bcf)
new_esEs24(vyy472, vyy482, ty_Double) → new_esEs18(vyy472, vyy482)
new_compare11(vyy3000, vyy400, True, cg, da) → LT
new_esEs7(@2(vyy470, vyy471), @2(vyy480, vyy481), cgd, cge) → new_asAs(new_esEs29(vyy470, vyy480, cgd), new_esEs28(vyy471, vyy481, cge))
new_ltEs6(Just(vyy3000), Just(vyy400), app(ty_[], bf)) → new_ltEs4(vyy3000, vyy400, bf)
new_sr0(Integer(vyy30000), Integer(vyy4010)) → Integer(new_primMulInt(vyy30000, vyy4010))
new_primPlusNat1(Succ(vyy10300), Succ(vyy400000)) → Succ(Succ(new_primPlusNat1(vyy10300, vyy400000)))
new_compare12(vyy3000, vyy400, True, ca) → LT
new_primEqInt(Neg(Succ(vyy4700)), Pos(vyy480)) → False
new_primEqInt(Pos(Succ(vyy4700)), Neg(vyy480)) → False
new_esEs27(vyy47, vyy48, app(ty_Maybe, bec)) → new_esEs5(vyy47, vyy48, bec)
new_foldFM2(EmptyFM, bgc, bgd) → []
new_esEs26(vyy470, vyy480, ty_Double) → new_esEs18(vyy470, vyy480)
new_ltEs6(Just(vyy3000), Just(vyy400), app(ty_Maybe, h)) → new_ltEs6(vyy3000, vyy400, h)
new_esEs26(vyy470, vyy480, app(ty_Ratio, cfd)) → new_esEs16(vyy470, vyy480, cfd)
new_esEs24(vyy472, vyy482, app(ty_[], cbc)) → new_esEs13(vyy472, vyy482, cbc)
new_ltEs6(Just(vyy3000), Just(vyy400), app(app(ty_Either, bg), bh)) → new_ltEs14(vyy3000, vyy400, bg, bh)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Float, bbh) → new_ltEs17(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4800))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4800))) → False
new_esEs10(Char(vyy470), Char(vyy480)) → new_primEqNat0(vyy470, vyy480)
new_esEs23(vyy470, vyy480, ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs29(vyy470, vyy480, ty_Integer) → new_esEs11(vyy470, vyy480)
new_compare31(vyy3000, vyy400, ty_Double) → new_compare8(vyy3000, vyy400)
new_primCompAux00(vyy88, EQ) → vyy88
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_esEs28(vyy471, vyy481, ty_Char) → new_esEs10(vyy471, vyy481)
new_compare24(vyy3000, vyy400, True) → EQ
new_esEs27(vyy47, vyy48, app(app(ty_@2, cgd), cge)) → new_esEs7(vyy47, vyy48, cgd, cge)
new_pePe(False, vyy47, vyy48, vyy66, cga) → new_asAs(new_esEs27(vyy47, vyy48, cga), vyy66)
new_esEs23(vyy470, vyy480, ty_Char) → new_esEs10(vyy470, vyy480)
new_esEs24(vyy472, vyy482, ty_Ordering) → new_esEs14(vyy472, vyy482)
new_compare24(vyy3000, vyy400, False) → new_compare14(vyy3000, vyy400, new_ltEs5(vyy3000, vyy400))
new_compare18(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare28(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_lt18(vyy3000, vyy400) → new_esEs9(new_compare7(vyy3000, vyy400))
new_lt10(vyy3001, vyy401, app(ty_Maybe, df)) → new_lt11(vyy3001, vyy401, df)
new_esEs29(vyy470, vyy480, app(app(ty_FiniteMap, ddh), dea)) → new_esEs15(vyy470, vyy480, ddh, dea)
new_esEs27(vyy47, vyy48, app(ty_Ratio, bge)) → new_esEs16(vyy47, vyy48, bge)
new_esEs5(Just(vyy470), Just(vyy480), ty_Ordering) → new_esEs14(vyy470, vyy480)
new_ltEs18(vyy3002, vyy402, ty_Float) → new_ltEs17(vyy3002, vyy402)
new_compare9(vyy3000, vyy400, cd, ce, cf) → new_compare26(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, cd, ce, cf), cd, ce, cf)
new_lt20(vyy3000, vyy400, ty_Double) → new_lt5(vyy3000, vyy400)
new_ltEs6(Just(vyy3000), Just(vyy400), app(app(ty_@2, bd), be)) → new_ltEs8(vyy3000, vyy400, bd, be)
new_lt9(vyy3000, vyy400, app(ty_[], db)) → new_lt15(vyy3000, vyy400, db)
new_esEs24(vyy472, vyy482, ty_Float) → new_esEs19(vyy472, vyy482)
new_compare16(vyy3000, vyy400) → new_compare25(vyy3000, vyy400, new_esEs17(vyy3000, vyy400))
new_primPlusNat0(Zero, vyy40000) → Succ(vyy40000)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_compare210(vyy3000, vyy400, True, cg, da) → EQ
new_esEs5(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, bfa), bfb)) → new_esEs15(vyy470, vyy480, bfa, bfb)
new_lt9(vyy3000, vyy400, ty_Int) → new_lt18(vyy3000, vyy400)
new_lt4(vyy3000, vyy400) → new_esEs9(new_compare6(vyy3000, vyy400))
new_esEs25(vyy471, vyy481, app(ty_Ratio, cdh)) → new_esEs16(vyy471, vyy481, cdh)
new_ltEs14(Left(vyy3000), Left(vyy400), app(ty_Maybe, bbg), bbh) → new_ltEs6(vyy3000, vyy400, bbg)
new_not0 → True
new_esEs22(vyy470, vyy480, ty_Integer) → new_esEs11(vyy470, vyy480)
new_esEs24(vyy472, vyy482, app(ty_Maybe, cbg)) → new_esEs5(vyy472, vyy482, cbg)
new_esEs8(Left(vyy470), Left(vyy480), app(ty_[], cgf), cgc) → new_esEs13(vyy470, vyy480, cgf)
new_ltEs14(Right(vyy3000), Right(vyy400), bda, ty_Float) → new_ltEs17(vyy3000, vyy400)
new_compare11(vyy3000, vyy400, False, cg, da) → GT
new_esEs25(vyy471, vyy481, ty_Integer) → new_esEs11(vyy471, vyy481)
new_compare30(vyy3000, vyy400, cg, da) → new_compare210(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, cg, da), cg, da)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_compare210(vyy3000, vyy400, False, cg, da) → new_compare11(vyy3000, vyy400, new_ltEs8(vyy3000, vyy400, cg, da), cg, da)
new_esEs20(vyy47, vyy48) → new_primEqInt(vyy47, vyy48)
new_esEs5(Just(vyy470), Just(vyy480), ty_Bool) → new_esEs17(vyy470, vyy480)
new_primMulInt(Pos(vyy30000), Pos(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_esEs8(Left(vyy470), Left(vyy480), app(ty_Ratio, chg), cgc) → new_esEs16(vyy470, vyy480, chg)
new_esEs24(vyy472, vyy482, ty_Integer) → new_esEs11(vyy472, vyy482)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Char, bbh) → new_ltEs12(vyy3000, vyy400)
new_esEs8(Right(vyy470), Right(vyy480), cgb, app(app(app(ty_@3, dac), dad), dae)) → new_esEs6(vyy470, vyy480, dac, dad, dae)
new_ltEs5(LT, GT) → True
new_esEs24(vyy472, vyy482, app(app(ty_FiniteMap, cbh), cca)) → new_esEs15(vyy472, vyy482, cbh, cca)
new_ltEs14(Right(vyy3000), Right(vyy400), bda, ty_Bool) → new_ltEs10(vyy3000, vyy400)
new_ltEs12(vyy300, vyy40) → new_not(new_compare15(vyy300, vyy40))
new_esEs5(Just(vyy470), Just(vyy480), ty_Double) → new_esEs18(vyy470, vyy480)
new_primMulInt(Neg(vyy30000), Neg(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_compare110(vyy3000, vyy400, True) → LT
new_esEs27(vyy47, vyy48, ty_Ordering) → new_esEs14(vyy47, vyy48)
new_primEqNat0(Zero, Succ(vyy4800)) → False
new_primEqNat0(Succ(vyy4700), Zero) → False
new_lt20(vyy3000, vyy400, app(app(ty_@2, gf), gg)) → new_lt12(vyy3000, vyy400, gf, gg)
new_esEs26(vyy470, vyy480, app(app(ty_@2, cfe), cff)) → new_esEs7(vyy470, vyy480, cfe, cff)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs13(vyy3000, vyy400)
new_compare110(vyy3000, vyy400, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vyy471, vyy481, app(app(app(ty_@3, dbh), dca), dcb)) → new_esEs6(vyy471, vyy481, dbh, dca, dcb)
new_esEs5(Just(vyy470), Just(vyy480), ty_Float) → new_esEs19(vyy470, vyy480)
new_esEs28(vyy471, vyy481, app(app(ty_Either, dcf), dcg)) → new_esEs8(vyy471, vyy481, dcf, dcg)
new_lt9(vyy3000, vyy400, ty_Float) → new_lt4(vyy3000, vyy400)
new_esEs27(vyy47, vyy48, app(app(app(ty_@3, cah), cba), cbb)) → new_esEs6(vyy47, vyy48, cah, cba, cbb)
new_compare31(vyy3000, vyy400, app(app(ty_@2, bbb), bbc)) → new_compare30(vyy3000, vyy400, bbb, bbc)
new_compare4(:(vyy3000, vyy3001), [], bae) → GT
new_lt10(vyy3001, vyy401, ty_Bool) → new_lt14(vyy3001, vyy401)
new_lt10(vyy3001, vyy401, app(ty_[], ed)) → new_lt15(vyy3001, vyy401, ed)
new_sizeFM(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), bgc, bgd) → vyy472
new_esEs26(vyy470, vyy480, ty_Ordering) → new_esEs14(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, ty_Bool) → new_ltEs10(vyy3001, vyy401)
new_ltEs14(Left(vyy3000), Left(vyy400), app(app(ty_@2, bcd), bce), bbh) → new_ltEs8(vyy3000, vyy400, bcd, bce)
new_pePe(True, vyy47, vyy48, vyy66, cga) → True
new_esEs26(vyy470, vyy480, app(ty_Maybe, ceg)) → new_esEs5(vyy470, vyy480, ceg)
new_compare31(vyy3000, vyy400, ty_Char) → new_compare15(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, app(ty_Maybe, baf)) → new_compare17(vyy3000, vyy400, baf)
new_esEs23(vyy470, vyy480, ty_Double) → new_esEs18(vyy470, vyy480)
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), bgc, bgd) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, bgc, bgd), vyy473, bgc, bgd)
new_esEs14(LT, EQ) → False
new_esEs14(EQ, LT) → False
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_esEs23(vyy470, vyy480, ty_Bool) → new_esEs17(vyy470, vyy480)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_ltEs16(vyy300, vyy40, bgb) → new_not(new_compare18(vyy300, vyy40, bgb))
new_lt20(vyy3000, vyy400, ty_Char) → new_lt7(vyy3000, vyy400)
new_esEs5(Just(vyy470), Just(vyy480), app(app(app(ty_@3, bee), bef), beg)) → new_esEs6(vyy470, vyy480, bee, bef, beg)
new_compare4([], :(vyy400, vyy401), bae) → LT
new_compare23(vyy3000, vyy400, True, ca) → EQ
new_lt10(vyy3001, vyy401, ty_Float) → new_lt4(vyy3001, vyy401)
new_lt20(vyy3000, vyy400, app(ty_Ratio, cfg)) → new_lt19(vyy3000, vyy400, cfg)
new_esEs8(Left(vyy470), Left(vyy480), app(app(ty_Either, che), chf), cgc) → new_esEs8(vyy470, vyy480, che, chf)
new_esEs8(Right(vyy470), Right(vyy480), cgb, ty_Char) → new_esEs10(vyy470, vyy480)
new_esEs23(vyy470, vyy480, app(ty_Ratio, cae)) → new_esEs16(vyy470, vyy480, cae)
new_esEs16(:%(vyy470, vyy471), :%(vyy480, vyy481), bge) → new_asAs(new_esEs22(vyy470, vyy480, bge), new_esEs21(vyy471, vyy481, bge))
new_esEs8(Left(vyy470), Left(vyy480), ty_Ordering, cgc) → new_esEs14(vyy470, vyy480)
new_esEs27(vyy47, vyy48, ty_Double) → new_esEs18(vyy47, vyy48)
new_lt11(vyy3000, vyy400, ca) → new_esEs9(new_compare17(vyy3000, vyy400, ca))
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs5(vyy3000, vyy400)
new_esEs14(EQ, GT) → False
new_esEs14(GT, EQ) → False
new_lt20(vyy3000, vyy400, app(ty_[], gh)) → new_lt15(vyy3000, vyy400, gh)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare31(vyy3000, vyy400, app(ty_[], bbd)) → new_compare4(vyy3000, vyy400, bbd)
new_esEs29(vyy470, vyy480, ty_Bool) → new_esEs17(vyy470, vyy480)
new_ltEs14(Left(vyy3000), Right(vyy400), bda, bbh) → True
new_lt20(vyy3000, vyy400, ty_@0) → new_lt13(vyy3000, vyy400)
new_ltEs10(True, False) → False
new_asAs(False, vyy79) → False
new_esEs8(Right(vyy470), Right(vyy480), cgb, ty_Ordering) → new_esEs14(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, app(app(ty_Either, bac), bad)) → new_ltEs14(vyy3001, vyy401, bac, bad)
new_primMulInt(Pos(vyy30000), Neg(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulInt(Neg(vyy30000), Pos(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_esEs8(Left(vyy470), Left(vyy480), ty_Bool, cgc) → new_esEs17(vyy470, vyy480)
new_esEs13([], :(vyy480, vyy481), bhc) → False
new_esEs13(:(vyy470, vyy471), [], bhc) → False
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40000)) → Zero
new_ltEs14(Right(vyy3000), Right(vyy400), bda, app(app(app(ty_@3, bdc), bdd), bde)) → new_ltEs7(vyy3000, vyy400, bdc, bdd, bde)
new_ltEs18(vyy3002, vyy402, ty_Ordering) → new_ltEs5(vyy3002, vyy402)
new_esEs23(vyy470, vyy480, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs6(vyy470, vyy480, bhe, bhf, bhg)
new_ltEs5(LT, EQ) → True
new_compare4(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_primCompAux0(vyy3000, vyy400, new_compare4(vyy3001, vyy401, bae), bae)
new_esEs28(vyy471, vyy481, ty_Int) → new_esEs20(vyy471, vyy481)
new_ltEs18(vyy3002, vyy402, app(ty_[], ff)) → new_ltEs4(vyy3002, vyy402, ff)
new_esEs23(vyy470, vyy480, app(app(ty_@2, caf), cag)) → new_esEs7(vyy470, vyy480, caf, cag)
new_esEs28(vyy471, vyy481, ty_Double) → new_esEs18(vyy471, vyy481)
new_not(EQ) → new_not0
new_ltEs14(Right(vyy3000), Right(vyy400), bda, app(app(ty_Either, bea), beb)) → new_ltEs14(vyy3000, vyy400, bea, beb)
new_ltEs14(Right(vyy3000), Right(vyy400), bda, ty_Double) → new_ltEs11(vyy3000, vyy400)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs17(vyy3000, vyy400)
new_esEs8(Right(vyy470), Right(vyy480), cgb, app(ty_[], dab)) → new_esEs13(vyy470, vyy480, dab)
new_esEs29(vyy470, vyy480, app(ty_Ratio, ded)) → new_esEs16(vyy470, vyy480, ded)
new_esEs23(vyy470, vyy480, app(ty_Maybe, bhh)) → new_esEs5(vyy470, vyy480, bhh)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Integer, bbh) → new_ltEs13(vyy3000, vyy400)
new_ltEs18(vyy3002, vyy402, ty_Char) → new_ltEs12(vyy3002, vyy402)
new_esEs25(vyy471, vyy481, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs6(vyy471, vyy481, cch, cda, cdb)
new_ltEs18(vyy3002, vyy402, app(app(ty_@2, fc), fd)) → new_ltEs8(vyy3002, vyy402, fc, fd)
new_esEs25(vyy471, vyy481, ty_Int) → new_esEs20(vyy471, vyy481)
new_lt14(vyy3000, vyy400) → new_esEs9(new_compare16(vyy3000, vyy400))
new_esEs14(GT, GT) → True
new_lt9(vyy3000, vyy400, app(ty_Maybe, ca)) → new_lt11(vyy3000, vyy400, ca)
new_esEs25(vyy471, vyy481, app(ty_[], ccg)) → new_esEs13(vyy471, vyy481, ccg)
new_esEs23(vyy470, vyy480, ty_@0) → new_esEs12(vyy470, vyy480)
new_esEs5(Nothing, Just(vyy480), bec) → False
new_esEs5(Just(vyy470), Nothing, bec) → False
new_compare211(vyy3000, vyy400, True, dc, dd) → EQ
new_ltEs6(Nothing, Nothing, bfh) → True
new_lt16(vyy3000, vyy400) → new_esEs9(new_compare28(vyy3000, vyy400))
new_ltEs14(Left(vyy3000), Left(vyy400), app(app(ty_Either, bcg), bch), bbh) → new_ltEs14(vyy3000, vyy400, bcg, bch)
new_esEs29(vyy470, vyy480, ty_Float) → new_esEs19(vyy470, vyy480)
new_esEs25(vyy471, vyy481, ty_Float) → new_esEs19(vyy471, vyy481)
new_compare19(vyy3000, vyy400) → new_compare24(vyy3000, vyy400, new_esEs14(vyy3000, vyy400))
new_lt12(vyy3000, vyy400, cg, da) → new_esEs9(new_compare30(vyy3000, vyy400, cg, da))
new_esEs28(vyy471, vyy481, ty_Bool) → new_esEs17(vyy471, vyy481)
new_ltEs13(vyy300, vyy40) → new_not(new_compare28(vyy300, vyy40))
new_compare31(vyy3000, vyy400, ty_Float) → new_compare6(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, ty_Int) → new_ltEs15(vyy3001, vyy401)
new_esEs29(vyy470, vyy480, ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs26(vyy470, vyy480, ty_Bool) → new_esEs17(vyy470, vyy480)
new_esEs27(vyy47, vyy48, ty_Int) → new_esEs20(vyy47, vyy48)
new_not(LT) → new_not0
new_lt6(vyy3000, vyy400, cd, ce, cf) → new_esEs9(new_compare9(vyy3000, vyy400, cd, ce, cf))
new_esEs25(vyy471, vyy481, ty_Double) → new_esEs18(vyy471, vyy481)
new_esEs5(Nothing, Nothing, bec) → True
new_esEs26(vyy470, vyy480, ty_Char) → new_esEs10(vyy470, vyy480)
new_ltEs18(vyy3002, vyy402, app(ty_Maybe, eg)) → new_ltEs6(vyy3002, vyy402, eg)
new_esEs28(vyy471, vyy481, app(ty_Maybe, dcc)) → new_esEs5(vyy471, vyy481, dcc)
new_esEs26(vyy470, vyy480, ty_Float) → new_esEs19(vyy470, vyy480)
new_esEs5(Just(vyy470), Just(vyy480), ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs29(vyy470, vyy480, app(app(app(ty_@3, ddd), dde), ddf)) → new_esEs6(vyy470, vyy480, ddd, dde, ddf)
new_esEs8(Left(vyy470), Left(vyy480), ty_@0, cgc) → new_esEs12(vyy470, vyy480)
new_esEs28(vyy471, vyy481, ty_Ordering) → new_esEs14(vyy471, vyy481)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Double, bbh) → new_ltEs11(vyy3000, vyy400)
new_ltEs14(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bca), bcb), bcc), bbh) → new_ltEs7(vyy3000, vyy400, bca, bcb, bcc)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs15(vyy3000, vyy400)
new_compare26(vyy3000, vyy400, True, cd, ce, cf) → EQ
new_compare31(vyy3000, vyy400, ty_Bool) → new_compare16(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, ty_Ordering) → new_ltEs5(vyy3001, vyy401)
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs10(True, True) → True
new_ltEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, cb, cc) → new_pePe(new_lt9(vyy3000, vyy400, de), vyy3000, vyy400, new_pePe(new_lt10(vyy3001, vyy401, cb), vyy3001, vyy401, new_ltEs18(vyy3002, vyy402, cc), cb), de)
new_esEs8(Right(vyy470), Right(vyy480), cgb, ty_Double) → new_esEs18(vyy470, vyy480)
new_asAs(True, vyy79) → vyy79
new_ltEs9(vyy300, vyy40) → new_not(new_compare29(vyy300, vyy40))
new_esEs5(Just(vyy470), Just(vyy480), ty_Integer) → new_esEs11(vyy470, vyy480)
new_primMulNat0(Succ(vyy300000), Succ(vyy40000)) → new_primPlusNat0(new_primMulNat0(vyy300000, Succ(vyy40000)), vyy40000)
new_esEs27(vyy47, vyy48, app(ty_[], bhc)) → new_esEs13(vyy47, vyy48, bhc)
new_ltEs5(GT, GT) → True
new_esEs27(vyy47, vyy48, ty_Integer) → new_esEs11(vyy47, vyy48)
new_compare31(vyy3000, vyy400, ty_Int) → new_compare7(vyy3000, vyy400)
new_esEs5(Just(vyy470), Just(vyy480), app(app(ty_@2, bff), bfg)) → new_esEs7(vyy470, vyy480, bff, bfg)
new_esEs8(Right(vyy470), Right(vyy480), cgb, ty_Integer) → new_esEs11(vyy470, vyy480)
new_esEs14(LT, LT) → True
new_ltEs19(vyy3001, vyy401, ty_@0) → new_ltEs9(vyy3001, vyy401)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Bool, bbh) → new_ltEs10(vyy3000, vyy400)
new_primCompAux0(vyy3000, vyy400, vyy84, bae) → new_primCompAux00(vyy84, new_compare31(vyy3000, vyy400, bae))
new_fmToList(vyy47, bgc, bgd) → new_foldFM2(vyy47, bgc, bgd)
new_ltEs19(vyy3001, vyy401, ty_Integer) → new_ltEs13(vyy3001, vyy401)
new_ltEs14(Right(vyy3000), Right(vyy400), bda, ty_Integer) → new_ltEs13(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, ty_Ordering) → new_esEs14(vyy471, vyy481)
new_ltEs14(Right(vyy3000), Right(vyy400), bda, app(ty_Maybe, bdb)) → new_ltEs6(vyy3000, vyy400, bdb)
new_ltEs6(Just(vyy3000), Just(vyy400), app(ty_Ratio, bga)) → new_ltEs16(vyy3000, vyy400, bga)
new_ltEs4(vyy300, vyy40, bae) → new_not(new_compare4(vyy300, vyy40, bae))
new_compare13(vyy3000, vyy400, True, cd, ce, cf) → LT
new_primCompAux00(vyy88, GT) → GT
new_lt5(vyy3000, vyy400) → new_esEs9(new_compare8(vyy3000, vyy400))
new_lt9(vyy3000, vyy400, ty_@0) → new_lt13(vyy3000, vyy400)
new_esEs8(Left(vyy470), Left(vyy480), app(app(ty_@2, chh), daa), cgc) → new_esEs7(vyy470, vyy480, chh, daa)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs8(Left(vyy470), Left(vyy480), ty_Char, cgc) → new_esEs10(vyy470, vyy480)
new_ltEs5(GT, EQ) → False
new_lt10(vyy3001, vyy401, ty_Int) → new_lt18(vyy3001, vyy401)
new_lt19(vyy3000, vyy400, bgf) → new_esEs9(new_compare18(vyy3000, vyy400, bgf))
new_ltEs18(vyy3002, vyy402, ty_Int) → new_ltEs15(vyy3002, vyy402)
new_esEs24(vyy472, vyy482, ty_@0) → new_esEs12(vyy472, vyy482)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs25(vyy471, vyy481, app(app(ty_Either, cdf), cdg)) → new_esEs8(vyy471, vyy481, cdf, cdg)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs23(vyy470, vyy480, app(ty_[], bhd)) → new_esEs13(vyy470, vyy480, bhd)
The set Q consists of the following terms:
new_ltEs18(x0, x1, ty_Char)
new_primCompAux00(x0, GT)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2, x3)
new_compare23(x0, x1, False, x2)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_lt20(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, True, x2, x3)
new_esEs27(x0, x1, ty_Integer)
new_compare25(x0, x1, False)
new_esEs23(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs6(Just(x0), Just(x1), ty_Integer)
new_esEs14(GT, EQ)
new_esEs14(EQ, GT)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt16(x0, x1)
new_esEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs18(Double(x0, x1), Double(x2, x3))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs29(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Int)
new_ltEs13(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_compare110(x0, x1, False)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_compare211(x0, x1, True, x2, x3)
new_compare7(x0, x1)
new_esEs9(EQ)
new_compare12(x0, x1, False, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs13([], :(x0, x1), x2)
new_esEs28(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Ordering)
new_lt19(x0, x1, x2)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs24(x0, x1, ty_Char)
new_esEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM2(EmptyFM, x0, x1)
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_compare10(x0, x1, False, x2, x3)
new_ltEs6(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(Just(x0), Just(x1), ty_Char)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_esEs8(Left(x0), Left(x1), ty_Integer, x2)
new_lt9(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Float)
new_ltEs6(Just(x0), Nothing, x1)
new_esEs8(Left(x0), Left(x1), ty_Char, x2)
new_esEs29(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs17(False, False)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt9(x0, x1, ty_Bool)
new_primMulNat0(Zero, Succ(x0))
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs18(x0, x1, ty_Ordering)
new_esEs14(LT, GT)
new_esEs14(GT, LT)
new_ltEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs8(Left(x0), Left(x1), ty_Bool, x2)
new_compare24(x0, x1, False)
new_esEs10(Char(x0), Char(x1))
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_Float)
new_esEs8(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs6(Just(x0), Just(x1), ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare29(@0, @0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(EQ, LT)
new_lt20(x0, x1, ty_@0)
new_ltEs5(LT, EQ)
new_esEs29(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_esEs5(Nothing, Nothing, x0)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs27(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs6(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_pePe(False, x0, x1, x2, x3)
new_esEs8(Right(x0), Right(x1), x2, ty_Float)
new_esEs12(@0, @0)
new_ltEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs6(Nothing, Nothing, x0)
new_compare12(x0, x1, True, x2)
new_compare6(Float(x0, x1), Float(x2, x3))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Zero)
new_compare17(x0, x1, x2)
new_esEs23(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs27(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Integer)
new_fmToList(x0, x1, x2)
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_lt9(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_lt18(x0, x1)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Integer)
new_esEs8(Left(x0), Right(x1), x2, x3)
new_esEs8(Right(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_compare26(x0, x1, True, x2, x3, x4)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Bool)
new_primPlusNat0(Zero, x0)
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare211(x0, x1, False, x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, ty_@0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt14(x0, x1)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Bool)
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_lt11(x0, x1, x2)
new_esEs24(x0, x1, ty_Double)
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare27(x0, x1, x2, x3)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare31(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_esEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs16(x0, x1, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), ty_Float, x2)
new_sizeFM(EmptyFM, x0, x1)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, Zero)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_not0
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs12(x0, x1)
new_compare30(x0, x1, x2, x3)
new_compare4([], :(x0, x1), x2)
new_esEs14(LT, LT)
new_esEs24(x0, x1, ty_Int)
new_ltEs10(False, False)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_esEs9(GT)
new_compare23(x0, x1, True, x2)
new_esEs8(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_asAs(True, x0)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_ltEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, app(ty_Ratio, x2))
new_esEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt9(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True)
new_ltEs18(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Int)
new_esEs13([], [], x0)
new_esEs26(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(True, x0, x1, x2, x3)
new_lt9(x0, x1, ty_@0)
new_compare24(x0, x1, True)
new_lt5(x0, x1)
new_primCompAux00(x0, LT)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(x0, x1, ty_Float)
new_asAs(False, x0)
new_primEqNat0(Zero, Succ(x0))
new_ltEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs5(Nothing, Just(x0), x1)
new_ltEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs28(x0, x1, ty_Int)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_not(GT)
new_primMulInt(Pos(x0), Pos(x1))
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare13(x0, x1, False, x2, x3, x4)
new_compare31(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_lt7(x0, x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_@0)
new_esEs20(x0, x1)
new_ltEs18(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare25(x0, x1, True)
new_ltEs19(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs11(Integer(x0), Integer(x1))
new_esEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs8(Right(x0), Right(x1), x2, ty_Bool)
new_lt9(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_Float)
new_lt9(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_compare9(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare28(Integer(x0), Integer(x1))
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Just(x0), Just(x1), ty_Ordering)
new_ltEs6(Just(x0), Just(x1), ty_Int)
new_esEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt8(x0, x1)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(LT)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(Nothing, Just(x0), x1)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_@0)
new_lt17(x0, x1, x2, x3)
new_compare4(:(x0, x1), :(x2, x3), x4)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare26(x0, x1, False, x2, x3, x4)
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), [], x2)
new_lt12(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Char)
new_esEs5(Just(x0), Nothing, x1)
new_compare15(Char(x0), Char(x1))
new_esEs13(:(x0, x1), [], x2)
new_primCmpNat0(Zero, Zero)
new_esEs15(x0, x1, x2, x3)
new_lt10(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare11(x0, x1, True, x2, x3)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs10(True, True)
new_lt13(x0, x1)
new_esEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt6(x0, x1, x2, x3, x4)
new_ltEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_@0)
new_esEs8(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Double)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(GT, GT)
new_ltEs19(x0, x1, ty_@0)
new_lt10(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux0(x0, x1, x2, x3)
new_compare11(x0, x1, False, x2, x3)
new_compare10(x0, x1, True, x2, x3)
new_esEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs4(x0, x1, x2)
new_esEs29(x0, x1, app(ty_[], x2))
new_not(EQ)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare31(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_compare31(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Bool)
new_ltEs6(Just(x0), Just(x1), ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs8(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs5(EQ, EQ)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primCompAux00(x0, EQ)
new_esEs14(EQ, LT)
new_esEs14(LT, EQ)
new_lt10(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Char)
new_sr(x0, x1)
new_ltEs15(x0, x1)
new_compare13(x0, x1, True, x2, x3, x4)
new_esEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs14(GT, GT)
new_lt15(x0, x1, x2)
new_primMulNat0(Succ(x0), Zero)
new_ltEs6(Just(x0), Just(x1), ty_Float)
new_lt9(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare19(x0, x1)
new_ltEs10(False, True)
new_ltEs10(True, False)
new_esEs26(x0, x1, ty_Integer)
new_compare14(x0, x1, False)
new_esEs28(x0, x1, ty_Bool)
new_ltEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Int)
new_compare4([], [], x0)
new_esEs17(False, True)
new_esEs17(True, False)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_compare16(x0, x1)
new_esEs14(EQ, EQ)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt9(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs9(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs29(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare8(Double(x0, x1), Double(x2, x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(x0, x1)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt10(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Char)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt20(x0, x1, ty_Char)
new_compare14(x0, x1, True)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs25(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_lt20(x0, x1, ty_Double)
new_not(LT)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs5(LT, LT)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs28(x0, x1, ty_Float)
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primCompAux(vyy3000, vyy400, vyy84, app(ty_[], bbd)) → new_compare(vyy3000, vyy400, bbd)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), hc, app(app(app(ty_@3, he), hf), hg)) → new_ltEs0(vyy3001, vyy401, he, hf, hg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), hc, app(app(ty_@2, hh), baa)) → new_ltEs1(vyy3001, vyy401, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), hc, app(app(ty_Either, bac), bad)) → new_ltEs3(vyy3001, vyy401, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_compare(vyy3001, vyy401, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_ltEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_primCompAux(vyy3000, vyy400, new_compare4(vyy3001, vyy401, bae), bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), hc, app(ty_Maybe, hd)) → new_ltEs(vyy3001, vyy401, hd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare1(vyy3000, vyy400, cd, ce, cf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, cd, ce, cf), cd, ce, cf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_primCompAux(vyy3000, vyy400, new_compare4(vyy3001, vyy401, bae), bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_lt(vyy3000, vyy400, ca) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, ca), ca)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_compare3(vyy3000, vyy400, cg, da) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, cg, da), cg, da)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, cb, app(app(app(ty_@3, eh), fa), fb)) → new_ltEs0(vyy3002, vyy402, eh, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_[], db), cb, cc) → new_compare(vyy3000, vyy400, db)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, cb, app(app(ty_@2, fc), fd)) → new_ltEs1(vyy3002, vyy402, fc, fd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, cb, app(app(ty_Either, fg), fh)) → new_ltEs3(vyy3002, vyy402, fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_Either, dc), dd), cb, cc) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, dc, dd), dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, cb, app(ty_Maybe, eg)) → new_ltEs(vyy3002, vyy402, eg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ba), bb), bc)) → new_ltEs0(vyy3000, vyy400, ba, bb, bc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_compare20(vyy3000, vyy400, False, cd, ce, cf) → new_ltEs0(vyy3000, vyy400, cd, ce, cf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4, 6 >= 5
- new_ltEs(Just(vyy3000), Just(vyy400), app(app(ty_@2, bd), be)) → new_ltEs1(vyy3000, vyy400, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_compare21(vyy3000, vyy400, False, cg, da) → new_ltEs1(vyy3000, vyy400, cg, da)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs(Just(vyy3000), Just(vyy400), app(app(ty_Either, bg), bh)) → new_ltEs3(vyy3000, vyy400, bg, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_compare22(vyy3000, vyy400, False, dc, dd) → new_ltEs3(vyy3000, vyy400, dc, dd)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs(Just(vyy3000), Just(vyy400), app(ty_Maybe, h)) → new_ltEs(vyy3000, vyy400, h)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_compare2(vyy3000, vyy400, False, ca) → new_ltEs(vyy3000, vyy400, ca)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3
- new_ltEs(Just(vyy3000), Just(vyy400), app(ty_[], bf)) → new_ltEs2(vyy3000, vyy400, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_Either, ha), hb), gb) → new_lt3(vyy3000, vyy400, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, app(app(ty_Either, ee), ef), cc) → new_lt3(vyy3001, vyy401, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_lt2(vyy3000, vyy400, db) → new_compare(vyy3000, vyy400, db)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
- new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_compare(vyy3001, vyy401, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_Maybe, ga), gb) → new_lt(vyy3000, vyy400, ga)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, app(ty_Maybe, df), cc) → new_lt(vyy3001, vyy401, df)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_primCompAux(vyy3000, vyy400, vyy84, app(app(ty_@2, bbb), bbc)) → new_compare3(vyy3000, vyy400, bbb, bbc)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_compare5(vyy3000, vyy400, dc, dd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, dc, dd), dc, dd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_lt3(vyy3000, vyy400, dc, dd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, dc, dd), dc, dd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_lt0(vyy3000, vyy400, cd, ce, cf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, cd, ce, cf), cd, ce, cf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_primCompAux(vyy3000, vyy400, vyy84, app(app(app(ty_@3, bag), bah), bba)) → new_compare1(vyy3000, vyy400, bag, bah, bba)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_@2, cg), da), cb, cc) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, cg, da), cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_lt1(vyy3000, vyy400, cg, da) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, cg, da), cg, da)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_compare0(vyy3000, vyy400, ca) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, ca), ca)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_Maybe, ca), cb, cc) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, ca), ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4
- new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), hc, app(ty_[], bab)) → new_ltEs2(vyy3001, vyy401, bab)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, cb, app(ty_[], ff)) → new_ltEs2(vyy3002, vyy402, ff)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_primCompAux(vyy3000, vyy400, vyy84, app(ty_Maybe, baf)) → new_compare0(vyy3000, vyy400, baf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_primCompAux(vyy3000, vyy400, vyy84, app(app(ty_Either, bbe), bbf)) → new_compare5(vyy3000, vyy400, bbe, bbf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_[], gh), gb) → new_lt2(vyy3000, vyy400, gh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, app(ty_[], ed), cc) → new_lt2(vyy3001, vyy401, ed)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(app(ty_@3, gc), gd), ge), gb) → new_lt0(vyy3000, vyy400, gc, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs1(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_@2, gf), gg), gb) → new_lt1(vyy3000, vyy400, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, app(app(app(ty_@3, dg), dh), ea), cc) → new_lt0(vyy3001, vyy401, dg, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(app(ty_@3, cd), ce), cf), cb, cc) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, cd, ce, cf), cd, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5, 3 > 6
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, app(app(ty_@2, eb), ec), cc) → new_lt1(vyy3001, vyy401, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(Right(vyy3000), Right(vyy400), bda, app(app(app(ty_@3, bdc), bdd), bde)) → new_ltEs0(vyy3000, vyy400, bdc, bdd, bde)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs3(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bca), bcb), bcc), bbh) → new_ltEs0(vyy3000, vyy400, bca, bcb, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs3(Right(vyy3000), Right(vyy400), bda, app(app(ty_@2, bdf), bdg)) → new_ltEs1(vyy3000, vyy400, bdf, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(Left(vyy3000), Left(vyy400), app(app(ty_@2, bcd), bce), bbh) → new_ltEs1(vyy3000, vyy400, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs3(Left(vyy3000), Left(vyy400), app(app(ty_Either, bcg), bch), bbh) → new_ltEs3(vyy3000, vyy400, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs3(Right(vyy3000), Right(vyy400), bda, app(app(ty_Either, bea), beb)) → new_ltEs3(vyy3000, vyy400, bea, beb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(Left(vyy3000), Left(vyy400), app(ty_Maybe, bbg), bbh) → new_ltEs(vyy3000, vyy400, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs3(Right(vyy3000), Right(vyy400), bda, app(ty_Maybe, bdb)) → new_ltEs(vyy3000, vyy400, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(Right(vyy3000), Right(vyy400), bda, app(ty_[], bdh)) → new_ltEs2(vyy3000, vyy400, bdh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(Left(vyy3000), Left(vyy400), app(ty_[], bcf), bbh) → new_ltEs2(vyy3000, vyy400, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE1(vyy65, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba, bb) → new_foldFM_LE2(vyy340, vyy341, new_foldFM_LE0(vyy65, vyy40, vyy343, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb)
new_foldFM_LE1(vyy65, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba, bb) → new_foldFM_LE(vyy65, vyy40, vyy343, h, ba, bb)
new_foldFM_LE1(vyy65, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba, bb) → new_foldFM_LE(vyy65, vyy40, vyy343, h, ba, bb)
new_foldFM_LE2(vyy340, vyy341, vyy73, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb) → new_foldFM_LE1(new_eltsFM_LE0(vyy340, vyy341, vyy73, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs14(vyy3440, Right(vyy40), ba, bb), h, ba, bb)
new_foldFM_LE1(vyy65, vyy40, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba, bb) → new_foldFM_LE1(vyy65, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs14(vyy3430, Right(vyy40), ba, bb), h, ba, bb)
new_foldFM_LE(vyy65, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba, bb) → new_foldFM_LE1(vyy65, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs14(vyy3430, Right(vyy40), ba, bb), h, ba, bb)
The TRS R consists of the following rules:
new_esEs28(vyy471, vyy481, app(ty_[], dcb)) → new_esEs13(vyy471, vyy481, dcb)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_@0, bbd) → new_ltEs9(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, app(ty_Ratio, cfb)) → new_ltEs16(vyy3001, vyy401, cfb)
new_ltEs18(vyy3002, vyy402, ty_@0) → new_ltEs9(vyy3002, vyy402)
new_ltEs10(False, True) → True
new_compare17(vyy3000, vyy400, ea) → new_compare23(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, ea), ea)
new_esEs13([], [], bea) → True
new_compare10(vyy3000, vyy400, True, bc, bd) → LT
new_esEs11(Integer(vyy470), Integer(vyy480)) → new_primEqInt(vyy470, vyy480)
new_ltEs5(EQ, GT) → True
new_esEs28(vyy471, vyy481, ty_Integer) → new_esEs11(vyy471, vyy481)
new_esEs26(vyy470, vyy480, ty_Integer) → new_esEs11(vyy470, vyy480)
new_ltEs6(Nothing, Just(vyy400), eb) → True
new_ltEs19(vyy3001, vyy401, ty_Double) → new_ltEs11(vyy3001, vyy401)
new_compare31(vyy3000, vyy400, app(app(app(ty_@3, dba), dbb), dbc)) → new_compare9(vyy3000, vyy400, dba, dbb, dbc)
new_esEs27(vyy47, vyy48, ty_Bool) → new_esEs17(vyy47, vyy48)
new_esEs23(vyy470, vyy480, ty_Float) → new_esEs19(vyy470, vyy480)
new_primMulNat0(Zero, Zero) → Zero
new_lt10(vyy3001, vyy401, app(app(ty_@2, hc), hd)) → new_lt12(vyy3001, vyy401, hc, hd)
new_lt20(vyy3000, vyy400, ty_Float) → new_lt4(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, app(ty_Ratio, dca)) → new_compare18(vyy3000, vyy400, dca)
new_compare13(vyy3000, vyy400, False, df, dg, dh) → GT
new_esEs5(Just(vyy470), Just(vyy480), app(ty_Ratio, db)) → new_esEs16(vyy470, vyy480, db)
new_esEs5(Just(vyy470), Just(vyy480), ty_@0) → new_esEs12(vyy470, vyy480)
new_esEs8(Right(vyy470), Right(vyy480), cfd, app(app(ty_FiniteMap, daa), dab)) → new_esEs15(vyy470, vyy480, daa, dab)
new_esEs9(LT) → True
new_lt20(vyy3000, vyy400, ty_Int) → new_lt18(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, ty_Bool) → new_esEs17(vyy471, vyy481)
new_esEs27(vyy47, vyy48, app(app(ty_FiniteMap, fg), fh)) → new_esEs15(vyy47, vyy48, fg, fh)
new_lt9(vyy3000, vyy400, app(ty_Ratio, gf)) → new_lt19(vyy3000, vyy400, gf)
new_not(GT) → False
new_esEs8(Right(vyy470), Right(vyy480), cfd, ty_@0) → new_esEs12(vyy470, vyy480)
new_lt9(vyy3000, vyy400, ty_Ordering) → new_lt8(vyy3000, vyy400)
new_esEs29(vyy470, vyy480, app(app(ty_Either, dee), def)) → new_esEs8(vyy470, vyy480, dee, def)
new_esEs8(Left(vyy470), Left(vyy480), ty_Integer, cfe) → new_esEs11(vyy470, vyy480)
new_esEs17(True, True) → True
new_lt17(vyy3000, vyy400, bc, bd) → new_esEs9(new_compare27(vyy3000, vyy400, bc, bd))
new_lt10(vyy3001, vyy401, ty_Ordering) → new_lt8(vyy3001, vyy401)
new_esEs8(Right(vyy470), Right(vyy480), cfd, app(ty_Ratio, dae)) → new_esEs16(vyy470, vyy480, dae)
new_ltEs15(vyy300, vyy40) → new_not(new_compare7(vyy300, vyy40))
new_esEs23(vyy470, vyy480, app(app(ty_FiniteMap, beg), beh)) → new_esEs15(vyy470, vyy480, beg, beh)
new_compare27(vyy3000, vyy400, bc, bd) → new_compare211(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, bc, bd), bc, bd)
new_ltEs11(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_esEs8(Right(vyy470), Right(vyy480), cfd, ty_Bool) → new_esEs17(vyy470, vyy480)
new_lt9(vyy3000, vyy400, app(app(app(ty_@3, df), dg), dh)) → new_lt6(vyy3000, vyy400, df, dg, dh)
new_esEs5(Just(vyy470), Just(vyy480), app(ty_Maybe, cd)) → new_esEs5(vyy470, vyy480, cd)
new_ltEs5(EQ, LT) → False
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt16(vyy3000, vyy400)
new_esEs12(@0, @0) → True
new_esEs28(vyy471, vyy481, ty_@0) → new_esEs12(vyy471, vyy481)
new_ltEs18(vyy3002, vyy402, ty_Bool) → new_ltEs10(vyy3002, vyy402)
new_ltEs10(False, False) → True
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, fg, fh) → :(@2(vyy470, vyy471), vyy102)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs10(vyy3000, vyy400)
new_lt8(vyy3000, vyy400) → new_esEs9(new_compare19(vyy3000, vyy400))
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt14(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, ty_Integer) → new_compare28(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, app(app(ty_@2, cee), cef)) → new_ltEs8(vyy3001, vyy401, cee, cef)
new_esEs25(vyy471, vyy481, app(app(ty_@2, cag), cah)) → new_esEs7(vyy471, vyy481, cag, cah)
new_ltEs18(vyy3002, vyy402, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs7(vyy3002, vyy402, bab, bac, bad)
new_compare31(vyy3000, vyy400, app(app(ty_Either, dbg), dbh)) → new_compare27(vyy3000, vyy400, dbg, dbh)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Char) → new_ltEs12(vyy3000, vyy400)
new_compare29(@0, @0) → EQ
new_compare31(vyy3000, vyy400, ty_@0) → new_compare29(vyy3000, vyy400)
new_esEs26(vyy470, vyy480, app(app(ty_FiniteMap, cbf), cbg)) → new_esEs15(vyy470, vyy480, cbf, cbg)
new_esEs23(vyy470, vyy480, app(app(ty_Either, bfa), bfb)) → new_esEs8(vyy470, vyy480, bfa, bfb)
new_compare15(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs26(vyy470, vyy480, app(app(ty_Either, cbh), cca)) → new_esEs8(vyy470, vyy480, cbh, cca)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, app(ty_[], bde)) → new_ltEs4(vyy3000, vyy400, bde)
new_compare8(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare7(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_foldFM_LE10(vyy65, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba, bb) → new_foldFM_LE20(vyy340, vyy341, new_foldFM_LE0(vyy65, vyy40, vyy343, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb)
new_esEs6(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), bff, bfg, bfh) → new_asAs(new_esEs26(vyy470, vyy480, bff), new_asAs(new_esEs25(vyy471, vyy481, bfg), new_esEs24(vyy472, vyy482, bfh)))
new_esEs28(vyy471, vyy481, app(app(ty_FiniteMap, dcg), dch)) → new_esEs15(vyy471, vyy481, dcg, dch)
new_lt9(vyy3000, vyy400, ty_Double) → new_lt5(vyy3000, vyy400)
new_esEs14(EQ, EQ) → True
new_ltEs18(vyy3002, vyy402, app(app(ty_Either, bah), bba)) → new_ltEs14(vyy3002, vyy402, bah, bba)
new_esEs27(vyy47, vyy48, ty_Float) → new_esEs19(vyy47, vyy48)
new_esEs28(vyy471, vyy481, app(ty_Ratio, ddc)) → new_esEs16(vyy471, vyy481, ddc)
new_ltEs14(Left(vyy3000), Left(vyy400), app(ty_Ratio, bce), bbd) → new_ltEs16(vyy3000, vyy400, bce)
new_esEs25(vyy471, vyy481, app(app(ty_FiniteMap, cab), cac)) → new_esEs15(vyy471, vyy481, cab, cac)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_lt7(vyy3000, vyy400) → new_esEs9(new_compare15(vyy3000, vyy400))
new_ltEs6(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ed), ee), ef)) → new_ltEs7(vyy3000, vyy400, ed, ee, ef)
new_compare14(vyy3000, vyy400, False) → GT
new_esEs25(vyy471, vyy481, ty_@0) → new_esEs12(vyy471, vyy481)
new_compare6(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare7(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs28(vyy471, vyy481, ty_Float) → new_esEs19(vyy471, vyy481)
new_esEs29(vyy470, vyy480, ty_Char) → new_esEs10(vyy470, vyy480)
new_esEs29(vyy470, vyy480, app(app(ty_@2, deh), dfa)) → new_esEs7(vyy470, vyy480, deh, dfa)
new_compare18(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare7(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs8(Right(vyy470), Right(vyy480), cfd, app(app(ty_@2, daf), dag)) → new_esEs7(vyy470, vyy480, daf, dag)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, app(ty_Ratio, bdh)) → new_ltEs16(vyy3000, vyy400, bdh)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Int, bbd) → new_ltEs15(vyy3000, vyy400)
new_lt10(vyy3001, vyy401, ty_Integer) → new_lt16(vyy3001, vyy401)
new_primEqNat0(Zero, Zero) → True
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Ordering, bbd) → new_ltEs5(vyy3000, vyy400)
new_esEs23(vyy470, vyy480, ty_Ordering) → new_esEs14(vyy470, vyy480)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Ordering) → new_ltEs5(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, True) → LT
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, app(app(ty_@2, bdc), bdd)) → new_ltEs8(vyy3000, vyy400, bdc, bdd)
new_ltEs19(vyy3001, vyy401, app(ty_[], ceg)) → new_ltEs4(vyy3001, vyy401, ceg)
new_lt9(vyy3000, vyy400, app(app(ty_Either, bc), bd)) → new_lt17(vyy3000, vyy400, bc, bd)
new_esEs8(Right(vyy470), Right(vyy480), cfd, ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs29(vyy470, vyy480, app(ty_[], ddf)) → new_esEs13(vyy470, vyy480, ddf)
new_esEs24(vyy472, vyy482, ty_Char) → new_esEs10(vyy472, vyy482)
new_esEs17(False, False) → True
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_compare12(vyy3000, vyy400, False, ea) → GT
new_sr(vyy3000, vyy400) → new_primMulInt(vyy3000, vyy400)
new_esEs24(vyy472, vyy482, ty_Bool) → new_esEs17(vyy472, vyy482)
new_esEs8(Right(vyy470), Right(vyy480), cfd, app(ty_Maybe, chh)) → new_esEs5(vyy470, vyy480, chh)
new_compare7(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_esEs8(Left(vyy470), Left(vyy480), ty_Float, cfe) → new_esEs19(vyy470, vyy480)
new_esEs24(vyy472, vyy482, app(app(ty_@2, bhc), bhd)) → new_esEs7(vyy472, vyy482, bhc, bhd)
new_esEs14(LT, GT) → False
new_esEs14(GT, LT) → False
new_esEs18(Double(vyy470, vyy471), Double(vyy480, vyy481)) → new_esEs20(new_sr(vyy470, vyy480), new_sr(vyy471, vyy481))
new_lt20(vyy3000, vyy400, app(ty_Maybe, ccg)) → new_lt11(vyy3000, vyy400, ccg)
new_primPlusNat0(Succ(vyy1030), vyy40000) → Succ(Succ(new_primPlusNat1(vyy1030, vyy40000)))
new_compare4([], [], de) → EQ
new_esEs27(vyy47, vyy48, ty_Char) → new_esEs10(vyy47, vyy48)
new_lt10(vyy3001, vyy401, ty_Double) → new_lt5(vyy3001, vyy401)
new_esEs5(Just(vyy470), Just(vyy480), app(app(ty_Either, cg), da)) → new_esEs8(vyy470, vyy480, cg, da)
new_esEs26(vyy470, vyy480, app(app(app(ty_@3, cbb), cbc), cbd)) → new_esEs6(vyy470, vyy480, cbb, cbc, cbd)
new_ltEs5(LT, LT) → True
new_esEs8(Right(vyy470), Right(vyy480), cfd, ty_Float) → new_esEs19(vyy470, vyy480)
new_lt20(vyy3000, vyy400, app(app(ty_Either, cdf), cdg)) → new_lt17(vyy3000, vyy400, cdf, cdg)
new_compare211(vyy3000, vyy400, False, bc, bd) → new_compare10(vyy3000, vyy400, new_ltEs14(vyy3000, vyy400, bc, bd), bc, bd)
new_foldFM_LE20(vyy340, vyy341, vyy73, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb) → new_foldFM_LE10(new_eltsFM_LE0(vyy340, vyy341, vyy73, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs14(vyy3440, Right(vyy40), ba, bb), h, ba, bb)
new_esEs8(Left(vyy470), Left(vyy480), ty_Int, cfe) → new_esEs20(vyy470, vyy480)
new_esEs21(vyy471, vyy481, ty_Int) → new_esEs20(vyy471, vyy481)
new_primEqInt(Neg(Succ(vyy4700)), Neg(Succ(vyy4800))) → new_primEqNat0(vyy4700, vyy4800)
new_ltEs8(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cce, ccf) → new_pePe(new_lt20(vyy3000, vyy400, cce), vyy3000, vyy400, new_ltEs19(vyy3001, vyy401, ccf), cce)
new_compare25(vyy3000, vyy400, True) → EQ
new_compare23(vyy3000, vyy400, False, ea) → new_compare12(vyy3000, vyy400, new_ltEs6(vyy3000, vyy400, ea), ea)
new_compare26(vyy3000, vyy400, False, df, dg, dh) → new_compare13(vyy3000, vyy400, new_ltEs7(vyy3000, vyy400, df, dg, dh), df, dg, dh)
new_foldFM_LE10(vyy65, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba, bb) → new_foldFM_LE3(vyy340, vyy341, new_foldFM_LE0(vyy65, vyy40, vyy343, h, ba, bb), vyy40, h, ba, bb)
new_esEs9(GT) → False
new_esEs26(vyy470, vyy480, app(ty_[], cba)) → new_esEs13(vyy470, vyy480, cba)
new_esEs13(:(vyy470, vyy471), :(vyy480, vyy481), bea) → new_asAs(new_esEs23(vyy470, vyy480, bea), new_esEs13(vyy471, vyy481, bea))
new_compare25(vyy3000, vyy400, False) → new_compare110(vyy3000, vyy400, new_ltEs10(vyy3000, vyy400))
new_primPlusNat1(Succ(vyy10300), Zero) → Succ(vyy10300)
new_primPlusNat1(Zero, Succ(vyy400000)) → Succ(vyy400000)
new_compare31(vyy3000, vyy400, ty_Ordering) → new_compare19(vyy3000, vyy400)
new_esEs9(EQ) → False
new_ltEs14(Right(vyy3000), Left(vyy400), bcf, bbd) → False
new_esEs8(Left(vyy470), Right(vyy480), cfd, cfe) → False
new_esEs8(Right(vyy470), Left(vyy480), cfd, cfe) → False
new_esEs8(Right(vyy470), Right(vyy480), cfd, app(app(ty_Either, dac), dad)) → new_esEs8(vyy470, vyy480, dac, dad)
new_lt9(vyy3000, vyy400, app(app(ty_@2, be), bf)) → new_lt12(vyy3000, vyy400, be, bf)
new_lt10(vyy3001, vyy401, app(ty_Ratio, hh)) → new_lt19(vyy3001, vyy401, hh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy472, vyy482, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs6(vyy472, vyy482, bgb, bgc, bgd)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Int) → new_ltEs15(vyy3000, vyy400)
new_esEs5(Just(vyy470), Just(vyy480), app(ty_[], bh)) → new_esEs13(vyy470, vyy480, bh)
new_lt9(vyy3000, vyy400, ty_Bool) → new_lt14(vyy3000, vyy400)
new_esEs21(vyy471, vyy481, ty_Integer) → new_esEs11(vyy471, vyy481)
new_lt13(vyy3000, vyy400) → new_esEs9(new_compare29(vyy3000, vyy400))
new_primEqInt(Neg(Zero), Neg(Succ(vyy4800))) → False
new_primEqInt(Neg(Succ(vyy4700)), Neg(Zero)) → False
new_ltEs19(vyy3001, vyy401, ty_Char) → new_ltEs12(vyy3001, vyy401)
new_lt9(vyy3000, vyy400, ty_Char) → new_lt7(vyy3000, vyy400)
new_esEs19(Float(vyy470, vyy471), Float(vyy480, vyy481)) → new_esEs20(new_sr(vyy470, vyy480), new_sr(vyy471, vyy481))
new_lt10(vyy3001, vyy401, ty_Char) → new_lt7(vyy3001, vyy401)
new_esEs27(vyy47, vyy48, app(app(ty_Either, cfd), cfe)) → new_esEs8(vyy47, vyy48, cfd, cfe)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt8(vyy3000, vyy400)
new_lt9(vyy3000, vyy400, ty_Integer) → new_lt16(vyy3000, vyy400)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), fg, fh) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, fg, fh), vyy4733, fg, fh)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs9(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs11(vyy3000, vyy400)
new_esEs24(vyy472, vyy482, ty_Int) → new_esEs20(vyy472, vyy482)
new_esEs28(vyy471, vyy481, app(app(ty_@2, ddd), dde)) → new_esEs7(vyy471, vyy481, ddd, dde)
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, cch), cda), cdb)) → new_lt6(vyy3000, vyy400, cch, cda, cdb)
new_ltEs18(vyy3002, vyy402, app(ty_Ratio, bbb)) → new_ltEs16(vyy3002, vyy402, bbb)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs5(EQ, EQ) → True
new_sizeFM(EmptyFM, fg, fh) → Pos(Zero)
new_ltEs18(vyy3002, vyy402, ty_Integer) → new_ltEs13(vyy3002, vyy402)
new_esEs29(vyy470, vyy480, ty_Ordering) → new_esEs14(vyy470, vyy480)
new_esEs22(vyy470, vyy480, ty_Int) → new_esEs20(vyy470, vyy480)
new_primEqInt(Pos(Succ(vyy4700)), Pos(Succ(vyy4800))) → new_primEqNat0(vyy4700, vyy4800)
new_ltEs19(vyy3001, vyy401, app(app(app(ty_@3, ceb), cec), ced)) → new_ltEs7(vyy3001, vyy401, ceb, cec, ced)
new_compare10(vyy3000, vyy400, False, bc, bd) → GT
new_esEs24(vyy472, vyy482, app(app(ty_Either, bgh), bha)) → new_esEs8(vyy472, vyy482, bgh, bha)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_@0) → new_ltEs9(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, app(ty_Maybe, caa)) → new_esEs5(vyy471, vyy481, caa)
new_esEs24(vyy472, vyy482, app(ty_Ratio, bhb)) → new_esEs16(vyy472, vyy482, bhb)
new_esEs29(vyy470, vyy480, app(ty_Maybe, deb)) → new_esEs5(vyy470, vyy480, deb)
new_esEs8(Left(vyy470), Left(vyy480), app(app(app(ty_@3, cga), cgb), cgc), cfe) → new_esEs6(vyy470, vyy480, cga, cgb, cgc)
new_esEs5(Just(vyy470), Just(vyy480), ty_Char) → new_esEs10(vyy470, vyy480)
new_esEs25(vyy471, vyy481, ty_Char) → new_esEs10(vyy471, vyy481)
new_primEqNat0(Succ(vyy4700), Succ(vyy4800)) → new_primEqNat0(vyy4700, vyy4800)
new_esEs27(vyy47, vyy48, ty_@0) → new_esEs12(vyy47, vyy48)
new_esEs23(vyy470, vyy480, ty_Integer) → new_esEs11(vyy470, vyy480)
new_foldFM_LE0(vyy65, vyy40, EmptyFM, h, ba, bb) → vyy65
new_esEs26(vyy470, vyy480, ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs26(vyy470, vyy480, ty_@0) → new_esEs12(vyy470, vyy480)
new_esEs8(Left(vyy470), Left(vyy480), app(ty_Maybe, cgd), cfe) → new_esEs5(vyy470, vyy480, cgd)
new_esEs29(vyy470, vyy480, ty_@0) → new_esEs12(vyy470, vyy480)
new_primCompAux00(vyy88, LT) → LT
new_esEs15(vyy47, vyy48, fg, fh) → new_asAs(new_esEs20(new_sizeFM(vyy47, fg, fh), new_sizeFM(vyy48, fg, fh)), new_esEs13(new_fmToList(vyy47, fg, fh), new_fmToList(vyy48, fg, fh), app(app(ty_@2, fg), fh)))
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_lt15(vyy3000, vyy400, ge) → new_esEs9(new_compare4(vyy3000, vyy400, ge))
new_lt10(vyy3001, vyy401, app(app(app(ty_@3, gh), ha), hb)) → new_lt6(vyy3001, vyy401, gh, ha, hb)
new_esEs8(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, cge), cgf), cfe) → new_esEs15(vyy470, vyy480, cge, cgf)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs12(vyy3000, vyy400)
new_ltEs17(vyy300, vyy40) → new_not(new_compare6(vyy300, vyy40))
new_ltEs18(vyy3002, vyy402, ty_Double) → new_ltEs11(vyy3002, vyy402)
new_lt10(vyy3001, vyy401, app(app(ty_Either, hf), hg)) → new_lt17(vyy3001, vyy401, hf, hg)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4800))) → False
new_primEqInt(Pos(Succ(vyy4700)), Pos(Zero)) → False
new_ltEs19(vyy3001, vyy401, app(ty_Maybe, cea)) → new_ltEs6(vyy3001, vyy401, cea)
new_compare28(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_ltEs6(Just(vyy3000), Nothing, eb) → False
new_esEs8(Left(vyy470), Left(vyy480), ty_Double, cfe) → new_esEs18(vyy470, vyy480)
new_ltEs5(GT, LT) → False
new_ltEs19(vyy3001, vyy401, ty_Float) → new_ltEs17(vyy3001, vyy401)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_esEs29(vyy470, vyy480, ty_Double) → new_esEs18(vyy470, vyy480)
new_ltEs14(Left(vyy3000), Left(vyy400), app(ty_[], bcb), bbd) → new_ltEs4(vyy3000, vyy400, bcb)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_lt10(vyy3001, vyy401, ty_@0) → new_lt13(vyy3001, vyy401)
new_esEs24(vyy472, vyy482, ty_Double) → new_esEs18(vyy472, vyy482)
new_compare11(vyy3000, vyy400, True, be, bf) → LT
new_esEs7(@2(vyy470, vyy471), @2(vyy480, vyy481), cff, cfg) → new_asAs(new_esEs29(vyy470, vyy480, cff), new_esEs28(vyy471, vyy481, cfg))
new_ltEs6(Just(vyy3000), Just(vyy400), app(ty_[], fa)) → new_ltEs4(vyy3000, vyy400, fa)
new_sr0(Integer(vyy30000), Integer(vyy4010)) → Integer(new_primMulInt(vyy30000, vyy4010))
new_primPlusNat1(Succ(vyy10300), Succ(vyy400000)) → Succ(Succ(new_primPlusNat1(vyy10300, vyy400000)))
new_compare12(vyy3000, vyy400, True, ea) → LT
new_primEqInt(Neg(Succ(vyy4700)), Pos(vyy480)) → False
new_primEqInt(Pos(Succ(vyy4700)), Neg(vyy480)) → False
new_foldFM_LE3(vyy340, vyy341, vyy72, vyy40, h, ba, bb) → new_eltsFM_LE0(vyy340, vyy341, vyy72, h, ba, bb)
new_esEs27(vyy47, vyy48, app(ty_Maybe, bg)) → new_esEs5(vyy47, vyy48, bg)
new_foldFM2(EmptyFM, fg, fh) → []
new_esEs26(vyy470, vyy480, ty_Double) → new_esEs18(vyy470, vyy480)
new_ltEs6(Just(vyy3000), Just(vyy400), app(ty_Maybe, ec)) → new_ltEs6(vyy3000, vyy400, ec)
new_esEs26(vyy470, vyy480, app(ty_Ratio, ccb)) → new_esEs16(vyy470, vyy480, ccb)
new_esEs24(vyy472, vyy482, app(ty_[], bga)) → new_esEs13(vyy472, vyy482, bga)
new_ltEs6(Just(vyy3000), Just(vyy400), app(app(ty_Either, fb), fc)) → new_ltEs14(vyy3000, vyy400, fb, fc)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Float, bbd) → new_ltEs17(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4800))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4800))) → False
new_esEs10(Char(vyy470), Char(vyy480)) → new_primEqNat0(vyy470, vyy480)
new_esEs23(vyy470, vyy480, ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs29(vyy470, vyy480, ty_Integer) → new_esEs11(vyy470, vyy480)
new_compare31(vyy3000, vyy400, ty_Double) → new_compare8(vyy3000, vyy400)
new_primCompAux00(vyy88, EQ) → vyy88
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_esEs28(vyy471, vyy481, ty_Char) → new_esEs10(vyy471, vyy481)
new_compare24(vyy3000, vyy400, True) → EQ
new_esEs27(vyy47, vyy48, app(app(ty_@2, cff), cfg)) → new_esEs7(vyy47, vyy48, cff, cfg)
new_pePe(False, vyy47, vyy48, vyy66, cfc) → new_asAs(new_esEs27(vyy47, vyy48, cfc), vyy66)
new_esEs23(vyy470, vyy480, ty_Char) → new_esEs10(vyy470, vyy480)
new_esEs24(vyy472, vyy482, ty_Ordering) → new_esEs14(vyy472, vyy482)
new_compare24(vyy3000, vyy400, False) → new_compare14(vyy3000, vyy400, new_ltEs5(vyy3000, vyy400))
new_compare18(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare28(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_lt18(vyy3000, vyy400) → new_esEs9(new_compare7(vyy3000, vyy400))
new_lt10(vyy3001, vyy401, app(ty_Maybe, gg)) → new_lt11(vyy3001, vyy401, gg)
new_esEs29(vyy470, vyy480, app(app(ty_FiniteMap, dec), ded)) → new_esEs15(vyy470, vyy480, dec, ded)
new_esEs27(vyy47, vyy48, app(ty_Ratio, ga)) → new_esEs16(vyy47, vyy48, ga)
new_esEs5(Just(vyy470), Just(vyy480), ty_Ordering) → new_esEs14(vyy470, vyy480)
new_ltEs18(vyy3002, vyy402, ty_Float) → new_ltEs17(vyy3002, vyy402)
new_compare9(vyy3000, vyy400, df, dg, dh) → new_compare26(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, df, dg, dh), df, dg, dh)
new_lt20(vyy3000, vyy400, ty_Double) → new_lt5(vyy3000, vyy400)
new_ltEs6(Just(vyy3000), Just(vyy400), app(app(ty_@2, eg), eh)) → new_ltEs8(vyy3000, vyy400, eg, eh)
new_lt9(vyy3000, vyy400, app(ty_[], ge)) → new_lt15(vyy3000, vyy400, ge)
new_esEs24(vyy472, vyy482, ty_Float) → new_esEs19(vyy472, vyy482)
new_compare16(vyy3000, vyy400) → new_compare25(vyy3000, vyy400, new_esEs17(vyy3000, vyy400))
new_primPlusNat0(Zero, vyy40000) → Succ(vyy40000)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_compare210(vyy3000, vyy400, True, be, bf) → EQ
new_esEs5(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, ce), cf)) → new_esEs15(vyy470, vyy480, ce, cf)
new_lt9(vyy3000, vyy400, ty_Int) → new_lt18(vyy3000, vyy400)
new_lt4(vyy3000, vyy400) → new_esEs9(new_compare6(vyy3000, vyy400))
new_esEs25(vyy471, vyy481, app(ty_Ratio, caf)) → new_esEs16(vyy471, vyy481, caf)
new_ltEs14(Left(vyy3000), Left(vyy400), app(ty_Maybe, bbc), bbd) → new_ltEs6(vyy3000, vyy400, bbc)
new_not0 → True
new_esEs22(vyy470, vyy480, ty_Integer) → new_esEs11(vyy470, vyy480)
new_esEs24(vyy472, vyy482, app(ty_Maybe, bge)) → new_esEs5(vyy472, vyy482, bge)
new_esEs8(Left(vyy470), Left(vyy480), app(ty_[], cfh), cfe) → new_esEs13(vyy470, vyy480, cfh)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Float) → new_ltEs17(vyy3000, vyy400)
new_compare11(vyy3000, vyy400, False, be, bf) → GT
new_esEs25(vyy471, vyy481, ty_Integer) → new_esEs11(vyy471, vyy481)
new_compare30(vyy3000, vyy400, be, bf) → new_compare210(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, be, bf), be, bf)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_compare210(vyy3000, vyy400, False, be, bf) → new_compare11(vyy3000, vyy400, new_ltEs8(vyy3000, vyy400, be, bf), be, bf)
new_esEs20(vyy47, vyy48) → new_primEqInt(vyy47, vyy48)
new_esEs5(Just(vyy470), Just(vyy480), ty_Bool) → new_esEs17(vyy470, vyy480)
new_primMulInt(Pos(vyy30000), Pos(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_esEs8(Left(vyy470), Left(vyy480), app(ty_Ratio, cha), cfe) → new_esEs16(vyy470, vyy480, cha)
new_esEs24(vyy472, vyy482, ty_Integer) → new_esEs11(vyy472, vyy482)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Char, bbd) → new_ltEs12(vyy3000, vyy400)
new_esEs8(Right(vyy470), Right(vyy480), cfd, app(app(app(ty_@3, che), chf), chg)) → new_esEs6(vyy470, vyy480, che, chf, chg)
new_ltEs5(LT, GT) → True
new_esEs24(vyy472, vyy482, app(app(ty_FiniteMap, bgf), bgg)) → new_esEs15(vyy472, vyy482, bgf, bgg)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Bool) → new_ltEs10(vyy3000, vyy400)
new_ltEs12(vyy300, vyy40) → new_not(new_compare15(vyy300, vyy40))
new_esEs5(Just(vyy470), Just(vyy480), ty_Double) → new_esEs18(vyy470, vyy480)
new_primMulInt(Neg(vyy30000), Neg(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_compare110(vyy3000, vyy400, True) → LT
new_esEs27(vyy47, vyy48, ty_Ordering) → new_esEs14(vyy47, vyy48)
new_primEqNat0(Zero, Succ(vyy4800)) → False
new_primEqNat0(Succ(vyy4700), Zero) → False
new_lt20(vyy3000, vyy400, app(app(ty_@2, cdc), cdd)) → new_lt12(vyy3000, vyy400, cdc, cdd)
new_esEs26(vyy470, vyy480, app(app(ty_@2, ccc), ccd)) → new_esEs7(vyy470, vyy480, ccc, ccd)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs13(vyy3000, vyy400)
new_compare110(vyy3000, vyy400, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vyy471, vyy481, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs6(vyy471, vyy481, dcc, dcd, dce)
new_esEs5(Just(vyy470), Just(vyy480), ty_Float) → new_esEs19(vyy470, vyy480)
new_esEs28(vyy471, vyy481, app(app(ty_Either, dda), ddb)) → new_esEs8(vyy471, vyy481, dda, ddb)
new_lt9(vyy3000, vyy400, ty_Float) → new_lt4(vyy3000, vyy400)
new_esEs27(vyy47, vyy48, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs6(vyy47, vyy48, bff, bfg, bfh)
new_compare31(vyy3000, vyy400, app(app(ty_@2, dbd), dbe)) → new_compare30(vyy3000, vyy400, dbd, dbe)
new_compare4(:(vyy3000, vyy3001), [], de) → GT
new_lt10(vyy3001, vyy401, ty_Bool) → new_lt14(vyy3001, vyy401)
new_lt10(vyy3001, vyy401, app(ty_[], he)) → new_lt15(vyy3001, vyy401, he)
new_sizeFM(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), fg, fh) → vyy472
new_esEs26(vyy470, vyy480, ty_Ordering) → new_esEs14(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, ty_Bool) → new_ltEs10(vyy3001, vyy401)
new_ltEs14(Left(vyy3000), Left(vyy400), app(app(ty_@2, bbh), bca), bbd) → new_ltEs8(vyy3000, vyy400, bbh, bca)
new_pePe(True, vyy47, vyy48, vyy66, cfc) → True
new_esEs26(vyy470, vyy480, app(ty_Maybe, cbe)) → new_esEs5(vyy470, vyy480, cbe)
new_compare31(vyy3000, vyy400, ty_Char) → new_compare15(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, app(ty_Maybe, dah)) → new_compare17(vyy3000, vyy400, dah)
new_esEs23(vyy470, vyy480, ty_Double) → new_esEs18(vyy470, vyy480)
new_foldFM_LE10(vyy65, vyy40, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba, bb) → new_foldFM_LE0(vyy65, vyy40, vyy343, h, ba, bb)
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), fg, fh) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, fg, fh), vyy473, fg, fh)
new_esEs14(LT, EQ) → False
new_esEs14(EQ, LT) → False
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_esEs23(vyy470, vyy480, ty_Bool) → new_esEs17(vyy470, vyy480)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_ltEs16(vyy300, vyy40, ff) → new_not(new_compare18(vyy300, vyy40, ff))
new_lt20(vyy3000, vyy400, ty_Char) → new_lt7(vyy3000, vyy400)
new_esEs5(Just(vyy470), Just(vyy480), app(app(app(ty_@3, ca), cb), cc)) → new_esEs6(vyy470, vyy480, ca, cb, cc)
new_compare4([], :(vyy400, vyy401), de) → LT
new_compare23(vyy3000, vyy400, True, ea) → EQ
new_lt10(vyy3001, vyy401, ty_Float) → new_lt4(vyy3001, vyy401)
new_lt20(vyy3000, vyy400, app(ty_Ratio, cdh)) → new_lt19(vyy3000, vyy400, cdh)
new_esEs8(Left(vyy470), Left(vyy480), app(app(ty_Either, cgg), cgh), cfe) → new_esEs8(vyy470, vyy480, cgg, cgh)
new_esEs8(Right(vyy470), Right(vyy480), cfd, ty_Char) → new_esEs10(vyy470, vyy480)
new_esEs23(vyy470, vyy480, app(ty_Ratio, bfc)) → new_esEs16(vyy470, vyy480, bfc)
new_esEs16(:%(vyy470, vyy471), :%(vyy480, vyy481), ga) → new_asAs(new_esEs22(vyy470, vyy480, ga), new_esEs21(vyy471, vyy481, ga))
new_eltsFM_LE0(vyy340, vyy341, vyy72, h, ba, bb) → :(vyy341, vyy72)
new_esEs8(Left(vyy470), Left(vyy480), ty_Ordering, cfe) → new_esEs14(vyy470, vyy480)
new_esEs27(vyy47, vyy48, ty_Double) → new_esEs18(vyy47, vyy48)
new_lt11(vyy3000, vyy400, ea) → new_esEs9(new_compare17(vyy3000, vyy400, ea))
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs5(vyy3000, vyy400)
new_esEs14(EQ, GT) → False
new_esEs14(GT, EQ) → False
new_lt20(vyy3000, vyy400, app(ty_[], cde)) → new_lt15(vyy3000, vyy400, cde)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare31(vyy3000, vyy400, app(ty_[], dbf)) → new_compare4(vyy3000, vyy400, dbf)
new_esEs29(vyy470, vyy480, ty_Bool) → new_esEs17(vyy470, vyy480)
new_ltEs14(Left(vyy3000), Right(vyy400), bcf, bbd) → True
new_lt20(vyy3000, vyy400, ty_@0) → new_lt13(vyy3000, vyy400)
new_ltEs10(True, False) → False
new_asAs(False, vyy79) → False
new_esEs8(Right(vyy470), Right(vyy480), cfd, ty_Ordering) → new_esEs14(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, app(app(ty_Either, ceh), cfa)) → new_ltEs14(vyy3001, vyy401, ceh, cfa)
new_primMulInt(Pos(vyy30000), Neg(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulInt(Neg(vyy30000), Pos(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_esEs8(Left(vyy470), Left(vyy480), ty_Bool, cfe) → new_esEs17(vyy470, vyy480)
new_esEs13([], :(vyy480, vyy481), bea) → False
new_esEs13(:(vyy470, vyy471), [], bea) → False
new_primMulNat0(Zero, Succ(vyy40000)) → Zero
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, app(app(app(ty_@3, bch), bda), bdb)) → new_ltEs7(vyy3000, vyy400, bch, bda, bdb)
new_ltEs18(vyy3002, vyy402, ty_Ordering) → new_ltEs5(vyy3002, vyy402)
new_esEs23(vyy470, vyy480, app(app(app(ty_@3, bec), bed), bee)) → new_esEs6(vyy470, vyy480, bec, bed, bee)
new_ltEs5(LT, EQ) → True
new_compare4(:(vyy3000, vyy3001), :(vyy400, vyy401), de) → new_primCompAux0(vyy3000, vyy400, new_compare4(vyy3001, vyy401, de), de)
new_esEs28(vyy471, vyy481, ty_Int) → new_esEs20(vyy471, vyy481)
new_ltEs18(vyy3002, vyy402, app(ty_[], bag)) → new_ltEs4(vyy3002, vyy402, bag)
new_esEs23(vyy470, vyy480, app(app(ty_@2, bfd), bfe)) → new_esEs7(vyy470, vyy480, bfd, bfe)
new_esEs28(vyy471, vyy481, ty_Double) → new_esEs18(vyy471, vyy481)
new_not(EQ) → new_not0
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, app(app(ty_Either, bdf), bdg)) → new_ltEs14(vyy3000, vyy400, bdf, bdg)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Double) → new_ltEs11(vyy3000, vyy400)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs17(vyy3000, vyy400)
new_esEs8(Right(vyy470), Right(vyy480), cfd, app(ty_[], chd)) → new_esEs13(vyy470, vyy480, chd)
new_esEs29(vyy470, vyy480, app(ty_Ratio, deg)) → new_esEs16(vyy470, vyy480, deg)
new_esEs23(vyy470, vyy480, app(ty_Maybe, bef)) → new_esEs5(vyy470, vyy480, bef)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Integer, bbd) → new_ltEs13(vyy3000, vyy400)
new_ltEs18(vyy3002, vyy402, ty_Char) → new_ltEs12(vyy3002, vyy402)
new_esEs25(vyy471, vyy481, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs6(vyy471, vyy481, bhf, bhg, bhh)
new_ltEs18(vyy3002, vyy402, app(app(ty_@2, bae), baf)) → new_ltEs8(vyy3002, vyy402, bae, baf)
new_esEs25(vyy471, vyy481, ty_Int) → new_esEs20(vyy471, vyy481)
new_lt14(vyy3000, vyy400) → new_esEs9(new_compare16(vyy3000, vyy400))
new_esEs14(GT, GT) → True
new_lt9(vyy3000, vyy400, app(ty_Maybe, ea)) → new_lt11(vyy3000, vyy400, ea)
new_esEs25(vyy471, vyy481, app(ty_[], bhe)) → new_esEs13(vyy471, vyy481, bhe)
new_esEs23(vyy470, vyy480, ty_@0) → new_esEs12(vyy470, vyy480)
new_esEs5(Nothing, Just(vyy480), bg) → False
new_esEs5(Just(vyy470), Nothing, bg) → False
new_compare211(vyy3000, vyy400, True, bc, bd) → EQ
new_ltEs6(Nothing, Nothing, eb) → True
new_lt16(vyy3000, vyy400) → new_esEs9(new_compare28(vyy3000, vyy400))
new_ltEs14(Left(vyy3000), Left(vyy400), app(app(ty_Either, bcc), bcd), bbd) → new_ltEs14(vyy3000, vyy400, bcc, bcd)
new_esEs29(vyy470, vyy480, ty_Float) → new_esEs19(vyy470, vyy480)
new_esEs25(vyy471, vyy481, ty_Float) → new_esEs19(vyy471, vyy481)
new_compare19(vyy3000, vyy400) → new_compare24(vyy3000, vyy400, new_esEs14(vyy3000, vyy400))
new_lt12(vyy3000, vyy400, be, bf) → new_esEs9(new_compare30(vyy3000, vyy400, be, bf))
new_esEs28(vyy471, vyy481, ty_Bool) → new_esEs17(vyy471, vyy481)
new_ltEs13(vyy300, vyy40) → new_not(new_compare28(vyy300, vyy40))
new_compare31(vyy3000, vyy400, ty_Float) → new_compare6(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, ty_Int) → new_ltEs15(vyy3001, vyy401)
new_esEs29(vyy470, vyy480, ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs26(vyy470, vyy480, ty_Bool) → new_esEs17(vyy470, vyy480)
new_esEs27(vyy47, vyy48, ty_Int) → new_esEs20(vyy47, vyy48)
new_not(LT) → new_not0
new_lt6(vyy3000, vyy400, df, dg, dh) → new_esEs9(new_compare9(vyy3000, vyy400, df, dg, dh))
new_esEs25(vyy471, vyy481, ty_Double) → new_esEs18(vyy471, vyy481)
new_esEs5(Nothing, Nothing, bg) → True
new_esEs26(vyy470, vyy480, ty_Char) → new_esEs10(vyy470, vyy480)
new_ltEs18(vyy3002, vyy402, app(ty_Maybe, baa)) → new_ltEs6(vyy3002, vyy402, baa)
new_esEs28(vyy471, vyy481, app(ty_Maybe, dcf)) → new_esEs5(vyy471, vyy481, dcf)
new_esEs26(vyy470, vyy480, ty_Float) → new_esEs19(vyy470, vyy480)
new_esEs5(Just(vyy470), Just(vyy480), ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs29(vyy470, vyy480, app(app(app(ty_@3, ddg), ddh), dea)) → new_esEs6(vyy470, vyy480, ddg, ddh, dea)
new_esEs8(Left(vyy470), Left(vyy480), ty_@0, cfe) → new_esEs12(vyy470, vyy480)
new_esEs28(vyy471, vyy481, ty_Ordering) → new_esEs14(vyy471, vyy481)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Double, bbd) → new_ltEs11(vyy3000, vyy400)
new_foldFM_LE0(vyy65, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba, bb) → new_foldFM_LE10(vyy65, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs14(vyy3430, Right(vyy40), ba, bb), h, ba, bb)
new_ltEs14(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bbe), bbf), bbg), bbd) → new_ltEs7(vyy3000, vyy400, bbe, bbf, bbg)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs15(vyy3000, vyy400)
new_compare26(vyy3000, vyy400, True, df, dg, dh) → EQ
new_compare31(vyy3000, vyy400, ty_Bool) → new_compare16(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, ty_Ordering) → new_ltEs5(vyy3001, vyy401)
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs10(True, True) → True
new_ltEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), gb, gc, gd) → new_pePe(new_lt9(vyy3000, vyy400, gb), vyy3000, vyy400, new_pePe(new_lt10(vyy3001, vyy401, gc), vyy3001, vyy401, new_ltEs18(vyy3002, vyy402, gd), gc), gb)
new_esEs8(Right(vyy470), Right(vyy480), cfd, ty_Double) → new_esEs18(vyy470, vyy480)
new_asAs(True, vyy79) → vyy79
new_ltEs9(vyy300, vyy40) → new_not(new_compare29(vyy300, vyy40))
new_esEs5(Just(vyy470), Just(vyy480), ty_Integer) → new_esEs11(vyy470, vyy480)
new_primMulNat0(Succ(vyy300000), Succ(vyy40000)) → new_primPlusNat0(new_primMulNat0(vyy300000, Succ(vyy40000)), vyy40000)
new_esEs27(vyy47, vyy48, app(ty_[], bea)) → new_esEs13(vyy47, vyy48, bea)
new_ltEs5(GT, GT) → True
new_esEs27(vyy47, vyy48, ty_Integer) → new_esEs11(vyy47, vyy48)
new_compare31(vyy3000, vyy400, ty_Int) → new_compare7(vyy3000, vyy400)
new_esEs5(Just(vyy470), Just(vyy480), app(app(ty_@2, dc), dd)) → new_esEs7(vyy470, vyy480, dc, dd)
new_esEs8(Right(vyy470), Right(vyy480), cfd, ty_Integer) → new_esEs11(vyy470, vyy480)
new_esEs14(LT, LT) → True
new_ltEs19(vyy3001, vyy401, ty_@0) → new_ltEs9(vyy3001, vyy401)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Bool, bbd) → new_ltEs10(vyy3000, vyy400)
new_primCompAux0(vyy3000, vyy400, vyy84, de) → new_primCompAux00(vyy84, new_compare31(vyy3000, vyy400, de))
new_fmToList(vyy47, fg, fh) → new_foldFM2(vyy47, fg, fh)
new_ltEs19(vyy3001, vyy401, ty_Integer) → new_ltEs13(vyy3001, vyy401)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Integer) → new_ltEs13(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, ty_Ordering) → new_esEs14(vyy471, vyy481)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, app(ty_Maybe, bcg)) → new_ltEs6(vyy3000, vyy400, bcg)
new_ltEs6(Just(vyy3000), Just(vyy400), app(ty_Ratio, fd)) → new_ltEs16(vyy3000, vyy400, fd)
new_ltEs4(vyy300, vyy40, de) → new_not(new_compare4(vyy300, vyy40, de))
new_compare13(vyy3000, vyy400, True, df, dg, dh) → LT
new_lt5(vyy3000, vyy400) → new_esEs9(new_compare8(vyy3000, vyy400))
new_primCompAux00(vyy88, GT) → GT
new_lt9(vyy3000, vyy400, ty_@0) → new_lt13(vyy3000, vyy400)
new_esEs8(Left(vyy470), Left(vyy480), app(app(ty_@2, chb), chc), cfe) → new_esEs7(vyy470, vyy480, chb, chc)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs5(GT, EQ) → False
new_esEs8(Left(vyy470), Left(vyy480), ty_Char, cfe) → new_esEs10(vyy470, vyy480)
new_lt10(vyy3001, vyy401, ty_Int) → new_lt18(vyy3001, vyy401)
new_lt19(vyy3000, vyy400, gf) → new_esEs9(new_compare18(vyy3000, vyy400, gf))
new_ltEs18(vyy3002, vyy402, ty_Int) → new_ltEs15(vyy3002, vyy402)
new_esEs24(vyy472, vyy482, ty_@0) → new_esEs12(vyy472, vyy482)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs25(vyy471, vyy481, app(app(ty_Either, cad), cae)) → new_esEs8(vyy471, vyy481, cad, cae)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs23(vyy470, vyy480, app(ty_[], beb)) → new_esEs13(vyy470, vyy480, beb)
The set Q consists of the following terms:
new_ltEs18(x0, x1, ty_Char)
new_primCompAux00(x0, GT)
new_lt20(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Integer)
new_esEs8(Right(x0), Right(x1), x2, ty_Int)
new_compare13(x0, x1, False, x2, x3, x4)
new_compare25(x0, x1, False)
new_esEs15(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs6(Just(x0), Just(x1), ty_Integer)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs14(GT, EQ)
new_esEs14(EQ, GT)
new_ltEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt16(x0, x1)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs18(Double(x0, x1), Double(x2, x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Int)
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_esEs5(Just(x0), Nothing, x1)
new_compare110(x0, x1, False)
new_esEs26(x0, x1, ty_@0)
new_compare9(x0, x1, x2, x3, x4)
new_compare7(x0, x1)
new_primCompAux0(x0, x1, x2, x3)
new_esEs9(EQ)
new_ltEs6(Nothing, Just(x0), x1)
new_esEs5(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Integer)
new_ltEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare12(x0, x1, False, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs19(Float(x0, x1), Float(x2, x3))
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Just(x0), Just(x1), ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Char)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, EmptyFM, True, x6, x7, x8)
new_ltEs6(Nothing, Nothing, x0)
new_esEs29(x0, x1, ty_Float)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1, ty_Ordering)
new_esEs17(False, False)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt9(x0, x1, ty_Bool)
new_primMulNat0(Zero, Succ(x0))
new_lt12(x0, x1, x2, x3)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs25(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs14(LT, GT)
new_esEs14(GT, LT)
new_esEs8(Right(x0), Right(x1), x2, ty_@0)
new_compare26(x0, x1, True, x2, x3, x4)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_foldFM_LE0(x0, x1, EmptyFM, x2, x3, x4)
new_compare24(x0, x1, False)
new_esEs10(Char(x0), Char(x1))
new_foldFM_LE3(x0, x1, x2, x3, x4, x5, x6)
new_lt20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_eltsFM_LE0(x0, x1, x2, x3, x4, x5)
new_ltEs6(Just(x0), Just(x1), ty_@0)
new_compare29(@0, @0)
new_esEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs5(EQ, LT)
new_compare30(x0, x1, x2, x3)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_lt20(x0, x1, ty_@0)
new_ltEs5(LT, EQ)
new_esEs29(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs27(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Int)
new_lt9(x0, x1, app(ty_[], x2))
new_ltEs6(Just(x0), Just(x1), ty_Double)
new_esEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs25(x0, x1, ty_Float)
new_esEs12(@0, @0)
new_compare27(x0, x1, x2, x3)
new_compare6(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Zero)
new_esEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs27(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, ty_Integer)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_lt9(x0, x1, ty_Int)
new_lt18(x0, x1)
new_compare10(x0, x1, True, x2, x3)
new_lt10(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Left(x0), Right(x1), x2, x3)
new_esEs8(Right(x0), Left(x1), x2, x3)
new_lt20(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs18(x0, x1, ty_Integer)
new_compare23(x0, x1, True, x2)
new_ltEs18(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_primPlusNat0(Zero, x0)
new_ltEs6(Just(x0), Nothing, x1)
new_compare4(:(x0, x1), :(x2, x3), x4)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_foldFM2(EmptyFM, x0, x1)
new_esEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs29(x0, x1, ty_Bool)
new_compare10(x0, x1, False, x2, x3)
new_esEs8(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_compare31(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Integer)
new_esEs8(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_not0
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs12(x0, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, x2)
new_esEs14(LT, LT)
new_esEs24(x0, x1, ty_Int)
new_ltEs10(False, False)
new_pePe(False, x0, x1, x2, x3)
new_esEs9(GT)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_lt11(x0, x1, x2)
new_lt10(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_esEs25(x0, x1, ty_Double)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_asAs(True, x0)
new_ltEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare31(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt9(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True)
new_fmToList(x0, x1, x2)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), ty_Char, x2)
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_foldFM_LE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_lt9(x0, x1, ty_@0)
new_compare24(x0, x1, True)
new_lt5(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(x0, x1, ty_Float)
new_asAs(False, x0)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Succ(x0))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_compare211(x0, x1, True, x2, x3)
new_esEs28(x0, x1, ty_Int)
new_not(GT)
new_primMulInt(Pos(x0), Pos(x1))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs5(Nothing, Just(x0), x1)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare13(x0, x1, True, x2, x3, x4)
new_lt17(x0, x1, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare11(x0, x1, True, x2, x3)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare31(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Integer)
new_lt7(x0, x1)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs8(Right(x0), Right(x1), x2, ty_Integer)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_@0)
new_esEs20(x0, x1)
new_ltEs18(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, x2)
new_ltEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare25(x0, x1, True)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs11(Integer(x0), Integer(x1))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13([], :(x0, x1), x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_ltEs4(x0, x1, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, ty_Float)
new_lt9(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs23(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare210(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs11(x0, x1)
new_esEs28(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_primPlusNat1(Zero, Succ(x0))
new_compare28(Integer(x0), Integer(x1))
new_compare4([], :(x0, x1), x2)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs8(Left(x0), Left(x1), ty_Float, x2)
new_ltEs6(Just(x0), Just(x1), ty_Ordering)
new_ltEs6(Just(x0), Just(x1), ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_lt8(x0, x1)
new_esEs9(LT)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs22(x0, x1, ty_Int)
new_esEs5(Nothing, Nothing, x0)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs27(x0, x1, ty_@0)
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Char)
new_compare15(Char(x0), Char(x1))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, ty_Double)
new_compare4([], [], x0)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare4(:(x0, x1), [], x2)
new_esEs8(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(True, True)
new_lt13(x0, x1)
new_esEs29(x0, x1, ty_Char)
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_@0)
new_compare23(x0, x1, False, x2)
new_esEs26(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Integer)
new_ltEs16(x0, x1, x2)
new_esEs26(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Float)
new_ltEs5(GT, GT)
new_ltEs19(x0, x1, ty_@0)
new_esEs8(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_@0)
new_pePe(True, x0, x1, x2, x3)
new_lt10(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_compare210(x0, x1, True, x2, x3)
new_compare12(x0, x1, True, x2)
new_sizeFM(EmptyFM, x0, x1)
new_lt9(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_not(EQ)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_compare31(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs19(x0, x1, ty_Char)
new_esEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, ty_Bool)
new_ltEs6(Just(x0), Just(x1), ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs13(:(x0, x1), [], x2)
new_esEs24(x0, x1, ty_@0)
new_esEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs5(EQ, EQ)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, EQ)
new_compare11(x0, x1, False, x2, x3)
new_esEs14(EQ, LT)
new_esEs14(LT, EQ)
new_esEs27(x0, x1, ty_Float)
new_ltEs6(Just(x0), Just(x1), app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_sr(x0, x1)
new_ltEs15(x0, x1)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(GT, GT)
new_ltEs6(Just(x0), Just(x1), ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM_LE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_lt9(x0, x1, app(ty_Ratio, x2))
new_compare19(x0, x1)
new_ltEs10(False, True)
new_ltEs10(True, False)
new_esEs26(x0, x1, ty_Integer)
new_compare14(x0, x1, False)
new_esEs28(x0, x1, ty_Bool)
new_compare31(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs17(False, True)
new_esEs17(True, False)
new_compare16(x0, x1)
new_esEs14(EQ, EQ)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt15(x0, x1, x2)
new_esEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt6(x0, x1, x2, x3, x4)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_compare18(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt9(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs9(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs29(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Float)
new_compare8(Double(x0, x1), Double(x2, x3))
new_ltEs17(x0, x1)
new_compare31(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), True, x11, x12, x13)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Char)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt20(x0, x1, ty_Char)
new_compare14(x0, x1, True)
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs25(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_esEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs13([], [], x0)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_not(LT)
new_compare211(x0, x1, False, x2, x3)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_ltEs5(LT, LT)
new_esEs28(x0, x1, ty_Float)
new_esEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM_LE2(vyy340, vyy341, vyy73, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb) → new_foldFM_LE1(new_eltsFM_LE0(vyy340, vyy341, vyy73, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs14(vyy3440, Right(vyy40), ba, bb), h, ba, bb)
The graph contains the following edges 4 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 >= 9, 11 >= 10, 12 >= 11
- new_foldFM_LE(vyy65, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba, bb) → new_foldFM_LE1(vyy65, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs14(vyy3430, Right(vyy40), ba, bb), h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 4 >= 9, 5 >= 10, 6 >= 11
- new_foldFM_LE1(vyy65, vyy40, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba, bb) → new_foldFM_LE1(vyy65, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs14(vyy3430, Right(vyy40), ba, bb), h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 > 3, 6 > 4, 6 > 5, 6 > 6, 6 > 7, 9 >= 9, 10 >= 10, 11 >= 11
- new_foldFM_LE1(vyy65, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba, bb) → new_foldFM_LE2(vyy340, vyy341, new_foldFM_LE0(vyy65, vyy40, vyy343, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb)
The graph contains the following edges 3 >= 1, 4 >= 2, 2 >= 4, 7 > 5, 7 > 6, 7 > 7, 7 > 8, 7 > 9, 9 >= 10, 10 >= 11, 11 >= 12
- new_foldFM_LE1(vyy65, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba, bb) → new_foldFM_LE(vyy65, vyy40, vyy343, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
- new_foldFM_LE1(vyy65, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba, bb) → new_foldFM_LE(vyy65, vyy40, vyy343, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE4(vyy71, vyy13, Branch(vyy1830, vyy1831, vyy1832, vyy1833, vyy1834), h, ba, bb) → new_foldFM_LE21(vyy71, vyy13, vyy1830, vyy1831, vyy1832, vyy1833, vyy1834, h, ba, bb)
new_foldFM_LE11(vyy71, vyy13, vyy180, vyy181, vyy182, vyy183, Branch(vyy1840, vyy1841, vyy1842, vyy1843, vyy1844), True, h, ba, bb) → new_foldFM_LE4(vyy71, vyy13, vyy183, h, ba, bb)
new_foldFM_LE11(vyy71, vyy13, vyy180, vyy181, vyy182, Branch(vyy1830, vyy1831, vyy1832, vyy1833, vyy1834), vyy184, False, h, ba, bb) → new_foldFM_LE21(vyy71, vyy13, vyy1830, vyy1831, vyy1832, vyy1833, vyy1834, h, ba, bb)
new_foldFM_LE11(vyy71, vyy13, vyy180, vyy181, vyy182, vyy183, EmptyFM, True, h, ba, bb) → new_foldFM_LE4(vyy71, vyy13, vyy183, h, ba, bb)
new_foldFM_LE21(vyy82, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, h, ba, bb) → new_foldFM_LE11(vyy82, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, new_ltEs14(vyy1840, Left(vyy13), ba, bb), h, ba, bb)
new_foldFM_LE11(vyy71, vyy13, vyy180, vyy181, vyy182, vyy183, Branch(vyy1840, vyy1841, vyy1842, vyy1843, vyy1844), True, h, ba, bb) → new_foldFM_LE21(new_eltsFM_LE0(vyy180, vyy181, new_foldFM_LE5(vyy71, vyy13, vyy183, h, ba, bb), h, ba, bb), vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, h, ba, bb)
The TRS R consists of the following rules:
new_esEs28(vyy471, vyy481, app(ty_[], dce)) → new_esEs13(vyy471, vyy481, dce)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_@0, bbd) → new_ltEs9(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, app(ty_Ratio, cfe)) → new_ltEs16(vyy3001, vyy401, cfe)
new_ltEs18(vyy3002, vyy402, ty_@0) → new_ltEs9(vyy3002, vyy402)
new_ltEs10(False, True) → True
new_compare17(vyy3000, vyy400, ea) → new_compare23(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, ea), ea)
new_esEs13([], [], bed) → True
new_compare10(vyy3000, vyy400, True, bc, bd) → LT
new_esEs11(Integer(vyy470), Integer(vyy480)) → new_primEqInt(vyy470, vyy480)
new_ltEs5(EQ, GT) → True
new_esEs28(vyy471, vyy481, ty_Integer) → new_esEs11(vyy471, vyy481)
new_esEs26(vyy470, vyy480, ty_Integer) → new_esEs11(vyy470, vyy480)
new_ltEs6(Nothing, Just(vyy400), eb) → True
new_ltEs19(vyy3001, vyy401, ty_Double) → new_ltEs11(vyy3001, vyy401)
new_foldFM_LE30(vyy80, vyy13, h, ba, bb) → vyy80
new_compare31(vyy3000, vyy400, app(app(app(ty_@3, dbd), dbe), dbf)) → new_compare9(vyy3000, vyy400, dbd, dbe, dbf)
new_esEs27(vyy47, vyy48, ty_Bool) → new_esEs17(vyy47, vyy48)
new_esEs23(vyy470, vyy480, ty_Float) → new_esEs19(vyy470, vyy480)
new_primMulNat0(Zero, Zero) → Zero
new_lt10(vyy3001, vyy401, app(app(ty_@2, hc), hd)) → new_lt12(vyy3001, vyy401, hc, hd)
new_lt20(vyy3000, vyy400, ty_Float) → new_lt4(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, app(ty_Ratio, dcd)) → new_compare18(vyy3000, vyy400, dcd)
new_compare13(vyy3000, vyy400, False, df, dg, dh) → GT
new_esEs5(Just(vyy470), Just(vyy480), app(ty_Ratio, db)) → new_esEs16(vyy470, vyy480, db)
new_esEs5(Just(vyy470), Just(vyy480), ty_@0) → new_esEs12(vyy470, vyy480)
new_esEs8(Right(vyy470), Right(vyy480), cfg, app(app(ty_FiniteMap, dad), dae)) → new_esEs15(vyy470, vyy480, dad, dae)
new_esEs9(LT) → True
new_lt20(vyy3000, vyy400, ty_Int) → new_lt18(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, ty_Bool) → new_esEs17(vyy471, vyy481)
new_esEs27(vyy47, vyy48, app(app(ty_FiniteMap, fg), fh)) → new_esEs15(vyy47, vyy48, fg, fh)
new_lt9(vyy3000, vyy400, app(ty_Ratio, gf)) → new_lt19(vyy3000, vyy400, gf)
new_not(GT) → False
new_esEs8(Right(vyy470), Right(vyy480), cfg, ty_@0) → new_esEs12(vyy470, vyy480)
new_lt9(vyy3000, vyy400, ty_Ordering) → new_lt8(vyy3000, vyy400)
new_esEs29(vyy470, vyy480, app(app(ty_Either, deh), dfa)) → new_esEs8(vyy470, vyy480, deh, dfa)
new_esEs8(Left(vyy470), Left(vyy480), ty_Integer, cfh) → new_esEs11(vyy470, vyy480)
new_esEs17(True, True) → True
new_lt17(vyy3000, vyy400, bc, bd) → new_esEs9(new_compare27(vyy3000, vyy400, bc, bd))
new_lt10(vyy3001, vyy401, ty_Ordering) → new_lt8(vyy3001, vyy401)
new_esEs8(Right(vyy470), Right(vyy480), cfg, app(ty_Ratio, dah)) → new_esEs16(vyy470, vyy480, dah)
new_ltEs15(vyy300, vyy40) → new_not(new_compare7(vyy300, vyy40))
new_esEs23(vyy470, vyy480, app(app(ty_FiniteMap, bfb), bfc)) → new_esEs15(vyy470, vyy480, bfb, bfc)
new_compare27(vyy3000, vyy400, bc, bd) → new_compare211(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, bc, bd), bc, bd)
new_ltEs11(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_esEs8(Right(vyy470), Right(vyy480), cfg, ty_Bool) → new_esEs17(vyy470, vyy480)
new_lt9(vyy3000, vyy400, app(app(app(ty_@3, df), dg), dh)) → new_lt6(vyy3000, vyy400, df, dg, dh)
new_esEs5(Just(vyy470), Just(vyy480), app(ty_Maybe, cd)) → new_esEs5(vyy470, vyy480, cd)
new_ltEs5(EQ, LT) → False
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt16(vyy3000, vyy400)
new_esEs12(@0, @0) → True
new_esEs28(vyy471, vyy481, ty_@0) → new_esEs12(vyy471, vyy481)
new_ltEs18(vyy3002, vyy402, ty_Bool) → new_ltEs10(vyy3002, vyy402)
new_ltEs10(False, False) → True
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, fg, fh) → :(@2(vyy470, vyy471), vyy102)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs10(vyy3000, vyy400)
new_lt8(vyy3000, vyy400) → new_esEs9(new_compare19(vyy3000, vyy400))
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt14(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, ty_Integer) → new_compare28(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, app(app(ty_@2, ceh), cfa)) → new_ltEs8(vyy3001, vyy401, ceh, cfa)
new_esEs25(vyy471, vyy481, app(app(ty_@2, cbb), cbc)) → new_esEs7(vyy471, vyy481, cbb, cbc)
new_ltEs18(vyy3002, vyy402, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs7(vyy3002, vyy402, bab, bac, bad)
new_compare31(vyy3000, vyy400, app(app(ty_Either, dcb), dcc)) → new_compare27(vyy3000, vyy400, dcb, dcc)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Char) → new_ltEs12(vyy3000, vyy400)
new_compare29(@0, @0) → EQ
new_compare31(vyy3000, vyy400, ty_@0) → new_compare29(vyy3000, vyy400)
new_esEs26(vyy470, vyy480, app(app(ty_FiniteMap, cca), ccb)) → new_esEs15(vyy470, vyy480, cca, ccb)
new_esEs23(vyy470, vyy480, app(app(ty_Either, bfd), bfe)) → new_esEs8(vyy470, vyy480, bfd, bfe)
new_compare15(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs26(vyy470, vyy480, app(app(ty_Either, ccc), ccd)) → new_esEs8(vyy470, vyy480, ccc, ccd)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, app(ty_[], bde)) → new_ltEs4(vyy3000, vyy400, bde)
new_compare8(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare7(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs6(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), bga, bgb, bgc) → new_asAs(new_esEs26(vyy470, vyy480, bga), new_asAs(new_esEs25(vyy471, vyy481, bgb), new_esEs24(vyy472, vyy482, bgc)))
new_esEs28(vyy471, vyy481, app(app(ty_FiniteMap, ddb), ddc)) → new_esEs15(vyy471, vyy481, ddb, ddc)
new_lt9(vyy3000, vyy400, ty_Double) → new_lt5(vyy3000, vyy400)
new_esEs14(EQ, EQ) → True
new_ltEs18(vyy3002, vyy402, app(app(ty_Either, bah), bba)) → new_ltEs14(vyy3002, vyy402, bah, bba)
new_esEs27(vyy47, vyy48, ty_Float) → new_esEs19(vyy47, vyy48)
new_esEs28(vyy471, vyy481, app(ty_Ratio, ddf)) → new_esEs16(vyy471, vyy481, ddf)
new_ltEs14(Left(vyy3000), Left(vyy400), app(ty_Ratio, bce), bbd) → new_ltEs16(vyy3000, vyy400, bce)
new_esEs25(vyy471, vyy481, app(app(ty_FiniteMap, cae), caf)) → new_esEs15(vyy471, vyy481, cae, caf)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_lt7(vyy3000, vyy400) → new_esEs9(new_compare15(vyy3000, vyy400))
new_ltEs6(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ed), ee), ef)) → new_ltEs7(vyy3000, vyy400, ed, ee, ef)
new_compare14(vyy3000, vyy400, False) → GT
new_esEs25(vyy471, vyy481, ty_@0) → new_esEs12(vyy471, vyy481)
new_compare6(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare7(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs28(vyy471, vyy481, ty_Float) → new_esEs19(vyy471, vyy481)
new_esEs29(vyy470, vyy480, ty_Char) → new_esEs10(vyy470, vyy480)
new_esEs29(vyy470, vyy480, app(app(ty_@2, dfc), dfd)) → new_esEs7(vyy470, vyy480, dfc, dfd)
new_compare18(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare7(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs8(Right(vyy470), Right(vyy480), cfg, app(app(ty_@2, dba), dbb)) → new_esEs7(vyy470, vyy480, dba, dbb)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, app(ty_Ratio, bdh)) → new_ltEs16(vyy3000, vyy400, bdh)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Int, bbd) → new_ltEs15(vyy3000, vyy400)
new_lt10(vyy3001, vyy401, ty_Integer) → new_lt16(vyy3001, vyy401)
new_primEqNat0(Zero, Zero) → True
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Ordering, bbd) → new_ltEs5(vyy3000, vyy400)
new_esEs23(vyy470, vyy480, ty_Ordering) → new_esEs14(vyy470, vyy480)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Ordering) → new_ltEs5(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, True) → LT
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, app(app(ty_@2, bdc), bdd)) → new_ltEs8(vyy3000, vyy400, bdc, bdd)
new_ltEs19(vyy3001, vyy401, app(ty_[], cfb)) → new_ltEs4(vyy3001, vyy401, cfb)
new_lt9(vyy3000, vyy400, app(app(ty_Either, bc), bd)) → new_lt17(vyy3000, vyy400, bc, bd)
new_esEs8(Right(vyy470), Right(vyy480), cfg, ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs29(vyy470, vyy480, app(ty_[], dea)) → new_esEs13(vyy470, vyy480, dea)
new_esEs24(vyy472, vyy482, ty_Char) → new_esEs10(vyy472, vyy482)
new_esEs17(False, False) → True
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_compare12(vyy3000, vyy400, False, ea) → GT
new_sr(vyy3000, vyy400) → new_primMulInt(vyy3000, vyy400)
new_esEs24(vyy472, vyy482, ty_Bool) → new_esEs17(vyy472, vyy482)
new_esEs8(Right(vyy470), Right(vyy480), cfg, app(ty_Maybe, dac)) → new_esEs5(vyy470, vyy480, dac)
new_compare7(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_esEs8(Left(vyy470), Left(vyy480), ty_Float, cfh) → new_esEs19(vyy470, vyy480)
new_esEs24(vyy472, vyy482, app(app(ty_@2, bhf), bhg)) → new_esEs7(vyy472, vyy482, bhf, bhg)
new_esEs14(LT, GT) → False
new_esEs14(GT, LT) → False
new_esEs18(Double(vyy470, vyy471), Double(vyy480, vyy481)) → new_esEs20(new_sr(vyy470, vyy480), new_sr(vyy471, vyy481))
new_lt20(vyy3000, vyy400, app(ty_Maybe, cdb)) → new_lt11(vyy3000, vyy400, cdb)
new_primPlusNat0(Succ(vyy1030), vyy40000) → Succ(Succ(new_primPlusNat1(vyy1030, vyy40000)))
new_compare4([], [], de) → EQ
new_esEs27(vyy47, vyy48, ty_Char) → new_esEs10(vyy47, vyy48)
new_lt10(vyy3001, vyy401, ty_Double) → new_lt5(vyy3001, vyy401)
new_esEs5(Just(vyy470), Just(vyy480), app(app(ty_Either, cg), da)) → new_esEs8(vyy470, vyy480, cg, da)
new_esEs26(vyy470, vyy480, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs6(vyy470, vyy480, cbe, cbf, cbg)
new_ltEs5(LT, LT) → True
new_esEs8(Right(vyy470), Right(vyy480), cfg, ty_Float) → new_esEs19(vyy470, vyy480)
new_lt20(vyy3000, vyy400, app(app(ty_Either, cea), ceb)) → new_lt17(vyy3000, vyy400, cea, ceb)
new_compare211(vyy3000, vyy400, False, bc, bd) → new_compare10(vyy3000, vyy400, new_ltEs14(vyy3000, vyy400, bc, bd), bc, bd)
new_esEs8(Left(vyy470), Left(vyy480), ty_Int, cfh) → new_esEs20(vyy470, vyy480)
new_esEs21(vyy471, vyy481, ty_Int) → new_esEs20(vyy471, vyy481)
new_primEqInt(Neg(Succ(vyy4700)), Neg(Succ(vyy4800))) → new_primEqNat0(vyy4700, vyy4800)
new_ltEs8(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cch, cda) → new_pePe(new_lt20(vyy3000, vyy400, cch), vyy3000, vyy400, new_ltEs19(vyy3001, vyy401, cda), cch)
new_compare25(vyy3000, vyy400, True) → EQ
new_compare23(vyy3000, vyy400, False, ea) → new_compare12(vyy3000, vyy400, new_ltEs6(vyy3000, vyy400, ea), ea)
new_compare26(vyy3000, vyy400, False, df, dg, dh) → new_compare13(vyy3000, vyy400, new_ltEs7(vyy3000, vyy400, df, dg, dh), df, dg, dh)
new_esEs9(GT) → False
new_esEs26(vyy470, vyy480, app(ty_[], cbd)) → new_esEs13(vyy470, vyy480, cbd)
new_esEs13(:(vyy470, vyy471), :(vyy480, vyy481), bed) → new_asAs(new_esEs23(vyy470, vyy480, bed), new_esEs13(vyy471, vyy481, bed))
new_compare25(vyy3000, vyy400, False) → new_compare110(vyy3000, vyy400, new_ltEs10(vyy3000, vyy400))
new_primPlusNat1(Succ(vyy10300), Zero) → Succ(vyy10300)
new_primPlusNat1(Zero, Succ(vyy400000)) → Succ(vyy400000)
new_foldFM_LE5(vyy71, vyy13, Branch(vyy1830, vyy1831, vyy1832, vyy1833, vyy1834), h, ba, bb) → new_foldFM_LE22(vyy71, vyy13, vyy1830, vyy1831, vyy1832, vyy1833, vyy1834, h, ba, bb)
new_compare31(vyy3000, vyy400, ty_Ordering) → new_compare19(vyy3000, vyy400)
new_esEs9(EQ) → False
new_ltEs14(Right(vyy3000), Left(vyy400), bcf, bbd) → False
new_esEs8(Left(vyy470), Right(vyy480), cfg, cfh) → False
new_esEs8(Right(vyy470), Left(vyy480), cfg, cfh) → False
new_esEs8(Right(vyy470), Right(vyy480), cfg, app(app(ty_Either, daf), dag)) → new_esEs8(vyy470, vyy480, daf, dag)
new_lt9(vyy3000, vyy400, app(app(ty_@2, be), bf)) → new_lt12(vyy3000, vyy400, be, bf)
new_lt10(vyy3001, vyy401, app(ty_Ratio, hh)) → new_lt19(vyy3001, vyy401, hh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy472, vyy482, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs6(vyy472, vyy482, bge, bgf, bgg)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Int) → new_ltEs15(vyy3000, vyy400)
new_esEs5(Just(vyy470), Just(vyy480), app(ty_[], bh)) → new_esEs13(vyy470, vyy480, bh)
new_lt9(vyy3000, vyy400, ty_Bool) → new_lt14(vyy3000, vyy400)
new_esEs21(vyy471, vyy481, ty_Integer) → new_esEs11(vyy471, vyy481)
new_lt13(vyy3000, vyy400) → new_esEs9(new_compare29(vyy3000, vyy400))
new_primEqInt(Neg(Zero), Neg(Succ(vyy4800))) → False
new_primEqInt(Neg(Succ(vyy4700)), Neg(Zero)) → False
new_ltEs19(vyy3001, vyy401, ty_Char) → new_ltEs12(vyy3001, vyy401)
new_lt9(vyy3000, vyy400, ty_Char) → new_lt7(vyy3000, vyy400)
new_esEs19(Float(vyy470, vyy471), Float(vyy480, vyy481)) → new_esEs20(new_sr(vyy470, vyy480), new_sr(vyy471, vyy481))
new_lt10(vyy3001, vyy401, ty_Char) → new_lt7(vyy3001, vyy401)
new_esEs27(vyy47, vyy48, app(app(ty_Either, cfg), cfh)) → new_esEs8(vyy47, vyy48, cfg, cfh)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt8(vyy3000, vyy400)
new_lt9(vyy3000, vyy400, ty_Integer) → new_lt16(vyy3000, vyy400)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), fg, fh) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, fg, fh), vyy4733, fg, fh)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs9(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs11(vyy3000, vyy400)
new_esEs24(vyy472, vyy482, ty_Int) → new_esEs20(vyy472, vyy482)
new_esEs28(vyy471, vyy481, app(app(ty_@2, ddg), ddh)) → new_esEs7(vyy471, vyy481, ddg, ddh)
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, cdc), cdd), cde)) → new_lt6(vyy3000, vyy400, cdc, cdd, cde)
new_ltEs18(vyy3002, vyy402, app(ty_Ratio, bbb)) → new_ltEs16(vyy3002, vyy402, bbb)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs5(EQ, EQ) → True
new_sizeFM(EmptyFM, fg, fh) → Pos(Zero)
new_ltEs18(vyy3002, vyy402, ty_Integer) → new_ltEs13(vyy3002, vyy402)
new_esEs29(vyy470, vyy480, ty_Ordering) → new_esEs14(vyy470, vyy480)
new_esEs22(vyy470, vyy480, ty_Int) → new_esEs20(vyy470, vyy480)
new_primEqInt(Pos(Succ(vyy4700)), Pos(Succ(vyy4800))) → new_primEqNat0(vyy4700, vyy4800)
new_ltEs19(vyy3001, vyy401, app(app(app(ty_@3, cee), cef), ceg)) → new_ltEs7(vyy3001, vyy401, cee, cef, ceg)
new_compare10(vyy3000, vyy400, False, bc, bd) → GT
new_esEs24(vyy472, vyy482, app(app(ty_Either, bhc), bhd)) → new_esEs8(vyy472, vyy482, bhc, bhd)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_@0) → new_ltEs9(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, app(ty_Maybe, cad)) → new_esEs5(vyy471, vyy481, cad)
new_esEs24(vyy472, vyy482, app(ty_Ratio, bhe)) → new_esEs16(vyy472, vyy482, bhe)
new_esEs29(vyy470, vyy480, app(ty_Maybe, dee)) → new_esEs5(vyy470, vyy480, dee)
new_foldFM_LE5(vyy71, vyy13, EmptyFM, h, ba, bb) → new_foldFM_LE30(vyy71, vyy13, h, ba, bb)
new_esEs8(Left(vyy470), Left(vyy480), app(app(app(ty_@3, cgd), cge), cgf), cfh) → new_esEs6(vyy470, vyy480, cgd, cge, cgf)
new_esEs5(Just(vyy470), Just(vyy480), ty_Char) → new_esEs10(vyy470, vyy480)
new_esEs25(vyy471, vyy481, ty_Char) → new_esEs10(vyy471, vyy481)
new_foldFM_LE12(vyy71, vyy13, vyy180, vyy181, vyy182, vyy183, Branch(vyy1840, vyy1841, vyy1842, vyy1843, vyy1844), True, h, ba, bb) → new_foldFM_LE22(new_eltsFM_LE0(vyy180, vyy181, new_foldFM_LE5(vyy71, vyy13, vyy183, h, ba, bb), h, ba, bb), vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, h, ba, bb)
new_primEqNat0(Succ(vyy4700), Succ(vyy4800)) → new_primEqNat0(vyy4700, vyy4800)
new_esEs27(vyy47, vyy48, ty_@0) → new_esEs12(vyy47, vyy48)
new_esEs23(vyy470, vyy480, ty_Integer) → new_esEs11(vyy470, vyy480)
new_esEs26(vyy470, vyy480, ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs26(vyy470, vyy480, ty_@0) → new_esEs12(vyy470, vyy480)
new_esEs8(Left(vyy470), Left(vyy480), app(ty_Maybe, cgg), cfh) → new_esEs5(vyy470, vyy480, cgg)
new_esEs29(vyy470, vyy480, ty_@0) → new_esEs12(vyy470, vyy480)
new_primCompAux00(vyy88, LT) → LT
new_esEs15(vyy47, vyy48, fg, fh) → new_asAs(new_esEs20(new_sizeFM(vyy47, fg, fh), new_sizeFM(vyy48, fg, fh)), new_esEs13(new_fmToList(vyy47, fg, fh), new_fmToList(vyy48, fg, fh), app(app(ty_@2, fg), fh)))
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_lt15(vyy3000, vyy400, ge) → new_esEs9(new_compare4(vyy3000, vyy400, ge))
new_lt10(vyy3001, vyy401, app(app(app(ty_@3, gh), ha), hb)) → new_lt6(vyy3001, vyy401, gh, ha, hb)
new_esEs8(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, cgh), cha), cfh) → new_esEs15(vyy470, vyy480, cgh, cha)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs12(vyy3000, vyy400)
new_ltEs17(vyy300, vyy40) → new_not(new_compare6(vyy300, vyy40))
new_ltEs18(vyy3002, vyy402, ty_Double) → new_ltEs11(vyy3002, vyy402)
new_lt10(vyy3001, vyy401, app(app(ty_Either, hf), hg)) → new_lt17(vyy3001, vyy401, hf, hg)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4800))) → False
new_primEqInt(Pos(Succ(vyy4700)), Pos(Zero)) → False
new_ltEs19(vyy3001, vyy401, app(ty_Maybe, ced)) → new_ltEs6(vyy3001, vyy401, ced)
new_compare28(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_ltEs6(Just(vyy3000), Nothing, eb) → False
new_esEs8(Left(vyy470), Left(vyy480), ty_Double, cfh) → new_esEs18(vyy470, vyy480)
new_ltEs5(GT, LT) → False
new_ltEs19(vyy3001, vyy401, ty_Float) → new_ltEs17(vyy3001, vyy401)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_esEs29(vyy470, vyy480, ty_Double) → new_esEs18(vyy470, vyy480)
new_ltEs14(Left(vyy3000), Left(vyy400), app(ty_[], bcb), bbd) → new_ltEs4(vyy3000, vyy400, bcb)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_lt10(vyy3001, vyy401, ty_@0) → new_lt13(vyy3001, vyy401)
new_esEs24(vyy472, vyy482, ty_Double) → new_esEs18(vyy472, vyy482)
new_compare11(vyy3000, vyy400, True, be, bf) → LT
new_esEs7(@2(vyy470, vyy471), @2(vyy480, vyy481), cga, cgb) → new_asAs(new_esEs29(vyy470, vyy480, cga), new_esEs28(vyy471, vyy481, cgb))
new_ltEs6(Just(vyy3000), Just(vyy400), app(ty_[], fa)) → new_ltEs4(vyy3000, vyy400, fa)
new_sr0(Integer(vyy30000), Integer(vyy4010)) → Integer(new_primMulInt(vyy30000, vyy4010))
new_primPlusNat1(Succ(vyy10300), Succ(vyy400000)) → Succ(Succ(new_primPlusNat1(vyy10300, vyy400000)))
new_compare12(vyy3000, vyy400, True, ea) → LT
new_primEqInt(Neg(Succ(vyy4700)), Pos(vyy480)) → False
new_primEqInt(Pos(Succ(vyy4700)), Neg(vyy480)) → False
new_esEs27(vyy47, vyy48, app(ty_Maybe, bg)) → new_esEs5(vyy47, vyy48, bg)
new_foldFM2(EmptyFM, fg, fh) → []
new_esEs26(vyy470, vyy480, ty_Double) → new_esEs18(vyy470, vyy480)
new_ltEs6(Just(vyy3000), Just(vyy400), app(ty_Maybe, ec)) → new_ltEs6(vyy3000, vyy400, ec)
new_esEs26(vyy470, vyy480, app(ty_Ratio, cce)) → new_esEs16(vyy470, vyy480, cce)
new_esEs24(vyy472, vyy482, app(ty_[], bgd)) → new_esEs13(vyy472, vyy482, bgd)
new_ltEs6(Just(vyy3000), Just(vyy400), app(app(ty_Either, fb), fc)) → new_ltEs14(vyy3000, vyy400, fb, fc)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Float, bbd) → new_ltEs17(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4800))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4800))) → False
new_esEs10(Char(vyy470), Char(vyy480)) → new_primEqNat0(vyy470, vyy480)
new_esEs23(vyy470, vyy480, ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs29(vyy470, vyy480, ty_Integer) → new_esEs11(vyy470, vyy480)
new_compare31(vyy3000, vyy400, ty_Double) → new_compare8(vyy3000, vyy400)
new_primCompAux00(vyy88, EQ) → vyy88
new_foldFM_LE12(vyy71, vyy13, vyy180, vyy181, vyy182, vyy183, vyy184, False, h, ba, bb) → new_foldFM_LE5(vyy71, vyy13, vyy183, h, ba, bb)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_esEs28(vyy471, vyy481, ty_Char) → new_esEs10(vyy471, vyy481)
new_compare24(vyy3000, vyy400, True) → EQ
new_esEs27(vyy47, vyy48, app(app(ty_@2, cga), cgb)) → new_esEs7(vyy47, vyy48, cga, cgb)
new_pePe(False, vyy47, vyy48, vyy66, cff) → new_asAs(new_esEs27(vyy47, vyy48, cff), vyy66)
new_esEs23(vyy470, vyy480, ty_Char) → new_esEs10(vyy470, vyy480)
new_esEs24(vyy472, vyy482, ty_Ordering) → new_esEs14(vyy472, vyy482)
new_compare24(vyy3000, vyy400, False) → new_compare14(vyy3000, vyy400, new_ltEs5(vyy3000, vyy400))
new_compare18(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare28(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_lt18(vyy3000, vyy400) → new_esEs9(new_compare7(vyy3000, vyy400))
new_lt10(vyy3001, vyy401, app(ty_Maybe, gg)) → new_lt11(vyy3001, vyy401, gg)
new_esEs29(vyy470, vyy480, app(app(ty_FiniteMap, def), deg)) → new_esEs15(vyy470, vyy480, def, deg)
new_esEs27(vyy47, vyy48, app(ty_Ratio, ga)) → new_esEs16(vyy47, vyy48, ga)
new_esEs5(Just(vyy470), Just(vyy480), ty_Ordering) → new_esEs14(vyy470, vyy480)
new_ltEs18(vyy3002, vyy402, ty_Float) → new_ltEs17(vyy3002, vyy402)
new_compare9(vyy3000, vyy400, df, dg, dh) → new_compare26(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, df, dg, dh), df, dg, dh)
new_lt20(vyy3000, vyy400, ty_Double) → new_lt5(vyy3000, vyy400)
new_ltEs6(Just(vyy3000), Just(vyy400), app(app(ty_@2, eg), eh)) → new_ltEs8(vyy3000, vyy400, eg, eh)
new_lt9(vyy3000, vyy400, app(ty_[], ge)) → new_lt15(vyy3000, vyy400, ge)
new_esEs24(vyy472, vyy482, ty_Float) → new_esEs19(vyy472, vyy482)
new_compare16(vyy3000, vyy400) → new_compare25(vyy3000, vyy400, new_esEs17(vyy3000, vyy400))
new_primPlusNat0(Zero, vyy40000) → Succ(vyy40000)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_compare210(vyy3000, vyy400, True, be, bf) → EQ
new_esEs5(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, ce), cf)) → new_esEs15(vyy470, vyy480, ce, cf)
new_lt9(vyy3000, vyy400, ty_Int) → new_lt18(vyy3000, vyy400)
new_lt4(vyy3000, vyy400) → new_esEs9(new_compare6(vyy3000, vyy400))
new_esEs25(vyy471, vyy481, app(ty_Ratio, cba)) → new_esEs16(vyy471, vyy481, cba)
new_ltEs14(Left(vyy3000), Left(vyy400), app(ty_Maybe, bbc), bbd) → new_ltEs6(vyy3000, vyy400, bbc)
new_not0 → True
new_esEs22(vyy470, vyy480, ty_Integer) → new_esEs11(vyy470, vyy480)
new_esEs24(vyy472, vyy482, app(ty_Maybe, bgh)) → new_esEs5(vyy472, vyy482, bgh)
new_esEs8(Left(vyy470), Left(vyy480), app(ty_[], cgc), cfh) → new_esEs13(vyy470, vyy480, cgc)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Float) → new_ltEs17(vyy3000, vyy400)
new_compare11(vyy3000, vyy400, False, be, bf) → GT
new_esEs25(vyy471, vyy481, ty_Integer) → new_esEs11(vyy471, vyy481)
new_compare30(vyy3000, vyy400, be, bf) → new_compare210(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, be, bf), be, bf)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_compare210(vyy3000, vyy400, False, be, bf) → new_compare11(vyy3000, vyy400, new_ltEs8(vyy3000, vyy400, be, bf), be, bf)
new_esEs20(vyy47, vyy48) → new_primEqInt(vyy47, vyy48)
new_esEs5(Just(vyy470), Just(vyy480), ty_Bool) → new_esEs17(vyy470, vyy480)
new_primMulInt(Pos(vyy30000), Pos(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_esEs8(Left(vyy470), Left(vyy480), app(ty_Ratio, chd), cfh) → new_esEs16(vyy470, vyy480, chd)
new_esEs24(vyy472, vyy482, ty_Integer) → new_esEs11(vyy472, vyy482)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Char, bbd) → new_ltEs12(vyy3000, vyy400)
new_esEs8(Right(vyy470), Right(vyy480), cfg, app(app(app(ty_@3, chh), daa), dab)) → new_esEs6(vyy470, vyy480, chh, daa, dab)
new_ltEs5(LT, GT) → True
new_esEs24(vyy472, vyy482, app(app(ty_FiniteMap, bha), bhb)) → new_esEs15(vyy472, vyy482, bha, bhb)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Bool) → new_ltEs10(vyy3000, vyy400)
new_ltEs12(vyy300, vyy40) → new_not(new_compare15(vyy300, vyy40))
new_esEs5(Just(vyy470), Just(vyy480), ty_Double) → new_esEs18(vyy470, vyy480)
new_primMulInt(Neg(vyy30000), Neg(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_compare110(vyy3000, vyy400, True) → LT
new_esEs27(vyy47, vyy48, ty_Ordering) → new_esEs14(vyy47, vyy48)
new_primEqNat0(Zero, Succ(vyy4800)) → False
new_primEqNat0(Succ(vyy4700), Zero) → False
new_foldFM_LE22(vyy82, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, h, ba, bb) → new_foldFM_LE12(vyy82, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, new_ltEs14(vyy1840, Left(vyy13), ba, bb), h, ba, bb)
new_lt20(vyy3000, vyy400, app(app(ty_@2, cdf), cdg)) → new_lt12(vyy3000, vyy400, cdf, cdg)
new_esEs26(vyy470, vyy480, app(app(ty_@2, ccf), ccg)) → new_esEs7(vyy470, vyy480, ccf, ccg)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs13(vyy3000, vyy400)
new_compare110(vyy3000, vyy400, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vyy471, vyy481, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs6(vyy471, vyy481, dcf, dcg, dch)
new_esEs5(Just(vyy470), Just(vyy480), ty_Float) → new_esEs19(vyy470, vyy480)
new_esEs28(vyy471, vyy481, app(app(ty_Either, ddd), dde)) → new_esEs8(vyy471, vyy481, ddd, dde)
new_lt9(vyy3000, vyy400, ty_Float) → new_lt4(vyy3000, vyy400)
new_esEs27(vyy47, vyy48, app(app(app(ty_@3, bga), bgb), bgc)) → new_esEs6(vyy47, vyy48, bga, bgb, bgc)
new_compare31(vyy3000, vyy400, app(app(ty_@2, dbg), dbh)) → new_compare30(vyy3000, vyy400, dbg, dbh)
new_compare4(:(vyy3000, vyy3001), [], de) → GT
new_lt10(vyy3001, vyy401, ty_Bool) → new_lt14(vyy3001, vyy401)
new_lt10(vyy3001, vyy401, app(ty_[], he)) → new_lt15(vyy3001, vyy401, he)
new_sizeFM(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), fg, fh) → vyy472
new_esEs26(vyy470, vyy480, ty_Ordering) → new_esEs14(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, ty_Bool) → new_ltEs10(vyy3001, vyy401)
new_ltEs14(Left(vyy3000), Left(vyy400), app(app(ty_@2, bbh), bca), bbd) → new_ltEs8(vyy3000, vyy400, bbh, bca)
new_pePe(True, vyy47, vyy48, vyy66, cff) → True
new_esEs26(vyy470, vyy480, app(ty_Maybe, cbh)) → new_esEs5(vyy470, vyy480, cbh)
new_compare31(vyy3000, vyy400, ty_Char) → new_compare15(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, app(ty_Maybe, dbc)) → new_compare17(vyy3000, vyy400, dbc)
new_esEs23(vyy470, vyy480, ty_Double) → new_esEs18(vyy470, vyy480)
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), fg, fh) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, fg, fh), vyy473, fg, fh)
new_esEs14(LT, EQ) → False
new_esEs14(EQ, LT) → False
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_esEs23(vyy470, vyy480, ty_Bool) → new_esEs17(vyy470, vyy480)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_ltEs16(vyy300, vyy40, ff) → new_not(new_compare18(vyy300, vyy40, ff))
new_lt20(vyy3000, vyy400, ty_Char) → new_lt7(vyy3000, vyy400)
new_esEs5(Just(vyy470), Just(vyy480), app(app(app(ty_@3, ca), cb), cc)) → new_esEs6(vyy470, vyy480, ca, cb, cc)
new_compare4([], :(vyy400, vyy401), de) → LT
new_compare23(vyy3000, vyy400, True, ea) → EQ
new_lt10(vyy3001, vyy401, ty_Float) → new_lt4(vyy3001, vyy401)
new_lt20(vyy3000, vyy400, app(ty_Ratio, cec)) → new_lt19(vyy3000, vyy400, cec)
new_esEs8(Left(vyy470), Left(vyy480), app(app(ty_Either, chb), chc), cfh) → new_esEs8(vyy470, vyy480, chb, chc)
new_esEs8(Right(vyy470), Right(vyy480), cfg, ty_Char) → new_esEs10(vyy470, vyy480)
new_esEs23(vyy470, vyy480, app(ty_Ratio, bff)) → new_esEs16(vyy470, vyy480, bff)
new_esEs16(:%(vyy470, vyy471), :%(vyy480, vyy481), ga) → new_asAs(new_esEs22(vyy470, vyy480, ga), new_esEs21(vyy471, vyy481, ga))
new_eltsFM_LE0(vyy340, vyy341, vyy72, bea, beb, bec) → :(vyy341, vyy72)
new_esEs8(Left(vyy470), Left(vyy480), ty_Ordering, cfh) → new_esEs14(vyy470, vyy480)
new_esEs27(vyy47, vyy48, ty_Double) → new_esEs18(vyy47, vyy48)
new_lt11(vyy3000, vyy400, ea) → new_esEs9(new_compare17(vyy3000, vyy400, ea))
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs5(vyy3000, vyy400)
new_esEs14(EQ, GT) → False
new_esEs14(GT, EQ) → False
new_lt20(vyy3000, vyy400, app(ty_[], cdh)) → new_lt15(vyy3000, vyy400, cdh)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare31(vyy3000, vyy400, app(ty_[], dca)) → new_compare4(vyy3000, vyy400, dca)
new_esEs29(vyy470, vyy480, ty_Bool) → new_esEs17(vyy470, vyy480)
new_ltEs14(Left(vyy3000), Right(vyy400), bcf, bbd) → True
new_lt20(vyy3000, vyy400, ty_@0) → new_lt13(vyy3000, vyy400)
new_ltEs10(True, False) → False
new_asAs(False, vyy79) → False
new_esEs8(Right(vyy470), Right(vyy480), cfg, ty_Ordering) → new_esEs14(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, app(app(ty_Either, cfc), cfd)) → new_ltEs14(vyy3001, vyy401, cfc, cfd)
new_primMulInt(Pos(vyy30000), Neg(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulInt(Neg(vyy30000), Pos(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_esEs8(Left(vyy470), Left(vyy480), ty_Bool, cfh) → new_esEs17(vyy470, vyy480)
new_esEs13([], :(vyy480, vyy481), bed) → False
new_esEs13(:(vyy470, vyy471), [], bed) → False
new_primMulNat0(Zero, Succ(vyy40000)) → Zero
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, app(app(app(ty_@3, bch), bda), bdb)) → new_ltEs7(vyy3000, vyy400, bch, bda, bdb)
new_ltEs18(vyy3002, vyy402, ty_Ordering) → new_ltEs5(vyy3002, vyy402)
new_esEs23(vyy470, vyy480, app(app(app(ty_@3, bef), beg), beh)) → new_esEs6(vyy470, vyy480, bef, beg, beh)
new_ltEs5(LT, EQ) → True
new_compare4(:(vyy3000, vyy3001), :(vyy400, vyy401), de) → new_primCompAux0(vyy3000, vyy400, new_compare4(vyy3001, vyy401, de), de)
new_esEs28(vyy471, vyy481, ty_Int) → new_esEs20(vyy471, vyy481)
new_ltEs18(vyy3002, vyy402, app(ty_[], bag)) → new_ltEs4(vyy3002, vyy402, bag)
new_esEs23(vyy470, vyy480, app(app(ty_@2, bfg), bfh)) → new_esEs7(vyy470, vyy480, bfg, bfh)
new_esEs28(vyy471, vyy481, ty_Double) → new_esEs18(vyy471, vyy481)
new_not(EQ) → new_not0
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, app(app(ty_Either, bdf), bdg)) → new_ltEs14(vyy3000, vyy400, bdf, bdg)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Double) → new_ltEs11(vyy3000, vyy400)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs17(vyy3000, vyy400)
new_esEs8(Right(vyy470), Right(vyy480), cfg, app(ty_[], chg)) → new_esEs13(vyy470, vyy480, chg)
new_esEs29(vyy470, vyy480, app(ty_Ratio, dfb)) → new_esEs16(vyy470, vyy480, dfb)
new_esEs23(vyy470, vyy480, app(ty_Maybe, bfa)) → new_esEs5(vyy470, vyy480, bfa)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Integer, bbd) → new_ltEs13(vyy3000, vyy400)
new_ltEs18(vyy3002, vyy402, ty_Char) → new_ltEs12(vyy3002, vyy402)
new_esEs25(vyy471, vyy481, app(app(app(ty_@3, caa), cab), cac)) → new_esEs6(vyy471, vyy481, caa, cab, cac)
new_ltEs18(vyy3002, vyy402, app(app(ty_@2, bae), baf)) → new_ltEs8(vyy3002, vyy402, bae, baf)
new_esEs25(vyy471, vyy481, ty_Int) → new_esEs20(vyy471, vyy481)
new_lt14(vyy3000, vyy400) → new_esEs9(new_compare16(vyy3000, vyy400))
new_esEs14(GT, GT) → True
new_lt9(vyy3000, vyy400, app(ty_Maybe, ea)) → new_lt11(vyy3000, vyy400, ea)
new_esEs25(vyy471, vyy481, app(ty_[], bhh)) → new_esEs13(vyy471, vyy481, bhh)
new_esEs23(vyy470, vyy480, ty_@0) → new_esEs12(vyy470, vyy480)
new_esEs5(Nothing, Just(vyy480), bg) → False
new_esEs5(Just(vyy470), Nothing, bg) → False
new_compare211(vyy3000, vyy400, True, bc, bd) → EQ
new_ltEs6(Nothing, Nothing, eb) → True
new_lt16(vyy3000, vyy400) → new_esEs9(new_compare28(vyy3000, vyy400))
new_ltEs14(Left(vyy3000), Left(vyy400), app(app(ty_Either, bcc), bcd), bbd) → new_ltEs14(vyy3000, vyy400, bcc, bcd)
new_esEs29(vyy470, vyy480, ty_Float) → new_esEs19(vyy470, vyy480)
new_esEs25(vyy471, vyy481, ty_Float) → new_esEs19(vyy471, vyy481)
new_compare19(vyy3000, vyy400) → new_compare24(vyy3000, vyy400, new_esEs14(vyy3000, vyy400))
new_lt12(vyy3000, vyy400, be, bf) → new_esEs9(new_compare30(vyy3000, vyy400, be, bf))
new_esEs28(vyy471, vyy481, ty_Bool) → new_esEs17(vyy471, vyy481)
new_ltEs13(vyy300, vyy40) → new_not(new_compare28(vyy300, vyy40))
new_compare31(vyy3000, vyy400, ty_Float) → new_compare6(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, ty_Int) → new_ltEs15(vyy3001, vyy401)
new_esEs29(vyy470, vyy480, ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs26(vyy470, vyy480, ty_Bool) → new_esEs17(vyy470, vyy480)
new_esEs27(vyy47, vyy48, ty_Int) → new_esEs20(vyy47, vyy48)
new_not(LT) → new_not0
new_lt6(vyy3000, vyy400, df, dg, dh) → new_esEs9(new_compare9(vyy3000, vyy400, df, dg, dh))
new_esEs25(vyy471, vyy481, ty_Double) → new_esEs18(vyy471, vyy481)
new_esEs5(Nothing, Nothing, bg) → True
new_esEs26(vyy470, vyy480, ty_Char) → new_esEs10(vyy470, vyy480)
new_ltEs18(vyy3002, vyy402, app(ty_Maybe, baa)) → new_ltEs6(vyy3002, vyy402, baa)
new_esEs28(vyy471, vyy481, app(ty_Maybe, dda)) → new_esEs5(vyy471, vyy481, dda)
new_esEs26(vyy470, vyy480, ty_Float) → new_esEs19(vyy470, vyy480)
new_esEs5(Just(vyy470), Just(vyy480), ty_Int) → new_esEs20(vyy470, vyy480)
new_esEs29(vyy470, vyy480, app(app(app(ty_@3, deb), dec), ded)) → new_esEs6(vyy470, vyy480, deb, dec, ded)
new_esEs8(Left(vyy470), Left(vyy480), ty_@0, cfh) → new_esEs12(vyy470, vyy480)
new_esEs28(vyy471, vyy481, ty_Ordering) → new_esEs14(vyy471, vyy481)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Double, bbd) → new_ltEs11(vyy3000, vyy400)
new_ltEs14(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bbe), bbf), bbg), bbd) → new_ltEs7(vyy3000, vyy400, bbe, bbf, bbg)
new_ltEs6(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs15(vyy3000, vyy400)
new_compare26(vyy3000, vyy400, True, df, dg, dh) → EQ
new_compare31(vyy3000, vyy400, ty_Bool) → new_compare16(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, ty_Ordering) → new_ltEs5(vyy3001, vyy401)
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs10(True, True) → True
new_ltEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), gb, gc, gd) → new_pePe(new_lt9(vyy3000, vyy400, gb), vyy3000, vyy400, new_pePe(new_lt10(vyy3001, vyy401, gc), vyy3001, vyy401, new_ltEs18(vyy3002, vyy402, gd), gc), gb)
new_esEs8(Right(vyy470), Right(vyy480), cfg, ty_Double) → new_esEs18(vyy470, vyy480)
new_asAs(True, vyy79) → vyy79
new_ltEs9(vyy300, vyy40) → new_not(new_compare29(vyy300, vyy40))
new_esEs5(Just(vyy470), Just(vyy480), ty_Integer) → new_esEs11(vyy470, vyy480)
new_primMulNat0(Succ(vyy300000), Succ(vyy40000)) → new_primPlusNat0(new_primMulNat0(vyy300000, Succ(vyy40000)), vyy40000)
new_esEs27(vyy47, vyy48, app(ty_[], bed)) → new_esEs13(vyy47, vyy48, bed)
new_ltEs5(GT, GT) → True
new_esEs27(vyy47, vyy48, ty_Integer) → new_esEs11(vyy47, vyy48)
new_compare31(vyy3000, vyy400, ty_Int) → new_compare7(vyy3000, vyy400)
new_esEs5(Just(vyy470), Just(vyy480), app(app(ty_@2, dc), dd)) → new_esEs7(vyy470, vyy480, dc, dd)
new_esEs8(Right(vyy470), Right(vyy480), cfg, ty_Integer) → new_esEs11(vyy470, vyy480)
new_esEs14(LT, LT) → True
new_ltEs19(vyy3001, vyy401, ty_@0) → new_ltEs9(vyy3001, vyy401)
new_ltEs14(Left(vyy3000), Left(vyy400), ty_Bool, bbd) → new_ltEs10(vyy3000, vyy400)
new_primCompAux0(vyy3000, vyy400, vyy84, de) → new_primCompAux00(vyy84, new_compare31(vyy3000, vyy400, de))
new_fmToList(vyy47, fg, fh) → new_foldFM2(vyy47, fg, fh)
new_ltEs19(vyy3001, vyy401, ty_Integer) → new_ltEs13(vyy3001, vyy401)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, ty_Integer) → new_ltEs13(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, ty_Ordering) → new_esEs14(vyy471, vyy481)
new_foldFM_LE12(vyy71, vyy13, vyy180, vyy181, vyy182, vyy183, EmptyFM, True, h, ba, bb) → new_foldFM_LE30(new_eltsFM_LE0(vyy180, vyy181, new_foldFM_LE5(vyy71, vyy13, vyy183, h, ba, bb), h, ba, bb), vyy13, h, ba, bb)
new_ltEs14(Right(vyy3000), Right(vyy400), bcf, app(ty_Maybe, bcg)) → new_ltEs6(vyy3000, vyy400, bcg)
new_ltEs6(Just(vyy3000), Just(vyy400), app(ty_Ratio, fd)) → new_ltEs16(vyy3000, vyy400, fd)
new_ltEs4(vyy300, vyy40, de) → new_not(new_compare4(vyy300, vyy40, de))
new_compare13(vyy3000, vyy400, True, df, dg, dh) → LT
new_lt5(vyy3000, vyy400) → new_esEs9(new_compare8(vyy3000, vyy400))
new_primCompAux00(vyy88, GT) → GT
new_lt9(vyy3000, vyy400, ty_@0) → new_lt13(vyy3000, vyy400)
new_esEs8(Left(vyy470), Left(vyy480), app(app(ty_@2, che), chf), cfh) → new_esEs7(vyy470, vyy480, che, chf)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs5(GT, EQ) → False
new_esEs8(Left(vyy470), Left(vyy480), ty_Char, cfh) → new_esEs10(vyy470, vyy480)
new_lt10(vyy3001, vyy401, ty_Int) → new_lt18(vyy3001, vyy401)
new_lt19(vyy3000, vyy400, gf) → new_esEs9(new_compare18(vyy3000, vyy400, gf))
new_ltEs18(vyy3002, vyy402, ty_Int) → new_ltEs15(vyy3002, vyy402)
new_esEs24(vyy472, vyy482, ty_@0) → new_esEs12(vyy472, vyy482)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs25(vyy471, vyy481, app(app(ty_Either, cag), cah)) → new_esEs8(vyy471, vyy481, cag, cah)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs23(vyy470, vyy480, app(ty_[], bee)) → new_esEs13(vyy470, vyy480, bee)
The set Q consists of the following terms:
new_ltEs18(x0, x1, ty_Char)
new_primCompAux00(x0, GT)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt20(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Integer)
new_compare13(x0, x1, False, x2, x3, x4)
new_compare25(x0, x1, False)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs15(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs6(Just(x0), Just(x1), ty_Integer)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs14(GT, EQ)
new_esEs14(EQ, GT)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt16(x0, x1)
new_esEs8(Right(x0), Right(x1), x2, ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs18(Double(x0, x1), Double(x2, x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs13(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_esEs5(Just(x0), Nothing, x1)
new_compare110(x0, x1, False)
new_esEs26(x0, x1, ty_@0)
new_compare9(x0, x1, x2, x3, x4)
new_compare7(x0, x1)
new_primCompAux0(x0, x1, x2, x3)
new_esEs9(EQ)
new_ltEs6(Nothing, Just(x0), x1)
new_esEs5(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Integer)
new_ltEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare12(x0, x1, False, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs13([], [], x0)
new_esEs24(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(Float(x0, x1), Float(x2, x3))
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Just(x0), Just(x1), ty_Char)
new_esEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, ty_Char)
new_ltEs6(Nothing, Nothing, x0)
new_esEs29(x0, x1, ty_Float)
new_esEs8(Left(x0), Left(x1), ty_@0, x2)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Ordering)
new_lt9(x0, x1, ty_Ordering)
new_eltsFM_LE0(x0, x1, x2, x3, x4, x5)
new_esEs17(False, False)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1, ty_Bool)
new_primMulNat0(Zero, Succ(x0))
new_esEs8(Left(x0), Right(x1), x2, x3)
new_esEs8(Right(x0), Left(x1), x2, x3)
new_lt12(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs14(LT, GT)
new_esEs14(GT, LT)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare26(x0, x1, True, x2, x3, x4)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare24(x0, x1, False)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs10(Char(x0), Char(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Integer)
new_esEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt9(x0, x1, ty_Float)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt10(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs6(Just(x0), Just(x1), ty_@0)
new_compare29(@0, @0)
new_esEs8(Left(x0), Left(x1), ty_Double, x2)
new_ltEs5(EQ, LT)
new_compare30(x0, x1, x2, x3)
new_lt20(x0, x1, ty_@0)
new_ltEs5(LT, EQ)
new_esEs29(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs27(x0, x1, ty_Char)
new_esEs8(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1, app(ty_[], x2))
new_ltEs6(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, ty_Float)
new_esEs12(@0, @0)
new_compare27(x0, x1, x2, x3)
new_compare6(Float(x0, x1), Float(x2, x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_foldFM_LE30(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Integer)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_lt9(x0, x1, ty_Int)
new_lt18(x0, x1)
new_compare10(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs8(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_compare23(x0, x1, True, x2)
new_ltEs18(x0, x1, ty_Int)
new_esEs8(Right(x0), Right(x1), x2, ty_Float)
new_esEs27(x0, x1, ty_Bool)
new_primPlusNat0(Zero, x0)
new_ltEs6(Just(x0), Nothing, x1)
new_compare4(:(x0, x1), :(x2, x3), x4)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt14(x0, x1)
new_esEs13([], :(x0, x1), x2)
new_foldFM2(EmptyFM, x0, x1)
new_esEs29(x0, x1, ty_Bool)
new_compare10(x0, x1, False, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Bool)
new_esEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs8(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_not0
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs12(x0, x1)
new_lt19(x0, x1, x2)
new_esEs14(LT, LT)
new_esEs24(x0, x1, ty_Int)
new_ltEs10(False, False)
new_esEs9(GT)
new_lt11(x0, x1, x2)
new_lt10(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_esEs25(x0, x1, ty_Double)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_asAs(True, x0)
new_ltEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt9(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True)
new_fmToList(x0, x1, x2)
new_ltEs18(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt9(x0, x1, ty_@0)
new_compare24(x0, x1, True)
new_lt5(x0, x1)
new_primCompAux00(x0, LT)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(x0, x1, ty_Float)
new_asAs(False, x0)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Succ(x0))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_compare211(x0, x1, True, x2, x3)
new_esEs28(x0, x1, ty_Int)
new_not(GT)
new_primMulInt(Pos(x0), Pos(x1))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs5(Nothing, Just(x0), x1)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare13(x0, x1, True, x2, x3, x4)
new_lt17(x0, x1, x2, x3)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare11(x0, x1, True, x2, x3)
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare31(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_@0)
new_esEs20(x0, x1)
new_ltEs18(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_compare17(x0, x1, x2)
new_ltEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_pePe(True, x0, x1, x2, x3)
new_compare25(x0, x1, True)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs27(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs11(Integer(x0), Integer(x1))
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), True, x11, x12, x13)
new_foldFM_LE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_esEs29(x0, x1, app(ty_[], x2))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_ltEs4(x0, x1, x2)
new_compare31(x0, x1, ty_Float)
new_lt9(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs23(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_compare210(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_esEs28(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_pePe(False, x0, x1, x2, x3)
new_primPlusNat1(Zero, Succ(x0))
new_compare31(x0, x1, app(ty_[], x2))
new_compare28(Integer(x0), Integer(x1))
new_compare4([], :(x0, x1), x2)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_esEs13(:(x0, x1), [], x2)
new_ltEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs8(Left(x0), Left(x1), ty_Char, x2)
new_ltEs6(Just(x0), Just(x1), ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs8(Left(x0), Left(x1), ty_Integer, x2)
new_lt8(x0, x1)
new_esEs9(LT)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Nothing, Nothing, x0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs27(x0, x1, ty_@0)
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_esEs25(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(Char(x0), Char(x1))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, ty_Double)
new_compare4([], [], x0)
new_lt20(x0, x1, ty_Ordering)
new_esEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare4(:(x0, x1), [], x2)
new_ltEs10(True, True)
new_lt13(x0, x1)
new_esEs8(Right(x0), Right(x1), x2, ty_Char)
new_esEs8(Right(x0), Right(x1), x2, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_@0)
new_compare23(x0, x1, False, x2)
new_esEs26(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Integer)
new_ltEs16(x0, x1, x2)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs5(GT, GT)
new_ltEs19(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, ty_@0)
new_lt10(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_compare210(x0, x1, True, x2, x3)
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(x0, x1, True, x2)
new_esEs8(Right(x0), Right(x1), x2, ty_Double)
new_sizeFM(EmptyFM, x0, x1)
new_lt9(x0, x1, app(ty_Maybe, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_not(EQ)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_compare31(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, EmptyFM, True, x6, x7, x8)
new_esEs24(x0, x1, ty_Bool)
new_ltEs6(Just(x0), Just(x1), ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs5(EQ, EQ)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs8(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, EQ)
new_compare11(x0, x1, False, x2, x3)
new_esEs14(EQ, LT)
new_esEs14(LT, EQ)
new_esEs27(x0, x1, ty_Float)
new_ltEs6(Just(x0), Just(x1), app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_sr(x0, x1)
new_ltEs15(x0, x1)
new_compare26(x0, x1, False, x2, x3, x4)
new_foldFM_LE5(x0, x1, EmptyFM, x2, x3, x4)
new_esEs14(GT, GT)
new_ltEs6(Just(x0), Just(x1), ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Int)
new_lt9(x0, x1, app(ty_Ratio, x2))
new_compare19(x0, x1)
new_ltEs10(False, True)
new_ltEs10(True, False)
new_esEs26(x0, x1, ty_Integer)
new_compare14(x0, x1, False)
new_esEs28(x0, x1, ty_Bool)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare31(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Int)
new_esEs17(False, True)
new_esEs17(True, False)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare16(x0, x1)
new_esEs14(EQ, EQ)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_lt15(x0, x1, x2)
new_lt6(x0, x1, x2, x3, x4)
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_compare18(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Float)
new_lt9(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs9(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs29(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Float)
new_compare8(Double(x0, x1), Double(x2, x3))
new_ltEs17(x0, x1)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt10(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Char)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt20(x0, x1, ty_Char)
new_compare14(x0, x1, True)
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs25(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_not(LT)
new_compare211(x0, x1, False, x2, x3)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(LT, LT)
new_esEs28(x0, x1, ty_Float)
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM_LE21(vyy82, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, h, ba, bb) → new_foldFM_LE11(vyy82, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, new_ltEs14(vyy1840, Left(vyy13), ba, bb), h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 9, 9 >= 10, 10 >= 11
- new_foldFM_LE4(vyy71, vyy13, Branch(vyy1830, vyy1831, vyy1832, vyy1833, vyy1834), h, ba, bb) → new_foldFM_LE21(vyy71, vyy13, vyy1830, vyy1831, vyy1832, vyy1833, vyy1834, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 4 >= 8, 5 >= 9, 6 >= 10
- new_foldFM_LE11(vyy71, vyy13, vyy180, vyy181, vyy182, vyy183, Branch(vyy1840, vyy1841, vyy1842, vyy1843, vyy1844), True, h, ba, bb) → new_foldFM_LE4(vyy71, vyy13, vyy183, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
- new_foldFM_LE11(vyy71, vyy13, vyy180, vyy181, vyy182, vyy183, EmptyFM, True, h, ba, bb) → new_foldFM_LE4(vyy71, vyy13, vyy183, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
- new_foldFM_LE11(vyy71, vyy13, vyy180, vyy181, vyy182, Branch(vyy1830, vyy1831, vyy1832, vyy1833, vyy1834), vyy184, False, h, ba, bb) → new_foldFM_LE21(vyy71, vyy13, vyy1830, vyy1831, vyy1832, vyy1833, vyy1834, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 > 3, 6 > 4, 6 > 5, 6 > 6, 6 > 7, 9 >= 8, 10 >= 9, 11 >= 10
- new_foldFM_LE11(vyy71, vyy13, vyy180, vyy181, vyy182, vyy183, Branch(vyy1840, vyy1841, vyy1842, vyy1843, vyy1844), True, h, ba, bb) → new_foldFM_LE21(new_eltsFM_LE0(vyy180, vyy181, new_foldFM_LE5(vyy71, vyy13, vyy183, h, ba, bb), h, ba, bb), vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, h, ba, bb)
The graph contains the following edges 2 >= 2, 7 > 3, 7 > 4, 7 > 5, 7 > 6, 7 > 7, 9 >= 8, 10 >= 9, 11 >= 10