YES 9.86
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
|
| ((keysFM_LE :: (Ord b, Ord a) => FiniteMap (Either a b) c -> Either a b -> [Either a b]) :: (Ord a, Ord b) => FiniteMap (Either a b) c -> Either a b -> [Either a 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 b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM (\key elt rest ->(key,elt) : rest) [] fm |
|
| | 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 b => (b -> c -> a -> a) -> a -> b -> FiniteMap b c -> a
| 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 | = |
|
|
|
| | keysFM_LE :: Ord a => FiniteMap a b -> a -> [a]
| keysFM_LE | fm fr | = | foldFM_LE (\key elt rest ->key : rest) [] fr fm |
|
| | 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 : rest
is transformed to
| keysFM_LE0 | key elt rest | = key : rest |
The following Lambda expression
\keyeltrest→(key,elt) : rest
is transformed to
| fmToList0 | key elt rest | = (key,elt) : rest |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
mainModule FiniteMap
|
| ((keysFM_LE :: (Ord b, Ord a) => FiniteMap (Either b a) c -> Either b a -> [Either b a]) :: (Ord a, Ord b) => FiniteMap (Either b a) c -> Either b a -> [Either 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 |
|
|
| | 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 b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> 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 | = |
|
|
|
| | keysFM_LE :: Ord a => FiniteMap a b -> a -> [a]
| keysFM_LE | fm fr | = | foldFM_LE keysFM_LE0 [] fr fm |
|
| |
| keysFM_LE0 | key elt rest | = | key : rest |
|
| | sizeFM :: FiniteMap a b -> 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
|
| ((keysFM_LE :: (Ord b, Ord c) => FiniteMap (Either b c) a -> Either b c -> [Either b c]) :: (Ord c, Ord b) => FiniteMap (Either b c) a -> Either b c -> [Either b 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 |
|
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| 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 _ 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 | = | 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 | = |
|
|
|
| | keysFM_LE :: Ord b => FiniteMap b a -> b -> [b]
| keysFM_LE | fm fr | = | foldFM_LE keysFM_LE0 [] fr fm |
|
| |
| keysFM_LE0 | key elt rest | = | key : rest |
|
| | 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
|
| ((keysFM_LE :: (Ord a, Ord c) => FiniteMap (Either c a) b -> Either c a -> [Either c a]) :: (Ord c, Ord a) => FiniteMap (Either c a) b -> Either c a -> [Either c a]) |
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 b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | 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 _ 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 | = | 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 | = |
|
|
|
| | keysFM_LE :: Ord a => FiniteMap a b -> a -> [a]
| keysFM_LE | fm fr | = | foldFM_LE keysFM_LE0 [] fr fm |
|
| |
| keysFM_LE0 | key elt rest | = | key : rest |
|
| | sizeFM :: FiniteMap a b -> 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
|
| ((keysFM_LE :: (Ord a, Ord b) => FiniteMap (Either a b) c -> Either a b -> [Either a b]) :: (Ord b, Ord a) => FiniteMap (Either a b) c -> Either a b -> [Either a 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 |
|
|
| | 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 b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> 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 | = |
|
|
|
| | keysFM_LE :: Ord a => FiniteMap a b -> a -> [a]
| keysFM_LE | fm fr | = | foldFM_LE keysFM_LE0 [] fr fm |
|
| |
| keysFM_LE0 | key elt rest | = | key : rest |
|
| | sizeFM :: FiniteMap a b -> 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_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 |
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
|
| ((keysFM_LE :: (Ord a, Ord b) => FiniteMap (Either b a) c -> Either b a -> [Either b a]) :: (Ord b, Ord a) => FiniteMap (Either b a) c -> Either b a -> [Either b a]) |
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 b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | 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 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 | = | 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 |
|
| | keysFM_LE :: Ord a => FiniteMap a b -> a -> [a]
| keysFM_LE | fm fr | = | foldFM_LE keysFM_LE0 [] fr fm |
|
| |
| keysFM_LE0 | key elt rest | = | key : rest |
|
| | 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) |
| reduce2D | vyw vyx | = gcd vyw vyx |
| reduce2Reduce1 | vyw vyx x y True | = error [] |
| reduce2Reduce1 | vyw vyx x y False | = reduce2Reduce0 vyw vyx x y otherwise |
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'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' | x vvy | = gcd0Gcd'2 x vvy |
| gcd0Gcd' | x y | = gcd0Gcd'0 x y |
| 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
|
| ((keysFM_LE :: (Ord b, Ord c) => FiniteMap (Either c b) a -> Either c b -> [Either c b]) :: (Ord b, Ord c) => FiniteMap (Either c b) a -> Either c b -> [Either 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 b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| 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 vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> 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 |
|
| | keysFM_LE :: Ord b => FiniteMap b a -> b -> [b]
| keysFM_LE | fm fr | = | foldFM_LE keysFM_LE0 [] fr fm |
|
| |
| keysFM_LE0 | key elt rest | = | key : rest |
|
| | 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
|
| (keysFM_LE :: (Ord b, Ord c) => FiniteMap (Either c b) a -> Either c b -> [Either 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 |
|
|
| | 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 vw 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 | = | 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 |
|
| | keysFM_LE :: Ord b => FiniteMap b a -> b -> [b]
| keysFM_LE | fm fr | = | foldFM_LE keysFM_LE0 [] fr fm |
|
| |
| keysFM_LE0 | key elt rest | = | key : rest |
|
| | 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_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
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ 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
↳ QDPSizeChangeProof
↳ 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
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ 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
↳ 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_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_[], bbd), bbc) → new_esEs0(vyy470, vyy480, bbd)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, bed), bee), beb) → new_esEs1(vyy470, vyy480, bed, bee)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(ty_[], be)) → new_esEs0(vyy472, vyy482, be)
new_esEs1(vyy47, vyy48, hb, hc) → new_esEs0(new_fmToList(vyy47, hb, hc), new_fmToList(vyy48, hb, hc), app(app(ty_@2, hb), hc))
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bca), bbc) → new_esEs3(vyy470, vyy480, bca)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, fg), fh), ga)) → new_esEs(vyy470, vyy480, fg, fh, ga)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(ty_Maybe, bae)) → new_esEs3(vyy471, vyy481, bae)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_Either, cc), cd)) → new_esEs4(vyy472, vyy482, cc, cd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs(vyy470, vyy480, bfd, bfe, bff)
new_esEs3(Just(vyy470), Just(vyy480), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs(vyy470, vyy480, bcd, bce, bcf)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_@2, bdb), bdc)) → new_esEs2(vyy470, vyy480, bdb, bdc)
new_esEs4(Left(vyy470), Left(vyy480), app(ty_[], bec), beb) → new_esEs0(vyy470, vyy480, bec)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_@2, bef), beg), beb) → new_esEs2(vyy470, vyy480, bef, beg)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bcb), bcc), bbc) → new_esEs4(vyy470, vyy480, bcb, bcc)
new_esEs4(Left(vyy470), Left(vyy480), app(app(app(ty_@3, bdg), bdh), bea), beb) → new_esEs(vyy470, vyy480, bdg, bdh, bea)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bah), bba), bbb), bbc) → new_esEs(vyy470, vyy480, bah, bba, bbb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_@2, bh), ca)) → new_esEs2(vyy472, vyy482, bh, ca)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_@2, bgb), bgc)) → new_esEs2(vyy470, vyy480, bgb, bgc)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_Either, fc), fd), ba, da) → new_esEs4(vyy470, vyy480, fc, fd)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), ff) → new_esEs0(vyy471, vyy481, ff)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_Maybe, fb), ba, da) → new_esEs3(vyy470, vyy480, fb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(ty_[], db), da) → new_esEs0(vyy471, vyy481, db)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, gg)) → new_esEs3(vyy470, vyy480, gg)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(ty_[], bfg)) → new_esEs0(vyy470, vyy480, bfg)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, gh), ha)) → new_esEs4(vyy470, vyy480, gh, ha)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, bch), bda)) → new_esEs1(vyy470, vyy480, bch, bda)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_@2, bac), bad)) → new_esEs2(vyy471, vyy481, bac, bad)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_FiniteMap, ef), eg), ba, da) → new_esEs1(vyy470, vyy480, ef, eg)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_FiniteMap, bbe), bbf), bbc) → new_esEs1(vyy470, vyy480, bbe, bbf)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bbg), bbh), bbc) → new_esEs2(vyy470, vyy480, bbg, bbh)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(app(ty_@3, eb), ec), ed), ba, da) → new_esEs(vyy470, vyy480, eb, ec, ed)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(app(ty_@3, he), hf), hg)) → new_esEs(vyy471, vyy481, he, hf, hg)
new_esEs3(Just(vyy470), Just(vyy480), app(ty_[], bcg)) → new_esEs0(vyy470, vyy480, bcg)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_FiniteMap, gc), gd)) → new_esEs1(vyy470, vyy480, gc, gd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(ty_Maybe, bgd)) → new_esEs3(vyy470, vyy480, bgd)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_@2, eh), fa), ba, da) → new_esEs2(vyy470, vyy480, eh, fa)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_FiniteMap, dc), dd), da) → new_esEs1(vyy471, vyy481, dc, dd)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_Either, bde), bdf)) → new_esEs4(vyy470, vyy480, bde, bdf)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_Either, dh), ea), da) → new_esEs4(vyy471, vyy481, dh, ea)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_Either, bfa), bfb), beb) → new_esEs4(vyy470, vyy480, bfa, bfb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_@2, de), df), da) → new_esEs2(vyy471, vyy481, de, df)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(app(ty_@3, ce), cf), cg), da) → new_esEs(vyy471, vyy481, ce, cf, cg)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_Either, baf), bag)) → new_esEs4(vyy471, vyy481, baf, bag)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(ty_Maybe, dg), da) → new_esEs3(vyy471, vyy481, dg)
new_esEs4(Left(vyy470), Left(vyy480), app(ty_Maybe, beh), beb) → new_esEs3(vyy470, vyy480, beh)
new_esEs3(Just(vyy470), Just(vyy480), app(ty_Maybe, bdd)) → new_esEs3(vyy470, vyy480, bdd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_FiniteMap, bfh), bga)) → new_esEs1(vyy470, vyy480, bfh, bga)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(ty_Maybe, cb)) → new_esEs3(vyy472, vyy482, cb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_[], ee), ba, da) → new_esEs0(vyy470, vyy480, ee)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(ty_[], hh)) → new_esEs0(vyy471, vyy481, hh)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_[], gb)) → new_esEs0(vyy470, vyy480, gb)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_FiniteMap, baa), bab)) → new_esEs1(vyy471, vyy481, baa, bab)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_@2, ge), gf)) → new_esEs2(vyy470, vyy480, ge, gf)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_FiniteMap, bf), bg)) → new_esEs1(vyy472, vyy482, bf, bg)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(app(ty_@3, bb), bc), bd)) → new_esEs(vyy472, vyy482, bb, bc, bd)
The TRS R consists of the following rules:
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, hb, hc) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), hb, hc) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, hb, hc), vyy4733, hb, hc)
new_fmToList(vyy47, hb, hc) → new_foldFM2(vyy47, hb, hc)
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), hb, hc) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, hb, hc), vyy473, hb, hc)
new_foldFM2(EmptyFM, hb, hc) → []
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs1(vyy47, vyy48, hb, hc) → new_esEs0(new_fmToList(vyy47, hb, hc), new_fmToList(vyy48, hb, hc), app(app(ty_@2, hb), hc)) at position [0] we obtained the following new rules:
new_esEs1(vyy47, vyy48, hb, hc) → new_esEs0(new_foldFM2(vyy47, hb, hc), new_fmToList(vyy48, hb, hc), app(app(ty_@2, hb), hc))
↳ 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_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_[], bbd), bbc) → new_esEs0(vyy470, vyy480, bbd)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, bed), bee), beb) → new_esEs1(vyy470, vyy480, bed, bee)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(ty_[], be)) → new_esEs0(vyy472, vyy482, be)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bca), bbc) → new_esEs3(vyy470, vyy480, bca)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(ty_Maybe, bae)) → new_esEs3(vyy471, vyy481, bae)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, fg), fh), ga)) → new_esEs(vyy470, vyy480, fg, fh, ga)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_Either, cc), cd)) → new_esEs4(vyy472, vyy482, cc, cd)
new_esEs3(Just(vyy470), Just(vyy480), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs(vyy470, vyy480, bcd, bce, bcf)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs(vyy470, vyy480, bfd, bfe, bff)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_@2, bdb), bdc)) → new_esEs2(vyy470, vyy480, bdb, bdc)
new_esEs4(Left(vyy470), Left(vyy480), app(ty_[], bec), beb) → new_esEs0(vyy470, vyy480, bec)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bcb), bcc), bbc) → new_esEs4(vyy470, vyy480, bcb, bcc)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_@2, bef), beg), beb) → new_esEs2(vyy470, vyy480, bef, beg)
new_esEs4(Left(vyy470), Left(vyy480), app(app(app(ty_@3, bdg), bdh), bea), beb) → new_esEs(vyy470, vyy480, bdg, bdh, bea)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bah), bba), bbb), bbc) → new_esEs(vyy470, vyy480, bah, bba, bbb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_@2, bh), ca)) → new_esEs2(vyy472, vyy482, bh, ca)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_@2, bgb), bgc)) → new_esEs2(vyy470, vyy480, bgb, bgc)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_Either, fc), fd), ba, da) → new_esEs4(vyy470, vyy480, fc, fd)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), ff) → new_esEs0(vyy471, vyy481, ff)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_Maybe, fb), ba, da) → new_esEs3(vyy470, vyy480, fb)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(ty_[], bfg)) → new_esEs0(vyy470, vyy480, bfg)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, gg)) → new_esEs3(vyy470, vyy480, gg)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(ty_[], db), da) → new_esEs0(vyy471, vyy481, db)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, gh), ha)) → new_esEs4(vyy470, vyy480, gh, ha)
new_esEs1(vyy47, vyy48, hb, hc) → new_esEs0(new_foldFM2(vyy47, hb, hc), new_fmToList(vyy48, hb, hc), app(app(ty_@2, hb), hc))
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, bch), bda)) → new_esEs1(vyy470, vyy480, bch, bda)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_@2, bac), bad)) → new_esEs2(vyy471, vyy481, bac, bad)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_FiniteMap, ef), eg), ba, da) → new_esEs1(vyy470, vyy480, ef, eg)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_FiniteMap, bbe), bbf), bbc) → new_esEs1(vyy470, vyy480, bbe, bbf)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bbg), bbh), bbc) → new_esEs2(vyy470, vyy480, bbg, bbh)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(app(ty_@3, eb), ec), ed), ba, da) → new_esEs(vyy470, vyy480, eb, ec, ed)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(app(ty_@3, he), hf), hg)) → new_esEs(vyy471, vyy481, he, hf, hg)
new_esEs3(Just(vyy470), Just(vyy480), app(ty_[], bcg)) → new_esEs0(vyy470, vyy480, bcg)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_FiniteMap, gc), gd)) → new_esEs1(vyy470, vyy480, gc, gd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(ty_Maybe, bgd)) → new_esEs3(vyy470, vyy480, bgd)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_FiniteMap, dc), dd), da) → new_esEs1(vyy471, vyy481, dc, dd)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_@2, eh), fa), ba, da) → new_esEs2(vyy470, vyy480, eh, fa)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_Either, bde), bdf)) → new_esEs4(vyy470, vyy480, bde, bdf)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_Either, dh), ea), da) → new_esEs4(vyy471, vyy481, dh, ea)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_@2, de), df), da) → new_esEs2(vyy471, vyy481, de, df)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_Either, bfa), bfb), beb) → new_esEs4(vyy470, vyy480, bfa, bfb)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_Either, baf), bag)) → new_esEs4(vyy471, vyy481, baf, bag)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(app(ty_@3, ce), cf), cg), da) → new_esEs(vyy471, vyy481, ce, cf, cg)
new_esEs4(Left(vyy470), Left(vyy480), app(ty_Maybe, beh), beb) → new_esEs3(vyy470, vyy480, beh)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(ty_Maybe, dg), da) → new_esEs3(vyy471, vyy481, dg)
new_esEs3(Just(vyy470), Just(vyy480), app(ty_Maybe, bdd)) → new_esEs3(vyy470, vyy480, bdd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_FiniteMap, bfh), bga)) → new_esEs1(vyy470, vyy480, bfh, bga)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(ty_Maybe, cb)) → new_esEs3(vyy472, vyy482, cb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_[], ee), ba, da) → new_esEs0(vyy470, vyy480, ee)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(ty_[], hh)) → new_esEs0(vyy471, vyy481, hh)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_[], gb)) → new_esEs0(vyy470, vyy480, gb)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_FiniteMap, baa), bab)) → new_esEs1(vyy471, vyy481, baa, bab)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_@2, ge), gf)) → new_esEs2(vyy470, vyy480, ge, gf)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(app(ty_@3, bb), bc), bd)) → new_esEs(vyy472, vyy482, bb, bc, bd)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_FiniteMap, bf), bg)) → new_esEs1(vyy472, vyy482, bf, bg)
The TRS R consists of the following rules:
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, hb, hc) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), hb, hc) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, hb, hc), vyy4733, hb, hc)
new_fmToList(vyy47, hb, hc) → new_foldFM2(vyy47, hb, hc)
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), hb, hc) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, hb, hc), vyy473, hb, hc)
new_foldFM2(EmptyFM, hb, hc) → []
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs1(vyy47, vyy48, hb, hc) → new_esEs0(new_foldFM2(vyy47, hb, hc), new_fmToList(vyy48, hb, hc), app(app(ty_@2, hb), hc)) at position [1] we obtained the following new rules:
new_esEs1(vyy47, vyy48, hb, hc) → new_esEs0(new_foldFM2(vyy47, hb, hc), new_foldFM2(vyy48, hb, hc), app(app(ty_@2, hb), hc))
↳ 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_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_[], bbd), bbc) → new_esEs0(vyy470, vyy480, bbd)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, bed), bee), beb) → new_esEs1(vyy470, vyy480, bed, bee)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(ty_[], be)) → new_esEs0(vyy472, vyy482, be)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bca), bbc) → new_esEs3(vyy470, vyy480, bca)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, fg), fh), ga)) → new_esEs(vyy470, vyy480, fg, fh, ga)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(ty_Maybe, bae)) → new_esEs3(vyy471, vyy481, bae)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_Either, cc), cd)) → new_esEs4(vyy472, vyy482, cc, cd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs(vyy470, vyy480, bfd, bfe, bff)
new_esEs3(Just(vyy470), Just(vyy480), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs(vyy470, vyy480, bcd, bce, bcf)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_@2, bdb), bdc)) → new_esEs2(vyy470, vyy480, bdb, bdc)
new_esEs4(Left(vyy470), Left(vyy480), app(ty_[], bec), beb) → new_esEs0(vyy470, vyy480, bec)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_@2, bef), beg), beb) → new_esEs2(vyy470, vyy480, bef, beg)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bcb), bcc), bbc) → new_esEs4(vyy470, vyy480, bcb, bcc)
new_esEs4(Left(vyy470), Left(vyy480), app(app(app(ty_@3, bdg), bdh), bea), beb) → new_esEs(vyy470, vyy480, bdg, bdh, bea)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bah), bba), bbb), bbc) → new_esEs(vyy470, vyy480, bah, bba, bbb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_@2, bh), ca)) → new_esEs2(vyy472, vyy482, bh, ca)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_@2, bgb), bgc)) → new_esEs2(vyy470, vyy480, bgb, bgc)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_Either, fc), fd), ba, da) → new_esEs4(vyy470, vyy480, fc, fd)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), ff) → new_esEs0(vyy471, vyy481, ff)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_Maybe, fb), ba, da) → new_esEs3(vyy470, vyy480, fb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(ty_[], db), da) → new_esEs0(vyy471, vyy481, db)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, gg)) → new_esEs3(vyy470, vyy480, gg)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(ty_[], bfg)) → new_esEs0(vyy470, vyy480, bfg)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, gh), ha)) → new_esEs4(vyy470, vyy480, gh, ha)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, bch), bda)) → new_esEs1(vyy470, vyy480, bch, bda)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_@2, bac), bad)) → new_esEs2(vyy471, vyy481, bac, bad)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_FiniteMap, ef), eg), ba, da) → new_esEs1(vyy470, vyy480, ef, eg)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_FiniteMap, bbe), bbf), bbc) → new_esEs1(vyy470, vyy480, bbe, bbf)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bbg), bbh), bbc) → new_esEs2(vyy470, vyy480, bbg, bbh)
new_esEs1(vyy47, vyy48, hb, hc) → new_esEs0(new_foldFM2(vyy47, hb, hc), new_foldFM2(vyy48, hb, hc), app(app(ty_@2, hb), hc))
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(app(ty_@3, eb), ec), ed), ba, da) → new_esEs(vyy470, vyy480, eb, ec, ed)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(app(ty_@3, he), hf), hg)) → new_esEs(vyy471, vyy481, he, hf, hg)
new_esEs3(Just(vyy470), Just(vyy480), app(ty_[], bcg)) → new_esEs0(vyy470, vyy480, bcg)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_FiniteMap, gc), gd)) → new_esEs1(vyy470, vyy480, gc, gd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(ty_Maybe, bgd)) → new_esEs3(vyy470, vyy480, bgd)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_@2, eh), fa), ba, da) → new_esEs2(vyy470, vyy480, eh, fa)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_FiniteMap, dc), dd), da) → new_esEs1(vyy471, vyy481, dc, dd)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_Either, bde), bdf)) → new_esEs4(vyy470, vyy480, bde, bdf)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_Either, dh), ea), da) → new_esEs4(vyy471, vyy481, dh, ea)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_Either, bfa), bfb), beb) → new_esEs4(vyy470, vyy480, bfa, bfb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_@2, de), df), da) → new_esEs2(vyy471, vyy481, de, df)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(app(ty_@3, ce), cf), cg), da) → new_esEs(vyy471, vyy481, ce, cf, cg)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_Either, baf), bag)) → new_esEs4(vyy471, vyy481, baf, bag)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(ty_Maybe, dg), da) → new_esEs3(vyy471, vyy481, dg)
new_esEs4(Left(vyy470), Left(vyy480), app(ty_Maybe, beh), beb) → new_esEs3(vyy470, vyy480, beh)
new_esEs3(Just(vyy470), Just(vyy480), app(ty_Maybe, bdd)) → new_esEs3(vyy470, vyy480, bdd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_FiniteMap, bfh), bga)) → new_esEs1(vyy470, vyy480, bfh, bga)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(ty_Maybe, cb)) → new_esEs3(vyy472, vyy482, cb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_[], ee), ba, da) → new_esEs0(vyy470, vyy480, ee)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(ty_[], hh)) → new_esEs0(vyy471, vyy481, hh)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_[], gb)) → new_esEs0(vyy470, vyy480, gb)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_FiniteMap, baa), bab)) → new_esEs1(vyy471, vyy481, baa, bab)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_@2, ge), gf)) → new_esEs2(vyy470, vyy480, ge, gf)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_FiniteMap, bf), bg)) → new_esEs1(vyy472, vyy482, bf, bg)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(app(ty_@3, bb), bc), bd)) → new_esEs(vyy472, vyy482, bb, bc, bd)
The TRS R consists of the following rules:
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, hb, hc) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), hb, hc) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, hb, hc), vyy4733, hb, hc)
new_fmToList(vyy47, hb, hc) → new_foldFM2(vyy47, hb, hc)
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), hb, hc) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, hb, hc), vyy473, hb, hc)
new_foldFM2(EmptyFM, hb, hc) → []
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_[], bbd), bbc) → new_esEs0(vyy470, vyy480, bbd)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, bed), bee), beb) → new_esEs1(vyy470, vyy480, bed, bee)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(ty_[], be)) → new_esEs0(vyy472, vyy482, be)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bca), bbc) → new_esEs3(vyy470, vyy480, bca)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, fg), fh), ga)) → new_esEs(vyy470, vyy480, fg, fh, ga)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(ty_Maybe, bae)) → new_esEs3(vyy471, vyy481, bae)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_Either, cc), cd)) → new_esEs4(vyy472, vyy482, cc, cd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs(vyy470, vyy480, bfd, bfe, bff)
new_esEs3(Just(vyy470), Just(vyy480), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs(vyy470, vyy480, bcd, bce, bcf)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_@2, bdb), bdc)) → new_esEs2(vyy470, vyy480, bdb, bdc)
new_esEs4(Left(vyy470), Left(vyy480), app(ty_[], bec), beb) → new_esEs0(vyy470, vyy480, bec)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bcb), bcc), bbc) → new_esEs4(vyy470, vyy480, bcb, bcc)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_@2, bef), beg), beb) → new_esEs2(vyy470, vyy480, bef, beg)
new_esEs4(Left(vyy470), Left(vyy480), app(app(app(ty_@3, bdg), bdh), bea), beb) → new_esEs(vyy470, vyy480, bdg, bdh, bea)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bah), bba), bbb), bbc) → new_esEs(vyy470, vyy480, bah, bba, bbb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_@2, bh), ca)) → new_esEs2(vyy472, vyy482, bh, ca)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_@2, bgb), bgc)) → new_esEs2(vyy470, vyy480, bgb, bgc)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_Either, fc), fd), ba, da) → new_esEs4(vyy470, vyy480, fc, fd)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), ff) → new_esEs0(vyy471, vyy481, ff)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_Maybe, fb), ba, da) → new_esEs3(vyy470, vyy480, fb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(ty_[], db), da) → new_esEs0(vyy471, vyy481, db)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, gg)) → new_esEs3(vyy470, vyy480, gg)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(ty_[], bfg)) → new_esEs0(vyy470, vyy480, bfg)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, gh), ha)) → new_esEs4(vyy470, vyy480, gh, ha)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, bch), bda)) → new_esEs1(vyy470, vyy480, bch, bda)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_@2, bac), bad)) → new_esEs2(vyy471, vyy481, bac, bad)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_FiniteMap, ef), eg), ba, da) → new_esEs1(vyy470, vyy480, ef, eg)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_FiniteMap, bbe), bbf), bbc) → new_esEs1(vyy470, vyy480, bbe, bbf)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bbg), bbh), bbc) → new_esEs2(vyy470, vyy480, bbg, bbh)
new_esEs1(vyy47, vyy48, hb, hc) → new_esEs0(new_foldFM2(vyy47, hb, hc), new_foldFM2(vyy48, hb, hc), app(app(ty_@2, hb), hc))
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(app(ty_@3, eb), ec), ed), ba, da) → new_esEs(vyy470, vyy480, eb, ec, ed)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(app(ty_@3, he), hf), hg)) → new_esEs(vyy471, vyy481, he, hf, hg)
new_esEs3(Just(vyy470), Just(vyy480), app(ty_[], bcg)) → new_esEs0(vyy470, vyy480, bcg)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_FiniteMap, gc), gd)) → new_esEs1(vyy470, vyy480, gc, gd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(ty_Maybe, bgd)) → new_esEs3(vyy470, vyy480, bgd)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_@2, eh), fa), ba, da) → new_esEs2(vyy470, vyy480, eh, fa)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_FiniteMap, dc), dd), da) → new_esEs1(vyy471, vyy481, dc, dd)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_Either, bde), bdf)) → new_esEs4(vyy470, vyy480, bde, bdf)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_Either, dh), ea), da) → new_esEs4(vyy471, vyy481, dh, ea)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_Either, bfa), bfb), beb) → new_esEs4(vyy470, vyy480, bfa, bfb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_@2, de), df), da) → new_esEs2(vyy471, vyy481, de, df)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(app(ty_@3, ce), cf), cg), da) → new_esEs(vyy471, vyy481, ce, cf, cg)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_Either, baf), bag)) → new_esEs4(vyy471, vyy481, baf, bag)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(ty_Maybe, dg), da) → new_esEs3(vyy471, vyy481, dg)
new_esEs4(Left(vyy470), Left(vyy480), app(ty_Maybe, beh), beb) → new_esEs3(vyy470, vyy480, beh)
new_esEs3(Just(vyy470), Just(vyy480), app(ty_Maybe, bdd)) → new_esEs3(vyy470, vyy480, bdd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_FiniteMap, bfh), bga)) → new_esEs1(vyy470, vyy480, bfh, bga)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(ty_Maybe, cb)) → new_esEs3(vyy472, vyy482, cb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_[], ee), ba, da) → new_esEs0(vyy470, vyy480, ee)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(ty_[], hh)) → new_esEs0(vyy471, vyy481, hh)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_[], gb)) → new_esEs0(vyy470, vyy480, gb)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_FiniteMap, baa), bab)) → new_esEs1(vyy471, vyy481, baa, bab)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_@2, ge), gf)) → new_esEs2(vyy470, vyy480, ge, gf)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_FiniteMap, bf), bg)) → new_esEs1(vyy472, vyy482, bf, bg)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(app(ty_@3, bb), bc), bd)) → new_esEs(vyy472, vyy482, bb, bc, bd)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), hb, hc) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, hb, hc), vyy473, hb, hc)
new_foldFM2(EmptyFM, hb, hc) → []
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, hb, hc) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), hb, hc) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, hb, hc), vyy4733, hb, hc)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_[], bbd), bbc) → new_esEs0(vyy470, vyy480, bbd)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, bed), bee), beb) → new_esEs1(vyy470, vyy480, bed, bee)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(ty_[], be)) → new_esEs0(vyy472, vyy482, be)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bca), bbc) → new_esEs3(vyy470, vyy480, bca)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, fg), fh), ga)) → new_esEs(vyy470, vyy480, fg, fh, ga)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(ty_Maybe, bae)) → new_esEs3(vyy471, vyy481, bae)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_Either, cc), cd)) → new_esEs4(vyy472, vyy482, cc, cd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs(vyy470, vyy480, bfd, bfe, bff)
new_esEs3(Just(vyy470), Just(vyy480), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs(vyy470, vyy480, bcd, bce, bcf)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_@2, bdb), bdc)) → new_esEs2(vyy470, vyy480, bdb, bdc)
new_esEs4(Left(vyy470), Left(vyy480), app(ty_[], bec), beb) → new_esEs0(vyy470, vyy480, bec)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bcb), bcc), bbc) → new_esEs4(vyy470, vyy480, bcb, bcc)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_@2, bef), beg), beb) → new_esEs2(vyy470, vyy480, bef, beg)
new_esEs4(Left(vyy470), Left(vyy480), app(app(app(ty_@3, bdg), bdh), bea), beb) → new_esEs(vyy470, vyy480, bdg, bdh, bea)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bah), bba), bbb), bbc) → new_esEs(vyy470, vyy480, bah, bba, bbb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_@2, bh), ca)) → new_esEs2(vyy472, vyy482, bh, ca)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_@2, bgb), bgc)) → new_esEs2(vyy470, vyy480, bgb, bgc)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_Either, fc), fd), ba, da) → new_esEs4(vyy470, vyy480, fc, fd)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), ff) → new_esEs0(vyy471, vyy481, ff)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_Maybe, fb), ba, da) → new_esEs3(vyy470, vyy480, fb)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(ty_[], bfg)) → new_esEs0(vyy470, vyy480, bfg)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, gg)) → new_esEs3(vyy470, vyy480, gg)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(ty_[], db), da) → new_esEs0(vyy471, vyy481, db)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, gh), ha)) → new_esEs4(vyy470, vyy480, gh, ha)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, bch), bda)) → new_esEs1(vyy470, vyy480, bch, bda)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_@2, bac), bad)) → new_esEs2(vyy471, vyy481, bac, bad)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_FiniteMap, ef), eg), ba, da) → new_esEs1(vyy470, vyy480, ef, eg)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_FiniteMap, bbe), bbf), bbc) → new_esEs1(vyy470, vyy480, bbe, bbf)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bbg), bbh), bbc) → new_esEs2(vyy470, vyy480, bbg, bbh)
new_esEs1(vyy47, vyy48, hb, hc) → new_esEs0(new_foldFM2(vyy47, hb, hc), new_foldFM2(vyy48, hb, hc), app(app(ty_@2, hb), hc))
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(app(ty_@3, eb), ec), ed), ba, da) → new_esEs(vyy470, vyy480, eb, ec, ed)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(app(ty_@3, he), hf), hg)) → new_esEs(vyy471, vyy481, he, hf, hg)
new_esEs3(Just(vyy470), Just(vyy480), app(ty_[], bcg)) → new_esEs0(vyy470, vyy480, bcg)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_FiniteMap, gc), gd)) → new_esEs1(vyy470, vyy480, gc, gd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(ty_Maybe, bgd)) → new_esEs3(vyy470, vyy480, bgd)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_@2, eh), fa), ba, da) → new_esEs2(vyy470, vyy480, eh, fa)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_FiniteMap, dc), dd), da) → new_esEs1(vyy471, vyy481, dc, dd)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_Either, bde), bdf)) → new_esEs4(vyy470, vyy480, bde, bdf)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_Either, dh), ea), da) → new_esEs4(vyy471, vyy481, dh, ea)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_Either, bfa), bfb), beb) → new_esEs4(vyy470, vyy480, bfa, bfb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_@2, de), df), da) → new_esEs2(vyy471, vyy481, de, df)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(app(ty_@3, ce), cf), cg), da) → new_esEs(vyy471, vyy481, ce, cf, cg)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_Either, baf), bag)) → new_esEs4(vyy471, vyy481, baf, bag)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(ty_Maybe, dg), da) → new_esEs3(vyy471, vyy481, dg)
new_esEs4(Left(vyy470), Left(vyy480), app(ty_Maybe, beh), beb) → new_esEs3(vyy470, vyy480, beh)
new_esEs3(Just(vyy470), Just(vyy480), app(ty_Maybe, bdd)) → new_esEs3(vyy470, vyy480, bdd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_FiniteMap, bfh), bga)) → new_esEs1(vyy470, vyy480, bfh, bga)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(ty_Maybe, cb)) → new_esEs3(vyy472, vyy482, cb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_[], ee), ba, da) → new_esEs0(vyy470, vyy480, ee)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(ty_[], hh)) → new_esEs0(vyy471, vyy481, hh)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_[], gb)) → new_esEs0(vyy470, vyy480, gb)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_FiniteMap, baa), bab)) → new_esEs1(vyy471, vyy481, baa, bab)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_@2, ge), gf)) → new_esEs2(vyy470, vyy480, ge, gf)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(app(ty_@3, bb), bc), bd)) → new_esEs(vyy472, vyy482, bb, bc, bd)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_FiniteMap, bf), bg)) → new_esEs1(vyy472, vyy482, bf, bg)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), hb, hc) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, hb, hc), vyy473, hb, hc)
new_foldFM2(EmptyFM, hb, hc) → []
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, hb, hc) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), hb, hc) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, hb, hc), vyy4733, hb, hc)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_[], bbd), bbc) → new_esEs0(vyy470, vyy480, bbd)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, bed), bee), beb) → new_esEs1(vyy470, vyy480, bed, bee)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(ty_[], be)) → new_esEs0(vyy472, vyy482, be)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_Either, cc), cd)) → new_esEs4(vyy472, vyy482, cc, cd)
new_esEs3(Just(vyy470), Just(vyy480), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs(vyy470, vyy480, bcd, bce, bcf)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_@2, bdb), bdc)) → new_esEs2(vyy470, vyy480, bdb, bdc)
new_esEs4(Left(vyy470), Left(vyy480), app(ty_[], bec), beb) → new_esEs0(vyy470, vyy480, bec)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_@2, bef), beg), beb) → new_esEs2(vyy470, vyy480, bef, beg)
new_esEs4(Left(vyy470), Left(vyy480), app(app(app(ty_@3, bdg), bdh), bea), beb) → new_esEs(vyy470, vyy480, bdg, bdh, bea)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_@2, bh), ca)) → new_esEs2(vyy472, vyy482, bh, ca)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_@2, bgb), bgc)) → new_esEs2(vyy470, vyy480, bgb, bgc)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_Either, fc), fd), ba, da) → new_esEs4(vyy470, vyy480, fc, fd)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), ff) → new_esEs0(vyy471, vyy481, ff)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_Maybe, fb), ba, da) → new_esEs3(vyy470, vyy480, fb)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(ty_[], bfg)) → new_esEs0(vyy470, vyy480, bfg)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(ty_[], db), da) → new_esEs0(vyy471, vyy481, db)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, bch), bda)) → new_esEs1(vyy470, vyy480, bch, bda)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_@2, bac), bad)) → new_esEs2(vyy471, vyy481, bac, bad)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_FiniteMap, ef), eg), ba, da) → new_esEs1(vyy470, vyy480, ef, eg)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_@2, bbg), bbh), bbc) → new_esEs2(vyy470, vyy480, bbg, bbh)
new_esEs1(vyy47, vyy48, hb, hc) → new_esEs0(new_foldFM2(vyy47, hb, hc), new_foldFM2(vyy48, hb, hc), app(app(ty_@2, hb), hc))
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(app(ty_@3, eb), ec), ed), ba, da) → new_esEs(vyy470, vyy480, eb, ec, ed)
new_esEs3(Just(vyy470), Just(vyy480), app(ty_[], bcg)) → new_esEs0(vyy470, vyy480, bcg)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(app(ty_@2, eh), fa), ba, da) → new_esEs2(vyy470, vyy480, eh, fa)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_FiniteMap, dc), dd), da) → new_esEs1(vyy471, vyy481, dc, dd)
new_esEs3(Just(vyy470), Just(vyy480), app(app(ty_Either, bde), bdf)) → new_esEs4(vyy470, vyy480, bde, bdf)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_Either, dh), ea), da) → new_esEs4(vyy471, vyy481, dh, ea)
new_esEs4(Left(vyy470), Left(vyy480), app(app(ty_Either, bfa), bfb), beb) → new_esEs4(vyy470, vyy480, bfa, bfb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(ty_@2, de), df), da) → new_esEs2(vyy471, vyy481, de, df)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(app(app(ty_@3, ce), cf), cg), da) → new_esEs(vyy471, vyy481, ce, cf, cg)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, app(ty_Maybe, dg), da) → new_esEs3(vyy471, vyy481, dg)
new_esEs4(Left(vyy470), Left(vyy480), app(ty_Maybe, beh), beb) → new_esEs3(vyy470, vyy480, beh)
new_esEs3(Just(vyy470), Just(vyy480), app(ty_Maybe, bdd)) → new_esEs3(vyy470, vyy480, bdd)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(ty_Maybe, cb)) → new_esEs3(vyy472, vyy482, cb)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), app(ty_[], ee), ba, da) → new_esEs0(vyy470, vyy480, ee)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(ty_[], hh)) → new_esEs0(vyy471, vyy481, hh)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_[], gb)) → new_esEs0(vyy470, vyy480, gb)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_@2, ge), gf)) → new_esEs2(vyy470, vyy480, ge, gf)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(app(ty_@3, bb), bc), bd)) → new_esEs(vyy472, vyy482, bb, bc, bd)
new_esEs(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), h, ba, app(app(ty_FiniteMap, bf), bg)) → new_esEs1(vyy472, vyy482, bf, bg)
The remaining pairs can at least be oriented weakly.
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bca), bbc) → new_esEs3(vyy470, vyy480, bca)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, fg), fh), ga)) → new_esEs(vyy470, vyy480, fg, fh, ga)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(ty_Maybe, bae)) → new_esEs3(vyy471, vyy481, bae)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs(vyy470, vyy480, bfd, bfe, bff)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bcb), bcc), bbc) → new_esEs4(vyy470, vyy480, bcb, bcc)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bah), bba), bbb), bbc) → new_esEs(vyy470, vyy480, bah, bba, bbb)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, gg)) → new_esEs3(vyy470, vyy480, gg)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, gh), ha)) → new_esEs4(vyy470, vyy480, gh, ha)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_FiniteMap, bbe), bbf), bbc) → new_esEs1(vyy470, vyy480, bbe, bbf)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(app(ty_@3, he), hf), hg)) → new_esEs(vyy471, vyy481, he, hf, hg)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_FiniteMap, gc), gd)) → new_esEs1(vyy470, vyy480, gc, gd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(ty_Maybe, bgd)) → new_esEs3(vyy470, vyy480, bgd)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_Either, baf), bag)) → new_esEs4(vyy471, vyy481, baf, bag)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_FiniteMap, bfh), bga)) → new_esEs1(vyy470, vyy480, bfh, bga)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_FiniteMap, baa), bab)) → new_esEs1(vyy471, vyy481, baa, bab)
Used ordering: Polynomial interpretation [25]:
POL(:(x1, x2)) = 1 + x1 + x2
POL(@2(x1, x2)) = 1 + x1 + x2
POL(@3(x1, x2, x3)) = 1 + x1 + x2 + x3
POL(Branch(x1, x2, x3, x4, x5)) = 1 + x1 + x2 + x4 + x5
POL(EmptyFM) = 1
POL(Just(x1)) = 1 + x1
POL(Left(x1)) = 1 + x1
POL(Right(x1)) = x1
POL([]) = 0
POL(app(x1, x2)) = 0
POL(new_esEs(x1, x2, x3, x4, x5)) = 1 + x2
POL(new_esEs0(x1, x2, x3)) = x2
POL(new_esEs1(x1, x2, x3, x4)) = 1 + x2
POL(new_esEs2(x1, x2, x3, x4)) = x2
POL(new_esEs3(x1, x2, x3)) = 1 + x2
POL(new_esEs4(x1, x2, x3, x4)) = 1 + x2
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = 1 + x1 + x2 + x3 + x4
POL(new_foldFM2(x1, x2, x3)) = x1
POL(ty_@2) = 0
POL(ty_@3) = 0
POL(ty_Either) = 0
POL(ty_FiniteMap) = 0
POL(ty_Maybe) = 0
POL(ty_[]) = 0
The following usable rules [17] were oriented:
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), hb, hc) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, hb, hc), vyy473, hb, hc)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), hb, hc) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, hb, hc), vyy4733, hb, hc)
new_foldFM2(EmptyFM, hb, hc) → []
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, hb, hc) → :(@2(vyy470, vyy471), vyy102)
↳ 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(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(app(ty_@3, bah), bba), bbb), bbc) → new_esEs(vyy470, vyy480, bah, bba, bbb)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(ty_Maybe, gg)) → new_esEs3(vyy470, vyy480, gg)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_Either, gh), ha)) → new_esEs4(vyy470, vyy480, gh, ha)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_Either, baf), bag)) → new_esEs4(vyy471, vyy481, baf, bag)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_FiniteMap, bfh), bga)) → new_esEs1(vyy470, vyy480, bfh, bga)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(ty_Maybe, bca), bbc) → new_esEs3(vyy470, vyy480, bca)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_FiniteMap, bbe), bbf), bbc) → new_esEs1(vyy470, vyy480, bbe, bbf)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(app(ty_@3, fg), fh), ga)) → new_esEs(vyy470, vyy480, fg, fh, ga)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(ty_Maybe, bae)) → new_esEs3(vyy471, vyy481, bae)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs(vyy470, vyy480, bfd, bfe, bff)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(app(ty_@3, he), hf), hg)) → new_esEs(vyy471, vyy481, he, hf, hg)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), hd, app(app(ty_FiniteMap, baa), bab)) → new_esEs1(vyy471, vyy481, baa, bab)
new_esEs0(:(vyy470, vyy471), :(vyy480, vyy481), app(app(ty_FiniteMap, gc), gd)) → new_esEs1(vyy470, vyy480, gc, gd)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy470, vyy480, bge, bgf)
new_esEs2(@2(vyy470, vyy471), @2(vyy480, vyy481), app(app(ty_Either, bcb), bcc), bbc) → new_esEs4(vyy470, vyy480, bcb, bcc)
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(ty_Maybe, bgd)) → new_esEs3(vyy470, vyy480, bgd)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), hb, hc) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, hb, hc), vyy473, hb, hc)
new_foldFM2(EmptyFM, hb, hc) → []
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, hb, hc) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), hb, hc) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, hb, hc), vyy4733, hb, hc)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 15 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
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy470, vyy480, bge, bgf)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), hb, hc) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, hb, hc), vyy473, hb, hc)
new_foldFM2(EmptyFM, hb, hc) → []
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, hb, hc) → :(@2(vyy470, vyy471), vyy102)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), hb, hc) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, hb, hc), vyy4733, hb, hc)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy470, vyy480, bge, bgf)
R is empty.
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
↳ 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
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(Right(vyy470), Right(vyy480), bfc, app(app(ty_Either, bge), bgf)) → 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(Right(vyy470), Right(vyy480), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy470, vyy480, bge, bgf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 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
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_lt3(vyy3000, vyy400, cb) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, cb), cb)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_@2, fc), fd), fb) → new_lt0(vyy3000, vyy400, fc, fd)
new_ltEs1(:(vyy3000, vyy3001), :(vyy400, vyy401), hd) → new_compare(vyy3001, vyy401, hd)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), hd) → new_primCompAux(vyy3000, vyy400, new_compare3(vyy3001, vyy401, hd), hd)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(app(ty_@2, cg), da), bd) → new_lt0(vyy3001, vyy401, cg, da)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_Maybe, ga), fb) → new_lt3(vyy3000, vyy400, ga)
new_lt(vyy3000, vyy400, h, ba, bb) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
new_ltEs2(Left(vyy3000), Left(vyy400), app(app(ty_Either, bbe), bbf), bba) → new_ltEs2(vyy3000, vyy400, bbe, bbf)
new_primCompAux(vyy3000, vyy400, vyy84, app(app(app(ty_@3, he), hf), hg)) → new_compare0(vyy3000, vyy400, he, hf, hg)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(app(ty_Either, dc), dd), bd) → new_lt2(vyy3001, vyy401, dc, dd)
new_compare5(vyy3000, vyy400, cb) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, cb), cb)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_Maybe, cb), bc, bd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, cb), cb)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(app(app(ty_@3, gc), gd), ge)) → new_ltEs(vyy3001, vyy401, gc, gd, ge)
new_ltEs2(Left(vyy3000), Left(vyy400), app(app(ty_@2, bbb), bbc), bba) → new_ltEs0(vyy3000, vyy400, bbb, bbc)
new_ltEs1(:(vyy3000, vyy3001), :(vyy400, vyy401), hd) → new_primCompAux(vyy3000, vyy400, new_compare3(vyy3001, vyy401, hd), hd)
new_ltEs2(Left(vyy3000), Left(vyy400), app(ty_Maybe, bbg), bba) → new_ltEs3(vyy3000, vyy400, bbg)
new_primCompAux(vyy3000, vyy400, vyy84, app(ty_[], bab)) → new_compare(vyy3000, vyy400, bab)
new_compare22(vyy3000, vyy400, False, cb) → new_ltEs3(vyy3000, vyy400, cb)
new_compare0(vyy3000, vyy400, h, ba, bb) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
new_ltEs3(Just(vyy3000), Just(vyy400), app(app(ty_Either, bdh), bea)) → new_ltEs2(vyy3000, vyy400, bdh, bea)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(app(ty_Either, ed), ee)) → new_ltEs2(vyy3002, vyy402, ed, ee)
new_compare20(vyy3000, vyy400, False, be, bf) → new_ltEs0(vyy3000, vyy400, be, bf)
new_ltEs2(Right(vyy3000), Right(vyy400), bbh, app(ty_[], bcf)) → new_ltEs1(vyy3000, vyy400, bcf)
new_ltEs2(Right(vyy3000), Right(vyy400), bbh, app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs(vyy3000, vyy400, bca, bcb, bcc)
new_ltEs2(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, baf), bag), bah), bba) → new_ltEs(vyy3000, vyy400, baf, bag, bah)
new_primCompAux(vyy3000, vyy400, vyy84, app(app(ty_Either, bac), bad)) → new_compare4(vyy3000, vyy400, bac, bad)
new_ltEs3(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs(vyy3000, vyy400, bdb, bdc, bdd)
new_lt2(vyy3000, vyy400, bh, ca) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bh, ca), bh, ca)
new_ltEs2(Right(vyy3000), Right(vyy400), bbh, app(app(ty_Either, bcg), bch)) → new_ltEs2(vyy3000, vyy400, bcg, bch)
new_compare21(vyy3000, vyy400, False, bh, ca) → new_ltEs2(vyy3000, vyy400, bh, ca)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_Either, bh), ca), bc, bd) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bh, ca), bh, ca)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(app(ty_@2, gf), gg)) → new_ltEs0(vyy3001, vyy401, gf, gg)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(ty_[], gh)) → new_ltEs1(vyy3001, vyy401, gh)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(app(ty_@3, h), ba), bb), bc, bd) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
new_compare4(vyy3000, vyy400, bh, ca) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bh, ca), bh, ca)
new_lt1(vyy3000, vyy400, bg) → new_compare(vyy3000, vyy400, bg)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(app(app(ty_@3, cd), ce), cf), bd) → new_lt(vyy3001, vyy401, cd, ce, cf)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(ty_Maybe, hc)) → new_ltEs3(vyy3001, vyy401, hc)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_[], ff), fb) → new_lt1(vyy3000, vyy400, ff)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(ty_Maybe, ef)) → new_ltEs3(vyy3002, vyy402, ef)
new_ltEs3(Just(vyy3000), Just(vyy400), app(app(ty_@2, bde), bdf)) → new_ltEs0(vyy3000, vyy400, bde, bdf)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(app(ty_Either, ha), hb)) → new_ltEs2(vyy3001, vyy401, ha, hb)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), hd) → new_compare(vyy3001, vyy401, hd)
new_lt0(vyy3000, vyy400, be, bf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
new_compare2(vyy3000, vyy400, False, h, ba, bb) → new_ltEs(vyy3000, vyy400, h, ba, bb)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_@2, be), bf), bc, bd) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
new_primCompAux(vyy3000, vyy400, vyy84, app(ty_Maybe, bae)) → new_compare5(vyy3000, vyy400, bae)
new_ltEs2(Right(vyy3000), Right(vyy400), bbh, app(app(ty_@2, bcd), bce)) → new_ltEs0(vyy3000, vyy400, bcd, bce)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(app(ty_@3, eg), eh), fa), fb) → new_lt(vyy3000, vyy400, eg, eh, fa)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_[], bg), bc, bd) → new_compare(vyy3000, vyy400, bg)
new_ltEs2(Right(vyy3000), Right(vyy400), bbh, app(ty_Maybe, bda)) → new_ltEs3(vyy3000, vyy400, bda)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(ty_[], db), bd) → new_lt1(vyy3001, vyy401, db)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(app(app(ty_@3, df), dg), dh)) → new_ltEs(vyy3002, vyy402, df, dg, dh)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(ty_Maybe, de), bd) → new_lt3(vyy3001, vyy401, de)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_Either, fg), fh), fb) → new_lt2(vyy3000, vyy400, fg, fh)
new_primCompAux(vyy3000, vyy400, vyy84, app(app(ty_@2, hh), baa)) → new_compare1(vyy3000, vyy400, hh, baa)
new_compare1(vyy3000, vyy400, be, bf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
new_ltEs3(Just(vyy3000), Just(vyy400), app(ty_Maybe, beb)) → new_ltEs3(vyy3000, vyy400, beb)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(app(ty_@2, ea), eb)) → new_ltEs0(vyy3002, vyy402, ea, eb)
new_ltEs2(Left(vyy3000), Left(vyy400), app(ty_[], bbd), bba) → new_ltEs1(vyy3000, vyy400, bbd)
new_ltEs3(Just(vyy3000), Just(vyy400), app(ty_[], bdg)) → new_ltEs1(vyy3000, vyy400, bdg)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(ty_[], ec)) → new_ltEs1(vyy3002, vyy402, ec)
The TRS R consists of the following rules:
new_esEs28(vyy470, vyy480, app(ty_[], chb)) → new_esEs13(vyy470, vyy480, chb)
new_ltEs14(vyy3002, vyy402, app(ty_Maybe, ef)) → new_ltEs7(vyy3002, vyy402, ef)
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, ty_Double) → new_ltEs18(vyy3000, vyy400)
new_compare3(:(vyy3000, vyy3001), :(vyy400, vyy401), hd) → new_primCompAux0(vyy3000, vyy400, new_compare3(vyy3001, vyy401, hd), hd)
new_esEs7(Left(vyy470), Left(vyy480), app(app(ty_Either, dbe), dbf), bfh) → new_esEs7(vyy470, vyy480, dbe, dbf)
new_esEs8(Just(vyy470), Just(vyy480), app(app(ty_@2, cea), ceb)) → new_esEs6(vyy470, vyy480, cea, ceb)
new_lt11(vyy3001, vyy401, ty_Bool) → new_lt17(vyy3001, vyy401)
new_esEs5(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), bee, bef, beg) → new_asAs(new_esEs26(vyy470, vyy480, bee), new_asAs(new_esEs25(vyy471, vyy481, bef), new_esEs24(vyy472, vyy482, beg)))
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs17(vyy3000, vyy400)
new_esEs24(vyy472, vyy482, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs5(vyy472, vyy482, bgb, bgc, bgd)
new_ltEs14(vyy3002, vyy402, ty_Integer) → new_ltEs9(vyy3002, vyy402)
new_esEs11(vyy47, vyy48, ty_Integer) → new_esEs18(vyy47, vyy48)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs17(Char(vyy470), Char(vyy480)) → new_primEqNat0(vyy470, vyy480)
new_esEs13([], [], beh) → True
new_esEs10(GT) → False
new_esEs24(vyy472, vyy482, ty_Char) → new_esEs17(vyy472, vyy482)
new_esEs23(vyy470, vyy480, ty_Integer) → new_esEs18(vyy470, vyy480)
new_compare10(vyy3000, vyy400, True, be, bf) → LT
new_esEs29(vyy470, vyy480, ty_Double) → new_esEs14(vyy470, vyy480)
new_esEs26(vyy470, vyy480, ty_Double) → new_esEs14(vyy470, vyy480)
new_ltEs5(EQ, GT) → True
new_ltEs14(vyy3002, vyy402, app(app(app(ty_@3, df), dg), dh)) → new_ltEs13(vyy3002, vyy402, df, dg, dh)
new_ltEs11(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, baf), bag), bah), bba) → new_ltEs13(vyy3000, vyy400, baf, bag, bah)
new_esEs25(vyy471, vyy481, ty_Char) → new_esEs17(vyy471, vyy481)
new_compare31(vyy3000, vyy400, ty_Int) → new_compare8(vyy3000, vyy400)
new_lt13(vyy3000, vyy400, h, ba, bb) → new_esEs10(new_compare32(vyy3000, vyy400, h, ba, bb))
new_esEs8(Just(vyy470), Just(vyy480), app(ty_Ratio, cec)) → new_esEs20(vyy470, vyy480, cec)
new_esEs29(vyy470, vyy480, app(ty_Ratio, dec)) → new_esEs20(vyy470, vyy480, dec)
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, ty_Ordering) → new_ltEs5(vyy3000, vyy400)
new_primMulNat0(Zero, Zero) → Zero
new_esEs7(Left(vyy470), Left(vyy480), app(app(app(ty_@3, dac), dad), dae), bfh) → new_esEs5(vyy470, vyy480, dac, dad, dae)
new_esEs26(vyy470, vyy480, ty_Float) → new_esEs15(vyy470, vyy480)
new_ltEs11(Right(vyy3000), Left(vyy400), bbh, bba) → False
new_esEs7(Right(vyy470), Right(vyy480), bfg, ty_Double) → new_esEs14(vyy470, vyy480)
new_esEs7(Left(vyy470), Left(vyy480), ty_Double, bfh) → new_esEs14(vyy470, vyy480)
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, app(app(ty_@2, bcd), bce)) → new_ltEs6(vyy3000, vyy400, bcd, bce)
new_compare9(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare25(vyy3000, vyy400, True, cb) → EQ
new_esEs7(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, dag), dah), bfh) → new_esEs19(vyy470, vyy480, dag, dah)
new_esEs8(Just(vyy470), Just(vyy480), ty_Integer) → new_esEs18(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, ty_Integer) → new_ltEs9(vyy3001, vyy401)
new_ltEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs13(vyy3000, vyy400, bdb, bdc, bdd)
new_ltEs17(vyy300, vyy40) → new_not(new_compare30(vyy300, vyy40))
new_not(GT) → False
new_esEs10(EQ) → False
new_ltEs14(vyy3002, vyy402, app(ty_[], ec)) → new_ltEs15(vyy3002, vyy402, ec)
new_esEs7(Right(vyy470), Right(vyy480), bfg, app(app(app(ty_@3, dbg), dbh), dca)) → new_esEs5(vyy470, vyy480, dbg, dbh, dca)
new_lt10(vyy3000, vyy400, ty_Float) → new_lt7(vyy3000, vyy400)
new_lt19(vyy3000, vyy400) → new_esEs10(new_compare30(vyy3000, vyy400))
new_lt8(vyy3000, vyy400, bga) → new_esEs10(new_compare7(vyy3000, vyy400, bga))
new_compare29(vyy3000, vyy400) → new_compare28(vyy3000, vyy400, new_esEs21(vyy3000, vyy400))
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs5(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, app(app(ty_@2, fc), fd)) → new_lt9(vyy3000, vyy400, fc, fd)
new_ltEs5(EQ, LT) → False
new_ltEs11(Left(vyy3000), Left(vyy400), ty_@0, bba) → new_ltEs10(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, ty_Double) → new_esEs14(vyy471, vyy481)
new_esEs25(vyy471, vyy481, ty_Bool) → new_esEs21(vyy471, vyy481)
new_esEs28(vyy470, vyy480, ty_Double) → new_esEs14(vyy470, vyy480)
new_esEs11(vyy47, vyy48, app(ty_Ratio, bfe)) → new_esEs20(vyy47, vyy48, bfe)
new_compare31(vyy3000, vyy400, app(app(ty_Either, bac), bad)) → new_compare33(vyy3000, vyy400, bac, bad)
new_compare15(vyy3000, vyy400, False) → GT
new_compare31(vyy3000, vyy400, ty_Char) → new_compare30(vyy3000, vyy400)
new_esEs28(vyy470, vyy480, ty_Bool) → new_esEs21(vyy470, vyy480)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt15(vyy3000, vyy400)
new_esEs28(vyy470, vyy480, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs5(vyy470, vyy480, cgg, cgh, cha)
new_lt4(vyy3000, vyy400) → new_esEs10(new_compare8(vyy3000, vyy400))
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Integer, bba) → new_ltEs9(vyy3000, vyy400)
new_esEs27(vyy471, vyy481, ty_Double) → new_esEs14(vyy471, vyy481)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs9(vyy3000, vyy400)
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, bfa, bfb) → :(@2(vyy470, vyy471), vyy102)
new_esEs8(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, cdg), cdh)) → new_esEs19(vyy470, vyy480, cdg, cdh)
new_esEs19(vyy47, vyy48, bfa, bfb) → new_asAs(new_esEs12(new_sizeFM(vyy47, bfa, bfb), new_sizeFM(vyy48, bfa, bfb)), new_esEs13(new_fmToList(vyy47, bfa, bfb), new_fmToList(vyy48, bfa, bfb), app(app(ty_@2, bfa), bfb)))
new_compare31(vyy3000, vyy400, app(app(ty_@2, hh), baa)) → new_compare27(vyy3000, vyy400, hh, baa)
new_esEs7(Left(vyy470), Right(vyy480), bfg, bfh) → False
new_esEs7(Right(vyy470), Left(vyy480), bfg, bfh) → False
new_lt14(vyy3000, vyy400) → new_esEs10(new_compare18(vyy3000, vyy400))
new_esEs27(vyy471, vyy481, ty_@0) → new_esEs16(vyy471, vyy481)
new_ltEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, fb) → new_pePe(new_lt20(vyy3000, vyy400, gb), vyy3000, vyy400, new_ltEs19(vyy3001, vyy401, fb), gb)
new_ltEs12(True, False) → False
new_compare23(vyy3000, vyy400, True) → EQ
new_esEs27(vyy471, vyy481, app(app(ty_Either, cge), cgf)) → new_esEs7(vyy471, vyy481, cge, cgf)
new_esEs28(vyy470, vyy480, ty_Integer) → new_esEs18(vyy470, vyy480)
new_lt11(vyy3001, vyy401, app(ty_Maybe, de)) → new_lt5(vyy3001, vyy401, de)
new_esEs27(vyy471, vyy481, ty_Ordering) → new_esEs9(vyy471, vyy481)
new_esEs29(vyy470, vyy480, ty_Float) → new_esEs15(vyy470, vyy480)
new_compare31(vyy3000, vyy400, ty_Bool) → new_compare29(vyy3000, vyy400)
new_ltEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, bde), bdf)) → new_ltEs6(vyy3000, vyy400, bde, bdf)
new_compare15(vyy3000, vyy400, True) → LT
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, eg), eh), fa)) → new_lt13(vyy3000, vyy400, eg, eh, fa)
new_compare11(vyy3000, vyy400, False, h, ba, bb) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs29(vyy470, vyy480, app(ty_Maybe, ded)) → new_esEs8(vyy470, vyy480, ded)
new_ltEs11(Left(vyy3000), Left(vyy400), app(ty_[], bbd), bba) → new_ltEs15(vyy3000, vyy400, bbd)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_esEs7(Left(vyy470), Left(vyy480), ty_Int, bfh) → new_esEs12(vyy470, vyy480)
new_lt9(vyy3000, vyy400, be, bf) → new_esEs10(new_compare27(vyy3000, vyy400, be, bf))
new_ltEs15(vyy300, vyy40, hd) → new_not(new_compare3(vyy300, vyy40, hd))
new_ltEs16(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_esEs25(vyy471, vyy481, app(app(ty_@2, cad), cae)) → new_esEs6(vyy471, vyy481, cad, cae)
new_lt10(vyy3000, vyy400, ty_Ordering) → new_lt15(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_lt11(vyy3001, vyy401, app(app(ty_Either, dc), dd)) → new_lt18(vyy3001, vyy401, dc, dd)
new_esEs11(vyy47, vyy48, app(app(ty_FiniteMap, bfa), bfb)) → new_esEs19(vyy47, vyy48, bfa, bfb)
new_esEs24(vyy472, vyy482, ty_Int) → new_esEs12(vyy472, vyy482)
new_esEs11(vyy47, vyy48, ty_Bool) → new_esEs21(vyy47, vyy48)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs10(vyy3000, vyy400)
new_esEs21(True, True) → True
new_esEs24(vyy472, vyy482, app(app(ty_Either, bhd), bhe)) → new_esEs7(vyy472, vyy482, bhd, bhe)
new_ltEs14(vyy3002, vyy402, app(app(ty_@2, ea), eb)) → new_ltEs6(vyy3002, vyy402, ea, eb)
new_esEs7(Right(vyy470), Right(vyy480), bfg, ty_Float) → new_esEs15(vyy470, vyy480)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Double, bba) → new_ltEs18(vyy3000, vyy400)
new_compare7(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare8(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs24(vyy472, vyy482, app(app(ty_@2, bgh), bha)) → new_esEs6(vyy472, vyy482, bgh, bha)
new_primEqNat0(Zero, Zero) → True
new_ltEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, bdh), bea)) → new_ltEs11(vyy3000, vyy400, bdh, bea)
new_ltEs12(False, False) → True
new_esEs26(vyy470, vyy480, ty_Char) → new_esEs17(vyy470, vyy480)
new_lt10(vyy3000, vyy400, app(ty_Ratio, bga)) → new_lt8(vyy3000, vyy400, bga)
new_esEs28(vyy470, vyy480, ty_@0) → new_esEs16(vyy470, vyy480)
new_esEs7(Left(vyy470), Left(vyy480), ty_Ordering, bfh) → new_esEs9(vyy470, vyy480)
new_lt20(vyy3000, vyy400, app(ty_Ratio, cfa)) → new_lt8(vyy3000, vyy400, cfa)
new_esEs26(vyy470, vyy480, ty_@0) → new_esEs16(vyy470, vyy480)
new_esEs29(vyy470, vyy480, app(ty_[], ddf)) → new_esEs13(vyy470, vyy480, ddf)
new_ltEs19(vyy3001, vyy401, ty_Float) → new_ltEs8(vyy3001, vyy401)
new_esEs25(vyy471, vyy481, ty_Integer) → new_esEs18(vyy471, vyy481)
new_compare25(vyy3000, vyy400, False, cb) → new_compare13(vyy3000, vyy400, new_ltEs7(vyy3000, vyy400, cb), cb)
new_ltEs14(vyy3002, vyy402, app(ty_Ratio, ccg)) → new_ltEs4(vyy3002, vyy402, ccg)
new_esEs20(:%(vyy470, vyy471), :%(vyy480, vyy481), bfe) → new_asAs(new_esEs23(vyy470, vyy480, bfe), new_esEs22(vyy471, vyy481, bfe))
new_sr(vyy3000, vyy400) → new_primMulInt(vyy3000, vyy400)
new_lt10(vyy3000, vyy400, ty_Int) → new_lt4(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, app(app(ty_FiniteMap, cab), cac)) → new_esEs19(vyy471, vyy481, cab, cac)
new_lt11(vyy3001, vyy401, app(ty_Ratio, ccf)) → new_lt8(vyy3001, vyy401, ccf)
new_esEs8(Just(vyy470), Just(vyy480), ty_Bool) → new_esEs21(vyy470, vyy480)
new_compare31(vyy3000, vyy400, ty_Double) → new_compare9(vyy3000, vyy400)
new_esEs26(vyy470, vyy480, ty_Int) → new_esEs12(vyy470, vyy480)
new_compare31(vyy3000, vyy400, app(app(app(ty_@3, he), hf), hg)) → new_compare32(vyy3000, vyy400, he, hf, hg)
new_esEs29(vyy470, vyy480, app(app(ty_FiniteMap, ddg), ddh)) → new_esEs19(vyy470, vyy480, ddg, ddh)
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, ty_Bool) → new_ltEs12(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy1030), vyy40000) → Succ(Succ(new_primPlusNat1(vyy1030, vyy40000)))
new_esEs7(Left(vyy470), Left(vyy480), ty_Bool, bfh) → new_esEs21(vyy470, vyy480)
new_esEs7(Right(vyy470), Right(vyy480), bfg, app(app(ty_Either, dda), ddb)) → new_esEs7(vyy470, vyy480, dda, ddb)
new_ltEs19(vyy3001, vyy401, ty_Bool) → new_ltEs12(vyy3001, vyy401)
new_ltEs5(LT, LT) → True
new_esEs7(Right(vyy470), Right(vyy480), bfg, app(ty_[], dcb)) → new_esEs13(vyy470, vyy480, dcb)
new_esEs23(vyy470, vyy480, ty_Int) → new_esEs12(vyy470, vyy480)
new_lt5(vyy3000, vyy400, cb) → new_esEs10(new_compare14(vyy3000, vyy400, cb))
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs16(vyy3000, vyy400)
new_esEs8(Just(vyy470), Nothing, bff) → False
new_esEs8(Nothing, Just(vyy480), bff) → False
new_esEs9(EQ, EQ) → True
new_ltEs14(vyy3002, vyy402, ty_Bool) → new_ltEs12(vyy3002, vyy402)
new_esEs29(vyy470, vyy480, ty_Int) → new_esEs12(vyy470, vyy480)
new_primEqInt(Neg(Succ(vyy4700)), Neg(Succ(vyy4800))) → new_primEqNat0(vyy4700, vyy4800)
new_esEs7(Right(vyy470), Right(vyy480), bfg, ty_Char) → new_esEs17(vyy470, vyy480)
new_lt11(vyy3001, vyy401, ty_@0) → new_lt12(vyy3001, vyy401)
new_esEs26(vyy470, vyy480, app(ty_Maybe, ccc)) → new_esEs8(vyy470, vyy480, ccc)
new_ltEs11(Left(vyy3000), Left(vyy400), app(app(ty_@2, bbb), bbc), bba) → new_ltEs6(vyy3000, vyy400, bbb, bbc)
new_lt10(vyy3000, vyy400, app(app(ty_Either, bh), ca)) → new_lt18(vyy3000, vyy400, bh, ca)
new_esEs26(vyy470, vyy480, app(ty_[], cbe)) → new_esEs13(vyy470, vyy480, cbe)
new_ltEs7(Just(vyy3000), Just(vyy400), app(ty_[], bdg)) → new_ltEs15(vyy3000, vyy400, bdg)
new_primPlusNat1(Zero, Succ(vyy400000)) → Succ(vyy400000)
new_primPlusNat1(Succ(vyy10300), Zero) → Succ(vyy10300)
new_esEs11(vyy47, vyy48, ty_Int) → new_esEs12(vyy47, vyy48)
new_lt20(vyy3000, vyy400, ty_Int) → new_lt4(vyy3000, vyy400)
new_esEs28(vyy470, vyy480, app(ty_Maybe, chh)) → new_esEs8(vyy470, vyy480, chh)
new_compare16(vyy3000, vyy400, True) → LT
new_compare3([], :(vyy400, vyy401), hd) → LT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs28(vyy470, vyy480, app(app(ty_FiniteMap, chc), chd)) → new_esEs19(vyy470, vyy480, chc, chd)
new_esEs7(Left(vyy470), Left(vyy480), app(app(ty_@2, dba), dbb), bfh) → new_esEs6(vyy470, vyy480, dba, dbb)
new_esEs27(vyy471, vyy481, ty_Int) → new_esEs12(vyy471, vyy481)
new_compare3(:(vyy3000, vyy3001), [], hd) → GT
new_compare11(vyy3000, vyy400, True, h, ba, bb) → LT
new_compare31(vyy3000, vyy400, app(ty_[], bab)) → new_compare3(vyy3000, vyy400, bab)
new_esEs11(vyy47, vyy48, app(app(app(ty_@3, bee), bef), beg)) → new_esEs5(vyy47, vyy48, bee, bef, beg)
new_esEs11(vyy47, vyy48, ty_Float) → new_esEs15(vyy47, vyy48)
new_compare8(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4800))) → False
new_primEqInt(Neg(Succ(vyy4700)), Neg(Zero)) → False
new_esEs25(vyy471, vyy481, ty_Ordering) → new_esEs9(vyy471, vyy481)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Char, bba) → new_ltEs17(vyy3000, vyy400)
new_compare26(vyy3000, vyy400, True, bh, ca) → EQ
new_compare24(vyy3000, vyy400, True, be, bf) → EQ
new_ltEs19(vyy3001, vyy401, ty_Char) → new_ltEs17(vyy3001, vyy401)
new_esEs22(vyy471, vyy481, ty_Int) → new_esEs12(vyy471, vyy481)
new_lt20(vyy3000, vyy400, app(ty_Maybe, ga)) → new_lt5(vyy3000, vyy400, ga)
new_esEs8(Just(vyy470), Just(vyy480), ty_Float) → new_esEs15(vyy470, vyy480)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), bfa, bfb) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, bfa, bfb), vyy4733, bfa, bfb)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs26(vyy470, vyy480, app(app(ty_Either, ccd), cce)) → new_esEs7(vyy470, vyy480, ccd, cce)
new_esEs27(vyy471, vyy481, ty_Float) → new_esEs15(vyy471, vyy481)
new_lt7(vyy3000, vyy400) → new_esEs10(new_compare17(vyy3000, vyy400))
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs19(vyy3001, vyy401, app(ty_Ratio, cfb)) → new_ltEs4(vyy3001, vyy401, cfb)
new_sizeFM(EmptyFM, bfa, bfb) → Pos(Zero)
new_ltEs5(EQ, EQ) → True
new_esEs7(Right(vyy470), Right(vyy480), bfg, app(app(ty_@2, dce), dcf)) → new_esEs6(vyy470, vyy480, dce, dcf)
new_primEqInt(Pos(Succ(vyy4700)), Pos(Succ(vyy4800))) → new_primEqNat0(vyy4700, vyy4800)
new_compare10(vyy3000, vyy400, False, be, bf) → GT
new_esEs28(vyy470, vyy480, ty_Char) → new_esEs17(vyy470, vyy480)
new_ltEs7(Nothing, Just(vyy400), ceg) → True
new_primEqNat0(Succ(vyy4700), Succ(vyy4800)) → new_primEqNat0(vyy4700, vyy4800)
new_compare28(vyy3000, vyy400, False) → new_compare15(vyy3000, vyy400, new_ltEs12(vyy3000, vyy400))
new_esEs24(vyy472, vyy482, ty_@0) → new_esEs16(vyy472, vyy482)
new_lt20(vyy3000, vyy400, ty_@0) → new_lt12(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, ty_Float) → new_compare17(vyy3000, vyy400)
new_esEs7(Right(vyy470), Right(vyy480), bfg, ty_Bool) → new_esEs21(vyy470, vyy480)
new_primCompAux00(vyy88, LT) → LT
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, ty_@0) → new_ltEs10(vyy3000, vyy400)
new_ltEs11(Left(vyy3000), Left(vyy400), app(ty_Ratio, cch), bba) → new_ltEs4(vyy3000, vyy400, cch)
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs27(vyy471, vyy481, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs5(vyy471, vyy481, cfc, cfd, cfe)
new_ltEs14(vyy3002, vyy402, ty_Int) → new_ltEs16(vyy3002, vyy402)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4800))) → False
new_primEqInt(Pos(Succ(vyy4700)), Pos(Zero)) → False
new_ltEs14(vyy3002, vyy402, ty_Ordering) → new_ltEs5(vyy3002, vyy402)
new_compare13(vyy3000, vyy400, True, cb) → LT
new_esEs24(vyy472, vyy482, ty_Float) → new_esEs15(vyy472, vyy482)
new_ltEs5(GT, LT) → False
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, app(app(ty_Either, bcg), bch)) → new_ltEs11(vyy3000, vyy400, bcg, bch)
new_lt10(vyy3000, vyy400, ty_@0) → new_lt12(vyy3000, vyy400)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs11(vyy47, vyy48, ty_@0) → new_esEs16(vyy47, vyy48)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_lt12(vyy3000, vyy400) → new_esEs10(new_compare12(vyy3000, vyy400))
new_ltEs14(vyy3002, vyy402, ty_@0) → new_ltEs10(vyy3002, vyy402)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_ltEs13(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, bd) → new_pePe(new_lt10(vyy3000, vyy400, cc), vyy3000, vyy400, new_pePe(new_lt11(vyy3001, vyy401, bc), vyy3001, vyy401, new_ltEs14(vyy3002, vyy402, bd), bc), cc)
new_compare210(vyy3000, vyy400, True, h, ba, bb) → EQ
new_esEs7(Right(vyy470), Right(vyy480), bfg, app(app(ty_FiniteMap, dcc), dcd)) → new_esEs19(vyy470, vyy480, dcc, dcd)
new_esEs8(Just(vyy470), Just(vyy480), ty_Char) → new_esEs17(vyy470, vyy480)
new_sr0(Integer(vyy30000), Integer(vyy4010)) → Integer(new_primMulInt(vyy30000, vyy4010))
new_primPlusNat1(Succ(vyy10300), Succ(vyy400000)) → Succ(Succ(new_primPlusNat1(vyy10300, vyy400000)))
new_lt11(vyy3001, vyy401, app(app(app(ty_@3, cd), ce), cf)) → new_lt13(vyy3001, vyy401, cd, ce, cf)
new_esEs7(Right(vyy470), Right(vyy480), bfg, app(ty_Maybe, dch)) → new_esEs8(vyy470, vyy480, dch)
new_primEqInt(Neg(Succ(vyy4700)), Pos(vyy480)) → False
new_primEqInt(Pos(Succ(vyy4700)), Neg(vyy480)) → False
new_esEs8(Just(vyy470), Just(vyy480), ty_Int) → new_esEs12(vyy470, vyy480)
new_foldFM2(EmptyFM, bfa, bfb) → []
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Float, bba) → new_ltEs8(vyy3000, vyy400)
new_esEs7(Left(vyy470), Left(vyy480), ty_Float, bfh) → new_esEs15(vyy470, vyy480)
new_compare18(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_esEs24(vyy472, vyy482, app(ty_[], bge)) → new_esEs13(vyy472, vyy482, bge)
new_ltEs10(vyy300, vyy40) → new_not(new_compare12(vyy300, vyy40))
new_primEqInt(Neg(Zero), Pos(Succ(vyy4800))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4800))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCompAux00(vyy88, EQ) → vyy88
new_esEs28(vyy470, vyy480, app(app(ty_Either, daa), dab)) → new_esEs7(vyy470, vyy480, daa, dab)
new_lt10(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs18(vyy3000, vyy400)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs8(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, ty_Double) → new_ltEs18(vyy3001, vyy401)
new_esEs25(vyy471, vyy481, ty_Float) → new_esEs15(vyy471, vyy481)
new_ltEs19(vyy3001, vyy401, app(app(app(ty_@3, gc), gd), ge)) → new_ltEs13(vyy3001, vyy401, gc, gd, ge)
new_esEs27(vyy471, vyy481, app(ty_Maybe, cgd)) → new_esEs8(vyy471, vyy481, cgd)
new_lt10(vyy3000, vyy400, app(ty_Maybe, cb)) → new_lt5(vyy3000, vyy400, cb)
new_esEs26(vyy470, vyy480, app(app(ty_FiniteMap, cbf), cbg)) → new_esEs19(vyy470, vyy480, cbf, cbg)
new_esEs26(vyy470, vyy480, ty_Bool) → new_esEs21(vyy470, vyy480)
new_lt11(vyy3001, vyy401, ty_Integer) → new_lt14(vyy3001, vyy401)
new_esEs24(vyy472, vyy482, ty_Integer) → new_esEs18(vyy472, vyy482)
new_compare12(@0, @0) → EQ
new_lt18(vyy3000, vyy400, bh, ca) → new_esEs10(new_compare33(vyy3000, vyy400, bh, ca))
new_ltEs4(vyy300, vyy40, bec) → new_not(new_compare7(vyy300, vyy40, bec))
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primPlusNat0(Zero, vyy40000) → Succ(vyy40000)
new_esEs11(vyy47, vyy48, ty_Ordering) → new_esEs9(vyy47, vyy48)
new_esEs9(GT, GT) → True
new_compare210(vyy3000, vyy400, False, h, ba, bb) → new_compare11(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, h, ba, bb), h, ba, bb)
new_not0 → True
new_esEs24(vyy472, vyy482, ty_Bool) → new_esEs21(vyy472, vyy482)
new_pePe(False, vyy47, vyy48, vyy66, bed) → new_asAs(new_esEs11(vyy47, vyy48, bed), vyy66)
new_compare28(vyy3000, vyy400, True) → EQ
new_lt20(vyy3000, vyy400, ty_Double) → new_lt6(vyy3000, vyy400)
new_esEs11(vyy47, vyy48, app(ty_[], beh)) → new_esEs13(vyy47, vyy48, beh)
new_ltEs8(vyy300, vyy40) → new_not(new_compare17(vyy300, vyy40))
new_esEs28(vyy470, vyy480, ty_Ordering) → new_esEs9(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, app(ty_[], gh)) → new_ltEs15(vyy3001, vyy401, gh)
new_ltEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, beb)) → new_ltEs7(vyy3000, vyy400, beb)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs7(Right(vyy470), Right(vyy480), bfg, ty_Ordering) → new_esEs9(vyy470, vyy480)
new_esEs8(Just(vyy470), Just(vyy480), app(app(ty_Either, cee), cef)) → new_esEs7(vyy470, vyy480, cee, cef)
new_esEs29(vyy470, vyy480, ty_@0) → new_esEs16(vyy470, vyy480)
new_primMulInt(Pos(vyy30000), Pos(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_ltEs18(vyy300, vyy40) → new_not(new_compare9(vyy300, vyy40))
new_esEs21(False, False) → True
new_compare23(vyy3000, vyy400, False) → new_compare16(vyy3000, vyy400, new_ltEs5(vyy3000, vyy400))
new_lt16(vyy3000, vyy400, bg) → new_esEs10(new_compare3(vyy3000, vyy400, bg))
new_esEs7(Left(vyy470), Left(vyy480), ty_Integer, bfh) → new_esEs18(vyy470, vyy480)
new_esEs27(vyy471, vyy481, ty_Char) → new_esEs17(vyy471, vyy481)
new_compare7(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare18(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_ltEs5(LT, GT) → True
new_esEs7(Right(vyy470), Right(vyy480), bfg, ty_Int) → new_esEs12(vyy470, vyy480)
new_compare6(vyy3000, vyy400) → new_compare23(vyy3000, vyy400, new_esEs9(vyy3000, vyy400))
new_esEs27(vyy471, vyy481, app(app(ty_@2, cga), cgb)) → new_esEs6(vyy471, vyy481, cga, cgb)
new_primMulInt(Neg(vyy30000), Neg(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_esEs11(vyy47, vyy48, ty_Double) → new_esEs14(vyy47, vyy48)
new_lt10(vyy3000, vyy400, ty_Double) → new_lt6(vyy3000, vyy400)
new_esEs29(vyy470, vyy480, app(app(ty_@2, dea), deb)) → new_esEs6(vyy470, vyy480, dea, deb)
new_esEs8(Just(vyy470), Just(vyy480), ty_Ordering) → new_esEs9(vyy470, vyy480)
new_esEs7(Right(vyy470), Right(vyy480), bfg, ty_Integer) → new_esEs18(vyy470, vyy480)
new_primEqNat0(Zero, Succ(vyy4800)) → False
new_primEqNat0(Succ(vyy4700), Zero) → False
new_lt20(vyy3000, vyy400, app(app(ty_Either, fg), fh)) → new_lt18(vyy3000, vyy400, fg, fh)
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs13(vyy3000, vyy400, bca, bcb, bcc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt10(vyy3000, vyy400, ty_Bool) → new_lt17(vyy3000, vyy400)
new_esEs7(Left(vyy470), Left(vyy480), ty_Char, bfh) → new_esEs17(vyy470, vyy480)
new_esEs25(vyy471, vyy481, ty_Int) → new_esEs12(vyy471, vyy481)
new_ltEs14(vyy3002, vyy402, ty_Float) → new_ltEs8(vyy3002, vyy402)
new_esEs15(Float(vyy470, vyy471), Float(vyy480, vyy481)) → new_esEs12(new_sr(vyy470, vyy480), new_sr(vyy471, vyy481))
new_esEs7(Left(vyy470), Left(vyy480), ty_@0, bfh) → new_esEs16(vyy470, vyy480)
new_lt10(vyy3000, vyy400, app(app(ty_@2, be), bf)) → new_lt9(vyy3000, vyy400, be, bf)
new_sizeFM(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), bfa, bfb) → vyy472
new_lt17(vyy3000, vyy400) → new_esEs10(new_compare29(vyy3000, vyy400))
new_ltEs7(Nothing, Nothing, ceg) → True
new_pePe(True, vyy47, vyy48, vyy66, bed) → True
new_esEs27(vyy471, vyy481, app(ty_Ratio, cgc)) → new_esEs20(vyy471, vyy481, cgc)
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), bfa, bfb) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, bfa, bfb), vyy473, bfa, bfb)
new_esEs29(vyy470, vyy480, app(app(app(ty_@3, ddc), ddd), dde)) → new_esEs5(vyy470, vyy480, ddc, ddd, dde)
new_esEs7(Left(vyy470), Left(vyy480), app(ty_Maybe, dbd), bfh) → new_esEs8(vyy470, vyy480, dbd)
new_compare13(vyy3000, vyy400, False, cb) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_compare32(vyy3000, vyy400, h, ba, bb) → new_compare210(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
new_esEs12(vyy47, vyy48) → new_primEqInt(vyy47, vyy48)
new_compare19(vyy3000, vyy400, True, bh, ca) → LT
new_compare31(vyy3000, vyy400, ty_Ordering) → new_compare6(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, app(ty_Ratio, cdb)) → new_compare7(vyy3000, vyy400, cdb)
new_lt11(vyy3001, vyy401, ty_Char) → new_lt19(vyy3001, vyy401)
new_lt11(vyy3001, vyy401, app(ty_[], db)) → new_lt16(vyy3001, vyy401, db)
new_esEs28(vyy470, vyy480, app(app(ty_@2, che), chf)) → new_esEs6(vyy470, vyy480, che, chf)
new_esEs11(vyy47, vyy48, app(app(ty_Either, bfg), bfh)) → new_esEs7(vyy47, vyy48, bfg, bfh)
new_lt20(vyy3000, vyy400, ty_Float) → new_lt7(vyy3000, vyy400)
new_ltEs11(Left(vyy3000), Left(vyy400), app(app(ty_Either, bbe), bbf), bba) → new_ltEs11(vyy3000, vyy400, bbe, bbf)
new_lt11(vyy3001, vyy401, ty_Ordering) → new_lt15(vyy3001, vyy401)
new_esEs7(Right(vyy470), Right(vyy480), bfg, ty_@0) → new_esEs16(vyy470, vyy480)
new_compare33(vyy3000, vyy400, bh, ca) → new_compare26(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bh, ca), bh, ca)
new_esEs10(LT) → True
new_lt20(vyy3000, vyy400, app(ty_[], ff)) → new_lt16(vyy3000, vyy400, ff)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Ordering, bba) → new_ltEs5(vyy3000, vyy400)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Int, bba) → new_ltEs16(vyy3000, vyy400)
new_esEs11(vyy47, vyy48, app(app(ty_@2, bfc), bfd)) → new_esEs6(vyy47, vyy48, bfc, bfd)
new_esEs8(Nothing, Nothing, bff) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt6(vyy3000, vyy400) → new_esEs10(new_compare9(vyy3000, vyy400))
new_compare17(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs19(vyy3001, vyy401, app(app(ty_@2, gf), gg)) → new_ltEs6(vyy3001, vyy401, gf, gg)
new_esEs11(vyy47, vyy48, app(ty_Maybe, bff)) → new_esEs8(vyy47, vyy48, bff)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs12(vyy3000, vyy400)
new_asAs(False, vyy79) → False
new_esEs14(Double(vyy470, vyy471), Double(vyy480, vyy481)) → new_esEs12(new_sr(vyy470, vyy480), new_sr(vyy471, vyy481))
new_compare3([], [], hd) → EQ
new_ltEs11(Left(vyy3000), Right(vyy400), bbh, bba) → True
new_primMulInt(Neg(vyy30000), Pos(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulInt(Pos(vyy30000), Neg(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, app(ty_[], bcf)) → new_ltEs15(vyy3000, vyy400, bcf)
new_primMulNat0(Zero, Succ(vyy40000)) → Zero
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_esEs22(vyy471, vyy481, ty_Integer) → new_esEs18(vyy471, vyy481)
new_esEs13(:(vyy470, vyy471), [], beh) → False
new_esEs13([], :(vyy480, vyy481), beh) → False
new_esEs25(vyy471, vyy481, ty_@0) → new_esEs16(vyy471, vyy481)
new_ltEs5(LT, EQ) → True
new_esEs7(Left(vyy470), Left(vyy480), app(ty_[], daf), bfh) → new_esEs13(vyy470, vyy480, daf)
new_compare27(vyy3000, vyy400, be, bf) → new_compare24(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
new_esEs29(vyy470, vyy480, ty_Char) → new_esEs17(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, ty_@0) → new_ltEs10(vyy3001, vyy401)
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, ty_Char) → new_ltEs17(vyy3000, vyy400)
new_esEs27(vyy471, vyy481, ty_Integer) → new_esEs18(vyy471, vyy481)
new_esEs18(Integer(vyy470), Integer(vyy480)) → new_primEqInt(vyy470, vyy480)
new_esEs8(Just(vyy470), Just(vyy480), app(app(app(ty_@3, cdc), cdd), cde)) → new_esEs5(vyy470, vyy480, cdc, cdd, cde)
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, app(ty_Ratio, cda)) → new_ltEs4(vyy3000, vyy400, cda)
new_not(EQ) → new_not0
new_ltEs12(True, True) → True
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, app(ty_Maybe, bda)) → new_ltEs7(vyy3000, vyy400, bda)
new_esEs27(vyy471, vyy481, app(app(ty_FiniteMap, cfg), cfh)) → new_esEs19(vyy471, vyy481, cfg, cfh)
new_compare14(vyy3000, vyy400, cb) → new_compare25(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, cb), cb)
new_ltEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, ceh)) → new_ltEs4(vyy3000, vyy400, ceh)
new_lt11(vyy3001, vyy401, ty_Int) → new_lt4(vyy3001, vyy401)
new_compare31(vyy3000, vyy400, app(ty_Maybe, bae)) → new_compare14(vyy3000, vyy400, bae)
new_compare31(vyy3000, vyy400, ty_Integer) → new_compare18(vyy3000, vyy400)
new_ltEs14(vyy3002, vyy402, ty_Double) → new_ltEs18(vyy3002, vyy402)
new_ltEs12(False, True) → True
new_esEs24(vyy472, vyy482, app(app(ty_FiniteMap, bgf), bgg)) → new_esEs19(vyy472, vyy482, bgf, bgg)
new_esEs16(@0, @0) → True
new_esEs25(vyy471, vyy481, app(ty_[], caa)) → new_esEs13(vyy471, vyy481, caa)
new_ltEs19(vyy3001, vyy401, ty_Int) → new_ltEs16(vyy3001, vyy401)
new_esEs8(Just(vyy470), Just(vyy480), app(ty_[], cdf)) → new_esEs13(vyy470, vyy480, cdf)
new_compare31(vyy3000, vyy400, ty_@0) → new_compare12(vyy3000, vyy400)
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, ty_Int) → new_ltEs16(vyy3000, vyy400)
new_ltEs14(vyy3002, vyy402, ty_Char) → new_ltEs17(vyy3002, vyy402)
new_ltEs7(Just(vyy3000), Nothing, ceg) → False
new_esEs27(vyy471, vyy481, ty_Bool) → new_esEs21(vyy471, vyy481)
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, ty_Integer) → new_ltEs9(vyy3000, vyy400)
new_esEs13(:(vyy470, vyy471), :(vyy480, vyy481), beh) → new_asAs(new_esEs29(vyy470, vyy480, beh), new_esEs13(vyy471, vyy481, beh))
new_esEs28(vyy470, vyy480, app(ty_Ratio, chg)) → new_esEs20(vyy470, vyy480, chg)
new_esEs24(vyy472, vyy482, app(ty_Maybe, bhc)) → new_esEs8(vyy472, vyy482, bhc)
new_esEs8(Just(vyy470), Just(vyy480), ty_@0) → new_esEs16(vyy470, vyy480)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_not(LT) → new_not0
new_esEs26(vyy470, vyy480, ty_Integer) → new_esEs18(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, app(ty_Maybe, hc)) → new_ltEs7(vyy3001, vyy401, hc)
new_esEs25(vyy471, vyy481, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs5(vyy471, vyy481, bhf, bhg, bhh)
new_lt15(vyy3000, vyy400) → new_esEs10(new_compare6(vyy3000, vyy400))
new_esEs29(vyy470, vyy480, app(app(ty_Either, dee), def)) → new_esEs7(vyy470, vyy480, dee, def)
new_lt10(vyy3000, vyy400, app(app(app(ty_@3, h), ba), bb)) → new_lt13(vyy3000, vyy400, h, ba, bb)
new_lt10(vyy3000, vyy400, app(ty_[], bg)) → new_lt16(vyy3000, vyy400, bg)
new_esEs24(vyy472, vyy482, ty_Ordering) → new_esEs9(vyy472, vyy482)
new_esEs29(vyy470, vyy480, ty_Bool) → new_esEs21(vyy470, vyy480)
new_esEs28(vyy470, vyy480, ty_Int) → new_esEs12(vyy470, vyy480)
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt14(vyy3000, vyy400)
new_esEs28(vyy470, vyy480, ty_Float) → new_esEs15(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, ty_Ordering) → new_ltEs5(vyy3001, vyy401)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(vyy470, vyy480, ty_Ordering) → new_esEs9(vyy470, vyy480)
new_esEs7(Left(vyy470), Left(vyy480), app(ty_Ratio, dbc), bfh) → new_esEs20(vyy470, vyy480, dbc)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Bool, bba) → new_ltEs12(vyy3000, vyy400)
new_ltEs11(Right(vyy3000), Right(vyy400), bbh, ty_Float) → new_ltEs8(vyy3000, vyy400)
new_asAs(True, vyy79) → vyy79
new_lt10(vyy3000, vyy400, ty_Integer) → new_lt14(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300000), Succ(vyy40000)) → new_primPlusNat0(new_primMulNat0(vyy300000, Succ(vyy40000)), vyy40000)
new_esEs26(vyy470, vyy480, app(app(app(ty_@3, cbb), cbc), cbd)) → new_esEs5(vyy470, vyy480, cbb, cbc, cbd)
new_lt11(vyy3001, vyy401, ty_Float) → new_lt7(vyy3001, vyy401)
new_esEs27(vyy471, vyy481, app(ty_[], cff)) → new_esEs13(vyy471, vyy481, cff)
new_esEs11(vyy47, vyy48, ty_Char) → new_esEs17(vyy47, vyy48)
new_compare30(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_ltEs5(GT, GT) → True
new_esEs8(Just(vyy470), Just(vyy480), ty_Double) → new_esEs14(vyy470, vyy480)
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt17(vyy3000, vyy400)
new_esEs8(Just(vyy470), Just(vyy480), app(ty_Maybe, ced)) → new_esEs8(vyy470, vyy480, ced)
new_esEs29(vyy470, vyy480, ty_Integer) → new_esEs18(vyy470, vyy480)
new_esEs7(Right(vyy470), Right(vyy480), bfg, app(ty_Ratio, dcg)) → new_esEs20(vyy470, vyy480, dcg)
new_primCompAux0(vyy3000, vyy400, vyy84, hd) → new_primCompAux00(vyy84, new_compare31(vyy3000, vyy400, hd))
new_fmToList(vyy47, bfa, bfb) → new_foldFM2(vyy47, bfa, bfb)
new_ltEs9(vyy300, vyy40) → new_not(new_compare18(vyy300, vyy40))
new_esEs26(vyy470, vyy480, app(app(ty_@2, cbh), cca)) → new_esEs6(vyy470, vyy480, cbh, cca)
new_ltEs19(vyy3001, vyy401, app(app(ty_Either, ha), hb)) → new_ltEs11(vyy3001, vyy401, ha, hb)
new_esEs21(True, False) → False
new_esEs21(False, True) → False
new_esEs24(vyy472, vyy482, app(ty_Ratio, bhb)) → new_esEs20(vyy472, vyy482, bhb)
new_ltEs14(vyy3002, vyy402, app(app(ty_Either, ed), ee)) → new_ltEs11(vyy3002, vyy402, ed, ee)
new_compare24(vyy3000, vyy400, False, be, bf) → new_compare10(vyy3000, vyy400, new_ltEs6(vyy3000, vyy400, be, bf), be, bf)
new_lt11(vyy3001, vyy401, ty_Double) → new_lt6(vyy3001, vyy401)
new_compare26(vyy3000, vyy400, False, bh, ca) → new_compare19(vyy3000, vyy400, new_ltEs11(vyy3000, vyy400, bh, ca), bh, ca)
new_compare19(vyy3000, vyy400, False, bh, ca) → GT
new_esEs9(LT, LT) → True
new_primCompAux00(vyy88, GT) → GT
new_esEs25(vyy471, vyy481, app(app(ty_Either, cah), cba)) → new_esEs7(vyy471, vyy481, cah, cba)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs25(vyy471, vyy481, app(ty_Maybe, cag)) → new_esEs8(vyy471, vyy481, cag)
new_lt11(vyy3001, vyy401, app(app(ty_@2, cg), da)) → new_lt9(vyy3001, vyy401, cg, da)
new_ltEs5(GT, EQ) → False
new_esEs29(vyy470, vyy480, ty_Ordering) → new_esEs9(vyy470, vyy480)
new_esEs6(@2(vyy470, vyy471), @2(vyy480, vyy481), bfc, bfd) → new_asAs(new_esEs28(vyy470, vyy480, bfc), new_esEs27(vyy471, vyy481, bfd))
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs25(vyy471, vyy481, app(ty_Ratio, caf)) → new_esEs20(vyy471, vyy481, caf)
new_esEs26(vyy470, vyy480, app(ty_Ratio, ccb)) → new_esEs20(vyy470, vyy480, ccb)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs24(vyy472, vyy482, ty_Double) → new_esEs14(vyy472, vyy482)
new_compare16(vyy3000, vyy400, False) → GT
new_ltEs11(Left(vyy3000), Left(vyy400), app(ty_Maybe, bbg), bba) → new_ltEs7(vyy3000, vyy400, bbg)
The set Q consists of the following terms:
new_lt20(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, GT)
new_lt20(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), ty_Int)
new_compare6(x0, x1)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt13(x0, x1, x2, x3, x4)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs29(x0, x1, ty_Double)
new_esEs8(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs8(Just(x0), Nothing, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_esEs26(x0, x1, ty_@0)
new_compare10(x0, x1, True, x2, x3)
new_esEs28(x0, x1, ty_Bool)
new_fmToList(x0, x1, x2)
new_compare23(x0, x1, True)
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt9(x0, x1, x2, x3)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Bool)
new_compare19(x0, x1, True, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs24(x0, x1, ty_Char)
new_ltEs11(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt8(x0, x1, x2)
new_ltEs11(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare31(x0, x1, app(ty_[], x2))
new_ltEs14(x0, x1, ty_Bool)
new_ltEs5(GT, EQ)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs5(EQ, GT)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_compare9(Double(x0, x1), Double(x2, x3))
new_compare8(x0, x1)
new_lt19(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs11(Right(x0), Right(x1), x2, ty_Bool)
new_lt11(x0, x1, ty_Bool)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs10(GT)
new_compare24(x0, x1, True, x2, x3)
new_esEs26(x0, x1, ty_Char)
new_esEs12(x0, x1)
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs29(x0, x1, ty_Float)
new_compare30(Char(x0), Char(x1))
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_lt11(x0, x1, ty_Int)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs16(@0, @0)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, ty_Integer)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs11(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Int)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_esEs13([], [], x0)
new_lt10(x0, x1, ty_Char)
new_ltEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs11(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs11(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare15(x0, x1, True)
new_ltEs5(EQ, LT)
new_lt20(x0, x1, ty_@0)
new_ltEs5(LT, EQ)
new_esEs29(x0, x1, ty_@0)
new_ltEs11(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_esEs8(Nothing, Nothing, x0)
new_primEqNat0(Zero, Zero)
new_compare24(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_@0)
new_ltEs11(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs14(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_ltEs14(x0, x1, ty_Int)
new_ltEs14(x0, x1, ty_Double)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs11(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs11(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare25(x0, x1, True, x2)
new_lt11(x0, x1, ty_Char)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(Right(x0), Left(x1), x2, x3)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(Left(x0), Right(x1), x2, x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs11(x0, x1, ty_Char)
new_compare12(@0, @0)
new_esEs25(x0, x1, ty_Float)
new_compare28(x0, x1, True)
new_esEs15(Float(x0, x1), Float(x2, x3))
new_lt5(x0, x1, x2)
new_esEs8(Nothing, Just(x0), x1)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Zero)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs11(Right(x0), Right(x1), x2, ty_Double)
new_esEs23(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs8(Just(x0), Just(x1), ty_Float)
new_sizeFM(EmptyFM, x0, x1)
new_compare3(:(x0, x1), [], x2)
new_compare14(x0, x1, x2)
new_ltEs11(Left(x0), Left(x1), ty_Float, x2)
new_lt11(x0, x1, ty_Double)
new_ltEs14(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs14(x0, x1, ty_Ordering)
new_compare3([], :(x0, x1), x2)
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt18(x0, x1, x2, x3)
new_ltEs11(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_pePe(False, x0, x1, x2, x3)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Zero, x0)
new_compare17(Float(x0, x1), Float(x2, x3))
new_ltEs16(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_foldFM2(EmptyFM, x0, x1)
new_lt10(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_pePe(True, x0, x1, x2, x3)
new_ltEs11(Left(x0), Left(x1), ty_Int, x2)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_lt14(x0, x1)
new_ltEs11(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_compare23(x0, x1, False)
new_esEs28(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Double)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(False, False)
new_compare31(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs11(Right(x0), Right(x1), x2, ty_Integer)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False)
new_compare33(x0, x1, x2, x3)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs11(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare11(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare3([], [], x0)
new_esEs27(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_Double)
new_lt11(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat1(Zero, Zero)
new_not0
new_esEs24(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, False, x2)
new_lt10(x0, x1, ty_@0)
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_ltEs7(Nothing, Just(x0), x1)
new_asAs(True, x0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs28(x0, x1, ty_Integer)
new_esEs13([], :(x0, x1), x2)
new_ltEs11(Right(x0), Right(x1), x2, ty_Ordering)
new_compare10(x0, x1, False, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs18(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_primCompAux00(x0, LT)
new_ltEs11(Right(x0), Right(x1), x2, ty_@0)
new_asAs(False, x0)
new_primEqNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_not(GT)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(GT, GT)
new_lt10(x0, x1, app(ty_[], x2))
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_ltEs7(Nothing, Nothing, x0)
new_ltEs10(x0, x1)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare26(x0, x1, True, x2, x3)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt11(x0, x1, ty_Float)
new_lt4(x0, x1)
new_compare31(x0, x1, ty_Ordering)
new_ltEs14(x0, x1, app(ty_Maybe, x2))
new_compare16(x0, x1, False)
new_compare32(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Ordering)
new_lt7(x0, x1)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_ltEs11(Left(x0), Left(x1), ty_Double, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs11(Right(x0), Right(x1), x2, ty_Int)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs11(x0, x1, ty_Integer)
new_esEs9(EQ, EQ)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare16(x0, x1, True)
new_compare13(x0, x1, False, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs11(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_compare31(x0, x1, ty_Float)
new_lt10(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Char)
new_primPlusNat0(Succ(x0), x1)
new_esEs8(Just(x0), Just(x1), ty_Double)
new_compare29(x0, x1)
new_compare13(x0, x1, True, x2)
new_lt15(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_lt17(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs22(x0, x1, ty_Int)
new_ltEs11(Left(x0), Left(x1), ty_Bool, x2)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs13(:(x0, x1), [], x2)
new_compare19(x0, x1, False, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare27(x0, x1, x2, x3)
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, ty_Double)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs12(False, True)
new_ltEs12(True, False)
new_ltEs14(x0, x1, ty_Float)
new_compare18(Integer(x0), Integer(x1))
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Char)
new_esEs10(EQ)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Float)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Zero, Zero)
new_esEs28(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Nothing, x1)
new_lt10(x0, x1, ty_Float)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1)
new_lt10(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Double)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(GT, GT)
new_esEs11(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_lt11(x0, x1, ty_Ordering)
new_ltEs11(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs14(x0, x1, ty_Char)
new_esEs10(LT)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs17(Char(x0), Char(x1))
new_lt11(x0, x1, ty_@0)
new_esEs21(True, True)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_ltEs4(x0, x1, x2)
new_lt16(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_not(EQ)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, ty_Int)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt6(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_@0)
new_esEs21(True, False)
new_esEs21(False, True)
new_compare15(x0, x1, False)
new_ltEs12(True, True)
new_ltEs5(EQ, EQ)
new_ltEs14(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(Left(x0), Left(x1), ty_Integer, x2)
new_primCompAux00(x0, EQ)
new_primEqNat0(Succ(x0), Zero)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_sr(x0, x1)
new_compare26(x0, x1, False, x2, x3)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_primCompAux0(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_esEs18(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare31(x0, x1, ty_Double)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_ltEs11(Left(x0), Left(x1), ty_@0, x2)
new_esEs27(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_sr0(Integer(x0), Integer(x1))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs11(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs11(Left(x0), Left(x1), app(ty_[], x2), x3)
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_esEs11(x0, x1, ty_Bool)
new_ltEs17(x0, x1)
new_esEs22(x0, x1, ty_Integer)
new_esEs21(False, False)
new_compare31(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs11(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs14(x0, x1, ty_Integer)
new_ltEs11(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, ty_Int)
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, ty_Char)
new_lt11(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Char)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs25(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, True, x2, x3, x4)
new_esEs19(x0, x1, x2, x3)
new_not(LT)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs9(LT, LT)
new_esEs25(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(LT, LT)
new_ltEs14(x0, x1, app(app(ty_Either, x2), x3))
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_compare22(vyy3000, vyy400, False, cb) → new_ltEs3(vyy3000, vyy400, cb)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3
- new_lt0(vyy3000, vyy400, be, bf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), hd) → new_compare(vyy3001, vyy401, hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), hd) → new_primCompAux(vyy3000, vyy400, new_compare3(vyy3001, vyy401, hd), hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_primCompAux(vyy3000, vyy400, vyy84, app(ty_[], bab)) → new_compare(vyy3000, vyy400, bab)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_lt3(vyy3000, vyy400, cb) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, cb), cb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_compare2(vyy3000, vyy400, False, h, ba, bb) → new_ltEs(vyy3000, vyy400, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4, 6 >= 5
- new_compare0(vyy3000, vyy400, h, ba, bb) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_ltEs1(:(vyy3000, vyy3001), :(vyy400, vyy401), hd) → new_primCompAux(vyy3000, vyy400, new_compare3(vyy3001, vyy401, hd), hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_lt2(vyy3000, vyy400, bh, ca) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bh, ca), bh, ca)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_primCompAux(vyy3000, vyy400, vyy84, app(ty_Maybe, bae)) → new_compare5(vyy3000, vyy400, bae)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(ty_Maybe, de), bd) → new_lt3(vyy3001, vyy401, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_Maybe, ga), fb) → new_lt3(vyy3000, vyy400, ga)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(app(ty_@2, ea), eb)) → new_ltEs0(vyy3002, vyy402, ea, eb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(ty_[], ec)) → new_ltEs1(vyy3002, vyy402, ec)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_[], bg), bc, bd) → new_compare(vyy3000, vyy400, bg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(app(app(ty_@3, df), dg), dh)) → new_ltEs(vyy3002, vyy402, df, dg, dh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(app(app(ty_@3, cd), ce), cf), bd) → new_lt(vyy3001, vyy401, cd, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(app(ty_@3, eg), eh), fa), fb) → new_lt(vyy3000, vyy400, eg, eh, fa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(app(ty_Either, ed), ee)) → new_ltEs2(vyy3002, vyy402, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(app(ty_@2, gf), gg)) → new_ltEs0(vyy3001, vyy401, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(ty_[], gh)) → new_ltEs1(vyy3001, vyy401, gh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(Just(vyy3000), Just(vyy400), app(ty_[], bdg)) → new_ltEs1(vyy3000, vyy400, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(app(app(ty_@3, gc), gd), ge)) → new_ltEs(vyy3001, vyy401, gc, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs3(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs(vyy3000, vyy400, bdb, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(app(ty_Either, ha), hb)) → new_ltEs2(vyy3001, vyy401, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(Just(vyy3000), Just(vyy400), app(app(ty_@2, bde), bdf)) → new_ltEs0(vyy3000, vyy400, bde, bdf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_compare20(vyy3000, vyy400, False, be, bf) → new_ltEs0(vyy3000, vyy400, be, bf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs3(Just(vyy3000), Just(vyy400), app(app(ty_Either, bdh), bea)) → new_ltEs2(vyy3000, vyy400, bdh, bea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_compare21(vyy3000, vyy400, False, bh, ca) → new_ltEs2(vyy3000, vyy400, bh, ca)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs3(Just(vyy3000), Just(vyy400), app(ty_Maybe, beb)) → new_ltEs3(vyy3000, vyy400, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_Maybe, cb), bc, bd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, cb), cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4
- new_compare5(vyy3000, vyy400, cb) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, cb), cb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_primCompAux(vyy3000, vyy400, vyy84, app(app(app(ty_@3, he), hf), hg)) → new_compare0(vyy3000, vyy400, he, hf, hg)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(ty_Maybe, ef)) → new_ltEs3(vyy3002, vyy402, ef)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(ty_Maybe, hc)) → new_ltEs3(vyy3001, vyy401, hc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_@2, be), bf), bc, bd) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_compare1(vyy3000, vyy400, be, bf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs1(:(vyy3000, vyy3001), :(vyy400, vyy401), hd) → new_compare(vyy3001, vyy401, hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_lt1(vyy3000, vyy400, bg) → new_compare(vyy3000, vyy400, bg)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
- new_compare4(vyy3000, vyy400, bh, ca) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bh, ca), bh, ca)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_lt(vyy3000, vyy400, h, ba, bb) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(app(ty_Either, dc), dd), bd) → new_lt2(vyy3001, vyy401, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_Either, fg), fh), fb) → new_lt2(vyy3000, vyy400, fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_Either, bh), ca), bc, bd) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bh, ca), bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_primCompAux(vyy3000, vyy400, vyy84, app(app(ty_Either, bac), bad)) → new_compare4(vyy3000, vyy400, bac, bad)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_primCompAux(vyy3000, vyy400, vyy84, app(app(ty_@2, hh), baa)) → new_compare1(vyy3000, vyy400, hh, baa)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(ty_[], db), bd) → new_lt1(vyy3001, vyy401, db)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_[], ff), fb) → new_lt1(vyy3000, vyy400, ff)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_@2, fc), fd), fb) → new_lt0(vyy3000, vyy400, fc, fd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(app(ty_@2, cg), da), bd) → new_lt0(vyy3001, vyy401, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(app(ty_@3, h), ba), bb), bc, bd) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5, 3 > 6
- new_ltEs2(Left(vyy3000), Left(vyy400), app(app(ty_@2, bbb), bbc), bba) → new_ltEs0(vyy3000, vyy400, bbb, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs2(Right(vyy3000), Right(vyy400), bbh, app(app(ty_@2, bcd), bce)) → new_ltEs0(vyy3000, vyy400, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs2(Right(vyy3000), Right(vyy400), bbh, app(ty_[], bcf)) → new_ltEs1(vyy3000, vyy400, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs2(Left(vyy3000), Left(vyy400), app(ty_[], bbd), bba) → new_ltEs1(vyy3000, vyy400, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs2(Right(vyy3000), Right(vyy400), bbh, app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs(vyy3000, vyy400, bca, bcb, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs2(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, baf), bag), bah), bba) → new_ltEs(vyy3000, vyy400, baf, bag, bah)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs2(Left(vyy3000), Left(vyy400), app(app(ty_Either, bbe), bbf), bba) → new_ltEs2(vyy3000, vyy400, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs2(Right(vyy3000), Right(vyy400), bbh, app(app(ty_Either, bcg), bch)) → new_ltEs2(vyy3000, vyy400, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs2(Left(vyy3000), Left(vyy400), app(ty_Maybe, bbg), bba) → new_ltEs3(vyy3000, vyy400, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs2(Right(vyy3000), Right(vyy400), bbh, app(ty_Maybe, bda)) → new_ltEs3(vyy3000, vyy400, bda)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 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_LE(vyy65, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba, bb) → new_foldFM_LE1(vyy65, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs11(vyy3430, Right(vyy40), h, ba), 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_ltEs11(vyy3430, Right(vyy40), h, ba), h, ba, bb)
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_LE2(vyy340, vyy341, vyy73, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb) → new_foldFM_LE1(new_keysFM_LE0(vyy340, vyy341, vyy73, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs11(vyy3440, Right(vyy40), h, ba), 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)
The TRS R consists of the following rules:
new_esEs28(vyy470, vyy480, app(ty_[], che)) → new_esEs13(vyy470, vyy480, che)
new_ltEs14(vyy3002, vyy402, app(ty_Maybe, bdg)) → new_ltEs7(vyy3002, vyy402, bdg)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Double) → new_ltEs18(vyy3000, vyy400)
new_compare3(:(vyy3000, vyy3001), :(vyy400, vyy401), dh) → new_primCompAux0(vyy3000, vyy400, new_compare3(vyy3001, vyy401, dh), dh)
new_esEs7(Left(vyy470), Left(vyy480), app(app(ty_Either, dbh), dca), da) → new_esEs7(vyy470, vyy480, dbh, dca)
new_esEs8(Just(vyy470), Just(vyy480), app(app(ty_@2, cag), cah)) → new_esEs6(vyy470, vyy480, cag, cah)
new_lt11(vyy3001, vyy401, ty_Bool) → new_lt17(vyy3001, vyy401)
new_esEs5(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), be, bf, bg) → new_asAs(new_esEs26(vyy470, vyy480, be), new_asAs(new_esEs25(vyy471, vyy481, bf), new_esEs24(vyy472, vyy482, bg)))
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs17(vyy3000, vyy400)
new_esEs24(vyy472, vyy482, app(app(app(ty_@3, ed), ee), ef)) → new_esEs5(vyy472, vyy482, ed, ee, ef)
new_ltEs14(vyy3002, vyy402, ty_Integer) → new_ltEs9(vyy3002, vyy402)
new_esEs11(vyy47, vyy48, ty_Integer) → new_esEs18(vyy47, vyy48)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs17(Char(vyy470), Char(vyy480)) → new_primEqNat0(vyy470, vyy480)
new_esEs13([], [], bh) → True
new_esEs10(GT) → False
new_esEs24(vyy472, vyy482, ty_Char) → new_esEs17(vyy472, vyy482)
new_esEs23(vyy470, vyy480, ty_Integer) → new_esEs18(vyy470, vyy480)
new_compare10(vyy3000, vyy400, True, db, dc) → LT
new_esEs29(vyy470, vyy480, ty_Double) → new_esEs14(vyy470, vyy480)
new_esEs26(vyy470, vyy480, ty_Double) → new_esEs14(vyy470, vyy480)
new_keysFM_LE0(vyy340, vyy341, vyy72, h, ba, bb) → :(vyy340, vyy72)
new_ltEs5(EQ, GT) → True
new_ltEs14(vyy3002, vyy402, app(app(app(ty_@3, bcg), bch), bda)) → new_ltEs13(vyy3002, vyy402, bcg, bch, bda)
new_ltEs11(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, beb), bec), bed), bea) → new_ltEs13(vyy3000, vyy400, beb, bec, bed)
new_esEs25(vyy471, vyy481, ty_Char) → new_esEs17(vyy471, vyy481)
new_compare31(vyy3000, vyy400, ty_Int) → new_compare8(vyy3000, vyy400)
new_lt13(vyy3000, vyy400, dd, de, df) → new_esEs10(new_compare32(vyy3000, vyy400, dd, de, df))
new_esEs8(Just(vyy470), Just(vyy480), app(ty_Ratio, cba)) → new_esEs20(vyy470, vyy480, cba)
new_esEs29(vyy470, vyy480, app(ty_Ratio, def)) → new_esEs20(vyy470, vyy480, def)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Ordering) → new_ltEs5(vyy3000, vyy400)
new_primMulNat0(Zero, Zero) → Zero
new_esEs7(Left(vyy470), Left(vyy480), app(app(app(ty_@3, daf), dag), dah), da) → new_esEs5(vyy470, vyy480, daf, dag, dah)
new_esEs26(vyy470, vyy480, ty_Float) → new_esEs15(vyy470, vyy480)
new_ltEs11(Right(vyy3000), Left(vyy400), bfd, bea) → False
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Double) → new_esEs14(vyy470, vyy480)
new_esEs7(Left(vyy470), Left(vyy480), ty_Double, da) → new_esEs14(vyy470, vyy480)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, app(app(ty_@2, bfh), bga)) → new_ltEs6(vyy3000, vyy400, bfh, bga)
new_compare9(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare25(vyy3000, vyy400, True, dg) → EQ
new_esEs7(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, dbb), dbc), da) → new_esEs19(vyy470, vyy480, dbb, dbc)
new_esEs8(Just(vyy470), Just(vyy480), ty_Integer) → new_esEs18(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, ty_Integer) → new_ltEs9(vyy3001, vyy401)
new_ltEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, cbf), cbg), cbh)) → new_ltEs13(vyy3000, vyy400, cbf, cbg, cbh)
new_ltEs17(vyy300, vyy40) → new_not(new_compare30(vyy300, vyy40))
new_not(GT) → False
new_esEs10(EQ) → False
new_ltEs14(vyy3002, vyy402, app(ty_[], bdd)) → new_ltEs15(vyy3002, vyy402, bdd)
new_foldFM_LE20(vyy340, vyy341, vyy73, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb) → new_foldFM_LE10(new_keysFM_LE0(vyy340, vyy341, vyy73, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs11(vyy3440, Right(vyy40), h, ba), h, ba, bb)
new_esEs7(Right(vyy470), Right(vyy480), cg, app(app(app(ty_@3, dcb), dcc), dcd)) → new_esEs5(vyy470, vyy480, dcb, dcc, dcd)
new_lt10(vyy3000, vyy400, ty_Float) → new_lt7(vyy3000, vyy400)
new_lt19(vyy3000, vyy400) → new_esEs10(new_compare30(vyy3000, vyy400))
new_lt8(vyy3000, vyy400, ec) → new_esEs10(new_compare7(vyy3000, vyy400, ec))
new_compare29(vyy3000, vyy400) → new_compare28(vyy3000, vyy400, new_esEs21(vyy3000, vyy400))
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs5(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, app(app(ty_@2, cde), cdf)) → new_lt9(vyy3000, vyy400, cde, cdf)
new_ltEs5(EQ, LT) → False
new_ltEs11(Left(vyy3000), Left(vyy400), ty_@0, bea) → new_ltEs10(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, ty_Double) → new_esEs14(vyy471, vyy481)
new_esEs25(vyy471, vyy481, ty_Bool) → new_esEs21(vyy471, vyy481)
new_esEs28(vyy470, vyy480, ty_Double) → new_esEs14(vyy470, vyy480)
new_esEs11(vyy47, vyy48, app(ty_Ratio, ce)) → new_esEs20(vyy47, vyy48, ce)
new_compare31(vyy3000, vyy400, app(app(ty_Either, bhe), bhf)) → new_compare33(vyy3000, vyy400, bhe, bhf)
new_compare15(vyy3000, vyy400, False) → GT
new_compare31(vyy3000, vyy400, ty_Char) → new_compare30(vyy3000, vyy400)
new_esEs28(vyy470, vyy480, ty_Bool) → new_esEs21(vyy470, vyy480)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt15(vyy3000, vyy400)
new_lt4(vyy3000, vyy400) → new_esEs10(new_compare8(vyy3000, vyy400))
new_esEs28(vyy470, vyy480, app(app(app(ty_@3, chb), chc), chd)) → new_esEs5(vyy470, vyy480, chb, chc, chd)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Integer, bea) → new_ltEs9(vyy3000, vyy400)
new_esEs27(vyy471, vyy481, ty_Double) → new_esEs14(vyy471, vyy481)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs9(vyy3000, vyy400)
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, ca, cb) → :(@2(vyy470, vyy471), vyy102)
new_esEs8(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, cae), caf)) → new_esEs19(vyy470, vyy480, cae, caf)
new_esEs19(vyy47, vyy48, ca, cb) → new_asAs(new_esEs12(new_sizeFM(vyy47, ca, cb), new_sizeFM(vyy48, ca, cb)), new_esEs13(new_fmToList(vyy47, ca, cb), new_fmToList(vyy48, ca, cb), app(app(ty_@2, ca), cb)))
new_compare31(vyy3000, vyy400, app(app(ty_@2, bhb), bhc)) → new_compare27(vyy3000, vyy400, bhb, bhc)
new_esEs7(Left(vyy470), Right(vyy480), cg, da) → False
new_esEs7(Right(vyy470), Left(vyy480), cg, da) → False
new_lt14(vyy3000, vyy400) → new_esEs10(new_compare18(vyy3000, vyy400))
new_esEs27(vyy471, vyy481, ty_@0) → new_esEs16(vyy471, vyy481)
new_ltEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cch, cda) → new_pePe(new_lt20(vyy3000, vyy400, cch), vyy3000, vyy400, new_ltEs19(vyy3001, vyy401, cda), cch)
new_ltEs12(True, False) → False
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_ltEs11(vyy3430, Right(vyy40), h, ba), h, ba, bb)
new_compare23(vyy3000, vyy400, True) → EQ
new_esEs27(vyy471, vyy481, app(app(ty_Either, cgh), cha)) → new_esEs7(vyy471, vyy481, cgh, cha)
new_esEs28(vyy470, vyy480, ty_Integer) → new_esEs18(vyy470, vyy480)
new_lt11(vyy3001, vyy401, app(ty_Maybe, bce)) → new_lt5(vyy3001, vyy401, bce)
new_esEs27(vyy471, vyy481, ty_Ordering) → new_esEs9(vyy471, vyy481)
new_esEs29(vyy470, vyy480, ty_Float) → new_esEs15(vyy470, vyy480)
new_compare31(vyy3000, vyy400, ty_Bool) → new_compare29(vyy3000, vyy400)
new_ltEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, cca), ccb)) → new_ltEs6(vyy3000, vyy400, cca, ccb)
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_compare15(vyy3000, vyy400, True) → LT
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, cdb), cdc), cdd)) → new_lt13(vyy3000, vyy400, cdb, cdc, cdd)
new_compare11(vyy3000, vyy400, False, dd, de, df) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs29(vyy470, vyy480, app(ty_Maybe, deg)) → new_esEs8(vyy470, vyy480, deg)
new_ltEs11(Left(vyy3000), Left(vyy400), app(ty_[], beg), bea) → new_ltEs15(vyy3000, vyy400, beg)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_esEs7(Left(vyy470), Left(vyy480), ty_Int, da) → new_esEs12(vyy470, vyy480)
new_lt9(vyy3000, vyy400, db, dc) → new_esEs10(new_compare27(vyy3000, vyy400, db, dc))
new_ltEs15(vyy300, vyy40, dh) → new_not(new_compare3(vyy300, vyy40, dh))
new_ltEs16(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_esEs25(vyy471, vyy481, app(app(ty_@2, gg), gh)) → new_esEs6(vyy471, vyy481, gg, gh)
new_lt10(vyy3000, vyy400, ty_Ordering) → new_lt15(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_lt11(vyy3001, vyy401, app(app(ty_Either, bcc), bcd)) → new_lt18(vyy3001, vyy401, bcc, bcd)
new_esEs11(vyy47, vyy48, app(app(ty_FiniteMap, ca), cb)) → new_esEs19(vyy47, vyy48, ca, cb)
new_esEs24(vyy472, vyy482, ty_Int) → new_esEs12(vyy472, vyy482)
new_esEs11(vyy47, vyy48, ty_Bool) → new_esEs21(vyy47, vyy48)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs10(vyy3000, vyy400)
new_esEs21(True, True) → True
new_esEs24(vyy472, vyy482, app(app(ty_Either, fg), fh)) → new_esEs7(vyy472, vyy482, fg, fh)
new_ltEs14(vyy3002, vyy402, app(app(ty_@2, bdb), bdc)) → new_ltEs6(vyy3002, vyy402, bdb, bdc)
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Float) → new_esEs15(vyy470, vyy480)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Double, bea) → new_ltEs18(vyy3000, vyy400)
new_compare7(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare8(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs24(vyy472, vyy482, app(app(ty_@2, fb), fc)) → new_esEs6(vyy472, vyy482, fb, fc)
new_primEqNat0(Zero, Zero) → True
new_ltEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, ccd), cce)) → new_ltEs11(vyy3000, vyy400, ccd, cce)
new_ltEs12(False, False) → True
new_esEs26(vyy470, vyy480, ty_Char) → new_esEs17(vyy470, vyy480)
new_lt10(vyy3000, vyy400, app(ty_Ratio, ec)) → new_lt8(vyy3000, vyy400, ec)
new_esEs28(vyy470, vyy480, ty_@0) → new_esEs16(vyy470, vyy480)
new_esEs7(Left(vyy470), Left(vyy480), ty_Ordering, da) → new_esEs9(vyy470, vyy480)
new_lt20(vyy3000, vyy400, app(ty_Ratio, cec)) → new_lt8(vyy3000, vyy400, cec)
new_esEs26(vyy470, vyy480, ty_@0) → new_esEs16(vyy470, vyy480)
new_esEs29(vyy470, vyy480, app(ty_[], dea)) → new_esEs13(vyy470, vyy480, dea)
new_ltEs19(vyy3001, vyy401, ty_Float) → new_ltEs8(vyy3001, vyy401)
new_esEs25(vyy471, vyy481, ty_Integer) → new_esEs18(vyy471, vyy481)
new_compare25(vyy3000, vyy400, False, dg) → new_compare13(vyy3000, vyy400, new_ltEs7(vyy3000, vyy400, dg), dg)
new_ltEs14(vyy3002, vyy402, app(ty_Ratio, bdh)) → new_ltEs4(vyy3002, vyy402, bdh)
new_esEs20(:%(vyy470, vyy471), :%(vyy480, vyy481), ce) → new_asAs(new_esEs23(vyy470, vyy480, ce), new_esEs22(vyy471, vyy481, ce))
new_sr(vyy3000, vyy400) → new_primMulInt(vyy3000, vyy400)
new_lt10(vyy3000, vyy400, ty_Int) → new_lt4(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, app(app(ty_FiniteMap, ge), gf)) → new_esEs19(vyy471, vyy481, ge, gf)
new_lt11(vyy3001, vyy401, app(ty_Ratio, bcf)) → new_lt8(vyy3001, vyy401, bcf)
new_esEs8(Just(vyy470), Just(vyy480), ty_Bool) → new_esEs21(vyy470, vyy480)
new_compare31(vyy3000, vyy400, ty_Double) → new_compare9(vyy3000, vyy400)
new_esEs26(vyy470, vyy480, ty_Int) → new_esEs12(vyy470, vyy480)
new_compare31(vyy3000, vyy400, app(app(app(ty_@3, bgg), bgh), bha)) → new_compare32(vyy3000, vyy400, bgg, bgh, bha)
new_esEs29(vyy470, vyy480, app(app(ty_FiniteMap, deb), dec)) → new_esEs19(vyy470, vyy480, deb, dec)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Bool) → new_ltEs12(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy1030), vyy40000) → Succ(Succ(new_primPlusNat1(vyy1030, vyy40000)))
new_esEs7(Left(vyy470), Left(vyy480), ty_Bool, da) → new_esEs21(vyy470, vyy480)
new_esEs7(Right(vyy470), Right(vyy480), cg, app(app(ty_Either, ddd), dde)) → new_esEs7(vyy470, vyy480, ddd, dde)
new_ltEs19(vyy3001, vyy401, ty_Bool) → new_ltEs12(vyy3001, vyy401)
new_ltEs5(LT, LT) → True
new_esEs7(Right(vyy470), Right(vyy480), cg, app(ty_[], dce)) → new_esEs13(vyy470, vyy480, dce)
new_esEs23(vyy470, vyy480, ty_Int) → new_esEs12(vyy470, vyy480)
new_lt5(vyy3000, vyy400, dg) → new_esEs10(new_compare14(vyy3000, vyy400, dg))
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs16(vyy3000, vyy400)
new_esEs8(Just(vyy470), Nothing, cf) → False
new_esEs8(Nothing, Just(vyy480), cf) → False
new_esEs9(EQ, EQ) → True
new_ltEs14(vyy3002, vyy402, ty_Bool) → new_ltEs12(vyy3002, vyy402)
new_esEs29(vyy470, vyy480, ty_Int) → new_esEs12(vyy470, vyy480)
new_primEqInt(Neg(Succ(vyy4700)), Neg(Succ(vyy4800))) → new_primEqNat0(vyy4700, vyy4800)
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Char) → new_esEs17(vyy470, vyy480)
new_lt11(vyy3001, vyy401, ty_@0) → new_lt12(vyy3001, vyy401)
new_esEs26(vyy470, vyy480, app(ty_Maybe, baf)) → new_esEs8(vyy470, vyy480, baf)
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_ltEs11(Left(vyy3000), Left(vyy400), app(app(ty_@2, bee), bef), bea) → new_ltEs6(vyy3000, vyy400, bee, bef)
new_lt10(vyy3000, vyy400, app(app(ty_Either, ea), eb)) → new_lt18(vyy3000, vyy400, ea, eb)
new_esEs26(vyy470, vyy480, app(ty_[], hh)) → new_esEs13(vyy470, vyy480, hh)
new_ltEs7(Just(vyy3000), Just(vyy400), app(ty_[], ccc)) → new_ltEs15(vyy3000, vyy400, ccc)
new_primPlusNat1(Zero, Succ(vyy400000)) → Succ(vyy400000)
new_primPlusNat1(Succ(vyy10300), Zero) → Succ(vyy10300)
new_esEs11(vyy47, vyy48, ty_Int) → new_esEs12(vyy47, vyy48)
new_lt20(vyy3000, vyy400, ty_Int) → new_lt4(vyy3000, vyy400)
new_esEs28(vyy470, vyy480, app(ty_Maybe, dac)) → new_esEs8(vyy470, vyy480, dac)
new_compare16(vyy3000, vyy400, True) → LT
new_compare3([], :(vyy400, vyy401), dh) → LT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs28(vyy470, vyy480, app(app(ty_FiniteMap, chf), chg)) → new_esEs19(vyy470, vyy480, chf, chg)
new_esEs7(Left(vyy470), Left(vyy480), app(app(ty_@2, dbd), dbe), da) → new_esEs6(vyy470, vyy480, dbd, dbe)
new_esEs27(vyy471, vyy481, ty_Int) → new_esEs12(vyy471, vyy481)
new_compare3(:(vyy3000, vyy3001), [], dh) → GT
new_compare11(vyy3000, vyy400, True, dd, de, df) → LT
new_compare31(vyy3000, vyy400, app(ty_[], bhd)) → new_compare3(vyy3000, vyy400, bhd)
new_esEs11(vyy47, vyy48, app(app(app(ty_@3, be), bf), bg)) → new_esEs5(vyy47, vyy48, be, bf, bg)
new_esEs11(vyy47, vyy48, ty_Float) → new_esEs15(vyy47, vyy48)
new_compare8(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4800))) → False
new_primEqInt(Neg(Succ(vyy4700)), Neg(Zero)) → False
new_esEs25(vyy471, vyy481, ty_Ordering) → new_esEs9(vyy471, vyy481)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Char, bea) → new_ltEs17(vyy3000, vyy400)
new_compare26(vyy3000, vyy400, True, ea, eb) → EQ
new_compare24(vyy3000, vyy400, True, db, dc) → EQ
new_ltEs19(vyy3001, vyy401, ty_Char) → new_ltEs17(vyy3001, vyy401)
new_esEs22(vyy471, vyy481, ty_Int) → new_esEs12(vyy471, vyy481)
new_lt20(vyy3000, vyy400, app(ty_Maybe, ceb)) → new_lt5(vyy3000, vyy400, ceb)
new_esEs8(Just(vyy470), Just(vyy480), ty_Float) → new_esEs15(vyy470, vyy480)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), ca, cb) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, ca, cb), vyy4733, ca, cb)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs26(vyy470, vyy480, app(app(ty_Either, bag), bah)) → new_esEs7(vyy470, vyy480, bag, bah)
new_esEs27(vyy471, vyy481, ty_Float) → new_esEs15(vyy471, vyy481)
new_lt7(vyy3000, vyy400) → new_esEs10(new_compare17(vyy3000, vyy400))
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs19(vyy3001, vyy401, app(ty_Ratio, cfe)) → new_ltEs4(vyy3001, vyy401, cfe)
new_sizeFM(EmptyFM, ca, cb) → Pos(Zero)
new_ltEs5(EQ, EQ) → True
new_esEs7(Right(vyy470), Right(vyy480), cg, app(app(ty_@2, dch), dda)) → new_esEs6(vyy470, vyy480, dch, dda)
new_primEqInt(Pos(Succ(vyy4700)), Pos(Succ(vyy4800))) → new_primEqNat0(vyy4700, vyy4800)
new_compare10(vyy3000, vyy400, False, db, dc) → GT
new_esEs28(vyy470, vyy480, ty_Char) → new_esEs17(vyy470, vyy480)
new_ltEs7(Nothing, Just(vyy400), cbe) → True
new_primEqNat0(Succ(vyy4700), Succ(vyy4800)) → new_primEqNat0(vyy4700, vyy4800)
new_compare28(vyy3000, vyy400, False) → new_compare15(vyy3000, vyy400, new_ltEs12(vyy3000, vyy400))
new_esEs24(vyy472, vyy482, ty_@0) → new_esEs16(vyy472, vyy482)
new_lt20(vyy3000, vyy400, ty_@0) → new_lt12(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, ty_Float) → new_compare17(vyy3000, vyy400)
new_foldFM_LE0(vyy65, vyy40, EmptyFM, h, ba, bb) → vyy65
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Bool) → new_esEs21(vyy470, vyy480)
new_primCompAux00(vyy88, LT) → LT
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_@0) → new_ltEs10(vyy3000, vyy400)
new_ltEs11(Left(vyy3000), Left(vyy400), app(ty_Ratio, bfc), bea) → new_ltEs4(vyy3000, vyy400, bfc)
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs27(vyy471, vyy481, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs5(vyy471, vyy481, cff, cfg, cfh)
new_ltEs14(vyy3002, vyy402, ty_Int) → new_ltEs16(vyy3002, vyy402)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4800))) → False
new_primEqInt(Pos(Succ(vyy4700)), Pos(Zero)) → False
new_ltEs14(vyy3002, vyy402, ty_Ordering) → new_ltEs5(vyy3002, vyy402)
new_compare13(vyy3000, vyy400, True, dg) → LT
new_esEs24(vyy472, vyy482, ty_Float) → new_esEs15(vyy472, vyy482)
new_ltEs5(GT, LT) → False
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, app(app(ty_Either, bgc), bgd)) → new_ltEs11(vyy3000, vyy400, bgc, bgd)
new_lt10(vyy3000, vyy400, ty_@0) → new_lt12(vyy3000, vyy400)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs11(vyy47, vyy48, ty_@0) → new_esEs16(vyy47, vyy48)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_lt12(vyy3000, vyy400) → new_esEs10(new_compare12(vyy3000, vyy400))
new_ltEs14(vyy3002, vyy402, ty_@0) → new_ltEs10(vyy3002, vyy402)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_ltEs13(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bba, bbb, bbc) → new_pePe(new_lt10(vyy3000, vyy400, bba), vyy3000, vyy400, new_pePe(new_lt11(vyy3001, vyy401, bbb), vyy3001, vyy401, new_ltEs14(vyy3002, vyy402, bbc), bbb), bba)
new_compare210(vyy3000, vyy400, True, dd, de, df) → EQ
new_esEs7(Right(vyy470), Right(vyy480), cg, app(app(ty_FiniteMap, dcf), dcg)) → new_esEs19(vyy470, vyy480, dcf, dcg)
new_esEs8(Just(vyy470), Just(vyy480), ty_Char) → new_esEs17(vyy470, vyy480)
new_sr0(Integer(vyy30000), Integer(vyy4010)) → Integer(new_primMulInt(vyy30000, vyy4010))
new_primPlusNat1(Succ(vyy10300), Succ(vyy400000)) → Succ(Succ(new_primPlusNat1(vyy10300, vyy400000)))
new_lt11(vyy3001, vyy401, app(app(app(ty_@3, bbe), bbf), bbg)) → new_lt13(vyy3001, vyy401, bbe, bbf, bbg)
new_esEs7(Right(vyy470), Right(vyy480), cg, app(ty_Maybe, ddc)) → new_esEs8(vyy470, vyy480, ddc)
new_primEqInt(Neg(Succ(vyy4700)), Pos(vyy480)) → False
new_primEqInt(Pos(Succ(vyy4700)), Neg(vyy480)) → False
new_esEs8(Just(vyy470), Just(vyy480), ty_Int) → new_esEs12(vyy470, vyy480)
new_foldFM2(EmptyFM, ca, cb) → []
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Float, bea) → new_ltEs8(vyy3000, vyy400)
new_esEs7(Left(vyy470), Left(vyy480), ty_Float, da) → new_esEs15(vyy470, vyy480)
new_compare18(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_esEs24(vyy472, vyy482, app(ty_[], eg)) → new_esEs13(vyy472, vyy482, eg)
new_ltEs10(vyy300, vyy40) → new_not(new_compare12(vyy300, vyy40))
new_primEqInt(Neg(Zero), Pos(Succ(vyy4800))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4800))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCompAux00(vyy88, EQ) → vyy88
new_esEs28(vyy470, vyy480, app(app(ty_Either, dad), dae)) → new_esEs7(vyy470, vyy480, dad, dae)
new_lt10(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs18(vyy3000, vyy400)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs8(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, ty_Double) → new_ltEs18(vyy3001, vyy401)
new_esEs25(vyy471, vyy481, ty_Float) → new_esEs15(vyy471, vyy481)
new_ltEs19(vyy3001, vyy401, app(app(app(ty_@3, ced), cee), cef)) → new_ltEs13(vyy3001, vyy401, ced, cee, cef)
new_esEs27(vyy471, vyy481, app(ty_Maybe, cgg)) → new_esEs8(vyy471, vyy481, cgg)
new_lt10(vyy3000, vyy400, app(ty_Maybe, dg)) → new_lt5(vyy3000, vyy400, dg)
new_esEs26(vyy470, vyy480, app(app(ty_FiniteMap, baa), bab)) → new_esEs19(vyy470, vyy480, baa, bab)
new_esEs26(vyy470, vyy480, ty_Bool) → new_esEs21(vyy470, vyy480)
new_lt11(vyy3001, vyy401, ty_Integer) → new_lt14(vyy3001, vyy401)
new_esEs24(vyy472, vyy482, ty_Integer) → new_esEs18(vyy472, vyy482)
new_compare12(@0, @0) → EQ
new_lt18(vyy3000, vyy400, ea, eb) → new_esEs10(new_compare33(vyy3000, vyy400, ea, eb))
new_ltEs4(vyy300, vyy40, bc) → new_not(new_compare7(vyy300, vyy40, bc))
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primPlusNat0(Zero, vyy40000) → Succ(vyy40000)
new_esEs11(vyy47, vyy48, ty_Ordering) → new_esEs9(vyy47, vyy48)
new_esEs9(GT, GT) → True
new_compare210(vyy3000, vyy400, False, dd, de, df) → new_compare11(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, dd, de, df), dd, de, df)
new_not0 → True
new_esEs24(vyy472, vyy482, ty_Bool) → new_esEs21(vyy472, vyy482)
new_pePe(False, vyy47, vyy48, vyy66, bd) → new_asAs(new_esEs11(vyy47, vyy48, bd), vyy66)
new_compare28(vyy3000, vyy400, True) → EQ
new_lt20(vyy3000, vyy400, ty_Double) → new_lt6(vyy3000, vyy400)
new_esEs11(vyy47, vyy48, app(ty_[], bh)) → new_esEs13(vyy47, vyy48, bh)
new_ltEs8(vyy300, vyy40) → new_not(new_compare17(vyy300, vyy40))
new_esEs28(vyy470, vyy480, ty_Ordering) → new_esEs9(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, app(ty_[], cfa)) → new_ltEs15(vyy3001, vyy401, cfa)
new_ltEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, ccf)) → new_ltEs7(vyy3000, vyy400, ccf)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Ordering) → new_esEs9(vyy470, vyy480)
new_esEs8(Just(vyy470), Just(vyy480), app(app(ty_Either, cbc), cbd)) → new_esEs7(vyy470, vyy480, cbc, cbd)
new_esEs29(vyy470, vyy480, ty_@0) → new_esEs16(vyy470, vyy480)
new_primMulInt(Pos(vyy30000), Pos(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_ltEs18(vyy300, vyy40) → new_not(new_compare9(vyy300, vyy40))
new_esEs21(False, False) → True
new_compare23(vyy3000, vyy400, False) → new_compare16(vyy3000, vyy400, new_ltEs5(vyy3000, vyy400))
new_lt16(vyy3000, vyy400, bbd) → new_esEs10(new_compare3(vyy3000, vyy400, bbd))
new_esEs7(Left(vyy470), Left(vyy480), ty_Integer, da) → new_esEs18(vyy470, vyy480)
new_esEs27(vyy471, vyy481, ty_Char) → new_esEs17(vyy471, vyy481)
new_compare7(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare18(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_ltEs5(LT, GT) → True
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Int) → new_esEs12(vyy470, vyy480)
new_compare6(vyy3000, vyy400) → new_compare23(vyy3000, vyy400, new_esEs9(vyy3000, vyy400))
new_esEs27(vyy471, vyy481, app(app(ty_@2, cgd), cge)) → new_esEs6(vyy471, vyy481, cgd, cge)
new_primMulInt(Neg(vyy30000), Neg(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_esEs11(vyy47, vyy48, ty_Double) → new_esEs14(vyy47, vyy48)
new_lt10(vyy3000, vyy400, ty_Double) → new_lt6(vyy3000, vyy400)
new_esEs29(vyy470, vyy480, app(app(ty_@2, ded), dee)) → new_esEs6(vyy470, vyy480, ded, dee)
new_esEs8(Just(vyy470), Just(vyy480), ty_Ordering) → new_esEs9(vyy470, vyy480)
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Integer) → new_esEs18(vyy470, vyy480)
new_primEqNat0(Zero, Succ(vyy4800)) → False
new_primEqNat0(Succ(vyy4700), Zero) → False
new_lt20(vyy3000, vyy400, app(app(ty_Either, cdh), cea)) → new_lt18(vyy3000, vyy400, cdh, cea)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, app(app(app(ty_@3, bfe), bff), bfg)) → new_ltEs13(vyy3000, vyy400, bfe, bff, bfg)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt10(vyy3000, vyy400, ty_Bool) → new_lt17(vyy3000, vyy400)
new_esEs7(Left(vyy470), Left(vyy480), ty_Char, da) → new_esEs17(vyy470, vyy480)
new_esEs25(vyy471, vyy481, ty_Int) → new_esEs12(vyy471, vyy481)
new_ltEs14(vyy3002, vyy402, ty_Float) → new_ltEs8(vyy3002, vyy402)
new_esEs15(Float(vyy470, vyy471), Float(vyy480, vyy481)) → new_esEs12(new_sr(vyy470, vyy480), new_sr(vyy471, vyy481))
new_esEs7(Left(vyy470), Left(vyy480), ty_@0, da) → new_esEs16(vyy470, vyy480)
new_lt10(vyy3000, vyy400, app(app(ty_@2, db), dc)) → new_lt9(vyy3000, vyy400, db, dc)
new_sizeFM(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), ca, cb) → vyy472
new_lt17(vyy3000, vyy400) → new_esEs10(new_compare29(vyy3000, vyy400))
new_ltEs7(Nothing, Nothing, cbe) → True
new_pePe(True, vyy47, vyy48, vyy66, bd) → True
new_esEs27(vyy471, vyy481, app(ty_Ratio, cgf)) → new_esEs20(vyy471, vyy481, cgf)
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), ca, cb) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, ca, cb), vyy473, ca, cb)
new_foldFM_LE10(vyy65, vyy40, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba, bb) → new_foldFM_LE0(vyy65, vyy40, vyy343, h, ba, bb)
new_esEs29(vyy470, vyy480, app(app(app(ty_@3, ddf), ddg), ddh)) → new_esEs5(vyy470, vyy480, ddf, ddg, ddh)
new_esEs7(Left(vyy470), Left(vyy480), app(ty_Maybe, dbg), da) → new_esEs8(vyy470, vyy480, dbg)
new_compare13(vyy3000, vyy400, False, dg) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_compare32(vyy3000, vyy400, dd, de, df) → new_compare210(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, dd, de, df), dd, de, df)
new_esEs12(vyy47, vyy48) → new_primEqInt(vyy47, vyy48)
new_compare19(vyy3000, vyy400, True, ea, eb) → LT
new_compare31(vyy3000, vyy400, ty_Ordering) → new_compare6(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, app(ty_Ratio, bhh)) → new_compare7(vyy3000, vyy400, bhh)
new_lt11(vyy3001, vyy401, ty_Char) → new_lt19(vyy3001, vyy401)
new_lt11(vyy3001, vyy401, app(ty_[], bcb)) → new_lt16(vyy3001, vyy401, bcb)
new_esEs28(vyy470, vyy480, app(app(ty_@2, chh), daa)) → new_esEs6(vyy470, vyy480, chh, daa)
new_esEs11(vyy47, vyy48, app(app(ty_Either, cg), da)) → new_esEs7(vyy47, vyy48, cg, da)
new_lt20(vyy3000, vyy400, ty_Float) → new_lt7(vyy3000, vyy400)
new_ltEs11(Left(vyy3000), Left(vyy400), app(app(ty_Either, beh), bfa), bea) → new_ltEs11(vyy3000, vyy400, beh, bfa)
new_lt11(vyy3001, vyy401, ty_Ordering) → new_lt15(vyy3001, vyy401)
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_@0) → new_esEs16(vyy470, vyy480)
new_compare33(vyy3000, vyy400, ea, eb) → new_compare26(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, ea, eb), ea, eb)
new_esEs10(LT) → True
new_lt20(vyy3000, vyy400, app(ty_[], cdg)) → new_lt16(vyy3000, vyy400, cdg)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Ordering, bea) → new_ltEs5(vyy3000, vyy400)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Int, bea) → new_ltEs16(vyy3000, vyy400)
new_esEs11(vyy47, vyy48, app(app(ty_@2, cc), cd)) → new_esEs6(vyy47, vyy48, cc, cd)
new_esEs8(Nothing, Nothing, cf) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt6(vyy3000, vyy400) → new_esEs10(new_compare9(vyy3000, vyy400))
new_compare17(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs19(vyy3001, vyy401, app(app(ty_@2, ceg), ceh)) → new_ltEs6(vyy3001, vyy401, ceg, ceh)
new_esEs11(vyy47, vyy48, app(ty_Maybe, cf)) → new_esEs8(vyy47, vyy48, cf)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs12(vyy3000, vyy400)
new_asAs(False, vyy79) → False
new_esEs14(Double(vyy470, vyy471), Double(vyy480, vyy481)) → new_esEs12(new_sr(vyy470, vyy480), new_sr(vyy471, vyy481))
new_compare3([], [], dh) → EQ
new_ltEs11(Left(vyy3000), Right(vyy400), bfd, bea) → True
new_primMulInt(Neg(vyy30000), Pos(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulInt(Pos(vyy30000), Neg(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, app(ty_[], bgb)) → new_ltEs15(vyy3000, vyy400, bgb)
new_primMulNat0(Zero, Succ(vyy40000)) → Zero
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_esEs22(vyy471, vyy481, ty_Integer) → new_esEs18(vyy471, vyy481)
new_esEs13(:(vyy470, vyy471), [], bh) → False
new_esEs13([], :(vyy480, vyy481), bh) → False
new_esEs25(vyy471, vyy481, ty_@0) → new_esEs16(vyy471, vyy481)
new_ltEs5(LT, EQ) → True
new_esEs7(Left(vyy470), Left(vyy480), app(ty_[], dba), da) → new_esEs13(vyy470, vyy480, dba)
new_compare27(vyy3000, vyy400, db, dc) → new_compare24(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, db, dc), db, dc)
new_esEs29(vyy470, vyy480, ty_Char) → new_esEs17(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, ty_@0) → new_ltEs10(vyy3001, vyy401)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Char) → new_ltEs17(vyy3000, vyy400)
new_esEs27(vyy471, vyy481, ty_Integer) → new_esEs18(vyy471, vyy481)
new_esEs18(Integer(vyy470), Integer(vyy480)) → new_primEqInt(vyy470, vyy480)
new_esEs8(Just(vyy470), Just(vyy480), app(app(app(ty_@3, caa), cab), cac)) → new_esEs5(vyy470, vyy480, caa, cab, cac)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, app(ty_Ratio, bgf)) → new_ltEs4(vyy3000, vyy400, bgf)
new_not(EQ) → new_not0
new_ltEs12(True, True) → True
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, app(ty_Maybe, bge)) → new_ltEs7(vyy3000, vyy400, bge)
new_esEs27(vyy471, vyy481, app(app(ty_FiniteMap, cgb), cgc)) → new_esEs19(vyy471, vyy481, cgb, cgc)
new_compare14(vyy3000, vyy400, dg) → new_compare25(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, dg), dg)
new_ltEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, ccg)) → new_ltEs4(vyy3000, vyy400, ccg)
new_lt11(vyy3001, vyy401, ty_Int) → new_lt4(vyy3001, vyy401)
new_compare31(vyy3000, vyy400, app(ty_Maybe, bhg)) → new_compare14(vyy3000, vyy400, bhg)
new_compare31(vyy3000, vyy400, ty_Integer) → new_compare18(vyy3000, vyy400)
new_ltEs14(vyy3002, vyy402, ty_Double) → new_ltEs18(vyy3002, vyy402)
new_ltEs12(False, True) → True
new_esEs24(vyy472, vyy482, app(app(ty_FiniteMap, eh), fa)) → new_esEs19(vyy472, vyy482, eh, fa)
new_esEs16(@0, @0) → True
new_esEs25(vyy471, vyy481, app(ty_[], gd)) → new_esEs13(vyy471, vyy481, gd)
new_ltEs19(vyy3001, vyy401, ty_Int) → new_ltEs16(vyy3001, vyy401)
new_esEs8(Just(vyy470), Just(vyy480), app(ty_[], cad)) → new_esEs13(vyy470, vyy480, cad)
new_compare31(vyy3000, vyy400, ty_@0) → new_compare12(vyy3000, vyy400)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Int) → new_ltEs16(vyy3000, vyy400)
new_ltEs14(vyy3002, vyy402, ty_Char) → new_ltEs17(vyy3002, vyy402)
new_ltEs7(Just(vyy3000), Nothing, cbe) → False
new_esEs27(vyy471, vyy481, ty_Bool) → new_esEs21(vyy471, vyy481)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Integer) → new_ltEs9(vyy3000, vyy400)
new_esEs13(:(vyy470, vyy471), :(vyy480, vyy481), bh) → new_asAs(new_esEs29(vyy470, vyy480, bh), new_esEs13(vyy471, vyy481, bh))
new_esEs28(vyy470, vyy480, app(ty_Ratio, dab)) → new_esEs20(vyy470, vyy480, dab)
new_esEs24(vyy472, vyy482, app(ty_Maybe, ff)) → new_esEs8(vyy472, vyy482, ff)
new_esEs8(Just(vyy470), Just(vyy480), ty_@0) → new_esEs16(vyy470, vyy480)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_not(LT) → new_not0
new_esEs26(vyy470, vyy480, ty_Integer) → new_esEs18(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, app(ty_Maybe, cfd)) → new_ltEs7(vyy3001, vyy401, cfd)
new_esEs25(vyy471, vyy481, app(app(app(ty_@3, ga), gb), gc)) → new_esEs5(vyy471, vyy481, ga, gb, gc)
new_lt15(vyy3000, vyy400) → new_esEs10(new_compare6(vyy3000, vyy400))
new_esEs29(vyy470, vyy480, app(app(ty_Either, deh), dfa)) → new_esEs7(vyy470, vyy480, deh, dfa)
new_lt10(vyy3000, vyy400, app(app(app(ty_@3, dd), de), df)) → new_lt13(vyy3000, vyy400, dd, de, df)
new_lt10(vyy3000, vyy400, app(ty_[], bbd)) → new_lt16(vyy3000, vyy400, bbd)
new_esEs24(vyy472, vyy482, ty_Ordering) → new_esEs9(vyy472, vyy482)
new_esEs29(vyy470, vyy480, ty_Bool) → new_esEs21(vyy470, vyy480)
new_esEs28(vyy470, vyy480, ty_Int) → new_esEs12(vyy470, vyy480)
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt14(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, ty_Ordering) → new_ltEs5(vyy3001, vyy401)
new_esEs28(vyy470, vyy480, ty_Float) → new_esEs15(vyy470, vyy480)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(vyy470, vyy480, ty_Ordering) → new_esEs9(vyy470, vyy480)
new_esEs7(Left(vyy470), Left(vyy480), app(ty_Ratio, dbf), da) → new_esEs20(vyy470, vyy480, dbf)
new_foldFM_LE3(vyy340, vyy341, vyy72, vyy40, h, ba, bb) → new_keysFM_LE0(vyy340, vyy341, vyy72, h, ba, bb)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Bool, bea) → new_ltEs12(vyy3000, vyy400)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Float) → new_ltEs8(vyy3000, vyy400)
new_asAs(True, vyy79) → vyy79
new_lt10(vyy3000, vyy400, ty_Integer) → new_lt14(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300000), Succ(vyy40000)) → new_primPlusNat0(new_primMulNat0(vyy300000, Succ(vyy40000)), vyy40000)
new_esEs26(vyy470, vyy480, app(app(app(ty_@3, he), hf), hg)) → new_esEs5(vyy470, vyy480, he, hf, hg)
new_lt11(vyy3001, vyy401, ty_Float) → new_lt7(vyy3001, vyy401)
new_esEs27(vyy471, vyy481, app(ty_[], cga)) → new_esEs13(vyy471, vyy481, cga)
new_esEs11(vyy47, vyy48, ty_Char) → new_esEs17(vyy47, vyy48)
new_compare30(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_ltEs5(GT, GT) → True
new_esEs8(Just(vyy470), Just(vyy480), ty_Double) → new_esEs14(vyy470, vyy480)
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt17(vyy3000, vyy400)
new_esEs8(Just(vyy470), Just(vyy480), app(ty_Maybe, cbb)) → new_esEs8(vyy470, vyy480, cbb)
new_esEs29(vyy470, vyy480, ty_Integer) → new_esEs18(vyy470, vyy480)
new_esEs7(Right(vyy470), Right(vyy480), cg, app(ty_Ratio, ddb)) → new_esEs20(vyy470, vyy480, ddb)
new_primCompAux0(vyy3000, vyy400, vyy84, dh) → new_primCompAux00(vyy84, new_compare31(vyy3000, vyy400, dh))
new_fmToList(vyy47, ca, cb) → new_foldFM2(vyy47, ca, cb)
new_ltEs9(vyy300, vyy40) → new_not(new_compare18(vyy300, vyy40))
new_esEs26(vyy470, vyy480, app(app(ty_@2, bac), bad)) → new_esEs6(vyy470, vyy480, bac, bad)
new_ltEs19(vyy3001, vyy401, app(app(ty_Either, cfb), cfc)) → new_ltEs11(vyy3001, vyy401, cfb, cfc)
new_esEs21(True, False) → False
new_esEs21(False, True) → False
new_esEs24(vyy472, vyy482, app(ty_Ratio, fd)) → new_esEs20(vyy472, vyy482, fd)
new_ltEs14(vyy3002, vyy402, app(app(ty_Either, bde), bdf)) → new_ltEs11(vyy3002, vyy402, bde, bdf)
new_compare24(vyy3000, vyy400, False, db, dc) → new_compare10(vyy3000, vyy400, new_ltEs6(vyy3000, vyy400, db, dc), db, dc)
new_lt11(vyy3001, vyy401, ty_Double) → new_lt6(vyy3001, vyy401)
new_compare26(vyy3000, vyy400, False, ea, eb) → new_compare19(vyy3000, vyy400, new_ltEs11(vyy3000, vyy400, ea, eb), ea, eb)
new_compare19(vyy3000, vyy400, False, ea, eb) → GT
new_esEs9(LT, LT) → True
new_primCompAux00(vyy88, GT) → GT
new_esEs25(vyy471, vyy481, app(app(ty_Either, hc), hd)) → new_esEs7(vyy471, vyy481, hc, hd)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs25(vyy471, vyy481, app(ty_Maybe, hb)) → new_esEs8(vyy471, vyy481, hb)
new_lt11(vyy3001, vyy401, app(app(ty_@2, bbh), bca)) → new_lt9(vyy3001, vyy401, bbh, bca)
new_ltEs5(GT, EQ) → False
new_esEs29(vyy470, vyy480, ty_Ordering) → new_esEs9(vyy470, vyy480)
new_esEs6(@2(vyy470, vyy471), @2(vyy480, vyy481), cc, cd) → new_asAs(new_esEs28(vyy470, vyy480, cc), new_esEs27(vyy471, vyy481, cd))
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs25(vyy471, vyy481, app(ty_Ratio, ha)) → new_esEs20(vyy471, vyy481, ha)
new_esEs26(vyy470, vyy480, app(ty_Ratio, bae)) → new_esEs20(vyy470, vyy480, bae)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs24(vyy472, vyy482, ty_Double) → new_esEs14(vyy472, vyy482)
new_compare16(vyy3000, vyy400, False) → GT
new_ltEs11(Left(vyy3000), Left(vyy400), app(ty_Maybe, bfb), bea) → new_ltEs7(vyy3000, vyy400, bfb)
The set Q consists of the following terms:
new_primCompAux00(x0, GT)
new_lt20(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Int)
new_compare6(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs11(Right(x0), Left(x1), x2, x3)
new_ltEs11(Left(x0), Right(x1), x2, x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs11(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare24(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs11(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt11(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Double)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Bool)
new_compare23(x0, x1, True)
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs13([], [], x0)
new_esEs24(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Double)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Bool)
new_ltEs8(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs13([], :(x0, x1), x2)
new_ltEs14(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_compare33(x0, x1, x2, x3)
new_compare9(Double(x0, x1), Double(x2, x3))
new_compare8(x0, x1)
new_lt19(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt11(x0, x1, ty_Bool)
new_ltEs11(Left(x0), Left(x1), ty_Int, x2)
new_ltEs11(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs10(GT)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, EmptyFM, True, x6, x7, x8)
new_esEs26(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs12(x0, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs29(x0, x1, ty_Float)
new_compare30(Char(x0), Char(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, ty_Ordering)
new_lt11(x0, x1, ty_Int)
new_compare13(x0, x1, False, x2)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs16(@0, @0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt11(x0, x1, ty_Integer)
new_ltEs11(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_ltEs15(x0, x1, x2)
new_primMulNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Char)
new_ltEs11(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt11(x0, x1, app(ty_[], x2))
new_foldFM_LE0(x0, x1, EmptyFM, x2, x3, x4)
new_ltEs14(x0, x1, ty_@0)
new_foldFM_LE3(x0, x1, x2, x3, x4, x5, x6)
new_esEs11(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs11(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare15(x0, x1, True)
new_ltEs5(EQ, LT)
new_lt20(x0, x1, ty_@0)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
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_esEs27(x0, x1, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_@0)
new_ltEs7(Nothing, Just(x0), x1)
new_esEs8(Just(x0), Nothing, x1)
new_lt5(x0, x1, x2)
new_ltEs14(x0, x1, ty_Int)
new_ltEs14(x0, x1, ty_Double)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt11(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs11(Left(x0), Left(x1), ty_Char, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_lt13(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_Char)
new_compare12(@0, @0)
new_compare32(x0, x1, x2, x3, x4)
new_ltEs11(Right(x0), Right(x1), x2, ty_Double)
new_esEs25(x0, x1, ty_Float)
new_compare28(x0, x1, True)
new_ltEs11(Left(x0), Left(x1), ty_Double, x2)
new_esEs15(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Zero)
new_ltEs11(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs23(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs4(x0, x1, x2)
new_keysFM_LE0(x0, x1, x2, x3, x4, x5)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs11(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(Just(x0), Just(x1), ty_Float)
new_lt11(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs14(x0, x1, ty_Ordering)
new_esEs8(Nothing, Just(x0), x1)
new_compare13(x0, x1, True, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primPlusNat0(Zero, x0)
new_compare17(Float(x0, x1), Float(x2, x3))
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs16(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_lt14(x0, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, x2, x3)
new_esEs8(Nothing, Nothing, x0)
new_esEs29(x0, x1, ty_Bool)
new_ltEs11(Right(x0), Right(x1), x2, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(Just(x0), Just(x1), ty_@0)
new_compare23(x0, x1, False)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Double)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs12(False, False)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare31(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, False)
new_compare26(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, ty_Integer)
new_compare10(x0, x1, False, x2, x3)
new_esEs13(:(x0, x1), [], x2)
new_esEs27(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0, x1, x2, x3)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_primPlusNat1(Zero, Zero)
new_not0
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs24(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, ty_@0)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, ty_Double)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs11(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Integer)
new_ltEs14(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1)
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_compare27(x0, x1, x2, x3)
new_ltEs11(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_compare14(x0, x1, x2)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primCompAux00(x0, LT)
new_asAs(False, x0)
new_primEqNat0(Zero, Succ(x0))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(GT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCompAux0(x0, x1, x2, x3)
new_esEs9(GT, GT)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs10(x0, x1)
new_compare3([], :(x0, x1), x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt11(x0, x1, ty_Float)
new_lt4(x0, x1)
new_compare31(x0, x1, ty_Ordering)
new_fmToList(x0, x1, x2)
new_ltEs14(x0, x1, app(ty_Ratio, x2))
new_compare16(x0, x1, False)
new_pePe(True, x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs11(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt7(x0, x1)
new_ltEs11(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, ty_Integer)
new_ltEs7(Nothing, Nothing, x0)
new_primEqNat0(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs11(x0, x1, ty_Integer)
new_esEs9(EQ, EQ)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_compare16(x0, x1, True)
new_ltEs14(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs29(x0, x1, app(ty_[], x2))
new_compare3(:(x0, x1), [], x2)
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_ltEs11(Right(x0), Right(x1), x2, ty_@0)
new_compare31(x0, x1, ty_Float)
new_lt10(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs8(Just(x0), Just(x1), ty_Double)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1)
new_lt15(x0, x1)
new_lt17(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sizeFM(EmptyFM, x0, x1)
new_ltEs14(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, ty_Double)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_lt18(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs12(False, True)
new_ltEs12(True, False)
new_ltEs14(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_compare18(Integer(x0), Integer(x1))
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Char)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs10(EQ)
new_esEs27(x0, x1, ty_Float)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Zero, Zero)
new_esEs28(x0, x1, ty_Float)
new_ltEs11(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare31(x0, x1, app(ty_[], x2))
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs11(Left(x0), Left(x1), ty_Integer, x2)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs11(Left(x0), Left(x1), ty_Bool, x2)
new_lt10(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_lt12(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt10(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs29(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_ltEs5(GT, GT)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_ltEs11(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_@0)
new_lt11(x0, x1, ty_Ordering)
new_lt9(x0, x1, x2, x3)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1, ty_Char)
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs10(LT)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs17(Char(x0), Char(x1))
new_lt11(x0, x1, ty_@0)
new_esEs21(True, True)
new_compare210(x0, x1, False, x2, x3, x4)
new_compare25(x0, x1, False, x2)
new_lt8(x0, x1, x2)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_not(EQ)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_compare31(x0, x1, ty_Int)
new_ltEs11(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, ty_Int)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt6(x0, x1)
new_compare25(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Char)
new_compare19(x0, x1, False, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs24(x0, x1, ty_Bool)
new_lt16(x0, x1, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_foldFM2(EmptyFM, x0, x1)
new_esEs24(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_@0)
new_esEs21(True, False)
new_esEs21(False, True)
new_ltEs12(True, True)
new_compare15(x0, x1, False)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(EQ, EQ)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare19(x0, x1, True, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, EQ)
new_ltEs11(Right(x0), Right(x1), x2, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_sr(x0, x1)
new_ltEs11(Right(x0), Right(x1), x2, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, True, x2, x3)
new_ltEs11(Left(x0), Left(x1), ty_@0, x2)
new_primMulNat0(Succ(x0), Zero)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_foldFM_LE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs8(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs18(Integer(x0), Integer(x1))
new_compare11(x0, x1, False, x2, x3, x4)
new_compare31(x0, x1, ty_Double)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_ltEs11(Left(x0), Left(x1), ty_Ordering, x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare3([], [], x0)
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_ltEs11(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs11(x0, x1, ty_Bool)
new_ltEs17(x0, x1)
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs21(False, False)
new_compare31(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs14(x0, x1, ty_Integer)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), True, x11, x12, x13)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs25(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs11(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_compare24(x0, x1, False, x2, x3)
new_not(LT)
new_compare11(x0, x1, True, x2, x3, x4)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs9(LT, LT)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs5(LT, LT)
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_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_ltEs11(vyy3430, Right(vyy40), h, ba), 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_LE2(vyy340, vyy341, vyy73, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb) → new_foldFM_LE1(new_keysFM_LE0(vyy340, vyy341, vyy73, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs11(vyy3440, Right(vyy40), h, ba), 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_ltEs11(vyy3430, Right(vyy40), h, ba), 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, 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_ltEs11(vyy1840, Left(vyy13), h, ba), 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_keysFM_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(vyy470, vyy480, app(ty_[], che)) → new_esEs13(vyy470, vyy480, che)
new_ltEs14(vyy3002, vyy402, app(ty_Maybe, bdg)) → new_ltEs7(vyy3002, vyy402, bdg)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Double) → new_ltEs18(vyy3000, vyy400)
new_compare3(:(vyy3000, vyy3001), :(vyy400, vyy401), dh) → new_primCompAux0(vyy3000, vyy400, new_compare3(vyy3001, vyy401, dh), dh)
new_esEs7(Left(vyy470), Left(vyy480), app(app(ty_Either, dcc), dcd), da) → new_esEs7(vyy470, vyy480, dcc, dcd)
new_esEs8(Just(vyy470), Just(vyy480), app(app(ty_@2, cag), cah)) → new_esEs6(vyy470, vyy480, cag, cah)
new_lt11(vyy3001, vyy401, ty_Bool) → new_lt17(vyy3001, vyy401)
new_esEs5(@3(vyy470, vyy471, vyy472), @3(vyy480, vyy481, vyy482), be, bf, bg) → new_asAs(new_esEs26(vyy470, vyy480, be), new_asAs(new_esEs25(vyy471, vyy481, bf), new_esEs24(vyy472, vyy482, bg)))
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs17(vyy3000, vyy400)
new_esEs24(vyy472, vyy482, app(app(app(ty_@3, ed), ee), ef)) → new_esEs5(vyy472, vyy482, ed, ee, ef)
new_ltEs14(vyy3002, vyy402, ty_Integer) → new_ltEs9(vyy3002, vyy402)
new_esEs11(vyy47, vyy48, ty_Integer) → new_esEs18(vyy47, vyy48)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_esEs17(Char(vyy470), Char(vyy480)) → new_primEqNat0(vyy470, vyy480)
new_esEs13([], [], bh) → True
new_esEs10(GT) → False
new_esEs24(vyy472, vyy482, ty_Char) → new_esEs17(vyy472, vyy482)
new_esEs23(vyy470, vyy480, ty_Integer) → new_esEs18(vyy470, vyy480)
new_compare10(vyy3000, vyy400, True, db, dc) → LT
new_esEs29(vyy470, vyy480, ty_Double) → new_esEs14(vyy470, vyy480)
new_esEs26(vyy470, vyy480, ty_Double) → new_esEs14(vyy470, vyy480)
new_keysFM_LE0(vyy340, vyy341, vyy72, daf, dag, dah) → :(vyy340, vyy72)
new_ltEs5(EQ, GT) → True
new_ltEs14(vyy3002, vyy402, app(app(app(ty_@3, bcg), bch), bda)) → new_ltEs13(vyy3002, vyy402, bcg, bch, bda)
new_ltEs11(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, beb), bec), bed), bea) → new_ltEs13(vyy3000, vyy400, beb, bec, bed)
new_esEs25(vyy471, vyy481, ty_Char) → new_esEs17(vyy471, vyy481)
new_foldFM_LE30(vyy80, vyy13, h, ba, bb) → vyy80
new_compare31(vyy3000, vyy400, ty_Int) → new_compare8(vyy3000, vyy400)
new_lt13(vyy3000, vyy400, dd, de, df) → new_esEs10(new_compare32(vyy3000, vyy400, dd, de, df))
new_esEs8(Just(vyy470), Just(vyy480), app(ty_Ratio, cba)) → new_esEs20(vyy470, vyy480, cba)
new_esEs29(vyy470, vyy480, app(ty_Ratio, dfa)) → new_esEs20(vyy470, vyy480, dfa)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Ordering) → new_ltEs5(vyy3000, vyy400)
new_primMulNat0(Zero, Zero) → Zero
new_esEs7(Left(vyy470), Left(vyy480), app(app(app(ty_@3, dba), dbb), dbc), da) → new_esEs5(vyy470, vyy480, dba, dbb, dbc)
new_esEs26(vyy470, vyy480, ty_Float) → new_esEs15(vyy470, vyy480)
new_ltEs11(Right(vyy3000), Left(vyy400), bfd, bea) → False
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Double) → new_esEs14(vyy470, vyy480)
new_esEs7(Left(vyy470), Left(vyy480), ty_Double, da) → new_esEs14(vyy470, vyy480)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, app(app(ty_@2, bfh), bga)) → new_ltEs6(vyy3000, vyy400, bfh, bga)
new_compare9(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare25(vyy3000, vyy400, True, dg) → EQ
new_esEs7(Left(vyy470), Left(vyy480), app(app(ty_FiniteMap, dbe), dbf), da) → new_esEs19(vyy470, vyy480, dbe, dbf)
new_esEs8(Just(vyy470), Just(vyy480), ty_Integer) → new_esEs18(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, ty_Integer) → new_ltEs9(vyy3001, vyy401)
new_ltEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, cbf), cbg), cbh)) → new_ltEs13(vyy3000, vyy400, cbf, cbg, cbh)
new_ltEs17(vyy300, vyy40) → new_not(new_compare30(vyy300, vyy40))
new_not(GT) → False
new_esEs10(EQ) → False
new_ltEs14(vyy3002, vyy402, app(ty_[], bdd)) → new_ltEs15(vyy3002, vyy402, bdd)
new_esEs7(Right(vyy470), Right(vyy480), cg, app(app(app(ty_@3, dce), dcf), dcg)) → new_esEs5(vyy470, vyy480, dce, dcf, dcg)
new_lt10(vyy3000, vyy400, ty_Float) → new_lt7(vyy3000, vyy400)
new_lt19(vyy3000, vyy400) → new_esEs10(new_compare30(vyy3000, vyy400))
new_lt8(vyy3000, vyy400, ec) → new_esEs10(new_compare7(vyy3000, vyy400, ec))
new_compare29(vyy3000, vyy400) → new_compare28(vyy3000, vyy400, new_esEs21(vyy3000, vyy400))
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs5(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, app(app(ty_@2, cde), cdf)) → new_lt9(vyy3000, vyy400, cde, cdf)
new_ltEs5(EQ, LT) → False
new_ltEs11(Left(vyy3000), Left(vyy400), ty_@0, bea) → new_ltEs10(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, ty_Double) → new_esEs14(vyy471, vyy481)
new_esEs25(vyy471, vyy481, ty_Bool) → new_esEs21(vyy471, vyy481)
new_esEs28(vyy470, vyy480, ty_Double) → new_esEs14(vyy470, vyy480)
new_esEs11(vyy47, vyy48, app(ty_Ratio, ce)) → new_esEs20(vyy47, vyy48, ce)
new_compare31(vyy3000, vyy400, app(app(ty_Either, bhe), bhf)) → new_compare33(vyy3000, vyy400, bhe, bhf)
new_compare15(vyy3000, vyy400, False) → GT
new_compare31(vyy3000, vyy400, ty_Char) → new_compare30(vyy3000, vyy400)
new_esEs28(vyy470, vyy480, ty_Bool) → new_esEs21(vyy470, vyy480)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt15(vyy3000, vyy400)
new_lt4(vyy3000, vyy400) → new_esEs10(new_compare8(vyy3000, vyy400))
new_esEs28(vyy470, vyy480, app(app(app(ty_@3, chb), chc), chd)) → new_esEs5(vyy470, vyy480, chb, chc, chd)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Integer, bea) → new_ltEs9(vyy3000, vyy400)
new_esEs27(vyy471, vyy481, ty_Double) → new_esEs14(vyy471, vyy481)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs9(vyy3000, vyy400)
new_foldFM0(vyy470, vyy471, vyy102, EmptyFM, ca, cb) → :(@2(vyy470, vyy471), vyy102)
new_esEs8(Just(vyy470), Just(vyy480), app(app(ty_FiniteMap, cae), caf)) → new_esEs19(vyy470, vyy480, cae, caf)
new_esEs19(vyy47, vyy48, ca, cb) → new_asAs(new_esEs12(new_sizeFM(vyy47, ca, cb), new_sizeFM(vyy48, ca, cb)), new_esEs13(new_fmToList(vyy47, ca, cb), new_fmToList(vyy48, ca, cb), app(app(ty_@2, ca), cb)))
new_compare31(vyy3000, vyy400, app(app(ty_@2, bhb), bhc)) → new_compare27(vyy3000, vyy400, bhb, bhc)
new_esEs7(Left(vyy470), Right(vyy480), cg, da) → False
new_esEs7(Right(vyy470), Left(vyy480), cg, da) → False
new_lt14(vyy3000, vyy400) → new_esEs10(new_compare18(vyy3000, vyy400))
new_esEs27(vyy471, vyy481, ty_@0) → new_esEs16(vyy471, vyy481)
new_ltEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cch, cda) → new_pePe(new_lt20(vyy3000, vyy400, cch), vyy3000, vyy400, new_ltEs19(vyy3001, vyy401, cda), cch)
new_ltEs12(True, False) → False
new_compare23(vyy3000, vyy400, True) → EQ
new_esEs27(vyy471, vyy481, app(app(ty_Either, cgh), cha)) → new_esEs7(vyy471, vyy481, cgh, cha)
new_esEs28(vyy470, vyy480, ty_Integer) → new_esEs18(vyy470, vyy480)
new_lt11(vyy3001, vyy401, app(ty_Maybe, bce)) → new_lt5(vyy3001, vyy401, bce)
new_esEs27(vyy471, vyy481, ty_Ordering) → new_esEs9(vyy471, vyy481)
new_esEs29(vyy470, vyy480, ty_Float) → new_esEs15(vyy470, vyy480)
new_compare31(vyy3000, vyy400, ty_Bool) → new_compare29(vyy3000, vyy400)
new_ltEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, cca), ccb)) → new_ltEs6(vyy3000, vyy400, cca, ccb)
new_compare15(vyy3000, vyy400, True) → LT
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, cdb), cdc), cdd)) → new_lt13(vyy3000, vyy400, cdb, cdc, cdd)
new_compare11(vyy3000, vyy400, False, dd, de, df) → GT
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs29(vyy470, vyy480, app(ty_Maybe, dfb)) → new_esEs8(vyy470, vyy480, dfb)
new_ltEs11(Left(vyy3000), Left(vyy400), app(ty_[], beg), bea) → new_ltEs15(vyy3000, vyy400, beg)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_esEs7(Left(vyy470), Left(vyy480), ty_Int, da) → new_esEs12(vyy470, vyy480)
new_lt9(vyy3000, vyy400, db, dc) → new_esEs10(new_compare27(vyy3000, vyy400, db, dc))
new_ltEs15(vyy300, vyy40, dh) → new_not(new_compare3(vyy300, vyy40, dh))
new_ltEs16(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_esEs25(vyy471, vyy481, app(app(ty_@2, gg), gh)) → new_esEs6(vyy471, vyy481, gg, gh)
new_lt10(vyy3000, vyy400, ty_Ordering) → new_lt15(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_lt11(vyy3001, vyy401, app(app(ty_Either, bcc), bcd)) → new_lt18(vyy3001, vyy401, bcc, bcd)
new_esEs11(vyy47, vyy48, app(app(ty_FiniteMap, ca), cb)) → new_esEs19(vyy47, vyy48, ca, cb)
new_esEs24(vyy472, vyy482, ty_Int) → new_esEs12(vyy472, vyy482)
new_esEs11(vyy47, vyy48, ty_Bool) → new_esEs21(vyy47, vyy48)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs10(vyy3000, vyy400)
new_esEs21(True, True) → True
new_esEs24(vyy472, vyy482, app(app(ty_Either, fg), fh)) → new_esEs7(vyy472, vyy482, fg, fh)
new_ltEs14(vyy3002, vyy402, app(app(ty_@2, bdb), bdc)) → new_ltEs6(vyy3002, vyy402, bdb, bdc)
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Float) → new_esEs15(vyy470, vyy480)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Double, bea) → new_ltEs18(vyy3000, vyy400)
new_compare7(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare8(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs24(vyy472, vyy482, app(app(ty_@2, fb), fc)) → new_esEs6(vyy472, vyy482, fb, fc)
new_primEqNat0(Zero, Zero) → True
new_ltEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, ccd), cce)) → new_ltEs11(vyy3000, vyy400, ccd, cce)
new_ltEs12(False, False) → True
new_esEs26(vyy470, vyy480, ty_Char) → new_esEs17(vyy470, vyy480)
new_lt10(vyy3000, vyy400, app(ty_Ratio, ec)) → new_lt8(vyy3000, vyy400, ec)
new_esEs28(vyy470, vyy480, ty_@0) → new_esEs16(vyy470, vyy480)
new_esEs7(Left(vyy470), Left(vyy480), ty_Ordering, da) → new_esEs9(vyy470, vyy480)
new_lt20(vyy3000, vyy400, app(ty_Ratio, cec)) → new_lt8(vyy3000, vyy400, cec)
new_esEs26(vyy470, vyy480, ty_@0) → new_esEs16(vyy470, vyy480)
new_esEs29(vyy470, vyy480, app(ty_[], ded)) → new_esEs13(vyy470, vyy480, ded)
new_ltEs19(vyy3001, vyy401, ty_Float) → new_ltEs8(vyy3001, vyy401)
new_esEs25(vyy471, vyy481, ty_Integer) → new_esEs18(vyy471, vyy481)
new_compare25(vyy3000, vyy400, False, dg) → new_compare13(vyy3000, vyy400, new_ltEs7(vyy3000, vyy400, dg), dg)
new_ltEs14(vyy3002, vyy402, app(ty_Ratio, bdh)) → new_ltEs4(vyy3002, vyy402, bdh)
new_esEs20(:%(vyy470, vyy471), :%(vyy480, vyy481), ce) → new_asAs(new_esEs23(vyy470, vyy480, ce), new_esEs22(vyy471, vyy481, ce))
new_foldFM_LE12(vyy71, vyy13, vyy180, vyy181, vyy182, vyy183, Branch(vyy1840, vyy1841, vyy1842, vyy1843, vyy1844), True, h, ba, bb) → new_foldFM_LE22(new_keysFM_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_sr(vyy3000, vyy400) → new_primMulInt(vyy3000, vyy400)
new_lt10(vyy3000, vyy400, ty_Int) → new_lt4(vyy3000, vyy400)
new_esEs25(vyy471, vyy481, app(app(ty_FiniteMap, ge), gf)) → new_esEs19(vyy471, vyy481, ge, gf)
new_lt11(vyy3001, vyy401, app(ty_Ratio, bcf)) → new_lt8(vyy3001, vyy401, bcf)
new_esEs8(Just(vyy470), Just(vyy480), ty_Bool) → new_esEs21(vyy470, vyy480)
new_compare31(vyy3000, vyy400, ty_Double) → new_compare9(vyy3000, vyy400)
new_esEs26(vyy470, vyy480, ty_Int) → new_esEs12(vyy470, vyy480)
new_compare31(vyy3000, vyy400, app(app(app(ty_@3, bgg), bgh), bha)) → new_compare32(vyy3000, vyy400, bgg, bgh, bha)
new_esEs29(vyy470, vyy480, app(app(ty_FiniteMap, dee), def)) → new_esEs19(vyy470, vyy480, dee, def)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Bool) → new_ltEs12(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy1030), vyy40000) → Succ(Succ(new_primPlusNat1(vyy1030, vyy40000)))
new_esEs7(Left(vyy470), Left(vyy480), ty_Bool, da) → new_esEs21(vyy470, vyy480)
new_esEs7(Right(vyy470), Right(vyy480), cg, app(app(ty_Either, ddg), ddh)) → new_esEs7(vyy470, vyy480, ddg, ddh)
new_ltEs19(vyy3001, vyy401, ty_Bool) → new_ltEs12(vyy3001, vyy401)
new_ltEs5(LT, LT) → True
new_esEs7(Right(vyy470), Right(vyy480), cg, app(ty_[], dch)) → new_esEs13(vyy470, vyy480, dch)
new_esEs23(vyy470, vyy480, ty_Int) → new_esEs12(vyy470, vyy480)
new_lt5(vyy3000, vyy400, dg) → new_esEs10(new_compare14(vyy3000, vyy400, dg))
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs16(vyy3000, vyy400)
new_esEs8(Just(vyy470), Nothing, cf) → False
new_esEs8(Nothing, Just(vyy480), cf) → False
new_esEs9(EQ, EQ) → True
new_ltEs14(vyy3002, vyy402, ty_Bool) → new_ltEs12(vyy3002, vyy402)
new_esEs29(vyy470, vyy480, ty_Int) → new_esEs12(vyy470, vyy480)
new_primEqInt(Neg(Succ(vyy4700)), Neg(Succ(vyy4800))) → new_primEqNat0(vyy4700, vyy4800)
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Char) → new_esEs17(vyy470, vyy480)
new_lt11(vyy3001, vyy401, ty_@0) → new_lt12(vyy3001, vyy401)
new_esEs26(vyy470, vyy480, app(ty_Maybe, baf)) → new_esEs8(vyy470, vyy480, baf)
new_ltEs11(Left(vyy3000), Left(vyy400), app(app(ty_@2, bee), bef), bea) → new_ltEs6(vyy3000, vyy400, bee, bef)
new_lt10(vyy3000, vyy400, app(app(ty_Either, ea), eb)) → new_lt18(vyy3000, vyy400, ea, eb)
new_esEs26(vyy470, vyy480, app(ty_[], hh)) → new_esEs13(vyy470, vyy480, hh)
new_ltEs7(Just(vyy3000), Just(vyy400), app(ty_[], ccc)) → new_ltEs15(vyy3000, vyy400, ccc)
new_primPlusNat1(Zero, Succ(vyy400000)) → Succ(vyy400000)
new_primPlusNat1(Succ(vyy10300), Zero) → Succ(vyy10300)
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_esEs11(vyy47, vyy48, ty_Int) → new_esEs12(vyy47, vyy48)
new_lt20(vyy3000, vyy400, ty_Int) → new_lt4(vyy3000, vyy400)
new_esEs28(vyy470, vyy480, app(ty_Maybe, dac)) → new_esEs8(vyy470, vyy480, dac)
new_compare16(vyy3000, vyy400, True) → LT
new_compare3([], :(vyy400, vyy401), dh) → LT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs28(vyy470, vyy480, app(app(ty_FiniteMap, chf), chg)) → new_esEs19(vyy470, vyy480, chf, chg)
new_esEs7(Left(vyy470), Left(vyy480), app(app(ty_@2, dbg), dbh), da) → new_esEs6(vyy470, vyy480, dbg, dbh)
new_esEs27(vyy471, vyy481, ty_Int) → new_esEs12(vyy471, vyy481)
new_compare3(:(vyy3000, vyy3001), [], dh) → GT
new_compare11(vyy3000, vyy400, True, dd, de, df) → LT
new_compare31(vyy3000, vyy400, app(ty_[], bhd)) → new_compare3(vyy3000, vyy400, bhd)
new_esEs11(vyy47, vyy48, app(app(app(ty_@3, be), bf), bg)) → new_esEs5(vyy47, vyy48, be, bf, bg)
new_esEs11(vyy47, vyy48, ty_Float) → new_esEs15(vyy47, vyy48)
new_compare8(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4800))) → False
new_primEqInt(Neg(Succ(vyy4700)), Neg(Zero)) → False
new_esEs25(vyy471, vyy481, ty_Ordering) → new_esEs9(vyy471, vyy481)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Char, bea) → new_ltEs17(vyy3000, vyy400)
new_compare26(vyy3000, vyy400, True, ea, eb) → EQ
new_compare24(vyy3000, vyy400, True, db, dc) → EQ
new_ltEs19(vyy3001, vyy401, ty_Char) → new_ltEs17(vyy3001, vyy401)
new_esEs22(vyy471, vyy481, ty_Int) → new_esEs12(vyy471, vyy481)
new_lt20(vyy3000, vyy400, app(ty_Maybe, ceb)) → new_lt5(vyy3000, vyy400, ceb)
new_esEs8(Just(vyy470), Just(vyy480), ty_Float) → new_esEs15(vyy470, vyy480)
new_foldFM0(vyy470, vyy471, vyy102, Branch(vyy4730, vyy4731, vyy4732, vyy4733, vyy4734), ca, cb) → new_foldFM0(vyy4730, vyy4731, new_foldFM0(vyy470, vyy471, vyy102, vyy4734, ca, cb), vyy4733, ca, cb)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs26(vyy470, vyy480, app(app(ty_Either, bag), bah)) → new_esEs7(vyy470, vyy480, bag, bah)
new_esEs27(vyy471, vyy481, ty_Float) → new_esEs15(vyy471, vyy481)
new_lt7(vyy3000, vyy400) → new_esEs10(new_compare17(vyy3000, vyy400))
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs19(vyy3001, vyy401, app(ty_Ratio, cfe)) → new_ltEs4(vyy3001, vyy401, cfe)
new_sizeFM(EmptyFM, ca, cb) → Pos(Zero)
new_ltEs5(EQ, EQ) → True
new_esEs7(Right(vyy470), Right(vyy480), cg, app(app(ty_@2, ddc), ddd)) → new_esEs6(vyy470, vyy480, ddc, ddd)
new_primEqInt(Pos(Succ(vyy4700)), Pos(Succ(vyy4800))) → new_primEqNat0(vyy4700, vyy4800)
new_compare10(vyy3000, vyy400, False, db, dc) → GT
new_esEs28(vyy470, vyy480, ty_Char) → new_esEs17(vyy470, vyy480)
new_foldFM_LE5(vyy71, vyy13, EmptyFM, h, ba, bb) → new_foldFM_LE30(vyy71, vyy13, h, ba, bb)
new_ltEs7(Nothing, Just(vyy400), cbe) → True
new_primEqNat0(Succ(vyy4700), Succ(vyy4800)) → new_primEqNat0(vyy4700, vyy4800)
new_compare28(vyy3000, vyy400, False) → new_compare15(vyy3000, vyy400, new_ltEs12(vyy3000, vyy400))
new_esEs24(vyy472, vyy482, ty_@0) → new_esEs16(vyy472, vyy482)
new_lt20(vyy3000, vyy400, ty_@0) → new_lt12(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, ty_Float) → new_compare17(vyy3000, vyy400)
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Bool) → new_esEs21(vyy470, vyy480)
new_primCompAux00(vyy88, LT) → LT
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_@0) → new_ltEs10(vyy3000, vyy400)
new_ltEs11(Left(vyy3000), Left(vyy400), app(ty_Ratio, bfc), bea) → new_ltEs4(vyy3000, vyy400, bfc)
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs27(vyy471, vyy481, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs5(vyy471, vyy481, cff, cfg, cfh)
new_ltEs14(vyy3002, vyy402, ty_Int) → new_ltEs16(vyy3002, vyy402)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4800))) → False
new_primEqInt(Pos(Succ(vyy4700)), Pos(Zero)) → False
new_ltEs14(vyy3002, vyy402, ty_Ordering) → new_ltEs5(vyy3002, vyy402)
new_compare13(vyy3000, vyy400, True, dg) → LT
new_esEs24(vyy472, vyy482, ty_Float) → new_esEs15(vyy472, vyy482)
new_ltEs5(GT, LT) → False
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, app(app(ty_Either, bgc), bgd)) → new_ltEs11(vyy3000, vyy400, bgc, bgd)
new_lt10(vyy3000, vyy400, ty_@0) → new_lt12(vyy3000, vyy400)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs11(vyy47, vyy48, ty_@0) → new_esEs16(vyy47, vyy48)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_lt12(vyy3000, vyy400) → new_esEs10(new_compare12(vyy3000, vyy400))
new_ltEs14(vyy3002, vyy402, ty_@0) → new_ltEs10(vyy3002, vyy402)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_ltEs13(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bba, bbb, bbc) → new_pePe(new_lt10(vyy3000, vyy400, bba), vyy3000, vyy400, new_pePe(new_lt11(vyy3001, vyy401, bbb), vyy3001, vyy401, new_ltEs14(vyy3002, vyy402, bbc), bbb), bba)
new_compare210(vyy3000, vyy400, True, dd, de, df) → EQ
new_esEs7(Right(vyy470), Right(vyy480), cg, app(app(ty_FiniteMap, dda), ddb)) → new_esEs19(vyy470, vyy480, dda, ddb)
new_esEs8(Just(vyy470), Just(vyy480), ty_Char) → new_esEs17(vyy470, vyy480)
new_sr0(Integer(vyy30000), Integer(vyy4010)) → Integer(new_primMulInt(vyy30000, vyy4010))
new_primPlusNat1(Succ(vyy10300), Succ(vyy400000)) → Succ(Succ(new_primPlusNat1(vyy10300, vyy400000)))
new_lt11(vyy3001, vyy401, app(app(app(ty_@3, bbe), bbf), bbg)) → new_lt13(vyy3001, vyy401, bbe, bbf, bbg)
new_esEs7(Right(vyy470), Right(vyy480), cg, app(ty_Maybe, ddf)) → new_esEs8(vyy470, vyy480, ddf)
new_primEqInt(Neg(Succ(vyy4700)), Pos(vyy480)) → False
new_primEqInt(Pos(Succ(vyy4700)), Neg(vyy480)) → False
new_esEs8(Just(vyy470), Just(vyy480), ty_Int) → new_esEs12(vyy470, vyy480)
new_foldFM2(EmptyFM, ca, cb) → []
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Float, bea) → new_ltEs8(vyy3000, vyy400)
new_esEs7(Left(vyy470), Left(vyy480), ty_Float, da) → new_esEs15(vyy470, vyy480)
new_compare18(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_esEs24(vyy472, vyy482, app(ty_[], eg)) → new_esEs13(vyy472, vyy482, eg)
new_ltEs10(vyy300, vyy40) → new_not(new_compare12(vyy300, vyy40))
new_primEqInt(Neg(Zero), Pos(Succ(vyy4800))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4800))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_foldFM_LE12(vyy71, vyy13, vyy180, vyy181, vyy182, vyy183, vyy184, False, h, ba, bb) → new_foldFM_LE5(vyy71, vyy13, vyy183, h, ba, bb)
new_primCompAux00(vyy88, EQ) → vyy88
new_esEs28(vyy470, vyy480, app(app(ty_Either, dad), dae)) → new_esEs7(vyy470, vyy480, dad, dae)
new_lt10(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs18(vyy3000, vyy400)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs8(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, ty_Double) → new_ltEs18(vyy3001, vyy401)
new_esEs25(vyy471, vyy481, ty_Float) → new_esEs15(vyy471, vyy481)
new_ltEs19(vyy3001, vyy401, app(app(app(ty_@3, ced), cee), cef)) → new_ltEs13(vyy3001, vyy401, ced, cee, cef)
new_esEs27(vyy471, vyy481, app(ty_Maybe, cgg)) → new_esEs8(vyy471, vyy481, cgg)
new_lt10(vyy3000, vyy400, app(ty_Maybe, dg)) → new_lt5(vyy3000, vyy400, dg)
new_esEs26(vyy470, vyy480, app(app(ty_FiniteMap, baa), bab)) → new_esEs19(vyy470, vyy480, baa, bab)
new_esEs26(vyy470, vyy480, ty_Bool) → new_esEs21(vyy470, vyy480)
new_lt11(vyy3001, vyy401, ty_Integer) → new_lt14(vyy3001, vyy401)
new_esEs24(vyy472, vyy482, ty_Integer) → new_esEs18(vyy472, vyy482)
new_compare12(@0, @0) → EQ
new_lt18(vyy3000, vyy400, ea, eb) → new_esEs10(new_compare33(vyy3000, vyy400, ea, eb))
new_ltEs4(vyy300, vyy40, bc) → new_not(new_compare7(vyy300, vyy40, bc))
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primPlusNat0(Zero, vyy40000) → Succ(vyy40000)
new_esEs11(vyy47, vyy48, ty_Ordering) → new_esEs9(vyy47, vyy48)
new_esEs9(GT, GT) → True
new_compare210(vyy3000, vyy400, False, dd, de, df) → new_compare11(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, dd, de, df), dd, de, df)
new_not0 → True
new_esEs24(vyy472, vyy482, ty_Bool) → new_esEs21(vyy472, vyy482)
new_pePe(False, vyy47, vyy48, vyy66, bd) → new_asAs(new_esEs11(vyy47, vyy48, bd), vyy66)
new_compare28(vyy3000, vyy400, True) → EQ
new_lt20(vyy3000, vyy400, ty_Double) → new_lt6(vyy3000, vyy400)
new_esEs11(vyy47, vyy48, app(ty_[], bh)) → new_esEs13(vyy47, vyy48, bh)
new_ltEs8(vyy300, vyy40) → new_not(new_compare17(vyy300, vyy40))
new_esEs28(vyy470, vyy480, ty_Ordering) → new_esEs9(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, app(ty_[], cfa)) → new_ltEs15(vyy3001, vyy401, cfa)
new_ltEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, ccf)) → new_ltEs7(vyy3000, vyy400, ccf)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Ordering) → new_esEs9(vyy470, vyy480)
new_esEs8(Just(vyy470), Just(vyy480), app(app(ty_Either, cbc), cbd)) → new_esEs7(vyy470, vyy480, cbc, cbd)
new_esEs29(vyy470, vyy480, ty_@0) → new_esEs16(vyy470, vyy480)
new_primMulInt(Pos(vyy30000), Pos(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_ltEs18(vyy300, vyy40) → new_not(new_compare9(vyy300, vyy40))
new_esEs21(False, False) → True
new_compare23(vyy3000, vyy400, False) → new_compare16(vyy3000, vyy400, new_ltEs5(vyy3000, vyy400))
new_lt16(vyy3000, vyy400, bbd) → new_esEs10(new_compare3(vyy3000, vyy400, bbd))
new_esEs7(Left(vyy470), Left(vyy480), ty_Integer, da) → new_esEs18(vyy470, vyy480)
new_esEs27(vyy471, vyy481, ty_Char) → new_esEs17(vyy471, vyy481)
new_compare7(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare18(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_ltEs5(LT, GT) → True
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Int) → new_esEs12(vyy470, vyy480)
new_compare6(vyy3000, vyy400) → new_compare23(vyy3000, vyy400, new_esEs9(vyy3000, vyy400))
new_esEs27(vyy471, vyy481, app(app(ty_@2, cgd), cge)) → new_esEs6(vyy471, vyy481, cgd, cge)
new_primMulInt(Neg(vyy30000), Neg(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_esEs11(vyy47, vyy48, ty_Double) → new_esEs14(vyy47, vyy48)
new_lt10(vyy3000, vyy400, ty_Double) → new_lt6(vyy3000, vyy400)
new_esEs29(vyy470, vyy480, app(app(ty_@2, deg), deh)) → new_esEs6(vyy470, vyy480, deg, deh)
new_esEs8(Just(vyy470), Just(vyy480), ty_Ordering) → new_esEs9(vyy470, vyy480)
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_Integer) → new_esEs18(vyy470, vyy480)
new_primEqNat0(Zero, Succ(vyy4800)) → False
new_primEqNat0(Succ(vyy4700), Zero) → False
new_lt20(vyy3000, vyy400, app(app(ty_Either, cdh), cea)) → new_lt18(vyy3000, vyy400, cdh, cea)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, app(app(app(ty_@3, bfe), bff), bfg)) → new_ltEs13(vyy3000, vyy400, bfe, bff, bfg)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt10(vyy3000, vyy400, ty_Bool) → new_lt17(vyy3000, vyy400)
new_esEs7(Left(vyy470), Left(vyy480), ty_Char, da) → new_esEs17(vyy470, vyy480)
new_esEs25(vyy471, vyy481, ty_Int) → new_esEs12(vyy471, vyy481)
new_ltEs14(vyy3002, vyy402, ty_Float) → new_ltEs8(vyy3002, vyy402)
new_esEs15(Float(vyy470, vyy471), Float(vyy480, vyy481)) → new_esEs12(new_sr(vyy470, vyy480), new_sr(vyy471, vyy481))
new_esEs7(Left(vyy470), Left(vyy480), ty_@0, da) → new_esEs16(vyy470, vyy480)
new_lt10(vyy3000, vyy400, app(app(ty_@2, db), dc)) → new_lt9(vyy3000, vyy400, db, dc)
new_sizeFM(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), ca, cb) → vyy472
new_lt17(vyy3000, vyy400) → new_esEs10(new_compare29(vyy3000, vyy400))
new_ltEs7(Nothing, Nothing, cbe) → True
new_pePe(True, vyy47, vyy48, vyy66, bd) → True
new_esEs27(vyy471, vyy481, app(ty_Ratio, cgf)) → new_esEs20(vyy471, vyy481, cgf)
new_foldFM2(Branch(vyy470, vyy471, vyy472, vyy473, vyy474), ca, cb) → new_foldFM0(vyy470, vyy471, new_foldFM2(vyy474, ca, cb), vyy473, ca, cb)
new_esEs29(vyy470, vyy480, app(app(app(ty_@3, dea), deb), dec)) → new_esEs5(vyy470, vyy480, dea, deb, dec)
new_esEs7(Left(vyy470), Left(vyy480), app(ty_Maybe, dcb), da) → new_esEs8(vyy470, vyy480, dcb)
new_compare13(vyy3000, vyy400, False, dg) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_compare32(vyy3000, vyy400, dd, de, df) → new_compare210(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, dd, de, df), dd, de, df)
new_esEs12(vyy47, vyy48) → new_primEqInt(vyy47, vyy48)
new_compare19(vyy3000, vyy400, True, ea, eb) → LT
new_compare31(vyy3000, vyy400, ty_Ordering) → new_compare6(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, app(ty_Ratio, bhh)) → new_compare7(vyy3000, vyy400, bhh)
new_lt11(vyy3001, vyy401, ty_Char) → new_lt19(vyy3001, vyy401)
new_lt11(vyy3001, vyy401, app(ty_[], bcb)) → new_lt16(vyy3001, vyy401, bcb)
new_esEs28(vyy470, vyy480, app(app(ty_@2, chh), daa)) → new_esEs6(vyy470, vyy480, chh, daa)
new_esEs11(vyy47, vyy48, app(app(ty_Either, cg), da)) → new_esEs7(vyy47, vyy48, cg, da)
new_lt20(vyy3000, vyy400, ty_Float) → new_lt7(vyy3000, vyy400)
new_ltEs11(Left(vyy3000), Left(vyy400), app(app(ty_Either, beh), bfa), bea) → new_ltEs11(vyy3000, vyy400, beh, bfa)
new_lt11(vyy3001, vyy401, ty_Ordering) → new_lt15(vyy3001, vyy401)
new_esEs7(Right(vyy470), Right(vyy480), cg, ty_@0) → new_esEs16(vyy470, vyy480)
new_compare33(vyy3000, vyy400, ea, eb) → new_compare26(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, ea, eb), ea, eb)
new_esEs10(LT) → True
new_lt20(vyy3000, vyy400, app(ty_[], cdg)) → new_lt16(vyy3000, vyy400, cdg)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Ordering, bea) → new_ltEs5(vyy3000, vyy400)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Int, bea) → new_ltEs16(vyy3000, vyy400)
new_esEs11(vyy47, vyy48, app(app(ty_@2, cc), cd)) → new_esEs6(vyy47, vyy48, cc, cd)
new_esEs8(Nothing, Nothing, cf) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt6(vyy3000, vyy400) → new_esEs10(new_compare9(vyy3000, vyy400))
new_compare17(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs19(vyy3001, vyy401, app(app(ty_@2, ceg), ceh)) → new_ltEs6(vyy3001, vyy401, ceg, ceh)
new_esEs11(vyy47, vyy48, app(ty_Maybe, cf)) → new_esEs8(vyy47, vyy48, cf)
new_ltEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs12(vyy3000, vyy400)
new_asAs(False, vyy79) → False
new_esEs14(Double(vyy470, vyy471), Double(vyy480, vyy481)) → new_esEs12(new_sr(vyy470, vyy480), new_sr(vyy471, vyy481))
new_compare3([], [], dh) → EQ
new_ltEs11(Left(vyy3000), Right(vyy400), bfd, bea) → True
new_primMulInt(Neg(vyy30000), Pos(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulInt(Pos(vyy30000), Neg(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, app(ty_[], bgb)) → new_ltEs15(vyy3000, vyy400, bgb)
new_primMulNat0(Zero, Succ(vyy40000)) → Zero
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_esEs22(vyy471, vyy481, ty_Integer) → new_esEs18(vyy471, vyy481)
new_esEs13(:(vyy470, vyy471), [], bh) → False
new_esEs13([], :(vyy480, vyy481), bh) → False
new_esEs25(vyy471, vyy481, ty_@0) → new_esEs16(vyy471, vyy481)
new_ltEs5(LT, EQ) → True
new_esEs7(Left(vyy470), Left(vyy480), app(ty_[], dbd), da) → new_esEs13(vyy470, vyy480, dbd)
new_compare27(vyy3000, vyy400, db, dc) → new_compare24(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, db, dc), db, dc)
new_esEs29(vyy470, vyy480, ty_Char) → new_esEs17(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, ty_@0) → new_ltEs10(vyy3001, vyy401)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Char) → new_ltEs17(vyy3000, vyy400)
new_esEs27(vyy471, vyy481, ty_Integer) → new_esEs18(vyy471, vyy481)
new_esEs18(Integer(vyy470), Integer(vyy480)) → new_primEqInt(vyy470, vyy480)
new_esEs8(Just(vyy470), Just(vyy480), app(app(app(ty_@3, caa), cab), cac)) → new_esEs5(vyy470, vyy480, caa, cab, cac)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, app(ty_Ratio, bgf)) → new_ltEs4(vyy3000, vyy400, bgf)
new_not(EQ) → new_not0
new_ltEs12(True, True) → True
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, app(ty_Maybe, bge)) → new_ltEs7(vyy3000, vyy400, bge)
new_esEs27(vyy471, vyy481, app(app(ty_FiniteMap, cgb), cgc)) → new_esEs19(vyy471, vyy481, cgb, cgc)
new_compare14(vyy3000, vyy400, dg) → new_compare25(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, dg), dg)
new_ltEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, ccg)) → new_ltEs4(vyy3000, vyy400, ccg)
new_lt11(vyy3001, vyy401, ty_Int) → new_lt4(vyy3001, vyy401)
new_compare31(vyy3000, vyy400, app(ty_Maybe, bhg)) → new_compare14(vyy3000, vyy400, bhg)
new_compare31(vyy3000, vyy400, ty_Integer) → new_compare18(vyy3000, vyy400)
new_ltEs14(vyy3002, vyy402, ty_Double) → new_ltEs18(vyy3002, vyy402)
new_ltEs12(False, True) → True
new_esEs24(vyy472, vyy482, app(app(ty_FiniteMap, eh), fa)) → new_esEs19(vyy472, vyy482, eh, fa)
new_esEs16(@0, @0) → True
new_esEs25(vyy471, vyy481, app(ty_[], gd)) → new_esEs13(vyy471, vyy481, gd)
new_ltEs19(vyy3001, vyy401, ty_Int) → new_ltEs16(vyy3001, vyy401)
new_esEs8(Just(vyy470), Just(vyy480), app(ty_[], cad)) → new_esEs13(vyy470, vyy480, cad)
new_compare31(vyy3000, vyy400, ty_@0) → new_compare12(vyy3000, vyy400)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Int) → new_ltEs16(vyy3000, vyy400)
new_ltEs14(vyy3002, vyy402, ty_Char) → new_ltEs17(vyy3002, vyy402)
new_ltEs7(Just(vyy3000), Nothing, cbe) → False
new_esEs27(vyy471, vyy481, ty_Bool) → new_esEs21(vyy471, vyy481)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Integer) → new_ltEs9(vyy3000, vyy400)
new_esEs13(:(vyy470, vyy471), :(vyy480, vyy481), bh) → new_asAs(new_esEs29(vyy470, vyy480, bh), new_esEs13(vyy471, vyy481, bh))
new_esEs28(vyy470, vyy480, app(ty_Ratio, dab)) → new_esEs20(vyy470, vyy480, dab)
new_esEs24(vyy472, vyy482, app(ty_Maybe, ff)) → new_esEs8(vyy472, vyy482, ff)
new_esEs8(Just(vyy470), Just(vyy480), ty_@0) → new_esEs16(vyy470, vyy480)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_not(LT) → new_not0
new_foldFM_LE22(vyy82, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, h, ba, bb) → new_foldFM_LE12(vyy82, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, new_ltEs11(vyy1840, Left(vyy13), h, ba), h, ba, bb)
new_esEs26(vyy470, vyy480, ty_Integer) → new_esEs18(vyy470, vyy480)
new_ltEs19(vyy3001, vyy401, app(ty_Maybe, cfd)) → new_ltEs7(vyy3001, vyy401, cfd)
new_esEs25(vyy471, vyy481, app(app(app(ty_@3, ga), gb), gc)) → new_esEs5(vyy471, vyy481, ga, gb, gc)
new_lt15(vyy3000, vyy400) → new_esEs10(new_compare6(vyy3000, vyy400))
new_esEs29(vyy470, vyy480, app(app(ty_Either, dfc), dfd)) → new_esEs7(vyy470, vyy480, dfc, dfd)
new_lt10(vyy3000, vyy400, app(app(app(ty_@3, dd), de), df)) → new_lt13(vyy3000, vyy400, dd, de, df)
new_lt10(vyy3000, vyy400, app(ty_[], bbd)) → new_lt16(vyy3000, vyy400, bbd)
new_esEs24(vyy472, vyy482, ty_Ordering) → new_esEs9(vyy472, vyy482)
new_esEs29(vyy470, vyy480, ty_Bool) → new_esEs21(vyy470, vyy480)
new_esEs28(vyy470, vyy480, ty_Int) → new_esEs12(vyy470, vyy480)
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt14(vyy3000, vyy400)
new_ltEs19(vyy3001, vyy401, ty_Ordering) → new_ltEs5(vyy3001, vyy401)
new_esEs28(vyy470, vyy480, ty_Float) → new_esEs15(vyy470, vyy480)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(vyy470, vyy480, ty_Ordering) → new_esEs9(vyy470, vyy480)
new_esEs7(Left(vyy470), Left(vyy480), app(ty_Ratio, dca), da) → new_esEs20(vyy470, vyy480, dca)
new_foldFM_LE12(vyy71, vyy13, vyy180, vyy181, vyy182, vyy183, EmptyFM, True, h, ba, bb) → new_foldFM_LE30(new_keysFM_LE0(vyy180, vyy181, new_foldFM_LE5(vyy71, vyy13, vyy183, h, ba, bb), h, ba, bb), vyy13, h, ba, bb)
new_ltEs11(Left(vyy3000), Left(vyy400), ty_Bool, bea) → new_ltEs12(vyy3000, vyy400)
new_ltEs11(Right(vyy3000), Right(vyy400), bfd, ty_Float) → new_ltEs8(vyy3000, vyy400)
new_asAs(True, vyy79) → vyy79
new_lt10(vyy3000, vyy400, ty_Integer) → new_lt14(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300000), Succ(vyy40000)) → new_primPlusNat0(new_primMulNat0(vyy300000, Succ(vyy40000)), vyy40000)
new_esEs26(vyy470, vyy480, app(app(app(ty_@3, he), hf), hg)) → new_esEs5(vyy470, vyy480, he, hf, hg)
new_lt11(vyy3001, vyy401, ty_Float) → new_lt7(vyy3001, vyy401)
new_esEs27(vyy471, vyy481, app(ty_[], cga)) → new_esEs13(vyy471, vyy481, cga)
new_esEs11(vyy47, vyy48, ty_Char) → new_esEs17(vyy47, vyy48)
new_compare30(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_ltEs5(GT, GT) → True
new_esEs8(Just(vyy470), Just(vyy480), ty_Double) → new_esEs14(vyy470, vyy480)
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt17(vyy3000, vyy400)
new_esEs8(Just(vyy470), Just(vyy480), app(ty_Maybe, cbb)) → new_esEs8(vyy470, vyy480, cbb)
new_esEs29(vyy470, vyy480, ty_Integer) → new_esEs18(vyy470, vyy480)
new_esEs7(Right(vyy470), Right(vyy480), cg, app(ty_Ratio, dde)) → new_esEs20(vyy470, vyy480, dde)
new_primCompAux0(vyy3000, vyy400, vyy84, dh) → new_primCompAux00(vyy84, new_compare31(vyy3000, vyy400, dh))
new_fmToList(vyy47, ca, cb) → new_foldFM2(vyy47, ca, cb)
new_ltEs9(vyy300, vyy40) → new_not(new_compare18(vyy300, vyy40))
new_esEs26(vyy470, vyy480, app(app(ty_@2, bac), bad)) → new_esEs6(vyy470, vyy480, bac, bad)
new_ltEs19(vyy3001, vyy401, app(app(ty_Either, cfb), cfc)) → new_ltEs11(vyy3001, vyy401, cfb, cfc)
new_esEs21(True, False) → False
new_esEs21(False, True) → False
new_esEs24(vyy472, vyy482, app(ty_Ratio, fd)) → new_esEs20(vyy472, vyy482, fd)
new_ltEs14(vyy3002, vyy402, app(app(ty_Either, bde), bdf)) → new_ltEs11(vyy3002, vyy402, bde, bdf)
new_compare24(vyy3000, vyy400, False, db, dc) → new_compare10(vyy3000, vyy400, new_ltEs6(vyy3000, vyy400, db, dc), db, dc)
new_lt11(vyy3001, vyy401, ty_Double) → new_lt6(vyy3001, vyy401)
new_compare26(vyy3000, vyy400, False, ea, eb) → new_compare19(vyy3000, vyy400, new_ltEs11(vyy3000, vyy400, ea, eb), ea, eb)
new_compare19(vyy3000, vyy400, False, ea, eb) → GT
new_esEs9(LT, LT) → True
new_primCompAux00(vyy88, GT) → GT
new_esEs25(vyy471, vyy481, app(app(ty_Either, hc), hd)) → new_esEs7(vyy471, vyy481, hc, hd)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs25(vyy471, vyy481, app(ty_Maybe, hb)) → new_esEs8(vyy471, vyy481, hb)
new_lt11(vyy3001, vyy401, app(app(ty_@2, bbh), bca)) → new_lt9(vyy3001, vyy401, bbh, bca)
new_ltEs5(GT, EQ) → False
new_esEs29(vyy470, vyy480, ty_Ordering) → new_esEs9(vyy470, vyy480)
new_esEs6(@2(vyy470, vyy471), @2(vyy480, vyy481), cc, cd) → new_asAs(new_esEs28(vyy470, vyy480, cc), new_esEs27(vyy471, vyy481, cd))
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs25(vyy471, vyy481, app(ty_Ratio, ha)) → new_esEs20(vyy471, vyy481, ha)
new_esEs26(vyy470, vyy480, app(ty_Ratio, bae)) → new_esEs20(vyy470, vyy480, bae)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs24(vyy472, vyy482, ty_Double) → new_esEs14(vyy472, vyy482)
new_compare16(vyy3000, vyy400, False) → GT
new_ltEs11(Left(vyy3000), Left(vyy400), app(ty_Maybe, bfb), bea) → new_ltEs7(vyy3000, vyy400, bfb)
The set Q consists of the following terms:
new_primCompAux00(x0, GT)
new_lt20(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Int)
new_compare6(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs11(Right(x0), Left(x1), x2, x3)
new_ltEs11(Left(x0), Right(x1), x2, x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs11(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare24(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs29(x0, x1, app(ty_[], x2))
new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs11(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt11(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Bool)
new_compare23(x0, x1, True)
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs13([], [], x0)
new_esEs24(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Double)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Bool)
new_ltEs8(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs13([], :(x0, x1), x2)
new_ltEs14(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_compare33(x0, x1, x2, x3)
new_compare9(Double(x0, x1), Double(x2, x3))
new_compare8(x0, x1)
new_lt19(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt11(x0, x1, ty_Bool)
new_ltEs11(Left(x0), Left(x1), ty_Int, x2)
new_ltEs11(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs10(GT)
new_esEs26(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs12(x0, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs29(x0, x1, ty_Float)
new_compare30(Char(x0), Char(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, ty_Ordering)
new_lt11(x0, x1, ty_Int)
new_compare13(x0, x1, False, x2)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs16(@0, @0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt11(x0, x1, ty_Integer)
new_ltEs11(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_ltEs15(x0, x1, x2)
new_primMulNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Char)
new_ltEs11(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt11(x0, x1, app(ty_[], x2))
new_ltEs14(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Ordering)
new_keysFM_LE0(x0, x1, x2, x3, x4, x5)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs11(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare15(x0, x1, True)
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_esEs27(x0, x1, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_@0)
new_ltEs7(Nothing, Just(x0), x1)
new_esEs8(Just(x0), Nothing, x1)
new_lt5(x0, x1, x2)
new_ltEs14(x0, x1, ty_Int)
new_ltEs14(x0, x1, ty_Double)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt11(x0, x1, ty_Char)
new_ltEs11(Left(x0), Left(x1), ty_Char, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_lt13(x0, x1, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs11(x0, x1, ty_Char)
new_compare12(@0, @0)
new_compare32(x0, x1, x2, x3, x4)
new_ltEs11(Right(x0), Right(x1), x2, ty_Double)
new_esEs25(x0, x1, ty_Float)
new_compare28(x0, x1, True)
new_ltEs11(Left(x0), Left(x1), ty_Double, x2)
new_esEs15(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Zero)
new_foldFM_LE30(x0, x1, x2, x3, x4)
new_ltEs11(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs23(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs4(x0, x1, x2)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs11(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(Just(x0), Just(x1), ty_Float)
new_lt11(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs14(x0, x1, ty_Ordering)
new_esEs8(Nothing, Just(x0), x1)
new_compare13(x0, x1, True, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primPlusNat0(Zero, x0)
new_compare17(Float(x0, x1), Float(x2, x3))
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs16(x0, x1)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_lt14(x0, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, x2, x3)
new_esEs8(Nothing, Nothing, x0)
new_esEs29(x0, x1, ty_Bool)
new_ltEs11(Right(x0), Right(x1), x2, ty_Bool)
new_esEs8(Just(x0), Just(x1), ty_@0)
new_compare23(x0, x1, False)
new_esEs28(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Double)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs12(False, False)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare31(x0, x1, ty_Bool)
new_ltEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare28(x0, x1, False)
new_compare26(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, ty_Integer)
new_compare10(x0, x1, False, x2, x3)
new_esEs13(:(x0, x1), [], x2)
new_esEs27(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_primPlusNat1(Zero, Zero)
new_not0
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, ty_@0)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs11(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Integer)
new_ltEs14(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_compare27(x0, x1, x2, x3)
new_ltEs11(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_compare14(x0, x1, x2)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primCompAux00(x0, LT)
new_asAs(False, x0)
new_primEqNat0(Zero, Succ(x0))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(GT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCompAux0(x0, x1, x2, x3)
new_esEs9(GT, GT)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs10(x0, x1)
new_compare3([], :(x0, x1), x2)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt11(x0, x1, ty_Float)
new_lt4(x0, x1)
new_compare31(x0, x1, ty_Ordering)
new_fmToList(x0, x1, x2)
new_ltEs14(x0, x1, app(ty_Ratio, x2))
new_compare16(x0, x1, False)
new_pePe(True, x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs11(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt7(x0, x1)
new_ltEs11(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, ty_Integer)
new_ltEs7(Nothing, Nothing, x0)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs11(x0, x1, ty_Integer)
new_esEs9(EQ, EQ)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_compare16(x0, x1, True)
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_ltEs14(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare3(:(x0, x1), [], x2)
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_ltEs11(Right(x0), Right(x1), x2, ty_@0)
new_compare31(x0, x1, ty_Float)
new_lt10(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(Just(x0), Just(x1), ty_Double)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1)
new_lt15(x0, x1)
new_lt17(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sizeFM(EmptyFM, x0, x1)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, ty_Double)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_lt18(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs12(False, True)
new_ltEs12(True, False)
new_ltEs14(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_compare18(Integer(x0), Integer(x1))
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Char)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs10(EQ)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Float)
new_primCmpNat0(Zero, Zero)
new_esEs28(x0, x1, ty_Float)
new_ltEs11(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare31(x0, x1, app(ty_[], x2))
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs11(Left(x0), Left(x1), ty_Integer, x2)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs11(Left(x0), Left(x1), ty_Bool, x2)
new_lt10(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_lt12(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt10(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs29(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_ltEs5(GT, GT)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_ltEs11(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_@0)
new_lt11(x0, x1, ty_Ordering)
new_lt9(x0, x1, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1, ty_Char)
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs10(LT)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs17(Char(x0), Char(x1))
new_lt11(x0, x1, ty_@0)
new_esEs21(True, True)
new_compare210(x0, x1, False, x2, x3, x4)
new_compare25(x0, x1, False, x2)
new_lt8(x0, x1, x2)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_not(EQ)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_compare31(x0, x1, ty_Int)
new_ltEs11(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, ty_Int)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt6(x0, x1)
new_compare25(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Char)
new_compare19(x0, x1, False, x2, x3)
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, EmptyFM, True, x6, x7, x8)
new_esEs24(x0, x1, ty_Bool)
new_lt16(x0, x1, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_foldFM2(EmptyFM, x0, x1)
new_esEs24(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_@0)
new_esEs21(True, False)
new_esEs21(False, True)
new_compare15(x0, x1, False)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs12(True, True)
new_ltEs5(EQ, EQ)
new_compare19(x0, x1, True, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, EQ)
new_ltEs11(Right(x0), Right(x1), x2, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_sr(x0, x1)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs11(Right(x0), Right(x1), x2, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_foldFM_LE5(x0, x1, EmptyFM, x2, x3, x4)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, True, x2, x3)
new_ltEs11(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs8(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs18(Integer(x0), Integer(x1))
new_compare11(x0, x1, False, x2, x3, x4)
new_compare31(x0, x1, ty_Double)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs11(Left(x0), Left(x1), ty_Ordering, x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare3([], [], x0)
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_ltEs11(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs11(x0, x1, ty_Bool)
new_ltEs17(x0, x1)
new_esEs22(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs21(False, False)
new_compare31(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs14(x0, x1, ty_Integer)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs25(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs11(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_compare24(x0, x1, False, x2, x3)
new_not(LT)
new_compare11(x0, x1, True, x2, x3, x4)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs9(LT, LT)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs5(LT, LT)
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_ltEs11(vyy1840, Left(vyy13), h, ba), 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_keysFM_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