YES 10.876
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 => FiniteMap (Maybe b) a -> Maybe b -> [Maybe b]) :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [Maybe 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 (\key elt rest ->(key,elt) : rest) [] fm |
|
| | 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 a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | 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 a => FiniteMap (Maybe a) b -> Maybe a -> [Maybe a]) :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [Maybe 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 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 :: (b -> a -> c -> c) -> c -> FiniteMap b a -> c
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord 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
|
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 a => FiniteMap (Maybe a) b -> Maybe a -> [Maybe a]) :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [Maybe 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 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 :: (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 -> 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 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 _ _ 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 b => FiniteMap (Maybe b) a -> Maybe b -> [Maybe b]) :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [Maybe 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 :: (a -> b -> c -> c) -> c -> FiniteMap a b -> c
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord 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 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
|
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 b => FiniteMap (Maybe b) a -> Maybe b -> [Maybe b]) :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [Maybe 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 b a -> [(b,a)]
| 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 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_LE1 | k z fr key elt vx fm_l fm_r True | = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = foldFM_LE k z fr fm_l |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
| foldFM_LE3 | k z fr EmptyFM | = z |
| foldFM_LE3 | vvu vvv vvw vvx | = foldFM_LE2 vvu vvv vvw vvx |
The following Function with conditions
| compare | x y |
| | | x == y | |
| | | x <= y | |
| | | otherwise | |
|
is transformed to
| compare | x y | = compare3 x y |
| compare2 | x y True | = EQ |
| compare2 | x y False | = compare1 x y (x <= y) |
| compare1 | x y True | = LT |
| compare1 | x y False | = compare0 x y otherwise |
| compare3 | x y | = compare2 x y (x == y) |
The following Function with conditions
| gcd' | x 0 | = x |
| gcd' | x y | = gcd' y (x `rem` y) |
is transformed to
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
| gcd'0 | x y | = gcd' y (x `rem` y) |
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
The following Function with conditions
| gcd | 0 0 | = error [] |
| gcd | x y | =
| gcd' (abs x) (abs y) |
| where |
| gcd' | x 0 | = x |
| gcd' | x y | = gcd' y (x `rem` y) |
|
|
is transformed to
| gcd | vwy vwz | = gcd3 vwy vwz |
| gcd | x y | = gcd0 x y |
| gcd0 | x y | =
| gcd' (abs x) (abs y) |
| where |
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
|
|
| gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
|
|
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
|
|
| gcd1 | True vwy vwz | = error [] |
| gcd1 | vxu vxv vxw | = gcd0 vxv vxw |
| gcd2 | True vwy vwz | = gcd1 (vwz == 0) vwy vwz |
| gcd2 | vxx vxy vxz | = gcd0 vxy vxz |
| gcd3 | vwy vwz | = gcd2 (vwy == 0) vwy vwz |
| gcd3 | vyu vyv | = gcd0 vyu vyv |
The following Function with conditions
is transformed to
| absReal1 | x True | = x |
| absReal1 | x False | = absReal0 x otherwise |
| absReal0 | x True | = `negate` x |
| absReal2 | x | = absReal1 x (x >= 0) |
The following Function with conditions
is transformed to
| undefined0 | True | = undefined |
| undefined1 | | = undefined0 False |
The following Function with conditions
| reduce | x y |
| | | y == 0 | |
| | | otherwise |
| = | x `quot` d :% (y `quot` d) |
|
|
| where | |
|
is transformed to
| reduce2 | x y | =
| reduce1 x y (y == 0) |
| where | |
|
| reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
| reduce1 | x y True | = error [] |
| reduce1 | x y False | = reduce0 x y otherwise |
|
|
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
mainModule FiniteMap
|
| ((keysFM_LE :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [Maybe b]) :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [Maybe 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 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 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 a b -> 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
| reduce2Reduce1 | vyw vyx x y True | = error [] |
| reduce2Reduce1 | vyw vyx x y False | = reduce2Reduce0 vyw vyx x y otherwise |
| reduce2D | vyw vyx | = gcd vyw vyx |
| reduce2Reduce0 | vyw vyx x y True | = x `quot` reduce2D vyw vyx :% (y `quot` reduce2D vyw vyx) |
The bindings of the following Let/Where expression
| gcd' (abs x) (abs y) |
| where |
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
|
|
| gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
|
|
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
|
are unpacked to the following functions on top level
| gcd0Gcd'0 | x y | = gcd0Gcd' y (x `rem` y) |
| 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'1 | True x vvy | = x |
| gcd0Gcd'1 | vvz vwu vwv | = gcd0Gcd'0 vwu vwv |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
mainModule FiniteMap
|
| ((keysFM_LE :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [Maybe a]) :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [Maybe 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 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 | = | 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
|
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 a => FiniteMap (Maybe a) b -> Maybe a -> [Maybe 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 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 -> c -> b -> b) -> b -> FiniteMap a c -> 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 b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | 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 | = | 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_foldFM(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, h, ba), vyy4133, h, ba)
new_foldFM(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM(vyy410, vyy411, vyy85, vyy4134, h, ba)
The TRS R consists of the following rules:
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, h, ba) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, h, ba), vyy4133, 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(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, h, ba), vyy4133, h, ba)
The graph contains the following edges 4 > 1, 4 > 2, 4 > 4, 5 >= 5, 6 >= 6
- new_foldFM(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM(vyy410, vyy411, vyy85, vyy4134, 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
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM1(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), h, ba) → new_foldFM1(vyy414, 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(vyy410, vyy411, vyy412, vyy413, vyy414), h, ba) → new_foldFM1(vyy414, 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
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primEqNat(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat(vyy4000, vyy4100)
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(vyy4000), Succ(vyy4100)) → new_primEqNat(vyy4000, vyy4100)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(vyy8600), Succ(vyy3001000)) → new_primPlusNat(vyy8600, vyy3001000)
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(vyy8600), Succ(vyy3001000)) → new_primPlusNat(vyy8600, vyy3001000)
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(vyy40000), Succ(vyy300100)) → new_primMulNat(vyy40000, Succ(vyy300100))
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(vyy40000), Succ(vyy300100)) → new_primMulNat(vyy40000, Succ(vyy300100))
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
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(app(ty_@3, ga), gb), gc), eb) → new_esEs1(vyy401, vyy411, ga, gb, gc)
new_esEs0(Just(vyy400), Just(vyy410), app(ty_Maybe, ce)) → new_esEs0(vyy400, vyy410, ce)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(app(ty_@3, hd), he), hf)) → new_esEs1(vyy402, vyy412, hd, he, hf)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdh) → new_esEs3(vyy400, vyy410, beg, beh)
new_esEs0(Just(vyy400), Just(vyy410), app(ty_[], cd)) → new_esEs(vyy400, vyy410, cd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs1(vyy400, vyy410, bah, bba, bbb)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_[], bdg), bdh) → new_esEs(vyy400, vyy410, bdg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_Maybe, hc)) → new_esEs0(vyy402, vyy412, hc)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, bag), baf) → new_esEs0(vyy400, vyy410, bag)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_@2, hg), hh)) → new_esEs2(vyy402, vyy412, hg, hh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, ba)) → new_esEs0(vyy400, vyy410, ba)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bbg), bbh), baf) → new_esEs4(vyy400, vyy410, bbg, bbh)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_@2, bee), bef), bdh) → new_esEs2(vyy400, vyy410, bee, bef)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, ca), cb)) → new_esEs4(vyy400, vyy410, ca, cb)
new_esEs4(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdh) → new_esEs1(vyy400, vyy410, beb, bec, bed)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_Maybe, bea), bdh) → new_esEs0(vyy400, vyy410, bea)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_Either, gh), ha), eb) → new_esEs4(vyy401, vyy411, gh, ha)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, fc), fd), ea, eb) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs3(vyy40, vyy41, bde, bdf) → new_esEs(new_fmToList(vyy40, bde, bdf), new_fmToList(vyy41, bde, bdf), app(app(ty_@2, bde), bdf))
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, bbe), bbf), baf) → new_esEs3(vyy400, vyy410, bbe, bbf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, eg), eh), ea, eb) → new_esEs2(vyy400, vyy410, eg, eh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_[], hb)) → new_esEs(vyy402, vyy412, hb)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_[], bfd)) → new_esEs(vyy400, vyy410, bfd)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_@2, bga), bgb)) → new_esEs2(vyy400, vyy410, bga, bgb)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_[], fg), eb) → new_esEs(vyy401, vyy411, fg)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vyy401, vyy411, bcd, bce, bcf)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_Maybe, bfe)) → new_esEs0(vyy400, vyy410, bfe)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs1(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_@2, gd), ge), eb) → new_esEs2(vyy401, vyy411, gd, ge)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_FiniteMap, bda), bdb)) → new_esEs3(vyy401, vyy411, bda, bdb)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_@2, bcg), bch)) → new_esEs2(vyy401, vyy411, bcg, bch)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, be), bf)) → new_esEs2(vyy400, vyy410, be, bf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_Maybe, fh), eb) → new_esEs0(vyy401, vyy411, fh)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bbc), bbd), baf) → new_esEs2(vyy400, vyy410, bbc, bbd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(ty_Maybe, bcc)) → new_esEs0(vyy401, vyy411, bcc)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_FiniteMap, gf), gg), eb) → new_esEs3(vyy401, vyy411, gf, gg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_Either, bac), bad)) → new_esEs4(vyy402, vyy412, bac, bad)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, ed), ee), ef), ea, eb) → new_esEs1(vyy400, vyy410, ed, ee, ef)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_@2, db), dc)) → new_esEs2(vyy400, vyy410, db, dc)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, dd), de)) → new_esEs3(vyy400, vyy410, dd, de)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), cc) → new_esEs(vyy401, vyy411, cc)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(ty_[], bcb)) → new_esEs(vyy401, vyy411, bcb)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs1(vyy400, vyy410, bb, bc, bd)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_Either, bfa), bfb), bdh) → new_esEs4(vyy400, vyy410, bfa, bfb)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_Either, bdc), bdd)) → new_esEs4(vyy401, vyy411, bdc, bdd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_FiniteMap, baa), bab)) → new_esEs3(vyy402, vyy412, baa, bab)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], dh), ea, eb) → new_esEs(vyy400, vyy410, dh)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_Either, df), dg)) → new_esEs4(vyy400, vyy410, df, dg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, ec), ea, eb) → new_esEs0(vyy400, vyy410, ec)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], bae), baf) → new_esEs(vyy400, vyy410, bae)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bg), bh)) → new_esEs3(vyy400, vyy410, bg, bh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, fa), fb), ea, eb) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs0(Just(vyy400), Just(vyy410), app(app(app(ty_@3, cf), cg), da)) → new_esEs1(vyy400, vyy410, cf, cg, da)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], h)) → new_esEs(vyy400, vyy410, h)
The TRS R consists of the following rules:
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bde, bdf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bde, bdf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bde, bdf), vyy4133, bde, bdf)
new_fmToList(vyy41, bde, bdf) → new_foldFM2(vyy41, bde, bdf)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bde, bdf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bde, bdf), vyy413, bde, bdf)
new_foldFM2(EmptyFM, bde, bdf) → []
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
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_esEs3(vyy40, vyy41, bde, bdf) → new_esEs(new_fmToList(vyy40, bde, bdf), new_fmToList(vyy41, bde, bdf), app(app(ty_@2, bde), bdf)) at position [0] we obtained the following new rules:
new_esEs3(vyy40, vyy41, bde, bdf) → new_esEs(new_foldFM2(vyy40, bde, bdf), new_fmToList(vyy41, bde, bdf), app(app(ty_@2, bde), bdf))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(app(ty_@3, ga), gb), gc), eb) → new_esEs1(vyy401, vyy411, ga, gb, gc)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdh) → new_esEs3(vyy400, vyy410, beg, beh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(app(ty_@3, hd), he), hf)) → new_esEs1(vyy402, vyy412, hd, he, hf)
new_esEs0(Just(vyy400), Just(vyy410), app(ty_Maybe, ce)) → new_esEs0(vyy400, vyy410, ce)
new_esEs0(Just(vyy400), Just(vyy410), app(ty_[], cd)) → new_esEs(vyy400, vyy410, cd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs1(vyy400, vyy410, bah, bba, bbb)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_[], bdg), bdh) → new_esEs(vyy400, vyy410, bdg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_Maybe, hc)) → new_esEs0(vyy402, vyy412, hc)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, bag), baf) → new_esEs0(vyy400, vyy410, bag)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_@2, hg), hh)) → new_esEs2(vyy402, vyy412, hg, hh)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_@2, bee), bef), bdh) → new_esEs2(vyy400, vyy410, bee, bef)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bbg), bbh), baf) → new_esEs4(vyy400, vyy410, bbg, bbh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, ba)) → new_esEs0(vyy400, vyy410, ba)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, ca), cb)) → new_esEs4(vyy400, vyy410, ca, cb)
new_esEs4(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdh) → new_esEs1(vyy400, vyy410, beb, bec, bed)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_Either, gh), ha), eb) → new_esEs4(vyy401, vyy411, gh, ha)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_Maybe, bea), bdh) → new_esEs0(vyy400, vyy410, bea)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, fc), fd), ea, eb) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, bbe), bbf), baf) → new_esEs3(vyy400, vyy410, bbe, bbf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, eg), eh), ea, eb) → new_esEs2(vyy400, vyy410, eg, eh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_[], hb)) → new_esEs(vyy402, vyy412, hb)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_@2, bga), bgb)) → new_esEs2(vyy400, vyy410, bga, bgb)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_[], bfd)) → new_esEs(vyy400, vyy410, bfd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_[], fg), eb) → new_esEs(vyy401, vyy411, fg)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vyy401, vyy411, bcd, bce, bcf)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_Maybe, bfe)) → new_esEs0(vyy400, vyy410, bfe)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs1(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_@2, gd), ge), eb) → new_esEs2(vyy401, vyy411, gd, ge)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_FiniteMap, bda), bdb)) → new_esEs3(vyy401, vyy411, bda, bdb)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_@2, bcg), bch)) → new_esEs2(vyy401, vyy411, bcg, bch)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, be), bf)) → new_esEs2(vyy400, vyy410, be, bf)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(ty_Maybe, bcc)) → new_esEs0(vyy401, vyy411, bcc)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bbc), bbd), baf) → new_esEs2(vyy400, vyy410, bbc, bbd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_Maybe, fh), eb) → new_esEs0(vyy401, vyy411, fh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_Either, bac), bad)) → new_esEs4(vyy402, vyy412, bac, bad)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_FiniteMap, gf), gg), eb) → new_esEs3(vyy401, vyy411, gf, gg)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, ed), ee), ef), ea, eb) → new_esEs1(vyy400, vyy410, ed, ee, ef)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_@2, db), dc)) → new_esEs2(vyy400, vyy410, db, dc)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, dd), de)) → new_esEs3(vyy400, vyy410, dd, de)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(ty_[], bcb)) → new_esEs(vyy401, vyy411, bcb)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), cc) → new_esEs(vyy401, vyy411, cc)
new_esEs3(vyy40, vyy41, bde, bdf) → new_esEs(new_foldFM2(vyy40, bde, bdf), new_fmToList(vyy41, bde, bdf), app(app(ty_@2, bde), bdf))
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs1(vyy400, vyy410, bb, bc, bd)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_Either, bfa), bfb), bdh) → new_esEs4(vyy400, vyy410, bfa, bfb)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_Either, bdc), bdd)) → new_esEs4(vyy401, vyy411, bdc, bdd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_FiniteMap, baa), bab)) → new_esEs3(vyy402, vyy412, baa, bab)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], dh), ea, eb) → new_esEs(vyy400, vyy410, dh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, ec), ea, eb) → new_esEs0(vyy400, vyy410, ec)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_Either, df), dg)) → new_esEs4(vyy400, vyy410, df, dg)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], bae), baf) → new_esEs(vyy400, vyy410, bae)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bg), bh)) → new_esEs3(vyy400, vyy410, bg, bh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, fa), fb), ea, eb) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], h)) → new_esEs(vyy400, vyy410, h)
new_esEs0(Just(vyy400), Just(vyy410), app(app(app(ty_@3, cf), cg), da)) → new_esEs1(vyy400, vyy410, cf, cg, da)
The TRS R consists of the following rules:
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bde, bdf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bde, bdf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bde, bdf), vyy4133, bde, bdf)
new_fmToList(vyy41, bde, bdf) → new_foldFM2(vyy41, bde, bdf)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bde, bdf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bde, bdf), vyy413, bde, bdf)
new_foldFM2(EmptyFM, bde, bdf) → []
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
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_esEs3(vyy40, vyy41, bde, bdf) → new_esEs(new_foldFM2(vyy40, bde, bdf), new_fmToList(vyy41, bde, bdf), app(app(ty_@2, bde), bdf)) at position [1] we obtained the following new rules:
new_esEs3(vyy40, vyy41, bde, bdf) → new_esEs(new_foldFM2(vyy40, bde, bdf), new_foldFM2(vyy41, bde, bdf), app(app(ty_@2, bde), bdf))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(app(ty_@3, ga), gb), gc), eb) → new_esEs1(vyy401, vyy411, ga, gb, gc)
new_esEs0(Just(vyy400), Just(vyy410), app(ty_Maybe, ce)) → new_esEs0(vyy400, vyy410, ce)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(app(ty_@3, hd), he), hf)) → new_esEs1(vyy402, vyy412, hd, he, hf)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdh) → new_esEs3(vyy400, vyy410, beg, beh)
new_esEs0(Just(vyy400), Just(vyy410), app(ty_[], cd)) → new_esEs(vyy400, vyy410, cd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs1(vyy400, vyy410, bah, bba, bbb)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_[], bdg), bdh) → new_esEs(vyy400, vyy410, bdg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_Maybe, hc)) → new_esEs0(vyy402, vyy412, hc)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, bag), baf) → new_esEs0(vyy400, vyy410, bag)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_@2, hg), hh)) → new_esEs2(vyy402, vyy412, hg, hh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, ba)) → new_esEs0(vyy400, vyy410, ba)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bbg), bbh), baf) → new_esEs4(vyy400, vyy410, bbg, bbh)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_@2, bee), bef), bdh) → new_esEs2(vyy400, vyy410, bee, bef)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, ca), cb)) → new_esEs4(vyy400, vyy410, ca, cb)
new_esEs4(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdh) → new_esEs1(vyy400, vyy410, beb, bec, bed)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_Maybe, bea), bdh) → new_esEs0(vyy400, vyy410, bea)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_Either, gh), ha), eb) → new_esEs4(vyy401, vyy411, gh, ha)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, fc), fd), ea, eb) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, bbe), bbf), baf) → new_esEs3(vyy400, vyy410, bbe, bbf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, eg), eh), ea, eb) → new_esEs2(vyy400, vyy410, eg, eh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_[], hb)) → new_esEs(vyy402, vyy412, hb)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_[], bfd)) → new_esEs(vyy400, vyy410, bfd)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_@2, bga), bgb)) → new_esEs2(vyy400, vyy410, bga, bgb)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_[], fg), eb) → new_esEs(vyy401, vyy411, fg)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vyy401, vyy411, bcd, bce, bcf)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_Maybe, bfe)) → new_esEs0(vyy400, vyy410, bfe)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs1(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_@2, gd), ge), eb) → new_esEs2(vyy401, vyy411, gd, ge)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_FiniteMap, bda), bdb)) → new_esEs3(vyy401, vyy411, bda, bdb)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_@2, bcg), bch)) → new_esEs2(vyy401, vyy411, bcg, bch)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, be), bf)) → new_esEs2(vyy400, vyy410, be, bf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_Maybe, fh), eb) → new_esEs0(vyy401, vyy411, fh)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bbc), bbd), baf) → new_esEs2(vyy400, vyy410, bbc, bbd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(ty_Maybe, bcc)) → new_esEs0(vyy401, vyy411, bcc)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_FiniteMap, gf), gg), eb) → new_esEs3(vyy401, vyy411, gf, gg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_Either, bac), bad)) → new_esEs4(vyy402, vyy412, bac, bad)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, ed), ee), ef), ea, eb) → new_esEs1(vyy400, vyy410, ed, ee, ef)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_@2, db), dc)) → new_esEs2(vyy400, vyy410, db, dc)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, dd), de)) → new_esEs3(vyy400, vyy410, dd, de)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), cc) → new_esEs(vyy401, vyy411, cc)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(ty_[], bcb)) → new_esEs(vyy401, vyy411, bcb)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs1(vyy400, vyy410, bb, bc, bd)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_Either, bfa), bfb), bdh) → new_esEs4(vyy400, vyy410, bfa, bfb)
new_esEs3(vyy40, vyy41, bde, bdf) → new_esEs(new_foldFM2(vyy40, bde, bdf), new_foldFM2(vyy41, bde, bdf), app(app(ty_@2, bde), bdf))
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_Either, bdc), bdd)) → new_esEs4(vyy401, vyy411, bdc, bdd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_FiniteMap, baa), bab)) → new_esEs3(vyy402, vyy412, baa, bab)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], dh), ea, eb) → new_esEs(vyy400, vyy410, dh)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_Either, df), dg)) → new_esEs4(vyy400, vyy410, df, dg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, ec), ea, eb) → new_esEs0(vyy400, vyy410, ec)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], bae), baf) → new_esEs(vyy400, vyy410, bae)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bg), bh)) → new_esEs3(vyy400, vyy410, bg, bh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, fa), fb), ea, eb) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs0(Just(vyy400), Just(vyy410), app(app(app(ty_@3, cf), cg), da)) → new_esEs1(vyy400, vyy410, cf, cg, da)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], h)) → new_esEs(vyy400, vyy410, h)
The TRS R consists of the following rules:
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bde, bdf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bde, bdf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bde, bdf), vyy4133, bde, bdf)
new_fmToList(vyy41, bde, bdf) → new_foldFM2(vyy41, bde, bdf)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bde, bdf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bde, bdf), vyy413, bde, bdf)
new_foldFM2(EmptyFM, bde, bdf) → []
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
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
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(app(ty_@3, ga), gb), gc), eb) → new_esEs1(vyy401, vyy411, ga, gb, gc)
new_esEs0(Just(vyy400), Just(vyy410), app(ty_Maybe, ce)) → new_esEs0(vyy400, vyy410, ce)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(app(ty_@3, hd), he), hf)) → new_esEs1(vyy402, vyy412, hd, he, hf)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdh) → new_esEs3(vyy400, vyy410, beg, beh)
new_esEs0(Just(vyy400), Just(vyy410), app(ty_[], cd)) → new_esEs(vyy400, vyy410, cd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs1(vyy400, vyy410, bah, bba, bbb)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_[], bdg), bdh) → new_esEs(vyy400, vyy410, bdg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_Maybe, hc)) → new_esEs0(vyy402, vyy412, hc)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, bag), baf) → new_esEs0(vyy400, vyy410, bag)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_@2, hg), hh)) → new_esEs2(vyy402, vyy412, hg, hh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, ba)) → new_esEs0(vyy400, vyy410, ba)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bbg), bbh), baf) → new_esEs4(vyy400, vyy410, bbg, bbh)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_@2, bee), bef), bdh) → new_esEs2(vyy400, vyy410, bee, bef)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, ca), cb)) → new_esEs4(vyy400, vyy410, ca, cb)
new_esEs4(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdh) → new_esEs1(vyy400, vyy410, beb, bec, bed)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_Maybe, bea), bdh) → new_esEs0(vyy400, vyy410, bea)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_Either, gh), ha), eb) → new_esEs4(vyy401, vyy411, gh, ha)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, fc), fd), ea, eb) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, bbe), bbf), baf) → new_esEs3(vyy400, vyy410, bbe, bbf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, eg), eh), ea, eb) → new_esEs2(vyy400, vyy410, eg, eh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_[], hb)) → new_esEs(vyy402, vyy412, hb)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_[], bfd)) → new_esEs(vyy400, vyy410, bfd)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_@2, bga), bgb)) → new_esEs2(vyy400, vyy410, bga, bgb)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_[], fg), eb) → new_esEs(vyy401, vyy411, fg)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vyy401, vyy411, bcd, bce, bcf)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_Maybe, bfe)) → new_esEs0(vyy400, vyy410, bfe)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs1(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_@2, gd), ge), eb) → new_esEs2(vyy401, vyy411, gd, ge)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_FiniteMap, bda), bdb)) → new_esEs3(vyy401, vyy411, bda, bdb)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_@2, bcg), bch)) → new_esEs2(vyy401, vyy411, bcg, bch)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, be), bf)) → new_esEs2(vyy400, vyy410, be, bf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_Maybe, fh), eb) → new_esEs0(vyy401, vyy411, fh)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bbc), bbd), baf) → new_esEs2(vyy400, vyy410, bbc, bbd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(ty_Maybe, bcc)) → new_esEs0(vyy401, vyy411, bcc)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_FiniteMap, gf), gg), eb) → new_esEs3(vyy401, vyy411, gf, gg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_Either, bac), bad)) → new_esEs4(vyy402, vyy412, bac, bad)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, ed), ee), ef), ea, eb) → new_esEs1(vyy400, vyy410, ed, ee, ef)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_@2, db), dc)) → new_esEs2(vyy400, vyy410, db, dc)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, dd), de)) → new_esEs3(vyy400, vyy410, dd, de)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), cc) → new_esEs(vyy401, vyy411, cc)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(ty_[], bcb)) → new_esEs(vyy401, vyy411, bcb)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs1(vyy400, vyy410, bb, bc, bd)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_Either, bfa), bfb), bdh) → new_esEs4(vyy400, vyy410, bfa, bfb)
new_esEs3(vyy40, vyy41, bde, bdf) → new_esEs(new_foldFM2(vyy40, bde, bdf), new_foldFM2(vyy41, bde, bdf), app(app(ty_@2, bde), bdf))
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_Either, bdc), bdd)) → new_esEs4(vyy401, vyy411, bdc, bdd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_FiniteMap, baa), bab)) → new_esEs3(vyy402, vyy412, baa, bab)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], dh), ea, eb) → new_esEs(vyy400, vyy410, dh)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_Either, df), dg)) → new_esEs4(vyy400, vyy410, df, dg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, ec), ea, eb) → new_esEs0(vyy400, vyy410, ec)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], bae), baf) → new_esEs(vyy400, vyy410, bae)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bg), bh)) → new_esEs3(vyy400, vyy410, bg, bh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, fa), fb), ea, eb) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs0(Just(vyy400), Just(vyy410), app(app(app(ty_@3, cf), cg), da)) → new_esEs1(vyy400, vyy410, cf, cg, da)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], h)) → new_esEs(vyy400, vyy410, h)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bde, bdf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bde, bdf), vyy413, bde, bdf)
new_foldFM2(EmptyFM, bde, bdf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bde, bdf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bde, bdf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bde, bdf), vyy4133, bde, bdf)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
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
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(app(ty_@3, ga), gb), gc), eb) → new_esEs1(vyy401, vyy411, ga, gb, gc)
new_esEs0(Just(vyy400), Just(vyy410), app(ty_Maybe, ce)) → new_esEs0(vyy400, vyy410, ce)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(app(ty_@3, hd), he), hf)) → new_esEs1(vyy402, vyy412, hd, he, hf)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdh) → new_esEs3(vyy400, vyy410, beg, beh)
new_esEs0(Just(vyy400), Just(vyy410), app(ty_[], cd)) → new_esEs(vyy400, vyy410, cd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs1(vyy400, vyy410, bah, bba, bbb)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_[], bdg), bdh) → new_esEs(vyy400, vyy410, bdg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_Maybe, hc)) → new_esEs0(vyy402, vyy412, hc)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, bag), baf) → new_esEs0(vyy400, vyy410, bag)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_@2, hg), hh)) → new_esEs2(vyy402, vyy412, hg, hh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, ba)) → new_esEs0(vyy400, vyy410, ba)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bbg), bbh), baf) → new_esEs4(vyy400, vyy410, bbg, bbh)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_@2, bee), bef), bdh) → new_esEs2(vyy400, vyy410, bee, bef)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, ca), cb)) → new_esEs4(vyy400, vyy410, ca, cb)
new_esEs4(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdh) → new_esEs1(vyy400, vyy410, beb, bec, bed)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_Either, gh), ha), eb) → new_esEs4(vyy401, vyy411, gh, ha)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_Maybe, bea), bdh) → new_esEs0(vyy400, vyy410, bea)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, fc), fd), ea, eb) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, bbe), bbf), baf) → new_esEs3(vyy400, vyy410, bbe, bbf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, eg), eh), ea, eb) → new_esEs2(vyy400, vyy410, eg, eh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_[], hb)) → new_esEs(vyy402, vyy412, hb)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_@2, bga), bgb)) → new_esEs2(vyy400, vyy410, bga, bgb)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_[], bfd)) → new_esEs(vyy400, vyy410, bfd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_[], fg), eb) → new_esEs(vyy401, vyy411, fg)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vyy401, vyy411, bcd, bce, bcf)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_Maybe, bfe)) → new_esEs0(vyy400, vyy410, bfe)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs1(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_@2, gd), ge), eb) → new_esEs2(vyy401, vyy411, gd, ge)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_FiniteMap, bda), bdb)) → new_esEs3(vyy401, vyy411, bda, bdb)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_@2, bcg), bch)) → new_esEs2(vyy401, vyy411, bcg, bch)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, be), bf)) → new_esEs2(vyy400, vyy410, be, bf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_Maybe, fh), eb) → new_esEs0(vyy401, vyy411, fh)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bbc), bbd), baf) → new_esEs2(vyy400, vyy410, bbc, bbd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(ty_Maybe, bcc)) → new_esEs0(vyy401, vyy411, bcc)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_FiniteMap, gf), gg), eb) → new_esEs3(vyy401, vyy411, gf, gg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_Either, bac), bad)) → new_esEs4(vyy402, vyy412, bac, bad)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, ed), ee), ef), ea, eb) → new_esEs1(vyy400, vyy410, ed, ee, ef)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_@2, db), dc)) → new_esEs2(vyy400, vyy410, db, dc)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, dd), de)) → new_esEs3(vyy400, vyy410, dd, de)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), cc) → new_esEs(vyy401, vyy411, cc)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(ty_[], bcb)) → new_esEs(vyy401, vyy411, bcb)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs1(vyy400, vyy410, bb, bc, bd)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_Either, bfa), bfb), bdh) → new_esEs4(vyy400, vyy410, bfa, bfb)
new_esEs3(vyy40, vyy41, bde, bdf) → new_esEs(new_foldFM2(vyy40, bde, bdf), new_foldFM2(vyy41, bde, bdf), app(app(ty_@2, bde), bdf))
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_Either, bdc), bdd)) → new_esEs4(vyy401, vyy411, bdc, bdd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_FiniteMap, baa), bab)) → new_esEs3(vyy402, vyy412, baa, bab)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], dh), ea, eb) → new_esEs(vyy400, vyy410, dh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, ec), ea, eb) → new_esEs0(vyy400, vyy410, ec)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_Either, df), dg)) → new_esEs4(vyy400, vyy410, df, dg)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], bae), baf) → new_esEs(vyy400, vyy410, bae)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bg), bh)) → new_esEs3(vyy400, vyy410, bg, bh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, fa), fb), ea, eb) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], h)) → new_esEs(vyy400, vyy410, h)
new_esEs0(Just(vyy400), Just(vyy410), app(app(app(ty_@3, cf), cg), da)) → new_esEs1(vyy400, vyy410, cf, cg, da)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bde, bdf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bde, bdf), vyy413, bde, bdf)
new_foldFM2(EmptyFM, bde, bdf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bde, bdf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bde, bdf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bde, bdf), vyy4133, bde, bdf)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
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_esEs0(Just(vyy400), Just(vyy410), app(ty_Maybe, ce)) → new_esEs0(vyy400, vyy410, ce)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_Maybe, hc)) → new_esEs0(vyy402, vyy412, hc)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, bag), baf) → new_esEs0(vyy400, vyy410, bag)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_@2, hg), hh)) → new_esEs2(vyy402, vyy412, hg, hh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, ba)) → new_esEs0(vyy400, vyy410, ba)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_@2, bee), bef), bdh) → new_esEs2(vyy400, vyy410, bee, bef)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_Maybe, bea), bdh) → new_esEs0(vyy400, vyy410, bea)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, eg), eh), ea, eb) → new_esEs2(vyy400, vyy410, eg, eh)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_@2, bga), bgb)) → new_esEs2(vyy400, vyy410, bga, bgb)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_Maybe, bfe)) → new_esEs0(vyy400, vyy410, bfe)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_@2, gd), ge), eb) → new_esEs2(vyy401, vyy411, gd, ge)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_@2, bcg), bch)) → new_esEs2(vyy401, vyy411, bcg, bch)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, be), bf)) → new_esEs2(vyy400, vyy410, be, bf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_Maybe, fh), eb) → new_esEs0(vyy401, vyy411, fh)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bbc), bbd), baf) → new_esEs2(vyy400, vyy410, bbc, bbd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(ty_Maybe, bcc)) → new_esEs0(vyy401, vyy411, bcc)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_@2, db), dc)) → new_esEs2(vyy400, vyy410, db, dc)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, ec), ea, eb) → new_esEs0(vyy400, vyy410, ec)
The remaining pairs can at least be oriented weakly.
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(app(ty_@3, ga), gb), gc), eb) → new_esEs1(vyy401, vyy411, ga, gb, gc)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(app(ty_@3, hd), he), hf)) → new_esEs1(vyy402, vyy412, hd, he, hf)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdh) → new_esEs3(vyy400, vyy410, beg, beh)
new_esEs0(Just(vyy400), Just(vyy410), app(ty_[], cd)) → new_esEs(vyy400, vyy410, cd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs1(vyy400, vyy410, bah, bba, bbb)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_[], bdg), bdh) → new_esEs(vyy400, vyy410, bdg)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bbg), bbh), baf) → new_esEs4(vyy400, vyy410, bbg, bbh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, ca), cb)) → new_esEs4(vyy400, vyy410, ca, cb)
new_esEs4(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdh) → new_esEs1(vyy400, vyy410, beb, bec, bed)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_Either, gh), ha), eb) → new_esEs4(vyy401, vyy411, gh, ha)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, fc), fd), ea, eb) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, bbe), bbf), baf) → new_esEs3(vyy400, vyy410, bbe, bbf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_[], hb)) → new_esEs(vyy402, vyy412, hb)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_[], bfd)) → new_esEs(vyy400, vyy410, bfd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_[], fg), eb) → new_esEs(vyy401, vyy411, fg)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vyy401, vyy411, bcd, bce, bcf)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs1(vyy400, vyy410, bff, bfg, bfh)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_FiniteMap, bda), bdb)) → new_esEs3(vyy401, vyy411, bda, bdb)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_FiniteMap, gf), gg), eb) → new_esEs3(vyy401, vyy411, gf, gg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_Either, bac), bad)) → new_esEs4(vyy402, vyy412, bac, bad)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, ed), ee), ef), ea, eb) → new_esEs1(vyy400, vyy410, ed, ee, ef)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, dd), de)) → new_esEs3(vyy400, vyy410, dd, de)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), cc) → new_esEs(vyy401, vyy411, cc)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(ty_[], bcb)) → new_esEs(vyy401, vyy411, bcb)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs1(vyy400, vyy410, bb, bc, bd)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_Either, bfa), bfb), bdh) → new_esEs4(vyy400, vyy410, bfa, bfb)
new_esEs3(vyy40, vyy41, bde, bdf) → new_esEs(new_foldFM2(vyy40, bde, bdf), new_foldFM2(vyy41, bde, bdf), app(app(ty_@2, bde), bdf))
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_Either, bdc), bdd)) → new_esEs4(vyy401, vyy411, bdc, bdd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_FiniteMap, baa), bab)) → new_esEs3(vyy402, vyy412, baa, bab)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], dh), ea, eb) → new_esEs(vyy400, vyy410, dh)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_Either, df), dg)) → new_esEs4(vyy400, vyy410, df, dg)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], bae), baf) → new_esEs(vyy400, vyy410, bae)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bg), bh)) → new_esEs3(vyy400, vyy410, bg, bh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, fa), fb), ea, eb) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], h)) → new_esEs(vyy400, vyy410, h)
new_esEs0(Just(vyy400), Just(vyy410), app(app(app(ty_@3, cf), cg), da)) → new_esEs1(vyy400, vyy410, cf, cg, da)
Used ordering: Polynomial interpretation [25]:
POL(:(x1, x2)) = 0
POL(@2(x1, x2)) = 0
POL(@3(x1, x2, x3)) = 0
POL(Branch(x1, x2, x3, x4, x5)) = 0
POL(EmptyFM) = 0
POL(Just(x1)) = 0
POL(Left(x1)) = 0
POL(Right(x1)) = 0
POL([]) = 0
POL(app(x1, x2)) = x1 + x2
POL(new_esEs(x1, x2, x3)) = x3
POL(new_esEs0(x1, x2, x3)) = x3
POL(new_esEs1(x1, x2, x3, x4, x5)) = x3 + x4 + x5
POL(new_esEs2(x1, x2, x3, x4)) = x3 + x4
POL(new_esEs3(x1, x2, x3, x4)) = 1 + x3 + x4
POL(new_esEs4(x1, x2, x3, x4)) = x3 + x4
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = 0
POL(new_foldFM2(x1, x2, x3)) = 0
POL(ty_@2) = 1
POL(ty_@3) = 0
POL(ty_Either) = 0
POL(ty_FiniteMap) = 1
POL(ty_Maybe) = 1
POL(ty_[]) = 0
The following usable rules [17] were oriented:
none
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vyy401, vyy411, bcd, bce, bcf)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs1(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(app(ty_@3, ga), gb), gc), eb) → new_esEs1(vyy401, vyy411, ga, gb, gc)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_FiniteMap, bda), bdb)) → new_esEs3(vyy401, vyy411, bda, bdb)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdh) → new_esEs3(vyy400, vyy410, beg, beh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(app(ty_@3, hd), he), hf)) → new_esEs1(vyy402, vyy412, hd, he, hf)
new_esEs0(Just(vyy400), Just(vyy410), app(ty_[], cd)) → new_esEs(vyy400, vyy410, cd)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs1(vyy400, vyy410, bah, bba, bbb)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_FiniteMap, gf), gg), eb) → new_esEs3(vyy401, vyy411, gf, gg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_Either, bac), bad)) → new_esEs4(vyy402, vyy412, bac, bad)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_[], bdg), bdh) → new_esEs(vyy400, vyy410, bdg)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bbg), bbh), baf) → new_esEs4(vyy400, vyy410, bbg, bbh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, ed), ee), ef), ea, eb) → new_esEs1(vyy400, vyy410, ed, ee, ef)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, dd), de)) → new_esEs3(vyy400, vyy410, dd, de)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(ty_[], bcb)) → new_esEs(vyy401, vyy411, bcb)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), cc) → new_esEs(vyy401, vyy411, cc)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs1(vyy400, vyy410, bb, bc, bd)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, ca), cb)) → new_esEs4(vyy400, vyy410, ca, cb)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_Either, bfa), bfb), bdh) → new_esEs4(vyy400, vyy410, bfa, bfb)
new_esEs4(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdh) → new_esEs1(vyy400, vyy410, beb, bec, bed)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), bca, app(app(ty_Either, bdc), bdd)) → new_esEs4(vyy401, vyy411, bdc, bdd)
new_esEs3(vyy40, vyy41, bde, bdf) → new_esEs(new_foldFM2(vyy40, bde, bdf), new_foldFM2(vyy41, bde, bdf), app(app(ty_@2, bde), bdf))
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_FiniteMap, baa), bab)) → new_esEs3(vyy402, vyy412, baa, bab)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], dh), ea, eb) → new_esEs(vyy400, vyy410, dh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_Either, gh), ha), eb) → new_esEs4(vyy401, vyy411, gh, ha)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, fc), fd), ea, eb) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs0(Just(vyy400), Just(vyy410), app(app(ty_Either, df), dg)) → new_esEs4(vyy400, vyy410, df, dg)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], bae), baf) → new_esEs(vyy400, vyy410, bae)
new_esEs2(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, bbe), bbf), baf) → new_esEs3(vyy400, vyy410, bbe, bbf)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bg), bh)) → new_esEs3(vyy400, vyy410, bg, bh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_[], hb)) → new_esEs(vyy402, vyy412, hb)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, fa), fb), ea, eb) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_[], bfd)) → new_esEs(vyy400, vyy410, bfd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_[], fg), eb) → new_esEs(vyy401, vyy411, fg)
new_esEs0(Just(vyy400), Just(vyy410), app(app(app(ty_@3, cf), cg), da)) → new_esEs1(vyy400, vyy410, cf, cg, da)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], h)) → new_esEs(vyy400, vyy410, h)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bde, bdf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bde, bdf), vyy413, bde, bdf)
new_foldFM2(EmptyFM, bde, bdf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bde, bdf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bde, bdf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bde, bdf), vyy4133, bde, bdf)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
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 12 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
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs1(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(app(ty_@3, ga), gb), gc), eb) → new_esEs1(vyy401, vyy411, ga, gb, gc)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdh) → new_esEs3(vyy400, vyy410, beg, beh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(app(ty_@3, hd), he), hf)) → new_esEs1(vyy402, vyy412, hd, he, hf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_FiniteMap, gf), gg), eb) → new_esEs3(vyy401, vyy411, gf, gg)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_Either, bac), bad)) → new_esEs4(vyy402, vyy412, bac, bad)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_[], bdg), bdh) → new_esEs(vyy400, vyy410, bdg)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, ed), ee), ef), ea, eb) → new_esEs1(vyy400, vyy410, ed, ee, ef)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), cc) → new_esEs(vyy401, vyy411, cc)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs1(vyy400, vyy410, bb, bc, bd)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, ca), cb)) → new_esEs4(vyy400, vyy410, ca, cb)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_Either, bfa), bfb), bdh) → new_esEs4(vyy400, vyy410, bfa, bfb)
new_esEs4(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdh) → new_esEs1(vyy400, vyy410, beb, bec, bed)
new_esEs3(vyy40, vyy41, bde, bdf) → new_esEs(new_foldFM2(vyy40, bde, bdf), new_foldFM2(vyy41, bde, bdf), app(app(ty_@2, bde), bdf))
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_FiniteMap, baa), bab)) → new_esEs3(vyy402, vyy412, baa, bab)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], dh), ea, eb) → new_esEs(vyy400, vyy410, dh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_Either, gh), ha), eb) → new_esEs4(vyy401, vyy411, gh, ha)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, fc), fd), ea, eb) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bg), bh)) → new_esEs3(vyy400, vyy410, bg, bh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_[], hb)) → new_esEs(vyy402, vyy412, hb)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, fa), fb), ea, eb) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_[], bfd)) → new_esEs(vyy400, vyy410, bfd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_[], fg), eb) → new_esEs(vyy401, vyy411, fg)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], h)) → new_esEs(vyy400, vyy410, h)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bde, bdf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bde, bdf), vyy413, bde, bdf)
new_foldFM2(EmptyFM, bde, bdf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bde, bdf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bde, bdf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bde, bdf), vyy4133, bde, bdf)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
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_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs1(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(app(ty_@3, ga), gb), gc), eb) → new_esEs1(vyy401, vyy411, ga, gb, gc)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(app(ty_@3, hd), he), hf)) → new_esEs1(vyy402, vyy412, hd, he, hf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_Either, bac), bad)) → new_esEs4(vyy402, vyy412, bac, bad)
new_esEs4(Left(vyy400), Left(vyy410), app(ty_[], bdg), bdh) → new_esEs(vyy400, vyy410, bdg)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_Either, bge), bgf)) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, ed), ee), ef), ea, eb) → new_esEs1(vyy400, vyy410, ed, ee, ef)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), cc) → new_esEs(vyy401, vyy411, cc)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs1(vyy400, vyy410, bb, bc, bd)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, ca), cb)) → new_esEs4(vyy400, vyy410, ca, cb)
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_Either, bfa), bfb), bdh) → new_esEs4(vyy400, vyy410, bfa, bfb)
new_esEs4(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdh) → new_esEs1(vyy400, vyy410, beb, bec, bed)
new_esEs3(vyy40, vyy41, bde, bdf) → new_esEs(new_foldFM2(vyy40, bde, bdf), new_foldFM2(vyy41, bde, bdf), app(app(ty_@2, bde), bdf))
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], dh), ea, eb) → new_esEs(vyy400, vyy410, dh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_Either, gh), ha), eb) → new_esEs4(vyy401, vyy411, gh, ha)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, fc), fd), ea, eb) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(ty_[], hb)) → new_esEs(vyy402, vyy412, hb)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(ty_[], bfd)) → new_esEs(vyy400, vyy410, bfd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(ty_[], fg), eb) → new_esEs(vyy401, vyy411, fg)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], h)) → new_esEs(vyy400, vyy410, h)
The remaining pairs can at least be oriented weakly.
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdh) → new_esEs3(vyy400, vyy410, beg, beh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_FiniteMap, gf), gg), eb) → new_esEs3(vyy401, vyy411, gf, gg)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_FiniteMap, baa), bab)) → new_esEs3(vyy402, vyy412, baa, bab)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bg), bh)) → new_esEs3(vyy400, vyy410, bg, bh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, fa), fb), ea, eb) → new_esEs3(vyy400, vyy410, fa, fb)
Used ordering: Polynomial interpretation [25]:
POL(:(x1, x2)) = 1 + x1 + x2
POL(@2(x1, x2)) = 0
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(Left(x1)) = 1 + x1
POL(Right(x1)) = 1 + x1
POL([]) = 0
POL(app(x1, x2)) = 0
POL(new_esEs(x1, x2, x3)) = x2
POL(new_esEs1(x1, x2, x3, x4, x5)) = x2
POL(new_esEs3(x1, x2, x3, x4)) = 1 + x2
POL(new_esEs4(x1, x2, x3, x4)) = x2
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = 1 + x1 + 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_[]) = 0
The following usable rules [17] were oriented:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bde, bdf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bde, bdf), vyy413, bde, bdf)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bde, bdf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bde, bdf), vyy4133, bde, bdf)
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bde, bdf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM2(EmptyFM, bde, bdf) → []
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdh) → new_esEs3(vyy400, vyy410, beg, beh)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, app(app(ty_FiniteMap, gf), gg), eb) → new_esEs3(vyy401, vyy411, gf, gg)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bg), bh)) → new_esEs3(vyy400, vyy410, bg, bh)
new_esEs4(Right(vyy400), Right(vyy410), bfc, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, fa), fb), ea, eb) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs1(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ff, ea, app(app(ty_FiniteMap, baa), bab)) → new_esEs3(vyy402, vyy412, baa, bab)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bde, bdf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bde, bdf), vyy413, bde, bdf)
new_foldFM2(EmptyFM, bde, bdf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bde, bdf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bde, bdf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bde, bdf), vyy4133, bde, bdf)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
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 0 SCCs with 6 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
↳ QDPSizeChangeProof
↳ 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
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_compare1(vyy3000, vyy400, eg) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, eg), eg)
new_primCompAux(vyy3000, vyy400, vyy67, app(app(ty_@2, bbe), bbf)) → new_compare5(vyy3000, vyy400, bbe, bbf)
new_compare22(vyy3000, vyy400, False, fg, fh) → new_ltEs3(vyy3000, vyy400, fg, fh)
new_ltEs(Just(vyy3000), Just(vyy400), app(ty_[], bf)) → new_ltEs2(vyy3000, vyy400, bf)
new_ltEs1(Left(vyy3000), Left(vyy400), app(app(ty_Either, gf), gg), gb) → new_ltEs1(vyy3000, vyy400, gf, gg)
new_ltEs1(Right(vyy3000), Right(vyy400), hc, app(app(app(ty_@3, he), hf), hg)) → new_ltEs0(vyy3000, vyy400, he, hf, hg)
new_compare3(vyy3000, vyy400, eh, fa, fb) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, eh, fa, fb), eh, fa, fb)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(ty_[], bcf)) → new_ltEs2(vyy3001, vyy401, bcf)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, app(app(ty_@2, ee), ef), df) → new_lt3(vyy3001, vyy401, ee, ef)
new_ltEs1(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, gc), gd), ge), gb) → new_ltEs0(vyy3000, vyy400, gc, gd, ge)
new_ltEs1(Left(vyy3000), Left(vyy400), app(ty_[], gh), gb) → new_ltEs2(vyy3000, vyy400, gh)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(app(ty_@3, eh), fa), fb), cb, df) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, eh, fa, fb), eh, fa, fb)
new_lt3(vyy3000, vyy400, fg, fh) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fg, fh), fg, fh)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, app(ty_[], ed), df) → new_lt2(vyy3001, vyy401, ed)
new_primCompAux(vyy3000, vyy400, vyy67, app(ty_[], bbd)) → new_compare(vyy3000, vyy400, bbd)
new_ltEs(Just(vyy3000), Just(vyy400), app(ty_Maybe, h)) → new_ltEs(vyy3000, vyy400, h)
new_lt(vyy3000, vyy400, eg) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, eg), eg)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, cb, app(app(ty_@2, dc), dd)) → new_ltEs3(vyy3002, vyy402, dc, dd)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_Maybe, eg), cb, df) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, eg), eg)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(ty_Maybe, bbh)) → new_ltEs(vyy3001, vyy401, bbh)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_Either, bdf), bdg), bdb) → new_lt1(vyy3000, vyy400, bdf, bdg)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_@2, fg), fh), cb, df) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fg, fh), fg, fh)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_[], ff), cb, df) → new_compare(vyy3000, vyy400, ff)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs0(vyy3001, vyy401, bca, bcb, bcc)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, app(app(app(ty_@3, dg), dh), ea), df) → new_lt0(vyy3001, vyy401, dg, dh, ea)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(ty_@2, bcg), bch)) → new_ltEs3(vyy3001, vyy401, bcg, bch)
new_compare21(vyy3000, vyy400, False, fc, fd) → new_ltEs1(vyy3000, vyy400, fc, fd)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(ty_Either, bcd), bce)) → new_ltEs1(vyy3001, vyy401, bcd, bce)
new_ltEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_primCompAux(vyy3000, vyy400, new_compare0(vyy3001, vyy401, bae), bae)
new_primCompAux(vyy3000, vyy400, vyy67, app(app(ty_Either, bbb), bbc)) → new_compare4(vyy3000, vyy400, bbb, bbc)
new_ltEs1(Left(vyy3000), Left(vyy400), app(ty_Maybe, ga), gb) → new_ltEs(vyy3000, vyy400, ga)
new_ltEs1(Right(vyy3000), Right(vyy400), hc, app(ty_Maybe, hd)) → new_ltEs(vyy3000, vyy400, hd)
new_ltEs1(Right(vyy3000), Right(vyy400), hc, app(ty_[], bab)) → new_ltEs2(vyy3000, vyy400, bab)
new_ltEs(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ba), bb), bc)) → new_ltEs0(vyy3000, vyy400, ba, bb, bc)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, app(app(ty_Either, eb), ec), df) → new_lt1(vyy3001, vyy401, eb, ec)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_Either, fc), fd), cb, df) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, fc, fd), fc, fd)
new_compare4(vyy3000, vyy400, fc, fd) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, fc, fd), fc, fd)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, cb, app(app(app(ty_@3, cd), ce), cf)) → new_ltEs0(vyy3002, vyy402, cd, ce, cf)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_@2, bea), beb), bdb) → new_lt3(vyy3000, vyy400, bea, beb)
new_compare2(vyy3000, vyy400, False, eg) → new_ltEs(vyy3000, vyy400, eg)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, cb, app(ty_[], db)) → new_ltEs2(vyy3002, vyy402, db)
new_ltEs(Just(vyy3000), Just(vyy400), app(app(ty_@2, bg), bh)) → new_ltEs3(vyy3000, vyy400, bg, bh)
new_ltEs(Just(vyy3000), Just(vyy400), app(app(ty_Either, bd), be)) → new_ltEs1(vyy3000, vyy400, bd, be)
new_ltEs1(Right(vyy3000), Right(vyy400), hc, app(app(ty_@2, bac), bad)) → new_ltEs3(vyy3000, vyy400, bac, bad)
new_ltEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_compare(vyy3001, vyy401, bae)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_compare(vyy3001, vyy401, bae)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, cb, app(app(ty_Either, cg), da)) → new_ltEs1(vyy3002, vyy402, cg, da)
new_primCompAux(vyy3000, vyy400, vyy67, app(ty_Maybe, baf)) → new_compare1(vyy3000, vyy400, baf)
new_primCompAux(vyy3000, vyy400, vyy67, app(app(app(ty_@3, bag), bah), bba)) → new_compare3(vyy3000, vyy400, bag, bah, bba)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_primCompAux(vyy3000, vyy400, new_compare0(vyy3001, vyy401, bae), bae)
new_ltEs1(Right(vyy3000), Right(vyy400), hc, app(app(ty_Either, hh), baa)) → new_ltEs1(vyy3000, vyy400, hh, baa)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, cb, app(ty_Maybe, cc)) → new_ltEs(vyy3002, vyy402, cc)
new_lt2(vyy3000, vyy400, ff) → new_compare(vyy3000, vyy400, ff)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_Maybe, bda), bdb) → new_lt(vyy3000, vyy400, bda)
new_compare5(vyy3000, vyy400, fg, fh) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fg, fh), fg, fh)
new_lt0(vyy3000, vyy400, eh, fa, fb) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, eh, fa, fb), eh, fa, fb)
new_compare20(vyy3000, vyy400, False, eh, fa, fb) → new_ltEs0(vyy3000, vyy400, eh, fa, fb)
new_lt1(vyy3000, vyy400, fc, fd) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, fc, fd), fc, fd)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(app(ty_@3, bdc), bdd), bde), bdb) → new_lt0(vyy3000, vyy400, bdc, bdd, bde)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, app(ty_Maybe, de), df) → new_lt(vyy3001, vyy401, de)
new_ltEs1(Left(vyy3000), Left(vyy400), app(app(ty_@2, ha), hb), gb) → new_ltEs3(vyy3000, vyy400, ha, hb)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_[], bdh), bdb) → new_lt2(vyy3000, vyy400, bdh)
The TRS R consists of the following rules:
new_esEs29(vyy400, vyy410, ty_Integer) → new_esEs17(vyy400, vyy410)
new_esEs28(vyy401, vyy411, ty_Integer) → new_esEs17(vyy401, vyy411)
new_compare18(vyy3000, vyy400) → new_compare210(vyy3000, vyy400, new_esEs14(vyy3000, vyy400))
new_compare31(vyy3000, vyy400, ty_Integer) → new_compare13(vyy3000, vyy400)
new_ltEs15(Right(vyy3000), Right(vyy400), hc, ty_Integer) → new_ltEs18(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, ty_Double) → new_esEs21(vyy401, vyy411)
new_esEs11(vyy40, vyy41, ty_Char) → new_esEs12(vyy40, vyy41)
new_esEs5(Just(vyy400), Just(vyy410), ty_@0) → new_esEs18(vyy400, vyy410)
new_esEs25(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_Either, bhe), bhf), bga) → new_esEs7(vyy400, vyy410, bhe, bhf)
new_compare29(vyy3000, vyy400, fg, fh) → new_compare26(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fg, fh), fg, fh)
new_ltEs9(vyy300, vyy40) → new_not(new_compare11(vyy300, vyy40))
new_lt19(vyy3001, vyy401, app(app(ty_Either, eb), ec)) → new_lt14(vyy3001, vyy401, eb, ec)
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, eh), fa), fb)) → new_lt12(vyy3000, vyy400, eh, fa, fb)
new_ltEs15(Right(vyy3000), Right(vyy400), hc, app(ty_Maybe, hd)) → new_ltEs8(vyy3000, vyy400, hd)
new_esEs5(Just(vyy400), Just(vyy410), ty_Integer) → new_esEs17(vyy400, vyy410)
new_compare10(vyy3000, vyy400, True, eh, fa, fb) → LT
new_lt19(vyy3001, vyy401, ty_Float) → new_lt9(vyy3001, vyy401)
new_esEs28(vyy401, vyy411, app(ty_[], chg)) → new_esEs15(vyy401, vyy411, chg)
new_compare110(vyy3000, vyy400, True, fc, fd) → LT
new_ltEs14(GT, GT) → True
new_ltEs8(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ba), bb), bc)) → new_ltEs13(vyy3000, vyy400, ba, bb, bc)
new_ltEs5(vyy3001, vyy401, ty_Char) → new_ltEs9(vyy3001, vyy401)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Ordering, gb) → new_ltEs14(vyy3000, vyy400)
new_esEs5(Just(vyy400), Just(vyy410), app(ty_[], dbe)) → new_esEs15(vyy400, vyy410, dbe)
new_esEs24(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_lt20(vyy3000, vyy400, app(app(ty_Either, fc), fd)) → new_lt14(vyy3000, vyy400, fc, fd)
new_compare7(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs20(vyy40, vyy41, bff, bfg) → new_asAs(new_esEs19(new_sizeFM(vyy40, bff, bfg), new_sizeFM(vyy41, bff, bfg)), new_esEs15(new_fmToList(vyy40, bff, bfg), new_fmToList(vyy41, bff, bfg), app(app(ty_@2, bff), bfg)))
new_compare31(vyy3000, vyy400, ty_Int) → new_compare8(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, ty_@0) → new_compare6(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs10(vyy3000, vyy400)
new_primMulNat0(Zero, Zero) → Zero
new_esEs29(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_ltEs5(vyy3001, vyy401, ty_@0) → new_ltEs10(vyy3001, vyy401)
new_esEs11(vyy40, vyy41, ty_Float) → new_esEs16(vyy40, vyy41)
new_lt20(vyy3000, vyy400, ty_Int) → new_lt11(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, app(ty_[], cgc)) → new_esEs15(vyy400, vyy410, cgc)
new_ltEs16(False, True) → True
new_esEs27(vyy400, vyy410, app(app(ty_FiniteMap, chb), chc)) → new_esEs20(vyy400, vyy410, chb, chc)
new_esEs9(LT) → True
new_esEs29(vyy400, vyy410, app(app(ty_FiniteMap, ddh), dea)) → new_esEs20(vyy400, vyy410, ddh, dea)
new_ltEs16(True, False) → False
new_not(GT) → False
new_esEs25(vyy401, vyy411, app(app(ty_FiniteMap, cdg), cdh)) → new_esEs20(vyy401, vyy411, cdg, cdh)
new_esEs27(vyy400, vyy410, app(app(ty_@2, cgh), cha)) → new_esEs8(vyy400, vyy410, cgh, cha)
new_ltEs19(vyy3002, vyy402, ty_Bool) → new_ltEs16(vyy3002, vyy402)
new_lt7(vyy3000, vyy400, ty_Float) → new_lt9(vyy3000, vyy400)
new_lt7(vyy3000, vyy400, ty_Ordering) → new_lt13(vyy3000, vyy400)
new_ltEs15(Right(vyy3000), Right(vyy400), hc, ty_Ordering) → new_ltEs14(vyy3000, vyy400)
new_ltEs11(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_compare0(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_primCompAux0(vyy3000, vyy400, new_compare0(vyy3001, vyy401, bae), bae)
new_esEs5(Just(vyy400), Just(vyy410), app(ty_Maybe, dbf)) → new_esEs5(vyy400, vyy410, dbf)
new_esEs27(vyy400, vyy410, ty_Bool) → new_esEs10(vyy400, vyy410)
new_esEs25(vyy401, vyy411, ty_Integer) → new_esEs17(vyy401, vyy411)
new_esEs7(Left(vyy400), Left(vyy410), ty_Ordering, bga) → new_esEs14(vyy400, vyy410)
new_ltEs15(Right(vyy3000), Right(vyy400), hc, app(app(ty_@2, bac), bad)) → new_ltEs4(vyy3000, vyy400, bac, bad)
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bff, bfg) → :(@2(vyy410, vyy411), vyy85)
new_ltEs16(True, True) → True
new_esEs17(Integer(vyy400), Integer(vyy410)) → new_primEqInt(vyy400, vyy410)
new_esEs26(vyy402, vyy412, ty_Bool) → new_esEs10(vyy402, vyy412)
new_esEs7(Left(vyy400), Right(vyy410), bfh, bga) → False
new_esEs7(Right(vyy400), Left(vyy410), bfh, bga) → False
new_esEs26(vyy402, vyy412, app(app(ty_@2, cfa), cfb)) → new_esEs8(vyy402, vyy412, cfa, cfb)
new_compare6(@0, @0) → EQ
new_ltEs19(vyy3002, vyy402, app(app(ty_@2, dc), dd)) → new_ltEs4(vyy3002, vyy402, dc, dd)
new_compare23(vyy3000, vyy400, True) → EQ
new_esEs27(vyy400, vyy410, app(app(ty_Either, chd), che)) → new_esEs7(vyy400, vyy410, chd, che)
new_ltEs14(GT, EQ) → False
new_lt19(vyy3001, vyy401, app(ty_[], ed)) → new_lt16(vyy3001, vyy401, ed)
new_esEs26(vyy402, vyy412, ty_Char) → new_esEs12(vyy402, vyy412)
new_compare31(vyy3000, vyy400, app(app(ty_@2, bbe), bbf)) → new_compare29(vyy3000, vyy400, bbe, bbf)
new_ltEs5(vyy3001, vyy401, app(app(ty_@2, bcg), bch)) → new_ltEs4(vyy3001, vyy401, bcg, bch)
new_ltEs6(vyy300, vyy40, cga) → new_not(new_compare14(vyy300, vyy40, cga))
new_lt7(vyy3000, vyy400, app(ty_Maybe, bda)) → new_lt10(vyy3000, vyy400, bda)
new_esEs14(EQ, EQ) → True
new_esEs25(vyy401, vyy411, ty_Double) → new_esEs21(vyy401, vyy411)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs16(vyy3000, vyy400)
new_lt19(vyy3001, vyy401, app(ty_Maybe, de)) → new_lt10(vyy3001, vyy401, de)
new_esEs11(vyy40, vyy41, app(ty_[], beg)) → new_esEs15(vyy40, vyy41, beg)
new_esEs29(vyy400, vyy410, app(ty_Ratio, dch)) → new_esEs13(vyy400, vyy410, dch)
new_compare111(vyy3000, vyy400, False) → GT
new_compare111(vyy3000, vyy400, True) → LT
new_ltEs5(vyy3001, vyy401, app(app(ty_Either, bcd), bce)) → new_ltEs15(vyy3001, vyy401, bcd, bce)
new_esEs27(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_ltEs8(Nothing, Just(vyy400), dee) → True
new_esEs8(@2(vyy400, vyy401), @2(vyy410, vyy411), bfd, bfe) → new_asAs(new_esEs27(vyy400, vyy410, bfd), new_esEs28(vyy401, vyy411, bfe))
new_esEs26(vyy402, vyy412, ty_Double) → new_esEs21(vyy402, vyy412)
new_esEs11(vyy40, vyy41, app(app(app(ty_@3, bfa), bfb), bfc)) → new_esEs6(vyy40, vyy41, bfa, bfb, bfc)
new_compare25(vyy3000, vyy400, True, eh, fa, fb) → EQ
new_esEs24(vyy400, vyy410, app(app(ty_FiniteMap, ccc), ccd)) → new_esEs20(vyy400, vyy410, ccc, ccd)
new_lt8(vyy3000, vyy400, bgb) → new_esEs9(new_compare14(vyy3000, vyy400, bgb))
new_compare31(vyy3000, vyy400, app(ty_Maybe, baf)) → new_compare30(vyy3000, vyy400, baf)
new_esEs24(vyy400, vyy410, app(app(ty_Either, cce), ccf)) → new_esEs7(vyy400, vyy410, cce, ccf)
new_esEs25(vyy401, vyy411, app(ty_Ratio, ccg)) → new_esEs13(vyy401, vyy411, ccg)
new_lt15(vyy3000, vyy400) → new_esEs9(new_compare9(vyy3000, vyy400))
new_esEs7(Right(vyy400), Right(vyy410), bfh, ty_Float) → new_esEs16(vyy400, vyy410)
new_compare0([], [], bae) → EQ
new_esEs27(vyy400, vyy410, ty_@0) → new_esEs18(vyy400, vyy410)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Integer, gb) → new_ltEs18(vyy3000, vyy400)
new_primEqNat0(Zero, Zero) → True
new_ltEs5(vyy3001, vyy401, ty_Int) → new_ltEs11(vyy3001, vyy401)
new_ltEs19(vyy3002, vyy402, ty_Integer) → new_ltEs18(vyy3002, vyy402)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Double, gb) → new_ltEs12(vyy3000, vyy400)
new_lt19(vyy3001, vyy401, ty_Double) → new_lt5(vyy3001, vyy401)
new_lt5(vyy3000, vyy400) → new_esEs9(new_compare7(vyy3000, vyy400))
new_lt20(vyy3000, vyy400, app(ty_Ratio, bgb)) → new_lt8(vyy3000, vyy400, bgb)
new_ltEs5(vyy3001, vyy401, app(ty_Maybe, bbh)) → new_ltEs8(vyy3001, vyy401, bbh)
new_lt7(vyy3000, vyy400, app(ty_[], bdh)) → new_lt16(vyy3000, vyy400, bdh)
new_esEs26(vyy402, vyy412, app(ty_Ratio, cec)) → new_esEs13(vyy402, vyy412, cec)
new_compare31(vyy3000, vyy400, ty_Ordering) → new_compare18(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, app(ty_Ratio, cgb)) → new_esEs13(vyy400, vyy410, cgb)
new_esEs27(vyy400, vyy410, ty_Char) → new_esEs12(vyy400, vyy410)
new_compare31(vyy3000, vyy400, app(ty_Ratio, ded)) → new_compare14(vyy3000, vyy400, ded)
new_compare110(vyy3000, vyy400, False, fc, fd) → GT
new_compare12(vyy3000, vyy400, False, eg) → GT
new_esEs7(Right(vyy400), Right(vyy410), bfh, app(app(app(ty_@3, cab), cac), cad)) → new_esEs6(vyy400, vyy410, cab, cac, cad)
new_sr(vyy400, vyy3001) → new_primMulInt(vyy400, vyy3001)
new_ltEs15(Right(vyy3000), Right(vyy400), hc, ty_Double) → new_ltEs12(vyy3000, vyy400)
new_ltEs14(EQ, LT) → False
new_lt20(vyy3000, vyy400, ty_Float) → new_lt9(vyy3000, vyy400)
new_esEs25(vyy401, vyy411, app(ty_[], cch)) → new_esEs15(vyy401, vyy411, cch)
new_ltEs8(Just(vyy3000), Just(vyy400), app(app(ty_Either, bd), be)) → new_ltEs15(vyy3000, vyy400, bd, be)
new_esEs7(Right(vyy400), Right(vyy410), bfh, app(ty_[], bhh)) → new_esEs15(vyy400, vyy410, bhh)
new_esEs24(vyy400, vyy410, ty_Char) → new_esEs12(vyy400, vyy410)
new_esEs14(GT, LT) → False
new_esEs14(LT, GT) → False
new_esEs15(:(vyy400, vyy401), :(vyy410, vyy411), beg) → new_asAs(new_esEs29(vyy400, vyy410, beg), new_esEs15(vyy401, vyy411, beg))
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Int, gb) → new_ltEs11(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy860), vyy300100) → Succ(Succ(new_primPlusNat1(vyy860, vyy300100)))
new_lt19(vyy3001, vyy401, ty_@0) → new_lt4(vyy3001, vyy401)
new_esEs25(vyy401, vyy411, ty_Float) → new_esEs16(vyy401, vyy411)
new_esEs7(Right(vyy400), Right(vyy410), bfh, app(app(ty_Either, cba), cbb)) → new_esEs7(vyy400, vyy410, cba, cbb)
new_esEs26(vyy402, vyy412, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs6(vyy402, vyy412, cef, ceg, ceh)
new_ltEs18(vyy300, vyy40) → new_not(new_compare13(vyy300, vyy40))
new_esEs7(Left(vyy400), Left(vyy410), app(ty_[], bgd), bga) → new_esEs15(vyy400, vyy410, bgd)
new_esEs7(Right(vyy400), Right(vyy410), bfh, ty_Char) → new_esEs12(vyy400, vyy410)
new_compare17(vyy3000, vyy400, True, fg, fh) → LT
new_ltEs19(vyy3002, vyy402, ty_Float) → new_ltEs7(vyy3002, vyy402)
new_esEs28(vyy401, vyy411, ty_Float) → new_esEs16(vyy401, vyy411)
new_lt20(vyy3000, vyy400, app(app(ty_@2, fg), fh)) → new_lt18(vyy3000, vyy400, fg, fh)
new_primEqInt(Neg(Succ(vyy4000)), Neg(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_esEs25(vyy401, vyy411, app(app(ty_@2, cde), cdf)) → new_esEs8(vyy401, vyy411, cde, cdf)
new_esEs9(GT) → False
new_compare10(vyy3000, vyy400, False, eh, fa, fb) → GT
new_lt7(vyy3000, vyy400, ty_Bool) → new_lt15(vyy3000, vyy400)
new_primPlusNat1(Zero, Succ(vyy3001000)) → Succ(vyy3001000)
new_primPlusNat1(Succ(vyy8600), Zero) → Succ(vyy8600)
new_lt20(vyy3000, vyy400, ty_Char) → new_lt6(vyy3000, vyy400)
new_compare9(vyy3000, vyy400) → new_compare23(vyy3000, vyy400, new_esEs10(vyy3000, vyy400))
new_ltEs12(vyy300, vyy40) → new_not(new_compare7(vyy300, vyy40))
new_esEs9(EQ) → False
new_ltEs15(Right(vyy3000), Right(vyy400), hc, app(app(app(ty_@3, he), hf), hg)) → new_ltEs13(vyy3000, vyy400, he, hf, hg)
new_compare16(vyy3000, vyy400, True) → LT
new_compare27(vyy3000, vyy400, False, fc, fd) → new_compare110(vyy3000, vyy400, new_ltEs15(vyy3000, vyy400, fc, fd), fc, fd)
new_esEs7(Right(vyy400), Right(vyy410), bfh, app(ty_Ratio, bhg)) → new_esEs13(vyy400, vyy410, bhg)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy400, vyy410, ty_Bool) → new_esEs10(vyy400, vyy410)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Ratio, bgc), bga) → new_esEs13(vyy400, vyy410, bgc)
new_esEs24(vyy400, vyy410, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs6(vyy400, vyy410, cbf, cbg, cbh)
new_esEs7(Right(vyy400), Right(vyy410), bfh, app(ty_Maybe, caa)) → new_esEs5(vyy400, vyy410, caa)
new_compare15(vyy3000, vyy400, eh, fa, fb) → new_compare25(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, eh, fa, fb), eh, fa, fb)
new_esEs29(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_compare8(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4100))) → False
new_primEqInt(Neg(Succ(vyy4000)), Neg(Zero)) → False
new_esEs11(vyy40, vyy41, ty_Int) → new_esEs19(vyy40, vyy41)
new_esEs5(Just(vyy400), Just(vyy410), ty_Float) → new_esEs16(vyy400, vyy410)
new_compare26(vyy3000, vyy400, True, fg, fh) → EQ
new_ltEs5(vyy3001, vyy401, app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs13(vyy3001, vyy401, bca, bcb, bcc)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt13(vyy3000, vyy400)
new_lt7(vyy3000, vyy400, ty_Integer) → new_lt17(vyy3000, vyy400)
new_esEs23(vyy401, vyy411, ty_Integer) → new_esEs17(vyy401, vyy411)
new_esEs7(Right(vyy400), Right(vyy410), bfh, ty_Ordering) → new_esEs14(vyy400, vyy410)
new_ltEs15(Left(vyy3000), Left(vyy400), app(ty_Maybe, ga), gb) → new_ltEs8(vyy3000, vyy400, ga)
new_esEs10(False, False) → True
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs14(vyy3000, vyy400)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bff, bfg) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bff, bfg), vyy4133, bff, bfg)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs28(vyy401, vyy411, ty_@0) → new_esEs18(vyy401, vyy411)
new_esEs26(vyy402, vyy412, app(app(ty_Either, cfe), cff)) → new_esEs7(vyy402, vyy412, cfe, cff)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs28(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs7(Left(vyy400), Left(vyy410), ty_Int, bga) → new_esEs19(vyy400, vyy410)
new_ltEs5(vyy3001, vyy401, app(ty_[], bcf)) → new_ltEs17(vyy3001, vyy401, bcf)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_sizeFM(EmptyFM, bff, bfg) → Pos(Zero)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, bhc), bhd), bga) → new_esEs20(vyy400, vyy410, bhc, bhd)
new_esEs26(vyy402, vyy412, ty_Integer) → new_esEs17(vyy402, vyy412)
new_esEs29(vyy400, vyy410, ty_Ordering) → new_esEs14(vyy400, vyy410)
new_ltEs17(vyy300, vyy40, bae) → new_not(new_compare0(vyy300, vyy40, bae))
new_primEqInt(Pos(Succ(vyy4000)), Pos(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_esEs11(vyy40, vyy41, ty_Double) → new_esEs21(vyy40, vyy41)
new_compare31(vyy3000, vyy400, ty_Float) → new_compare28(vyy3000, vyy400)
new_esEs16(Float(vyy400, vyy401), Float(vyy410, vyy411)) → new_esEs19(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_compare27(vyy3000, vyy400, True, fc, fd) → EQ
new_esEs25(vyy401, vyy411, app(ty_Maybe, cda)) → new_esEs5(vyy401, vyy411, cda)
new_esEs29(vyy400, vyy410, app(ty_Maybe, ddb)) → new_esEs5(vyy400, vyy410, ddb)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs11(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, app(app(ty_FiniteMap, daf), dag)) → new_esEs20(vyy401, vyy411, daf, dag)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs7(vyy3000, vyy400)
new_primEqNat0(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat0(vyy4000, vyy4100)
new_esEs11(vyy40, vyy41, app(app(ty_FiniteMap, bff), bfg)) → new_esEs20(vyy40, vyy41, bff, bfg)
new_esEs27(vyy400, vyy410, ty_Integer) → new_esEs17(vyy400, vyy410)
new_ltEs5(vyy3001, vyy401, app(ty_Ratio, bec)) → new_ltEs6(vyy3001, vyy401, bec)
new_esEs26(vyy402, vyy412, app(app(ty_FiniteMap, cfc), cfd)) → new_esEs20(vyy402, vyy412, cfc, cfd)
new_ltEs4(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, bdb) → new_pePe(new_lt7(vyy3000, vyy400, bbg), vyy3000, vyy400, new_ltEs5(vyy3001, vyy401, bdb), bbg)
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt17(vyy3000, vyy400)
new_primCompAux00(vyy71, LT) → LT
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_lt20(vyy3000, vyy400, ty_@0) → new_lt4(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, app(ty_[], db)) → new_ltEs17(vyy3002, vyy402, db)
new_compare24(vyy3000, vyy400, False, eg) → new_compare12(vyy3000, vyy400, new_ltEs8(vyy3000, vyy400, eg), eg)
new_ltEs8(Just(vyy3000), Nothing, dee) → False
new_compare31(vyy3000, vyy400, ty_Char) → new_compare11(vyy3000, vyy400)
new_esEs15([], [], beg) → True
new_primEqInt(Pos(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Succ(vyy4000)), Pos(Zero)) → False
new_ltEs15(Right(vyy3000), Right(vyy400), hc, ty_Char) → new_ltEs9(vyy3000, vyy400)
new_ltEs8(Just(vyy3000), Just(vyy400), app(ty_Ratio, def)) → new_ltEs6(vyy3000, vyy400, def)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_esEs6(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), bfa, bfb, bfc) → new_asAs(new_esEs24(vyy400, vyy410, bfa), new_asAs(new_esEs25(vyy401, vyy411, bfb), new_esEs26(vyy402, vyy412, bfc)))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_primPlusNat1(Succ(vyy8600), Succ(vyy3001000)) → Succ(Succ(new_primPlusNat1(vyy8600, vyy3001000)))
new_compare12(vyy3000, vyy400, True, eg) → LT
new_primEqInt(Neg(Succ(vyy4000)), Pos(vyy410)) → False
new_primEqInt(Pos(Succ(vyy4000)), Neg(vyy410)) → False
new_esEs24(vyy400, vyy410, app(ty_Ratio, cbc)) → new_esEs13(vyy400, vyy410, cbc)
new_lt12(vyy3000, vyy400, eh, fa, fb) → new_esEs9(new_compare15(vyy3000, vyy400, eh, fa, fb))
new_esEs7(Left(vyy400), Left(vyy410), ty_Integer, bga) → new_esEs17(vyy400, vyy410)
new_compare14(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare13(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_esEs27(vyy400, vyy410, app(ty_Maybe, cgd)) → new_esEs5(vyy400, vyy410, cgd)
new_foldFM2(EmptyFM, bff, bfg) → []
new_esEs25(vyy401, vyy411, ty_Char) → new_esEs12(vyy401, vyy411)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4100))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCompAux00(vyy71, EQ) → vyy71
new_esEs28(vyy401, vyy411, app(app(ty_Either, dah), dba)) → new_esEs7(vyy401, vyy411, dah, dba)
new_ltEs15(Right(vyy3000), Right(vyy400), hc, app(ty_Ratio, cfh)) → new_ltEs6(vyy3000, vyy400, cfh)
new_compare25(vyy3000, vyy400, False, eh, fa, fb) → new_compare10(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, eh, fa, fb), eh, fa, fb)
new_esEs5(Just(vyy400), Just(vyy410), ty_Bool) → new_esEs10(vyy400, vyy410)
new_esEs24(vyy400, vyy410, ty_Ordering) → new_esEs14(vyy400, vyy410)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_@0, gb) → new_ltEs10(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, app(app(ty_Either, bbb), bbc)) → new_compare19(vyy3000, vyy400, bbb, bbc)
new_ltEs19(vyy3002, vyy402, app(app(app(ty_@3, cd), ce), cf)) → new_ltEs13(vyy3002, vyy402, cd, ce, cf)
new_lt7(vyy3000, vyy400, app(app(ty_@2, bea), beb)) → new_lt18(vyy3000, vyy400, bea, beb)
new_esEs5(Just(vyy400), Just(vyy410), ty_Ordering) → new_esEs14(vyy400, vyy410)
new_compare17(vyy3000, vyy400, False, fg, fh) → GT
new_esEs25(vyy401, vyy411, ty_Bool) → new_esEs10(vyy401, vyy411)
new_esEs26(vyy402, vyy412, ty_Float) → new_esEs16(vyy402, vyy412)
new_lt20(vyy3000, vyy400, ty_Double) → new_lt5(vyy3000, vyy400)
new_esEs12(Char(vyy400), Char(vyy410)) → new_primEqNat0(vyy400, vyy410)
new_esEs23(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs11(vyy40, vyy41, ty_Ordering) → new_esEs14(vyy40, vyy41)
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt15(vyy3000, vyy400)
new_compare24(vyy3000, vyy400, True, eg) → EQ
new_esEs29(vyy400, vyy410, ty_@0) → new_esEs18(vyy400, vyy410)
new_esEs5(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, dcd), dce)) → new_esEs20(vyy400, vyy410, dcd, dce)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primPlusNat0(Zero, vyy300100) → Succ(vyy300100)
new_lt19(vyy3001, vyy401, ty_Int) → new_lt11(vyy3001, vyy401)
new_compare31(vyy3000, vyy400, ty_Double) → new_compare7(vyy3000, vyy400)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs12(vyy3000, vyy400)
new_esEs29(vyy400, vyy410, app(app(ty_@2, ddf), ddg)) → new_esEs8(vyy400, vyy410, ddf, ddg)
new_lt19(vyy3001, vyy401, ty_Integer) → new_lt17(vyy3001, vyy401)
new_compare19(vyy3000, vyy400, fc, fd) → new_compare27(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, fc, fd), fc, fd)
new_lt4(vyy3000, vyy400) → new_esEs9(new_compare6(vyy3000, vyy400))
new_esEs7(Left(vyy400), Left(vyy410), ty_@0, bga) → new_esEs18(vyy400, vyy410)
new_ltEs14(LT, LT) → True
new_compare30(vyy3000, vyy400, eg) → new_compare24(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, eg), eg)
new_lt7(vyy3000, vyy400, ty_Double) → new_lt5(vyy3000, vyy400)
new_lt10(vyy3000, vyy400, eg) → new_esEs9(new_compare30(vyy3000, vyy400, eg))
new_not0 → True
new_compare0(:(vyy3000, vyy3001), [], bae) → GT
new_lt19(vyy3001, vyy401, app(app(ty_@2, ee), ef)) → new_lt18(vyy3001, vyy401, ee, ef)
new_lt19(vyy3001, vyy401, app(app(app(ty_@3, dg), dh), ea)) → new_lt12(vyy3001, vyy401, dg, dh, ea)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Float, gb) → new_ltEs7(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, app(app(ty_Either, cg), da)) → new_ltEs15(vyy3002, vyy402, cg, da)
new_pePe(False, vyy40, vyy41, vyy57, bee) → new_asAs(new_esEs11(vyy40, vyy41, bee), vyy57)
new_ltEs5(vyy3001, vyy401, ty_Float) → new_ltEs7(vyy3001, vyy401)
new_esEs5(Just(vyy400), Just(vyy410), ty_Char) → new_esEs12(vyy400, vyy410)
new_esEs24(vyy400, vyy410, app(ty_Maybe, cbe)) → new_esEs5(vyy400, vyy410, cbe)
new_lt18(vyy3000, vyy400, fg, fh) → new_esEs9(new_compare29(vyy3000, vyy400, fg, fh))
new_esEs5(Just(vyy400), Just(vyy410), app(app(ty_@2, dcb), dcc)) → new_esEs8(vyy400, vyy410, dcb, dcc)
new_esEs5(Just(vyy400), Just(vyy410), app(ty_Ratio, dbd)) → new_esEs13(vyy400, vyy410, dbd)
new_lt19(vyy3001, vyy401, ty_Char) → new_lt6(vyy3001, vyy401)
new_esEs7(Right(vyy400), Right(vyy410), bfh, ty_@0) → new_esEs18(vyy400, vyy410)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs11(vyy40, vyy41, app(ty_Maybe, beh)) → new_esEs5(vyy40, vyy41, beh)
new_esEs7(Left(vyy400), Left(vyy410), ty_Bool, bga) → new_esEs10(vyy400, vyy410)
new_primMulInt(Pos(vyy4000), Pos(vyy30010)) → Pos(new_primMulNat0(vyy4000, vyy30010))
new_lt17(vyy3000, vyy400) → new_esEs9(new_compare13(vyy3000, vyy400))
new_ltEs5(vyy3001, vyy401, ty_Ordering) → new_ltEs14(vyy3001, vyy401)
new_esEs7(Left(vyy400), Left(vyy410), ty_Char, bga) → new_esEs12(vyy400, vyy410)
new_esEs10(True, True) → True
new_ltEs15(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, gc), gd), ge), gb) → new_ltEs13(vyy3000, vyy400, gc, gd, ge)
new_ltEs19(vyy3002, vyy402, app(ty_Maybe, cc)) → new_ltEs8(vyy3002, vyy402, cc)
new_lt7(vyy3000, vyy400, app(app(app(ty_@3, bdc), bdd), bde)) → new_lt12(vyy3000, vyy400, bdc, bdd, bde)
new_primMulInt(Neg(vyy4000), Neg(vyy30010)) → Pos(new_primMulNat0(vyy4000, vyy30010))
new_ltEs19(vyy3002, vyy402, app(ty_Ratio, dbb)) → new_ltEs6(vyy3002, vyy402, dbb)
new_esEs27(vyy400, vyy410, ty_Ordering) → new_esEs14(vyy400, vyy410)
new_primEqNat0(Succ(vyy4000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4100)) → False
new_lt20(vyy3000, vyy400, app(ty_Maybe, eg)) → new_lt10(vyy3000, vyy400, eg)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vyy401, vyy411, app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(vyy401, vyy411, daa, dab, dac)
new_esEs7(Right(vyy400), Right(vyy410), bfh, app(app(ty_@2, cae), caf)) → new_esEs8(vyy400, vyy410, cae, caf)
new_esEs27(vyy400, vyy410, app(app(app(ty_@3, cge), cgf), cgg)) → new_esEs6(vyy400, vyy410, cge, cgf, cgg)
new_compare210(vyy3000, vyy400, True) → EQ
new_sizeFM(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bff, bfg) → vyy412
new_lt7(vyy3000, vyy400, app(ty_Ratio, bed)) → new_lt8(vyy3000, vyy400, bed)
new_esEs26(vyy402, vyy412, ty_Ordering) → new_esEs14(vyy402, vyy412)
new_pePe(True, vyy40, vyy41, vyy57, bee) → True
new_esEs26(vyy402, vyy412, app(ty_Maybe, cee)) → new_esEs5(vyy402, vyy412, cee)
new_ltEs19(vyy3002, vyy402, ty_Char) → new_ltEs9(vyy3002, vyy402)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bff, bfg) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bff, bfg), vyy413, bff, bfg)
new_ltEs15(Right(vyy3000), Right(vyy400), hc, app(ty_[], bab)) → new_ltEs17(vyy3000, vyy400, bab)
new_esEs14(EQ, LT) → False
new_esEs14(LT, EQ) → False
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs5(Just(vyy400), Just(vyy410), app(app(app(ty_@3, dbg), dbh), dca)) → new_esEs6(vyy400, vyy410, dbg, dbh, dca)
new_ltEs5(vyy3001, vyy401, ty_Bool) → new_ltEs16(vyy3001, vyy401)
new_ltEs19(vyy3002, vyy402, ty_Int) → new_ltEs11(vyy3002, vyy402)
new_esEs5(Just(vyy400), Just(vyy410), ty_Double) → new_esEs21(vyy400, vyy410)
new_esEs15([], :(vyy410, vyy411), beg) → False
new_esEs15(:(vyy400, vyy401), [], beg) → False
new_esEs29(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_esEs11(vyy40, vyy41, app(app(ty_Either, bfh), bga)) → new_esEs7(vyy40, vyy41, bfh, bga)
new_ltEs19(vyy3002, vyy402, ty_Ordering) → new_ltEs14(vyy3002, vyy402)
new_ltEs8(Just(vyy3000), Just(vyy400), app(ty_[], bf)) → new_ltEs17(vyy3000, vyy400, bf)
new_compare31(vyy3000, vyy400, ty_Bool) → new_compare9(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, app(ty_[], ff)) → new_lt16(vyy3000, vyy400, ff)
new_esEs19(vyy40, vyy41) → new_primEqInt(vyy40, vyy41)
new_esEs29(vyy400, vyy410, ty_Bool) → new_esEs10(vyy400, vyy410)
new_esEs14(GT, EQ) → False
new_esEs14(EQ, GT) → False
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs8(Just(vyy3000), Just(vyy400), app(ty_Maybe, h)) → new_ltEs8(vyy3000, vyy400, h)
new_lt19(vyy3001, vyy401, ty_Ordering) → new_lt13(vyy3001, vyy401)
new_compare28(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt7(vyy3000, vyy400, ty_@0) → new_lt4(vyy3000, vyy400)
new_asAs(False, vyy66) → False
new_esEs5(Just(vyy400), Just(vyy410), app(app(ty_Either, dcf), dcg)) → new_esEs7(vyy400, vyy410, dcf, dcg)
new_primMulInt(Pos(vyy4000), Neg(vyy30010)) → Neg(new_primMulNat0(vyy4000, vyy30010))
new_primMulInt(Neg(vyy4000), Pos(vyy30010)) → Neg(new_primMulNat0(vyy4000, vyy30010))
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_@2, bha), bhb), bga) → new_esEs8(vyy400, vyy410, bha, bhb)
new_ltEs15(Right(vyy3000), Right(vyy400), hc, ty_Float) → new_ltEs7(vyy3000, vyy400)
new_esEs29(vyy400, vyy410, ty_Char) → new_esEs12(vyy400, vyy410)
new_primMulNat0(Succ(vyy40000), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy300100)) → Zero
new_ltEs15(Right(vyy3000), Right(vyy400), hc, ty_@0) → new_ltEs10(vyy3000, vyy400)
new_esEs11(vyy40, vyy41, app(app(ty_@2, bfd), bfe)) → new_esEs8(vyy40, vyy41, bfd, bfe)
new_ltEs8(Just(vyy3000), Just(vyy400), app(app(ty_@2, bg), bh)) → new_ltEs4(vyy3000, vyy400, bg, bh)
new_ltEs19(vyy3002, vyy402, ty_@0) → new_ltEs10(vyy3002, vyy402)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs18(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, ty_Double) → new_ltEs12(vyy3002, vyy402)
new_ltEs14(GT, LT) → False
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Char, gb) → new_ltEs9(vyy3000, vyy400)
new_not(EQ) → new_not0
new_esEs24(vyy400, vyy410, ty_Integer) → new_esEs17(vyy400, vyy410)
new_lt16(vyy3000, vyy400, ff) → new_esEs9(new_compare0(vyy3000, vyy400, ff))
new_compare31(vyy3000, vyy400, app(ty_[], bbd)) → new_compare0(vyy3000, vyy400, bbd)
new_ltEs15(Right(vyy3000), Right(vyy400), hc, ty_Bool) → new_ltEs16(vyy3000, vyy400)
new_esEs26(vyy402, vyy412, ty_@0) → new_esEs18(vyy402, vyy412)
new_esEs25(vyy401, vyy411, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs6(vyy401, vyy411, cdb, cdc, cdd)
new_esEs7(Right(vyy400), Right(vyy410), bfh, ty_Int) → new_esEs19(vyy400, vyy410)
new_esEs14(GT, GT) → True
new_esEs25(vyy401, vyy411, ty_@0) → new_esEs18(vyy401, vyy411)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs9(vyy3000, vyy400)
new_lt14(vyy3000, vyy400, fc, fd) → new_esEs9(new_compare19(vyy3000, vyy400, fc, fd))
new_lt19(vyy3001, vyy401, ty_Bool) → new_lt15(vyy3001, vyy401)
new_esEs7(Left(vyy400), Left(vyy410), app(app(app(ty_@3, bgf), bgg), bgh), bga) → new_esEs6(vyy400, vyy410, bgf, bgg, bgh)
new_lt7(vyy3000, vyy400, ty_Char) → new_lt6(vyy3000, vyy400)
new_esEs5(Just(vyy400), Nothing, beh) → False
new_esEs5(Nothing, Just(vyy410), beh) → False
new_esEs11(vyy40, vyy41, app(ty_Ratio, bef)) → new_esEs13(vyy40, vyy41, bef)
new_esEs26(vyy402, vyy412, app(ty_[], ced)) → new_esEs15(vyy402, vyy412, ced)
new_esEs28(vyy401, vyy411, app(ty_Ratio, chf)) → new_esEs13(vyy401, vyy411, chf)
new_esEs22(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_ltEs15(Left(vyy3000), Left(vyy400), app(ty_[], gh), gb) → new_ltEs17(vyy3000, vyy400, gh)
new_ltEs14(LT, GT) → True
new_ltEs8(Nothing, Nothing, dee) → True
new_esEs7(Right(vyy400), Right(vyy410), bfh, ty_Integer) → new_esEs17(vyy400, vyy410)
new_not(LT) → new_not0
new_compare13(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_ltEs14(LT, EQ) → True
new_esEs26(vyy402, vyy412, ty_Int) → new_esEs19(vyy402, vyy412)
new_esEs5(Nothing, Nothing, beh) → True
new_esEs28(vyy401, vyy411, app(ty_Maybe, chh)) → new_esEs5(vyy401, vyy411, chh)
new_lt6(vyy3000, vyy400) → new_esEs9(new_compare11(vyy3000, vyy400))
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Maybe, bge), bga) → new_esEs5(vyy400, vyy410, bge)
new_esEs29(vyy400, vyy410, app(app(app(ty_@3, ddc), ddd), dde)) → new_esEs6(vyy400, vyy410, ddc, ddd, dde)
new_esEs22(vyy400, vyy410, ty_Integer) → new_esEs17(vyy400, vyy410)
new_esEs29(vyy400, vyy410, app(app(ty_Either, deb), dec)) → new_esEs7(vyy400, vyy410, deb, dec)
new_lt9(vyy3000, vyy400) → new_esEs9(new_compare28(vyy3000, vyy400))
new_compare26(vyy3000, vyy400, False, fg, fh) → new_compare17(vyy3000, vyy400, new_ltEs4(vyy3000, vyy400, fg, fh), fg, fh)
new_ltEs15(Left(vyy3000), Left(vyy400), app(ty_Ratio, cfg), gb) → new_ltEs6(vyy3000, vyy400, cfg)
new_esEs28(vyy401, vyy411, ty_Ordering) → new_esEs14(vyy401, vyy411)
new_ltEs15(Right(vyy3000), Right(vyy400), hc, app(app(ty_Either, hh), baa)) → new_ltEs15(vyy3000, vyy400, hh, baa)
new_lt7(vyy3000, vyy400, ty_Int) → new_lt11(vyy3000, vyy400)
new_esEs24(vyy400, vyy410, ty_@0) → new_esEs18(vyy400, vyy410)
new_esEs28(vyy401, vyy411, ty_Bool) → new_esEs10(vyy401, vyy411)
new_esEs28(vyy401, vyy411, app(app(ty_@2, dad), dae)) → new_esEs8(vyy401, vyy411, dad, dae)
new_compare14(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare8(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs11(vyy40, vyy41, ty_Integer) → new_esEs17(vyy40, vyy41)
new_compare31(vyy3000, vyy400, app(app(app(ty_@3, bag), bah), bba)) → new_compare15(vyy3000, vyy400, bag, bah, bba)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Bool, gb) → new_ltEs16(vyy3000, vyy400)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vyy400, vyy401), bae) → LT
new_esEs11(vyy40, vyy41, ty_@0) → new_esEs18(vyy40, vyy41)
new_asAs(True, vyy66) → vyy66
new_esEs24(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_ltEs14(EQ, EQ) → True
new_esEs21(Double(vyy400, vyy401), Double(vyy410, vyy411)) → new_esEs19(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_compare11(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_primMulNat0(Succ(vyy40000), Succ(vyy300100)) → new_primPlusNat0(new_primMulNat0(vyy40000, Succ(vyy300100)), vyy300100)
new_ltEs5(vyy3001, vyy401, ty_Integer) → new_ltEs18(vyy3001, vyy401)
new_esEs10(True, False) → False
new_esEs10(False, True) → False
new_esEs14(LT, LT) → True
new_ltEs7(vyy300, vyy40) → new_not(new_compare28(vyy300, vyy40))
new_lt7(vyy3000, vyy400, app(app(ty_Either, bdf), bdg)) → new_lt14(vyy3000, vyy400, bdf, bdg)
new_ltEs16(False, False) → True
new_esEs24(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_esEs18(@0, @0) → True
new_primCompAux0(vyy3000, vyy400, vyy67, bae) → new_primCompAux00(vyy67, new_compare31(vyy3000, vyy400, bae))
new_lt11(vyy3000, vyy400) → new_esEs9(new_compare8(vyy3000, vyy400))
new_fmToList(vyy41, bff, bfg) → new_foldFM2(vyy41, bff, bfg)
new_esEs29(vyy400, vyy410, app(ty_[], dda)) → new_esEs15(vyy400, vyy410, dda)
new_ltEs15(Left(vyy3000), Left(vyy400), app(app(ty_Either, gf), gg), gb) → new_ltEs15(vyy3000, vyy400, gf, gg)
new_esEs25(vyy401, vyy411, ty_Ordering) → new_esEs14(vyy401, vyy411)
new_ltEs15(Left(vyy3000), Right(vyy400), hc, gb) → True
new_ltEs15(Right(vyy3000), Right(vyy400), hc, ty_Int) → new_ltEs11(vyy3000, vyy400)
new_esEs24(vyy400, vyy410, app(app(ty_@2, cca), ccb)) → new_esEs8(vyy400, vyy410, cca, ccb)
new_esEs5(Just(vyy400), Just(vyy410), ty_Int) → new_esEs19(vyy400, vyy410)
new_esEs7(Left(vyy400), Left(vyy410), ty_Double, bga) → new_esEs21(vyy400, vyy410)
new_lt19(vyy3001, vyy401, app(ty_Ratio, dbc)) → new_lt8(vyy3001, vyy401, dbc)
new_compare210(vyy3000, vyy400, False) → new_compare111(vyy3000, vyy400, new_ltEs14(vyy3000, vyy400))
new_ltEs5(vyy3001, vyy401, ty_Double) → new_ltEs12(vyy3001, vyy401)
new_ltEs10(vyy300, vyy40) → new_not(new_compare6(vyy300, vyy40))
new_esEs7(Right(vyy400), Right(vyy410), bfh, ty_Double) → new_esEs21(vyy400, vyy410)
new_ltEs13(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, cb, df) → new_pePe(new_lt20(vyy3000, vyy400, ca), vyy3000, vyy400, new_pePe(new_lt19(vyy3001, vyy401, cb), vyy3001, vyy401, new_ltEs19(vyy3002, vyy402, df), cb), ca)
new_primCompAux00(vyy71, GT) → GT
new_esEs25(vyy401, vyy411, app(app(ty_Either, cea), ceb)) → new_esEs7(vyy401, vyy411, cea, ceb)
new_esEs7(Left(vyy400), Left(vyy410), ty_Float, bga) → new_esEs16(vyy400, vyy410)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs7(Right(vyy400), Right(vyy410), bfh, ty_Bool) → new_esEs10(vyy400, vyy410)
new_ltEs14(EQ, GT) → True
new_ltEs15(Right(vyy3000), Left(vyy400), hc, gb) → False
new_esEs24(vyy400, vyy410, app(ty_[], cbd)) → new_esEs15(vyy400, vyy410, cbd)
new_ltEs15(Left(vyy3000), Left(vyy400), app(app(ty_@2, ha), hb), gb) → new_ltEs4(vyy3000, vyy400, ha, hb)
new_esEs28(vyy401, vyy411, ty_Char) → new_esEs12(vyy401, vyy411)
new_lt13(vyy3000, vyy400) → new_esEs9(new_compare18(vyy3000, vyy400))
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs11(vyy40, vyy41, ty_Bool) → new_esEs10(vyy40, vyy41)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs7(Right(vyy400), Right(vyy410), bfh, app(app(ty_FiniteMap, cag), cah)) → new_esEs20(vyy400, vyy410, cag, cah)
new_compare16(vyy3000, vyy400, False) → GT
new_compare23(vyy3000, vyy400, False) → new_compare16(vyy3000, vyy400, new_ltEs16(vyy3000, vyy400))
new_esEs13(:%(vyy400, vyy401), :%(vyy410, vyy411), bef) → new_asAs(new_esEs22(vyy400, vyy410, bef), new_esEs23(vyy401, vyy411, bef))
The set Q consists of the following terms:
new_lt20(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs8(Nothing, Just(x0), x1)
new_lt20(x0, x1, ty_Integer)
new_ltEs16(True, True)
new_esEs18(@0, @0)
new_compare18(x0, x1)
new_compare17(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_esEs14(EQ, GT)
new_esEs14(GT, EQ)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_ltEs15(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs15(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_compare15(x0, x1, x2, x3, x4)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(Right(x0), Right(x1), x2, ty_@0)
new_esEs9(EQ)
new_compare23(x0, x1, True)
new_esEs27(x0, x1, ty_Float)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs5(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs11(x0, x1, ty_Float)
new_esEs11(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primCompAux00(x0, GT)
new_esEs28(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_lt19(x0, x1, ty_Ordering)
new_compare8(x0, x1)
new_esEs5(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs15(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare13(Integer(x0), Integer(x1))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_pePe(True, x0, x1, x2, x3)
new_compare0([], :(x0, x1), x2)
new_ltEs5(x0, x1, ty_Int)
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_asAs(False, x0)
new_compare110(x0, x1, False, x2, x3)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_esEs25(x0, x1, ty_Int)
new_esEs14(GT, LT)
new_esEs14(LT, GT)
new_compare25(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs15(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, ty_Char)
new_primCompAux00(x0, EQ)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_lt20(x0, x1, ty_Float)
new_ltEs15(Right(x0), Left(x1), x2, x3)
new_ltEs15(Left(x0), Right(x1), x2, x3)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_ltEs5(x0, x1, ty_@0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs15(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, ty_@0)
new_lt7(x0, x1, ty_Double)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs11(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs8(Just(x0), Nothing, x1)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Int)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_compare31(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Zero)
new_lt7(x0, x1, ty_Char)
new_esEs10(True, False)
new_esEs10(False, True)
new_ltEs15(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs11(x0, x1, app(ty_[], x2))
new_compare24(x0, x1, False, x2)
new_esEs11(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Float)
new_ltEs15(Right(x0), Right(x1), x2, ty_Integer)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs5(Nothing, Just(x0), x1)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Int)
new_lt7(x0, x1, app(ty_[], x2))
new_compare12(x0, x1, True, x2)
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs15(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs16(Float(x0, x1), Float(x2, x3))
new_primPlusNat1(Succ(x0), Zero)
new_pePe(False, x0, x1, x2, x3)
new_lt7(x0, x1, ty_Ordering)
new_ltEs15(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_esEs17(Integer(x0), Integer(x1))
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs15([], [], x0)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt8(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare17(x0, x1, False, x2, x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare0(:(x0, x1), [], x2)
new_compare23(x0, x1, False)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True, x2, x3)
new_ltEs15(Left(x0), Left(x1), ty_Int, x2)
new_compare31(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare12(x0, x1, False, x2)
new_ltEs8(Nothing, Nothing, x0)
new_esEs27(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, x2, x3)
new_lt7(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt19(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Zero, Zero)
new_esEs11(x0, x1, ty_Double)
new_not0
new_esEs29(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_compare27(x0, x1, True, x2, x3)
new_ltEs12(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs14(LT, LT)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs15(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs10(True, True)
new_esEs9(GT)
new_ltEs14(LT, LT)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs11(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt7(x0, x1, ty_Integer)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs5(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, x2)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(x0, x1)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Char)
new_ltEs18(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, ty_Bool)
new_lt5(x0, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare26(x0, x1, True, x2, x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs6(x0, x1, x2)
new_esEs15([], :(x0, x1), x2)
new_esEs25(x0, x1, ty_Float)
new_not(GT)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_compare111(x0, x1, True)
new_ltEs10(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_compare24(x0, x1, True, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs15(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_compare31(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_esEs15(:(x0, x1), [], x2)
new_compare16(x0, x1, False)
new_esEs24(x0, x1, ty_Integer)
new_ltEs15(Right(x0), Right(x1), x2, ty_Double)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_sr(x0, x1)
new_compare29(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Bool)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare16(x0, x1, True)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Float)
new_compare26(x0, x1, False, x2, x3)
new_lt7(x0, x1, ty_Float)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs15(Left(x0), Left(x1), ty_Float, x2)
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Char)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_lt15(x0, x1)
new_lt17(x0, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Left(x0), Left(x1), ty_Char, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primPlusNat0(Zero, x0)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Integer)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs9(LT)
new_ltEs16(True, False)
new_ltEs16(False, True)
new_primCompAux00(x0, LT)
new_compare6(@0, @0)
new_esEs24(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_primEqNat0(Zero, Succ(x0))
new_fmToList(x0, x1, x2)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Float)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare10(x0, x1, True, x2, x3, x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs22(x0, x1, ty_Int)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Zero, Zero)
new_ltEs15(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_esEs10(False, False)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_lt20(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Bool)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs15(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs28(x0, x1, ty_Int)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs29(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Char)
new_lt13(x0, x1)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, ty_@0)
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare30(x0, x1, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, app(ty_[], x2))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Double)
new_esEs5(Nothing, Nothing, x0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt7(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Ordering)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_esEs12(Char(x0), Char(x1))
new_esEs11(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_ltEs15(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat0(Succ(x0), x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs29(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_ltEs15(Right(x0), Right(x1), x2, ty_Char)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, True)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs14(GT, GT)
new_esEs24(x0, x1, ty_Char)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs15(Right(x0), Right(x1), x2, ty_Float)
new_not(EQ)
new_ltEs17(x0, x1, x2)
new_compare31(x0, x1, ty_Int)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, ty_Integer)
new_lt6(x0, x1)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare9(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_compare11(Char(x0), Char(x1))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt11(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_ltEs15(Right(x0), Right(x1), x2, ty_Bool)
new_compare28(Float(x0, x1), Float(x2, x3))
new_esEs14(LT, EQ)
new_esEs14(EQ, LT)
new_esEs22(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Double)
new_lt14(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Double)
new_esEs14(GT, GT)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Ordering)
new_compare111(x0, x1, False)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs21(Double(x0, x1), Double(x2, x3))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare31(x0, x1, ty_Double)
new_esEs14(EQ, EQ)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, False, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_lt19(x0, x1, ty_Int)
new_lt19(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs9(x0, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Float)
new_lt18(x0, x1, x2, x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_foldFM2(EmptyFM, x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_compare31(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Bool)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt20(x0, x1, ty_Char)
new_asAs(True, x0)
new_lt12(x0, x1, x2, x3, x4)
new_compare27(x0, x1, False, x2, x3)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, x2)
new_compare0([], [], x0)
new_esEs24(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_ltEs16(False, False)
new_not(LT)
new_ltEs19(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
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_compare2(vyy3000, vyy400, False, eg) → new_ltEs(vyy3000, vyy400, eg)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3
- new_primCompAux(vyy3000, vyy400, vyy67, app(ty_Maybe, baf)) → new_compare1(vyy3000, vyy400, baf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_compare5(vyy3000, vyy400, fg, fh) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fg, fh), fg, fh)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_primCompAux(vyy3000, vyy400, new_compare0(vyy3001, vyy401, bae), bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_primCompAux(vyy3000, vyy400, new_compare0(vyy3001, vyy401, bae), bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(ty_Maybe, bbh)) → new_ltEs(vyy3001, vyy401, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_compare(vyy3001, vyy401, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(ty_Either, bcd), bce)) → new_ltEs1(vyy3001, vyy401, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_@2, fg), fh), cb, df) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fg, fh), fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_lt3(vyy3000, vyy400, fg, fh) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fg, fh), fg, fh)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, cb, app(ty_Maybe, cc)) → new_ltEs(vyy3002, vyy402, cc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs(Just(vyy3000), Just(vyy400), app(ty_Maybe, h)) → new_ltEs(vyy3000, vyy400, h)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, cb, app(app(ty_Either, cg), da)) → new_ltEs1(vyy3002, vyy402, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_compare20(vyy3000, vyy400, False, eh, fa, fb) → new_ltEs0(vyy3000, vyy400, eh, fa, fb)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4, 6 >= 5
- new_primCompAux(vyy3000, vyy400, vyy67, app(app(app(ty_@3, bag), bah), bba)) → new_compare3(vyy3000, vyy400, bag, bah, bba)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(ty_@2, bcg), bch)) → new_ltEs3(vyy3001, vyy401, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, cb, app(app(ty_@2, dc), dd)) → new_ltEs3(vyy3002, vyy402, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs0(vyy3001, vyy401, bca, bcb, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, cb, app(app(app(ty_@3, cd), ce), cf)) → new_ltEs0(vyy3002, vyy402, cd, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_ltEs(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ba), bb), bc)) → new_ltEs0(vyy3000, vyy400, ba, bb, bc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_@2, bea), beb), bdb) → new_lt3(vyy3000, vyy400, bea, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, app(app(ty_@2, ee), ef), df) → new_lt3(vyy3001, vyy401, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare22(vyy3000, vyy400, False, fg, fh) → new_ltEs3(vyy3000, vyy400, fg, fh)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs(Just(vyy3000), Just(vyy400), app(app(ty_@2, bg), bh)) → new_ltEs3(vyy3000, vyy400, bg, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_lt2(vyy3000, vyy400, ff) → new_compare(vyy3000, vyy400, ff)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_Maybe, bda), bdb) → new_lt(vyy3000, vyy400, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, app(ty_Maybe, de), df) → new_lt(vyy3001, vyy401, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs(Just(vyy3000), Just(vyy400), app(app(ty_Either, bd), be)) → new_ltEs1(vyy3000, vyy400, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_compare21(vyy3000, vyy400, False, fc, fd) → new_ltEs1(vyy3000, vyy400, fc, fd)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs(Just(vyy3000), Just(vyy400), app(ty_[], bf)) → new_ltEs2(vyy3000, vyy400, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_compare(vyy3001, vyy401, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_lt1(vyy3000, vyy400, fc, fd) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, fc, fd), fc, fd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_lt0(vyy3000, vyy400, eh, fa, fb) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, eh, fa, fb), eh, fa, fb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_Either, fc), fd), cb, df) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, fc, fd), fc, fd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_compare4(vyy3000, vyy400, fc, fd) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, fc, fd), fc, fd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(ty_[], bcf)) → new_ltEs2(vyy3001, vyy401, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, cb, app(ty_[], db)) → new_ltEs2(vyy3002, vyy402, db)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_primCompAux(vyy3000, vyy400, vyy67, app(app(ty_Either, bbb), bbc)) → new_compare4(vyy3000, vyy400, bbb, bbc)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_Maybe, eg), cb, df) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, eg), eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4
- new_compare3(vyy3000, vyy400, eh, fa, fb) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, eh, fa, fb), eh, fa, fb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_[], ff), cb, df) → new_compare(vyy3000, vyy400, ff)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_primCompAux(vyy3000, vyy400, vyy67, app(ty_[], bbd)) → new_compare(vyy3000, vyy400, bbd)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_primCompAux(vyy3000, vyy400, vyy67, app(app(ty_@2, bbe), bbf)) → new_compare5(vyy3000, vyy400, bbe, bbf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_compare1(vyy3000, vyy400, eg) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, eg), eg)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_lt(vyy3000, vyy400, eg) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, eg), eg)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_[], bdh), bdb) → new_lt2(vyy3000, vyy400, bdh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, app(ty_[], ed), df) → new_lt2(vyy3001, vyy401, ed)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(app(ty_@3, bdc), bdd), bde), bdb) → new_lt0(vyy3000, vyy400, bdc, bdd, bde)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_Either, bdf), bdg), bdb) → new_lt1(vyy3000, vyy400, bdf, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, app(app(app(ty_@3, dg), dh), ea), df) → new_lt0(vyy3001, vyy401, dg, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(app(ty_@3, eh), fa), fb), cb, df) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, eh, fa, fb), eh, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5, 3 > 6
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ca, app(app(ty_Either, eb), ec), df) → new_lt1(vyy3001, vyy401, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs1(Left(vyy3000), Left(vyy400), app(ty_Maybe, ga), gb) → new_ltEs(vyy3000, vyy400, ga)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs1(Right(vyy3000), Right(vyy400), hc, app(ty_Maybe, hd)) → new_ltEs(vyy3000, vyy400, hd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs1(Left(vyy3000), Left(vyy400), app(app(ty_Either, gf), gg), gb) → new_ltEs1(vyy3000, vyy400, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs1(Right(vyy3000), Right(vyy400), hc, app(app(ty_Either, hh), baa)) → new_ltEs1(vyy3000, vyy400, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs1(Right(vyy3000), Right(vyy400), hc, app(app(ty_@2, bac), bad)) → new_ltEs3(vyy3000, vyy400, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs1(Left(vyy3000), Left(vyy400), app(app(ty_@2, ha), hb), gb) → new_ltEs3(vyy3000, vyy400, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs1(Right(vyy3000), Right(vyy400), hc, app(app(app(ty_@3, he), hf), hg)) → new_ltEs0(vyy3000, vyy400, he, hf, hg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs1(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, gc), gd), ge), gb) → new_ltEs0(vyy3000, vyy400, gc, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs1(Left(vyy3000), Left(vyy400), app(ty_[], gh), gb) → new_ltEs2(vyy3000, vyy400, gh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs1(Right(vyy3000), Right(vyy400), hc, app(ty_[], bab)) → new_ltEs2(vyy3000, vyy400, bab)
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_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE(vyy26, vyy40, vyy343, h, ba)
new_foldFM_LE(vyy26, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE1(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Just(vyy40), h), h, ba)
new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE2(vyy340, vyy341, new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE2(vyy340, vyy341, vyy30, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE1(new_keysFM_LE0(vyy340, vyy341, vyy30, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs8(vyy3440, Just(vyy40), h), h, ba)
new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE1(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Just(vyy40), h), h, ba)
new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE(vyy26, vyy40, vyy343, h, ba)
The TRS R consists of the following rules:
new_esEs28(vyy401, vyy411, ty_Integer) → new_esEs17(vyy401, vyy411)
new_esEs29(vyy400, vyy410, ty_Integer) → new_esEs17(vyy400, vyy410)
new_compare18(vyy3000, vyy400) → new_compare210(vyy3000, vyy400, new_esEs14(vyy3000, vyy400))
new_compare31(vyy3000, vyy400, ty_Integer) → new_compare13(vyy3000, vyy400)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Integer) → new_ltEs18(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, ty_Double) → new_esEs21(vyy401, vyy411)
new_esEs11(vyy40, vyy41, ty_Char) → new_esEs12(vyy40, vyy41)
new_esEs5(Just(vyy400), Just(vyy410), ty_@0) → new_esEs18(vyy400, vyy410)
new_esEs25(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_Either, hg), hh), gb) → new_esEs7(vyy400, vyy410, hg, hh)
new_compare29(vyy3000, vyy400, cba, cbb) → new_compare26(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, cba, cbb), cba, cbb)
new_ltEs9(vyy300, vyy40) → new_not(new_compare11(vyy300, vyy40))
new_lt19(vyy3001, vyy401, app(app(ty_Either, cgg), cgh)) → new_lt14(vyy3001, vyy401, cgg, cgh)
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, bb), bc), bd)) → new_lt12(vyy3000, vyy400, bb, bc, bd)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, app(ty_Maybe, bhf)) → new_ltEs8(vyy3000, vyy400, bhf)
new_esEs5(Just(vyy400), Just(vyy410), ty_Integer) → new_esEs17(vyy400, vyy410)
new_compare10(vyy3000, vyy400, True, bb, bc, bd) → LT
new_lt19(vyy3001, vyy401, ty_Float) → new_lt9(vyy3001, vyy401)
new_esEs28(vyy401, vyy411, app(ty_[], cch)) → new_esEs15(vyy401, vyy411, cch)
new_compare110(vyy3000, vyy400, True, cec, ced) → LT
new_ltEs14(GT, GT) → True
new_ltEs8(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, dea), deb), dec)) → new_ltEs13(vyy3000, vyy400, dea, deb, dec)
new_ltEs5(vyy3001, vyy401, ty_Char) → new_ltEs9(vyy3001, vyy401)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Ordering, bgb) → new_ltEs14(vyy3000, vyy400)
new_esEs5(Just(vyy400), Just(vyy410), app(ty_[], che)) → new_esEs15(vyy400, vyy410, che)
new_esEs24(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_lt20(vyy3000, vyy400, app(app(ty_Either, cec), ced)) → new_lt14(vyy3000, vyy400, cec, ced)
new_compare7(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs20(vyy40, vyy41, fg, fh) → new_asAs(new_esEs19(new_sizeFM(vyy40, fg, fh), new_sizeFM(vyy41, fg, fh)), new_esEs15(new_fmToList(vyy40, fg, fh), new_fmToList(vyy41, fg, fh), app(app(ty_@2, fg), fh)))
new_compare31(vyy3000, vyy400, ty_Int) → new_compare8(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, ty_@0) → new_compare6(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs10(vyy3000, vyy400)
new_primMulNat0(Zero, Zero) → Zero
new_esEs29(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_ltEs5(vyy3001, vyy401, ty_@0) → new_ltEs10(vyy3001, vyy401)
new_esEs11(vyy40, vyy41, ty_Float) → new_esEs16(vyy40, vyy41)
new_lt20(vyy3000, vyy400, ty_Int) → new_lt11(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, app(ty_[], cbd)) → new_esEs15(vyy400, vyy410, cbd)
new_ltEs16(False, True) → True
new_esEs27(vyy400, vyy410, app(app(ty_FiniteMap, ccc), ccd)) → new_esEs20(vyy400, vyy410, ccc, ccd)
new_esEs9(LT) → True
new_esEs29(vyy400, vyy410, app(app(ty_FiniteMap, dbh), dca)) → new_esEs20(vyy400, vyy410, dbh, dca)
new_ltEs16(True, False) → False
new_not(GT) → False
new_esEs25(vyy401, vyy411, app(app(ty_FiniteMap, bea), beb)) → new_esEs20(vyy401, vyy411, bea, beb)
new_esEs27(vyy400, vyy410, app(app(ty_@2, cca), ccb)) → new_esEs8(vyy400, vyy410, cca, ccb)
new_ltEs19(vyy3002, vyy402, ty_Bool) → new_ltEs16(vyy3002, vyy402)
new_lt7(vyy3000, vyy400, ty_Float) → new_lt9(vyy3000, vyy400)
new_lt7(vyy3000, vyy400, ty_Ordering) → new_lt13(vyy3000, vyy400)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Ordering) → new_ltEs14(vyy3000, vyy400)
new_ltEs11(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_compare0(:(vyy3000, vyy3001), :(vyy400, vyy401), gd) → new_primCompAux0(vyy3000, vyy400, new_compare0(vyy3001, vyy401, gd), gd)
new_esEs5(Just(vyy400), Just(vyy410), app(ty_Maybe, chf)) → new_esEs5(vyy400, vyy410, chf)
new_esEs27(vyy400, vyy410, ty_Bool) → new_esEs10(vyy400, vyy410)
new_esEs25(vyy401, vyy411, ty_Integer) → new_esEs17(vyy401, vyy411)
new_esEs7(Left(vyy400), Left(vyy410), ty_Ordering, gb) → new_esEs14(vyy400, vyy410)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, app(app(ty_@2, cae), caf)) → new_ltEs4(vyy3000, vyy400, cae, caf)
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, fg, fh) → :(@2(vyy410, vyy411), vyy85)
new_ltEs16(True, True) → True
new_esEs17(Integer(vyy400), Integer(vyy410)) → new_primEqInt(vyy400, vyy410)
new_esEs26(vyy402, vyy412, ty_Bool) → new_esEs10(vyy402, vyy412)
new_esEs7(Left(vyy400), Right(vyy410), ga, gb) → False
new_esEs7(Right(vyy400), Left(vyy410), ga, gb) → False
new_esEs26(vyy402, vyy412, app(app(ty_@2, bfc), bfd)) → new_esEs8(vyy402, vyy412, bfc, bfd)
new_compare6(@0, @0) → EQ
new_ltEs19(vyy3002, vyy402, app(app(ty_@2, cfh), cga)) → new_ltEs4(vyy3002, vyy402, cfh, cga)
new_compare23(vyy3000, vyy400, True) → EQ
new_esEs27(vyy400, vyy410, app(app(ty_Either, cce), ccf)) → new_esEs7(vyy400, vyy410, cce, ccf)
new_ltEs14(GT, EQ) → False
new_lt19(vyy3001, vyy401, app(ty_[], cha)) → new_lt16(vyy3001, vyy401, cha)
new_esEs26(vyy402, vyy412, ty_Char) → new_esEs12(vyy402, vyy412)
new_compare31(vyy3000, vyy400, app(app(ty_@2, ddd), dde)) → new_compare29(vyy3000, vyy400, ddd, dde)
new_ltEs5(vyy3001, vyy401, app(app(ty_@2, cg), da)) → new_ltEs4(vyy3001, vyy401, cg, da)
new_ltEs6(vyy300, vyy40, cag) → new_not(new_compare14(vyy300, vyy40, cag))
new_lt7(vyy3000, vyy400, app(ty_Maybe, dc)) → new_lt10(vyy3000, vyy400, dc)
new_esEs14(EQ, EQ) → True
new_esEs25(vyy401, vyy411, ty_Double) → new_esEs21(vyy401, vyy411)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs16(vyy3000, vyy400)
new_lt19(vyy3001, vyy401, app(ty_Maybe, cgc)) → new_lt10(vyy3001, vyy401, cgc)
new_esEs11(vyy40, vyy41, app(ty_[], eg)) → new_esEs15(vyy40, vyy41, eg)
new_esEs29(vyy400, vyy410, app(ty_Ratio, dah)) → new_esEs13(vyy400, vyy410, dah)
new_compare111(vyy3000, vyy400, False) → GT
new_compare111(vyy3000, vyy400, True) → LT
new_ltEs5(vyy3001, vyy401, app(app(ty_Either, cd), ce)) → new_ltEs15(vyy3001, vyy401, cd, ce)
new_esEs27(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_ltEs8(Nothing, Just(vyy400), ddf) → True
new_foldFM_LE20(vyy340, vyy341, vyy30, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE10(new_keysFM_LE0(vyy340, vyy341, vyy30, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs8(vyy3440, Just(vyy40), h), h, ba)
new_esEs8(@2(vyy400, vyy401), @2(vyy410, vyy411), fd, ff) → new_asAs(new_esEs27(vyy400, vyy410, fd), new_esEs28(vyy401, vyy411, ff))
new_esEs26(vyy402, vyy412, ty_Double) → new_esEs21(vyy402, vyy412)
new_esEs11(vyy40, vyy41, app(app(app(ty_@3, fa), fb), fc)) → new_esEs6(vyy40, vyy41, fa, fb, fc)
new_keysFM_LE0(vyy340, vyy341, vyy27, h, ba) → :(vyy340, vyy27)
new_compare25(vyy3000, vyy400, True, bb, bc, bd) → EQ
new_esEs24(vyy400, vyy410, app(app(ty_FiniteMap, bce), bcf)) → new_esEs20(vyy400, vyy410, bce, bcf)
new_lt8(vyy3000, vyy400, gc) → new_esEs9(new_compare14(vyy3000, vyy400, gc))
new_compare31(vyy3000, vyy400, app(ty_Maybe, dce)) → new_compare30(vyy3000, vyy400, dce)
new_esEs24(vyy400, vyy410, app(app(ty_Either, bcg), bch)) → new_esEs7(vyy400, vyy410, bcg, bch)
new_esEs25(vyy401, vyy411, app(ty_Ratio, bda)) → new_esEs13(vyy401, vyy411, bda)
new_lt15(vyy3000, vyy400) → new_esEs9(new_compare9(vyy3000, vyy400))
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Float) → new_esEs16(vyy400, vyy410)
new_compare0([], [], gd) → EQ
new_esEs27(vyy400, vyy410, ty_@0) → new_esEs18(vyy400, vyy410)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Integer, bgb) → new_ltEs18(vyy3000, vyy400)
new_primEqNat0(Zero, Zero) → True
new_ltEs5(vyy3001, vyy401, ty_Int) → new_ltEs11(vyy3001, vyy401)
new_ltEs19(vyy3002, vyy402, ty_Integer) → new_ltEs18(vyy3002, vyy402)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Double, bgb) → new_ltEs12(vyy3000, vyy400)
new_lt19(vyy3001, vyy401, ty_Double) → new_lt5(vyy3001, vyy401)
new_lt5(vyy3000, vyy400) → new_esEs9(new_compare7(vyy3000, vyy400))
new_lt20(vyy3000, vyy400, app(ty_Ratio, gc)) → new_lt8(vyy3000, vyy400, gc)
new_ltEs5(vyy3001, vyy401, app(ty_Maybe, bh)) → new_ltEs8(vyy3001, vyy401, bh)
new_lt7(vyy3000, vyy400, app(ty_[], ea)) → new_lt16(vyy3000, vyy400, ea)
new_esEs26(vyy402, vyy412, app(ty_Ratio, bee)) → new_esEs13(vyy402, vyy412, bee)
new_compare31(vyy3000, vyy400, ty_Ordering) → new_compare18(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, app(ty_Ratio, cbc)) → new_esEs13(vyy400, vyy410, cbc)
new_esEs27(vyy400, vyy410, ty_Char) → new_esEs12(vyy400, vyy410)
new_compare31(vyy3000, vyy400, app(ty_Ratio, dcd)) → new_compare14(vyy3000, vyy400, dcd)
new_compare110(vyy3000, vyy400, False, cec, ced) → GT
new_compare12(vyy3000, vyy400, False, ed) → GT
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(app(ty_@3, bad), bae), baf)) → new_esEs6(vyy400, vyy410, bad, bae, baf)
new_sr(vyy400, vyy3001) → new_primMulInt(vyy400, vyy3001)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Double) → new_ltEs12(vyy3000, vyy400)
new_ltEs14(EQ, LT) → False
new_lt20(vyy3000, vyy400, ty_Float) → new_lt9(vyy3000, vyy400)
new_esEs25(vyy401, vyy411, app(ty_[], bdb)) → new_esEs15(vyy401, vyy411, bdb)
new_ltEs8(Just(vyy3000), Just(vyy400), app(app(ty_Either, ded), dee)) → new_ltEs15(vyy3000, vyy400, ded, dee)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(ty_[], bab)) → new_esEs15(vyy400, vyy410, bab)
new_esEs24(vyy400, vyy410, ty_Char) → new_esEs12(vyy400, vyy410)
new_esEs14(GT, LT) → False
new_esEs14(LT, GT) → False
new_esEs15(:(vyy400, vyy401), :(vyy410, vyy411), eg) → new_asAs(new_esEs29(vyy400, vyy410, eg), new_esEs15(vyy401, vyy411, eg))
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Int, bgb) → new_ltEs11(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy860), vyy300100) → Succ(Succ(new_primPlusNat1(vyy860, vyy300100)))
new_lt19(vyy3001, vyy401, ty_@0) → new_lt4(vyy3001, vyy401)
new_esEs25(vyy401, vyy411, ty_Float) → new_esEs16(vyy401, vyy411)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(ty_Either, bbc), bbd)) → new_esEs7(vyy400, vyy410, bbc, bbd)
new_esEs26(vyy402, vyy412, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs6(vyy402, vyy412, beh, bfa, bfb)
new_ltEs18(vyy300, vyy40) → new_not(new_compare13(vyy300, vyy40))
new_esEs7(Left(vyy400), Left(vyy410), app(ty_[], gf), gb) → new_esEs15(vyy400, vyy410, gf)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Char) → new_esEs12(vyy400, vyy410)
new_compare17(vyy3000, vyy400, True, cba, cbb) → LT
new_ltEs19(vyy3002, vyy402, ty_Float) → new_ltEs7(vyy3002, vyy402)
new_esEs28(vyy401, vyy411, ty_Float) → new_esEs16(vyy401, vyy411)
new_lt20(vyy3000, vyy400, app(app(ty_@2, cba), cbb)) → new_lt18(vyy3000, vyy400, cba, cbb)
new_primEqInt(Neg(Succ(vyy4000)), Neg(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_esEs25(vyy401, vyy411, app(app(ty_@2, bdg), bdh)) → new_esEs8(vyy401, vyy411, bdg, bdh)
new_esEs9(GT) → False
new_compare10(vyy3000, vyy400, False, bb, bc, bd) → GT
new_lt7(vyy3000, vyy400, ty_Bool) → new_lt15(vyy3000, vyy400)
new_primPlusNat1(Zero, Succ(vyy3001000)) → Succ(vyy3001000)
new_primPlusNat1(Succ(vyy8600), Zero) → Succ(vyy8600)
new_lt20(vyy3000, vyy400, ty_Char) → new_lt6(vyy3000, vyy400)
new_compare9(vyy3000, vyy400) → new_compare23(vyy3000, vyy400, new_esEs10(vyy3000, vyy400))
new_ltEs12(vyy300, vyy40) → new_not(new_compare7(vyy300, vyy40))
new_esEs9(EQ) → False
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, app(app(app(ty_@3, bhg), bhh), caa)) → new_ltEs13(vyy3000, vyy400, bhg, bhh, caa)
new_compare16(vyy3000, vyy400, True) → LT
new_compare27(vyy3000, vyy400, False, cec, ced) → new_compare110(vyy3000, vyy400, new_ltEs15(vyy3000, vyy400, cec, ced), cec, ced)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(ty_Ratio, baa)) → new_esEs13(vyy400, vyy410, baa)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy400, vyy410, ty_Bool) → new_esEs10(vyy400, vyy410)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Ratio, ge), gb) → new_esEs13(vyy400, vyy410, ge)
new_esEs24(vyy400, vyy410, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs6(vyy400, vyy410, bbh, bca, bcb)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(ty_Maybe, bac)) → new_esEs5(vyy400, vyy410, bac)
new_compare15(vyy3000, vyy400, bb, bc, bd) → new_compare25(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, bb, bc, bd), bb, bc, bd)
new_esEs29(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_compare8(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4100))) → False
new_primEqInt(Neg(Succ(vyy4000)), Neg(Zero)) → False
new_esEs11(vyy40, vyy41, ty_Int) → new_esEs19(vyy40, vyy41)
new_esEs5(Just(vyy400), Just(vyy410), ty_Float) → new_esEs16(vyy400, vyy410)
new_compare26(vyy3000, vyy400, True, cba, cbb) → EQ
new_ltEs5(vyy3001, vyy401, app(app(app(ty_@3, ca), cb), cc)) → new_ltEs13(vyy3001, vyy401, ca, cb, cc)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt13(vyy3000, vyy400)
new_lt7(vyy3000, vyy400, ty_Integer) → new_lt17(vyy3000, vyy400)
new_esEs23(vyy401, vyy411, ty_Integer) → new_esEs17(vyy401, vyy411)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Ordering) → new_esEs14(vyy400, vyy410)
new_ltEs15(Left(vyy3000), Left(vyy400), app(ty_Maybe, bgc), bgb) → new_ltEs8(vyy3000, vyy400, bgc)
new_esEs10(False, False) → True
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs14(vyy3000, vyy400)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), fg, fh) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, fg, fh), vyy4133, fg, fh)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs28(vyy401, vyy411, ty_@0) → new_esEs18(vyy401, vyy411)
new_esEs26(vyy402, vyy412, app(app(ty_Either, bfg), bfh)) → new_esEs7(vyy402, vyy412, bfg, bfh)
new_esEs28(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs7(Left(vyy400), Left(vyy410), ty_Int, gb) → new_esEs19(vyy400, vyy410)
new_ltEs5(vyy3001, vyy401, app(ty_[], cf)) → new_ltEs17(vyy3001, vyy401, cf)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_sizeFM(EmptyFM, fg, fh) → Pos(Zero)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, he), hf), gb) → new_esEs20(vyy400, vyy410, he, hf)
new_esEs26(vyy402, vyy412, ty_Integer) → new_esEs17(vyy402, vyy412)
new_esEs29(vyy400, vyy410, ty_Ordering) → new_esEs14(vyy400, vyy410)
new_ltEs17(vyy300, vyy40, gd) → new_not(new_compare0(vyy300, vyy40, gd))
new_primEqInt(Pos(Succ(vyy4000)), Pos(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_esEs11(vyy40, vyy41, ty_Double) → new_esEs21(vyy40, vyy41)
new_compare31(vyy3000, vyy400, ty_Float) → new_compare28(vyy3000, vyy400)
new_esEs16(Float(vyy400, vyy401), Float(vyy410, vyy411)) → new_esEs19(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_compare27(vyy3000, vyy400, True, cec, ced) → EQ
new_esEs25(vyy401, vyy411, app(ty_Maybe, bdc)) → new_esEs5(vyy401, vyy411, bdc)
new_esEs29(vyy400, vyy410, app(ty_Maybe, dbb)) → new_esEs5(vyy400, vyy410, dbb)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs11(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, app(app(ty_FiniteMap, cdg), cdh)) → new_esEs20(vyy401, vyy411, cdg, cdh)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs7(vyy3000, vyy400)
new_primEqNat0(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat0(vyy4000, vyy4100)
new_esEs11(vyy40, vyy41, app(app(ty_FiniteMap, fg), fh)) → new_esEs20(vyy40, vyy41, fg, fh)
new_esEs27(vyy400, vyy410, ty_Integer) → new_esEs17(vyy400, vyy410)
new_ltEs5(vyy3001, vyy401, app(ty_Ratio, bg)) → new_ltEs6(vyy3001, vyy401, bg)
new_esEs26(vyy402, vyy412, app(app(ty_FiniteMap, bfe), bff)) → new_esEs20(vyy402, vyy412, bfe, bff)
new_ltEs4(@2(vyy3000, vyy3001), @2(vyy400, vyy401), be, bf) → new_pePe(new_lt7(vyy3000, vyy400, be), vyy3000, vyy400, new_ltEs5(vyy3001, vyy401, bf), be)
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt17(vyy3000, vyy400)
new_primCompAux00(vyy71, LT) → LT
new_foldFM_LE0(vyy26, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE10(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Just(vyy40), h), h, ba)
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_lt20(vyy3000, vyy400, ty_@0) → new_lt4(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, app(ty_[], cfg)) → new_ltEs17(vyy3002, vyy402, cfg)
new_compare24(vyy3000, vyy400, False, ed) → new_compare12(vyy3000, vyy400, new_ltEs8(vyy3000, vyy400, ed), ed)
new_ltEs8(Just(vyy3000), Nothing, ddf) → False
new_compare31(vyy3000, vyy400, ty_Char) → new_compare11(vyy3000, vyy400)
new_esEs15([], [], eg) → True
new_primEqInt(Pos(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Succ(vyy4000)), Pos(Zero)) → False
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Char) → new_ltEs9(vyy3000, vyy400)
new_ltEs8(Just(vyy3000), Just(vyy400), app(ty_Ratio, ddg)) → new_ltEs6(vyy3000, vyy400, ddg)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_esEs6(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), fa, fb, fc) → new_asAs(new_esEs24(vyy400, vyy410, fa), new_asAs(new_esEs25(vyy401, vyy411, fb), new_esEs26(vyy402, vyy412, fc)))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_primPlusNat1(Succ(vyy8600), Succ(vyy3001000)) → Succ(Succ(new_primPlusNat1(vyy8600, vyy3001000)))
new_compare12(vyy3000, vyy400, True, ed) → LT
new_primEqInt(Neg(Succ(vyy4000)), Pos(vyy410)) → False
new_primEqInt(Pos(Succ(vyy4000)), Neg(vyy410)) → False
new_esEs24(vyy400, vyy410, app(ty_Ratio, bbe)) → new_esEs13(vyy400, vyy410, bbe)
new_lt12(vyy3000, vyy400, bb, bc, bd) → new_esEs9(new_compare15(vyy3000, vyy400, bb, bc, bd))
new_esEs7(Left(vyy400), Left(vyy410), ty_Integer, gb) → new_esEs17(vyy400, vyy410)
new_compare14(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare13(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_esEs27(vyy400, vyy410, app(ty_Maybe, cbe)) → new_esEs5(vyy400, vyy410, cbe)
new_foldFM2(EmptyFM, fg, fh) → []
new_foldFM_LE10(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba) → new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba)
new_esEs25(vyy401, vyy411, ty_Char) → new_esEs12(vyy401, vyy411)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4100))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCompAux00(vyy71, EQ) → vyy71
new_esEs28(vyy401, vyy411, app(app(ty_Either, cea), ceb)) → new_esEs7(vyy401, vyy411, cea, ceb)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, app(ty_Ratio, bhe)) → new_ltEs6(vyy3000, vyy400, bhe)
new_compare25(vyy3000, vyy400, False, bb, bc, bd) → new_compare10(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, bb, bc, bd), bb, bc, bd)
new_esEs5(Just(vyy400), Just(vyy410), ty_Bool) → new_esEs10(vyy400, vyy410)
new_esEs24(vyy400, vyy410, ty_Ordering) → new_esEs14(vyy400, vyy410)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_@0, bgb) → new_ltEs10(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, app(app(ty_Either, dda), ddb)) → new_compare19(vyy3000, vyy400, dda, ddb)
new_ltEs19(vyy3002, vyy402, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs13(vyy3002, vyy402, cfb, cfc, cfd)
new_lt7(vyy3000, vyy400, app(app(ty_@2, eb), ec)) → new_lt18(vyy3000, vyy400, eb, ec)
new_esEs5(Just(vyy400), Just(vyy410), ty_Ordering) → new_esEs14(vyy400, vyy410)
new_compare17(vyy3000, vyy400, False, cba, cbb) → GT
new_esEs25(vyy401, vyy411, ty_Bool) → new_esEs10(vyy401, vyy411)
new_esEs26(vyy402, vyy412, ty_Float) → new_esEs16(vyy402, vyy412)
new_lt20(vyy3000, vyy400, ty_Double) → new_lt5(vyy3000, vyy400)
new_esEs12(Char(vyy400), Char(vyy410)) → new_primEqNat0(vyy400, vyy410)
new_esEs23(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs11(vyy40, vyy41, ty_Ordering) → new_esEs14(vyy40, vyy41)
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt15(vyy3000, vyy400)
new_compare24(vyy3000, vyy400, True, ed) → EQ
new_esEs5(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, dad), dae)) → new_esEs20(vyy400, vyy410, dad, dae)
new_esEs29(vyy400, vyy410, ty_@0) → new_esEs18(vyy400, vyy410)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primPlusNat0(Zero, vyy300100) → Succ(vyy300100)
new_lt19(vyy3001, vyy401, ty_Int) → new_lt11(vyy3001, vyy401)
new_compare31(vyy3000, vyy400, ty_Double) → new_compare7(vyy3000, vyy400)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs12(vyy3000, vyy400)
new_lt19(vyy3001, vyy401, ty_Integer) → new_lt17(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, app(app(ty_@2, dbf), dbg)) → new_esEs8(vyy400, vyy410, dbf, dbg)
new_compare19(vyy3000, vyy400, cec, ced) → new_compare27(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, cec, ced), cec, ced)
new_lt4(vyy3000, vyy400) → new_esEs9(new_compare6(vyy3000, vyy400))
new_esEs7(Left(vyy400), Left(vyy410), ty_@0, gb) → new_esEs18(vyy400, vyy410)
new_ltEs14(LT, LT) → True
new_compare30(vyy3000, vyy400, ed) → new_compare24(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, ed), ed)
new_lt7(vyy3000, vyy400, ty_Double) → new_lt5(vyy3000, vyy400)
new_lt10(vyy3000, vyy400, ed) → new_esEs9(new_compare30(vyy3000, vyy400, ed))
new_not0 → True
new_compare0(:(vyy3000, vyy3001), [], gd) → GT
new_lt19(vyy3001, vyy401, app(app(ty_@2, chb), chc)) → new_lt18(vyy3001, vyy401, chb, chc)
new_lt19(vyy3001, vyy401, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt12(vyy3001, vyy401, cgd, cge, cgf)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Float, bgb) → new_ltEs7(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, app(app(ty_Either, cfe), cff)) → new_ltEs15(vyy3002, vyy402, cfe, cff)
new_pePe(False, vyy40, vyy41, vyy57, ee) → new_asAs(new_esEs11(vyy40, vyy41, ee), vyy57)
new_ltEs5(vyy3001, vyy401, ty_Float) → new_ltEs7(vyy3001, vyy401)
new_esEs5(Just(vyy400), Just(vyy410), ty_Char) → new_esEs12(vyy400, vyy410)
new_esEs24(vyy400, vyy410, app(ty_Maybe, bbg)) → new_esEs5(vyy400, vyy410, bbg)
new_lt18(vyy3000, vyy400, cba, cbb) → new_esEs9(new_compare29(vyy3000, vyy400, cba, cbb))
new_esEs5(Just(vyy400), Just(vyy410), app(app(ty_@2, dab), dac)) → new_esEs8(vyy400, vyy410, dab, dac)
new_esEs5(Just(vyy400), Just(vyy410), app(ty_Ratio, chd)) → new_esEs13(vyy400, vyy410, chd)
new_lt19(vyy3001, vyy401, ty_Char) → new_lt6(vyy3001, vyy401)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_@0) → new_esEs18(vyy400, vyy410)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs11(vyy40, vyy41, app(ty_Maybe, eh)) → new_esEs5(vyy40, vyy41, eh)
new_esEs7(Left(vyy400), Left(vyy410), ty_Bool, gb) → new_esEs10(vyy400, vyy410)
new_primMulInt(Pos(vyy4000), Pos(vyy30010)) → Pos(new_primMulNat0(vyy4000, vyy30010))
new_lt17(vyy3000, vyy400) → new_esEs9(new_compare13(vyy3000, vyy400))
new_ltEs5(vyy3001, vyy401, ty_Ordering) → new_ltEs14(vyy3001, vyy401)
new_esEs7(Left(vyy400), Left(vyy410), ty_Char, gb) → new_esEs12(vyy400, vyy410)
new_esEs10(True, True) → True
new_ltEs15(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bgd), bge), bgf), bgb) → new_ltEs13(vyy3000, vyy400, bgd, bge, bgf)
new_ltEs19(vyy3002, vyy402, app(ty_Maybe, cfa)) → new_ltEs8(vyy3002, vyy402, cfa)
new_lt7(vyy3000, vyy400, app(app(app(ty_@3, dd), de), df)) → new_lt12(vyy3000, vyy400, dd, de, df)
new_primMulInt(Neg(vyy4000), Neg(vyy30010)) → Pos(new_primMulNat0(vyy4000, vyy30010))
new_ltEs19(vyy3002, vyy402, app(ty_Ratio, ceh)) → new_ltEs6(vyy3002, vyy402, ceh)
new_esEs27(vyy400, vyy410, ty_Ordering) → new_esEs14(vyy400, vyy410)
new_primEqNat0(Succ(vyy4000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4100)) → False
new_lt20(vyy3000, vyy400, app(ty_Maybe, ed)) → new_lt10(vyy3000, vyy400, ed)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vyy401, vyy411, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs6(vyy401, vyy411, cdb, cdc, cdd)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(ty_@2, bag), bah)) → new_esEs8(vyy400, vyy410, bag, bah)
new_esEs27(vyy400, vyy410, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs6(vyy400, vyy410, cbf, cbg, cbh)
new_compare210(vyy3000, vyy400, True) → EQ
new_sizeFM(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), fg, fh) → vyy412
new_lt7(vyy3000, vyy400, app(ty_Ratio, db)) → new_lt8(vyy3000, vyy400, db)
new_foldFM_LE10(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE3(vyy340, vyy341, new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba), vyy40, h, ba)
new_esEs26(vyy402, vyy412, ty_Ordering) → new_esEs14(vyy402, vyy412)
new_pePe(True, vyy40, vyy41, vyy57, ee) → True
new_esEs26(vyy402, vyy412, app(ty_Maybe, beg)) → new_esEs5(vyy402, vyy412, beg)
new_ltEs19(vyy3002, vyy402, ty_Char) → new_ltEs9(vyy3002, vyy402)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), fg, fh) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, fg, fh), vyy413, fg, fh)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, app(ty_[], cad)) → new_ltEs17(vyy3000, vyy400, cad)
new_esEs14(EQ, LT) → False
new_esEs14(LT, EQ) → False
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs5(Just(vyy400), Just(vyy410), app(app(app(ty_@3, chg), chh), daa)) → new_esEs6(vyy400, vyy410, chg, chh, daa)
new_ltEs5(vyy3001, vyy401, ty_Bool) → new_ltEs16(vyy3001, vyy401)
new_ltEs19(vyy3002, vyy402, ty_Int) → new_ltEs11(vyy3002, vyy402)
new_esEs5(Just(vyy400), Just(vyy410), ty_Double) → new_esEs21(vyy400, vyy410)
new_esEs15([], :(vyy410, vyy411), eg) → False
new_esEs15(:(vyy400, vyy401), [], eg) → False
new_esEs29(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_esEs11(vyy40, vyy41, app(app(ty_Either, ga), gb)) → new_esEs7(vyy40, vyy41, ga, gb)
new_ltEs19(vyy3002, vyy402, ty_Ordering) → new_ltEs14(vyy3002, vyy402)
new_ltEs8(Just(vyy3000), Just(vyy400), app(ty_[], def)) → new_ltEs17(vyy3000, vyy400, def)
new_compare31(vyy3000, vyy400, ty_Bool) → new_compare9(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, app(ty_[], cah)) → new_lt16(vyy3000, vyy400, cah)
new_esEs19(vyy40, vyy41) → new_primEqInt(vyy40, vyy41)
new_esEs29(vyy400, vyy410, ty_Bool) → new_esEs10(vyy400, vyy410)
new_esEs14(GT, EQ) → False
new_esEs14(EQ, GT) → False
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs8(Just(vyy3000), Just(vyy400), app(ty_Maybe, ddh)) → new_ltEs8(vyy3000, vyy400, ddh)
new_lt19(vyy3001, vyy401, ty_Ordering) → new_lt13(vyy3001, vyy401)
new_compare28(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt7(vyy3000, vyy400, ty_@0) → new_lt4(vyy3000, vyy400)
new_asAs(False, vyy66) → False
new_esEs5(Just(vyy400), Just(vyy410), app(app(ty_Either, daf), dag)) → new_esEs7(vyy400, vyy410, daf, dag)
new_primMulInt(Pos(vyy4000), Neg(vyy30010)) → Neg(new_primMulNat0(vyy4000, vyy30010))
new_primMulInt(Neg(vyy4000), Pos(vyy30010)) → Neg(new_primMulNat0(vyy4000, vyy30010))
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_@2, hc), hd), gb) → new_esEs8(vyy400, vyy410, hc, hd)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Float) → new_ltEs7(vyy3000, vyy400)
new_esEs29(vyy400, vyy410, ty_Char) → new_esEs12(vyy400, vyy410)
new_primMulNat0(Zero, Succ(vyy300100)) → Zero
new_primMulNat0(Succ(vyy40000), Zero) → Zero
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_@0) → new_ltEs10(vyy3000, vyy400)
new_esEs11(vyy40, vyy41, app(app(ty_@2, fd), ff)) → new_esEs8(vyy40, vyy41, fd, ff)
new_ltEs8(Just(vyy3000), Just(vyy400), app(app(ty_@2, deg), deh)) → new_ltEs4(vyy3000, vyy400, deg, deh)
new_ltEs19(vyy3002, vyy402, ty_@0) → new_ltEs10(vyy3002, vyy402)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs18(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, ty_Double) → new_ltEs12(vyy3002, vyy402)
new_ltEs14(GT, LT) → False
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Char, bgb) → new_ltEs9(vyy3000, vyy400)
new_not(EQ) → new_not0
new_esEs24(vyy400, vyy410, ty_Integer) → new_esEs17(vyy400, vyy410)
new_lt16(vyy3000, vyy400, cah) → new_esEs9(new_compare0(vyy3000, vyy400, cah))
new_compare31(vyy3000, vyy400, app(ty_[], ddc)) → new_compare0(vyy3000, vyy400, ddc)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Bool) → new_ltEs16(vyy3000, vyy400)
new_esEs26(vyy402, vyy412, ty_@0) → new_esEs18(vyy402, vyy412)
new_esEs25(vyy401, vyy411, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs6(vyy401, vyy411, bdd, bde, bdf)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Int) → new_esEs19(vyy400, vyy410)
new_esEs14(GT, GT) → True
new_esEs25(vyy401, vyy411, ty_@0) → new_esEs18(vyy401, vyy411)
new_foldFM_LE10(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE20(vyy340, vyy341, new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs9(vyy3000, vyy400)
new_lt14(vyy3000, vyy400, cec, ced) → new_esEs9(new_compare19(vyy3000, vyy400, cec, ced))
new_lt19(vyy3001, vyy401, ty_Bool) → new_lt15(vyy3001, vyy401)
new_esEs7(Left(vyy400), Left(vyy410), app(app(app(ty_@3, gh), ha), hb), gb) → new_esEs6(vyy400, vyy410, gh, ha, hb)
new_lt7(vyy3000, vyy400, ty_Char) → new_lt6(vyy3000, vyy400)
new_esEs5(Just(vyy400), Nothing, eh) → False
new_esEs5(Nothing, Just(vyy410), eh) → False
new_esEs11(vyy40, vyy41, app(ty_Ratio, ef)) → new_esEs13(vyy40, vyy41, ef)
new_esEs26(vyy402, vyy412, app(ty_[], bef)) → new_esEs15(vyy402, vyy412, bef)
new_esEs28(vyy401, vyy411, app(ty_Ratio, ccg)) → new_esEs13(vyy401, vyy411, ccg)
new_esEs22(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_foldFM_LE3(vyy340, vyy341, vyy29, vyy40, h, ba) → new_keysFM_LE0(vyy340, vyy341, vyy29, h, ba)
new_ltEs15(Left(vyy3000), Left(vyy400), app(ty_[], bha), bgb) → new_ltEs17(vyy3000, vyy400, bha)
new_ltEs14(LT, GT) → True
new_ltEs8(Nothing, Nothing, ddf) → True
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Integer) → new_esEs17(vyy400, vyy410)
new_not(LT) → new_not0
new_compare13(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_ltEs14(LT, EQ) → True
new_esEs26(vyy402, vyy412, ty_Int) → new_esEs19(vyy402, vyy412)
new_esEs5(Nothing, Nothing, eh) → True
new_esEs28(vyy401, vyy411, app(ty_Maybe, cda)) → new_esEs5(vyy401, vyy411, cda)
new_lt6(vyy3000, vyy400) → new_esEs9(new_compare11(vyy3000, vyy400))
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Maybe, gg), gb) → new_esEs5(vyy400, vyy410, gg)
new_esEs29(vyy400, vyy410, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs6(vyy400, vyy410, dbc, dbd, dbe)
new_esEs22(vyy400, vyy410, ty_Integer) → new_esEs17(vyy400, vyy410)
new_esEs29(vyy400, vyy410, app(app(ty_Either, dcb), dcc)) → new_esEs7(vyy400, vyy410, dcb, dcc)
new_lt9(vyy3000, vyy400) → new_esEs9(new_compare28(vyy3000, vyy400))
new_compare26(vyy3000, vyy400, False, cba, cbb) → new_compare17(vyy3000, vyy400, new_ltEs4(vyy3000, vyy400, cba, cbb), cba, cbb)
new_ltEs15(Left(vyy3000), Left(vyy400), app(ty_Ratio, bga), bgb) → new_ltEs6(vyy3000, vyy400, bga)
new_esEs28(vyy401, vyy411, ty_Ordering) → new_esEs14(vyy401, vyy411)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, app(app(ty_Either, cab), cac)) → new_ltEs15(vyy3000, vyy400, cab, cac)
new_lt7(vyy3000, vyy400, ty_Int) → new_lt11(vyy3000, vyy400)
new_esEs24(vyy400, vyy410, ty_@0) → new_esEs18(vyy400, vyy410)
new_esEs28(vyy401, vyy411, ty_Bool) → new_esEs10(vyy401, vyy411)
new_esEs28(vyy401, vyy411, app(app(ty_@2, cde), cdf)) → new_esEs8(vyy401, vyy411, cde, cdf)
new_compare14(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare8(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs11(vyy40, vyy41, ty_Integer) → new_esEs17(vyy40, vyy41)
new_compare31(vyy3000, vyy400, app(app(app(ty_@3, dcf), dcg), dch)) → new_compare15(vyy3000, vyy400, dcf, dcg, dch)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Bool, bgb) → new_ltEs16(vyy3000, vyy400)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vyy400, vyy401), gd) → LT
new_esEs11(vyy40, vyy41, ty_@0) → new_esEs18(vyy40, vyy41)
new_asAs(True, vyy66) → vyy66
new_esEs24(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_ltEs14(EQ, EQ) → True
new_esEs21(Double(vyy400, vyy401), Double(vyy410, vyy411)) → new_esEs19(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_compare11(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_primMulNat0(Succ(vyy40000), Succ(vyy300100)) → new_primPlusNat0(new_primMulNat0(vyy40000, Succ(vyy300100)), vyy300100)
new_ltEs5(vyy3001, vyy401, ty_Integer) → new_ltEs18(vyy3001, vyy401)
new_esEs10(True, False) → False
new_esEs10(False, True) → False
new_esEs14(LT, LT) → True
new_ltEs7(vyy300, vyy40) → new_not(new_compare28(vyy300, vyy40))
new_lt7(vyy3000, vyy400, app(app(ty_Either, dg), dh)) → new_lt14(vyy3000, vyy400, dg, dh)
new_ltEs16(False, False) → True
new_esEs24(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_esEs18(@0, @0) → True
new_primCompAux0(vyy3000, vyy400, vyy67, gd) → new_primCompAux00(vyy67, new_compare31(vyy3000, vyy400, gd))
new_lt11(vyy3000, vyy400) → new_esEs9(new_compare8(vyy3000, vyy400))
new_fmToList(vyy41, fg, fh) → new_foldFM2(vyy41, fg, fh)
new_esEs29(vyy400, vyy410, app(ty_[], dba)) → new_esEs15(vyy400, vyy410, dba)
new_ltEs15(Left(vyy3000), Left(vyy400), app(app(ty_Either, bgg), bgh), bgb) → new_ltEs15(vyy3000, vyy400, bgg, bgh)
new_esEs25(vyy401, vyy411, ty_Ordering) → new_esEs14(vyy401, vyy411)
new_ltEs15(Left(vyy3000), Right(vyy400), bhd, bgb) → True
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Int) → new_ltEs11(vyy3000, vyy400)
new_esEs24(vyy400, vyy410, app(app(ty_@2, bcc), bcd)) → new_esEs8(vyy400, vyy410, bcc, bcd)
new_esEs5(Just(vyy400), Just(vyy410), ty_Int) → new_esEs19(vyy400, vyy410)
new_esEs7(Left(vyy400), Left(vyy410), ty_Double, gb) → new_esEs21(vyy400, vyy410)
new_lt19(vyy3001, vyy401, app(ty_Ratio, cgb)) → new_lt8(vyy3001, vyy401, cgb)
new_compare210(vyy3000, vyy400, False) → new_compare111(vyy3000, vyy400, new_ltEs14(vyy3000, vyy400))
new_ltEs5(vyy3001, vyy401, ty_Double) → new_ltEs12(vyy3001, vyy401)
new_ltEs10(vyy300, vyy40) → new_not(new_compare6(vyy300, vyy40))
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Double) → new_esEs21(vyy400, vyy410)
new_ltEs13(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cee, cef, ceg) → new_pePe(new_lt20(vyy3000, vyy400, cee), vyy3000, vyy400, new_pePe(new_lt19(vyy3001, vyy401, cef), vyy3001, vyy401, new_ltEs19(vyy3002, vyy402, ceg), cef), cee)
new_primCompAux00(vyy71, GT) → GT
new_esEs25(vyy401, vyy411, app(app(ty_Either, bec), bed)) → new_esEs7(vyy401, vyy411, bec, bed)
new_esEs7(Left(vyy400), Left(vyy410), ty_Float, gb) → new_esEs16(vyy400, vyy410)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Bool) → new_esEs10(vyy400, vyy410)
new_ltEs14(EQ, GT) → True
new_ltEs15(Right(vyy3000), Left(vyy400), bhd, bgb) → False
new_esEs24(vyy400, vyy410, app(ty_[], bbf)) → new_esEs15(vyy400, vyy410, bbf)
new_ltEs15(Left(vyy3000), Left(vyy400), app(app(ty_@2, bhb), bhc), bgb) → new_ltEs4(vyy3000, vyy400, bhb, bhc)
new_esEs28(vyy401, vyy411, ty_Char) → new_esEs12(vyy401, vyy411)
new_lt13(vyy3000, vyy400) → new_esEs9(new_compare18(vyy3000, vyy400))
new_foldFM_LE0(vyy26, vyy40, EmptyFM, h, ba) → vyy26
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs11(vyy40, vyy41, ty_Bool) → new_esEs10(vyy40, vyy41)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(ty_FiniteMap, bba), bbb)) → new_esEs20(vyy400, vyy410, bba, bbb)
new_compare16(vyy3000, vyy400, False) → GT
new_compare23(vyy3000, vyy400, False) → new_compare16(vyy3000, vyy400, new_ltEs16(vyy3000, vyy400))
new_esEs13(:%(vyy400, vyy401), :%(vyy410, vyy411), ef) → new_asAs(new_esEs22(vyy400, vyy410, ef), new_esEs23(vyy401, vyy411, ef))
The set Q consists of the following terms:
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs15(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs16(True, True)
new_esEs18(@0, @0)
new_compare18(x0, x1)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs14(EQ, GT)
new_esEs14(GT, EQ)
new_pePe(True, x0, x1, x2, x3)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs5(Nothing, Just(x0), x1)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, EmptyFM, True, x6, x7)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(EQ)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(Right(x0), Right(x1), x2, ty_Int)
new_compare23(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Float)
new_compare19(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs11(x0, x1, ty_Float)
new_primCompAux00(x0, GT)
new_esEs28(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_ltEs15(Right(x0), Left(x1), x2, x3)
new_ltEs15(Left(x0), Right(x1), x2, x3)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Ordering)
new_compare8(x0, x1)
new_compare17(x0, x1, True, x2, x3)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs5(x0, x1, ty_Char)
new_compare13(Integer(x0), Integer(x1))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_asAs(False, x0)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare10(x0, x1, True, x2, x3, x4)
new_lt16(x0, x1, x2)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs15([], [], x0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_primMulNat0(Succ(x0), Zero)
new_esEs25(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(GT, LT)
new_esEs14(LT, GT)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_compare12(x0, x1, False, x2)
new_compare30(x0, x1, x2)
new_esEs28(x0, x1, ty_Char)
new_ltEs8(Nothing, Just(x0), x1)
new_ltEs5(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_primCompAux00(x0, EQ)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_lt20(x0, x1, ty_Float)
new_esEs15([], :(x0, x1), x2)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, ty_@0)
new_esEs11(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs8(Just(x0), Nothing, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_esEs27(x0, x1, ty_@0)
new_lt7(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs11(x0, x1, ty_@0)
new_ltEs15(Right(x0), Right(x1), x2, ty_Double)
new_compare26(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Integer)
new_foldFM_LE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_pePe(False, x0, x1, x2, x3)
new_primMulNat0(Zero, Zero)
new_lt7(x0, x1, ty_Char)
new_esEs10(True, False)
new_esEs10(False, True)
new_esEs11(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare27(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_foldFM_LE0(x0, x1, EmptyFM, x2, x3)
new_ltEs15(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs17(x0, x1, x2)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Int)
new_fmToList(x0, x1, x2)
new_compare24(x0, x1, False, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16(Float(x0, x1), Float(x2, x3))
new_primPlusNat1(Succ(x0), Zero)
new_ltEs15(Right(x0), Right(x1), x2, ty_Float)
new_lt7(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_esEs17(Integer(x0), Integer(x1))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_foldFM2(EmptyFM, x0, x1)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, False, x2, x3)
new_compare23(x0, x1, False)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Bool)
new_lt8(x0, x1, x2)
new_compare31(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_lt7(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt19(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_compare15(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_Double)
new_not0
new_esEs29(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_ltEs12(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Nothing, x1)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs14(LT, LT)
new_esEs10(True, True)
new_esEs9(GT)
new_ltEs14(LT, LT)
new_esEs11(x0, x1, ty_Int)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_lt7(x0, x1, ty_Integer)
new_ltEs15(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs5(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs24(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs7(x0, x1)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Char)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Integer)
new_esEs5(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_ltEs18(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, ty_Bool)
new_lt10(x0, x1, x2)
new_ltEs15(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt5(x0, x1)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs6(x0, x1, x2)
new_esEs25(x0, x1, ty_Float)
new_not(GT)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare111(x0, x1, True)
new_ltEs10(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare210(x0, x1, False)
new_foldFM_LE3(x0, x1, x2, x3, x4, x5)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs15(Left(x0), Left(x1), ty_Double, x2)
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_compare31(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_compare16(x0, x1, False)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs24(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs15(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), True, x11, x12)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_ltEs15(Left(x0), Left(x1), ty_Bool, x2)
new_compare24(x0, x1, True, x2)
new_sr(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare16(x0, x1, True)
new_esEs28(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Ordering)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt7(x0, x1, ty_Float)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Double)
new_lt14(x0, x1, x2, x3)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1)
new_lt17(x0, x1)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs5(x0, x1, app(ty_[], x2))
new_primPlusNat0(Zero, x0)
new_ltEs15(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Integer)
new_ltEs15(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs9(LT)
new_ltEs16(True, False)
new_ltEs16(False, True)
new_primCompAux00(x0, LT)
new_compare6(@0, @0)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_ltEs15(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, x2, x3)
new_primCmpNat0(Zero, Zero)
new_esEs10(False, False)
new_lt20(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt19(x0, x1, ty_Bool)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_compare0([], [], x0)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, ty_Int)
new_compare10(x0, x1, False, x2, x3, x4)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_compare12(x0, x1, True, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_lt18(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Double)
new_compare29(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt7(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Ordering)
new_compare26(x0, x1, False, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs14(LT, GT)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs14(GT, LT)
new_esEs12(Char(x0), Char(x1))
new_esEs11(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare210(x0, x1, True)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs15(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs8(Nothing, Nothing, x0)
new_ltEs14(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_esEs24(x0, x1, ty_Char)
new_foldFM_LE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8)
new_primCompAux0(x0, x1, x2, x3)
new_not(EQ)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, ty_Int)
new_keysFM_LE0(x0, x1, x2, x3, x4)
new_compare31(x0, x1, ty_Integer)
new_lt6(x0, x1)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_compare9(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_compare11(Char(x0), Char(x1))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, app(ty_[], x2))
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt11(x0, x1)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(Float(x0, x1), Float(x2, x3))
new_esEs14(LT, EQ)
new_esEs14(EQ, LT)
new_esEs22(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Double)
new_compare110(x0, x1, False, x2, x3)
new_esEs15(:(x0, x1), [], x2)
new_esEs26(x0, x1, ty_Double)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Double)
new_esEs14(GT, GT)
new_ltEs15(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare111(x0, x1, False)
new_esEs5(Nothing, Nothing, x0)
new_compare110(x0, x1, True, x2, x3)
new_esEs21(Double(x0, x1), Double(x2, x3))
new_compare31(x0, x1, ty_Double)
new_esEs14(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_lt19(x0, x1, ty_Int)
new_lt19(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Int)
new_ltEs15(Left(x0), Left(x1), ty_Char, x2)
new_ltEs9(x0, x1)
new_esEs28(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs15(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs19(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Bool)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare0([], :(x0, x1), x2)
new_lt20(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare0(:(x0, x1), [], x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_ltEs16(False, False)
new_not(LT)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
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_LE(vyy26, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE1(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Just(vyy40), h), h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 4 >= 9, 5 >= 10
- new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE1(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Just(vyy40), h), h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 > 3, 6 > 4, 6 > 5, 6 > 6, 6 > 7, 9 >= 9, 10 >= 10
- new_foldFM_LE2(vyy340, vyy341, vyy30, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE1(new_keysFM_LE0(vyy340, vyy341, vyy30, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs8(vyy3440, Just(vyy40), h), h, ba)
The graph contains the following edges 4 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 >= 9, 11 >= 10
- new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE2(vyy340, vyy341, new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
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
- new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE(vyy26, vyy40, vyy343, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5
- new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE(vyy26, vyy40, vyy343, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5
↳ 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
↳ UsableRulesProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Nothing, h), h, ba)
new_foldFM_LE21(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE11(new_keysFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs8(vyy3440, Nothing, h), h, ba)
new_foldFM_LE4(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Nothing, h), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE21(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The TRS R consists of the following rules:
new_esEs28(vyy401, vyy411, ty_Integer) → new_esEs17(vyy401, vyy411)
new_esEs29(vyy400, vyy410, ty_Integer) → new_esEs17(vyy400, vyy410)
new_compare18(vyy3000, vyy400) → new_compare210(vyy3000, vyy400, new_esEs14(vyy3000, vyy400))
new_compare31(vyy3000, vyy400, ty_Integer) → new_compare13(vyy3000, vyy400)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Integer) → new_ltEs18(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, ty_Double) → new_esEs21(vyy401, vyy411)
new_esEs11(vyy40, vyy41, ty_Char) → new_esEs12(vyy40, vyy41)
new_esEs5(Just(vyy400), Just(vyy410), ty_@0) → new_esEs18(vyy400, vyy410)
new_esEs25(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_Either, hg), hh), gb) → new_esEs7(vyy400, vyy410, hg, hh)
new_compare29(vyy3000, vyy400, cba, cbb) → new_compare26(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, cba, cbb), cba, cbb)
new_ltEs9(vyy300, vyy40) → new_not(new_compare11(vyy300, vyy40))
new_lt19(vyy3001, vyy401, app(app(ty_Either, cgg), cgh)) → new_lt14(vyy3001, vyy401, cgg, cgh)
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, bb), bc), bd)) → new_lt12(vyy3000, vyy400, bb, bc, bd)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, app(ty_Maybe, bhf)) → new_ltEs8(vyy3000, vyy400, bhf)
new_esEs5(Just(vyy400), Just(vyy410), ty_Integer) → new_esEs17(vyy400, vyy410)
new_compare10(vyy3000, vyy400, True, bb, bc, bd) → LT
new_lt19(vyy3001, vyy401, ty_Float) → new_lt9(vyy3001, vyy401)
new_esEs28(vyy401, vyy411, app(ty_[], cch)) → new_esEs15(vyy401, vyy411, cch)
new_compare110(vyy3000, vyy400, True, cec, ced) → LT
new_ltEs14(GT, GT) → True
new_ltEs8(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, dea), deb), dec)) → new_ltEs13(vyy3000, vyy400, dea, deb, dec)
new_ltEs5(vyy3001, vyy401, ty_Char) → new_ltEs9(vyy3001, vyy401)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Ordering, bgb) → new_ltEs14(vyy3000, vyy400)
new_esEs5(Just(vyy400), Just(vyy410), app(ty_[], che)) → new_esEs15(vyy400, vyy410, che)
new_esEs24(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_lt20(vyy3000, vyy400, app(app(ty_Either, cec), ced)) → new_lt14(vyy3000, vyy400, cec, ced)
new_compare7(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs20(vyy40, vyy41, fg, fh) → new_asAs(new_esEs19(new_sizeFM(vyy40, fg, fh), new_sizeFM(vyy41, fg, fh)), new_esEs15(new_fmToList(vyy40, fg, fh), new_fmToList(vyy41, fg, fh), app(app(ty_@2, fg), fh)))
new_compare31(vyy3000, vyy400, ty_Int) → new_compare8(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, ty_@0) → new_compare6(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs10(vyy3000, vyy400)
new_primMulNat0(Zero, Zero) → Zero
new_esEs29(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_ltEs5(vyy3001, vyy401, ty_@0) → new_ltEs10(vyy3001, vyy401)
new_foldFM_LE30(vyy340, vyy341, vyy27, h, ba) → new_keysFM_LE0(vyy340, vyy341, vyy27, h, ba)
new_esEs11(vyy40, vyy41, ty_Float) → new_esEs16(vyy40, vyy41)
new_lt20(vyy3000, vyy400, ty_Int) → new_lt11(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, app(ty_[], cbd)) → new_esEs15(vyy400, vyy410, cbd)
new_ltEs16(False, True) → True
new_esEs27(vyy400, vyy410, app(app(ty_FiniteMap, ccc), ccd)) → new_esEs20(vyy400, vyy410, ccc, ccd)
new_esEs9(LT) → True
new_esEs29(vyy400, vyy410, app(app(ty_FiniteMap, dbh), dca)) → new_esEs20(vyy400, vyy410, dbh, dca)
new_ltEs16(True, False) → False
new_not(GT) → False
new_esEs25(vyy401, vyy411, app(app(ty_FiniteMap, bea), beb)) → new_esEs20(vyy401, vyy411, bea, beb)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE30(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), h, ba)
new_esEs27(vyy400, vyy410, app(app(ty_@2, cca), ccb)) → new_esEs8(vyy400, vyy410, cca, ccb)
new_ltEs19(vyy3002, vyy402, ty_Bool) → new_ltEs16(vyy3002, vyy402)
new_lt7(vyy3000, vyy400, ty_Float) → new_lt9(vyy3000, vyy400)
new_lt7(vyy3000, vyy400, ty_Ordering) → new_lt13(vyy3000, vyy400)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Ordering) → new_ltEs14(vyy3000, vyy400)
new_ltEs11(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE22(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_compare0(:(vyy3000, vyy3001), :(vyy400, vyy401), gd) → new_primCompAux0(vyy3000, vyy400, new_compare0(vyy3001, vyy401, gd), gd)
new_esEs5(Just(vyy400), Just(vyy410), app(ty_Maybe, chf)) → new_esEs5(vyy400, vyy410, chf)
new_esEs27(vyy400, vyy410, ty_Bool) → new_esEs10(vyy400, vyy410)
new_esEs25(vyy401, vyy411, ty_Integer) → new_esEs17(vyy401, vyy411)
new_esEs7(Left(vyy400), Left(vyy410), ty_Ordering, gb) → new_esEs14(vyy400, vyy410)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, app(app(ty_@2, cae), caf)) → new_ltEs4(vyy3000, vyy400, cae, caf)
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, fg, fh) → :(@2(vyy410, vyy411), vyy85)
new_ltEs16(True, True) → True
new_esEs17(Integer(vyy400), Integer(vyy410)) → new_primEqInt(vyy400, vyy410)
new_esEs26(vyy402, vyy412, ty_Bool) → new_esEs10(vyy402, vyy412)
new_esEs7(Left(vyy400), Right(vyy410), ga, gb) → False
new_esEs7(Right(vyy400), Left(vyy410), ga, gb) → False
new_esEs26(vyy402, vyy412, app(app(ty_@2, bfc), bfd)) → new_esEs8(vyy402, vyy412, bfc, bfd)
new_compare6(@0, @0) → EQ
new_ltEs19(vyy3002, vyy402, app(app(ty_@2, cfh), cga)) → new_ltEs4(vyy3002, vyy402, cfh, cga)
new_compare23(vyy3000, vyy400, True) → EQ
new_esEs27(vyy400, vyy410, app(app(ty_Either, cce), ccf)) → new_esEs7(vyy400, vyy410, cce, ccf)
new_ltEs14(GT, EQ) → False
new_lt19(vyy3001, vyy401, app(ty_[], cha)) → new_lt16(vyy3001, vyy401, cha)
new_esEs26(vyy402, vyy412, ty_Char) → new_esEs12(vyy402, vyy412)
new_compare31(vyy3000, vyy400, app(app(ty_@2, ddd), dde)) → new_compare29(vyy3000, vyy400, ddd, dde)
new_ltEs5(vyy3001, vyy401, app(app(ty_@2, cg), da)) → new_ltEs4(vyy3001, vyy401, cg, da)
new_ltEs6(vyy300, vyy40, cag) → new_not(new_compare14(vyy300, vyy40, cag))
new_lt7(vyy3000, vyy400, app(ty_Maybe, dc)) → new_lt10(vyy3000, vyy400, dc)
new_esEs14(EQ, EQ) → True
new_esEs25(vyy401, vyy411, ty_Double) → new_esEs21(vyy401, vyy411)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs16(vyy3000, vyy400)
new_lt19(vyy3001, vyy401, app(ty_Maybe, cgc)) → new_lt10(vyy3001, vyy401, cgc)
new_esEs11(vyy40, vyy41, app(ty_[], eg)) → new_esEs15(vyy40, vyy41, eg)
new_esEs29(vyy400, vyy410, app(ty_Ratio, dah)) → new_esEs13(vyy400, vyy410, dah)
new_compare111(vyy3000, vyy400, False) → GT
new_compare111(vyy3000, vyy400, True) → LT
new_ltEs5(vyy3001, vyy401, app(app(ty_Either, cd), ce)) → new_ltEs15(vyy3001, vyy401, cd, ce)
new_esEs27(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_ltEs8(Nothing, Just(vyy400), ddf) → True
new_esEs8(@2(vyy400, vyy401), @2(vyy410, vyy411), fd, ff) → new_asAs(new_esEs27(vyy400, vyy410, fd), new_esEs28(vyy401, vyy411, ff))
new_esEs26(vyy402, vyy412, ty_Double) → new_esEs21(vyy402, vyy412)
new_esEs11(vyy40, vyy41, app(app(app(ty_@3, fa), fb), fc)) → new_esEs6(vyy40, vyy41, fa, fb, fc)
new_keysFM_LE0(vyy340, vyy341, vyy27, h, ba) → :(vyy340, vyy27)
new_compare25(vyy3000, vyy400, True, bb, bc, bd) → EQ
new_esEs24(vyy400, vyy410, app(app(ty_FiniteMap, bce), bcf)) → new_esEs20(vyy400, vyy410, bce, bcf)
new_lt8(vyy3000, vyy400, gc) → new_esEs9(new_compare14(vyy3000, vyy400, gc))
new_compare31(vyy3000, vyy400, app(ty_Maybe, dce)) → new_compare30(vyy3000, vyy400, dce)
new_esEs24(vyy400, vyy410, app(app(ty_Either, bcg), bch)) → new_esEs7(vyy400, vyy410, bcg, bch)
new_esEs25(vyy401, vyy411, app(ty_Ratio, bda)) → new_esEs13(vyy401, vyy411, bda)
new_lt15(vyy3000, vyy400) → new_esEs9(new_compare9(vyy3000, vyy400))
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Float) → new_esEs16(vyy400, vyy410)
new_compare0([], [], gd) → EQ
new_esEs27(vyy400, vyy410, ty_@0) → new_esEs18(vyy400, vyy410)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Integer, bgb) → new_ltEs18(vyy3000, vyy400)
new_primEqNat0(Zero, Zero) → True
new_ltEs5(vyy3001, vyy401, ty_Int) → new_ltEs11(vyy3001, vyy401)
new_ltEs19(vyy3002, vyy402, ty_Integer) → new_ltEs18(vyy3002, vyy402)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Double, bgb) → new_ltEs12(vyy3000, vyy400)
new_lt19(vyy3001, vyy401, ty_Double) → new_lt5(vyy3001, vyy401)
new_lt5(vyy3000, vyy400) → new_esEs9(new_compare7(vyy3000, vyy400))
new_foldFM_LE5(vyy24, EmptyFM, h, ba) → vyy24
new_lt20(vyy3000, vyy400, app(ty_Ratio, gc)) → new_lt8(vyy3000, vyy400, gc)
new_ltEs5(vyy3001, vyy401, app(ty_Maybe, bh)) → new_ltEs8(vyy3001, vyy401, bh)
new_lt7(vyy3000, vyy400, app(ty_[], ea)) → new_lt16(vyy3000, vyy400, ea)
new_esEs26(vyy402, vyy412, app(ty_Ratio, bee)) → new_esEs13(vyy402, vyy412, bee)
new_compare31(vyy3000, vyy400, ty_Ordering) → new_compare18(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, app(ty_Ratio, cbc)) → new_esEs13(vyy400, vyy410, cbc)
new_esEs27(vyy400, vyy410, ty_Char) → new_esEs12(vyy400, vyy410)
new_compare31(vyy3000, vyy400, app(ty_Ratio, dcd)) → new_compare14(vyy3000, vyy400, dcd)
new_compare110(vyy3000, vyy400, False, cec, ced) → GT
new_compare12(vyy3000, vyy400, False, ed) → GT
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(app(ty_@3, bad), bae), baf)) → new_esEs6(vyy400, vyy410, bad, bae, baf)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Double) → new_ltEs12(vyy3000, vyy400)
new_sr(vyy400, vyy3001) → new_primMulInt(vyy400, vyy3001)
new_ltEs14(EQ, LT) → False
new_lt20(vyy3000, vyy400, ty_Float) → new_lt9(vyy3000, vyy400)
new_esEs25(vyy401, vyy411, app(ty_[], bdb)) → new_esEs15(vyy401, vyy411, bdb)
new_ltEs8(Just(vyy3000), Just(vyy400), app(app(ty_Either, ded), dee)) → new_ltEs15(vyy3000, vyy400, ded, dee)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(ty_[], bab)) → new_esEs15(vyy400, vyy410, bab)
new_esEs24(vyy400, vyy410, ty_Char) → new_esEs12(vyy400, vyy410)
new_esEs14(GT, LT) → False
new_esEs14(LT, GT) → False
new_esEs15(:(vyy400, vyy401), :(vyy410, vyy411), eg) → new_asAs(new_esEs29(vyy400, vyy410, eg), new_esEs15(vyy401, vyy411, eg))
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Int, bgb) → new_ltEs11(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy860), vyy300100) → Succ(Succ(new_primPlusNat1(vyy860, vyy300100)))
new_lt19(vyy3001, vyy401, ty_@0) → new_lt4(vyy3001, vyy401)
new_esEs25(vyy401, vyy411, ty_Float) → new_esEs16(vyy401, vyy411)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(ty_Either, bbc), bbd)) → new_esEs7(vyy400, vyy410, bbc, bbd)
new_esEs26(vyy402, vyy412, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs6(vyy402, vyy412, beh, bfa, bfb)
new_ltEs18(vyy300, vyy40) → new_not(new_compare13(vyy300, vyy40))
new_esEs7(Left(vyy400), Left(vyy410), app(ty_[], gf), gb) → new_esEs15(vyy400, vyy410, gf)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Char) → new_esEs12(vyy400, vyy410)
new_compare17(vyy3000, vyy400, True, cba, cbb) → LT
new_ltEs19(vyy3002, vyy402, ty_Float) → new_ltEs7(vyy3002, vyy402)
new_esEs28(vyy401, vyy411, ty_Float) → new_esEs16(vyy401, vyy411)
new_lt20(vyy3000, vyy400, app(app(ty_@2, cba), cbb)) → new_lt18(vyy3000, vyy400, cba, cbb)
new_primEqInt(Neg(Succ(vyy4000)), Neg(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_esEs25(vyy401, vyy411, app(app(ty_@2, bdg), bdh)) → new_esEs8(vyy401, vyy411, bdg, bdh)
new_esEs9(GT) → False
new_compare10(vyy3000, vyy400, False, bb, bc, bd) → GT
new_lt7(vyy3000, vyy400, ty_Bool) → new_lt15(vyy3000, vyy400)
new_primPlusNat1(Zero, Succ(vyy3001000)) → Succ(vyy3001000)
new_primPlusNat1(Succ(vyy8600), Zero) → Succ(vyy8600)
new_lt20(vyy3000, vyy400, ty_Char) → new_lt6(vyy3000, vyy400)
new_compare9(vyy3000, vyy400) → new_compare23(vyy3000, vyy400, new_esEs10(vyy3000, vyy400))
new_ltEs12(vyy300, vyy40) → new_not(new_compare7(vyy300, vyy40))
new_esEs9(EQ) → False
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, app(app(app(ty_@3, bhg), bhh), caa)) → new_ltEs13(vyy3000, vyy400, bhg, bhh, caa)
new_compare16(vyy3000, vyy400, True) → LT
new_compare27(vyy3000, vyy400, False, cec, ced) → new_compare110(vyy3000, vyy400, new_ltEs15(vyy3000, vyy400, cec, ced), cec, ced)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(ty_Ratio, baa)) → new_esEs13(vyy400, vyy410, baa)
new_foldFM_LE22(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE12(new_keysFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs8(vyy3440, Nothing, h), h, ba)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba) → new_foldFM_LE5(vyy24, vyy343, h, ba)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy400, vyy410, ty_Bool) → new_esEs10(vyy400, vyy410)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Ratio, ge), gb) → new_esEs13(vyy400, vyy410, ge)
new_esEs24(vyy400, vyy410, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs6(vyy400, vyy410, bbh, bca, bcb)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(ty_Maybe, bac)) → new_esEs5(vyy400, vyy410, bac)
new_compare15(vyy3000, vyy400, bb, bc, bd) → new_compare25(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, bb, bc, bd), bb, bc, bd)
new_esEs29(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_compare8(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4100))) → False
new_primEqInt(Neg(Succ(vyy4000)), Neg(Zero)) → False
new_esEs11(vyy40, vyy41, ty_Int) → new_esEs19(vyy40, vyy41)
new_esEs5(Just(vyy400), Just(vyy410), ty_Float) → new_esEs16(vyy400, vyy410)
new_compare26(vyy3000, vyy400, True, cba, cbb) → EQ
new_ltEs5(vyy3001, vyy401, app(app(app(ty_@3, ca), cb), cc)) → new_ltEs13(vyy3001, vyy401, ca, cb, cc)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt13(vyy3000, vyy400)
new_lt7(vyy3000, vyy400, ty_Integer) → new_lt17(vyy3000, vyy400)
new_esEs23(vyy401, vyy411, ty_Integer) → new_esEs17(vyy401, vyy411)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Ordering) → new_esEs14(vyy400, vyy410)
new_ltEs15(Left(vyy3000), Left(vyy400), app(ty_Maybe, bgc), bgb) → new_ltEs8(vyy3000, vyy400, bgc)
new_esEs10(False, False) → True
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs14(vyy3000, vyy400)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), fg, fh) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, fg, fh), vyy4133, fg, fh)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs28(vyy401, vyy411, ty_@0) → new_esEs18(vyy401, vyy411)
new_esEs26(vyy402, vyy412, app(app(ty_Either, bfg), bfh)) → new_esEs7(vyy402, vyy412, bfg, bfh)
new_esEs28(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs7(Left(vyy400), Left(vyy410), ty_Int, gb) → new_esEs19(vyy400, vyy410)
new_ltEs5(vyy3001, vyy401, app(ty_[], cf)) → new_ltEs17(vyy3001, vyy401, cf)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_sizeFM(EmptyFM, fg, fh) → Pos(Zero)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, he), hf), gb) → new_esEs20(vyy400, vyy410, he, hf)
new_esEs26(vyy402, vyy412, ty_Integer) → new_esEs17(vyy402, vyy412)
new_esEs29(vyy400, vyy410, ty_Ordering) → new_esEs14(vyy400, vyy410)
new_ltEs17(vyy300, vyy40, gd) → new_not(new_compare0(vyy300, vyy40, gd))
new_primEqInt(Pos(Succ(vyy4000)), Pos(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_esEs11(vyy40, vyy41, ty_Double) → new_esEs21(vyy40, vyy41)
new_compare31(vyy3000, vyy400, ty_Float) → new_compare28(vyy3000, vyy400)
new_esEs16(Float(vyy400, vyy401), Float(vyy410, vyy411)) → new_esEs19(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_compare27(vyy3000, vyy400, True, cec, ced) → EQ
new_esEs25(vyy401, vyy411, app(ty_Maybe, bdc)) → new_esEs5(vyy401, vyy411, bdc)
new_esEs29(vyy400, vyy410, app(ty_Maybe, dbb)) → new_esEs5(vyy400, vyy410, dbb)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs11(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, app(app(ty_FiniteMap, cdg), cdh)) → new_esEs20(vyy401, vyy411, cdg, cdh)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs7(vyy3000, vyy400)
new_primEqNat0(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat0(vyy4000, vyy4100)
new_esEs11(vyy40, vyy41, app(app(ty_FiniteMap, fg), fh)) → new_esEs20(vyy40, vyy41, fg, fh)
new_esEs27(vyy400, vyy410, ty_Integer) → new_esEs17(vyy400, vyy410)
new_ltEs5(vyy3001, vyy401, app(ty_Ratio, bg)) → new_ltEs6(vyy3001, vyy401, bg)
new_esEs26(vyy402, vyy412, app(app(ty_FiniteMap, bfe), bff)) → new_esEs20(vyy402, vyy412, bfe, bff)
new_ltEs4(@2(vyy3000, vyy3001), @2(vyy400, vyy401), be, bf) → new_pePe(new_lt7(vyy3000, vyy400, be), vyy3000, vyy400, new_ltEs5(vyy3001, vyy401, bf), be)
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt17(vyy3000, vyy400)
new_primCompAux00(vyy71, LT) → LT
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_lt20(vyy3000, vyy400, ty_@0) → new_lt4(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, app(ty_[], cfg)) → new_ltEs17(vyy3002, vyy402, cfg)
new_compare24(vyy3000, vyy400, False, ed) → new_compare12(vyy3000, vyy400, new_ltEs8(vyy3000, vyy400, ed), ed)
new_ltEs8(Just(vyy3000), Nothing, ddf) → False
new_compare31(vyy3000, vyy400, ty_Char) → new_compare11(vyy3000, vyy400)
new_esEs15([], [], eg) → True
new_primEqInt(Pos(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Succ(vyy4000)), Pos(Zero)) → False
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Char) → new_ltEs9(vyy3000, vyy400)
new_ltEs8(Just(vyy3000), Just(vyy400), app(ty_Ratio, ddg)) → new_ltEs6(vyy3000, vyy400, ddg)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_esEs6(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), fa, fb, fc) → new_asAs(new_esEs24(vyy400, vyy410, fa), new_asAs(new_esEs25(vyy401, vyy411, fb), new_esEs26(vyy402, vyy412, fc)))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_primPlusNat1(Succ(vyy8600), Succ(vyy3001000)) → Succ(Succ(new_primPlusNat1(vyy8600, vyy3001000)))
new_compare12(vyy3000, vyy400, True, ed) → LT
new_primEqInt(Neg(Succ(vyy4000)), Pos(vyy410)) → False
new_primEqInt(Pos(Succ(vyy4000)), Neg(vyy410)) → False
new_esEs24(vyy400, vyy410, app(ty_Ratio, bbe)) → new_esEs13(vyy400, vyy410, bbe)
new_lt12(vyy3000, vyy400, bb, bc, bd) → new_esEs9(new_compare15(vyy3000, vyy400, bb, bc, bd))
new_esEs7(Left(vyy400), Left(vyy410), ty_Integer, gb) → new_esEs17(vyy400, vyy410)
new_compare14(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare13(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_esEs27(vyy400, vyy410, app(ty_Maybe, cbe)) → new_esEs5(vyy400, vyy410, cbe)
new_foldFM2(EmptyFM, fg, fh) → []
new_esEs25(vyy401, vyy411, ty_Char) → new_esEs12(vyy401, vyy411)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4100))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCompAux00(vyy71, EQ) → vyy71
new_esEs28(vyy401, vyy411, app(app(ty_Either, cea), ceb)) → new_esEs7(vyy401, vyy411, cea, ceb)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, app(ty_Ratio, bhe)) → new_ltEs6(vyy3000, vyy400, bhe)
new_compare25(vyy3000, vyy400, False, bb, bc, bd) → new_compare10(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, bb, bc, bd), bb, bc, bd)
new_esEs5(Just(vyy400), Just(vyy410), ty_Bool) → new_esEs10(vyy400, vyy410)
new_esEs24(vyy400, vyy410, ty_Ordering) → new_esEs14(vyy400, vyy410)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_@0, bgb) → new_ltEs10(vyy3000, vyy400)
new_compare31(vyy3000, vyy400, app(app(ty_Either, dda), ddb)) → new_compare19(vyy3000, vyy400, dda, ddb)
new_ltEs19(vyy3002, vyy402, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs13(vyy3002, vyy402, cfb, cfc, cfd)
new_lt7(vyy3000, vyy400, app(app(ty_@2, eb), ec)) → new_lt18(vyy3000, vyy400, eb, ec)
new_esEs5(Just(vyy400), Just(vyy410), ty_Ordering) → new_esEs14(vyy400, vyy410)
new_compare17(vyy3000, vyy400, False, cba, cbb) → GT
new_esEs25(vyy401, vyy411, ty_Bool) → new_esEs10(vyy401, vyy411)
new_esEs26(vyy402, vyy412, ty_Float) → new_esEs16(vyy402, vyy412)
new_lt20(vyy3000, vyy400, ty_Double) → new_lt5(vyy3000, vyy400)
new_esEs12(Char(vyy400), Char(vyy410)) → new_primEqNat0(vyy400, vyy410)
new_esEs23(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs11(vyy40, vyy41, ty_Ordering) → new_esEs14(vyy40, vyy41)
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt15(vyy3000, vyy400)
new_compare24(vyy3000, vyy400, True, ed) → EQ
new_esEs5(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, dad), dae)) → new_esEs20(vyy400, vyy410, dad, dae)
new_esEs29(vyy400, vyy410, ty_@0) → new_esEs18(vyy400, vyy410)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primPlusNat0(Zero, vyy300100) → Succ(vyy300100)
new_lt19(vyy3001, vyy401, ty_Int) → new_lt11(vyy3001, vyy401)
new_compare31(vyy3000, vyy400, ty_Double) → new_compare7(vyy3000, vyy400)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs12(vyy3000, vyy400)
new_lt19(vyy3001, vyy401, ty_Integer) → new_lt17(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, app(app(ty_@2, dbf), dbg)) → new_esEs8(vyy400, vyy410, dbf, dbg)
new_compare19(vyy3000, vyy400, cec, ced) → new_compare27(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, cec, ced), cec, ced)
new_lt4(vyy3000, vyy400) → new_esEs9(new_compare6(vyy3000, vyy400))
new_esEs7(Left(vyy400), Left(vyy410), ty_@0, gb) → new_esEs18(vyy400, vyy410)
new_ltEs14(LT, LT) → True
new_compare30(vyy3000, vyy400, ed) → new_compare24(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, ed), ed)
new_lt7(vyy3000, vyy400, ty_Double) → new_lt5(vyy3000, vyy400)
new_lt10(vyy3000, vyy400, ed) → new_esEs9(new_compare30(vyy3000, vyy400, ed))
new_not0 → True
new_compare0(:(vyy3000, vyy3001), [], gd) → GT
new_lt19(vyy3001, vyy401, app(app(ty_@2, chb), chc)) → new_lt18(vyy3001, vyy401, chb, chc)
new_lt19(vyy3001, vyy401, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt12(vyy3001, vyy401, cgd, cge, cgf)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Float, bgb) → new_ltEs7(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, app(app(ty_Either, cfe), cff)) → new_ltEs15(vyy3002, vyy402, cfe, cff)
new_pePe(False, vyy40, vyy41, vyy57, ee) → new_asAs(new_esEs11(vyy40, vyy41, ee), vyy57)
new_ltEs5(vyy3001, vyy401, ty_Float) → new_ltEs7(vyy3001, vyy401)
new_esEs5(Just(vyy400), Just(vyy410), ty_Char) → new_esEs12(vyy400, vyy410)
new_esEs24(vyy400, vyy410, app(ty_Maybe, bbg)) → new_esEs5(vyy400, vyy410, bbg)
new_lt18(vyy3000, vyy400, cba, cbb) → new_esEs9(new_compare29(vyy3000, vyy400, cba, cbb))
new_esEs5(Just(vyy400), Just(vyy410), app(app(ty_@2, dab), dac)) → new_esEs8(vyy400, vyy410, dab, dac)
new_esEs5(Just(vyy400), Just(vyy410), app(ty_Ratio, chd)) → new_esEs13(vyy400, vyy410, chd)
new_lt19(vyy3001, vyy401, ty_Char) → new_lt6(vyy3001, vyy401)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_@0) → new_esEs18(vyy400, vyy410)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs11(vyy40, vyy41, app(ty_Maybe, eh)) → new_esEs5(vyy40, vyy41, eh)
new_esEs7(Left(vyy400), Left(vyy410), ty_Bool, gb) → new_esEs10(vyy400, vyy410)
new_primMulInt(Pos(vyy4000), Pos(vyy30010)) → Pos(new_primMulNat0(vyy4000, vyy30010))
new_lt17(vyy3000, vyy400) → new_esEs9(new_compare13(vyy3000, vyy400))
new_ltEs5(vyy3001, vyy401, ty_Ordering) → new_ltEs14(vyy3001, vyy401)
new_esEs7(Left(vyy400), Left(vyy410), ty_Char, gb) → new_esEs12(vyy400, vyy410)
new_esEs10(True, True) → True
new_ltEs15(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bgd), bge), bgf), bgb) → new_ltEs13(vyy3000, vyy400, bgd, bge, bgf)
new_ltEs19(vyy3002, vyy402, app(ty_Maybe, cfa)) → new_ltEs8(vyy3002, vyy402, cfa)
new_lt7(vyy3000, vyy400, app(app(app(ty_@3, dd), de), df)) → new_lt12(vyy3000, vyy400, dd, de, df)
new_primMulInt(Neg(vyy4000), Neg(vyy30010)) → Pos(new_primMulNat0(vyy4000, vyy30010))
new_ltEs19(vyy3002, vyy402, app(ty_Ratio, ceh)) → new_ltEs6(vyy3002, vyy402, ceh)
new_esEs27(vyy400, vyy410, ty_Ordering) → new_esEs14(vyy400, vyy410)
new_primEqNat0(Succ(vyy4000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4100)) → False
new_lt20(vyy3000, vyy400, app(ty_Maybe, ed)) → new_lt10(vyy3000, vyy400, ed)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vyy401, vyy411, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs6(vyy401, vyy411, cdb, cdc, cdd)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(ty_@2, bag), bah)) → new_esEs8(vyy400, vyy410, bag, bah)
new_esEs27(vyy400, vyy410, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs6(vyy400, vyy410, cbf, cbg, cbh)
new_compare210(vyy3000, vyy400, True) → EQ
new_sizeFM(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), fg, fh) → vyy412
new_lt7(vyy3000, vyy400, app(ty_Ratio, db)) → new_lt8(vyy3000, vyy400, db)
new_esEs26(vyy402, vyy412, ty_Ordering) → new_esEs14(vyy402, vyy412)
new_pePe(True, vyy40, vyy41, vyy57, ee) → True
new_esEs26(vyy402, vyy412, app(ty_Maybe, beg)) → new_esEs5(vyy402, vyy412, beg)
new_ltEs19(vyy3002, vyy402, ty_Char) → new_ltEs9(vyy3002, vyy402)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), fg, fh) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, fg, fh), vyy413, fg, fh)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, app(ty_[], cad)) → new_ltEs17(vyy3000, vyy400, cad)
new_esEs14(EQ, LT) → False
new_esEs14(LT, EQ) → False
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs5(Just(vyy400), Just(vyy410), app(app(app(ty_@3, chg), chh), daa)) → new_esEs6(vyy400, vyy410, chg, chh, daa)
new_ltEs5(vyy3001, vyy401, ty_Bool) → new_ltEs16(vyy3001, vyy401)
new_ltEs19(vyy3002, vyy402, ty_Int) → new_ltEs11(vyy3002, vyy402)
new_esEs5(Just(vyy400), Just(vyy410), ty_Double) → new_esEs21(vyy400, vyy410)
new_esEs15([], :(vyy410, vyy411), eg) → False
new_esEs15(:(vyy400, vyy401), [], eg) → False
new_esEs29(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_esEs11(vyy40, vyy41, app(app(ty_Either, ga), gb)) → new_esEs7(vyy40, vyy41, ga, gb)
new_ltEs19(vyy3002, vyy402, ty_Ordering) → new_ltEs14(vyy3002, vyy402)
new_ltEs8(Just(vyy3000), Just(vyy400), app(ty_[], def)) → new_ltEs17(vyy3000, vyy400, def)
new_compare31(vyy3000, vyy400, ty_Bool) → new_compare9(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, app(ty_[], cah)) → new_lt16(vyy3000, vyy400, cah)
new_esEs19(vyy40, vyy41) → new_primEqInt(vyy40, vyy41)
new_esEs29(vyy400, vyy410, ty_Bool) → new_esEs10(vyy400, vyy410)
new_esEs14(GT, EQ) → False
new_esEs14(EQ, GT) → False
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs8(Just(vyy3000), Just(vyy400), app(ty_Maybe, ddh)) → new_ltEs8(vyy3000, vyy400, ddh)
new_lt19(vyy3001, vyy401, ty_Ordering) → new_lt13(vyy3001, vyy401)
new_compare28(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt7(vyy3000, vyy400, ty_@0) → new_lt4(vyy3000, vyy400)
new_foldFM_LE5(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE12(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Nothing, h), h, ba)
new_asAs(False, vyy66) → False
new_esEs5(Just(vyy400), Just(vyy410), app(app(ty_Either, daf), dag)) → new_esEs7(vyy400, vyy410, daf, dag)
new_primMulInt(Pos(vyy4000), Neg(vyy30010)) → Neg(new_primMulNat0(vyy4000, vyy30010))
new_primMulInt(Neg(vyy4000), Pos(vyy30010)) → Neg(new_primMulNat0(vyy4000, vyy30010))
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_@2, hc), hd), gb) → new_esEs8(vyy400, vyy410, hc, hd)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Float) → new_ltEs7(vyy3000, vyy400)
new_esEs29(vyy400, vyy410, ty_Char) → new_esEs12(vyy400, vyy410)
new_primMulNat0(Zero, Succ(vyy300100)) → Zero
new_primMulNat0(Succ(vyy40000), Zero) → Zero
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_@0) → new_ltEs10(vyy3000, vyy400)
new_esEs11(vyy40, vyy41, app(app(ty_@2, fd), ff)) → new_esEs8(vyy40, vyy41, fd, ff)
new_ltEs8(Just(vyy3000), Just(vyy400), app(app(ty_@2, deg), deh)) → new_ltEs4(vyy3000, vyy400, deg, deh)
new_ltEs19(vyy3002, vyy402, ty_@0) → new_ltEs10(vyy3002, vyy402)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs18(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, ty_Double) → new_ltEs12(vyy3002, vyy402)
new_ltEs14(GT, LT) → False
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Char, bgb) → new_ltEs9(vyy3000, vyy400)
new_not(EQ) → new_not0
new_esEs24(vyy400, vyy410, ty_Integer) → new_esEs17(vyy400, vyy410)
new_lt16(vyy3000, vyy400, cah) → new_esEs9(new_compare0(vyy3000, vyy400, cah))
new_compare31(vyy3000, vyy400, app(ty_[], ddc)) → new_compare0(vyy3000, vyy400, ddc)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Bool) → new_ltEs16(vyy3000, vyy400)
new_esEs26(vyy402, vyy412, ty_@0) → new_esEs18(vyy402, vyy412)
new_esEs25(vyy401, vyy411, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs6(vyy401, vyy411, bdd, bde, bdf)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Int) → new_esEs19(vyy400, vyy410)
new_esEs14(GT, GT) → True
new_esEs25(vyy401, vyy411, ty_@0) → new_esEs18(vyy401, vyy411)
new_ltEs8(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs9(vyy3000, vyy400)
new_lt14(vyy3000, vyy400, cec, ced) → new_esEs9(new_compare19(vyy3000, vyy400, cec, ced))
new_lt19(vyy3001, vyy401, ty_Bool) → new_lt15(vyy3001, vyy401)
new_esEs7(Left(vyy400), Left(vyy410), app(app(app(ty_@3, gh), ha), hb), gb) → new_esEs6(vyy400, vyy410, gh, ha, hb)
new_lt7(vyy3000, vyy400, ty_Char) → new_lt6(vyy3000, vyy400)
new_esEs5(Just(vyy400), Nothing, eh) → False
new_esEs5(Nothing, Just(vyy410), eh) → False
new_esEs11(vyy40, vyy41, app(ty_Ratio, ef)) → new_esEs13(vyy40, vyy41, ef)
new_esEs26(vyy402, vyy412, app(ty_[], bef)) → new_esEs15(vyy402, vyy412, bef)
new_esEs28(vyy401, vyy411, app(ty_Ratio, ccg)) → new_esEs13(vyy401, vyy411, ccg)
new_esEs22(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_ltEs15(Left(vyy3000), Left(vyy400), app(ty_[], bha), bgb) → new_ltEs17(vyy3000, vyy400, bha)
new_ltEs14(LT, GT) → True
new_ltEs8(Nothing, Nothing, ddf) → True
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Integer) → new_esEs17(vyy400, vyy410)
new_not(LT) → new_not0
new_compare13(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_ltEs14(LT, EQ) → True
new_esEs26(vyy402, vyy412, ty_Int) → new_esEs19(vyy402, vyy412)
new_esEs5(Nothing, Nothing, eh) → True
new_esEs28(vyy401, vyy411, app(ty_Maybe, cda)) → new_esEs5(vyy401, vyy411, cda)
new_lt6(vyy3000, vyy400) → new_esEs9(new_compare11(vyy3000, vyy400))
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Maybe, gg), gb) → new_esEs5(vyy400, vyy410, gg)
new_esEs29(vyy400, vyy410, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs6(vyy400, vyy410, dbc, dbd, dbe)
new_esEs22(vyy400, vyy410, ty_Integer) → new_esEs17(vyy400, vyy410)
new_esEs29(vyy400, vyy410, app(app(ty_Either, dcb), dcc)) → new_esEs7(vyy400, vyy410, dcb, dcc)
new_lt9(vyy3000, vyy400) → new_esEs9(new_compare28(vyy3000, vyy400))
new_compare26(vyy3000, vyy400, False, cba, cbb) → new_compare17(vyy3000, vyy400, new_ltEs4(vyy3000, vyy400, cba, cbb), cba, cbb)
new_ltEs15(Left(vyy3000), Left(vyy400), app(ty_Ratio, bga), bgb) → new_ltEs6(vyy3000, vyy400, bga)
new_esEs28(vyy401, vyy411, ty_Ordering) → new_esEs14(vyy401, vyy411)
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, app(app(ty_Either, cab), cac)) → new_ltEs15(vyy3000, vyy400, cab, cac)
new_lt7(vyy3000, vyy400, ty_Int) → new_lt11(vyy3000, vyy400)
new_esEs24(vyy400, vyy410, ty_@0) → new_esEs18(vyy400, vyy410)
new_esEs28(vyy401, vyy411, ty_Bool) → new_esEs10(vyy401, vyy411)
new_esEs28(vyy401, vyy411, app(app(ty_@2, cde), cdf)) → new_esEs8(vyy401, vyy411, cde, cdf)
new_compare14(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare8(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs11(vyy40, vyy41, ty_Integer) → new_esEs17(vyy40, vyy41)
new_compare31(vyy3000, vyy400, app(app(app(ty_@3, dcf), dcg), dch)) → new_compare15(vyy3000, vyy400, dcf, dcg, dch)
new_ltEs15(Left(vyy3000), Left(vyy400), ty_Bool, bgb) → new_ltEs16(vyy3000, vyy400)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vyy400, vyy401), gd) → LT
new_esEs11(vyy40, vyy41, ty_@0) → new_esEs18(vyy40, vyy41)
new_asAs(True, vyy66) → vyy66
new_esEs24(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_ltEs14(EQ, EQ) → True
new_esEs21(Double(vyy400, vyy401), Double(vyy410, vyy411)) → new_esEs19(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_compare11(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_primMulNat0(Succ(vyy40000), Succ(vyy300100)) → new_primPlusNat0(new_primMulNat0(vyy40000, Succ(vyy300100)), vyy300100)
new_ltEs5(vyy3001, vyy401, ty_Integer) → new_ltEs18(vyy3001, vyy401)
new_esEs10(True, False) → False
new_esEs10(False, True) → False
new_esEs14(LT, LT) → True
new_ltEs7(vyy300, vyy40) → new_not(new_compare28(vyy300, vyy40))
new_lt7(vyy3000, vyy400, app(app(ty_Either, dg), dh)) → new_lt14(vyy3000, vyy400, dg, dh)
new_ltEs16(False, False) → True
new_esEs24(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_esEs18(@0, @0) → True
new_primCompAux0(vyy3000, vyy400, vyy67, gd) → new_primCompAux00(vyy67, new_compare31(vyy3000, vyy400, gd))
new_lt11(vyy3000, vyy400) → new_esEs9(new_compare8(vyy3000, vyy400))
new_fmToList(vyy41, fg, fh) → new_foldFM2(vyy41, fg, fh)
new_esEs29(vyy400, vyy410, app(ty_[], dba)) → new_esEs15(vyy400, vyy410, dba)
new_ltEs15(Left(vyy3000), Left(vyy400), app(app(ty_Either, bgg), bgh), bgb) → new_ltEs15(vyy3000, vyy400, bgg, bgh)
new_esEs25(vyy401, vyy411, ty_Ordering) → new_esEs14(vyy401, vyy411)
new_ltEs15(Left(vyy3000), Right(vyy400), bhd, bgb) → True
new_ltEs15(Right(vyy3000), Right(vyy400), bhd, ty_Int) → new_ltEs11(vyy3000, vyy400)
new_esEs24(vyy400, vyy410, app(app(ty_@2, bcc), bcd)) → new_esEs8(vyy400, vyy410, bcc, bcd)
new_esEs5(Just(vyy400), Just(vyy410), ty_Int) → new_esEs19(vyy400, vyy410)
new_esEs7(Left(vyy400), Left(vyy410), ty_Double, gb) → new_esEs21(vyy400, vyy410)
new_lt19(vyy3001, vyy401, app(ty_Ratio, cgb)) → new_lt8(vyy3001, vyy401, cgb)
new_compare210(vyy3000, vyy400, False) → new_compare111(vyy3000, vyy400, new_ltEs14(vyy3000, vyy400))
new_ltEs5(vyy3001, vyy401, ty_Double) → new_ltEs12(vyy3001, vyy401)
new_ltEs10(vyy300, vyy40) → new_not(new_compare6(vyy300, vyy40))
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Double) → new_esEs21(vyy400, vyy410)
new_ltEs13(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cee, cef, ceg) → new_pePe(new_lt20(vyy3000, vyy400, cee), vyy3000, vyy400, new_pePe(new_lt19(vyy3001, vyy401, cef), vyy3001, vyy401, new_ltEs19(vyy3002, vyy402, ceg), cef), cee)
new_primCompAux00(vyy71, GT) → GT
new_esEs25(vyy401, vyy411, app(app(ty_Either, bec), bed)) → new_esEs7(vyy401, vyy411, bec, bed)
new_esEs7(Left(vyy400), Left(vyy410), ty_Float, gb) → new_esEs16(vyy400, vyy410)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Bool) → new_esEs10(vyy400, vyy410)
new_ltEs14(EQ, GT) → True
new_ltEs15(Right(vyy3000), Left(vyy400), bhd, bgb) → False
new_esEs24(vyy400, vyy410, app(ty_[], bbf)) → new_esEs15(vyy400, vyy410, bbf)
new_ltEs15(Left(vyy3000), Left(vyy400), app(app(ty_@2, bhb), bhc), bgb) → new_ltEs4(vyy3000, vyy400, bhb, bhc)
new_esEs28(vyy401, vyy411, ty_Char) → new_esEs12(vyy401, vyy411)
new_lt13(vyy3000, vyy400) → new_esEs9(new_compare18(vyy3000, vyy400))
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs11(vyy40, vyy41, ty_Bool) → new_esEs10(vyy40, vyy41)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(ty_FiniteMap, bba), bbb)) → new_esEs20(vyy400, vyy410, bba, bbb)
new_compare16(vyy3000, vyy400, False) → GT
new_compare23(vyy3000, vyy400, False) → new_compare16(vyy3000, vyy400, new_ltEs16(vyy3000, vyy400))
new_esEs13(:%(vyy400, vyy401), :%(vyy410, vyy411), ef) → new_asAs(new_esEs22(vyy400, vyy410, ef), new_esEs23(vyy401, vyy411, ef))
The set Q consists of the following terms:
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs15(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs16(True, True)
new_esEs18(@0, @0)
new_compare18(x0, x1)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs14(EQ, GT)
new_esEs14(GT, EQ)
new_pePe(True, x0, x1, x2, x3)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs5(Nothing, Just(x0), x1)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(EQ)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(Right(x0), Right(x1), x2, ty_Int)
new_compare23(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Float)
new_compare19(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_foldFM_LE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs11(x0, x1, ty_Float)
new_primCompAux00(x0, GT)
new_esEs28(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_ltEs15(Right(x0), Left(x1), x2, x3)
new_ltEs15(Left(x0), Right(x1), x2, x3)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Ordering)
new_compare8(x0, x1)
new_compare17(x0, x1, True, x2, x3)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs5(x0, x1, ty_Char)
new_compare13(Integer(x0), Integer(x1))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_asAs(False, x0)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare10(x0, x1, True, x2, x3, x4)
new_lt16(x0, x1, x2)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs15([], [], x0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_esEs25(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(GT, LT)
new_esEs14(LT, GT)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_compare12(x0, x1, False, x2)
new_compare30(x0, x1, x2)
new_esEs28(x0, x1, ty_Char)
new_ltEs8(Nothing, Just(x0), x1)
new_ltEs5(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_primCompAux00(x0, EQ)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_lt20(x0, x1, ty_Float)
new_esEs15([], :(x0, x1), x2)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, ty_@0)
new_esEs11(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs8(Just(x0), Nothing, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_esEs27(x0, x1, ty_@0)
new_lt7(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs11(x0, x1, ty_@0)
new_ltEs15(Right(x0), Right(x1), x2, ty_Double)
new_compare26(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Integer)
new_pePe(False, x0, x1, x2, x3)
new_primMulNat0(Zero, Zero)
new_lt7(x0, x1, ty_Char)
new_esEs10(True, False)
new_esEs10(False, True)
new_esEs11(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare27(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs15(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs17(x0, x1, x2)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Int)
new_fmToList(x0, x1, x2)
new_compare24(x0, x1, False, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16(Float(x0, x1), Float(x2, x3))
new_primPlusNat1(Succ(x0), Zero)
new_ltEs15(Right(x0), Right(x1), x2, ty_Float)
new_lt7(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_esEs17(Integer(x0), Integer(x1))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_foldFM2(EmptyFM, x0, x1)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, False, x2, x3)
new_compare23(x0, x1, False)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Bool)
new_lt8(x0, x1, x2)
new_compare31(x0, x1, ty_Bool)
new_foldFM_LE5(x0, EmptyFM, x1, x2)
new_esEs27(x0, x1, ty_Int)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_lt7(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt19(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_compare15(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_Double)
new_not0
new_esEs29(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_ltEs12(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Nothing, x1)
new_foldFM_LE12(x0, x1, x2, x3, x4, EmptyFM, True, x5, x6)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs14(LT, LT)
new_esEs10(True, True)
new_esEs9(GT)
new_ltEs14(LT, LT)
new_esEs11(x0, x1, ty_Int)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_lt7(x0, x1, ty_Integer)
new_ltEs15(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs5(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs24(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs7(x0, x1)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Char)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Integer)
new_esEs5(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_ltEs18(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, ty_Bool)
new_lt10(x0, x1, x2)
new_ltEs15(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt5(x0, x1)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs6(x0, x1, x2)
new_esEs25(x0, x1, ty_Float)
new_not(GT)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare111(x0, x1, True)
new_ltEs10(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs15(Left(x0), Left(x1), ty_Double, x2)
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_compare31(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_compare16(x0, x1, False)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs24(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs15(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_ltEs15(Left(x0), Left(x1), ty_Bool, x2)
new_compare24(x0, x1, True, x2)
new_sr(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare16(x0, x1, True)
new_esEs28(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_ltEs5(x0, x1, ty_Ordering)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt7(x0, x1, ty_Float)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Double)
new_lt14(x0, x1, x2, x3)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1)
new_lt17(x0, x1)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs5(x0, x1, app(ty_[], x2))
new_primPlusNat0(Zero, x0)
new_ltEs15(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Integer)
new_ltEs15(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs9(LT)
new_ltEs16(True, False)
new_ltEs16(False, True)
new_primCompAux00(x0, LT)
new_compare6(@0, @0)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_ltEs15(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, x2, x3)
new_primCmpNat0(Zero, Zero)
new_esEs10(False, False)
new_lt20(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt19(x0, x1, ty_Bool)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_compare0([], [], x0)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, ty_Int)
new_compare10(x0, x1, False, x2, x3, x4)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_compare12(x0, x1, True, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_foldFM_LE12(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), True, x10, x11)
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_lt18(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Double)
new_compare29(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt7(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Ordering)
new_compare26(x0, x1, False, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs14(LT, GT)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs14(GT, LT)
new_esEs12(Char(x0), Char(x1))
new_esEs11(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare210(x0, x1, True)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs15(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs8(Nothing, Nothing, x0)
new_ltEs14(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_esEs24(x0, x1, ty_Char)
new_primCompAux0(x0, x1, x2, x3)
new_not(EQ)
new_foldFM_LE5(x0, Branch(x1, x2, x3, x4, x5), x6, x7)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, ty_Int)
new_keysFM_LE0(x0, x1, x2, x3, x4)
new_compare31(x0, x1, ty_Integer)
new_lt6(x0, x1)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_compare9(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_compare11(Char(x0), Char(x1))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, app(ty_[], x2))
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt11(x0, x1)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(Float(x0, x1), Float(x2, x3))
new_esEs14(LT, EQ)
new_esEs14(EQ, LT)
new_esEs22(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Double)
new_compare110(x0, x1, False, x2, x3)
new_esEs15(:(x0, x1), [], x2)
new_esEs26(x0, x1, ty_Double)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Double)
new_esEs14(GT, GT)
new_ltEs15(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare111(x0, x1, False)
new_esEs5(Nothing, Nothing, x0)
new_compare110(x0, x1, True, x2, x3)
new_esEs21(Double(x0, x1), Double(x2, x3))
new_compare31(x0, x1, ty_Double)
new_esEs14(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_lt19(x0, x1, ty_Int)
new_lt19(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Int)
new_ltEs15(Left(x0), Left(x1), ty_Char, x2)
new_ltEs9(x0, x1)
new_esEs28(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs15(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs19(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Bool)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare0([], :(x0, x1), x2)
new_lt20(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare0(:(x0, x1), [], x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_ltEs16(False, False)
new_not(LT)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_foldFM_LE30(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
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
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Nothing, h), h, ba)
new_foldFM_LE21(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE11(new_keysFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs8(vyy3440, Nothing, h), h, ba)
new_foldFM_LE4(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Nothing, h), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE21(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The TRS R consists of the following rules:
new_ltEs8(Just(vyy3000), Nothing, ddf) → False
new_ltEs8(Nothing, Nothing, ddf) → True
new_foldFM_LE5(vyy24, EmptyFM, h, ba) → vyy24
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE22(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE22(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE12(new_keysFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs8(vyy3440, Nothing, h), h, ba)
new_foldFM_LE5(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE12(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Nothing, h), h, ba)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba) → new_foldFM_LE5(vyy24, vyy343, h, ba)
new_keysFM_LE0(vyy340, vyy341, vyy27, h, ba) → :(vyy340, vyy27)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE30(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), h, ba)
new_foldFM_LE30(vyy340, vyy341, vyy27, h, ba) → new_keysFM_LE0(vyy340, vyy341, vyy27, h, ba)
The set Q consists of the following terms:
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs15(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs16(True, True)
new_esEs18(@0, @0)
new_compare18(x0, x1)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs14(EQ, GT)
new_esEs14(GT, EQ)
new_pePe(True, x0, x1, x2, x3)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs5(Nothing, Just(x0), x1)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(EQ)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(Right(x0), Right(x1), x2, ty_Int)
new_compare23(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Float)
new_compare19(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_foldFM_LE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs11(x0, x1, ty_Float)
new_primCompAux00(x0, GT)
new_esEs28(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_ltEs15(Right(x0), Left(x1), x2, x3)
new_ltEs15(Left(x0), Right(x1), x2, x3)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Ordering)
new_compare8(x0, x1)
new_compare17(x0, x1, True, x2, x3)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs5(x0, x1, ty_Char)
new_compare13(Integer(x0), Integer(x1))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_asAs(False, x0)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare10(x0, x1, True, x2, x3, x4)
new_lt16(x0, x1, x2)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs15([], [], x0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_esEs25(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(GT, LT)
new_esEs14(LT, GT)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_compare12(x0, x1, False, x2)
new_compare30(x0, x1, x2)
new_esEs28(x0, x1, ty_Char)
new_ltEs8(Nothing, Just(x0), x1)
new_ltEs5(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_primCompAux00(x0, EQ)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_lt20(x0, x1, ty_Float)
new_esEs15([], :(x0, x1), x2)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, ty_@0)
new_esEs11(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs8(Just(x0), Nothing, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_esEs27(x0, x1, ty_@0)
new_lt7(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs11(x0, x1, ty_@0)
new_ltEs15(Right(x0), Right(x1), x2, ty_Double)
new_compare26(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Integer)
new_pePe(False, x0, x1, x2, x3)
new_primMulNat0(Zero, Zero)
new_lt7(x0, x1, ty_Char)
new_esEs10(True, False)
new_esEs10(False, True)
new_esEs11(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare27(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs15(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs17(x0, x1, x2)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Int)
new_fmToList(x0, x1, x2)
new_compare24(x0, x1, False, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16(Float(x0, x1), Float(x2, x3))
new_primPlusNat1(Succ(x0), Zero)
new_ltEs15(Right(x0), Right(x1), x2, ty_Float)
new_lt7(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_esEs17(Integer(x0), Integer(x1))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_foldFM2(EmptyFM, x0, x1)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, False, x2, x3)
new_compare23(x0, x1, False)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Bool)
new_lt8(x0, x1, x2)
new_compare31(x0, x1, ty_Bool)
new_foldFM_LE5(x0, EmptyFM, x1, x2)
new_esEs27(x0, x1, ty_Int)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_lt7(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt19(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_compare15(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_Double)
new_not0
new_esEs29(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_ltEs12(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Nothing, x1)
new_foldFM_LE12(x0, x1, x2, x3, x4, EmptyFM, True, x5, x6)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs14(LT, LT)
new_esEs10(True, True)
new_esEs9(GT)
new_ltEs14(LT, LT)
new_esEs11(x0, x1, ty_Int)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_lt7(x0, x1, ty_Integer)
new_ltEs15(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs5(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs24(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs7(x0, x1)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Char)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Integer)
new_esEs5(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_ltEs18(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, ty_Bool)
new_lt10(x0, x1, x2)
new_ltEs15(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt5(x0, x1)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs6(x0, x1, x2)
new_esEs25(x0, x1, ty_Float)
new_not(GT)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare111(x0, x1, True)
new_ltEs10(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs15(Left(x0), Left(x1), ty_Double, x2)
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_compare31(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_compare16(x0, x1, False)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs24(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs15(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_ltEs15(Left(x0), Left(x1), ty_Bool, x2)
new_compare24(x0, x1, True, x2)
new_sr(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare16(x0, x1, True)
new_esEs28(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_ltEs5(x0, x1, ty_Ordering)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt7(x0, x1, ty_Float)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Double)
new_lt14(x0, x1, x2, x3)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1)
new_lt17(x0, x1)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs5(x0, x1, app(ty_[], x2))
new_primPlusNat0(Zero, x0)
new_ltEs15(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Integer)
new_ltEs15(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs9(LT)
new_ltEs16(True, False)
new_ltEs16(False, True)
new_primCompAux00(x0, LT)
new_compare6(@0, @0)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_ltEs15(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, x2, x3)
new_primCmpNat0(Zero, Zero)
new_esEs10(False, False)
new_lt20(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt19(x0, x1, ty_Bool)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_compare0([], [], x0)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, ty_Int)
new_compare10(x0, x1, False, x2, x3, x4)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_compare12(x0, x1, True, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_foldFM_LE12(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), True, x10, x11)
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_lt18(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Double)
new_compare29(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt7(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Ordering)
new_compare26(x0, x1, False, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs14(LT, GT)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs14(GT, LT)
new_esEs12(Char(x0), Char(x1))
new_esEs11(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare210(x0, x1, True)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs15(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs8(Nothing, Nothing, x0)
new_ltEs14(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_esEs24(x0, x1, ty_Char)
new_primCompAux0(x0, x1, x2, x3)
new_not(EQ)
new_foldFM_LE5(x0, Branch(x1, x2, x3, x4, x5), x6, x7)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, ty_Int)
new_keysFM_LE0(x0, x1, x2, x3, x4)
new_compare31(x0, x1, ty_Integer)
new_lt6(x0, x1)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_compare9(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_compare11(Char(x0), Char(x1))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, app(ty_[], x2))
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt11(x0, x1)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(Float(x0, x1), Float(x2, x3))
new_esEs14(LT, EQ)
new_esEs14(EQ, LT)
new_esEs22(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Double)
new_compare110(x0, x1, False, x2, x3)
new_esEs15(:(x0, x1), [], x2)
new_esEs26(x0, x1, ty_Double)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Double)
new_esEs14(GT, GT)
new_ltEs15(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare111(x0, x1, False)
new_esEs5(Nothing, Nothing, x0)
new_compare110(x0, x1, True, x2, x3)
new_esEs21(Double(x0, x1), Double(x2, x3))
new_compare31(x0, x1, ty_Double)
new_esEs14(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_lt19(x0, x1, ty_Int)
new_lt19(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Int)
new_ltEs15(Left(x0), Left(x1), ty_Char, x2)
new_ltEs9(x0, x1)
new_esEs28(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs15(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs19(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Bool)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare0([], :(x0, x1), x2)
new_lt20(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare0(:(x0, x1), [], x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_ltEs16(False, False)
new_not(LT)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_foldFM_LE30(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
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_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs15(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs16(True, True)
new_esEs18(@0, @0)
new_compare18(x0, x1)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs14(EQ, GT)
new_esEs14(GT, EQ)
new_pePe(True, x0, x1, x2, x3)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs5(Nothing, Just(x0), x1)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(EQ)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(Right(x0), Right(x1), x2, ty_Int)
new_compare23(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Float)
new_compare19(x0, x1, x2, x3)
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs11(x0, x1, ty_Float)
new_primCompAux00(x0, GT)
new_esEs28(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_ltEs15(Right(x0), Left(x1), x2, x3)
new_ltEs15(Left(x0), Right(x1), x2, x3)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Ordering)
new_compare8(x0, x1)
new_compare17(x0, x1, True, x2, x3)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs5(x0, x1, ty_Char)
new_compare13(Integer(x0), Integer(x1))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_asAs(False, x0)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare10(x0, x1, True, x2, x3, x4)
new_lt16(x0, x1, x2)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs15([], [], x0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_esEs25(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(GT, LT)
new_esEs14(LT, GT)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_compare12(x0, x1, False, x2)
new_compare30(x0, x1, x2)
new_esEs28(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_primCompAux00(x0, EQ)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_lt20(x0, x1, ty_Float)
new_esEs15([], :(x0, x1), x2)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, ty_@0)
new_esEs11(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_esEs27(x0, x1, ty_@0)
new_lt7(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs11(x0, x1, ty_@0)
new_ltEs15(Right(x0), Right(x1), x2, ty_Double)
new_compare26(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Integer)
new_pePe(False, x0, x1, x2, x3)
new_primMulNat0(Zero, Zero)
new_lt7(x0, x1, ty_Char)
new_esEs10(True, False)
new_esEs10(False, True)
new_esEs11(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare27(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs15(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs17(x0, x1, x2)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Int)
new_fmToList(x0, x1, x2)
new_compare24(x0, x1, False, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16(Float(x0, x1), Float(x2, x3))
new_primPlusNat1(Succ(x0), Zero)
new_ltEs15(Right(x0), Right(x1), x2, ty_Float)
new_lt7(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_esEs17(Integer(x0), Integer(x1))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_foldFM2(EmptyFM, x0, x1)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, False, x2, x3)
new_compare23(x0, x1, False)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Bool)
new_lt8(x0, x1, x2)
new_compare31(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_compare15(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_Double)
new_not0
new_esEs29(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_ltEs12(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Nothing, x1)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs14(LT, LT)
new_esEs10(True, True)
new_esEs9(GT)
new_ltEs14(LT, LT)
new_esEs11(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_lt7(x0, x1, ty_Integer)
new_ltEs15(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs5(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs24(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs7(x0, x1)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Char)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Integer)
new_esEs5(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_ltEs18(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, ty_Bool)
new_lt10(x0, x1, x2)
new_ltEs15(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt5(x0, x1)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs6(x0, x1, x2)
new_esEs25(x0, x1, ty_Float)
new_not(GT)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare111(x0, x1, True)
new_ltEs10(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs15(Left(x0), Left(x1), ty_Double, x2)
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_compare31(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_compare16(x0, x1, False)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs24(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs15(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_ltEs15(Left(x0), Left(x1), ty_Bool, x2)
new_compare24(x0, x1, True, x2)
new_sr(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare16(x0, x1, True)
new_esEs28(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Ordering)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt7(x0, x1, ty_Float)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Double)
new_lt14(x0, x1, x2, x3)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1)
new_lt17(x0, x1)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs5(x0, x1, app(ty_[], x2))
new_primPlusNat0(Zero, x0)
new_ltEs15(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Integer)
new_ltEs15(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs9(LT)
new_ltEs16(True, False)
new_ltEs16(False, True)
new_primCompAux00(x0, LT)
new_compare6(@0, @0)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_ltEs15(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, x2, x3)
new_primCmpNat0(Zero, Zero)
new_esEs10(False, False)
new_lt20(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt19(x0, x1, ty_Bool)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_compare0([], [], x0)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, ty_Int)
new_compare10(x0, x1, False, x2, x3, x4)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_compare12(x0, x1, True, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Double)
new_compare29(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt7(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Ordering)
new_compare26(x0, x1, False, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs14(LT, GT)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs14(GT, LT)
new_esEs12(Char(x0), Char(x1))
new_esEs11(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare210(x0, x1, True)
new_ltEs15(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_esEs24(x0, x1, ty_Char)
new_primCompAux0(x0, x1, x2, x3)
new_not(EQ)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Integer)
new_lt6(x0, x1)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_compare9(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_compare11(Char(x0), Char(x1))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, app(ty_[], x2))
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt11(x0, x1)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(Float(x0, x1), Float(x2, x3))
new_esEs14(LT, EQ)
new_esEs14(EQ, LT)
new_esEs22(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Double)
new_compare110(x0, x1, False, x2, x3)
new_esEs15(:(x0, x1), [], x2)
new_esEs26(x0, x1, ty_Double)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Double)
new_esEs14(GT, GT)
new_ltEs15(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare111(x0, x1, False)
new_esEs5(Nothing, Nothing, x0)
new_compare110(x0, x1, True, x2, x3)
new_esEs21(Double(x0, x1), Double(x2, x3))
new_compare31(x0, x1, ty_Double)
new_esEs14(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_lt19(x0, x1, ty_Int)
new_lt19(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Int)
new_ltEs15(Left(x0), Left(x1), ty_Char, x2)
new_ltEs9(x0, x1)
new_esEs28(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs15(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs19(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Bool)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare0([], :(x0, x1), x2)
new_lt20(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare0(:(x0, x1), [], x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_ltEs16(False, False)
new_not(LT)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
↳ 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
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Nothing, h), h, ba)
new_foldFM_LE21(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE11(new_keysFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs8(vyy3440, Nothing, h), h, ba)
new_foldFM_LE4(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Nothing, h), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE21(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The TRS R consists of the following rules:
new_ltEs8(Just(vyy3000), Nothing, ddf) → False
new_ltEs8(Nothing, Nothing, ddf) → True
new_foldFM_LE5(vyy24, EmptyFM, h, ba) → vyy24
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE22(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE22(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE12(new_keysFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs8(vyy3440, Nothing, h), h, ba)
new_foldFM_LE5(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE12(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Nothing, h), h, ba)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba) → new_foldFM_LE5(vyy24, vyy343, h, ba)
new_keysFM_LE0(vyy340, vyy341, vyy27, h, ba) → :(vyy340, vyy27)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE30(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), h, ba)
new_foldFM_LE30(vyy340, vyy341, vyy27, h, ba) → new_keysFM_LE0(vyy340, vyy341, vyy27, h, ba)
The set Q consists of the following terms:
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_foldFM_LE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_ltEs8(Nothing, Just(x0), x1)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs8(Just(x0), Nothing, x1)
new_foldFM_LE5(x0, EmptyFM, x1, x2)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_foldFM_LE12(x0, x1, x2, x3, x4, EmptyFM, True, x5, x6)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_foldFM_LE12(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), True, x10, x11)
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs8(Nothing, Nothing, x0)
new_foldFM_LE5(x0, Branch(x1, x2, x3, x4, x5), x6, x7)
new_keysFM_LE0(x0, x1, x2, x3, x4)
new_foldFM_LE30(x0, x1, x2, x3, x4)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
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_LE4(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Nothing, h), h, ba)
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 8, 4 >= 9
- new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs8(vyy3430, Nothing, h), h, ba)
The graph contains the following edges 1 >= 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 8 >= 8, 9 >= 9
- new_foldFM_LE21(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE11(new_keysFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs8(vyy3440, Nothing, h), h, ba)
The graph contains the following edges 4 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 8, 10 >= 9
- new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE21(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
The graph contains the following edges 2 >= 1, 3 >= 2, 6 > 4, 6 > 5, 6 > 6, 6 > 7, 6 > 8, 8 >= 9, 9 >= 10
- new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The graph contains the following edges 1 >= 1, 5 >= 2, 8 >= 3, 9 >= 4
- new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The graph contains the following edges 1 >= 1, 5 >= 2, 8 >= 3, 9 >= 4