YES 9.357 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



HASKELL
  ↳ LR

mainModule FiniteMap
  ((eltsFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [b]) :: Ord a => FiniteMap a b  ->  a  ->  [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 b a) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a]
eltsFM_LE fm fr foldFM_LE (\key elt rest ->elt : rest) [] fr fm

  fmToList :: FiniteMap b a  ->  [(b,a)]
fmToList fm foldFM (\key elt rest ->(key,elt: rest) [] fm

  foldFM :: (a  ->  c  ->  b  ->  b ->  b  ->  FiniteMap a c  ->  b
foldFM k z EmptyFM z
foldFM k z (Branch key elt _ fm_l fm_rfoldFM k (k key elt (foldFM k z fm_r)) fm_l

  foldFM_LE :: Ord c => (c  ->  a  ->  b  ->  b ->  b  ->  c  ->  FiniteMap c a  ->  b
foldFM_LE k z fr EmptyFM z
foldFM_LE k z fr (Branch key elt _ fm_l fm_r
 | key <= fr = 
foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r
 | otherwise = 
foldFM_LE k z fr fm_l

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch _ _ size _ _) size


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Lambda Reductions:
The following Lambda expression
\keyeltrest→(key,elt: rest

is transformed to
fmToList0 key elt rest = (key,elt: rest

The following Lambda expression
\keyeltrestelt : rest

is transformed to
eltsFM_LE0 key elt rest = elt : rest



↳ HASKELL
  ↳ LR
HASKELL
      ↳ CR

mainModule FiniteMap
  ((eltsFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [b]) :: Ord a => FiniteMap a b  ->  a  ->  [b])

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a


  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a]
eltsFM_LE fm fr foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest elt : rest

  fmToList :: FiniteMap a b  ->  [(a,b)]
fmToList fm foldFM fmToList0 [] fm

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (a  ->  c  ->  b  ->  b ->  b  ->  FiniteMap a c  ->  b
foldFM k z EmptyFM z
foldFM k z (Branch key elt _ fm_l fm_rfoldFM 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 = 
foldFM_LE k z fr fm_l

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch _ _ size _ _) size


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Case Reductions:
The following Case expression
case compare x y of
 EQ → o
 LT → LT
 GT → GT

is transformed to
primCompAux0 o EQ = o
primCompAux0 o LT = LT
primCompAux0 o GT = GT



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
HASKELL
          ↳ IFR

mainModule FiniteMap
  ((eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a]) :: Ord b => FiniteMap b a  ->  b  ->  [a])

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b


  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a]
eltsFM_LE fm fr foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest elt : rest

  fmToList :: FiniteMap b a  ->  [(b,a)]
fmToList fm foldFM fmToList0 [] fm

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (c  ->  a  ->  b  ->  b ->  b  ->  FiniteMap c a  ->  b
foldFM k z EmptyFM z
foldFM k z (Branch key elt _ fm_l fm_rfoldFM 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 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 = 
foldFM_LE k z fr fm_l

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch _ _ size _ _) size


module Maybe where
  import qualified FiniteMap
import qualified Prelude



If Reductions:
The following If expression
if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero

is transformed to
primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y))
primDivNatS0 x y False = Zero

The following If expression
if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x

is transformed to
primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y)
primModNatS0 x y False = Succ x



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
HASKELL
              ↳ BR

mainModule FiniteMap
  ((eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a]) :: Ord b => FiniteMap b a  ->  b  ->  [a])

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b


  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  eltsFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_LE fm fr foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest elt : rest

  fmToList :: FiniteMap b a  ->  [(b,a)]
fmToList fm foldFM fmToList0 [] fm

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (b  ->  c  ->  a  ->  a ->  a  ->  FiniteMap b c  ->  a
foldFM k z EmptyFM z
foldFM k z (Branch key elt _ fm_l fm_rfoldFM 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 = 
foldFM_LE k z fr fm_l

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch _ _ size _ _) size


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
HASKELL
                  ↳ COR

mainModule FiniteMap
  ((eltsFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [b]) :: Ord a => FiniteMap a b  ->  a  ->  [b])

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a


  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  eltsFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_LE fm fr foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest elt : rest

  fmToList :: FiniteMap b a  ->  [(b,a)]
fmToList fm foldFM fmToList0 [] fm

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (a  ->  b  ->  c  ->  c ->  c  ->  FiniteMap a b  ->  c
foldFM k z EmptyFM z
foldFM k z (Branch key elt vw fm_l fm_rfoldFM 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 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 = 
foldFM_LE k z fr fm_l

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch vy vz size wu wvsize


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
 = foldFM_LE k z fr fm_l

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
 = EQ
 | x <= y
 = LT
 | otherwise
 = GT

is transformed to
compare x y = compare3 x y

compare1 x y True = LT
compare1 x y False = compare0 x y otherwise

compare2 x y True = EQ
compare2 x y False = compare1 x y (x <= y)

compare0 x y True = GT

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
absReal x
 | x >= 0
 = x
 | otherwise
 = `negate` x

is transformed to
absReal x = absReal2 x

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
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

The following Function with conditions
reduce x y
 | y == 0
 = error []
 | otherwise
 = x `quot` d :% (y `quot` d)
where 
d  = gcd x y

is transformed to
reduce x y = reduce2 x y

reduce2 x y = 
reduce1 x y (y == 0)
where 
d  = gcd x y
reduce0 x y True = x `quot` d :% (y `quot` d)
reduce1 x y True = error []
reduce1 x y False = reduce0 x y otherwise



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
HASKELL
                      ↳ LetRed

mainModule FiniteMap
  ((eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a]) :: Ord b => FiniteMap b a  ->  b  ->  [a])

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a


  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  eltsFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_LE fm fr foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest elt : rest

  fmToList :: FiniteMap a b  ->  [(a,b)]
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_rfoldFM k (k key elt (foldFM k z fm_r)) fm_l

  foldFM_LE :: Ord a => (a  ->  c  ->  b  ->  b ->  b  ->  a  ->  FiniteMap a c  ->  b
foldFM_LE k z fr EmptyFM foldFM_LE3 k z fr EmptyFM
foldFM_LE k z fr (Branch key elt vx fm_l fm_rfoldFM_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_rfoldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr)

  
foldFM_LE3 k z fr EmptyFM z
foldFM_LE3 vvu vvv vvw vvx foldFM_LE2 vvu vvv vvw vvx

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch vy vz size wu wvsize


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 
d  = gcd x y
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

reduce2Reduce0 vyw vyx x y True = x `quot` reduce2D vyw vyx :% (y `quot` reduce2D vyw vyx)

reduce2D vyw vyx = gcd vyw vyx

The bindings of the following Let/Where expression
gcd' (abs x) (abs y)
where 
gcd' x vvy = gcd'2 x vvy
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x vvy = x
gcd'1 vvz vwu vwv = gcd'0 vwu vwv
gcd'2 x vvy = gcd'1 (vvy == 0) x vvy
gcd'2 vww vwx = gcd'0 vww vwx

are unpacked to the following functions on top level
gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y)

gcd0Gcd'1 True x vvy = x
gcd0Gcd'1 vvz vwu vwv = gcd0Gcd'0 vwu vwv

gcd0Gcd'2 x vvy = gcd0Gcd'1 (vvy == 0) x vvy
gcd0Gcd'2 vww vwx = gcd0Gcd'0 vww vwx

gcd0Gcd' x vvy = gcd0Gcd'2 x vvy
gcd0Gcd' x y = gcd0Gcd'0 x y



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
HASKELL
                          ↳ NumRed

mainModule FiniteMap
  ((eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a]) :: Ord b => FiniteMap b a  ->  b  ->  [a])

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b


  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  eltsFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_LE fm fr foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest elt : rest

  fmToList :: FiniteMap b a  ->  [(b,a)]
fmToList fm foldFM fmToList0 [] fm

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (b  ->  a  ->  c  ->  c ->  c  ->  FiniteMap b a  ->  c
foldFM k z EmptyFM z
foldFM k z (Branch key elt vw fm_l fm_rfoldFM 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_rfoldFM_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_rfoldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr)

  
foldFM_LE3 k z fr EmptyFM z
foldFM_LE3 vvu vvv vvw vvx foldFM_LE2 vvu vvv vvw vvx

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch vy vz size wu wvsize


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
HASKELL
                              ↳ Narrow

mainModule FiniteMap
  (eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a])

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a


  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a]
eltsFM_LE fm fr foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest elt : rest

  fmToList :: FiniteMap 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_rfoldFM k (k key elt (foldFM k z fm_r)) fm_l

  foldFM_LE :: Ord b => (b  ->  c  ->  a  ->  a ->  a  ->  b  ->  FiniteMap b c  ->  a
foldFM_LE k z fr EmptyFM foldFM_LE3 k z fr EmptyFM
foldFM_LE k z fr (Branch key elt vx fm_l fm_rfoldFM_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_rfoldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr)

  
foldFM_LE3 k z fr EmptyFM z
foldFM_LE3 vvu vvv vvw vvx foldFM_LE2 vvu vvv vvw vvx

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM Pos Zero
sizeFM (Branch vy vz size wu wvsize


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

Q DP problem:
The TRS P consists of the following rules:

new_primPlusNat(Succ(vyy12600), Succ(vyy41000)) → new_primPlusNat(vyy12600, vyy41000)

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:



↳ 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

Q DP problem:
The TRS P consists of the following rules:

new_primMulNat(Succ(vyy30000), Succ(vyy4100)) → new_primMulNat(vyy30000, Succ(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:



↳ 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

Q DP problem:
The TRS P consists of the following rules:

new_foldFM(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), h, ba) → new_foldFM(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, h, ba), vyy7933, h, ba)
new_foldFM(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), h, ba) → new_foldFM(vyy790, vyy791, vyy125, vyy7934, h, ba)

The TRS R consists of the following rules:

new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, h, ba) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), h, ba) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, h, ba), vyy7933, 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:



↳ 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

Q DP problem:
The TRS P consists of the following rules:

new_foldFM1(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), h, ba) → new_foldFM1(vyy794, 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:



↳ 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

Q DP problem:
The TRS P consists of the following rules:

new_primEqNat(Succ(vyy7800), Succ(vyy7900)) → new_primEqNat(vyy7800, vyy7900)

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:



↳ 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

Q DP problem:
The TRS P consists of the following rules:

new_esEs2(Just(vyy780), Just(vyy790), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy780, vyy790, hg, hh, baa)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy780, vyy790, bde, bdf)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(ty_[], bcd)) → new_esEs(vyy780, vyy790, bcd)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, bec), bed), bee), bdh) → new_esEs1(vyy780, vyy790, bec, bed, bee)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_FiniteMap, gb), gc)) → new_esEs0(vyy782, vyy792, gb, gc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(app(ty_@3, eh), fa), fb), da) → new_esEs1(vyy781, vyy791, eh, fa, fb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_Either, fd), ff), da) → new_esEs3(vyy781, vyy791, fd, ff)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_FiniteMap, bfe), bff)) → new_esEs0(vyy781, vyy791, bfe, bff)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy780, vyy790, bdc, bdd)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(app(ty_@3, gd), ge), gf)) → new_esEs1(vyy782, vyy792, gd, ge, gf)
new_esEs3(Left(vyy780), Left(vyy790), app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs1(vyy780, vyy790, bbc, bbd, bbe)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_Maybe, bab)) → new_esEs2(vyy780, vyy790, bab)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy780, vyy790, bbg, bbh)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_Either, bgc), bgd)) → new_esEs3(vyy781, vyy791, bgc, bgd)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bg), bh)) → new_esEs3(vyy780, vyy790, bg, bh)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_Maybe, bgb)) → new_esEs2(vyy781, vyy791, bgb)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy780, vyy790, bca, bcb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_@2, hb), hc)) → new_esEs4(vyy782, vyy792, hb, hc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, dg), cg, da) → new_esEs2(vyy780, vyy790, dg)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(ty_Maybe, bdb)) → new_esEs2(vyy780, vyy790, bdb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, ca), cb)) → new_esEs4(vyy780, vyy790, ca, cb)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_Either, bac), bad)) → new_esEs3(vyy780, vyy790, bac, bad)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_[], ga)) → new_esEs(vyy782, vyy792, ga)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_@2, bge), bgf)) → new_esEs4(vyy781, vyy791, bge, bgf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_[], ee), da) → new_esEs(vyy781, vyy791, ee)
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_fmToList(vyy78, cd, ce), new_fmToList(vyy79, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, bef), bdh) → new_esEs2(vyy780, vyy790, bef)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_[], hd)) → new_esEs(vyy780, vyy790, hd)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, bba), bbb), bah) → new_esEs0(vyy780, vyy790, bba, bbb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_FiniteMap, ef), eg), da) → new_esEs0(vyy781, vyy791, ef, eg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_Either, gh), ha)) → new_esEs3(vyy782, vyy792, gh, ha)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, bfa), bfb), bdh) → new_esEs4(vyy780, vyy790, bfa, bfb)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs1(vyy780, vyy790, bcg, bch, bda)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_[], bag), bah) → new_esEs(vyy780, vyy790, bag)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy780, vyy790, bce, bcf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_[], bfd)) → new_esEs(vyy781, vyy791, bfd)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, bf)) → new_esEs2(vyy780, vyy790, bf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, db), dc), cg, da) → new_esEs0(vyy780, vyy790, db, dc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_@2, fg), fh), da) → new_esEs4(vyy781, vyy791, fg, fh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, dd), de), df), cg, da) → new_esEs1(vyy780, vyy790, dd, de, df)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_Maybe, bbf), bah) → new_esEs2(vyy780, vyy790, bbf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_Maybe, fc), da) → new_esEs2(vyy781, vyy791, fc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bc), bd), be)) → new_esEs1(vyy780, vyy790, bc, bd, be)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, bea), beb), bdh) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs1(vyy781, vyy791, bfg, bfh, bga)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], bdg), bdh) → new_esEs(vyy780, vyy790, bdg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, eb), ec), cg, da) → new_esEs4(vyy780, vyy790, eb, ec)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, beg), beh), bdh) → new_esEs3(vyy780, vyy790, beg, beh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], cf), cg, da) → new_esEs(vyy780, vyy790, cf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_Maybe, gg)) → new_esEs2(vyy782, vyy792, gg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, dh), ea), cg, da) → new_esEs3(vyy780, vyy790, dh, ea)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_@2, bae), baf)) → new_esEs4(vyy780, vyy790, bae, baf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], h)) → new_esEs(vyy780, vyy790, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy780, vyy790, ba, bb)

The TRS R consists of the following rules:

new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)
new_fmToList(vyy79, cd, ce) → new_foldFM2(vyy79, cd, ce)
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []

The set Q consists of the following terms:

new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_fmToList(vyy78, cd, ce), new_fmToList(vyy79, cd, ce), app(app(ty_@2, cd), ce)) at position [0] we obtained the following new rules:

new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_fmToList(vyy79, cd, ce), app(app(ty_@2, cd), ce))



↳ 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

Q DP problem:
The TRS P consists of the following rules:

new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy780, vyy790, bde, bdf)
new_esEs2(Just(vyy780), Just(vyy790), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy780, vyy790, hg, hh, baa)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(ty_[], bcd)) → new_esEs(vyy780, vyy790, bcd)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, bec), bed), bee), bdh) → new_esEs1(vyy780, vyy790, bec, bed, bee)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(app(ty_@3, eh), fa), fb), da) → new_esEs1(vyy781, vyy791, eh, fa, fb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_FiniteMap, gb), gc)) → new_esEs0(vyy782, vyy792, gb, gc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_Either, fd), ff), da) → new_esEs3(vyy781, vyy791, fd, ff)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy780, vyy790, bdc, bdd)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_FiniteMap, bfe), bff)) → new_esEs0(vyy781, vyy791, bfe, bff)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(app(ty_@3, gd), ge), gf)) → new_esEs1(vyy782, vyy792, gd, ge, gf)
new_esEs3(Left(vyy780), Left(vyy790), app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs1(vyy780, vyy790, bbc, bbd, bbe)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_Maybe, bab)) → new_esEs2(vyy780, vyy790, bab)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy780, vyy790, bbg, bbh)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_Either, bgc), bgd)) → new_esEs3(vyy781, vyy791, bgc, bgd)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bg), bh)) → new_esEs3(vyy780, vyy790, bg, bh)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_Maybe, bgb)) → new_esEs2(vyy781, vyy791, bgb)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy780, vyy790, bca, bcb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_@2, hb), hc)) → new_esEs4(vyy782, vyy792, hb, hc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, dg), cg, da) → new_esEs2(vyy780, vyy790, dg)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(ty_Maybe, bdb)) → new_esEs2(vyy780, vyy790, bdb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, ca), cb)) → new_esEs4(vyy780, vyy790, ca, cb)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_@2, bge), bgf)) → new_esEs4(vyy781, vyy791, bge, bgf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_[], ga)) → new_esEs(vyy782, vyy792, ga)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_Either, bac), bad)) → new_esEs3(vyy780, vyy790, bac, bad)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_[], ee), da) → new_esEs(vyy781, vyy791, ee)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, bef), bdh) → new_esEs2(vyy780, vyy790, bef)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_[], hd)) → new_esEs(vyy780, vyy790, hd)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, bba), bbb), bah) → new_esEs0(vyy780, vyy790, bba, bbb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_FiniteMap, ef), eg), da) → new_esEs0(vyy781, vyy791, ef, eg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_Either, gh), ha)) → new_esEs3(vyy782, vyy792, gh, ha)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, bfa), bfb), bdh) → new_esEs4(vyy780, vyy790, bfa, bfb)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs1(vyy780, vyy790, bcg, bch, bda)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_[], bag), bah) → new_esEs(vyy780, vyy790, bag)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy780, vyy790, bce, bcf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, bf)) → new_esEs2(vyy780, vyy790, bf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_[], bfd)) → new_esEs(vyy781, vyy791, bfd)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, db), dc), cg, da) → new_esEs0(vyy780, vyy790, db, dc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, dd), de), df), cg, da) → new_esEs1(vyy780, vyy790, dd, de, df)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_@2, fg), fh), da) → new_esEs4(vyy781, vyy791, fg, fh)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_Maybe, bbf), bah) → new_esEs2(vyy780, vyy790, bbf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_Maybe, fc), da) → new_esEs2(vyy781, vyy791, fc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bc), bd), be)) → new_esEs1(vyy780, vyy790, bc, bd, be)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, bea), beb), bdh) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs1(vyy781, vyy791, bfg, bfh, bga)
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_fmToList(vyy79, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], bdg), bdh) → new_esEs(vyy780, vyy790, bdg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, eb), ec), cg, da) → new_esEs4(vyy780, vyy790, eb, ec)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_Maybe, gg)) → new_esEs2(vyy782, vyy792, gg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], cf), cg, da) → new_esEs(vyy780, vyy790, cf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, beg), beh), bdh) → new_esEs3(vyy780, vyy790, beg, beh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, dh), ea), cg, da) → new_esEs3(vyy780, vyy790, dh, ea)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_@2, bae), baf)) → new_esEs4(vyy780, vyy790, bae, baf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], h)) → new_esEs(vyy780, vyy790, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy780, vyy790, ba, bb)

The TRS R consists of the following rules:

new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)
new_fmToList(vyy79, cd, ce) → new_foldFM2(vyy79, cd, ce)
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []

The set Q consists of the following terms:

new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_fmToList(vyy79, cd, ce), app(app(ty_@2, cd), ce)) at position [1] we obtained the following new rules:

new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_foldFM2(vyy79, cd, ce), app(app(ty_@2, cd), ce))



↳ 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

Q DP problem:
The TRS P consists of the following rules:

new_esEs2(Just(vyy780), Just(vyy790), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy780, vyy790, hg, hh, baa)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy780, vyy790, bde, bdf)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(ty_[], bcd)) → new_esEs(vyy780, vyy790, bcd)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, bec), bed), bee), bdh) → new_esEs1(vyy780, vyy790, bec, bed, bee)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_FiniteMap, gb), gc)) → new_esEs0(vyy782, vyy792, gb, gc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(app(ty_@3, eh), fa), fb), da) → new_esEs1(vyy781, vyy791, eh, fa, fb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_Either, fd), ff), da) → new_esEs3(vyy781, vyy791, fd, ff)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_FiniteMap, bfe), bff)) → new_esEs0(vyy781, vyy791, bfe, bff)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy780, vyy790, bdc, bdd)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(app(ty_@3, gd), ge), gf)) → new_esEs1(vyy782, vyy792, gd, ge, gf)
new_esEs3(Left(vyy780), Left(vyy790), app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs1(vyy780, vyy790, bbc, bbd, bbe)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_Maybe, bab)) → new_esEs2(vyy780, vyy790, bab)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy780, vyy790, bbg, bbh)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_Either, bgc), bgd)) → new_esEs3(vyy781, vyy791, bgc, bgd)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bg), bh)) → new_esEs3(vyy780, vyy790, bg, bh)
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_foldFM2(vyy79, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_Maybe, bgb)) → new_esEs2(vyy781, vyy791, bgb)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy780, vyy790, bca, bcb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_@2, hb), hc)) → new_esEs4(vyy782, vyy792, hb, hc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, dg), cg, da) → new_esEs2(vyy780, vyy790, dg)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(ty_Maybe, bdb)) → new_esEs2(vyy780, vyy790, bdb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, ca), cb)) → new_esEs4(vyy780, vyy790, ca, cb)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_Either, bac), bad)) → new_esEs3(vyy780, vyy790, bac, bad)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_[], ga)) → new_esEs(vyy782, vyy792, ga)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_@2, bge), bgf)) → new_esEs4(vyy781, vyy791, bge, bgf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_[], ee), da) → new_esEs(vyy781, vyy791, ee)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, bef), bdh) → new_esEs2(vyy780, vyy790, bef)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_[], hd)) → new_esEs(vyy780, vyy790, hd)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, bba), bbb), bah) → new_esEs0(vyy780, vyy790, bba, bbb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_FiniteMap, ef), eg), da) → new_esEs0(vyy781, vyy791, ef, eg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_Either, gh), ha)) → new_esEs3(vyy782, vyy792, gh, ha)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, bfa), bfb), bdh) → new_esEs4(vyy780, vyy790, bfa, bfb)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs1(vyy780, vyy790, bcg, bch, bda)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_[], bag), bah) → new_esEs(vyy780, vyy790, bag)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy780, vyy790, bce, bcf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_[], bfd)) → new_esEs(vyy781, vyy791, bfd)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, bf)) → new_esEs2(vyy780, vyy790, bf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, db), dc), cg, da) → new_esEs0(vyy780, vyy790, db, dc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_@2, fg), fh), da) → new_esEs4(vyy781, vyy791, fg, fh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, dd), de), df), cg, da) → new_esEs1(vyy780, vyy790, dd, de, df)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_Maybe, bbf), bah) → new_esEs2(vyy780, vyy790, bbf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_Maybe, fc), da) → new_esEs2(vyy781, vyy791, fc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bc), bd), be)) → new_esEs1(vyy780, vyy790, bc, bd, be)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, bea), beb), bdh) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs1(vyy781, vyy791, bfg, bfh, bga)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], bdg), bdh) → new_esEs(vyy780, vyy790, bdg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, eb), ec), cg, da) → new_esEs4(vyy780, vyy790, eb, ec)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, beg), beh), bdh) → new_esEs3(vyy780, vyy790, beg, beh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], cf), cg, da) → new_esEs(vyy780, vyy790, cf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_Maybe, gg)) → new_esEs2(vyy782, vyy792, gg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, dh), ea), cg, da) → new_esEs3(vyy780, vyy790, dh, ea)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_@2, bae), baf)) → new_esEs4(vyy780, vyy790, bae, baf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], h)) → new_esEs(vyy780, vyy790, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy780, vyy790, ba, bb)

The TRS R consists of the following rules:

new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)
new_fmToList(vyy79, cd, ce) → new_foldFM2(vyy79, cd, ce)
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []

The set Q consists of the following terms:

new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ Rewriting
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
QDP
                                                ↳ QReductionProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_esEs2(Just(vyy780), Just(vyy790), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy780, vyy790, hg, hh, baa)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy780, vyy790, bde, bdf)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(ty_[], bcd)) → new_esEs(vyy780, vyy790, bcd)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, bec), bed), bee), bdh) → new_esEs1(vyy780, vyy790, bec, bed, bee)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_FiniteMap, gb), gc)) → new_esEs0(vyy782, vyy792, gb, gc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(app(ty_@3, eh), fa), fb), da) → new_esEs1(vyy781, vyy791, eh, fa, fb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_Either, fd), ff), da) → new_esEs3(vyy781, vyy791, fd, ff)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_FiniteMap, bfe), bff)) → new_esEs0(vyy781, vyy791, bfe, bff)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy780, vyy790, bdc, bdd)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(app(ty_@3, gd), ge), gf)) → new_esEs1(vyy782, vyy792, gd, ge, gf)
new_esEs3(Left(vyy780), Left(vyy790), app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs1(vyy780, vyy790, bbc, bbd, bbe)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_Maybe, bab)) → new_esEs2(vyy780, vyy790, bab)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy780, vyy790, bbg, bbh)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_Either, bgc), bgd)) → new_esEs3(vyy781, vyy791, bgc, bgd)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bg), bh)) → new_esEs3(vyy780, vyy790, bg, bh)
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_foldFM2(vyy79, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_Maybe, bgb)) → new_esEs2(vyy781, vyy791, bgb)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy780, vyy790, bca, bcb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_@2, hb), hc)) → new_esEs4(vyy782, vyy792, hb, hc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, dg), cg, da) → new_esEs2(vyy780, vyy790, dg)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(ty_Maybe, bdb)) → new_esEs2(vyy780, vyy790, bdb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, ca), cb)) → new_esEs4(vyy780, vyy790, ca, cb)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_Either, bac), bad)) → new_esEs3(vyy780, vyy790, bac, bad)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_[], ga)) → new_esEs(vyy782, vyy792, ga)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_@2, bge), bgf)) → new_esEs4(vyy781, vyy791, bge, bgf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_[], ee), da) → new_esEs(vyy781, vyy791, ee)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, bef), bdh) → new_esEs2(vyy780, vyy790, bef)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_[], hd)) → new_esEs(vyy780, vyy790, hd)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, bba), bbb), bah) → new_esEs0(vyy780, vyy790, bba, bbb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_FiniteMap, ef), eg), da) → new_esEs0(vyy781, vyy791, ef, eg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_Either, gh), ha)) → new_esEs3(vyy782, vyy792, gh, ha)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, bfa), bfb), bdh) → new_esEs4(vyy780, vyy790, bfa, bfb)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs1(vyy780, vyy790, bcg, bch, bda)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_[], bag), bah) → new_esEs(vyy780, vyy790, bag)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy780, vyy790, bce, bcf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_[], bfd)) → new_esEs(vyy781, vyy791, bfd)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, bf)) → new_esEs2(vyy780, vyy790, bf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, db), dc), cg, da) → new_esEs0(vyy780, vyy790, db, dc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_@2, fg), fh), da) → new_esEs4(vyy781, vyy791, fg, fh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, dd), de), df), cg, da) → new_esEs1(vyy780, vyy790, dd, de, df)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_Maybe, bbf), bah) → new_esEs2(vyy780, vyy790, bbf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_Maybe, fc), da) → new_esEs2(vyy781, vyy791, fc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bc), bd), be)) → new_esEs1(vyy780, vyy790, bc, bd, be)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, bea), beb), bdh) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs1(vyy781, vyy791, bfg, bfh, bga)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], bdg), bdh) → new_esEs(vyy780, vyy790, bdg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, eb), ec), cg, da) → new_esEs4(vyy780, vyy790, eb, ec)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, beg), beh), bdh) → new_esEs3(vyy780, vyy790, beg, beh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], cf), cg, da) → new_esEs(vyy780, vyy790, cf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_Maybe, gg)) → new_esEs2(vyy782, vyy792, gg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, dh), ea), cg, da) → new_esEs3(vyy780, vyy790, dh, ea)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_@2, bae), baf)) → new_esEs4(vyy780, vyy790, bae, baf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], h)) → new_esEs(vyy780, vyy790, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy780, vyy790, ba, bb)

The TRS R consists of the following rules:

new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)

The set Q consists of the following terms:

new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_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

Q DP problem:
The TRS P consists of the following rules:

new_esEs2(Just(vyy780), Just(vyy790), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy780, vyy790, hg, hh, baa)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy780, vyy790, bde, bdf)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(ty_[], bcd)) → new_esEs(vyy780, vyy790, bcd)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, bec), bed), bee), bdh) → new_esEs1(vyy780, vyy790, bec, bed, bee)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_FiniteMap, gb), gc)) → new_esEs0(vyy782, vyy792, gb, gc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(app(ty_@3, eh), fa), fb), da) → new_esEs1(vyy781, vyy791, eh, fa, fb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_Either, fd), ff), da) → new_esEs3(vyy781, vyy791, fd, ff)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_FiniteMap, bfe), bff)) → new_esEs0(vyy781, vyy791, bfe, bff)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy780, vyy790, bdc, bdd)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(app(ty_@3, gd), ge), gf)) → new_esEs1(vyy782, vyy792, gd, ge, gf)
new_esEs3(Left(vyy780), Left(vyy790), app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs1(vyy780, vyy790, bbc, bbd, bbe)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_Maybe, bab)) → new_esEs2(vyy780, vyy790, bab)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy780, vyy790, bbg, bbh)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_Either, bgc), bgd)) → new_esEs3(vyy781, vyy791, bgc, bgd)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bg), bh)) → new_esEs3(vyy780, vyy790, bg, bh)
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_foldFM2(vyy79, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_Maybe, bgb)) → new_esEs2(vyy781, vyy791, bgb)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy780, vyy790, bca, bcb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_@2, hb), hc)) → new_esEs4(vyy782, vyy792, hb, hc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, dg), cg, da) → new_esEs2(vyy780, vyy790, dg)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(ty_Maybe, bdb)) → new_esEs2(vyy780, vyy790, bdb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, ca), cb)) → new_esEs4(vyy780, vyy790, ca, cb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_[], ga)) → new_esEs(vyy782, vyy792, ga)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_Either, bac), bad)) → new_esEs3(vyy780, vyy790, bac, bad)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_@2, bge), bgf)) → new_esEs4(vyy781, vyy791, bge, bgf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_[], ee), da) → new_esEs(vyy781, vyy791, ee)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, bef), bdh) → new_esEs2(vyy780, vyy790, bef)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_[], hd)) → new_esEs(vyy780, vyy790, hd)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, bba), bbb), bah) → new_esEs0(vyy780, vyy790, bba, bbb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_FiniteMap, ef), eg), da) → new_esEs0(vyy781, vyy791, ef, eg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_Either, gh), ha)) → new_esEs3(vyy782, vyy792, gh, ha)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, bfa), bfb), bdh) → new_esEs4(vyy780, vyy790, bfa, bfb)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs1(vyy780, vyy790, bcg, bch, bda)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_[], bag), bah) → new_esEs(vyy780, vyy790, bag)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy780, vyy790, bce, bcf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_[], bfd)) → new_esEs(vyy781, vyy791, bfd)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, bf)) → new_esEs2(vyy780, vyy790, bf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, db), dc), cg, da) → new_esEs0(vyy780, vyy790, db, dc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_@2, fg), fh), da) → new_esEs4(vyy781, vyy791, fg, fh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, dd), de), df), cg, da) → new_esEs1(vyy780, vyy790, dd, de, df)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_Maybe, bbf), bah) → new_esEs2(vyy780, vyy790, bbf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_Maybe, fc), da) → new_esEs2(vyy781, vyy791, fc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bc), bd), be)) → new_esEs1(vyy780, vyy790, bc, bd, be)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, bea), beb), bdh) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs1(vyy781, vyy791, bfg, bfh, bga)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], bdg), bdh) → new_esEs(vyy780, vyy790, bdg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, eb), ec), cg, da) → new_esEs4(vyy780, vyy790, eb, ec)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_Maybe, gg)) → new_esEs2(vyy782, vyy792, gg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], cf), cg, da) → new_esEs(vyy780, vyy790, cf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, beg), beh), bdh) → new_esEs3(vyy780, vyy790, beg, beh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, dh), ea), cg, da) → new_esEs3(vyy780, vyy790, dh, ea)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_@2, bae), baf)) → new_esEs4(vyy780, vyy790, bae, baf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], h)) → new_esEs(vyy780, vyy790, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy780, vyy790, ba, bb)

The TRS R consists of the following rules:

new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)

The set Q consists of the following terms:

new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)

We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].


The following pairs can be oriented strictly and are deleted.


new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy780, vyy790, bde, bdf)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(ty_[], bcd)) → new_esEs(vyy780, vyy790, bcd)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy780, vyy790, bdc, bdd)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bg), bh)) → new_esEs3(vyy780, vyy790, bg, bh)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(ty_Maybe, bdb)) → new_esEs2(vyy780, vyy790, bdb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, ca), cb)) → new_esEs4(vyy780, vyy790, ca, cb)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs1(vyy780, vyy790, bcg, bch, bda)
new_esEs3(Right(vyy780), Right(vyy790), bcc, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy780, vyy790, bce, bcf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, bf)) → new_esEs2(vyy780, vyy790, bf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bc), bd), be)) → new_esEs1(vyy780, vyy790, bc, bd, be)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], h)) → new_esEs(vyy780, vyy790, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy780, vyy790, ba, bb)
The remaining pairs can at least be oriented weakly.

new_esEs2(Just(vyy780), Just(vyy790), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy780, vyy790, hg, hh, baa)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, bec), bed), bee), bdh) → new_esEs1(vyy780, vyy790, bec, bed, bee)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_FiniteMap, gb), gc)) → new_esEs0(vyy782, vyy792, gb, gc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(app(ty_@3, eh), fa), fb), da) → new_esEs1(vyy781, vyy791, eh, fa, fb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_Either, fd), ff), da) → new_esEs3(vyy781, vyy791, fd, ff)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_FiniteMap, bfe), bff)) → new_esEs0(vyy781, vyy791, bfe, bff)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(app(ty_@3, gd), ge), gf)) → new_esEs1(vyy782, vyy792, gd, ge, gf)
new_esEs3(Left(vyy780), Left(vyy790), app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs1(vyy780, vyy790, bbc, bbd, bbe)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_Maybe, bab)) → new_esEs2(vyy780, vyy790, bab)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy780, vyy790, bbg, bbh)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_Either, bgc), bgd)) → new_esEs3(vyy781, vyy791, bgc, bgd)
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_foldFM2(vyy79, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_Maybe, bgb)) → new_esEs2(vyy781, vyy791, bgb)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy780, vyy790, bca, bcb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_@2, hb), hc)) → new_esEs4(vyy782, vyy792, hb, hc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, dg), cg, da) → new_esEs2(vyy780, vyy790, dg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_[], ga)) → new_esEs(vyy782, vyy792, ga)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_Either, bac), bad)) → new_esEs3(vyy780, vyy790, bac, bad)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_@2, bge), bgf)) → new_esEs4(vyy781, vyy791, bge, bgf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_[], ee), da) → new_esEs(vyy781, vyy791, ee)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, bef), bdh) → new_esEs2(vyy780, vyy790, bef)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_[], hd)) → new_esEs(vyy780, vyy790, hd)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, bba), bbb), bah) → new_esEs0(vyy780, vyy790, bba, bbb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_FiniteMap, ef), eg), da) → new_esEs0(vyy781, vyy791, ef, eg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_Either, gh), ha)) → new_esEs3(vyy782, vyy792, gh, ha)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, bfa), bfb), bdh) → new_esEs4(vyy780, vyy790, bfa, bfb)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_[], bag), bah) → new_esEs(vyy780, vyy790, bag)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_[], bfd)) → new_esEs(vyy781, vyy791, bfd)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, db), dc), cg, da) → new_esEs0(vyy780, vyy790, db, dc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_@2, fg), fh), da) → new_esEs4(vyy781, vyy791, fg, fh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, dd), de), df), cg, da) → new_esEs1(vyy780, vyy790, dd, de, df)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_Maybe, bbf), bah) → new_esEs2(vyy780, vyy790, bbf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_Maybe, fc), da) → new_esEs2(vyy781, vyy791, fc)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, bea), beb), bdh) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs1(vyy781, vyy791, bfg, bfh, bga)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], bdg), bdh) → new_esEs(vyy780, vyy790, bdg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, eb), ec), cg, da) → new_esEs4(vyy780, vyy790, eb, ec)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_Maybe, gg)) → new_esEs2(vyy782, vyy792, gg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], cf), cg, da) → new_esEs(vyy780, vyy790, cf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, beg), beh), bdh) → new_esEs3(vyy780, vyy790, beg, beh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, dh), ea), cg, da) → new_esEs3(vyy780, vyy790, dh, ea)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_@2, bae), baf)) → new_esEs4(vyy780, vyy790, bae, baf)
Used ordering: Polynomial interpretation [25]:

POL(:(x1, x2)) = 1 + x1 + x2   
POL(@2(x1, x2)) = x1 + x2   
POL(@3(x1, x2, x3)) = x1 + x2 + x3   
POL(Branch(x1, x2, x3, x4, x5)) = x1 + x2 + x4 + x5   
POL(EmptyFM) = 1   
POL(Just(x1)) = x1   
POL(Left(x1)) = x1   
POL(Right(x1)) = 1 + x1   
POL([]) = 0   
POL(app(x1, x2)) = 0   
POL(new_esEs(x1, x2, x3)) = x1   
POL(new_esEs0(x1, x2, x3, x4)) = x1   
POL(new_esEs1(x1, x2, x3, x4, x5)) = x1   
POL(new_esEs2(x1, x2, x3)) = x1   
POL(new_esEs3(x1, x2, x3, x4)) = x1   
POL(new_esEs4(x1, x2, x3, x4)) = x1   
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = x1 + x2 + x3 + x4   
POL(new_foldFM2(x1, x2, x3)) = x1   
POL(ty_@2) = 0   
POL(ty_@3) = 0   
POL(ty_Either) = 0   
POL(ty_FiniteMap) = 0   
POL(ty_Maybe) = 0   
POL(ty_[]) = 0   

The following usable rules [17] were oriented:

new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)



↳ 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

Q DP problem:
The TRS P consists of the following rules:

new_esEs2(Just(vyy780), Just(vyy790), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy780, vyy790, hg, hh, baa)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, bef), bdh) → new_esEs2(vyy780, vyy790, bef)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, bec), bed), bee), bdh) → new_esEs1(vyy780, vyy790, bec, bed, bee)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_[], hd)) → new_esEs(vyy780, vyy790, hd)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(app(ty_@3, eh), fa), fb), da) → new_esEs1(vyy781, vyy791, eh, fa, fb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_FiniteMap, gb), gc)) → new_esEs0(vyy782, vyy792, gb, gc)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, bba), bbb), bah) → new_esEs0(vyy780, vyy790, bba, bbb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_Either, fd), ff), da) → new_esEs3(vyy781, vyy791, fd, ff)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_FiniteMap, ef), eg), da) → new_esEs0(vyy781, vyy791, ef, eg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_Either, gh), ha)) → new_esEs3(vyy782, vyy792, gh, ha)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, bfa), bfb), bdh) → new_esEs4(vyy780, vyy790, bfa, bfb)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_FiniteMap, bfe), bff)) → new_esEs0(vyy781, vyy791, bfe, bff)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(app(ty_@3, gd), ge), gf)) → new_esEs1(vyy782, vyy792, gd, ge, gf)
new_esEs3(Left(vyy780), Left(vyy790), app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs1(vyy780, vyy790, bbc, bbd, bbe)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_[], bag), bah) → new_esEs(vyy780, vyy790, bag)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_Maybe, bab)) → new_esEs2(vyy780, vyy790, bab)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy780, vyy790, bbg, bbh)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_[], bfd)) → new_esEs(vyy781, vyy791, bfd)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, db), dc), cg, da) → new_esEs0(vyy780, vyy790, db, dc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, dd), de), df), cg, da) → new_esEs1(vyy780, vyy790, dd, de, df)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_@2, fg), fh), da) → new_esEs4(vyy781, vyy791, fg, fh)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_Maybe, bbf), bah) → new_esEs2(vyy780, vyy790, bbf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_Either, bgc), bgd)) → new_esEs3(vyy781, vyy791, bgc, bgd)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_Maybe, fc), da) → new_esEs2(vyy781, vyy791, fc)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, bea), beb), bdh) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_foldFM2(vyy79, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs1(vyy781, vyy791, bfg, bfh, bga)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], bdg), bdh) → new_esEs(vyy780, vyy790, bdg)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_Maybe, bgb)) → new_esEs2(vyy781, vyy791, bgb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, eb), ec), cg, da) → new_esEs4(vyy780, vyy790, eb, ec)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, beg), beh), bdh) → new_esEs3(vyy780, vyy790, beg, beh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], cf), cg, da) → new_esEs(vyy780, vyy790, cf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_Maybe, gg)) → new_esEs2(vyy782, vyy792, gg)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy780, vyy790, bca, bcb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_@2, hb), hc)) → new_esEs4(vyy782, vyy792, hb, hc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, dg), cg, da) → new_esEs2(vyy780, vyy790, dg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, dh), ea), cg, da) → new_esEs3(vyy780, vyy790, dh, ea)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_@2, bae), baf)) → new_esEs4(vyy780, vyy790, bae, baf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_[], ga)) → new_esEs(vyy782, vyy792, ga)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_Either, bac), bad)) → new_esEs3(vyy780, vyy790, bac, bad)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_@2, bge), bgf)) → new_esEs4(vyy781, vyy791, bge, bgf)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_[], ee), da) → new_esEs(vyy781, vyy791, ee)

The TRS R consists of the following rules:

new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)

The set Q consists of the following terms:

new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 15 less nodes.

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ Rewriting
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ QDP
                                                    ↳ QDPOrderProof
                                                      ↳ QDP
                                                        ↳ DependencyGraphProof
QDP
                                                            ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_esEs2(Just(vyy780), Just(vyy790), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy780, vyy790, hg, hh, baa)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, bef), bdh) → new_esEs2(vyy780, vyy790, bef)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, bec), bed), bee), bdh) → new_esEs1(vyy780, vyy790, bec, bed, bee)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(app(ty_@3, eh), fa), fb), da) → new_esEs1(vyy781, vyy791, eh, fa, fb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_Either, fd), ff), da) → new_esEs3(vyy781, vyy791, fd, ff)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_Either, gh), ha)) → new_esEs3(vyy782, vyy792, gh, ha)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, bfa), bfb), bdh) → new_esEs4(vyy780, vyy790, bfa, bfb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(app(ty_@3, gd), ge), gf)) → new_esEs1(vyy782, vyy792, gd, ge, gf)
new_esEs3(Left(vyy780), Left(vyy790), app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs1(vyy780, vyy790, bbc, bbd, bbe)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_Maybe, bab)) → new_esEs2(vyy780, vyy790, bab)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy780, vyy790, bbg, bbh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_@2, fg), fh), da) → new_esEs4(vyy781, vyy791, fg, fh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, dd), de), df), cg, da) → new_esEs1(vyy780, vyy790, dd, de, df)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_Maybe, bbf), bah) → new_esEs2(vyy780, vyy790, bbf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_Either, bgc), bgd)) → new_esEs3(vyy781, vyy791, bgc, bgd)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_Maybe, fc), da) → new_esEs2(vyy781, vyy791, fc)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs1(vyy781, vyy791, bfg, bfh, bga)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_Maybe, bgb)) → new_esEs2(vyy781, vyy791, bgb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, eb), ec), cg, da) → new_esEs4(vyy780, vyy790, eb, ec)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_Maybe, gg)) → new_esEs2(vyy782, vyy792, gg)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy780, vyy790, bca, bcb)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, beg), beh), bdh) → new_esEs3(vyy780, vyy790, beg, beh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_@2, hb), hc)) → new_esEs4(vyy782, vyy792, hb, hc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, dg), cg, da) → new_esEs2(vyy780, vyy790, dg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, dh), ea), cg, da) → new_esEs3(vyy780, vyy790, dh, ea)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_@2, bae), baf)) → new_esEs4(vyy780, vyy790, bae, baf)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_Either, bac), bad)) → new_esEs3(vyy780, vyy790, bac, bad)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_@2, bge), bgf)) → new_esEs4(vyy781, vyy791, bge, bgf)

The TRS R consists of the following rules:

new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)

The set Q consists of the following terms:

new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ Rewriting
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ QDP
                                                    ↳ QDPOrderProof
                                                      ↳ QDP
                                                        ↳ DependencyGraphProof
                                                          ↳ QDP
                                                            ↳ UsableRulesProof
QDP
                                                                ↳ QReductionProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_esEs2(Just(vyy780), Just(vyy790), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy780, vyy790, hg, hh, baa)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, bef), bdh) → new_esEs2(vyy780, vyy790, bef)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, bec), bed), bee), bdh) → new_esEs1(vyy780, vyy790, bec, bed, bee)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(app(ty_@3, eh), fa), fb), da) → new_esEs1(vyy781, vyy791, eh, fa, fb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_Either, fd), ff), da) → new_esEs3(vyy781, vyy791, fd, ff)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_Either, gh), ha)) → new_esEs3(vyy782, vyy792, gh, ha)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, bfa), bfb), bdh) → new_esEs4(vyy780, vyy790, bfa, bfb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(app(ty_@3, gd), ge), gf)) → new_esEs1(vyy782, vyy792, gd, ge, gf)
new_esEs3(Left(vyy780), Left(vyy790), app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs1(vyy780, vyy790, bbc, bbd, bbe)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_Maybe, bab)) → new_esEs2(vyy780, vyy790, bab)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy780, vyy790, bbg, bbh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_@2, fg), fh), da) → new_esEs4(vyy781, vyy791, fg, fh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, dd), de), df), cg, da) → new_esEs1(vyy780, vyy790, dd, de, df)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_Maybe, bbf), bah) → new_esEs2(vyy780, vyy790, bbf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_Either, bgc), bgd)) → new_esEs3(vyy781, vyy791, bgc, bgd)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_Maybe, fc), da) → new_esEs2(vyy781, vyy791, fc)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs1(vyy781, vyy791, bfg, bfh, bga)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_Maybe, bgb)) → new_esEs2(vyy781, vyy791, bgb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, eb), ec), cg, da) → new_esEs4(vyy780, vyy790, eb, ec)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_Maybe, gg)) → new_esEs2(vyy782, vyy792, gg)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy780, vyy790, bca, bcb)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, beg), beh), bdh) → new_esEs3(vyy780, vyy790, beg, beh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_@2, hb), hc)) → new_esEs4(vyy782, vyy792, hb, hc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, dg), cg, da) → new_esEs2(vyy780, vyy790, dg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, dh), ea), cg, da) → new_esEs3(vyy780, vyy790, dh, ea)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_@2, bae), baf)) → new_esEs4(vyy780, vyy790, bae, baf)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_Either, bac), bad)) → new_esEs3(vyy780, vyy790, bac, bad)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_@2, bge), bgf)) → new_esEs4(vyy781, vyy791, bge, bgf)

R is empty.
The set Q consists of the following terms:

new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ Rewriting
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ QDP
                                                    ↳ QDPOrderProof
                                                      ↳ QDP
                                                        ↳ DependencyGraphProof
                                                          ↳ QDP
                                                            ↳ UsableRulesProof
                                                              ↳ QDP
                                                                ↳ QReductionProof
QDP
                                                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_esEs2(Just(vyy780), Just(vyy790), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy780, vyy790, hg, hh, baa)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, bef), bdh) → new_esEs2(vyy780, vyy790, bef)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, bec), bed), bee), bdh) → new_esEs1(vyy780, vyy790, bec, bed, bee)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(app(ty_@3, eh), fa), fb), da) → new_esEs1(vyy781, vyy791, eh, fa, fb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_Either, fd), ff), da) → new_esEs3(vyy781, vyy791, fd, ff)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_Either, gh), ha)) → new_esEs3(vyy782, vyy792, gh, ha)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, bfa), bfb), bdh) → new_esEs4(vyy780, vyy790, bfa, bfb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(app(ty_@3, gd), ge), gf)) → new_esEs1(vyy782, vyy792, gd, ge, gf)
new_esEs3(Left(vyy780), Left(vyy790), app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs1(vyy780, vyy790, bbc, bbd, bbe)
new_esEs2(Just(vyy780), Just(vyy790), app(ty_Maybe, bab)) → new_esEs2(vyy780, vyy790, bab)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy780, vyy790, bbg, bbh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, dd), de), df), cg, da) → new_esEs1(vyy780, vyy790, dd, de, df)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(app(ty_@2, fg), fh), da) → new_esEs4(vyy781, vyy791, fg, fh)
new_esEs3(Left(vyy780), Left(vyy790), app(ty_Maybe, bbf), bah) → new_esEs2(vyy780, vyy790, bbf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_Either, bgc), bgd)) → new_esEs3(vyy781, vyy791, bgc, bgd)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, app(ty_Maybe, fc), da) → new_esEs2(vyy781, vyy791, fc)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs1(vyy781, vyy791, bfg, bfh, bga)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(ty_Maybe, bgb)) → new_esEs2(vyy781, vyy791, bgb)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, eb), ec), cg, da) → new_esEs4(vyy780, vyy790, eb, ec)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(ty_Maybe, gg)) → new_esEs2(vyy782, vyy792, gg)
new_esEs3(Left(vyy780), Left(vyy790), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy780, vyy790, bca, bcb)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, beg), beh), bdh) → new_esEs3(vyy780, vyy790, beg, beh)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ed, cg, app(app(ty_@2, hb), hc)) → new_esEs4(vyy782, vyy792, hb, hc)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, dg), cg, da) → new_esEs2(vyy780, vyy790, dg)
new_esEs1(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, dh), ea), cg, da) → new_esEs3(vyy780, vyy790, dh, ea)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_@2, bae), baf)) → new_esEs4(vyy780, vyy790, bae, baf)
new_esEs4(@2(vyy780, vyy781), @2(vyy790, vyy791), bfc, app(app(ty_@2, bge), bgf)) → new_esEs4(vyy781, vyy791, bge, bgf)
new_esEs2(Just(vyy780), Just(vyy790), app(app(ty_Either, bac), bad)) → new_esEs3(vyy780, vyy790, bac, bad)

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:



↳ 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

Q DP problem:
The TRS P consists of the following rules:

new_primCmpNat(Succ(vyy3000), Succ(vyy400)) → new_primCmpNat(vyy3000, vyy400)

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:



↳ 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

Q DP problem:
The TRS P consists of the following rules:

new_ltEs0(Left(vyy300), Left(vyy40), app(ty_[], ga), fb) → new_ltEs3(vyy300, vyy40, ga)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(app(ty_@2, bbd), bbe), bah) → new_lt2(vyy300, vyy40, bbd, bbe)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(ty_[], bbf), bah) → new_lt3(vyy300, vyy40, bbf)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), cc, bc, app(app(ty_@2, ed), ee)) → new_ltEs2(vyy302, vyy42, ed, ee)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), bbg, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs(vyy301, vyy41, bbh, bca, bcb)
new_ltEs0(Right(vyy300), Right(vyy40), gb, app(app(app(ty_@3, gc), gd), ge)) → new_ltEs(vyy300, vyy40, gc, gd, ge)
new_lt(vyy300, vyy40, h, ba, bb) → new_compare2(vyy300, vyy40, new_esEs5(vyy300, vyy40, h, ba, bb), h, ba, bb)
new_primCompAux(vyy300, vyy40, vyy107, app(app(app(ty_@3, bdb), bdc), bdd)) → new_compare0(vyy300, vyy40, bdb, bdc, bdd)
new_ltEs1(Just(vyy300), Just(vyy40), app(ty_Maybe, baa)) → new_ltEs1(vyy300, vyy40, baa)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(app(ty_Either, bba), bbb), bah) → new_lt0(vyy300, vyy40, bba, bbb)
new_ltEs0(Left(vyy300), Left(vyy40), app(app(ty_Either, fc), fd), fb) → new_ltEs0(vyy300, vyy40, fc, fd)
new_ltEs1(Just(vyy300), Just(vyy40), app(app(app(ty_@3, hd), he), hf)) → new_ltEs(vyy300, vyy40, hd, he, hf)
new_primCompAux(vyy300, vyy40, vyy107, app(ty_[], beb)) → new_compare(vyy300, vyy40, beb)
new_ltEs3(:(vyy300, vyy301), :(vyy40, vyy41), bda) → new_compare(vyy301, vyy41, bda)
new_compare0(vyy300, vyy40, h, ba, bb) → new_compare2(vyy300, vyy40, new_esEs5(vyy300, vyy40, h, ba, bb), h, ba, bb)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), bbg, app(ty_[], bch)) → new_ltEs3(vyy301, vyy41, bch)
new_ltEs1(Just(vyy300), Just(vyy40), app(app(ty_Either, hg), hh)) → new_ltEs0(vyy300, vyy40, hg, hh)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(app(ty_Either, be), bf), bc, bd) → new_compare20(vyy300, vyy40, new_esEs6(vyy300, vyy40, be, bf), be, bf)
new_ltEs0(Left(vyy300), Left(vyy40), app(app(app(ty_@3, eg), eh), fa), fb) → new_ltEs(vyy300, vyy40, eg, eh, fa)
new_compare(:(vyy300, vyy301), :(vyy40, vyy41), bda) → new_primCompAux(vyy300, vyy40, new_compare5(vyy301, vyy41, bda), bda)
new_compare20(vyy300, vyy40, False, be, bf) → new_ltEs0(vyy300, vyy40, be, bf)
new_ltEs3(:(vyy300, vyy301), :(vyy40, vyy41), bda) → new_primCompAux(vyy300, vyy40, new_compare5(vyy301, vyy41, bda), bda)
new_primCompAux(vyy300, vyy40, vyy107, app(app(ty_Either, bde), bdf)) → new_compare1(vyy300, vyy40, bde, bdf)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(app(ty_@2, bh), ca), bc, bd) → new_compare22(vyy300, vyy40, new_esEs8(vyy300, vyy40, bh, ca), bh, ca)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(app(app(ty_@3, h), ba), bb), bc, bd) → new_compare2(vyy300, vyy40, new_esEs5(vyy300, vyy40, h, ba, bb), h, ba, bb)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), cc, app(app(ty_@2, dc), dd), bd) → new_lt2(vyy301, vyy41, dc, dd)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(ty_Maybe, bbc), bah) → new_lt1(vyy300, vyy40, bbc)
new_ltEs1(Just(vyy300), Just(vyy40), app(app(ty_@2, bab), bac)) → new_ltEs2(vyy300, vyy40, bab, bac)
new_ltEs0(Right(vyy300), Right(vyy40), gb, app(app(ty_Either, gf), gg)) → new_ltEs0(vyy300, vyy40, gf, gg)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), bbg, app(ty_Maybe, bce)) → new_ltEs1(vyy301, vyy41, bce)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(app(app(ty_@3, bae), baf), bag), bah) → new_lt(vyy300, vyy40, bae, baf, bag)
new_ltEs0(Right(vyy300), Right(vyy40), gb, app(ty_[], hc)) → new_ltEs3(vyy300, vyy40, hc)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), cc, app(app(app(ty_@3, cd), ce), cf), bd) → new_lt(vyy301, vyy41, cd, ce, cf)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), cc, bc, app(ty_Maybe, ec)) → new_ltEs1(vyy302, vyy42, ec)
new_lt2(vyy300, vyy40, bh, ca) → new_compare22(vyy300, vyy40, new_esEs8(vyy300, vyy40, bh, ca), bh, ca)
new_lt1(vyy300, vyy40, bg) → new_compare21(vyy300, vyy40, new_esEs7(vyy300, vyy40, bg), bg)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), cc, bc, app(app(ty_Either, ea), eb)) → new_ltEs0(vyy302, vyy42, ea, eb)
new_ltEs0(Left(vyy300), Left(vyy40), app(app(ty_@2, fg), fh), fb) → new_ltEs2(vyy300, vyy40, fg, fh)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), bbg, app(app(ty_@2, bcf), bcg)) → new_ltEs2(vyy301, vyy41, bcf, bcg)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), cc, bc, app(ty_[], ef)) → new_ltEs3(vyy302, vyy42, ef)
new_compare(:(vyy300, vyy301), :(vyy40, vyy41), bda) → new_compare(vyy301, vyy41, bda)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), cc, app(ty_[], de), bd) → new_lt3(vyy301, vyy41, de)
new_lt3(vyy300, vyy40, cb) → new_compare(vyy300, vyy40, cb)
new_lt0(vyy300, vyy40, be, bf) → new_compare20(vyy300, vyy40, new_esEs6(vyy300, vyy40, be, bf), be, bf)
new_compare2(vyy300, vyy40, False, h, ba, bb) → new_ltEs(vyy300, vyy40, h, ba, bb)
new_compare3(vyy300, vyy40, bg) → new_compare21(vyy300, vyy40, new_esEs7(vyy300, vyy40, bg), bg)
new_ltEs1(Just(vyy300), Just(vyy40), app(ty_[], bad)) → new_ltEs3(vyy300, vyy40, bad)
new_ltEs0(Right(vyy300), Right(vyy40), gb, app(app(ty_@2, ha), hb)) → new_ltEs2(vyy300, vyy40, ha, hb)
new_primCompAux(vyy300, vyy40, vyy107, app(app(ty_@2, bdh), bea)) → new_compare4(vyy300, vyy40, bdh, bea)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), bbg, app(app(ty_Either, bcc), bcd)) → new_ltEs0(vyy301, vyy41, bcc, bcd)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(ty_[], cb), bc, bd) → new_compare(vyy300, vyy40, cb)
new_compare4(vyy300, vyy40, bh, ca) → new_compare22(vyy300, vyy40, new_esEs8(vyy300, vyy40, bh, ca), bh, ca)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(ty_Maybe, bg), bc, bd) → new_compare21(vyy300, vyy40, new_esEs7(vyy300, vyy40, bg), bg)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), cc, bc, app(app(app(ty_@3, df), dg), dh)) → new_ltEs(vyy302, vyy42, df, dg, dh)
new_compare22(vyy300, vyy40, False, bh, ca) → new_ltEs2(vyy300, vyy40, bh, ca)
new_ltEs0(Right(vyy300), Right(vyy40), gb, app(ty_Maybe, gh)) → new_ltEs1(vyy300, vyy40, gh)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), cc, app(ty_Maybe, db), bd) → new_lt1(vyy301, vyy41, db)
new_compare21(vyy300, vyy40, False, bg) → new_ltEs1(vyy300, vyy40, bg)
new_compare1(vyy300, vyy40, be, bf) → new_compare20(vyy300, vyy40, new_esEs6(vyy300, vyy40, be, bf), be, bf)
new_primCompAux(vyy300, vyy40, vyy107, app(ty_Maybe, bdg)) → new_compare3(vyy300, vyy40, bdg)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), cc, app(app(ty_Either, cg), da), bd) → new_lt0(vyy301, vyy41, cg, da)
new_ltEs0(Left(vyy300), Left(vyy40), app(ty_Maybe, ff), fb) → new_ltEs1(vyy300, vyy40, ff)

The TRS R consists of the following rules:

new_esEs7(Just(vyy780), Just(vyy790), app(ty_Maybe, cgd)) → new_esEs7(vyy780, vyy790, cgd)
new_ltEs19(vyy302, vyy42, ty_Ordering) → new_ltEs12(vyy302, vyy42)
new_compare28(Float(vyy300, vyy301), Float(vyy40, vyy41)) → new_compare29(new_sr(vyy300, vyy40), new_sr(vyy301, vyy41))
new_lt19(vyy300, vyy40, ty_Char) → new_lt7(vyy300, vyy40)
new_lt19(vyy300, vyy40, ty_Int) → new_lt18(vyy300, vyy40)
new_lt19(vyy300, vyy40, app(app(ty_Either, be), bf)) → new_lt14(vyy300, vyy40, be, bf)
new_esEs20(True, True) → True
new_lt16(vyy300, vyy40, bg) → new_esEs14(new_compare9(vyy300, vyy40, bg))
new_compare9(vyy300, vyy40, bg) → new_compare25(vyy300, vyy40, new_esEs7(vyy300, vyy40, bg), bg)
new_esEs17(vyy782, vyy792, ty_Ordering) → new_esEs25(vyy782, vyy792)
new_lt14(vyy300, vyy40, be, bf) → new_esEs14(new_compare6(vyy300, vyy40, be, bf))
new_esEs15(vyy780, vyy790, ty_Char) → new_esEs24(vyy780, vyy790)
new_compare15(vyy300, vyy40, app(app(app(ty_@3, bdb), bdc), bdd)) → new_compare17(vyy300, vyy40, bdb, bdc, bdd)
new_esEs6(Left(vyy780), Left(vyy790), ty_Char, cfe) → new_esEs24(vyy780, vyy790)
new_ltEs12(LT, GT) → True
new_ltEs11(Left(vyy300), Left(vyy40), ty_Char, fb) → new_ltEs15(vyy300, vyy40)
new_ltEs19(vyy302, vyy42, ty_Char) → new_ltEs15(vyy302, vyy42)
new_compare110(vyy300, vyy40, True, bh, ca) → LT
new_esEs29(vyy780, vyy790, ty_Integer) → new_esEs13(vyy780, vyy790)
new_esEs17(vyy782, vyy792, ty_Char) → new_esEs24(vyy782, vyy792)
new_ltEs18(Just(vyy300), Just(vyy40), app(ty_Maybe, baa)) → new_ltEs18(vyy300, vyy40, baa)
new_esEs27(vyy781, vyy791, app(ty_Maybe, ceb)) → new_esEs7(vyy781, vyy791, ceb)
new_lt20(vyy301, vyy41, app(app(ty_Either, cg), da)) → new_lt14(vyy301, vyy41, cg, da)
new_esEs25(GT, GT) → True
new_compare14(vyy300, vyy40, True, h, ba, bb) → LT
new_lt7(vyy300, vyy40) → new_esEs14(new_compare16(vyy300, vyy40))
new_esEs28(vyy78, vyy79, ty_Float) → new_esEs21(vyy78, vyy79)
new_ltEs14(vyy301, vyy41, app(app(ty_@2, bcf), bcg)) → new_ltEs8(vyy301, vyy41, bcf, bcg)
new_esEs7(Just(vyy780), Just(vyy790), app(app(ty_Either, cgf), cgg)) → new_esEs6(vyy780, vyy790, cgf, cgg)
new_primMulNat0(Zero, Zero) → Zero
new_lt12(vyy300, vyy40, app(app(ty_@2, bbd), bbe)) → new_lt4(vyy300, vyy40, bbd, bbe)
new_ltEs14(vyy301, vyy41, ty_Ordering) → new_ltEs12(vyy301, vyy41)
new_ltEs11(Right(vyy300), Left(vyy40), gb, fb) → False
new_esEs6(Right(vyy780), Right(vyy790), cfd, ty_Float) → new_esEs21(vyy780, vyy790)
new_ltEs12(LT, LT) → True
new_esEs6(Right(vyy780), Right(vyy790), cfd, app(ty_Ratio, dcb)) → new_esEs9(vyy780, vyy790, dcb)
new_esEs26(vyy780, vyy790, ty_@0) → new_esEs22(vyy780, vyy790)
new_compare25(vyy300, vyy40, True, bg) → EQ
new_ltEs18(Just(vyy300), Just(vyy40), ty_Bool) → new_ltEs4(vyy300, vyy40)
new_esEs27(vyy781, vyy791, ty_Bool) → new_esEs20(vyy781, vyy791)
new_esEs26(vyy780, vyy790, ty_Ordering) → new_esEs25(vyy780, vyy790)
new_lt20(vyy301, vyy41, ty_Int) → new_lt18(vyy301, vyy41)
new_lt12(vyy300, vyy40, ty_Integer) → new_lt6(vyy300, vyy40)
new_not(GT) → False
new_lt19(vyy300, vyy40, app(app(app(ty_@3, h), ba), bb)) → new_lt9(vyy300, vyy40, h, ba, bb)
new_esEs29(vyy780, vyy790, app(ty_Maybe, dde)) → new_esEs7(vyy780, vyy790, dde)
new_compare18(vyy300, vyy40) → new_compare23(vyy300, vyy40, new_esEs20(vyy300, vyy40))
new_esEs27(vyy781, vyy791, app(app(ty_@2, cef), ceg)) → new_esEs8(vyy781, vyy791, cef, ceg)
new_esEs27(vyy781, vyy791, app(ty_Ratio, cec)) → new_esEs9(vyy781, vyy791, cec)
new_esEs10(vyy780, vyy790, ty_Int) → new_esEs12(vyy780, vyy790)
new_esEs16(vyy781, vyy791, app(app(ty_Either, bhc), bhd)) → new_esEs6(vyy781, vyy791, bhc, bhd)
new_ltEs12(LT, EQ) → True
new_compare17(vyy300, vyy40, h, ba, bb) → new_compare210(vyy300, vyy40, new_esEs5(vyy300, vyy40, h, ba, bb), h, ba, bb)
new_esEs15(vyy780, vyy790, app(app(app(ty_@3, bfb), bfc), bfd)) → new_esEs5(vyy780, vyy790, bfb, bfc, bfd)
new_ltEs11(Left(vyy300), Left(vyy40), app(ty_Maybe, ff), fb) → new_ltEs18(vyy300, vyy40, ff)
new_ltEs19(vyy302, vyy42, ty_Bool) → new_ltEs4(vyy302, vyy42)
new_ltEs4(False, True) → True
new_ltEs18(Just(vyy300), Just(vyy40), ty_Float) → new_ltEs17(vyy300, vyy40)
new_esEs27(vyy781, vyy791, ty_Integer) → new_esEs13(vyy781, vyy791)
new_esEs6(Right(vyy780), Right(vyy790), cfd, app(app(ty_FiniteMap, dbd), dbe)) → new_esEs19(vyy780, vyy790, dbd, dbe)
new_esEs16(vyy781, vyy791, app(app(ty_FiniteMap, bgd), bge)) → new_esEs19(vyy781, vyy791, bgd, bge)
new_esEs6(Right(vyy780), Right(vyy790), cfd, ty_Ordering) → new_esEs25(vyy780, vyy790)
new_ltEs6(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), cc, bc, bd) → new_pePe(new_lt19(vyy300, vyy40, cc), vyy300, vyy40, new_pePe(new_lt20(vyy301, vyy41, bc), vyy301, vyy41, new_ltEs19(vyy302, vyy42, bd), bc), cc)
new_esEs28(vyy78, vyy79, app(app(app(ty_@3, bed), bee), bef)) → new_esEs5(vyy78, vyy79, bed, bee, bef)
new_esEs7(Just(vyy780), Just(vyy790), app(ty_Ratio, cge)) → new_esEs9(vyy780, vyy790, cge)
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cbc, cbd) → :(@2(vyy790, vyy791), vyy125)
new_ltEs19(vyy302, vyy42, app(app(ty_@2, ed), ee)) → new_ltEs8(vyy302, vyy42, ed, ee)
new_esEs6(Left(vyy780), Left(vyy790), ty_Int, cfe) → new_esEs12(vyy780, vyy790)
new_ltEs11(Left(vyy300), Left(vyy40), ty_Bool, fb) → new_ltEs4(vyy300, vyy40)
new_ltEs4(True, True) → True
new_esEs26(vyy780, vyy790, app(app(ty_@2, cdb), cdc)) → new_esEs8(vyy780, vyy790, cdb, cdc)
new_esEs18(:(vyy780, vyy781), [], cfb) → False
new_esEs18([], :(vyy790, vyy791), cfb) → False
new_esEs17(vyy782, vyy792, app(app(ty_FiniteMap, bhh), caa)) → new_esEs19(vyy782, vyy792, bhh, caa)
new_esEs26(vyy780, vyy790, ty_Bool) → new_esEs20(vyy780, vyy790)
new_lt12(vyy300, vyy40, app(app(ty_Either, bba), bbb)) → new_lt14(vyy300, vyy40, bba, bbb)
new_esEs17(vyy782, vyy792, app(ty_Maybe, cae)) → new_esEs7(vyy782, vyy792, cae)
new_esEs18(:(vyy780, vyy781), :(vyy790, vyy791), cfb) → new_asAs(new_esEs29(vyy780, vyy790, cfb), new_esEs18(vyy781, vyy791, cfb))
new_compare23(vyy300, vyy40, True) → EQ
new_lt19(vyy300, vyy40, ty_Integer) → new_lt6(vyy300, vyy40)
new_esEs16(vyy781, vyy791, ty_Ordering) → new_esEs25(vyy781, vyy791)
new_lt12(vyy300, vyy40, ty_Int) → new_lt18(vyy300, vyy40)
new_esEs16(vyy781, vyy791, app(ty_Ratio, bhb)) → new_esEs9(vyy781, vyy791, bhb)
new_esEs15(vyy780, vyy790, ty_Ordering) → new_esEs25(vyy780, vyy790)
new_ltEs18(Just(vyy300), Just(vyy40), app(app(ty_@2, bab), bac)) → new_ltEs8(vyy300, vyy40, bab, bac)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Char) → new_ltEs15(vyy300, vyy40)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Ordering) → new_ltEs12(vyy300, vyy40)
new_ltEs14(vyy301, vyy41, app(ty_Maybe, bce)) → new_ltEs18(vyy301, vyy41, bce)
new_lt20(vyy301, vyy41, app(ty_Maybe, db)) → new_lt16(vyy301, vyy41, db)
new_primCmpNat0(Zero, Succ(vyy400)) → LT
new_lt12(vyy300, vyy40, ty_@0) → new_lt11(vyy300, vyy40)
new_ltEs18(Just(vyy300), Just(vyy40), app(ty_Ratio, ded)) → new_ltEs10(vyy300, vyy40, ded)
new_esEs8(@2(vyy780, vyy781), @2(vyy790, vyy791), cbf, cbg) → new_asAs(new_esEs26(vyy780, vyy790, cbf), new_esEs27(vyy781, vyy791, cbg))
new_ltEs11(Right(vyy300), Right(vyy40), gb, ty_Int) → new_ltEs9(vyy300, vyy40)
new_esEs15(vyy780, vyy790, ty_Bool) → new_esEs20(vyy780, vyy790)
new_esEs6(Right(vyy780), Left(vyy790), cfd, cfe) → False
new_esEs6(Left(vyy780), Right(vyy790), cfd, cfe) → False
new_ltEs11(Left(vyy300), Left(vyy40), ty_Double, fb) → new_ltEs5(vyy300, vyy40)
new_ltEs11(Left(vyy300), Left(vyy40), ty_Int, fb) → new_ltEs9(vyy300, vyy40)
new_compare15(vyy300, vyy40, ty_Double) → new_compare8(vyy300, vyy40)
new_compare8(Double(vyy300, vyy301), Double(vyy40, vyy41)) → new_compare29(new_sr(vyy300, vyy40), new_sr(vyy301, vyy41))
new_ltEs17(vyy30, vyy4) → new_not(new_compare28(vyy30, vyy4))
new_ltEs15(vyy30, vyy4) → new_not(new_compare16(vyy30, vyy4))
new_ltEs16(vyy30, vyy4) → new_not(new_compare27(vyy30, vyy4))
new_esEs17(vyy782, vyy792, ty_@0) → new_esEs22(vyy782, vyy792)
new_ltEs11(Right(vyy300), Right(vyy40), gb, ty_Bool) → new_ltEs4(vyy300, vyy40)
new_ltEs18(Just(vyy300), Just(vyy40), app(app(app(ty_@3, hd), he), hf)) → new_ltEs6(vyy300, vyy40, hd, he, hf)
new_primEqNat0(Zero, Zero) → True
new_compare26(vyy300, vyy40, True) → EQ
new_lt12(vyy300, vyy40, ty_Char) → new_lt7(vyy300, vyy40)
new_compare11(vyy300, vyy40, True, bg) → LT
new_primMulNat0(Succ(vyy30000), Succ(vyy4100)) → new_primPlusNat1(new_primMulNat0(vyy30000, Succ(vyy4100)), vyy4100)
new_compare111(vyy300, vyy40, False, be, bf) → GT
new_ltEs11(Right(vyy300), Right(vyy40), gb, ty_Integer) → new_ltEs7(vyy300, vyy40)
new_compare29(vyy30, vyy4) → new_primCmpInt(vyy30, vyy4)
new_esEs6(Right(vyy780), Right(vyy790), cfd, app(app(ty_Either, dcc), dcd)) → new_esEs6(vyy780, vyy790, dcc, dcd)
new_lt8(vyy300, vyy40) → new_esEs14(new_compare28(vyy300, vyy40))
new_esEs28(vyy78, vyy79, ty_Ordering) → new_esEs25(vyy78, vyy79)
new_esEs15(vyy780, vyy790, app(app(ty_FiniteMap, beh), bfa)) → new_esEs19(vyy780, vyy790, beh, bfa)
new_ltEs11(Left(vyy300), Left(vyy40), ty_Float, fb) → new_ltEs17(vyy300, vyy40)
new_compare110(vyy300, vyy40, False, bh, ca) → GT
new_lt13(vyy300, vyy40) → new_esEs14(new_compare18(vyy300, vyy40))
new_compare19(:%(vyy300, vyy301), :%(vyy40, vyy41), ty_Int) → new_compare29(new_sr(vyy300, vyy41), new_sr(vyy40, vyy301))
new_ltEs18(Just(vyy300), Just(vyy40), app(ty_[], bad)) → new_ltEs13(vyy300, vyy40, bad)
new_sr(vyy300, vyy41) → new_primMulInt(vyy300, vyy41)
new_esEs28(vyy78, vyy79, app(app(ty_Either, cfd), cfe)) → new_esEs6(vyy78, vyy79, cfd, cfe)
new_esEs7(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, cfg), cfh)) → new_esEs19(vyy780, vyy790, cfg, cfh)
new_esEs17(vyy782, vyy792, app(app(app(ty_@3, cab), cac), cad)) → new_esEs5(vyy782, vyy792, cab, cac, cad)
new_esEs29(vyy780, vyy790, ty_Bool) → new_esEs20(vyy780, vyy790)
new_esEs26(vyy780, vyy790, ty_Int) → new_esEs12(vyy780, vyy790)
new_ltEs7(vyy30, vyy4) → new_not(new_compare13(vyy30, vyy4))
new_esEs19(vyy78, vyy79, cbc, cbd) → new_asAs(new_esEs12(new_sizeFM(vyy78, cbc, cbd), new_sizeFM(vyy79, cbc, cbd)), new_esEs18(new_fmToList(vyy78, cbc, cbd), new_fmToList(vyy79, cbc, cbd), app(app(ty_@2, cbc), cbd)))
new_esEs29(vyy780, vyy790, app(app(ty_FiniteMap, dch), dda)) → new_esEs19(vyy780, vyy790, dch, dda)
new_lt12(vyy300, vyy40, app(ty_Maybe, bbc)) → new_lt16(vyy300, vyy40, bbc)
new_compare15(vyy300, vyy40, app(ty_[], beb)) → new_compare5(vyy300, vyy40, beb)
new_esEs29(vyy780, vyy790, ty_Float) → new_esEs21(vyy780, vyy790)
new_esEs6(Right(vyy780), Right(vyy790), cfd, ty_Bool) → new_esEs20(vyy780, vyy790)
new_lt20(vyy301, vyy41, ty_Double) → new_lt17(vyy301, vyy41)
new_compare23(vyy300, vyy40, False) → new_compare10(vyy300, vyy40, new_ltEs4(vyy300, vyy40))
new_ltEs14(vyy301, vyy41, app(ty_Ratio, chc)) → new_ltEs10(vyy301, vyy41, chc)
new_esEs25(EQ, EQ) → True
new_esEs13(Integer(vyy780), Integer(vyy790)) → new_primEqInt(vyy780, vyy790)
new_esEs15(vyy780, vyy790, ty_Double) → new_esEs23(vyy780, vyy790)
new_esEs27(vyy781, vyy791, ty_Float) → new_esEs21(vyy781, vyy791)
new_esEs29(vyy780, vyy790, ty_Int) → new_esEs12(vyy780, vyy790)
new_ltEs8(@2(vyy300, vyy301), @2(vyy40, vyy41), bbg, bah) → new_pePe(new_lt12(vyy300, vyy40, bbg), vyy300, vyy40, new_ltEs14(vyy301, vyy41, bah), bbg)
new_esEs7(Just(vyy780), Just(vyy790), ty_Ordering) → new_esEs25(vyy780, vyy790)
new_primEqInt(Neg(Succ(vyy7800)), Neg(Succ(vyy7900))) → new_primEqNat0(vyy7800, vyy7900)
new_ltEs11(Right(vyy300), Right(vyy40), gb, app(app(ty_@2, ha), hb)) → new_ltEs8(vyy300, vyy40, ha, hb)
new_esEs14(EQ) → False
new_compare15(vyy300, vyy40, ty_Integer) → new_compare13(vyy300, vyy40)
new_lt19(vyy300, vyy40, app(app(ty_@2, bh), ca)) → new_lt4(vyy300, vyy40, bh, ca)
new_ltEs19(vyy302, vyy42, ty_Double) → new_ltEs5(vyy302, vyy42)
new_esEs15(vyy780, vyy790, ty_Integer) → new_esEs13(vyy780, vyy790)
new_ltEs11(Right(vyy300), Right(vyy40), gb, app(ty_Ratio, def)) → new_ltEs10(vyy300, vyy40, def)
new_ltEs11(Right(vyy300), Right(vyy40), gb, app(ty_[], hc)) → new_ltEs13(vyy300, vyy40, hc)
new_esEs11(vyy781, vyy791, ty_Int) → new_esEs12(vyy781, vyy791)
new_esEs6(Right(vyy780), Right(vyy790), cfd, app(app(ty_@2, dce), dcf)) → new_esEs8(vyy780, vyy790, dce, dcf)
new_compare211(vyy300, vyy40, False, bh, ca) → new_compare110(vyy300, vyy40, new_ltEs8(vyy300, vyy40, bh, ca), bh, ca)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs6(Left(vyy780), Left(vyy790), ty_Integer, cfe) → new_esEs13(vyy780, vyy790)
new_esEs17(vyy782, vyy792, app(ty_[], bhg)) → new_esEs18(vyy782, vyy792, bhg)
new_esEs28(vyy78, vyy79, app(app(ty_FiniteMap, cbc), cbd)) → new_esEs19(vyy78, vyy79, cbc, cbd)
new_esEs27(vyy781, vyy791, ty_Int) → new_esEs12(vyy781, vyy791)
new_compare15(vyy300, vyy40, app(ty_Ratio, cbe)) → new_compare19(vyy300, vyy40, cbe)
new_ltEs12(EQ, EQ) → True
new_esEs29(vyy780, vyy790, ty_Char) → new_esEs24(vyy780, vyy790)
new_ltEs5(vyy30, vyy4) → new_not(new_compare8(vyy30, vyy4))
new_compare7(vyy300, vyy40, bh, ca) → new_compare211(vyy300, vyy40, new_esEs8(vyy300, vyy40, bh, ca), bh, ca)
new_primEqInt(Neg(Zero), Neg(Succ(vyy7900))) → False
new_primEqInt(Neg(Succ(vyy7800)), Neg(Zero)) → False
new_esEs10(vyy780, vyy790, ty_Integer) → new_esEs13(vyy780, vyy790)
new_primPlusNat1(Zero, vyy4100) → Succ(vyy4100)
new_esEs25(LT, LT) → True
new_esEs28(vyy78, vyy79, ty_Char) → new_esEs24(vyy78, vyy79)
new_compare24(vyy300, vyy40, True, be, bf) → EQ
new_esEs26(vyy780, vyy790, app(ty_[], cbh)) → new_esEs18(vyy780, vyy790, cbh)
new_compare15(vyy300, vyy40, ty_Int) → new_compare29(vyy300, vyy40)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cbc, cbd) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cbc, cbd), vyy7933, cbc, cbd)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs15(vyy780, vyy790, app(ty_Ratio, bff)) → new_esEs9(vyy780, vyy790, bff)
new_primCmpNat0(Succ(vyy3000), Succ(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_sizeFM(EmptyFM, cbc, cbd) → Pos(Zero)
new_esEs15(vyy780, vyy790, ty_Float) → new_esEs21(vyy780, vyy790)
new_compare5(:(vyy300, vyy301), [], bda) → GT
new_compare112(vyy300, vyy40, True) → LT
new_compare11(vyy300, vyy40, False, bg) → GT
new_primEqInt(Pos(Succ(vyy7800)), Pos(Succ(vyy7900))) → new_primEqNat0(vyy7800, vyy7900)
new_esEs17(vyy782, vyy792, app(ty_Ratio, caf)) → new_esEs9(vyy782, vyy792, caf)
new_esEs7(Just(vyy780), Just(vyy790), ty_Double) → new_esEs23(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), app(app(app(ty_@3, dab), dac), dad), cfe) → new_esEs5(vyy780, vyy790, dab, dac, dad)
new_lt12(vyy300, vyy40, ty_Ordering) → new_lt10(vyy300, vyy40)
new_esEs7(Just(vyy780), Just(vyy790), app(app(ty_@2, cgh), cha)) → new_esEs8(vyy780, vyy790, cgh, cha)
new_ltEs19(vyy302, vyy42, app(ty_Ratio, chf)) → new_ltEs10(vyy302, vyy42, chf)
new_primEqNat0(Succ(vyy7800), Succ(vyy7900)) → new_primEqNat0(vyy7800, vyy7900)
new_lt5(vyy300, vyy40, cb) → new_esEs14(new_compare5(vyy300, vyy40, cb))
new_esEs6(Left(vyy780), Left(vyy790), app(ty_Ratio, daf), cfe) → new_esEs9(vyy780, vyy790, daf)
new_compare5(:(vyy300, vyy301), :(vyy40, vyy41), bda) → new_primCompAux0(vyy300, vyy40, new_compare5(vyy301, vyy41, bda), bda)
new_esEs6(Right(vyy780), Right(vyy790), cfd, ty_Integer) → new_esEs13(vyy780, vyy790)
new_primCompAux00(vyy111, LT) → LT
new_lt12(vyy300, vyy40, ty_Bool) → new_lt13(vyy300, vyy40)
new_primCmpInt(Neg(Succ(vyy3000)), Neg(vyy40)) → new_primCmpNat0(vyy40, Succ(vyy3000))
new_esEs27(vyy781, vyy791, ty_Double) → new_esEs23(vyy781, vyy791)
new_esEs17(vyy782, vyy792, ty_Bool) → new_esEs20(vyy782, vyy792)
new_esEs27(vyy781, vyy791, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs5(vyy781, vyy791, cdg, cdh, cea)
new_primCompAux0(vyy300, vyy40, vyy107, bda) → new_primCompAux00(vyy107, new_compare15(vyy300, vyy40, bda))
new_esEs6(Left(vyy780), Left(vyy790), ty_@0, cfe) → new_esEs22(vyy780, vyy790)
new_esEs7(Nothing, Nothing, cfc) → True
new_compare25(vyy300, vyy40, False, bg) → new_compare11(vyy300, vyy40, new_ltEs18(vyy300, vyy40, bg), bg)
new_primEqInt(Pos(Zero), Pos(Succ(vyy7900))) → False
new_primEqInt(Pos(Succ(vyy7800)), Pos(Zero)) → False
new_esEs6(Right(vyy780), Right(vyy790), cfd, ty_@0) → new_esEs22(vyy780, vyy790)
new_primPlusNat0(Zero, Succ(vyy41000)) → Succ(vyy41000)
new_primPlusNat0(Succ(vyy12600), Zero) → Succ(vyy12600)
new_ltEs19(vyy302, vyy42, ty_Float) → new_ltEs17(vyy302, vyy42)
new_ltEs11(Right(vyy300), Right(vyy40), gb, app(app(ty_Either, gf), gg)) → new_ltEs11(vyy300, vyy40, gf, gg)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs17(vyy782, vyy792, ty_Double) → new_esEs23(vyy782, vyy792)
new_ltEs18(Nothing, Nothing, dec) → True
new_esEs6(Right(vyy780), Right(vyy790), cfd, app(ty_Maybe, dca)) → new_esEs7(vyy780, vyy790, dca)
new_primCmpNat0(Succ(vyy3000), Zero) → GT
new_lt20(vyy301, vyy41, app(app(ty_@2, dc), dd)) → new_lt4(vyy301, vyy41, dc, dd)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy400))) → LT
new_compare210(vyy300, vyy40, True, h, ba, bb) → EQ
new_esEs27(vyy781, vyy791, ty_Char) → new_esEs24(vyy781, vyy791)
new_compare14(vyy300, vyy40, False, h, ba, bb) → GT
new_sr0(Integer(vyy3000), Integer(vyy410)) → Integer(new_primMulInt(vyy3000, vyy410))
new_esEs17(vyy782, vyy792, app(app(ty_Either, cag), cah)) → new_esEs6(vyy782, vyy792, cag, cah)
new_primEqInt(Neg(Succ(vyy7800)), Pos(vyy790)) → False
new_primEqInt(Pos(Succ(vyy7800)), Neg(vyy790)) → False
new_esEs7(Just(vyy780), Nothing, cfc) → False
new_esEs7(Nothing, Just(vyy790), cfc) → False
new_lt19(vyy300, vyy40, app(ty_Ratio, chd)) → new_lt15(vyy300, vyy40, chd)
new_foldFM2(EmptyFM, cbc, cbd) → []
new_lt19(vyy300, vyy40, app(ty_Maybe, bg)) → new_lt16(vyy300, vyy40, bg)
new_ltEs12(GT, EQ) → False
new_compare15(vyy300, vyy40, app(app(ty_@2, bdh), bea)) → new_compare7(vyy300, vyy40, bdh, bea)
new_esEs20(False, False) → True
new_ltEs18(Just(vyy300), Just(vyy40), app(app(ty_Either, hg), hh)) → new_ltEs11(vyy300, vyy40, hg, hh)
new_esEs21(Float(vyy780, vyy781), Float(vyy790, vyy791)) → new_esEs12(new_sr(vyy780, vyy790), new_sr(vyy781, vyy791))
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_@2, dba), dbb), cfe) → new_esEs8(vyy780, vyy790, dba, dbb)
new_lt12(vyy300, vyy40, ty_Float) → new_lt8(vyy300, vyy40)
new_primEqInt(Neg(Zero), Pos(Succ(vyy7900))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy7900))) → False
new_ltEs18(Just(vyy300), Just(vyy40), ty_Double) → new_ltEs5(vyy300, vyy40)
new_primCompAux00(vyy111, EQ) → vyy111
new_primCmpInt(Pos(Zero), Pos(Succ(vyy400))) → new_primCmpNat0(Zero, Succ(vyy400))
new_esEs25(GT, LT) → False
new_esEs25(LT, GT) → False
new_lt20(vyy301, vyy41, ty_Bool) → new_lt13(vyy301, vyy41)
new_ltEs11(Left(vyy300), Left(vyy40), app(app(ty_@2, fg), fh), fb) → new_ltEs8(vyy300, vyy40, fg, fh)
new_lt20(vyy301, vyy41, app(app(app(ty_@3, cd), ce), cf)) → new_lt9(vyy301, vyy41, cd, ce, cf)
new_lt19(vyy300, vyy40, ty_@0) → new_lt11(vyy300, vyy40)
new_lt20(vyy301, vyy41, ty_Integer) → new_lt6(vyy301, vyy41)
new_ltEs14(vyy301, vyy41, ty_Float) → new_ltEs17(vyy301, vyy41)
new_lt19(vyy300, vyy40, app(ty_[], cb)) → new_lt5(vyy300, vyy40, cb)
new_esEs17(vyy782, vyy792, app(app(ty_@2, cba), cbb)) → new_esEs8(vyy782, vyy792, cba, cbb)
new_esEs28(vyy78, vyy79, ty_Double) → new_esEs23(vyy78, vyy79)
new_esEs15(vyy780, vyy790, ty_@0) → new_esEs22(vyy780, vyy790)
new_esEs17(vyy782, vyy792, ty_Int) → new_esEs12(vyy782, vyy792)
new_esEs15(vyy780, vyy790, app(ty_Maybe, bfe)) → new_esEs7(vyy780, vyy790, bfe)
new_esEs23(Double(vyy780, vyy781), Double(vyy790, vyy791)) → new_esEs12(new_sr(vyy780, vyy790), new_sr(vyy781, vyy791))
new_pePe(False, vyy78, vyy79, vyy97, cfa) → new_asAs(new_esEs28(vyy78, vyy79, cfa), vyy97)
new_esEs26(vyy780, vyy790, app(app(ty_FiniteMap, cca), ccb)) → new_esEs19(vyy780, vyy790, cca, ccb)
new_ltEs11(Left(vyy300), Left(vyy40), app(app(app(ty_@3, eg), eh), fa), fb) → new_ltEs6(vyy300, vyy40, eg, eh, fa)
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_Either, dag), dah), cfe) → new_esEs6(vyy780, vyy790, dag, dah)
new_ltEs13(vyy30, vyy4, bda) → new_not(new_compare5(vyy30, vyy4, bda))
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, chh), daa), cfe) → new_esEs19(vyy780, vyy790, chh, daa)
new_ltEs18(Just(vyy300), Nothing, dec) → False
new_ltEs18(Just(vyy300), Just(vyy40), ty_@0) → new_ltEs16(vyy300, vyy40)
new_primCmpInt(Pos(Succ(vyy3000)), Pos(vyy40)) → new_primCmpNat0(Succ(vyy3000), vyy40)
new_esEs27(vyy781, vyy791, ty_@0) → new_esEs22(vyy781, vyy791)
new_esEs29(vyy780, vyy790, app(app(ty_@2, dea), deb)) → new_esEs8(vyy780, vyy790, dea, deb)
new_esEs16(vyy781, vyy791, app(ty_[], bgc)) → new_esEs18(vyy781, vyy791, bgc)
new_esEs7(Just(vyy780), Just(vyy790), ty_Bool) → new_esEs20(vyy780, vyy790)
new_not0True
new_esEs16(vyy781, vyy791, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs5(vyy781, vyy791, bgf, bgg, bgh)
new_ltEs11(Right(vyy300), Right(vyy40), gb, ty_Double) → new_ltEs5(vyy300, vyy40)
new_ltEs19(vyy302, vyy42, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(vyy302, vyy42, df, dg, dh)
new_esEs27(vyy781, vyy791, app(ty_[], cdd)) → new_esEs18(vyy781, vyy791, cdd)
new_esEs27(vyy781, vyy791, app(app(ty_Either, ced), cee)) → new_esEs6(vyy781, vyy791, ced, cee)
new_esEs14(GT) → False
new_esEs16(vyy781, vyy791, ty_Double) → new_esEs23(vyy781, vyy791)
new_esEs15(vyy780, vyy790, app(app(ty_Either, bfg), bfh)) → new_esEs6(vyy780, vyy790, bfg, bfh)
new_esEs16(vyy781, vyy791, app(app(ty_@2, bhe), bhf)) → new_esEs8(vyy781, vyy791, bhe, bhf)
new_compare16(Char(vyy300), Char(vyy40)) → new_primCmpNat0(vyy300, vyy40)
new_primCmpInt(Pos(Succ(vyy3000)), Neg(vyy40)) → GT
new_ltEs19(vyy302, vyy42, ty_Int) → new_ltEs9(vyy302, vyy42)
new_esEs28(vyy78, vyy79, app(ty_Maybe, cfc)) → new_esEs7(vyy78, vyy79, cfc)
new_ltEs11(Left(vyy300), Left(vyy40), app(ty_[], ga), fb) → new_ltEs13(vyy300, vyy40, ga)
new_lt19(vyy300, vyy40, ty_Ordering) → new_lt10(vyy300, vyy40)
new_esEs26(vyy780, vyy790, ty_Char) → new_esEs24(vyy780, vyy790)
new_primMulInt(Pos(vyy3000), Pos(vyy410)) → Pos(new_primMulNat0(vyy3000, vyy410))
new_lt12(vyy300, vyy40, app(app(app(ty_@3, bae), baf), bag)) → new_lt9(vyy300, vyy40, bae, baf, bag)
new_ltEs11(Right(vyy300), Right(vyy40), gb, app(app(app(ty_@3, gc), gd), ge)) → new_ltEs6(vyy300, vyy40, gc, gd, ge)
new_lt12(vyy300, vyy40, app(ty_[], bbf)) → new_lt5(vyy300, vyy40, bbf)
new_compare24(vyy300, vyy40, False, be, bf) → new_compare111(vyy300, vyy40, new_ltEs11(vyy300, vyy40, be, bf), be, bf)
new_primMulInt(Neg(vyy3000), Neg(vyy410)) → Pos(new_primMulNat0(vyy3000, vyy410))
new_esEs24(Char(vyy780), Char(vyy790)) → new_primEqNat0(vyy780, vyy790)
new_ltEs12(EQ, GT) → True
new_esEs28(vyy78, vyy79, app(ty_Ratio, bec)) → new_esEs9(vyy78, vyy79, bec)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Integer) → new_ltEs7(vyy300, vyy40)
new_primEqNat0(Succ(vyy7800), Zero) → False
new_primEqNat0(Zero, Succ(vyy7900)) → False
new_lt17(vyy300, vyy40) → new_esEs14(new_compare8(vyy300, vyy40))
new_ltEs14(vyy301, vyy41, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs6(vyy301, vyy41, bbh, bca, bcb)
new_primPlusNat0(Zero, Zero) → Zero
new_lt20(vyy301, vyy41, app(ty_Ratio, che)) → new_lt15(vyy301, vyy41, che)
new_lt10(vyy300, vyy40) → new_esEs14(new_compare12(vyy300, vyy40))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare15(vyy300, vyy40, ty_@0) → new_compare27(vyy300, vyy40)
new_lt19(vyy300, vyy40, ty_Double) → new_lt17(vyy300, vyy40)
new_lt11(vyy300, vyy40) → new_esEs14(new_compare27(vyy300, vyy40))
new_ltEs14(vyy301, vyy41, ty_Char) → new_ltEs15(vyy301, vyy41)
new_lt12(vyy300, vyy40, app(ty_Ratio, chb)) → new_lt15(vyy300, vyy40, chb)
new_esEs25(GT, EQ) → False
new_esEs25(EQ, GT) → False
new_sizeFM(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cbc, cbd) → vyy792
new_ltEs4(True, False) → False
new_esEs29(vyy780, vyy790, app(app(ty_Either, ddg), ddh)) → new_esEs6(vyy780, vyy790, ddg, ddh)
new_pePe(True, vyy78, vyy79, vyy97, cfa) → True
new_esEs6(Left(vyy780), Left(vyy790), app(ty_[], chg), cfe) → new_esEs18(vyy780, vyy790, chg)
new_primPlusNat1(Succ(vyy1260), vyy4100) → Succ(Succ(new_primPlusNat0(vyy1260, vyy4100)))
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cbc, cbd) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cbc, cbd), vyy793, cbc, cbd)
new_esEs29(vyy780, vyy790, app(app(app(ty_@3, ddb), ddc), ddd)) → new_esEs5(vyy780, vyy790, ddb, ddc, ddd)
new_esEs29(vyy780, vyy790, ty_Ordering) → new_esEs25(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), ty_Ordering, cfe) → new_esEs25(vyy780, vyy790)
new_ltEs14(vyy301, vyy41, ty_@0) → new_ltEs16(vyy301, vyy41)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy400))) → new_primCmpNat0(Succ(vyy400), Zero)
new_esEs6(Left(vyy780), Left(vyy790), ty_Bool, cfe) → new_esEs20(vyy780, vyy790)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy400))) → GT
new_esEs6(Left(vyy780), Left(vyy790), app(ty_Maybe, dae), cfe) → new_esEs7(vyy780, vyy790, dae)
new_esEs27(vyy781, vyy791, ty_Ordering) → new_esEs25(vyy781, vyy791)
new_esEs12(vyy78, vyy79) → new_primEqInt(vyy78, vyy79)
new_esEs16(vyy781, vyy791, ty_@0) → new_esEs22(vyy781, vyy791)
new_lt20(vyy301, vyy41, ty_Char) → new_lt7(vyy301, vyy41)
new_esEs20(False, True) → False
new_esEs20(True, False) → False
new_esEs15(vyy780, vyy790, app(app(ty_@2, bga), bgb)) → new_esEs8(vyy780, vyy790, bga, bgb)
new_compare26(vyy300, vyy40, False) → new_compare112(vyy300, vyy40, new_ltEs12(vyy300, vyy40))
new_esEs15(vyy780, vyy790, ty_Int) → new_esEs12(vyy780, vyy790)
new_ltEs11(Left(vyy300), Left(vyy40), app(app(ty_Either, fc), fd), fb) → new_ltEs11(vyy300, vyy40, fc, fd)
new_compare5([], :(vyy40, vyy41), bda) → LT
new_esEs7(Just(vyy780), Just(vyy790), ty_Char) → new_esEs24(vyy780, vyy790)
new_esEs7(Just(vyy780), Just(vyy790), app(app(app(ty_@3, cga), cgb), cgc)) → new_esEs5(vyy780, vyy790, cga, cgb, cgc)
new_esEs29(vyy780, vyy790, app(ty_Ratio, ddf)) → new_esEs9(vyy780, vyy790, ddf)
new_ltEs11(Left(vyy300), Left(vyy40), ty_Integer, fb) → new_ltEs7(vyy300, vyy40)
new_esEs17(vyy782, vyy792, ty_Integer) → new_esEs13(vyy782, vyy792)
new_esEs28(vyy78, vyy79, app(ty_[], cfb)) → new_esEs18(vyy78, vyy79, cfb)
new_esEs5(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bed, bee, bef) → new_asAs(new_esEs15(vyy780, vyy790, bed), new_asAs(new_esEs16(vyy781, vyy791, bee), new_esEs17(vyy782, vyy792, bef)))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs28(vyy78, vyy79, ty_Bool) → new_esEs20(vyy78, vyy79)
new_ltEs14(vyy301, vyy41, ty_Double) → new_ltEs5(vyy301, vyy41)
new_lt19(vyy300, vyy40, ty_Bool) → new_lt13(vyy300, vyy40)
new_esEs7(Just(vyy780), Just(vyy790), app(ty_[], cff)) → new_esEs18(vyy780, vyy790, cff)
new_esEs6(Right(vyy780), Right(vyy790), cfd, ty_Double) → new_esEs23(vyy780, vyy790)
new_esEs17(vyy782, vyy792, ty_Float) → new_esEs21(vyy782, vyy792)
new_asAs(False, vyy106) → False
new_esEs16(vyy781, vyy791, ty_Integer) → new_esEs13(vyy781, vyy791)
new_esEs29(vyy780, vyy790, ty_@0) → new_esEs22(vyy780, vyy790)
new_primMulInt(Pos(vyy3000), Neg(vyy410)) → Neg(new_primMulNat0(vyy3000, vyy410))
new_primMulInt(Neg(vyy3000), Pos(vyy410)) → Neg(new_primMulNat0(vyy3000, vyy410))
new_ltEs11(Left(vyy300), Right(vyy40), gb, fb) → True
new_ltEs11(Right(vyy300), Right(vyy40), gb, ty_Ordering) → new_ltEs12(vyy300, vyy40)
new_primMulNat0(Succ(vyy30000), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy4100)) → Zero
new_esEs18([], [], cfb) → True
new_esEs26(vyy780, vyy790, ty_Integer) → new_esEs13(vyy780, vyy790)
new_compare6(vyy300, vyy40, be, bf) → new_compare24(vyy300, vyy40, new_esEs6(vyy300, vyy40, be, bf), be, bf)
new_ltEs12(GT, GT) → True
new_compare19(:%(vyy300, vyy301), :%(vyy40, vyy41), ty_Integer) → new_compare13(new_sr0(vyy300, vyy41), new_sr0(vyy40, vyy301))
new_ltEs14(vyy301, vyy41, ty_Integer) → new_ltEs7(vyy301, vyy41)
new_compare210(vyy300, vyy40, False, h, ba, bb) → new_compare14(vyy300, vyy40, new_ltEs6(vyy300, vyy40, h, ba, bb), h, ba, bb)
new_esEs26(vyy780, vyy790, app(ty_Maybe, ccf)) → new_esEs7(vyy780, vyy790, ccf)
new_esEs6(Left(vyy780), Left(vyy790), ty_Float, cfe) → new_esEs21(vyy780, vyy790)
new_ltEs18(Nothing, Just(vyy40), dec) → True
new_lt19(vyy300, vyy40, ty_Float) → new_lt8(vyy300, vyy40)
new_ltEs11(Right(vyy300), Right(vyy40), gb, app(ty_Maybe, gh)) → new_ltEs18(vyy300, vyy40, gh)
new_lt20(vyy301, vyy41, ty_Float) → new_lt8(vyy301, vyy41)
new_not(EQ) → new_not0
new_esEs26(vyy780, vyy790, app(ty_Ratio, ccg)) → new_esEs9(vyy780, vyy790, ccg)
new_compare15(vyy300, vyy40, ty_Char) → new_compare16(vyy300, vyy40)
new_esEs11(vyy781, vyy791, ty_Integer) → new_esEs13(vyy781, vyy791)
new_esEs27(vyy781, vyy791, app(app(ty_FiniteMap, cde), cdf)) → new_esEs19(vyy781, vyy791, cde, cdf)
new_esEs15(vyy780, vyy790, app(ty_[], beg)) → new_esEs18(vyy780, vyy790, beg)
new_ltEs11(Right(vyy300), Right(vyy40), gb, ty_@0) → new_ltEs16(vyy300, vyy40)
new_ltEs4(False, False) → True
new_esEs28(vyy78, vyy79, ty_Integer) → new_esEs13(vyy78, vyy79)
new_lt12(vyy300, vyy40, ty_Double) → new_lt17(vyy300, vyy40)
new_esEs16(vyy781, vyy791, ty_Int) → new_esEs12(vyy781, vyy791)
new_ltEs11(Right(vyy300), Right(vyy40), gb, ty_Float) → new_ltEs17(vyy300, vyy40)
new_ltEs11(Left(vyy300), Left(vyy40), app(ty_Ratio, dee), fb) → new_ltEs10(vyy300, vyy40, dee)
new_esEs25(EQ, LT) → False
new_esEs25(LT, EQ) → False
new_compare211(vyy300, vyy40, True, bh, ca) → EQ
new_esEs29(vyy780, vyy790, ty_Double) → new_esEs23(vyy780, vyy790)
new_esEs16(vyy781, vyy791, app(ty_Maybe, bha)) → new_esEs7(vyy781, vyy791, bha)
new_esEs7(Just(vyy780), Just(vyy790), ty_Int) → new_esEs12(vyy780, vyy790)
new_esEs7(Just(vyy780), Just(vyy790), ty_Integer) → new_esEs13(vyy780, vyy790)
new_ltEs12(EQ, LT) → False
new_esEs9(:%(vyy780, vyy781), :%(vyy790, vyy791), bec) → new_asAs(new_esEs10(vyy780, vyy790, bec), new_esEs11(vyy781, vyy791, bec))
new_ltEs18(Just(vyy300), Just(vyy40), ty_Int) → new_ltEs9(vyy300, vyy40)
new_not(LT) → new_not0
new_compare13(Integer(vyy300), Integer(vyy40)) → new_primCmpInt(vyy300, vyy40)
new_esEs26(vyy780, vyy790, ty_Float) → new_esEs21(vyy780, vyy790)
new_esEs7(Just(vyy780), Just(vyy790), ty_Float) → new_esEs21(vyy780, vyy790)
new_compare112(vyy300, vyy40, False) → GT
new_esEs6(Right(vyy780), Right(vyy790), cfd, ty_Int) → new_esEs12(vyy780, vyy790)
new_esEs16(vyy781, vyy791, ty_Char) → new_esEs24(vyy781, vyy791)
new_esEs7(Just(vyy780), Just(vyy790), ty_@0) → new_esEs22(vyy780, vyy790)
new_esEs16(vyy781, vyy791, ty_Bool) → new_esEs20(vyy781, vyy791)
new_compare12(vyy300, vyy40) → new_compare26(vyy300, vyy40, new_esEs25(vyy300, vyy40))
new_ltEs19(vyy302, vyy42, ty_Integer) → new_ltEs7(vyy302, vyy42)
new_esEs6(Right(vyy780), Right(vyy790), cfd, app(ty_[], dbc)) → new_esEs18(vyy780, vyy790, dbc)
new_primPlusNat0(Succ(vyy12600), Succ(vyy41000)) → Succ(Succ(new_primPlusNat0(vyy12600, vyy41000)))
new_esEs28(vyy78, vyy79, ty_Int) → new_esEs12(vyy78, vyy79)
new_esEs28(vyy78, vyy79, app(app(ty_@2, cbf), cbg)) → new_esEs8(vyy78, vyy79, cbf, cbg)
new_esEs26(vyy780, vyy790, app(app(ty_Either, cch), cda)) → new_esEs6(vyy780, vyy790, cch, cda)
new_lt20(vyy301, vyy41, ty_Ordering) → new_lt10(vyy301, vyy41)
new_esEs26(vyy780, vyy790, ty_Double) → new_esEs23(vyy780, vyy790)
new_esEs29(vyy780, vyy790, app(ty_[], dcg)) → new_esEs18(vyy780, vyy790, dcg)
new_compare111(vyy300, vyy40, True, be, bf) → LT
new_esEs28(vyy78, vyy79, ty_@0) → new_esEs22(vyy78, vyy79)
new_asAs(True, vyy106) → vyy106
new_ltEs9(vyy30, vyy4) → new_not(new_compare29(vyy30, vyy4))
new_compare27(@0, @0) → EQ
new_esEs26(vyy780, vyy790, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs5(vyy780, vyy790, ccc, ccd, cce)
new_ltEs11(Left(vyy300), Left(vyy40), ty_@0, fb) → new_ltEs16(vyy300, vyy40)
new_lt15(vyy300, vyy40, chd) → new_esEs14(new_compare19(vyy300, vyy40, chd))
new_ltEs10(vyy30, vyy4, ceh) → new_not(new_compare19(vyy30, vyy4, ceh))
new_ltEs11(Right(vyy300), Right(vyy40), gb, ty_Char) → new_ltEs15(vyy300, vyy40)
new_compare15(vyy300, vyy40, ty_Bool) → new_compare18(vyy300, vyy40)
new_compare15(vyy300, vyy40, app(ty_Maybe, bdg)) → new_compare9(vyy300, vyy40, bdg)
new_ltEs14(vyy301, vyy41, app(ty_[], bch)) → new_ltEs13(vyy301, vyy41, bch)
new_lt20(vyy301, vyy41, ty_@0) → new_lt11(vyy301, vyy41)
new_fmToList(vyy79, cbc, cbd) → new_foldFM2(vyy79, cbc, cbd)
new_esEs6(Left(vyy780), Left(vyy790), ty_Double, cfe) → new_esEs23(vyy780, vyy790)
new_ltEs19(vyy302, vyy42, app(app(ty_Either, ea), eb)) → new_ltEs11(vyy302, vyy42, ea, eb)
new_lt20(vyy301, vyy41, app(ty_[], de)) → new_lt5(vyy301, vyy41, de)
new_compare15(vyy300, vyy40, app(app(ty_Either, bde), bdf)) → new_compare6(vyy300, vyy40, bde, bdf)
new_compare5([], [], bda) → EQ
new_ltEs14(vyy301, vyy41, app(app(ty_Either, bcc), bcd)) → new_ltEs11(vyy301, vyy41, bcc, bcd)
new_lt9(vyy300, vyy40, h, ba, bb) → new_esEs14(new_compare17(vyy300, vyy40, h, ba, bb))
new_compare10(vyy300, vyy40, True) → LT
new_lt18(vyy300, vyy40) → new_esEs14(new_compare29(vyy300, vyy40))
new_compare10(vyy300, vyy40, False) → GT
new_primCompAux00(vyy111, GT) → GT
new_esEs14(LT) → True
new_lt6(vyy300, vyy40) → new_esEs14(new_compare13(vyy300, vyy40))
new_ltEs14(vyy301, vyy41, ty_Int) → new_ltEs9(vyy301, vyy41)
new_ltEs12(GT, LT) → False
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vyy780), Right(vyy790), cfd, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs5(vyy780, vyy790, dbf, dbg, dbh)
new_esEs16(vyy781, vyy791, ty_Float) → new_esEs21(vyy781, vyy791)
new_ltEs19(vyy302, vyy42, ty_@0) → new_ltEs16(vyy302, vyy42)
new_ltEs11(Left(vyy300), Left(vyy40), ty_Ordering, fb) → new_ltEs12(vyy300, vyy40)
new_ltEs19(vyy302, vyy42, app(ty_[], ef)) → new_ltEs13(vyy302, vyy42, ef)
new_compare15(vyy300, vyy40, ty_Float) → new_compare28(vyy300, vyy40)
new_esEs22(@0, @0) → True
new_ltEs19(vyy302, vyy42, app(ty_Maybe, ec)) → new_ltEs18(vyy302, vyy42, ec)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs6(Right(vyy780), Right(vyy790), cfd, ty_Char) → new_esEs24(vyy780, vyy790)
new_ltEs14(vyy301, vyy41, ty_Bool) → new_ltEs4(vyy301, vyy41)
new_primCmpInt(Neg(Succ(vyy3000)), Pos(vyy40)) → LT
new_compare15(vyy300, vyy40, ty_Ordering) → new_compare12(vyy300, vyy40)
new_lt4(vyy300, vyy40, bh, ca) → new_esEs14(new_compare7(vyy300, vyy40, bh, ca))

The set Q consists of the following terms:

new_esEs29(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_compare15(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs19(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(LT, LT)
new_compare210(x0, x1, False, x2, x3, x4)
new_fmToList(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt12(x0, x1, ty_Bool)
new_ltEs14(x0, x1, ty_Int)
new_esEs16(x0, x1, ty_Integer)
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs12(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs11(Right(x0), Right(x1), x2, ty_@0)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_asAs(True, x0)
new_ltEs11(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs11(Left(x0), Left(x1), ty_Char, x2)
new_esEs17(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(False, x0)
new_esEs14(EQ)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(x0, x1, x2)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs16(x0, x1, app(app(ty_@2, x2), x3))
new_compare14(x0, x1, True, x2, x3, x4)
new_compare15(x0, x1, ty_Integer)
new_ltEs11(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs29(x0, x1, ty_Double)
new_ltEs12(GT, GT)
new_esEs17(x0, x1, ty_Ordering)
new_esEs16(x0, x1, app(app(ty_Either, x2), x3))
new_lt15(x0, x1, x2)
new_esEs29(x0, x1, ty_Integer)
new_compare11(x0, x1, True, x2)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_ltEs14(x0, x1, ty_Double)
new_ltEs11(Right(x0), Right(x1), x2, ty_Bool)
new_compare15(x0, x1, ty_Double)
new_ltEs11(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare5(:(x0, x1), :(x2, x3), x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt12(x0, x1, ty_Int)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs25(LT, LT)
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_primCompAux00(x0, GT)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs11(Right(x0), Right(x1), x2, ty_Char)
new_ltEs11(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs16(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare26(x0, x1, True)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs18(:(x0, x1), [], x2)
new_esEs22(@0, @0)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_compare112(x0, x1, True)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Zero, Zero)
new_ltEs11(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, ty_Char)
new_compare5(:(x0, x1), [], x2)
new_ltEs4(True, True)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs14(x0, x1, ty_@0)
new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_compare24(x0, x1, True, x2, x3)
new_ltEs14(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17(x0, x1, ty_Double)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs16(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare15(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs17(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_lt7(x0, x1)
new_compare15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt14(x0, x1, x2, x3)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs25(GT, GT)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_compare17(x0, x1, x2, x3, x4)
new_compare19(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs11(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_compare5([], [], x0)
new_compare18(x0, x1)
new_esEs29(x0, x1, ty_@0)
new_esEs18([], [], x0)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_compare11(x0, x1, False, x2)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs15(x0, x1, ty_Integer)
new_esEs20(True, True)
new_lt19(x0, x1, ty_@0)
new_esEs17(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_esEs24(Char(x0), Char(x1))
new_esEs25(EQ, GT)
new_esEs25(GT, EQ)
new_ltEs4(False, False)
new_lt20(x0, x1, ty_Char)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_lt12(x0, x1, ty_Double)
new_esEs7(Nothing, Just(x0), x1)
new_lt19(x0, x1, ty_Char)
new_primCmpNat0(Zero, Succ(x0))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs9(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs29(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs11(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(True, False)
new_esEs20(False, True)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_esEs16(x0, x1, ty_Char)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs20(False, False)
new_esEs15(x0, x1, ty_Bool)
new_ltEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs28(x0, x1, ty_Int)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs13(Integer(x0), Integer(x1))
new_not0
new_ltEs11(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16(x0, x1, app(ty_[], x2))
new_primPlusNat0(Zero, Zero)
new_compare211(x0, x1, False, x2, x3)
new_esEs16(x0, x1, ty_Ordering)
new_compare12(x0, x1)
new_compare28(Float(x0, x1), Float(x2, x3))
new_ltEs11(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Float)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs15(x0, x1, ty_@0)
new_esEs25(LT, GT)
new_esEs25(GT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs11(Right(x0), Left(x1), x2, x3)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs11(Left(x0), Right(x1), x2, x3)
new_esEs26(x0, x1, ty_Bool)
new_lt18(x0, x1)
new_ltEs11(Left(x0), Left(x1), ty_Float, x2)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
new_compare8(Double(x0, x1), Double(x2, x3))
new_esEs21(Float(x0, x1), Float(x2, x3))
new_esEs28(x0, x1, ty_Bool)
new_ltEs12(GT, EQ)
new_ltEs12(EQ, GT)
new_compare25(x0, x1, False, x2)
new_primEqNat0(Succ(x0), Zero)
new_esEs27(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_@0)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_not(GT)
new_esEs18([], :(x0, x1), x2)
new_esEs11(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_pePe(False, x0, x1, x2, x3)
new_lt19(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_esEs14(LT)
new_ltEs7(x0, x1)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_compare23(x0, x1, True)
new_pePe(True, x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare9(x0, x1, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs16(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs17(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), x1)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare24(x0, x1, False, x2, x3)
new_lt12(x0, x1, ty_Ordering)
new_esEs17(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs5(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_ltEs11(Right(x0), Right(x1), x2, ty_Double)
new_ltEs12(EQ, EQ)
new_primCompAux00(x0, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs11(Right(x0), Right(x1), x2, ty_Float)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare29(x0, x1)
new_ltEs14(x0, x1, app(ty_[], x2))
new_lt10(x0, x1)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_ltEs11(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs26(x0, x1, ty_Double)
new_ltEs17(x0, x1)
new_esEs25(EQ, EQ)
new_lt19(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs11(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, ty_@0)
new_ltEs16(x0, x1)
new_compare25(x0, x1, True, x2)
new_esEs11(x0, x1, ty_Int)
new_lt8(x0, x1)
new_compare26(x0, x1, False)
new_lt11(x0, x1)
new_esEs15(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs14(x0, x1, app(ty_Ratio, x2))
new_compare15(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs11(Right(x0), Right(x1), x2, ty_Ordering)
new_compare15(x0, x1, ty_Int)
new_primCompAux00(x0, EQ)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs14(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Int)
new_esEs17(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs16(x0, x1, app(ty_Ratio, x2))
new_esEs14(GT)
new_esEs27(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Ordering)
new_sizeFM(EmptyFM, x0, x1)
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Nothing, Nothing, x0)
new_lt19(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17(x0, x1, app(ty_Ratio, x2))
new_compare15(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_compare13(Integer(x0), Integer(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs14(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Zero, Zero)
new_esEs27(x0, x1, ty_@0)
new_lt12(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs14(x0, x1, ty_Bool)
new_compare111(x0, x1, False, x2, x3)
new_ltEs4(False, True)
new_compare15(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(True, False)
new_ltEs14(x0, x1, ty_Ordering)
new_ltEs11(Left(x0), Left(x1), ty_Int, x2)
new_lt9(x0, x1, x2, x3, x4)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_compare15(x0, x1, app(ty_Maybe, x2))
new_esEs15(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs29(x0, x1, ty_Int)
new_lt12(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_compare110(x0, x1, False, x2, x3)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs14(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs13(x0, x1, x2)
new_lt5(x0, x1, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt12(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Nothing, Just(x0), x1)
new_esEs16(x0, x1, ty_@0)
new_esEs16(x0, x1, ty_Int)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_lt16(x0, x1, x2)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_lt20(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_compare7(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Float)
new_esEs17(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt12(x0, x1, ty_@0)
new_esEs17(x0, x1, ty_@0)
new_esEs16(x0, x1, app(ty_Maybe, x2))
new_primPlusNat0(Zero, Succ(x0))
new_not(EQ)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare112(x0, x1, False)
new_esEs15(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_compare210(x0, x1, True, x2, x3, x4)
new_compare110(x0, x1, True, x2, x3)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat1(Zero, x0)
new_esEs7(Just(x0), Nothing, x1)
new_compare5([], :(x0, x1), x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs16(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_esEs7(Nothing, Nothing, x0)
new_ltEs19(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs11(Left(x0), Left(x1), ty_Double, x2)
new_sr0(Integer(x0), Integer(x1))
new_compare111(x0, x1, True, x2, x3)
new_lt4(x0, x1, x2, x3)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs11(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_compare14(x0, x1, False, x2, x3, x4)
new_ltEs11(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_lt13(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_Integer)
new_compare10(x0, x1, True)
new_esEs15(x0, x1, ty_Ordering)
new_ltEs14(x0, x1, ty_Integer)
new_esEs19(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs12(EQ, LT)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs12(LT, EQ)
new_compare16(Char(x0), Char(x1))
new_esEs15(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs14(x0, x1, app(ty_Maybe, x2))
new_esEs17(x0, x1, ty_Char)
new_compare27(@0, @0)
new_primPlusNat0(Succ(x0), Zero)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs27(x0, x1, ty_Bool)
new_esEs17(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare15(x0, x1, app(ty_Ratio, x2))
new_ltEs11(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs11(Right(x0), Right(x1), x2, ty_Int)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs12(GT, LT)
new_ltEs12(LT, GT)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs23(Double(x0, x1), Double(x2, x3))
new_lt12(x0, x1, ty_Char)
new_esEs25(EQ, LT)
new_esEs25(LT, EQ)
new_compare19(:%(x0, x1), :%(x2, x3), ty_Int)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(x0, x1, ty_Float)
new_lt6(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs15(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, ty_Float)
new_esEs17(x0, x1, app(ty_Maybe, x2))
new_esEs17(x0, x1, app(ty_[], x2))
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs15(x0, x1, ty_Char)
new_compare15(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, False)
new_esEs15(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, ty_Double)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_not(LT)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs11(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare15(x0, x1, app(app(ty_Either, x2), x3))
new_compare211(x0, x1, True, x2, x3)
new_esEs26(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_[], x2))
new_foldFM2(EmptyFM, x0, x1)
new_ltEs18(Just(x0), Just(x1), ty_Float)

We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:



↳ 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

Q DP problem:
The TRS P consists of the following rules:

new_foldFM_LE1(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, EmptyFM, True, h, ba) → new_foldFM_LE(vyy61, vyy62, vyy66, h, ba)
new_foldFM_LE(vyy61, vyy62, Branch(vyy660, vyy661, vyy662, vyy663, vyy664), h, ba) → new_foldFM_LE1(vyy61, vyy62, vyy660, vyy661, vyy662, vyy663, vyy664, new_ltEs20(vyy660, vyy62, ba), h, ba)
new_foldFM_LE1(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, Branch(vyy670, vyy671, vyy672, vyy673, vyy674), True, h, ba) → new_foldFM_LE2(vyy63, vyy64, new_foldFM_LE0(vyy61, vyy62, vyy66, h, ba), vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, h, ba)
new_foldFM_LE2(vyy63, vyy64, vyy96, vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, h, ba) → new_foldFM_LE1(new_eltsFM_LE0(vyy63, vyy64, vyy96, h, ba), vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, new_ltEs21(vyy670, vyy62, ba), h, ba)
new_foldFM_LE1(vyy61, vyy62, vyy63, vyy64, vyy65, Branch(vyy660, vyy661, vyy662, vyy663, vyy664), vyy67, False, h, ba) → new_foldFM_LE1(vyy61, vyy62, vyy660, vyy661, vyy662, vyy663, vyy664, new_ltEs20(vyy660, vyy62, ba), h, ba)
new_foldFM_LE1(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, Branch(vyy670, vyy671, vyy672, vyy673, vyy674), True, h, ba) → new_foldFM_LE(vyy61, vyy62, vyy66, h, ba)

The TRS R consists of the following rules:

new_esEs7(Just(vyy780), Just(vyy790), app(ty_Maybe, bab)) → new_esEs7(vyy780, vyy790, bab)
new_ltEs20(vyy660, vyy62, app(ty_Maybe, cf)) → new_ltEs18(vyy660, vyy62, cf)
new_ltEs20(vyy660, vyy62, ty_Bool) → new_ltEs4(vyy660, vyy62)
new_ltEs19(vyy302, vyy42, ty_Ordering) → new_ltEs12(vyy302, vyy42)
new_compare28(Float(vyy300, vyy301), Float(vyy40, vyy41)) → new_compare29(new_sr(vyy300, vyy40), new_sr(vyy301, vyy41))
new_lt19(vyy300, vyy40, ty_Char) → new_lt7(vyy300, vyy40)
new_ltEs20(vyy660, vyy62, ty_Int) → new_ltEs9(vyy660, vyy62)
new_lt19(vyy300, vyy40, app(app(ty_Either, bb), bc)) → new_lt14(vyy300, vyy40, bb, bc)
new_lt19(vyy300, vyy40, ty_Int) → new_lt18(vyy300, vyy40)
new_esEs20(True, True) → True
new_lt16(vyy300, vyy40, bd) → new_esEs14(new_compare9(vyy300, vyy40, bd))
new_compare9(vyy300, vyy40, bd) → new_compare25(vyy300, vyy40, new_esEs7(vyy300, vyy40, bd), bd)
new_esEs17(vyy782, vyy792, ty_Ordering) → new_esEs25(vyy782, vyy792)
new_lt14(vyy300, vyy40, bb, bc) → new_esEs14(new_compare6(vyy300, vyy40, bb, bc))
new_ltEs21(vyy670, vyy62, ty_Char) → new_ltEs15(vyy670, vyy62)
new_esEs15(vyy780, vyy790, ty_Char) → new_esEs24(vyy780, vyy790)
new_compare15(vyy300, vyy40, app(app(app(ty_@3, cff), cfg), cfh)) → new_compare17(vyy300, vyy40, cff, cfg, cfh)
new_esEs6(Left(vyy780), Left(vyy790), ty_Char, bdh) → new_esEs24(vyy780, vyy790)
new_ltEs12(LT, GT) → True
new_ltEs11(Left(vyy300), Left(vyy40), ty_Char, dde) → new_ltEs15(vyy300, vyy40)
new_ltEs19(vyy302, vyy42, ty_Char) → new_ltEs15(vyy302, vyy42)
new_compare110(vyy300, vyy40, True, gf, gg) → LT
new_esEs29(vyy780, vyy790, ty_Integer) → new_esEs13(vyy780, vyy790)
new_esEs17(vyy782, vyy792, ty_Char) → new_esEs24(vyy782, vyy792)
new_ltEs18(Just(vyy300), Just(vyy40), app(ty_Maybe, bhh)) → new_ltEs18(vyy300, vyy40, bhh)
new_esEs27(vyy781, vyy791, app(ty_Maybe, fh)) → new_esEs7(vyy781, vyy791, fh)
new_lt20(vyy301, vyy41, app(app(ty_Either, chh), daa)) → new_lt14(vyy301, vyy41, chh, daa)
new_esEs25(GT, GT) → True
new_compare14(vyy300, vyy40, True, be, bf, bg) → LT
new_lt7(vyy300, vyy40) → new_esEs14(new_compare16(vyy300, vyy40))
new_esEs28(vyy78, vyy79, ty_Float) → new_esEs21(vyy78, vyy79)
new_ltEs21(vyy670, vyy62, app(app(ty_@2, cg), da)) → new_ltEs8(vyy670, vyy62, cg, da)
new_esEs7(Just(vyy780), Just(vyy790), app(app(ty_Either, bad), bae)) → new_esEs6(vyy780, vyy790, bad, bae)
new_ltEs14(vyy301, vyy41, app(app(ty_@2, bdc), bdd)) → new_ltEs8(vyy301, vyy41, bdc, bdd)
new_primMulNat0(Zero, Zero) → Zero
new_lt12(vyy300, vyy40, app(app(ty_@2, bca), bcb)) → new_lt4(vyy300, vyy40, bca, bcb)
new_ltEs14(vyy301, vyy41, ty_Ordering) → new_ltEs12(vyy301, vyy41)
new_ltEs11(Right(vyy300), Left(vyy40), deh, dde) → False
new_esEs6(Right(vyy780), Right(vyy790), bfd, ty_Float) → new_esEs21(vyy780, vyy790)
new_ltEs12(LT, LT) → True
new_esEs6(Right(vyy780), Right(vyy790), bfd, app(ty_Ratio, bgd)) → new_esEs9(vyy780, vyy790, bgd)
new_esEs26(vyy780, vyy790, ty_@0) → new_esEs22(vyy780, vyy790)
new_compare25(vyy300, vyy40, True, bd) → EQ
new_ltEs18(Just(vyy300), Just(vyy40), ty_Bool) → new_ltEs4(vyy300, vyy40)
new_esEs27(vyy781, vyy791, ty_Bool) → new_esEs20(vyy781, vyy791)
new_esEs26(vyy780, vyy790, ty_Ordering) → new_esEs25(vyy780, vyy790)
new_lt20(vyy301, vyy41, ty_Int) → new_lt18(vyy301, vyy41)
new_lt12(vyy300, vyy40, ty_Integer) → new_lt6(vyy300, vyy40)
new_not(GT) → False
new_lt19(vyy300, vyy40, app(app(app(ty_@3, be), bf), bg)) → new_lt9(vyy300, vyy40, be, bf, bg)
new_esEs29(vyy780, vyy790, app(ty_Maybe, dcg)) → new_esEs7(vyy780, vyy790, dcg)
new_compare18(vyy300, vyy40) → new_compare23(vyy300, vyy40, new_esEs20(vyy300, vyy40))
new_esEs27(vyy781, vyy791, app(app(ty_@2, gd), ge)) → new_esEs8(vyy781, vyy791, gd, ge)
new_esEs27(vyy781, vyy791, app(ty_Ratio, ga)) → new_esEs9(vyy781, vyy791, ga)
new_esEs10(vyy780, vyy790, ty_Int) → new_esEs12(vyy780, vyy790)
new_esEs16(vyy781, vyy791, app(app(ty_Either, cde), cdf)) → new_esEs6(vyy781, vyy791, cde, cdf)
new_compare17(vyy300, vyy40, be, bf, bg) → new_compare210(vyy300, vyy40, new_esEs5(vyy300, vyy40, be, bf, bg), be, bf, bg)
new_ltEs12(LT, EQ) → True
new_esEs15(vyy780, vyy790, app(app(app(ty_@3, cbd), cbe), cbf)) → new_esEs5(vyy780, vyy790, cbd, cbe, cbf)
new_ltEs11(Left(vyy300), Left(vyy40), app(ty_Maybe, ded), dde) → new_ltEs18(vyy300, vyy40, ded)
new_ltEs19(vyy302, vyy42, ty_Bool) → new_ltEs4(vyy302, vyy42)
new_ltEs4(False, True) → True
new_ltEs18(Just(vyy300), Just(vyy40), ty_Float) → new_ltEs17(vyy300, vyy40)
new_esEs27(vyy781, vyy791, ty_Integer) → new_esEs13(vyy781, vyy791)
new_esEs6(Right(vyy780), Right(vyy790), bfd, app(app(ty_FiniteMap, bff), bfg)) → new_esEs19(vyy780, vyy790, bff, bfg)
new_esEs16(vyy781, vyy791, app(app(ty_FiniteMap, ccf), ccg)) → new_esEs19(vyy781, vyy791, ccf, ccg)
new_esEs6(Right(vyy780), Right(vyy790), bfd, ty_Ordering) → new_esEs25(vyy780, vyy790)
new_ltEs6(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), chb, chc, chd) → new_pePe(new_lt19(vyy300, vyy40, chb), vyy300, vyy40, new_pePe(new_lt20(vyy301, vyy41, chc), vyy301, vyy41, new_ltEs19(vyy302, vyy42, chd), chc), chb)
new_esEs28(vyy78, vyy79, app(app(app(ty_@3, caf), cag), cah)) → new_esEs5(vyy78, vyy79, caf, cag, cah)
new_esEs7(Just(vyy780), Just(vyy790), app(ty_Ratio, bac)) → new_esEs9(vyy780, vyy790, bac)
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, ha, hb) → :(@2(vyy790, vyy791), vyy125)
new_ltEs19(vyy302, vyy42, app(app(ty_@2, dbf), dbg)) → new_ltEs8(vyy302, vyy42, dbf, dbg)
new_esEs6(Left(vyy780), Left(vyy790), ty_Int, bdh) → new_esEs12(vyy780, vyy790)
new_ltEs11(Left(vyy300), Left(vyy40), ty_Bool, dde) → new_ltEs4(vyy300, vyy40)
new_ltEs4(True, True) → True
new_ltEs20(vyy660, vyy62, app(app(ty_Either, cc), cd)) → new_ltEs11(vyy660, vyy62, cc, cd)
new_esEs26(vyy780, vyy790, app(app(ty_@2, eg), eh)) → new_esEs8(vyy780, vyy790, eg, eh)
new_esEs18(:(vyy780, vyy781), [], cha) → False
new_esEs18([], :(vyy790, vyy791), cha) → False
new_esEs17(vyy782, vyy792, app(app(ty_FiniteMap, ceb), cec)) → new_esEs19(vyy782, vyy792, ceb, cec)
new_esEs26(vyy780, vyy790, ty_Bool) → new_esEs20(vyy780, vyy790)
new_esEs17(vyy782, vyy792, app(ty_Maybe, ceg)) → new_esEs7(vyy782, vyy792, ceg)
new_lt12(vyy300, vyy40, app(app(ty_Either, bbe), bbf)) → new_lt14(vyy300, vyy40, bbe, bbf)
new_compare23(vyy300, vyy40, True) → EQ
new_esEs18(:(vyy780, vyy781), :(vyy790, vyy791), cha) → new_asAs(new_esEs29(vyy780, vyy790, cha), new_esEs18(vyy781, vyy791, cha))
new_esEs16(vyy781, vyy791, ty_Ordering) → new_esEs25(vyy781, vyy791)
new_ltEs20(vyy660, vyy62, app(app(ty_@2, cg), da)) → new_ltEs8(vyy660, vyy62, cg, da)
new_lt19(vyy300, vyy40, ty_Integer) → new_lt6(vyy300, vyy40)
new_lt12(vyy300, vyy40, ty_Int) → new_lt18(vyy300, vyy40)
new_esEs16(vyy781, vyy791, app(ty_Ratio, cdd)) → new_esEs9(vyy781, vyy791, cdd)
new_esEs15(vyy780, vyy790, ty_Ordering) → new_esEs25(vyy780, vyy790)
new_ltEs20(vyy660, vyy62, ty_Double) → new_ltEs5(vyy660, vyy62)
new_ltEs20(vyy660, vyy62, app(ty_[], db)) → new_ltEs13(vyy660, vyy62, db)
new_ltEs21(vyy670, vyy62, ty_Int) → new_ltEs9(vyy670, vyy62)
new_ltEs18(Just(vyy300), Just(vyy40), app(app(ty_@2, caa), cab)) → new_ltEs8(vyy300, vyy40, caa, cab)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Char) → new_ltEs15(vyy300, vyy40)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Ordering) → new_ltEs12(vyy300, vyy40)
new_ltEs14(vyy301, vyy41, app(ty_Maybe, bdb)) → new_ltEs18(vyy301, vyy41, bdb)
new_lt20(vyy301, vyy41, app(ty_Maybe, dac)) → new_lt16(vyy301, vyy41, dac)
new_ltEs20(vyy660, vyy62, ty_Ordering) → new_ltEs12(vyy660, vyy62)
new_primCmpNat0(Zero, Succ(vyy400)) → LT
new_lt12(vyy300, vyy40, ty_@0) → new_lt11(vyy300, vyy40)
new_ltEs18(Just(vyy300), Just(vyy40), app(ty_Ratio, bhg)) → new_ltEs10(vyy300, vyy40, bhg)
new_esEs8(@2(vyy780, vyy781), @2(vyy790, vyy791), dc, dd) → new_asAs(new_esEs26(vyy780, vyy790, dc), new_esEs27(vyy781, vyy791, dd))
new_ltEs11(Right(vyy300), Right(vyy40), deh, ty_Int) → new_ltEs9(vyy300, vyy40)
new_esEs15(vyy780, vyy790, ty_Bool) → new_esEs20(vyy780, vyy790)
new_esEs6(Left(vyy780), Right(vyy790), bfd, bdh) → False
new_esEs6(Right(vyy780), Left(vyy790), bfd, bdh) → False
new_ltEs11(Left(vyy300), Left(vyy40), ty_Double, dde) → new_ltEs5(vyy300, vyy40)
new_ltEs11(Left(vyy300), Left(vyy40), ty_Int, dde) → new_ltEs9(vyy300, vyy40)
new_compare15(vyy300, vyy40, ty_Double) → new_compare8(vyy300, vyy40)
new_compare8(Double(vyy300, vyy301), Double(vyy40, vyy41)) → new_compare29(new_sr(vyy300, vyy40), new_sr(vyy301, vyy41))
new_ltEs17(vyy30, vyy4) → new_not(new_compare28(vyy30, vyy4))
new_ltEs15(vyy30, vyy4) → new_not(new_compare16(vyy30, vyy4))
new_ltEs16(vyy30, vyy4) → new_not(new_compare27(vyy30, vyy4))
new_esEs17(vyy782, vyy792, ty_@0) → new_esEs22(vyy782, vyy792)
new_ltEs11(Right(vyy300), Right(vyy40), deh, ty_Bool) → new_ltEs4(vyy300, vyy40)
new_ltEs18(Just(vyy300), Just(vyy40), app(app(app(ty_@3, bhb), bhc), bhd)) → new_ltEs6(vyy300, vyy40, bhb, bhc, bhd)
new_primEqNat0(Zero, Zero) → True
new_compare26(vyy300, vyy40, True) → EQ
new_lt12(vyy300, vyy40, ty_Char) → new_lt7(vyy300, vyy40)
new_compare11(vyy300, vyy40, True, bd) → LT
new_primMulNat0(Succ(vyy30000), Succ(vyy4100)) → new_primPlusNat1(new_primMulNat0(vyy30000, Succ(vyy4100)), vyy4100)
new_compare111(vyy300, vyy40, False, bb, bc) → GT
new_ltEs11(Right(vyy300), Right(vyy40), deh, ty_Integer) → new_ltEs7(vyy300, vyy40)
new_compare29(vyy30, vyy4) → new_primCmpInt(vyy30, vyy4)
new_lt8(vyy300, vyy40) → new_esEs14(new_compare28(vyy300, vyy40))
new_esEs6(Right(vyy780), Right(vyy790), bfd, app(app(ty_Either, bge), bgf)) → new_esEs6(vyy780, vyy790, bge, bgf)
new_esEs28(vyy78, vyy79, ty_Ordering) → new_esEs25(vyy78, vyy79)
new_esEs15(vyy780, vyy790, app(app(ty_FiniteMap, cbb), cbc)) → new_esEs19(vyy780, vyy790, cbb, cbc)
new_ltEs11(Left(vyy300), Left(vyy40), ty_Float, dde) → new_ltEs17(vyy300, vyy40)
new_compare110(vyy300, vyy40, False, gf, gg) → GT
new_lt13(vyy300, vyy40) → new_esEs14(new_compare18(vyy300, vyy40))
new_compare19(:%(vyy300, vyy301), :%(vyy40, vyy41), ty_Int) → new_compare29(new_sr(vyy300, vyy41), new_sr(vyy40, vyy301))
new_ltEs18(Just(vyy300), Just(vyy40), app(ty_[], cac)) → new_ltEs13(vyy300, vyy40, cac)
new_sr(vyy300, vyy41) → new_primMulInt(vyy300, vyy41)
new_ltEs21(vyy670, vyy62, ty_Float) → new_ltEs17(vyy670, vyy62)
new_esEs28(vyy78, vyy79, app(app(ty_Either, bfd), bdh)) → new_esEs6(vyy78, vyy79, bfd, bdh)
new_esEs17(vyy782, vyy792, app(app(app(ty_@3, ced), cee), cef)) → new_esEs5(vyy782, vyy792, ced, cee, cef)
new_esEs7(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, he), hf)) → new_esEs19(vyy780, vyy790, he, hf)
new_esEs29(vyy780, vyy790, ty_Bool) → new_esEs20(vyy780, vyy790)
new_ltEs7(vyy30, vyy4) → new_not(new_compare13(vyy30, vyy4))
new_esEs19(vyy78, vyy79, ha, hb) → new_asAs(new_esEs12(new_sizeFM(vyy78, ha, hb), new_sizeFM(vyy79, ha, hb)), new_esEs18(new_fmToList(vyy78, ha, hb), new_fmToList(vyy79, ha, hb), app(app(ty_@2, ha), hb)))
new_esEs26(vyy780, vyy790, ty_Int) → new_esEs12(vyy780, vyy790)
new_esEs29(vyy780, vyy790, app(app(ty_FiniteMap, dcb), dcc)) → new_esEs19(vyy780, vyy790, dcb, dcc)
new_lt12(vyy300, vyy40, app(ty_Maybe, bbh)) → new_lt16(vyy300, vyy40, bbh)
new_compare15(vyy300, vyy40, app(ty_[], cgg)) → new_compare5(vyy300, vyy40, cgg)
new_esEs29(vyy780, vyy790, ty_Float) → new_esEs21(vyy780, vyy790)
new_esEs6(Right(vyy780), Right(vyy790), bfd, ty_Bool) → new_esEs20(vyy780, vyy790)
new_compare23(vyy300, vyy40, False) → new_compare10(vyy300, vyy40, new_ltEs4(vyy300, vyy40))
new_lt20(vyy301, vyy41, ty_Double) → new_lt17(vyy301, vyy41)
new_ltEs14(vyy301, vyy41, app(ty_Ratio, bda)) → new_ltEs10(vyy301, vyy41, bda)
new_esEs25(EQ, EQ) → True
new_esEs13(Integer(vyy780), Integer(vyy790)) → new_primEqInt(vyy780, vyy790)
new_esEs15(vyy780, vyy790, ty_Double) → new_esEs23(vyy780, vyy790)
new_esEs27(vyy781, vyy791, ty_Float) → new_esEs21(vyy781, vyy791)
new_esEs29(vyy780, vyy790, ty_Int) → new_esEs12(vyy780, vyy790)
new_ltEs8(@2(vyy300, vyy301), @2(vyy40, vyy41), bah, bba) → new_pePe(new_lt12(vyy300, vyy40, bah), vyy300, vyy40, new_ltEs14(vyy301, vyy41, bba), bah)
new_esEs7(Just(vyy780), Just(vyy790), ty_Ordering) → new_esEs25(vyy780, vyy790)
new_primEqInt(Neg(Succ(vyy7800)), Neg(Succ(vyy7900))) → new_primEqNat0(vyy7800, vyy7900)
new_ltEs11(Right(vyy300), Right(vyy40), deh, app(app(ty_@2, dfh), dga)) → new_ltEs8(vyy300, vyy40, dfh, dga)
new_compare15(vyy300, vyy40, ty_Integer) → new_compare13(vyy300, vyy40)
new_esEs14(EQ) → False
new_lt19(vyy300, vyy40, app(app(ty_@2, gf), gg)) → new_lt4(vyy300, vyy40, gf, gg)
new_esEs15(vyy780, vyy790, ty_Integer) → new_esEs13(vyy780, vyy790)
new_ltEs19(vyy302, vyy42, ty_Double) → new_ltEs5(vyy302, vyy42)
new_ltEs11(Right(vyy300), Right(vyy40), deh, app(ty_Ratio, dff)) → new_ltEs10(vyy300, vyy40, dff)
new_ltEs11(Right(vyy300), Right(vyy40), deh, app(ty_[], dgb)) → new_ltEs13(vyy300, vyy40, dgb)
new_esEs11(vyy781, vyy791, ty_Int) → new_esEs12(vyy781, vyy791)
new_ltEs21(vyy670, vyy62, ty_Double) → new_ltEs5(vyy670, vyy62)
new_esEs6(Right(vyy780), Right(vyy790), bfd, app(app(ty_@2, bgg), bgh)) → new_esEs8(vyy780, vyy790, bgg, bgh)
new_compare211(vyy300, vyy40, False, gf, gg) → new_compare110(vyy300, vyy40, new_ltEs8(vyy300, vyy40, gf, gg), gf, gg)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs28(vyy78, vyy79, app(app(ty_FiniteMap, ha), hb)) → new_esEs19(vyy78, vyy79, ha, hb)
new_esEs17(vyy782, vyy792, app(ty_[], cea)) → new_esEs18(vyy782, vyy792, cea)
new_esEs6(Left(vyy780), Left(vyy790), ty_Integer, bdh) → new_esEs13(vyy780, vyy790)
new_esEs27(vyy781, vyy791, ty_Int) → new_esEs12(vyy781, vyy791)
new_compare15(vyy300, vyy40, app(ty_Ratio, cgc)) → new_compare19(vyy300, vyy40, cgc)
new_ltEs12(EQ, EQ) → True
new_esEs29(vyy780, vyy790, ty_Char) → new_esEs24(vyy780, vyy790)
new_ltEs5(vyy30, vyy4) → new_not(new_compare8(vyy30, vyy4))
new_compare7(vyy300, vyy40, gf, gg) → new_compare211(vyy300, vyy40, new_esEs8(vyy300, vyy40, gf, gg), gf, gg)
new_primEqInt(Neg(Zero), Neg(Succ(vyy7900))) → False
new_primEqInt(Neg(Succ(vyy7800)), Neg(Zero)) → False
new_esEs10(vyy780, vyy790, ty_Integer) → new_esEs13(vyy780, vyy790)
new_primPlusNat1(Zero, vyy4100) → Succ(vyy4100)
new_esEs25(LT, LT) → True
new_esEs28(vyy78, vyy79, ty_Char) → new_esEs24(vyy78, vyy79)
new_compare24(vyy300, vyy40, True, bb, bc) → EQ
new_ltEs21(vyy670, vyy62, ty_Bool) → new_ltEs4(vyy670, vyy62)
new_esEs26(vyy780, vyy790, app(ty_[], de)) → new_esEs18(vyy780, vyy790, de)
new_compare15(vyy300, vyy40, ty_Int) → new_compare29(vyy300, vyy40)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), ha, hb) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, ha, hb), vyy7933, ha, hb)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs21(vyy670, vyy62, ty_Ordering) → new_ltEs12(vyy670, vyy62)
new_esEs15(vyy780, vyy790, app(ty_Ratio, cbh)) → new_esEs9(vyy780, vyy790, cbh)
new_primCmpNat0(Succ(vyy3000), Succ(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_sizeFM(EmptyFM, ha, hb) → Pos(Zero)
new_esEs15(vyy780, vyy790, ty_Float) → new_esEs21(vyy780, vyy790)
new_compare5(:(vyy300, vyy301), [], cad) → GT
new_compare11(vyy300, vyy40, False, bd) → GT
new_compare112(vyy300, vyy40, True) → LT
new_primEqInt(Pos(Succ(vyy7800)), Pos(Succ(vyy7900))) → new_primEqNat0(vyy7800, vyy7900)
new_esEs17(vyy782, vyy792, app(ty_Ratio, ceh)) → new_esEs9(vyy782, vyy792, ceh)
new_esEs7(Just(vyy780), Just(vyy790), ty_Double) → new_esEs23(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), app(app(app(ty_@3, bec), bed), bee), bdh) → new_esEs5(vyy780, vyy790, bec, bed, bee)
new_lt12(vyy300, vyy40, ty_Ordering) → new_lt10(vyy300, vyy40)
new_esEs7(Just(vyy780), Just(vyy790), app(app(ty_@2, baf), bag)) → new_esEs8(vyy780, vyy790, baf, bag)
new_ltEs20(vyy660, vyy62, ty_@0) → new_ltEs16(vyy660, vyy62)
new_ltEs19(vyy302, vyy42, app(ty_Ratio, dbd)) → new_ltEs10(vyy302, vyy42, dbd)
new_primEqNat0(Succ(vyy7800), Succ(vyy7900)) → new_primEqNat0(vyy7800, vyy7900)
new_lt5(vyy300, vyy40, cfe) → new_esEs14(new_compare5(vyy300, vyy40, cfe))
new_ltEs21(vyy670, vyy62, app(ty_Ratio, ce)) → new_ltEs10(vyy670, vyy62, ce)
new_esEs6(Left(vyy780), Left(vyy790), app(ty_Ratio, beg), bdh) → new_esEs9(vyy780, vyy790, beg)
new_compare5(:(vyy300, vyy301), :(vyy40, vyy41), cad) → new_primCompAux0(vyy300, vyy40, new_compare5(vyy301, vyy41, cad), cad)
new_primCompAux00(vyy111, LT) → LT
new_esEs6(Right(vyy780), Right(vyy790), bfd, ty_Integer) → new_esEs13(vyy780, vyy790)
new_lt12(vyy300, vyy40, ty_Bool) → new_lt13(vyy300, vyy40)
new_primCmpInt(Neg(Succ(vyy3000)), Neg(vyy40)) → new_primCmpNat0(vyy40, Succ(vyy3000))
new_esEs27(vyy781, vyy791, ty_Double) → new_esEs23(vyy781, vyy791)
new_esEs17(vyy782, vyy792, ty_Bool) → new_esEs20(vyy782, vyy792)
new_esEs27(vyy781, vyy791, app(app(app(ty_@3, fd), ff), fg)) → new_esEs5(vyy781, vyy791, fd, ff, fg)
new_primCompAux0(vyy300, vyy40, vyy107, cad) → new_primCompAux00(vyy107, new_compare15(vyy300, vyy40, cad))
new_esEs6(Left(vyy780), Left(vyy790), ty_@0, bdh) → new_esEs22(vyy780, vyy790)
new_esEs7(Nothing, Nothing, hc) → True
new_compare25(vyy300, vyy40, False, bd) → new_compare11(vyy300, vyy40, new_ltEs18(vyy300, vyy40, bd), bd)
new_primEqInt(Pos(Zero), Pos(Succ(vyy7900))) → False
new_primEqInt(Pos(Succ(vyy7800)), Pos(Zero)) → False
new_esEs6(Right(vyy780), Right(vyy790), bfd, ty_@0) → new_esEs22(vyy780, vyy790)
new_primPlusNat0(Zero, Succ(vyy41000)) → Succ(vyy41000)
new_primPlusNat0(Succ(vyy12600), Zero) → Succ(vyy12600)
new_ltEs19(vyy302, vyy42, ty_Float) → new_ltEs17(vyy302, vyy42)
new_ltEs11(Right(vyy300), Right(vyy40), deh, app(app(ty_Either, dfd), dfe)) → new_ltEs11(vyy300, vyy40, dfd, dfe)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs17(vyy782, vyy792, ty_Double) → new_esEs23(vyy782, vyy792)
new_ltEs18(Nothing, Nothing, bha) → True
new_esEs6(Right(vyy780), Right(vyy790), bfd, app(ty_Maybe, bgc)) → new_esEs7(vyy780, vyy790, bgc)
new_primCmpNat0(Succ(vyy3000), Zero) → GT
new_lt20(vyy301, vyy41, app(app(ty_@2, dad), dae)) → new_lt4(vyy301, vyy41, dad, dae)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy400))) → LT
new_ltEs21(vyy670, vyy62, app(app(app(ty_@3, bh), ca), cb)) → new_ltEs6(vyy670, vyy62, bh, ca, cb)
new_compare210(vyy300, vyy40, True, be, bf, bg) → EQ
new_esEs27(vyy781, vyy791, ty_Char) → new_esEs24(vyy781, vyy791)
new_sr0(Integer(vyy3000), Integer(vyy410)) → Integer(new_primMulInt(vyy3000, vyy410))
new_compare14(vyy300, vyy40, False, be, bf, bg) → GT
new_esEs17(vyy782, vyy792, app(app(ty_Either, cfa), cfb)) → new_esEs6(vyy782, vyy792, cfa, cfb)
new_primEqInt(Neg(Succ(vyy7800)), Pos(vyy790)) → False
new_primEqInt(Pos(Succ(vyy7800)), Neg(vyy790)) → False
new_esEs7(Nothing, Just(vyy790), hc) → False
new_esEs7(Just(vyy780), Nothing, hc) → False
new_lt19(vyy300, vyy40, app(ty_Ratio, bdf)) → new_lt15(vyy300, vyy40, bdf)
new_foldFM2(EmptyFM, ha, hb) → []
new_compare15(vyy300, vyy40, app(app(ty_@2, cge), cgf)) → new_compare7(vyy300, vyy40, cge, cgf)
new_ltEs12(GT, EQ) → False
new_lt19(vyy300, vyy40, app(ty_Maybe, bd)) → new_lt16(vyy300, vyy40, bd)
new_esEs20(False, False) → True
new_ltEs18(Just(vyy300), Just(vyy40), app(app(ty_Either, bhe), bhf)) → new_ltEs11(vyy300, vyy40, bhe, bhf)
new_foldFM_LE10(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, vyy67, False, h, ba) → new_foldFM_LE0(vyy61, vyy62, vyy66, h, ba)
new_foldFM_LE0(vyy61, vyy62, Branch(vyy660, vyy661, vyy662, vyy663, vyy664), h, ba) → new_foldFM_LE10(vyy61, vyy62, vyy660, vyy661, vyy662, vyy663, vyy664, new_ltEs20(vyy660, vyy62, ba), h, ba)
new_esEs21(Float(vyy780, vyy781), Float(vyy790, vyy791)) → new_esEs12(new_sr(vyy780, vyy790), new_sr(vyy781, vyy791))
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_@2, bfb), bfc), bdh) → new_esEs8(vyy780, vyy790, bfb, bfc)
new_lt12(vyy300, vyy40, ty_Float) → new_lt8(vyy300, vyy40)
new_primEqInt(Neg(Zero), Pos(Succ(vyy7900))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy7900))) → False
new_ltEs18(Just(vyy300), Just(vyy40), ty_Double) → new_ltEs5(vyy300, vyy40)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy400))) → new_primCmpNat0(Zero, Succ(vyy400))
new_primCompAux00(vyy111, EQ) → vyy111
new_esEs25(LT, GT) → False
new_esEs25(GT, LT) → False
new_lt20(vyy301, vyy41, ty_Bool) → new_lt13(vyy301, vyy41)
new_ltEs11(Left(vyy300), Left(vyy40), app(app(ty_@2, dee), def), dde) → new_ltEs8(vyy300, vyy40, dee, def)
new_eltsFM_LE0(vyy63, vyy64, vyy95, h, ba) → :(vyy64, vyy95)
new_lt20(vyy301, vyy41, app(app(app(ty_@3, che), chf), chg)) → new_lt9(vyy301, vyy41, che, chf, chg)
new_lt19(vyy300, vyy40, ty_@0) → new_lt11(vyy300, vyy40)
new_ltEs14(vyy301, vyy41, ty_Float) → new_ltEs17(vyy301, vyy41)
new_lt20(vyy301, vyy41, ty_Integer) → new_lt6(vyy301, vyy41)
new_esEs17(vyy782, vyy792, app(app(ty_@2, cfc), cfd)) → new_esEs8(vyy782, vyy792, cfc, cfd)
new_lt19(vyy300, vyy40, app(ty_[], cfe)) → new_lt5(vyy300, vyy40, cfe)
new_esEs28(vyy78, vyy79, ty_Double) → new_esEs23(vyy78, vyy79)
new_esEs15(vyy780, vyy790, ty_@0) → new_esEs22(vyy780, vyy790)
new_esEs17(vyy782, vyy792, ty_Int) → new_esEs12(vyy782, vyy792)
new_esEs15(vyy780, vyy790, app(ty_Maybe, cbg)) → new_esEs7(vyy780, vyy790, cbg)
new_esEs23(Double(vyy780, vyy781), Double(vyy790, vyy791)) → new_esEs12(new_sr(vyy780, vyy790), new_sr(vyy781, vyy791))
new_pePe(False, vyy78, vyy79, vyy97, cgh) → new_asAs(new_esEs28(vyy78, vyy79, cgh), vyy97)
new_esEs26(vyy780, vyy790, app(app(ty_FiniteMap, df), dg)) → new_esEs19(vyy780, vyy790, df, dg)
new_ltEs20(vyy660, vyy62, app(app(app(ty_@3, bh), ca), cb)) → new_ltEs6(vyy660, vyy62, bh, ca, cb)
new_ltEs11(Left(vyy300), Left(vyy40), app(app(app(ty_@3, ddf), ddg), ddh), dde) → new_ltEs6(vyy300, vyy40, ddf, ddg, ddh)
new_ltEs13(vyy30, vyy4, cad) → new_not(new_compare5(vyy30, vyy4, cad))
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_Either, beh), bfa), bdh) → new_esEs6(vyy780, vyy790, beh, bfa)
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, bea), beb), bdh) → new_esEs19(vyy780, vyy790, bea, beb)
new_ltEs20(vyy660, vyy62, app(ty_Ratio, ce)) → new_ltEs10(vyy660, vyy62, ce)
new_ltEs18(Just(vyy300), Just(vyy40), ty_@0) → new_ltEs16(vyy300, vyy40)
new_ltEs18(Just(vyy300), Nothing, bha) → False
new_primCmpInt(Pos(Succ(vyy3000)), Pos(vyy40)) → new_primCmpNat0(Succ(vyy3000), vyy40)
new_esEs27(vyy781, vyy791, ty_@0) → new_esEs22(vyy781, vyy791)
new_esEs29(vyy780, vyy790, app(app(ty_@2, ddc), ddd)) → new_esEs8(vyy780, vyy790, ddc, ddd)
new_esEs16(vyy781, vyy791, app(ty_[], cce)) → new_esEs18(vyy781, vyy791, cce)
new_esEs7(Just(vyy780), Just(vyy790), ty_Bool) → new_esEs20(vyy780, vyy790)
new_esEs16(vyy781, vyy791, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs5(vyy781, vyy791, cch, cda, cdb)
new_not0True
new_ltEs11(Right(vyy300), Right(vyy40), deh, ty_Double) → new_ltEs5(vyy300, vyy40)
new_ltEs19(vyy302, vyy42, app(app(app(ty_@3, dag), dah), dba)) → new_ltEs6(vyy302, vyy42, dag, dah, dba)
new_esEs27(vyy781, vyy791, app(app(ty_Either, gb), gc)) → new_esEs6(vyy781, vyy791, gb, gc)
new_esEs27(vyy781, vyy791, app(ty_[], fa)) → new_esEs18(vyy781, vyy791, fa)
new_esEs14(GT) → False
new_esEs16(vyy781, vyy791, ty_Double) → new_esEs23(vyy781, vyy791)
new_esEs15(vyy780, vyy790, app(app(ty_Either, cca), ccb)) → new_esEs6(vyy780, vyy790, cca, ccb)
new_compare16(Char(vyy300), Char(vyy40)) → new_primCmpNat0(vyy300, vyy40)
new_esEs16(vyy781, vyy791, app(app(ty_@2, cdg), cdh)) → new_esEs8(vyy781, vyy791, cdg, cdh)
new_primCmpInt(Pos(Succ(vyy3000)), Neg(vyy40)) → GT
new_ltEs19(vyy302, vyy42, ty_Int) → new_ltEs9(vyy302, vyy42)
new_esEs28(vyy78, vyy79, app(ty_Maybe, hc)) → new_esEs7(vyy78, vyy79, hc)
new_ltEs11(Left(vyy300), Left(vyy40), app(ty_[], deg), dde) → new_ltEs13(vyy300, vyy40, deg)
new_lt19(vyy300, vyy40, ty_Ordering) → new_lt10(vyy300, vyy40)
new_esEs26(vyy780, vyy790, ty_Char) → new_esEs24(vyy780, vyy790)
new_primMulInt(Pos(vyy3000), Pos(vyy410)) → Pos(new_primMulNat0(vyy3000, vyy410))
new_lt12(vyy300, vyy40, app(app(app(ty_@3, bbb), bbc), bbd)) → new_lt9(vyy300, vyy40, bbb, bbc, bbd)
new_ltEs11(Right(vyy300), Right(vyy40), deh, app(app(app(ty_@3, dfa), dfb), dfc)) → new_ltEs6(vyy300, vyy40, dfa, dfb, dfc)
new_lt12(vyy300, vyy40, app(ty_[], bcc)) → new_lt5(vyy300, vyy40, bcc)
new_compare24(vyy300, vyy40, False, bb, bc) → new_compare111(vyy300, vyy40, new_ltEs11(vyy300, vyy40, bb, bc), bb, bc)
new_primMulInt(Neg(vyy3000), Neg(vyy410)) → Pos(new_primMulNat0(vyy3000, vyy410))
new_esEs24(Char(vyy780), Char(vyy790)) → new_primEqNat0(vyy780, vyy790)
new_ltEs12(EQ, GT) → True
new_esEs28(vyy78, vyy79, app(ty_Ratio, cae)) → new_esEs9(vyy78, vyy79, cae)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Integer) → new_ltEs7(vyy300, vyy40)
new_ltEs20(vyy660, vyy62, ty_Float) → new_ltEs17(vyy660, vyy62)
new_primEqNat0(Zero, Succ(vyy7900)) → False
new_primEqNat0(Succ(vyy7800), Zero) → False
new_lt17(vyy300, vyy40) → new_esEs14(new_compare8(vyy300, vyy40))
new_ltEs14(vyy301, vyy41, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs6(vyy301, vyy41, bcd, bce, bcf)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs21(vyy670, vyy62, ty_Integer) → new_ltEs7(vyy670, vyy62)
new_lt20(vyy301, vyy41, app(ty_Ratio, dab)) → new_lt15(vyy301, vyy41, dab)
new_lt10(vyy300, vyy40) → new_esEs14(new_compare12(vyy300, vyy40))
new_ltEs20(vyy660, vyy62, ty_Char) → new_ltEs15(vyy660, vyy62)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare15(vyy300, vyy40, ty_@0) → new_compare27(vyy300, vyy40)
new_lt19(vyy300, vyy40, ty_Double) → new_lt17(vyy300, vyy40)
new_lt11(vyy300, vyy40) → new_esEs14(new_compare27(vyy300, vyy40))
new_lt12(vyy300, vyy40, app(ty_Ratio, bbg)) → new_lt15(vyy300, vyy40, bbg)
new_ltEs14(vyy301, vyy41, ty_Char) → new_ltEs15(vyy301, vyy41)
new_esEs25(EQ, GT) → False
new_esEs25(GT, EQ) → False
new_sizeFM(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), ha, hb) → vyy792
new_ltEs4(True, False) → False
new_esEs29(vyy780, vyy790, app(app(ty_Either, dda), ddb)) → new_esEs6(vyy780, vyy790, dda, ddb)
new_foldFM_LE10(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, EmptyFM, True, h, ba) → new_foldFM_LE3(vyy63, vyy64, new_foldFM_LE0(vyy61, vyy62, vyy66, h, ba), vyy62, h, ba)
new_ltEs21(vyy670, vyy62, app(ty_Maybe, cf)) → new_ltEs18(vyy670, vyy62, cf)
new_pePe(True, vyy78, vyy79, vyy97, cgh) → True
new_primPlusNat1(Succ(vyy1260), vyy4100) → Succ(Succ(new_primPlusNat0(vyy1260, vyy4100)))
new_esEs6(Left(vyy780), Left(vyy790), app(ty_[], bdg), bdh) → new_esEs18(vyy780, vyy790, bdg)
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), ha, hb) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, ha, hb), vyy793, ha, hb)
new_esEs29(vyy780, vyy790, app(app(app(ty_@3, dcd), dce), dcf)) → new_esEs5(vyy780, vyy790, dcd, dce, dcf)
new_esEs29(vyy780, vyy790, ty_Ordering) → new_esEs25(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), ty_Ordering, bdh) → new_esEs25(vyy780, vyy790)
new_ltEs14(vyy301, vyy41, ty_@0) → new_ltEs16(vyy301, vyy41)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy400))) → new_primCmpNat0(Succ(vyy400), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy400))) → GT
new_esEs6(Left(vyy780), Left(vyy790), ty_Bool, bdh) → new_esEs20(vyy780, vyy790)
new_esEs27(vyy781, vyy791, ty_Ordering) → new_esEs25(vyy781, vyy791)
new_esEs6(Left(vyy780), Left(vyy790), app(ty_Maybe, bef), bdh) → new_esEs7(vyy780, vyy790, bef)
new_esEs16(vyy781, vyy791, ty_@0) → new_esEs22(vyy781, vyy791)
new_esEs12(vyy78, vyy79) → new_primEqInt(vyy78, vyy79)
new_lt20(vyy301, vyy41, ty_Char) → new_lt7(vyy301, vyy41)
new_esEs20(True, False) → False
new_esEs20(False, True) → False
new_esEs15(vyy780, vyy790, app(app(ty_@2, ccc), ccd)) → new_esEs8(vyy780, vyy790, ccc, ccd)
new_compare26(vyy300, vyy40, False) → new_compare112(vyy300, vyy40, new_ltEs12(vyy300, vyy40))
new_esEs15(vyy780, vyy790, ty_Int) → new_esEs12(vyy780, vyy790)
new_ltEs11(Left(vyy300), Left(vyy40), app(app(ty_Either, dea), deb), dde) → new_ltEs11(vyy300, vyy40, dea, deb)
new_compare5([], :(vyy40, vyy41), cad) → LT
new_ltEs21(vyy670, vyy62, ty_@0) → new_ltEs16(vyy670, vyy62)
new_esEs7(Just(vyy780), Just(vyy790), ty_Char) → new_esEs24(vyy780, vyy790)
new_esEs7(Just(vyy780), Just(vyy790), app(app(app(ty_@3, hg), hh), baa)) → new_esEs5(vyy780, vyy790, hg, hh, baa)
new_esEs29(vyy780, vyy790, app(ty_Ratio, dch)) → new_esEs9(vyy780, vyy790, dch)
new_ltEs11(Left(vyy300), Left(vyy40), ty_Integer, dde) → new_ltEs7(vyy300, vyy40)
new_esEs17(vyy782, vyy792, ty_Integer) → new_esEs13(vyy782, vyy792)
new_esEs28(vyy78, vyy79, app(ty_[], cha)) → new_esEs18(vyy78, vyy79, cha)
new_esEs5(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), caf, cag, cah) → new_asAs(new_esEs15(vyy780, vyy790, caf), new_asAs(new_esEs16(vyy781, vyy791, cag), new_esEs17(vyy782, vyy792, cah)))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs28(vyy78, vyy79, ty_Bool) → new_esEs20(vyy78, vyy79)
new_ltEs14(vyy301, vyy41, ty_Double) → new_ltEs5(vyy301, vyy41)
new_lt19(vyy300, vyy40, ty_Bool) → new_lt13(vyy300, vyy40)
new_esEs7(Just(vyy780), Just(vyy790), app(ty_[], hd)) → new_esEs18(vyy780, vyy790, hd)
new_esEs6(Right(vyy780), Right(vyy790), bfd, ty_Double) → new_esEs23(vyy780, vyy790)
new_esEs17(vyy782, vyy792, ty_Float) → new_esEs21(vyy782, vyy792)
new_esEs16(vyy781, vyy791, ty_Integer) → new_esEs13(vyy781, vyy791)
new_asAs(False, vyy106) → False
new_esEs29(vyy780, vyy790, ty_@0) → new_esEs22(vyy780, vyy790)
new_primMulInt(Neg(vyy3000), Pos(vyy410)) → Neg(new_primMulNat0(vyy3000, vyy410))
new_primMulInt(Pos(vyy3000), Neg(vyy410)) → Neg(new_primMulNat0(vyy3000, vyy410))
new_ltEs11(Left(vyy300), Right(vyy40), deh, dde) → True
new_ltEs11(Right(vyy300), Right(vyy40), deh, ty_Ordering) → new_ltEs12(vyy300, vyy40)
new_primMulNat0(Succ(vyy30000), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy4100)) → Zero
new_esEs18([], [], cha) → True
new_esEs26(vyy780, vyy790, ty_Integer) → new_esEs13(vyy780, vyy790)
new_ltEs20(vyy660, vyy62, ty_Integer) → new_ltEs7(vyy660, vyy62)
new_ltEs21(vyy670, vyy62, app(app(ty_Either, cc), cd)) → new_ltEs11(vyy670, vyy62, cc, cd)
new_compare6(vyy300, vyy40, bb, bc) → new_compare24(vyy300, vyy40, new_esEs6(vyy300, vyy40, bb, bc), bb, bc)
new_ltEs12(GT, GT) → True
new_ltEs14(vyy301, vyy41, ty_Integer) → new_ltEs7(vyy301, vyy41)
new_compare19(:%(vyy300, vyy301), :%(vyy40, vyy41), ty_Integer) → new_compare13(new_sr0(vyy300, vyy41), new_sr0(vyy40, vyy301))
new_compare210(vyy300, vyy40, False, be, bf, bg) → new_compare14(vyy300, vyy40, new_ltEs6(vyy300, vyy40, be, bf, bg), be, bf, bg)
new_esEs26(vyy780, vyy790, app(ty_Maybe, ec)) → new_esEs7(vyy780, vyy790, ec)
new_ltEs18(Nothing, Just(vyy40), bha) → True
new_esEs6(Left(vyy780), Left(vyy790), ty_Float, bdh) → new_esEs21(vyy780, vyy790)
new_lt19(vyy300, vyy40, ty_Float) → new_lt8(vyy300, vyy40)
new_ltEs11(Right(vyy300), Right(vyy40), deh, app(ty_Maybe, dfg)) → new_ltEs18(vyy300, vyy40, dfg)
new_not(EQ) → new_not0
new_esEs26(vyy780, vyy790, app(ty_Ratio, ed)) → new_esEs9(vyy780, vyy790, ed)
new_lt20(vyy301, vyy41, ty_Float) → new_lt8(vyy301, vyy41)
new_compare15(vyy300, vyy40, ty_Char) → new_compare16(vyy300, vyy40)
new_esEs11(vyy781, vyy791, ty_Integer) → new_esEs13(vyy781, vyy791)
new_esEs27(vyy781, vyy791, app(app(ty_FiniteMap, fb), fc)) → new_esEs19(vyy781, vyy791, fb, fc)
new_esEs15(vyy780, vyy790, app(ty_[], cba)) → new_esEs18(vyy780, vyy790, cba)
new_ltEs11(Right(vyy300), Right(vyy40), deh, ty_@0) → new_ltEs16(vyy300, vyy40)
new_ltEs4(False, False) → True
new_foldFM_LE20(vyy63, vyy64, vyy96, vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, h, ba) → new_foldFM_LE10(new_eltsFM_LE0(vyy63, vyy64, vyy96, h, ba), vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, new_ltEs21(vyy670, vyy62, ba), h, ba)
new_esEs28(vyy78, vyy79, ty_Integer) → new_esEs13(vyy78, vyy79)
new_foldFM_LE10(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, Branch(vyy670, vyy671, vyy672, vyy673, vyy674), True, h, ba) → new_foldFM_LE20(vyy63, vyy64, new_foldFM_LE0(vyy61, vyy62, vyy66, h, ba), vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, h, ba)
new_lt12(vyy300, vyy40, ty_Double) → new_lt17(vyy300, vyy40)
new_esEs16(vyy781, vyy791, ty_Int) → new_esEs12(vyy781, vyy791)
new_ltEs11(Right(vyy300), Right(vyy40), deh, ty_Float) → new_ltEs17(vyy300, vyy40)
new_ltEs11(Left(vyy300), Left(vyy40), app(ty_Ratio, dec), dde) → new_ltEs10(vyy300, vyy40, dec)
new_esEs25(LT, EQ) → False
new_esEs25(EQ, LT) → False
new_compare211(vyy300, vyy40, True, gf, gg) → EQ
new_foldFM_LE3(vyy63, vyy64, vyy95, vyy62, h, ba) → new_eltsFM_LE0(vyy63, vyy64, vyy95, h, ba)
new_esEs29(vyy780, vyy790, ty_Double) → new_esEs23(vyy780, vyy790)
new_esEs16(vyy781, vyy791, app(ty_Maybe, cdc)) → new_esEs7(vyy781, vyy791, cdc)
new_esEs7(Just(vyy780), Just(vyy790), ty_Int) → new_esEs12(vyy780, vyy790)
new_esEs7(Just(vyy780), Just(vyy790), ty_Integer) → new_esEs13(vyy780, vyy790)
new_esEs9(:%(vyy780, vyy781), :%(vyy790, vyy791), cae) → new_asAs(new_esEs10(vyy780, vyy790, cae), new_esEs11(vyy781, vyy791, cae))
new_ltEs12(EQ, LT) → False
new_ltEs18(Just(vyy300), Just(vyy40), ty_Int) → new_ltEs9(vyy300, vyy40)
new_not(LT) → new_not0
new_compare13(Integer(vyy300), Integer(vyy40)) → new_primCmpInt(vyy300, vyy40)
new_esEs26(vyy780, vyy790, ty_Float) → new_esEs21(vyy780, vyy790)
new_esEs7(Just(vyy780), Just(vyy790), ty_Float) → new_esEs21(vyy780, vyy790)
new_compare112(vyy300, vyy40, False) → GT
new_esEs6(Right(vyy780), Right(vyy790), bfd, ty_Int) → new_esEs12(vyy780, vyy790)
new_esEs16(vyy781, vyy791, ty_Char) → new_esEs24(vyy781, vyy791)
new_esEs7(Just(vyy780), Just(vyy790), ty_@0) → new_esEs22(vyy780, vyy790)
new_esEs16(vyy781, vyy791, ty_Bool) → new_esEs20(vyy781, vyy791)
new_compare12(vyy300, vyy40) → new_compare26(vyy300, vyy40, new_esEs25(vyy300, vyy40))
new_ltEs19(vyy302, vyy42, ty_Integer) → new_ltEs7(vyy302, vyy42)
new_esEs6(Right(vyy780), Right(vyy790), bfd, app(ty_[], bfe)) → new_esEs18(vyy780, vyy790, bfe)
new_esEs28(vyy78, vyy79, ty_Int) → new_esEs12(vyy78, vyy79)
new_primPlusNat0(Succ(vyy12600), Succ(vyy41000)) → Succ(Succ(new_primPlusNat0(vyy12600, vyy41000)))
new_esEs28(vyy78, vyy79, app(app(ty_@2, dc), dd)) → new_esEs8(vyy78, vyy79, dc, dd)
new_esEs26(vyy780, vyy790, app(app(ty_Either, ee), ef)) → new_esEs6(vyy780, vyy790, ee, ef)
new_esEs26(vyy780, vyy790, ty_Double) → new_esEs23(vyy780, vyy790)
new_lt20(vyy301, vyy41, ty_Ordering) → new_lt10(vyy301, vyy41)
new_esEs29(vyy780, vyy790, app(ty_[], dca)) → new_esEs18(vyy780, vyy790, dca)
new_compare111(vyy300, vyy40, True, bb, bc) → LT
new_esEs28(vyy78, vyy79, ty_@0) → new_esEs22(vyy78, vyy79)
new_ltEs9(vyy30, vyy4) → new_not(new_compare29(vyy30, vyy4))
new_asAs(True, vyy106) → vyy106
new_compare27(@0, @0) → EQ
new_esEs26(vyy780, vyy790, app(app(app(ty_@3, dh), ea), eb)) → new_esEs5(vyy780, vyy790, dh, ea, eb)
new_ltEs11(Left(vyy300), Left(vyy40), ty_@0, dde) → new_ltEs16(vyy300, vyy40)
new_lt15(vyy300, vyy40, bdf) → new_esEs14(new_compare19(vyy300, vyy40, bdf))
new_ltEs10(vyy30, vyy4, gh) → new_not(new_compare19(vyy30, vyy4, gh))
new_ltEs11(Right(vyy300), Right(vyy40), deh, ty_Char) → new_ltEs15(vyy300, vyy40)
new_compare15(vyy300, vyy40, ty_Bool) → new_compare18(vyy300, vyy40)
new_compare15(vyy300, vyy40, app(ty_Maybe, cgd)) → new_compare9(vyy300, vyy40, cgd)
new_ltEs14(vyy301, vyy41, app(ty_[], bde)) → new_ltEs13(vyy301, vyy41, bde)
new_lt20(vyy301, vyy41, ty_@0) → new_lt11(vyy301, vyy41)
new_fmToList(vyy79, ha, hb) → new_foldFM2(vyy79, ha, hb)
new_esEs6(Left(vyy780), Left(vyy790), ty_Double, bdh) → new_esEs23(vyy780, vyy790)
new_lt20(vyy301, vyy41, app(ty_[], daf)) → new_lt5(vyy301, vyy41, daf)
new_ltEs19(vyy302, vyy42, app(app(ty_Either, dbb), dbc)) → new_ltEs11(vyy302, vyy42, dbb, dbc)
new_compare15(vyy300, vyy40, app(app(ty_Either, cga), cgb)) → new_compare6(vyy300, vyy40, cga, cgb)
new_compare5([], [], cad) → EQ
new_ltEs14(vyy301, vyy41, app(app(ty_Either, bcg), bch)) → new_ltEs11(vyy301, vyy41, bcg, bch)
new_lt9(vyy300, vyy40, be, bf, bg) → new_esEs14(new_compare17(vyy300, vyy40, be, bf, bg))
new_compare10(vyy300, vyy40, True) → LT
new_lt18(vyy300, vyy40) → new_esEs14(new_compare29(vyy300, vyy40))
new_compare10(vyy300, vyy40, False) → GT
new_primCompAux00(vyy111, GT) → GT
new_esEs14(LT) → True
new_lt6(vyy300, vyy40) → new_esEs14(new_compare13(vyy300, vyy40))
new_ltEs14(vyy301, vyy41, ty_Int) → new_ltEs9(vyy301, vyy41)
new_ltEs21(vyy670, vyy62, app(ty_[], db)) → new_ltEs13(vyy670, vyy62, db)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs12(GT, LT) → False
new_esEs6(Right(vyy780), Right(vyy790), bfd, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs5(vyy780, vyy790, bfh, bga, bgb)
new_esEs16(vyy781, vyy791, ty_Float) → new_esEs21(vyy781, vyy791)
new_ltEs19(vyy302, vyy42, ty_@0) → new_ltEs16(vyy302, vyy42)
new_ltEs11(Left(vyy300), Left(vyy40), ty_Ordering, dde) → new_ltEs12(vyy300, vyy40)
new_ltEs19(vyy302, vyy42, app(ty_[], dbh)) → new_ltEs13(vyy302, vyy42, dbh)
new_compare15(vyy300, vyy40, ty_Float) → new_compare28(vyy300, vyy40)
new_foldFM_LE0(vyy61, vyy62, EmptyFM, h, ba) → vyy61
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(vyy302, vyy42, app(ty_Maybe, dbe)) → new_ltEs18(vyy302, vyy42, dbe)
new_esEs22(@0, @0) → True
new_ltEs14(vyy301, vyy41, ty_Bool) → new_ltEs4(vyy301, vyy41)
new_esEs6(Right(vyy780), Right(vyy790), bfd, ty_Char) → new_esEs24(vyy780, vyy790)
new_primCmpInt(Neg(Succ(vyy3000)), Pos(vyy40)) → LT
new_compare15(vyy300, vyy40, ty_Ordering) → new_compare12(vyy300, vyy40)
new_lt4(vyy300, vyy40, gf, gg) → new_esEs14(new_compare7(vyy300, vyy40, gf, gg))

The set Q consists of the following terms:

new_lt20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs11(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_compare210(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, ty_Double)
new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(LT, LT)
new_foldFM_LE0(x0, x1, EmptyFM, x2, x3)
new_ltEs20(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt12(x0, x1, ty_Bool)
new_ltEs14(x0, x1, ty_Int)
new_esEs16(x0, x1, ty_Integer)
new_compare14(x0, x1, True, x2, x3, x4)
new_esEs12(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_compare111(x0, x1, False, x2, x3)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(Left(x0), Left(x1), ty_Float, x2)
new_ltEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_esEs17(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs19(x0, x1, x2, x3)
new_asAs(False, x0)
new_esEs14(EQ)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare15(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare111(x0, x1, True, x2, x3)
new_ltEs11(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs16(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare24(x0, x1, False, x2, x3)
new_esEs29(x0, x1, ty_Double)
new_ltEs12(GT, GT)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs17(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs14(x0, x1, app(ty_Ratio, x2))
new_foldFM_LE3(x0, x1, x2, x3, x4, x5)
new_esEs17(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs29(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs14(x0, x1, ty_Double)
new_foldFM2(EmptyFM, x0, x1)
new_compare15(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_compare15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(Left(x0), Left(x1), ty_Char, x2)
new_lt12(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs25(LT, LT)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare7(x0, x1, x2, x3)
new_esEs6(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs21(x0, x1, ty_Integer)
new_ltEs18(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, GT)
new_esEs18([], [], x0)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs16(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_@0)
new_esEs17(x0, x1, app(app(ty_@2, x2), x3))
new_compare26(x0, x1, True)
new_esEs18([], :(x0, x1), x2)
new_esEs22(@0, @0)
new_esEs28(x0, x1, app(ty_[], x2))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_compare112(x0, x1, True)
new_primEqNat0(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt12(x0, x1, app(ty_Ratio, x2))
new_ltEs4(True, True)
new_compare211(x0, x1, True, x2, x3)
new_ltEs14(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_compare5(:(x0, x1), [], x2)
new_esEs17(x0, x1, ty_Double)
new_pePe(False, x0, x1, x2, x3)
new_compare15(x0, x1, ty_Bool)
new_esEs17(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_lt7(x0, x1)
new_esEs25(GT, GT)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Nothing, Nothing, x0)
new_compare19(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs29(x0, x1, ty_@0)
new_compare18(x0, x1)
new_ltEs20(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs14(x0, x1, app(app(ty_@2, x2), x3))
new_compare14(x0, x1, False, x2, x3, x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs11(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_compare210(x0, x1, False, x2, x3, x4)
new_ltEs21(x0, x1, ty_Double)
new_compare5(:(x0, x1), :(x2, x3), x4)
new_ltEs13(x0, x1, x2)
new_esEs15(x0, x1, ty_Integer)
new_esEs20(True, True)
new_lt19(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_compare5([], :(x0, x1), x2)
new_compare25(x0, x1, True, x2)
new_esEs28(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True, x2, x3)
new_esEs24(Char(x0), Char(x1))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs25(GT, EQ)
new_esEs25(EQ, GT)
new_ltEs11(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs4(False, False)
new_lt20(x0, x1, ty_Char)
new_ltEs10(x0, x1, x2)
new_esEs17(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1, ty_Double)
new_primCmpNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Char)
new_esEs16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs9(x0, x1)
new_ltEs11(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, ty_Bool)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(False, True)
new_esEs20(True, False)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs28(x0, x1, ty_@0)
new_esEs16(x0, x1, ty_Char)
new_esEs20(False, False)
new_lt9(x0, x1, x2, x3, x4)
new_esEs15(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Integer)
new_compare11(x0, x1, True, x2)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs28(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_not0
new_compare15(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(ty_[], x2))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare110(x0, x1, False, x2, x3)
new_primPlusNat0(Zero, Zero)
new_ltEs11(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Nothing, Just(x0), x1)
new_fmToList(x0, x1, x2)
new_compare211(x0, x1, False, x2, x3)
new_lt16(x0, x1, x2)
new_ltEs11(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs16(x0, x1, ty_Ordering)
new_compare12(x0, x1)
new_ltEs20(x0, x1, ty_Bool)
new_compare25(x0, x1, False, x2)
new_compare28(Float(x0, x1), Float(x2, x3))
new_ltEs14(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Char)
new_esEs16(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_ltEs11(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Integer)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs15(x0, x1, ty_@0)
new_esEs25(GT, LT)
new_esEs25(LT, GT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, EmptyFM, True, x6, x7)
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Bool)
new_lt18(x0, x1)
new_ltEs11(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs11(Right(x0), Right(x1), x2, ty_@0)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs11(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare8(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs21(Float(x0, x1), Float(x2, x3))
new_esEs16(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Bool)
new_ltEs12(GT, EQ)
new_ltEs12(EQ, GT)
new_primEqNat0(Succ(x0), Zero)
new_esEs27(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_not(GT)
new_esEs11(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs18(:(x0, x1), [], x2)
new_lt4(x0, x1, x2, x3)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt19(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_esEs14(LT)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs7(x0, x1)
new_lt5(x0, x1, x2)
new_lt17(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_compare23(x0, x1, True)
new_ltEs14(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare15(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs16(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Int)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_primPlusNat1(Succ(x0), x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_lt12(x0, x1, ty_Ordering)
new_esEs17(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(x0, x1)
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Just(x0), Nothing, x1)
new_pePe(True, x0, x1, x2, x3)
new_ltEs12(EQ, EQ)
new_primCompAux00(x0, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Float)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare29(x0, x1)
new_lt10(x0, x1)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs26(x0, x1, ty_Double)
new_ltEs11(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs17(x0, x1)
new_esEs25(EQ, EQ)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, False, x2)
new_lt20(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_ltEs16(x0, x1)
new_esEs11(x0, x1, ty_Int)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1)
new_compare26(x0, x1, False)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), True, x11, x12)
new_lt11(x0, x1)
new_esEs15(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_compare15(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs15(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, ty_Int)
new_esEs16(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, EQ)
new_ltEs14(x0, x1, ty_Char)
new_ltEs11(Left(x0), Left(x1), ty_Double, x2)
new_ltEs11(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt19(x0, x1, ty_Int)
new_esEs14(GT)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare6(x0, x1, x2, x3)
new_lt19(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs11(Right(x0), Right(x1), x2, ty_Int)
new_compare15(x0, x1, ty_Ordering)
new_compare13(Integer(x0), Integer(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_eltsFM_LE0(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Zero, Zero)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs11(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_@0)
new_lt12(x0, x1, ty_Float)
new_esEs16(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(x0, x1, ty_Bool)
new_ltEs4(False, True)
new_ltEs4(True, False)
new_ltEs14(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs11(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs11(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_lt15(x0, x1, x2)
new_ltEs21(x0, x1, ty_Char)
new_esEs17(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare17(x0, x1, x2, x3, x4)
new_sizeFM(EmptyFM, x0, x1)
new_ltEs14(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs21(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt12(x0, x1, ty_Integer)
new_esEs16(x0, x1, ty_@0)
new_esEs16(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Float)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs18(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_Float)
new_esEs17(x0, x1, ty_Integer)
new_ltEs11(Left(x0), Left(x1), ty_Int, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs11(Left(x0), Left(x1), ty_@0, x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt12(x0, x1, ty_@0)
new_esEs17(x0, x1, ty_@0)
new_compare24(x0, x1, True, x2, x3)
new_primPlusNat0(Zero, Succ(x0))
new_not(EQ)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare112(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, ty_Int)
new_compare5([], [], x0)
new_compare9(x0, x1, x2)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, x0)
new_esEs16(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs15(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_esEs15(x0, x1, app(ty_Ratio, x2))
new_esEs15(x0, x1, app(ty_[], x2))
new_ltEs11(Left(x0), Right(x1), x2, x3)
new_ltEs11(Right(x0), Left(x1), x2, x3)
new_sr0(Integer(x0), Integer(x1))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_lt14(x0, x1, x2, x3)
new_compare15(x0, x1, app(ty_Ratio, x2))
new_foldFM_LE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs17(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1)
new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(Right(x0), Right(x1), x2, ty_Bool)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_Integer)
new_esEs16(x0, x1, app(ty_Ratio, x2))
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True)
new_esEs15(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs11(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs14(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs12(EQ, LT)
new_ltEs12(LT, EQ)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_compare16(Char(x0), Char(x1))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs17(x0, x1, ty_Char)
new_compare27(@0, @0)
new_primPlusNat0(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs27(x0, x1, ty_Bool)
new_esEs17(x0, x1, ty_Bool)
new_esEs17(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Int)
new_ltEs21(x0, x1, ty_Float)
new_ltEs11(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs12(GT, LT)
new_ltEs12(LT, GT)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs23(Double(x0, x1), Double(x2, x3))
new_compare15(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Char)
new_esEs25(LT, EQ)
new_esEs25(EQ, LT)
new_primMulNat0(Succ(x0), Zero)
new_compare19(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(x0, x1, ty_Float)
new_lt6(x0, x1)
new_ltEs15(x0, x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs15(x0, x1, ty_Float)
new_ltEs11(Right(x0), Right(x1), x2, ty_Float)
new_esEs15(x0, x1, ty_Char)
new_compare23(x0, x1, False)
new_foldFM_LE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8)
new_esEs15(x0, x1, ty_Double)
new_not(LT)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs26(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), ty_Float)

We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: