YES 9.059000000000001 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



HASKELL
  ↳ LR

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Lambda Reductions:
The following Lambda expression
\keyeltrestkey : rest

is transformed to
keysFM_LE0 key elt rest = key : rest

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

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



↳ HASKELL
  ↳ LR
HASKELL
      ↳ CR

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (a  ->  b  ->  c  ->  c ->  c  ->  FiniteMap a b  ->  c
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

  keysFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_LE fm fr foldFM_LE keysFM_LE0 [] fr fm

  
keysFM_LE0 key elt rest key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
HASKELL
          ↳ IFR

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

  keysFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_LE fm fr foldFM_LE keysFM_LE0 [] fr fm

  
keysFM_LE0 key elt rest key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

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

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



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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
fmToList0 key elt rest (key,elt: rest

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

  keysFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [b]
keysFM_LE fm fr foldFM_LE keysFM_LE0 [] fr fm

  
keysFM_LE0 key elt rest key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Replaced joker patterns by fresh variables and removed binding patterns.

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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
fmToList0 key elt rest (key,elt: rest

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

  keysFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_LE fm fr foldFM_LE keysFM_LE0 [] fr fm

  
keysFM_LE0 key elt rest key : rest

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch vy vz size wu 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_LE0 k z fr key elt vx fm_l fm_r True = foldFM_LE k z fr fm_l

foldFM_LE1 k z fr key elt vx fm_l fm_r True = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r
foldFM_LE1 k z fr key elt vx fm_l fm_r False = foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise

foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) = foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr)

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

The following Function with conditions
compare x y
 | x == y
 = EQ
 | x <= y
 = LT
 | otherwise
 = GT

is transformed to
compare x y = compare3 x y

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

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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (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 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

  keysFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [b]
keysFM_LE fm fr foldFM_LE keysFM_LE0 [] fr fm

  
keysFM_LE0 key elt rest key : rest

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch vy vz size wu 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'1 True x vvy = x
gcd0Gcd'1 vvz vwu vwv = gcd0Gcd'0 vwu vwv

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

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

gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y)



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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
fmToList0 key elt rest (key,elt: rest

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

  foldFM_LE :: Ord a => (a  ->  b  ->  c  ->  c ->  c  ->  a  ->  FiniteMap a b  ->  c
foldFM_LE k z fr EmptyFM foldFM_LE3 k z fr EmptyFM
foldFM_LE k z fr (Branch key elt vx fm_l fm_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

  keysFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [b]
keysFM_LE fm fr foldFM_LE keysFM_LE0 [] fr fm

  
keysFM_LE0 key elt rest key : rest

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch vy vz size wu 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
  (keysFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [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

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

  
fmToList0 key elt rest (key,elt: rest

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

  foldFM_LE :: Ord a => (a  ->  b  ->  c  ->  c ->  c  ->  a  ->  FiniteMap a b  ->  c
foldFM_LE k z fr EmptyFM foldFM_LE3 k z fr EmptyFM
foldFM_LE k z fr (Branch key elt vx fm_l fm_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

  keysFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_LE fm fr foldFM_LE keysFM_LE0 [] fr fm

  
keysFM_LE0 key elt rest key : rest

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM 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_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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                    ↳ QDPSizeChangeProof
                                  ↳ 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
                                  ↳ QDP
                                  ↳ QDP
QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primMulNat(Succ(vyy30100), Succ(vyy4100)) → new_primMulNat(vyy30100, 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
                                  ↳ QDP
                                  ↳ QDP
QDP
                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bge)) → new_esEs4(vyy780, vyy790, bge)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_@2, bch), bda), bcg) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_[], bag)) → new_esEs(vyy780, vyy790, bag)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, bee), bef), bba, bcg) → new_esEs2(vyy780, vyy790, bee, bef)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(vyy780, vyy790, bg, bh, ca)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, bfb), bba, bcg) → new_esEs4(vyy780, vyy790, bfb)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_Either, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_[], bdh), bcg) → new_esEs(vyy781, vyy791, bdh)
new_esEs2(Left(vyy780), Left(vyy790), app(app(app(ty_@3, gg), gh), ha), gb) → new_esEs3(vyy780, vyy790, gg, gh, ha)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bea), beb), bba, bcg) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_Maybe, bdg), bcg) → new_esEs4(vyy781, vyy791, bdg)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy781, vyy791, db, dc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
new_esEs4(Just(vyy780), Just(vyy790), app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs3(vyy780, vyy790, bgb, bgc, bgd)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_Either, baa), bab)) → new_esEs2(vyy780, vyy790, baa, bab)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_Either, dd), de)) → new_esEs2(vyy781, vyy791, dd, de)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, ff), ee) → new_esEs4(vyy780, vyy790, ff)
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_esEs2(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_[], hc), gb) → new_esEs(vyy780, vyy790, hc)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, ec), ed), ee) → new_esEs0(vyy780, vyy790, ec, ed)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_FiniteMap, bce), bcf), bcg) → new_esEs0(vyy781, vyy791, bce, bcf)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, eh), fa), ee) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_Either, bfh), bga)) → new_esEs2(vyy780, vyy790, bfh, bga)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_Maybe, ea)) → new_esEs4(vyy781, vyy791, ea)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(app(ty_@3, df), dg), dh)) → new_esEs3(vyy781, vyy791, df, dg, dh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs3(vyy782, vyy792, bbh, bca, bcb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_[], bcd)) → new_esEs(vyy782, vyy792, bcd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bec), bed), bba, bcg) → new_esEs1(vyy780, vyy790, bec, bed)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_FiniteMap, cg), da)) → new_esEs0(vyy781, vyy791, cg, da)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bfc), bba, bcg) → new_esEs(vyy780, vyy790, bfc)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy780, vyy790, hg, hh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_Either, bdb), bdc), bcg) → new_esEs2(vyy781, vyy791, bdb, bdc)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_[], eb)) → new_esEs(vyy781, vyy791, eb)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_Maybe, hb), gb) → new_esEs4(vyy780, vyy790, hb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], fg), ee) → new_esEs(vyy780, vyy790, fg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_Either, bbf), bbg)) → new_esEs2(vyy782, vyy792, bbf, bbg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_Maybe, bcc)) → new_esEs4(vyy782, vyy792, bcc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bc), bd)) → new_esEs1(vyy780, vyy790, bc, bd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(app(ty_@3, bdd), bde), bdf), bcg) → new_esEs3(vyy781, vyy791, bdd, bde, bdf)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_Maybe, baf)) → new_esEs4(vyy780, vyy790, baf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), h) → new_esEs(vyy781, vyy791, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, be), bf)) → new_esEs2(vyy780, vyy790, be, bf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_@2, bbd), bbe)) → new_esEs1(vyy782, vyy792, bbd, bbe)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, fb), fc), fd), ee) → new_esEs3(vyy780, vyy790, fb, fc, fd)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgf)) → new_esEs(vyy780, vyy790, bgf)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(app(ty_@3, bac), bad), bae)) → new_esEs3(vyy780, vyy790, bac, bad, bae)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], cc)) → new_esEs(vyy780, vyy790, cc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, beg), beh), bfa), bba, bcg) → new_esEs3(vyy780, vyy790, beg, beh, bfa)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_FiniteMap, bbb), bbc)) → new_esEs0(vyy782, vyy792, bbb, bbc)
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_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bge)) → new_esEs4(vyy780, vyy790, bge)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_@2, bch), bda), bcg) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, bee), bef), bba, bcg) → new_esEs2(vyy780, vyy790, bee, bef)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_[], bag)) → new_esEs(vyy780, vyy790, bag)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, bfb), bba, bcg) → new_esEs4(vyy780, vyy790, bfb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(vyy780, vyy790, bg, bh, ca)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_[], bdh), bcg) → new_esEs(vyy781, vyy791, bdh)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_Either, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs2(Left(vyy780), Left(vyy790), app(app(app(ty_@3, gg), gh), ha), gb) → new_esEs3(vyy780, vyy790, gg, gh, ha)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bea), beb), bba, bcg) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy781, vyy791, db, dc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_Maybe, bdg), bcg) → new_esEs4(vyy781, vyy791, bdg)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
new_esEs4(Just(vyy780), Just(vyy790), app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs3(vyy780, vyy790, bgb, bgc, bgd)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_Either, baa), bab)) → new_esEs2(vyy780, vyy790, baa, bab)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_Either, dd), de)) → new_esEs2(vyy781, vyy791, dd, de)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, ff), ee) → new_esEs4(vyy780, vyy790, ff)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_FiniteMap, bce), bcf), bcg) → new_esEs0(vyy781, vyy791, bce, bcf)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, ec), ed), ee) → new_esEs0(vyy780, vyy790, ec, ed)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_[], hc), gb) → new_esEs(vyy780, vyy790, hc)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, eh), fa), ee) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_Maybe, ea)) → new_esEs4(vyy781, vyy791, ea)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_Either, bfh), bga)) → new_esEs2(vyy780, vyy790, bfh, bga)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(app(ty_@3, df), dg), dh)) → new_esEs3(vyy781, vyy791, df, dg, dh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs3(vyy782, vyy792, bbh, bca, bcb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_[], bcd)) → new_esEs(vyy782, vyy792, bcd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bec), bed), bba, bcg) → new_esEs1(vyy780, vyy790, bec, bed)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_FiniteMap, cg), da)) → new_esEs0(vyy781, vyy791, cg, da)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy780, vyy790, hg, hh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bfc), bba, bcg) → new_esEs(vyy780, vyy790, bfc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_Either, bdb), bdc), bcg) → new_esEs2(vyy781, vyy791, bdb, bdc)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_[], eb)) → new_esEs(vyy781, vyy791, eb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], fg), ee) → new_esEs(vyy780, vyy790, fg)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_Maybe, hb), gb) → new_esEs4(vyy780, vyy790, hb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_Either, bbf), bbg)) → new_esEs2(vyy782, vyy792, bbf, bbg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_Maybe, bcc)) → new_esEs4(vyy782, vyy792, bcc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(app(ty_@3, bdd), bde), bdf), bcg) → new_esEs3(vyy781, vyy791, bdd, bde, bdf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bc), bd)) → new_esEs1(vyy780, vyy790, bc, bd)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_Maybe, baf)) → new_esEs4(vyy780, vyy790, baf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), h) → new_esEs(vyy781, vyy791, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, be), bf)) → new_esEs2(vyy780, vyy790, be, bf)
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_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_@2, bbd), bbe)) → new_esEs1(vyy782, vyy792, bbd, bbe)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, fb), fc), fd), ee) → new_esEs3(vyy780, vyy790, fb, fc, fd)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgf)) → new_esEs(vyy780, vyy790, bgf)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(app(ty_@3, bac), bad), bae)) → new_esEs3(vyy780, vyy790, bac, bad, bae)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], cc)) → new_esEs(vyy780, vyy790, cc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_FiniteMap, bbb), bbc)) → new_esEs0(vyy782, vyy792, bbb, bbc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, beg), beh), bfa), bba, bcg) → new_esEs3(vyy780, vyy790, beg, beh, bfa)
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_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bge)) → new_esEs4(vyy780, vyy790, bge)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_@2, bch), bda), bcg) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_[], bag)) → new_esEs(vyy780, vyy790, bag)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, bee), bef), bba, bcg) → new_esEs2(vyy780, vyy790, bee, bef)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(vyy780, vyy790, bg, bh, ca)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, bfb), bba, bcg) → new_esEs4(vyy780, vyy790, bfb)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_Either, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_[], bdh), bcg) → new_esEs(vyy781, vyy791, bdh)
new_esEs2(Left(vyy780), Left(vyy790), app(app(app(ty_@3, gg), gh), ha), gb) → new_esEs3(vyy780, vyy790, gg, gh, ha)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bea), beb), bba, bcg) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_Maybe, bdg), bcg) → new_esEs4(vyy781, vyy791, bdg)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy781, vyy791, db, dc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
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(Just(vyy780), Just(vyy790), app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs3(vyy780, vyy790, bgb, bgc, bgd)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_Either, baa), bab)) → new_esEs2(vyy780, vyy790, baa, bab)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_Either, dd), de)) → new_esEs2(vyy781, vyy791, dd, de)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, ff), ee) → new_esEs4(vyy780, vyy790, ff)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_[], hc), gb) → new_esEs(vyy780, vyy790, hc)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, ec), ed), ee) → new_esEs0(vyy780, vyy790, ec, ed)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_FiniteMap, bce), bcf), bcg) → new_esEs0(vyy781, vyy791, bce, bcf)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, eh), fa), ee) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_Either, bfh), bga)) → new_esEs2(vyy780, vyy790, bfh, bga)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_Maybe, ea)) → new_esEs4(vyy781, vyy791, ea)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(app(ty_@3, df), dg), dh)) → new_esEs3(vyy781, vyy791, df, dg, dh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs3(vyy782, vyy792, bbh, bca, bcb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_[], bcd)) → new_esEs(vyy782, vyy792, bcd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bec), bed), bba, bcg) → new_esEs1(vyy780, vyy790, bec, bed)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_FiniteMap, cg), da)) → new_esEs0(vyy781, vyy791, cg, da)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bfc), bba, bcg) → new_esEs(vyy780, vyy790, bfc)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy780, vyy790, hg, hh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_Either, bdb), bdc), bcg) → new_esEs2(vyy781, vyy791, bdb, bdc)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_[], eb)) → new_esEs(vyy781, vyy791, eb)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_Maybe, hb), gb) → new_esEs4(vyy780, vyy790, hb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], fg), ee) → new_esEs(vyy780, vyy790, fg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_Either, bbf), bbg)) → new_esEs2(vyy782, vyy792, bbf, bbg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_Maybe, bcc)) → new_esEs4(vyy782, vyy792, bcc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bc), bd)) → new_esEs1(vyy780, vyy790, bc, bd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(app(ty_@3, bdd), bde), bdf), bcg) → new_esEs3(vyy781, vyy791, bdd, bde, bdf)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_Maybe, baf)) → new_esEs4(vyy780, vyy790, baf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), h) → new_esEs(vyy781, vyy791, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, be), bf)) → new_esEs2(vyy780, vyy790, be, bf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_@2, bbd), bbe)) → new_esEs1(vyy782, vyy792, bbd, bbe)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, fb), fc), fd), ee) → new_esEs3(vyy780, vyy790, fb, fc, fd)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgf)) → new_esEs(vyy780, vyy790, bgf)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(app(ty_@3, bac), bad), bae)) → new_esEs3(vyy780, vyy790, bac, bad, bae)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], cc)) → new_esEs(vyy780, vyy790, cc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, beg), beh), bfa), bba, bcg) → new_esEs3(vyy780, vyy790, beg, beh, bfa)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_FiniteMap, bbb), bbc)) → new_esEs0(vyy782, vyy792, bbb, bbc)
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_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bge)) → new_esEs4(vyy780, vyy790, bge)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_@2, bch), bda), bcg) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_[], bag)) → new_esEs(vyy780, vyy790, bag)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, bee), bef), bba, bcg) → new_esEs2(vyy780, vyy790, bee, bef)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(vyy780, vyy790, bg, bh, ca)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, bfb), bba, bcg) → new_esEs4(vyy780, vyy790, bfb)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_Either, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_[], bdh), bcg) → new_esEs(vyy781, vyy791, bdh)
new_esEs2(Left(vyy780), Left(vyy790), app(app(app(ty_@3, gg), gh), ha), gb) → new_esEs3(vyy780, vyy790, gg, gh, ha)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bea), beb), bba, bcg) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_Maybe, bdg), bcg) → new_esEs4(vyy781, vyy791, bdg)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy781, vyy791, db, dc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
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(Just(vyy780), Just(vyy790), app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs3(vyy780, vyy790, bgb, bgc, bgd)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_Either, baa), bab)) → new_esEs2(vyy780, vyy790, baa, bab)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_Either, dd), de)) → new_esEs2(vyy781, vyy791, dd, de)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, ff), ee) → new_esEs4(vyy780, vyy790, ff)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_FiniteMap, bce), bcf), bcg) → new_esEs0(vyy781, vyy791, bce, bcf)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_[], hc), gb) → new_esEs(vyy780, vyy790, hc)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, ec), ed), ee) → new_esEs0(vyy780, vyy790, ec, ed)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, eh), fa), ee) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_Either, bfh), bga)) → new_esEs2(vyy780, vyy790, bfh, bga)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_Maybe, ea)) → new_esEs4(vyy781, vyy791, ea)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(app(ty_@3, df), dg), dh)) → new_esEs3(vyy781, vyy791, df, dg, dh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs3(vyy782, vyy792, bbh, bca, bcb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_[], bcd)) → new_esEs(vyy782, vyy792, bcd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bec), bed), bba, bcg) → new_esEs1(vyy780, vyy790, bec, bed)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_FiniteMap, cg), da)) → new_esEs0(vyy781, vyy791, cg, da)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bfc), bba, bcg) → new_esEs(vyy780, vyy790, bfc)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy780, vyy790, hg, hh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_Either, bdb), bdc), bcg) → new_esEs2(vyy781, vyy791, bdb, bdc)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_[], eb)) → new_esEs(vyy781, vyy791, eb)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_Maybe, hb), gb) → new_esEs4(vyy780, vyy790, hb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], fg), ee) → new_esEs(vyy780, vyy790, fg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_Either, bbf), bbg)) → new_esEs2(vyy782, vyy792, bbf, bbg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_Maybe, bcc)) → new_esEs4(vyy782, vyy792, bcc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bc), bd)) → new_esEs1(vyy780, vyy790, bc, bd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(app(ty_@3, bdd), bde), bdf), bcg) → new_esEs3(vyy781, vyy791, bdd, bde, bdf)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_Maybe, baf)) → new_esEs4(vyy780, vyy790, baf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), h) → new_esEs(vyy781, vyy791, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, be), bf)) → new_esEs2(vyy780, vyy790, be, bf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_@2, bbd), bbe)) → new_esEs1(vyy782, vyy792, bbd, bbe)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, fb), fc), fd), ee) → new_esEs3(vyy780, vyy790, fb, fc, fd)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgf)) → new_esEs(vyy780, vyy790, bgf)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(app(ty_@3, bac), bad), bae)) → new_esEs3(vyy780, vyy790, bac, bad, bae)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], cc)) → new_esEs(vyy780, vyy790, cc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, beg), beh), bfa), bba, bcg) → new_esEs3(vyy780, vyy790, beg, beh, bfa)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_FiniteMap, bbb), bbc)) → new_esEs0(vyy782, vyy792, bbb, bbc)
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_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bge)) → new_esEs4(vyy780, vyy790, bge)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_@2, bch), bda), bcg) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_[], bag)) → new_esEs(vyy780, vyy790, bag)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, bee), bef), bba, bcg) → new_esEs2(vyy780, vyy790, bee, bef)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(vyy780, vyy790, bg, bh, ca)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, bfb), bba, bcg) → new_esEs4(vyy780, vyy790, bfb)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_Either, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_[], bdh), bcg) → new_esEs(vyy781, vyy791, bdh)
new_esEs2(Left(vyy780), Left(vyy790), app(app(app(ty_@3, gg), gh), ha), gb) → new_esEs3(vyy780, vyy790, gg, gh, ha)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bea), beb), bba, bcg) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy781, vyy791, db, dc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_Maybe, bdg), bcg) → new_esEs4(vyy781, vyy791, bdg)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
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(Just(vyy780), Just(vyy790), app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs3(vyy780, vyy790, bgb, bgc, bgd)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_Either, baa), bab)) → new_esEs2(vyy780, vyy790, baa, bab)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_Either, dd), de)) → new_esEs2(vyy781, vyy791, dd, de)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, ff), ee) → new_esEs4(vyy780, vyy790, ff)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_[], hc), gb) → new_esEs(vyy780, vyy790, hc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_FiniteMap, bce), bcf), bcg) → new_esEs0(vyy781, vyy791, bce, bcf)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, ec), ed), ee) → new_esEs0(vyy780, vyy790, ec, ed)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, eh), fa), ee) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_Either, bfh), bga)) → new_esEs2(vyy780, vyy790, bfh, bga)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_Maybe, ea)) → new_esEs4(vyy781, vyy791, ea)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(app(ty_@3, df), dg), dh)) → new_esEs3(vyy781, vyy791, df, dg, dh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs3(vyy782, vyy792, bbh, bca, bcb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_[], bcd)) → new_esEs(vyy782, vyy792, bcd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bec), bed), bba, bcg) → new_esEs1(vyy780, vyy790, bec, bed)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_FiniteMap, cg), da)) → new_esEs0(vyy781, vyy791, cg, da)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bfc), bba, bcg) → new_esEs(vyy780, vyy790, bfc)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy780, vyy790, hg, hh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_Either, bdb), bdc), bcg) → new_esEs2(vyy781, vyy791, bdb, bdc)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_[], eb)) → new_esEs(vyy781, vyy791, eb)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_Maybe, hb), gb) → new_esEs4(vyy780, vyy790, hb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], fg), ee) → new_esEs(vyy780, vyy790, fg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_Either, bbf), bbg)) → new_esEs2(vyy782, vyy792, bbf, bbg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_Maybe, bcc)) → new_esEs4(vyy782, vyy792, bcc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bc), bd)) → new_esEs1(vyy780, vyy790, bc, bd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(app(ty_@3, bdd), bde), bdf), bcg) → new_esEs3(vyy781, vyy791, bdd, bde, bdf)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_Maybe, baf)) → new_esEs4(vyy780, vyy790, baf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), h) → new_esEs(vyy781, vyy791, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, be), bf)) → new_esEs2(vyy780, vyy790, be, bf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_@2, bbd), bbe)) → new_esEs1(vyy782, vyy792, bbd, bbe)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, fb), fc), fd), ee) → new_esEs3(vyy780, vyy790, fb, fc, fd)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgf)) → new_esEs(vyy780, vyy790, bgf)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(app(ty_@3, bac), bad), bae)) → new_esEs3(vyy780, vyy790, bac, bad, bae)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], cc)) → new_esEs(vyy780, vyy790, cc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_FiniteMap, bbb), bbc)) → new_esEs0(vyy782, vyy792, bbb, bbc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, beg), beh), bfa), bba, bcg) → new_esEs3(vyy780, vyy790, beg, beh, bfa)
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(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, bee), bef), bba, bcg) → new_esEs2(vyy780, vyy790, bee, bef)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(vyy780, vyy790, bg, bh, ca)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_Either, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs2(Left(vyy780), Left(vyy790), app(app(app(ty_@3, gg), gh), ha), gb) → new_esEs3(vyy780, vyy790, gg, gh, ha)
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(Just(vyy780), Just(vyy790), app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs3(vyy780, vyy790, bgb, bgc, bgd)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_Either, baa), bab)) → new_esEs2(vyy780, vyy790, baa, bab)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_Either, dd), de)) → new_esEs2(vyy781, vyy791, dd, de)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, eh), fa), ee) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_Either, bfh), bga)) → new_esEs2(vyy780, vyy790, bfh, bga)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(app(ty_@3, df), dg), dh)) → new_esEs3(vyy781, vyy791, df, dg, dh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs3(vyy782, vyy792, bbh, bca, bcb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_Either, bdb), bdc), bcg) → new_esEs2(vyy781, vyy791, bdb, bdc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_Either, bbf), bbg)) → new_esEs2(vyy782, vyy792, bbf, bbg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(app(ty_@3, bdd), bde), bdf), bcg) → new_esEs3(vyy781, vyy791, bdd, bde, bdf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, be), bf)) → new_esEs2(vyy780, vyy790, be, bf)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, fb), fc), fd), ee) → new_esEs3(vyy780, vyy790, fb, fc, fd)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(app(ty_@3, bac), bad), bae)) → new_esEs3(vyy780, vyy790, bac, bad, bae)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, beg), beh), bfa), bba, bcg) → new_esEs3(vyy780, vyy790, beg, beh, bfa)
The remaining pairs can at least be oriented weakly.

new_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bge)) → new_esEs4(vyy780, vyy790, bge)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_@2, bch), bda), bcg) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_[], bag)) → new_esEs(vyy780, vyy790, bag)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, bfb), bba, bcg) → new_esEs4(vyy780, vyy790, bfb)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_[], bdh), bcg) → new_esEs(vyy781, vyy791, bdh)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bea), beb), bba, bcg) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy781, vyy791, db, dc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_Maybe, bdg), bcg) → new_esEs4(vyy781, vyy791, bdg)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, ff), ee) → new_esEs4(vyy780, vyy790, ff)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_[], hc), gb) → new_esEs(vyy780, vyy790, hc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_FiniteMap, bce), bcf), bcg) → new_esEs0(vyy781, vyy791, bce, bcf)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, ec), ed), ee) → new_esEs0(vyy780, vyy790, ec, ed)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_Maybe, ea)) → new_esEs4(vyy781, vyy791, ea)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_[], bcd)) → new_esEs(vyy782, vyy792, bcd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bec), bed), bba, bcg) → new_esEs1(vyy780, vyy790, bec, bed)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_FiniteMap, cg), da)) → new_esEs0(vyy781, vyy791, cg, da)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bfc), bba, bcg) → new_esEs(vyy780, vyy790, bfc)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy780, vyy790, hg, hh)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_[], eb)) → new_esEs(vyy781, vyy791, eb)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_Maybe, hb), gb) → new_esEs4(vyy780, vyy790, hb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], fg), ee) → new_esEs(vyy780, vyy790, fg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_Maybe, bcc)) → new_esEs4(vyy782, vyy792, bcc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bc), bd)) → new_esEs1(vyy780, vyy790, bc, bd)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_Maybe, baf)) → new_esEs4(vyy780, vyy790, baf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), h) → new_esEs(vyy781, vyy791, h)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_@2, bbd), bbe)) → new_esEs1(vyy782, vyy792, bbd, bbe)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgf)) → new_esEs(vyy780, vyy790, bgf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], cc)) → new_esEs(vyy780, vyy790, cc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_FiniteMap, bbb), bbc)) → new_esEs0(vyy782, vyy792, bbb, bbc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy780, vyy790, ba, bb)
Used ordering: Polynomial interpretation [25]:

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

The following usable rules [17] were oriented: none



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

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

new_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bge)) → new_esEs4(vyy780, vyy790, bge)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_@2, bch), bda), bcg) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_[], hc), gb) → new_esEs(vyy780, vyy790, hc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(app(ty_FiniteMap, bce), bcf), bcg) → new_esEs0(vyy781, vyy791, bce, bcf)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, ec), ed), ee) → new_esEs0(vyy780, vyy790, ec, ed)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_Maybe, ea)) → new_esEs4(vyy781, vyy791, ea)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_[], bag)) → new_esEs(vyy780, vyy790, bag)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_[], bcd)) → new_esEs(vyy782, vyy792, bcd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bec), bed), bba, bcg) → new_esEs1(vyy780, vyy790, bec, bed)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, bfb), bba, bcg) → new_esEs4(vyy780, vyy790, bfb)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_FiniteMap, cg), da)) → new_esEs0(vyy781, vyy791, cg, da)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bfc), bba, bcg) → new_esEs(vyy780, vyy790, bfc)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy780, vyy790, hg, hh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_[], bdh), bcg) → new_esEs(vyy781, vyy791, bdh)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_[], eb)) → new_esEs(vyy781, vyy791, eb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bea), beb), bba, bcg) → new_esEs0(vyy780, vyy790, bea, beb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], fg), ee) → new_esEs(vyy780, vyy790, fg)
new_esEs2(Left(vyy780), Left(vyy790), app(ty_Maybe, hb), gb) → new_esEs4(vyy780, vyy790, hb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(ty_Maybe, bcc)) → new_esEs4(vyy782, vyy792, bcc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bc), bd)) → new_esEs1(vyy780, vyy790, bc, bd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, app(ty_Maybe, bdg), bcg) → new_esEs4(vyy781, vyy791, bdg)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy781, vyy791, db, dc)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(ty_Maybe, baf)) → new_esEs4(vyy780, vyy790, baf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), h) → new_esEs(vyy781, vyy791, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_@2, bbd), bbe)) → new_esEs1(vyy782, vyy792, bbd, bbe)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgf)) → new_esEs(vyy780, vyy790, bgf)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, ff), ee) → new_esEs4(vyy780, vyy790, ff)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], cc)) → new_esEs(vyy780, vyy790, cc)
new_esEs2(Left(vyy780), Left(vyy790), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs2(Right(vyy780), Right(vyy790), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy780, vyy790, he, hf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bah, bba, app(app(ty_FiniteMap, bbb), bbc)) → new_esEs0(vyy782, vyy792, bbb, bbc)
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.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 24 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_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bge)) → new_esEs4(vyy780, vyy790, bge)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), h) → new_esEs(vyy781, vyy791, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_Maybe, ea)) → new_esEs4(vyy781, vyy791, ea)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgf)) → new_esEs(vyy780, vyy790, bgf)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, ff), ee) → new_esEs4(vyy780, vyy790, ff)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_[], eb)) → new_esEs(vyy781, vyy791, eb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], fg), ee) → new_esEs(vyy780, vyy790, fg)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], cc)) → new_esEs(vyy780, vyy790, cc)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy781, vyy791, db, dc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bc), bd)) → new_esEs1(vyy780, vyy790, bc, bd)

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_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bge)) → new_esEs4(vyy780, vyy790, bge)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), h) → new_esEs(vyy781, vyy791, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_Maybe, ea)) → new_esEs4(vyy781, vyy791, ea)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgf)) → new_esEs(vyy780, vyy790, bgf)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, ff), ee) → new_esEs4(vyy780, vyy790, ff)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_[], eb)) → new_esEs(vyy781, vyy791, eb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], fg), ee) → new_esEs(vyy780, vyy790, fg)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], cc)) → new_esEs(vyy780, vyy790, cc)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy781, vyy791, db, dc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bc), bd)) → new_esEs1(vyy780, vyy790, bc, bd)

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_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bge)) → new_esEs4(vyy780, vyy790, bge)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), h) → new_esEs(vyy781, vyy791, h)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_Maybe, ea)) → new_esEs4(vyy781, vyy791, ea)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgf)) → new_esEs(vyy780, vyy790, bgf)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, ff), ee) → new_esEs4(vyy780, vyy790, ff)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(ty_[], eb)) → new_esEs(vyy781, vyy791, eb)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], fg), ee) → new_esEs(vyy780, vyy790, fg)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], cc)) → new_esEs(vyy780, vyy790, cc)
new_esEs1(@2(vyy780, vyy781), @2(vyy790, vyy791), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy781, vyy791, db, dc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bc), bd)) → new_esEs1(vyy780, vyy790, bc, bd)

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_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), ef, app(app(ty_Either, gd), ge), gc) → new_lt0(vyy301, vyy41, gd, ge)
new_compare1(vyy300, vyy40, hd) → new_compare2(vyy300, vyy40, new_esEs5(vyy300, vyy40, hd), hd)
new_primCompAux(vyy300, vyy40, vyy107, app(app(ty_@2, bbe), bbf)) → new_compare5(vyy300, vyy40, bbe, bbf)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), ef, app(ty_[], ha), gc) → new_lt2(vyy301, vyy41, ha)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), ef, app(app(app(ty_@3, gf), gg), gh), gc) → new_lt1(vyy301, vyy41, gf, gg, gh)
new_compare22(vyy300, vyy40, False, bac, bad) → new_ltEs3(vyy300, vyy40, bac, bad)
new_ltEs3(@2(vyy300, vyy301), @2(vyy40, vyy41), app(app(app(ty_@3, bde), bdf), bdg), bdb) → new_lt1(vyy300, vyy40, bde, bdf, bdg)
new_ltEs(Just(vyy300), Just(vyy40), app(ty_[], bf)) → new_ltEs2(vyy300, vyy40, bf)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), ef, eg, app(app(ty_@2, fh), ga)) → new_ltEs3(vyy302, vyy42, fh, ga)
new_ltEs3(@2(vyy300, vyy301), @2(vyy40, vyy41), bbg, app(app(app(ty_@3, bcc), bcd), bce)) → new_ltEs1(vyy301, vyy41, bcc, bcd, bce)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(app(ty_@2, bac), bad), eg, gc) → new_compare22(vyy300, vyy40, new_esEs8(vyy300, vyy40, bac, bad), bac, bad)
new_ltEs(Just(vyy300), Just(vyy40), app(app(ty_Either, ba), bb)) → new_ltEs0(vyy300, vyy40, ba, bb)
new_compare21(vyy300, vyy40, False, hg, hh, baa) → new_ltEs1(vyy300, vyy40, hg, hh, baa)
new_ltEs3(@2(vyy300, vyy301), @2(vyy40, vyy41), bbg, app(ty_[], bcf)) → new_ltEs2(vyy301, vyy41, bcf)
new_lt1(vyy300, vyy40, hg, hh, baa) → new_compare21(vyy300, vyy40, new_esEs7(vyy300, vyy40, hg, hh, baa), hg, hh, baa)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(ty_[], bab), eg, gc) → new_compare(vyy300, vyy40, bab)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), ef, app(app(ty_@2, hb), hc), gc) → new_lt3(vyy301, vyy41, hb, hc)
new_ltEs3(@2(vyy300, vyy301), @2(vyy40, vyy41), app(app(ty_Either, bdc), bdd), bdb) → new_lt0(vyy300, vyy40, bdc, bdd)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(app(ty_Either, he), hf), eg, gc) → new_compare20(vyy300, vyy40, new_esEs6(vyy300, vyy40, he, hf), he, hf)
new_ltEs(Just(vyy300), Just(vyy40), app(app(app(ty_@3, bc), bd), be)) → new_ltEs1(vyy300, vyy40, bc, bd, be)
new_ltEs0(Left(vyy300), Left(vyy40), app(app(ty_Either, cc), cd), cb) → new_ltEs0(vyy300, vyy40, cc, cd)
new_lt3(vyy300, vyy40, bac, bad) → new_compare22(vyy300, vyy40, new_esEs8(vyy300, vyy40, bac, bad), bac, bad)
new_ltEs3(@2(vyy300, vyy301), @2(vyy40, vyy41), bbg, app(app(ty_Either, bca), bcb)) → new_ltEs0(vyy301, vyy41, bca, bcb)
new_compare4(vyy300, vyy40, hg, hh, baa) → new_compare21(vyy300, vyy40, new_esEs7(vyy300, vyy40, hg, hh, baa), hg, hh, baa)
new_lt(vyy300, vyy40, hd) → new_compare2(vyy300, vyy40, new_esEs5(vyy300, vyy40, hd), hd)
new_ltEs(Just(vyy300), Just(vyy40), app(ty_Maybe, h)) → new_ltEs(vyy300, vyy40, h)
new_primCompAux(vyy300, vyy40, vyy107, app(ty_[], bbd)) → new_compare(vyy300, vyy40, bbd)
new_compare3(vyy300, vyy40, he, hf) → new_compare20(vyy300, vyy40, new_esEs6(vyy300, vyy40, he, hf), he, hf)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(ty_Maybe, hd), eg, gc) → new_compare2(vyy300, vyy40, new_esEs5(vyy300, vyy40, hd), hd)
new_ltEs3(@2(vyy300, vyy301), @2(vyy40, vyy41), bbg, app(ty_Maybe, bbh)) → new_ltEs(vyy301, vyy41, bbh)
new_compare20(vyy300, vyy40, False, he, hf) → new_ltEs0(vyy300, vyy40, he, hf)
new_ltEs3(@2(vyy300, vyy301), @2(vyy40, vyy41), bbg, app(app(ty_@2, bcg), bch)) → new_ltEs3(vyy301, vyy41, bcg, bch)
new_ltEs2(:(vyy300, vyy301), :(vyy40, vyy41), bae) → new_primCompAux(vyy300, vyy40, new_compare0(vyy301, vyy41, bae), bae)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), ef, eg, app(app(ty_Either, fa), fb)) → new_ltEs0(vyy302, vyy42, fa, fb)
new_ltEs0(Left(vyy300), Left(vyy40), app(ty_Maybe, ca), cb) → new_ltEs(vyy300, vyy40, ca)
new_ltEs0(Left(vyy300), Left(vyy40), app(ty_[], da), cb) → new_ltEs2(vyy300, vyy40, da)
new_ltEs0(Right(vyy300), Right(vyy40), dd, app(app(ty_Either, df), dg)) → new_ltEs0(vyy300, vyy40, df, dg)
new_ltEs3(@2(vyy300, vyy301), @2(vyy40, vyy41), app(app(ty_@2, bea), beb), bdb) → new_lt3(vyy300, vyy40, bea, beb)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), ef, app(ty_Maybe, gb), gc) → new_lt(vyy301, vyy41, gb)
new_ltEs0(Left(vyy300), Left(vyy40), app(app(ty_@2, db), dc), cb) → new_ltEs3(vyy300, vyy40, db, dc)
new_compare2(vyy300, vyy40, False, hd) → new_ltEs(vyy300, vyy40, hd)
new_ltEs(Just(vyy300), Just(vyy40), app(app(ty_@2, bg), bh)) → new_ltEs3(vyy300, vyy40, bg, bh)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(app(app(ty_@3, hg), hh), baa), eg, gc) → new_compare21(vyy300, vyy40, new_esEs7(vyy300, vyy40, hg, hh, baa), hg, hh, baa)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), ef, eg, app(ty_[], fg)) → new_ltEs2(vyy302, vyy42, fg)
new_ltEs2(:(vyy300, vyy301), :(vyy40, vyy41), bae) → new_compare(vyy301, vyy41, bae)
new_ltEs0(Right(vyy300), Right(vyy40), dd, app(ty_Maybe, de)) → new_ltEs(vyy300, vyy40, de)
new_compare(:(vyy300, vyy301), :(vyy40, vyy41), bae) → new_compare(vyy301, vyy41, bae)
new_primCompAux(vyy300, vyy40, vyy107, app(ty_Maybe, baf)) → new_compare1(vyy300, vyy40, baf)
new_primCompAux(vyy300, vyy40, vyy107, app(app(ty_Either, bag), bah)) → new_compare3(vyy300, vyy40, bag, bah)
new_lt0(vyy300, vyy40, he, hf) → new_compare20(vyy300, vyy40, new_esEs6(vyy300, vyy40, he, hf), he, hf)
new_compare(:(vyy300, vyy301), :(vyy40, vyy41), bae) → new_primCompAux(vyy300, vyy40, new_compare0(vyy301, vyy41, bae), bae)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), ef, eg, app(ty_Maybe, eh)) → new_ltEs(vyy302, vyy42, eh)
new_ltEs1(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), ef, eg, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs1(vyy302, vyy42, fc, fd, ff)
new_lt2(vyy300, vyy40, bab) → new_compare(vyy300, vyy40, bab)
new_ltEs3(@2(vyy300, vyy301), @2(vyy40, vyy41), app(ty_Maybe, bda), bdb) → new_lt(vyy300, vyy40, bda)
new_compare5(vyy300, vyy40, bac, bad) → new_compare22(vyy300, vyy40, new_esEs8(vyy300, vyy40, bac, bad), bac, bad)
new_ltEs0(Right(vyy300), Right(vyy40), dd, app(ty_[], ec)) → new_ltEs2(vyy300, vyy40, ec)
new_ltEs0(Left(vyy300), Left(vyy40), app(app(app(ty_@3, ce), cf), cg), cb) → new_ltEs1(vyy300, vyy40, ce, cf, cg)
new_ltEs0(Right(vyy300), Right(vyy40), dd, app(app(ty_@2, ed), ee)) → new_ltEs3(vyy300, vyy40, ed, ee)
new_primCompAux(vyy300, vyy40, vyy107, app(app(app(ty_@3, bba), bbb), bbc)) → new_compare4(vyy300, vyy40, bba, bbb, bbc)
new_ltEs3(@2(vyy300, vyy301), @2(vyy40, vyy41), app(ty_[], bdh), bdb) → new_lt2(vyy300, vyy40, bdh)
new_ltEs0(Right(vyy300), Right(vyy40), dd, app(app(app(ty_@3, dh), ea), eb)) → new_ltEs1(vyy300, vyy40, dh, ea, eb)

The TRS R consists of the following rules:

new_lt6(vyy301, vyy41, ty_Char) → new_lt11(vyy301, vyy41)
new_ltEs18(vyy30, vyy4, che) → new_not(new_compare6(vyy30, vyy4, che))
new_lt20(vyy300, vyy40, ty_Int) → new_lt16(vyy300, vyy40)
new_esEs18(Char(vyy780), Char(vyy790)) → new_primEqNat0(vyy780, vyy790)
new_esEs24(vyy780, vyy790, app(ty_Ratio, cge)) → new_esEs15(vyy780, vyy790, cge)
new_compare9(Char(vyy300), Char(vyy40)) → new_primCmpNat0(vyy300, vyy40)
new_ltEs17(LT, LT) → True
new_lt7(vyy300, vyy40, app(ty_[], bab)) → new_lt15(vyy300, vyy40, bab)
new_compare30(vyy300, vyy40, he, hf) → new_compare24(vyy300, vyy40, new_esEs6(vyy300, vyy40, he, hf), he, hf)
new_lt6(vyy301, vyy41, ty_@0) → new_lt8(vyy301, vyy41)
new_ltEs5(Right(vyy300), Right(vyy40), dd, ty_Float) → new_ltEs12(vyy300, vyy40)
new_esEs26(vyy781, vyy791, app(ty_Ratio, dce)) → new_esEs15(vyy781, vyy791, dce)
new_lt20(vyy300, vyy40, ty_Char) → new_lt11(vyy300, vyy40)
new_compare10(vyy300, vyy40, True, bac, bad) → LT
new_compare26(vyy300, vyy40, False, hg, hh, baa) → new_compare16(vyy300, vyy40, new_ltEs8(vyy300, vyy40, hg, hh, baa), hg, hh, baa)
new_compare16(vyy300, vyy40, False, hg, hh, baa) → GT
new_esEs27(vyy780, vyy790, ty_Ordering) → new_esEs19(vyy780, vyy790)
new_ltEs19(vyy301, vyy41, app(ty_Maybe, bbh)) → new_ltEs11(vyy301, vyy41, bbh)
new_esEs13(vyy78, vyy79, bhg, bhh) → new_asAs(new_esEs10(new_sizeFM(vyy78, bhg, bhh), new_sizeFM(vyy79, bhg, bhh)), new_esEs17(new_fmToList(vyy78, bhg, bhh), new_fmToList(vyy79, bhg, bhh), app(app(ty_@2, bhg), bhh)))
new_esEs23(vyy781, vyy791, app(ty_[], cff)) → new_esEs17(vyy781, vyy791, cff)
new_esEs6(Left(vyy780), Left(vyy790), app(ty_Ratio, bfb), bec) → new_esEs15(vyy780, vyy790, bfb)
new_ltEs11(Just(vyy300), Just(vyy40), ty_Bool) → new_ltEs16(vyy300, vyy40)
new_primMulNat0(Zero, Zero) → Zero
new_esEs25(vyy780, vyy790, ty_Double) → new_esEs12(vyy780, vyy790)
new_ltEs9(vyy302, vyy42, ty_Int) → new_ltEs15(vyy302, vyy42)
new_lt7(vyy300, vyy40, app(app(ty_Either, he), hf)) → new_lt13(vyy300, vyy40, he, hf)
new_esEs6(Left(vyy780), Left(vyy790), app(app(app(ty_@3, bfc), bfd), bfe), bec) → new_esEs7(vyy780, vyy790, bfc, bfd, bfe)
new_compare19(vyy300, vyy40, app(app(ty_@2, bbe), bbf)) → new_compare31(vyy300, vyy40, bbe, bbf)
new_compare19(vyy300, vyy40, app(app(app(ty_@3, bba), bbb), bbc)) → new_compare18(vyy300, vyy40, bba, bbb, bbc)
new_esEs25(vyy780, vyy790, app(app(ty_Either, dag), dah)) → new_esEs6(vyy780, vyy790, dag, dah)
new_lt20(vyy300, vyy40, app(app(ty_Either, bdc), bdd)) → new_lt13(vyy300, vyy40, bdc, bdd)
new_lt7(vyy300, vyy40, app(app(app(ty_@3, hg), hh), baa)) → new_lt14(vyy300, vyy40, hg, hh, baa)
new_lt20(vyy300, vyy40, ty_@0) → new_lt8(vyy300, vyy40)
new_esEs20(EQ) → False
new_ltEs16(False, True) → True
new_esEs15(:%(vyy780, vyy781), :%(vyy790, vyy791), cac) → new_asAs(new_esEs29(vyy780, vyy790, cac), new_esEs28(vyy781, vyy791, cac))
new_ltEs16(True, False) → False
new_not(GT) → False
new_esEs26(vyy781, vyy791, ty_Float) → new_esEs9(vyy781, vyy791)
new_esEs27(vyy780, vyy790, app(app(ty_@2, dde), ddf)) → new_esEs8(vyy780, vyy790, dde, ddf)
new_ltEs19(vyy301, vyy41, ty_Bool) → new_ltEs16(vyy301, vyy41)
new_esEs6(Left(vyy780), Left(vyy790), ty_Bool, bec) → new_esEs11(vyy780, vyy790)
new_ltEs9(vyy302, vyy42, ty_@0) → new_ltEs10(vyy302, vyy42)
new_ltEs6(vyy30, vyy4) → new_not(new_compare7(vyy30, vyy4))
new_esEs6(Right(vyy780), Right(vyy790), bfh, app(ty_Ratio, bgg)) → new_esEs15(vyy780, vyy790, bgg)
new_compare19(vyy300, vyy40, app(ty_[], bbd)) → new_compare0(vyy300, vyy40, bbd)
new_primCompAux0(vyy300, vyy40, vyy107, bae) → new_primCompAux00(vyy107, new_compare19(vyy300, vyy40, bae))
new_ltEs5(Left(vyy300), Right(vyy40), dd, cb) → True
new_compare0(:(vyy300, vyy301), :(vyy40, vyy41), bae) → new_primCompAux0(vyy300, vyy40, new_compare0(vyy301, vyy41, bae), bae)
new_esEs21(vyy78, vyy79, app(app(app(ty_@3, cad), cae), caf)) → new_esEs7(vyy78, vyy79, cad, cae, caf)
new_ltEs9(vyy302, vyy42, ty_Ordering) → new_ltEs17(vyy302, vyy42)
new_ltEs5(Right(vyy300), Right(vyy40), dd, app(app(ty_@2, ed), ee)) → new_ltEs4(vyy300, vyy40, ed, ee)
new_esEs5(Just(vyy780), Just(vyy790), app(ty_Maybe, ccc)) → new_esEs5(vyy780, vyy790, ccc)
new_ltEs5(Right(vyy300), Right(vyy40), dd, app(app(ty_Either, df), dg)) → new_ltEs5(vyy300, vyy40, df, dg)
new_lt20(vyy300, vyy40, ty_Float) → new_lt12(vyy300, vyy40)
new_esEs12(Double(vyy780, vyy781), Double(vyy790, vyy791)) → new_esEs10(new_sr(vyy780, vyy790), new_sr(vyy781, vyy791))
new_esEs21(vyy78, vyy79, app(app(ty_Either, bfh), bec)) → new_esEs6(vyy78, vyy79, bfh, bec)
new_esEs26(vyy781, vyy791, ty_Integer) → new_esEs14(vyy781, vyy791)
new_compare15(vyy300, vyy40, False) → GT
new_ltEs11(Just(vyy300), Just(vyy40), app(app(app(ty_@3, bc), bd), be)) → new_ltEs8(vyy300, vyy40, bc, bd, be)
new_ltEs11(Just(vyy300), Just(vyy40), ty_Double) → new_ltEs14(vyy300, vyy40)
new_lt7(vyy300, vyy40, ty_Integer) → new_lt10(vyy300, vyy40)
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, bhg, bhh) → :(@2(vyy790, vyy791), vyy125)
new_ltEs5(Right(vyy300), Left(vyy40), dd, cb) → False
new_ltEs16(True, True) → True
new_ltEs17(EQ, LT) → False
new_esEs21(vyy78, vyy79, app(app(ty_@2, caa), cab)) → new_esEs8(vyy78, vyy79, caa, cab)
new_lt6(vyy301, vyy41, ty_Bool) → new_lt18(vyy301, vyy41)
new_esEs19(GT, GT) → True
new_esEs26(vyy781, vyy791, app(app(ty_@2, dca), dcb)) → new_esEs8(vyy781, vyy791, dca, dcb)
new_esEs27(vyy780, vyy790, ty_@0) → new_esEs16(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), ty_Char, bec) → new_esEs18(vyy780, vyy790)
new_ltEs19(vyy301, vyy41, app(app(ty_@2, bcg), bch)) → new_ltEs4(vyy301, vyy41, bcg, bch)
new_esEs6(Right(vyy780), Right(vyy790), bfh, app(app(ty_FiniteMap, bga), bgb)) → new_esEs13(vyy780, vyy790, bga, bgb)
new_lt20(vyy300, vyy40, app(app(ty_@2, bea), beb)) → new_lt17(vyy300, vyy40, bea, beb)
new_ltEs19(vyy301, vyy41, ty_Integer) → new_ltEs6(vyy301, vyy41)
new_compare15(vyy300, vyy40, True) → LT
new_ltEs5(Left(vyy300), Left(vyy40), ty_Float, cb) → new_ltEs12(vyy300, vyy40)
new_esEs5(Just(vyy780), Just(vyy790), ty_Ordering) → new_esEs19(vyy780, vyy790)
new_esEs27(vyy780, vyy790, app(ty_[], def)) → new_esEs17(vyy780, vyy790, def)
new_ltEs5(Left(vyy300), Left(vyy40), app(app(app(ty_@3, ce), cf), cg), cb) → new_ltEs8(vyy300, vyy40, ce, cf, cg)
new_ltEs19(vyy301, vyy41, app(ty_Ratio, chc)) → new_ltEs18(vyy301, vyy41, chc)
new_esEs14(Integer(vyy780), Integer(vyy790)) → new_primEqInt(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), ty_Integer, bec) → new_esEs14(vyy780, vyy790)
new_lt6(vyy301, vyy41, app(ty_Ratio, ccf)) → new_lt4(vyy301, vyy41, ccf)
new_esEs23(vyy781, vyy791, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs7(vyy781, vyy791, cfb, cfc, cfd)
new_primCmpNat0(Zero, Succ(vyy400)) → LT
new_esEs27(vyy780, vyy790, app(app(app(ty_@3, deb), dec), ded)) → new_esEs7(vyy780, vyy790, deb, dec, ded)
new_ltEs9(vyy302, vyy42, app(ty_Maybe, eh)) → new_ltEs11(vyy302, vyy42, eh)
new_esEs26(vyy781, vyy791, ty_Double) → new_esEs12(vyy781, vyy791)
new_lt20(vyy300, vyy40, app(app(app(ty_@3, bde), bdf), bdg)) → new_lt14(vyy300, vyy40, bde, bdf, bdg)
new_esEs8(@2(vyy780, vyy781), @2(vyy790, vyy791), caa, cab) → new_asAs(new_esEs27(vyy780, vyy790, caa), new_esEs26(vyy781, vyy791, cab))
new_esEs26(vyy781, vyy791, ty_Bool) → new_esEs11(vyy781, vyy791)
new_ltEs5(Right(vyy300), Right(vyy40), dd, ty_Integer) → new_ltEs6(vyy300, vyy40)
new_esEs6(Left(vyy780), Right(vyy790), bfh, bec) → False
new_esEs6(Right(vyy780), Left(vyy790), bfh, bec) → False
new_compare19(vyy300, vyy40, app(app(ty_Either, bag), bah)) → new_compare30(vyy300, vyy40, bag, bah)
new_esEs23(vyy781, vyy791, ty_Char) → new_esEs18(vyy781, vyy791)
new_esEs5(Just(vyy780), Just(vyy790), app(ty_[], ccd)) → new_esEs17(vyy780, vyy790, ccd)
new_compare0([], [], bae) → EQ
new_esEs23(vyy781, vyy791, ty_@0) → new_esEs16(vyy781, vyy791)
new_primEqNat0(Zero, Zero) → True
new_compare6(:%(vyy300, vyy301), :%(vyy40, vyy41), ty_Integer) → new_compare7(new_sr0(vyy300, vyy41), new_sr0(vyy40, vyy301))
new_ltEs11(Nothing, Just(vyy40), daa) → True
new_ltEs11(Just(vyy300), Just(vyy40), app(ty_Maybe, h)) → new_ltEs11(vyy300, vyy40, h)
new_primMulNat0(Succ(vyy30100), Succ(vyy4100)) → new_primPlusNat1(new_primMulNat0(vyy30100, Succ(vyy4100)), vyy4100)
new_lt7(vyy300, vyy40, app(ty_Ratio, bhe)) → new_lt4(vyy300, vyy40, bhe)
new_esEs23(vyy781, vyy791, app(app(ty_Either, ceg), ceh)) → new_esEs6(vyy781, vyy791, ceg, ceh)
new_esEs6(Right(vyy780), Right(vyy790), bfh, ty_@0) → new_esEs16(vyy780, vyy790)
new_compare18(vyy300, vyy40, hg, hh, baa) → new_compare26(vyy300, vyy40, new_esEs7(vyy300, vyy40, hg, hh, baa), hg, hh, baa)
new_ltEs5(Left(vyy300), Left(vyy40), ty_Int, cb) → new_ltEs15(vyy300, vyy40)
new_esEs26(vyy781, vyy791, ty_@0) → new_esEs16(vyy781, vyy791)
new_esEs6(Right(vyy780), Right(vyy790), bfh, app(app(ty_Either, bge), bgf)) → new_esEs6(vyy780, vyy790, bge, bgf)
new_ltEs15(vyy30, vyy4) → new_not(new_compare13(vyy30, vyy4))
new_esEs6(Right(vyy780), Right(vyy790), bfh, ty_Char) → new_esEs18(vyy780, vyy790)
new_compare19(vyy300, vyy40, ty_Integer) → new_compare7(vyy300, vyy40)
new_ltEs17(GT, LT) → False
new_esEs5(Just(vyy780), Just(vyy790), app(ty_Ratio, cbg)) → new_esEs15(vyy780, vyy790, cbg)
new_sr(vyy301, vyy41) → new_primMulInt(vyy301, vyy41)
new_esEs5(Just(vyy780), Just(vyy790), ty_Integer) → new_esEs14(vyy780, vyy790)
new_lt7(vyy300, vyy40, ty_Int) → new_lt16(vyy300, vyy40)
new_ltEs5(Left(vyy300), Left(vyy40), app(ty_[], da), cb) → new_ltEs13(vyy300, vyy40, da)
new_esEs26(vyy781, vyy791, ty_Ordering) → new_esEs19(vyy781, vyy791)
new_esEs5(Just(vyy780), Just(vyy790), ty_Char) → new_esEs18(vyy780, vyy790)
new_esEs21(vyy78, vyy79, ty_Float) → new_esEs9(vyy78, vyy79)
new_esEs23(vyy781, vyy791, ty_Float) → new_esEs9(vyy781, vyy791)
new_ltEs11(Just(vyy300), Just(vyy40), ty_Float) → new_ltEs12(vyy300, vyy40)
new_esEs21(vyy78, vyy79, ty_Ordering) → new_esEs19(vyy78, vyy79)
new_esEs5(Just(vyy780), Just(vyy790), ty_Double) → new_esEs12(vyy780, vyy790)
new_compare25(vyy300, vyy40, False) → new_compare15(vyy300, vyy40, new_ltEs16(vyy300, vyy40))
new_ltEs5(Left(vyy300), Left(vyy40), app(app(ty_@2, db), dc), cb) → new_ltEs4(vyy300, vyy40, db, dc)
new_lt6(vyy301, vyy41, app(app(ty_Either, gd), ge)) → new_lt13(vyy301, vyy41, gd, ge)
new_esEs6(Left(vyy780), Left(vyy790), ty_Float, bec) → new_esEs9(vyy780, vyy790)
new_compare25(vyy300, vyy40, True) → EQ
new_ltEs5(Left(vyy300), Left(vyy40), ty_Ordering, cb) → new_ltEs17(vyy300, vyy40)
new_primEqInt(Neg(Succ(vyy7800)), Neg(Succ(vyy7900))) → new_primEqNat0(vyy7800, vyy7900)
new_esEs25(vyy780, vyy790, app(app(ty_@2, dae), daf)) → new_esEs8(vyy780, vyy790, dae, daf)
new_esEs25(vyy780, vyy790, ty_Bool) → new_esEs11(vyy780, vyy790)
new_esEs6(Right(vyy780), Right(vyy790), bfh, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs7(vyy780, vyy790, bgh, bha, bhb)
new_ltEs17(LT, GT) → True
new_esEs19(EQ, EQ) → True
new_ltEs5(Right(vyy300), Right(vyy40), dd, ty_Double) → new_ltEs14(vyy300, vyy40)
new_esEs22(vyy782, vyy792, ty_Ordering) → new_esEs19(vyy782, vyy792)
new_ltEs5(Right(vyy300), Right(vyy40), dd, ty_Ordering) → new_ltEs17(vyy300, vyy40)
new_esEs21(vyy78, vyy79, ty_@0) → new_esEs16(vyy78, vyy79)
new_ltEs9(vyy302, vyy42, ty_Double) → new_ltEs14(vyy302, vyy42)
new_esEs6(Right(vyy780), Right(vyy790), bfh, app(app(ty_@2, bgc), bgd)) → new_esEs8(vyy780, vyy790, bgc, bgd)
new_lt7(vyy300, vyy40, ty_Ordering) → new_lt19(vyy300, vyy40)
new_esEs26(vyy781, vyy791, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs7(vyy781, vyy791, dcf, dcg, dch)
new_esEs25(vyy780, vyy790, ty_Char) → new_esEs18(vyy780, vyy790)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Just(vyy780), Just(vyy790), ty_Int) → new_esEs10(vyy780, vyy790)
new_compare19(vyy300, vyy40, ty_Double) → new_compare12(vyy300, vyy40)
new_esEs25(vyy780, vyy790, app(ty_Ratio, dba)) → new_esEs15(vyy780, vyy790, dba)
new_ltEs11(Just(vyy300), Just(vyy40), ty_Int) → new_ltEs15(vyy300, vyy40)
new_primEqInt(Neg(Zero), Neg(Succ(vyy7900))) → False
new_primEqInt(Neg(Succ(vyy7800)), Neg(Zero)) → False
new_primPlusNat1(Zero, vyy4100) → Succ(vyy4100)
new_compare111(vyy300, vyy40, True, hd) → LT
new_ltEs5(Left(vyy300), Left(vyy40), ty_Integer, cb) → new_ltEs6(vyy300, vyy40)
new_lt7(vyy300, vyy40, ty_Float) → new_lt12(vyy300, vyy40)
new_esEs6(Right(vyy780), Right(vyy790), bfh, app(ty_[], bhd)) → new_esEs17(vyy780, vyy790, bhd)
new_ltEs4(@2(vyy300, vyy301), @2(vyy40, vyy41), bbg, bdb) → new_pePe(new_lt20(vyy300, vyy40, bbg), vyy300, vyy40, new_ltEs19(vyy301, vyy41, bdb), bbg)
new_compare24(vyy300, vyy40, True, he, hf) → EQ
new_esEs23(vyy781, vyy791, ty_Ordering) → new_esEs19(vyy781, vyy791)
new_ltEs11(Just(vyy300), Just(vyy40), ty_Char) → new_ltEs7(vyy300, vyy40)
new_lt6(vyy301, vyy41, ty_Float) → new_lt12(vyy301, vyy41)
new_ltEs17(EQ, EQ) → True
new_lt9(vyy300, vyy40, hd) → new_esEs20(new_compare29(vyy300, vyy40, hd))
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), bhg, bhh) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, bhg, bhh), vyy7933, bhg, bhh)
new_ltEs19(vyy301, vyy41, ty_Ordering) → new_ltEs17(vyy301, vyy41)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs23(vyy781, vyy791, ty_Integer) → new_esEs14(vyy781, vyy791)
new_lt6(vyy301, vyy41, ty_Double) → new_lt5(vyy301, vyy41)
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, bed), bee), bec) → new_esEs13(vyy780, vyy790, bed, bee)
new_esEs19(EQ, LT) → False
new_esEs19(LT, EQ) → False
new_primCmpNat0(Succ(vyy3000), Succ(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_sizeFM(EmptyFM, bhg, bhh) → Pos(Zero)
new_lt15(vyy300, vyy40, bab) → new_esEs20(new_compare0(vyy300, vyy40, bab))
new_esEs25(vyy780, vyy790, app(app(ty_FiniteMap, dac), dad)) → new_esEs13(vyy780, vyy790, dac, dad)
new_esEs11(False, False) → True
new_primEqInt(Pos(Succ(vyy7800)), Pos(Succ(vyy7900))) → new_primEqNat0(vyy7800, vyy7900)
new_compare10(vyy300, vyy40, False, bac, bad) → GT
new_ltEs5(Left(vyy300), Left(vyy40), app(app(ty_Either, cc), cd), cb) → new_ltEs5(vyy300, vyy40, cc, cd)
new_esEs25(vyy780, vyy790, app(ty_Maybe, dbe)) → new_esEs5(vyy780, vyy790, dbe)
new_lt20(vyy300, vyy40, ty_Ordering) → new_lt19(vyy300, vyy40)
new_ltEs5(Right(vyy300), Right(vyy40), dd, app(ty_Maybe, de)) → new_ltEs11(vyy300, vyy40, de)
new_esEs5(Just(vyy780), Just(vyy790), ty_Bool) → new_esEs11(vyy780, vyy790)
new_esEs26(vyy781, vyy791, app(app(ty_FiniteMap, dbg), dbh)) → new_esEs13(vyy781, vyy791, dbg, dbh)
new_esEs6(Left(vyy780), Left(vyy790), ty_@0, bec) → new_esEs16(vyy780, vyy790)
new_primEqNat0(Succ(vyy7800), Succ(vyy7900)) → new_primEqNat0(vyy7800, vyy7900)
new_esEs17(:(vyy780, vyy781), :(vyy790, vyy791), cah) → new_asAs(new_esEs25(vyy780, vyy790, cah), new_esEs17(vyy781, vyy791, cah))
new_esEs24(vyy780, vyy790, ty_@0) → new_esEs16(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), app(ty_[], bfg), bec) → new_esEs17(vyy780, vyy790, bfg)
new_lt7(vyy300, vyy40, app(app(ty_@2, bac), bad)) → new_lt17(vyy300, vyy40, bac, bad)
new_ltEs9(vyy302, vyy42, app(app(ty_@2, fh), ga)) → new_ltEs4(vyy302, vyy42, fh, ga)
new_ltEs19(vyy301, vyy41, ty_Double) → new_ltEs14(vyy301, vyy41)
new_esEs29(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_primCompAux00(vyy111, LT) → LT
new_esEs27(vyy780, vyy790, app(ty_Ratio, dea)) → new_esEs15(vyy780, vyy790, dea)
new_compare12(Double(vyy300, vyy301), Double(vyy40, vyy41)) → new_compare13(new_sr(vyy300, vyy40), new_sr(vyy301, vyy41))
new_lt16(vyy300, vyy40) → new_esEs20(new_compare13(vyy300, vyy40))
new_primCmpInt(Neg(Succ(vyy3000)), Neg(vyy40)) → new_primCmpNat0(vyy40, Succ(vyy3000))
new_esEs24(vyy780, vyy790, ty_Float) → new_esEs9(vyy780, vyy790)
new_esEs6(Right(vyy780), Right(vyy790), bfh, app(ty_Maybe, bhc)) → new_esEs5(vyy780, vyy790, bhc)
new_esEs6(Right(vyy780), Right(vyy790), bfh, ty_Float) → new_esEs9(vyy780, vyy790)
new_primEqInt(Pos(Succ(vyy7800)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy7900))) → False
new_ltEs8(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), ef, eg, gc) → new_pePe(new_lt7(vyy300, vyy40, ef), vyy300, vyy40, new_pePe(new_lt6(vyy301, vyy41, eg), vyy301, vyy41, new_ltEs9(vyy302, vyy42, gc), eg), ef)
new_primPlusNat0(Zero, Succ(vyy41000)) → Succ(vyy41000)
new_primPlusNat0(Succ(vyy12600), Zero) → Succ(vyy12600)
new_primCmpNat0(Zero, Zero) → EQ
new_lt6(vyy301, vyy41, ty_Integer) → new_lt10(vyy301, vyy41)
new_primCmpNat0(Succ(vyy3000), Zero) → GT
new_lt18(vyy300, vyy40) → new_esEs20(new_compare8(vyy300, vyy40))
new_esEs22(vyy782, vyy792, ty_Integer) → new_esEs14(vyy782, vyy792)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy400))) → LT
new_compare11(vyy300, vyy40, True, he, hf) → LT
new_ltEs11(Just(vyy300), Just(vyy40), app(ty_[], bf)) → new_ltEs13(vyy300, vyy40, bf)
new_sr0(Integer(vyy400), Integer(vyy3010)) → Integer(new_primMulInt(vyy400, vyy3010))
new_primEqInt(Pos(Succ(vyy7800)), Neg(vyy790)) → False
new_primEqInt(Neg(Succ(vyy7800)), Pos(vyy790)) → False
new_esEs25(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_ltEs5(Right(vyy300), Right(vyy40), dd, ty_Int) → new_ltEs15(vyy300, vyy40)
new_compare6(:%(vyy300, vyy301), :%(vyy40, vyy41), ty_Int) → new_compare13(new_sr(vyy300, vyy41), new_sr(vyy40, vyy301))
new_compare210(vyy300, vyy40, True, hd) → EQ
new_foldFM2(EmptyFM, bhg, bhh) → []
new_esEs27(vyy780, vyy790, app(ty_Maybe, dee)) → new_esEs5(vyy780, vyy790, dee)
new_esEs6(Right(vyy780), Right(vyy790), bfh, ty_Ordering) → new_esEs19(vyy780, vyy790)
new_ltEs5(Left(vyy300), Left(vyy40), ty_Double, cb) → new_ltEs14(vyy300, vyy40)
new_ltEs9(vyy302, vyy42, app(app(ty_Either, fa), fb)) → new_ltEs5(vyy302, vyy42, fa, fb)
new_esEs27(vyy780, vyy790, ty_Double) → new_esEs12(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_@2, bef), beg), bec) → new_esEs8(vyy780, vyy790, bef, beg)
new_primEqInt(Neg(Zero), Pos(Succ(vyy7900))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy7900))) → False
new_lt5(vyy300, vyy40) → new_esEs20(new_compare12(vyy300, vyy40))
new_esEs26(vyy781, vyy791, ty_Int) → new_esEs10(vyy781, vyy791)
new_esEs26(vyy781, vyy791, app(ty_[], ddb)) → new_esEs17(vyy781, vyy791, ddb)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy400))) → new_primCmpNat0(Zero, Succ(vyy400))
new_primCompAux00(vyy111, EQ) → vyy111
new_esEs22(vyy782, vyy792, app(app(ty_FiniteMap, ccg), cch)) → new_esEs13(vyy782, vyy792, ccg, cch)
new_esEs23(vyy781, vyy791, ty_Bool) → new_esEs11(vyy781, vyy791)
new_lt20(vyy300, vyy40, app(ty_Ratio, chd)) → new_lt4(vyy300, vyy40, chd)
new_lt7(vyy300, vyy40, app(ty_Maybe, hd)) → new_lt9(vyy300, vyy40, hd)
new_esEs22(vyy782, vyy792, ty_@0) → new_esEs16(vyy782, vyy792)
new_ltEs5(Left(vyy300), Left(vyy40), app(ty_Ratio, chg), cb) → new_ltEs18(vyy300, vyy40, chg)
new_esEs7(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), cad, cae, caf) → new_asAs(new_esEs24(vyy780, vyy790, cad), new_asAs(new_esEs23(vyy781, vyy791, cae), new_esEs22(vyy782, vyy792, caf)))
new_esEs21(vyy78, vyy79, app(ty_[], cah)) → new_esEs17(vyy78, vyy79, cah)
new_ltEs11(Just(vyy300), Just(vyy40), ty_@0) → new_ltEs10(vyy300, vyy40)
new_esEs21(vyy78, vyy79, ty_Char) → new_esEs18(vyy78, vyy79)
new_ltEs11(Just(vyy300), Just(vyy40), app(ty_Ratio, dab)) → new_ltEs18(vyy300, vyy40, dab)
new_lt20(vyy300, vyy40, ty_Double) → new_lt5(vyy300, vyy40)
new_lt6(vyy301, vyy41, app(app(ty_@2, hb), hc)) → new_lt17(vyy301, vyy41, hb, hc)
new_compare17(vyy300, vyy40) → new_compare27(vyy300, vyy40, new_esEs19(vyy300, vyy40))
new_esEs21(vyy78, vyy79, ty_Integer) → new_esEs14(vyy78, vyy79)
new_lt17(vyy300, vyy40, bac, bad) → new_esEs20(new_compare31(vyy300, vyy40, bac, bad))
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_Either, beh), bfa), bec) → new_esEs6(vyy780, vyy790, beh, bfa)
new_esEs23(vyy781, vyy791, app(app(ty_FiniteMap, cec), ced)) → new_esEs13(vyy781, vyy791, cec, ced)
new_lt10(vyy300, vyy40) → new_esEs20(new_compare7(vyy300, vyy40))
new_primCmpInt(Pos(Succ(vyy3000)), Pos(vyy40)) → new_primCmpNat0(Succ(vyy3000), vyy40)
new_lt8(vyy300, vyy40) → new_esEs20(new_compare28(vyy300, vyy40))
new_esEs24(vyy780, vyy790, app(app(ty_Either, cgc), cgd)) → new_esEs6(vyy780, vyy790, cgc, cgd)
new_esEs24(vyy780, vyy790, ty_Ordering) → new_esEs19(vyy780, vyy790)
new_lt7(vyy300, vyy40, ty_Double) → new_lt5(vyy300, vyy40)
new_not0True
new_compare0(:(vyy300, vyy301), [], bae) → GT
new_esEs24(vyy780, vyy790, app(ty_[], chb)) → new_esEs17(vyy780, vyy790, chb)
new_ltEs9(vyy302, vyy42, app(ty_Ratio, cce)) → new_ltEs18(vyy302, vyy42, cce)
new_esEs21(vyy78, vyy79, app(ty_Ratio, cac)) → new_esEs15(vyy78, vyy79, cac)
new_esEs27(vyy780, vyy790, app(app(ty_Either, ddg), ddh)) → new_esEs6(vyy780, vyy790, ddg, ddh)
new_esEs24(vyy780, vyy790, app(ty_Maybe, cha)) → new_esEs5(vyy780, vyy790, cha)
new_esEs5(Just(vyy780), Just(vyy790), app(app(ty_@2, cbc), cbd)) → new_esEs8(vyy780, vyy790, cbc, cbd)
new_lt6(vyy301, vyy41, app(ty_[], ha)) → new_lt15(vyy301, vyy41, ha)
new_esEs19(GT, LT) → False
new_esEs19(LT, GT) → False
new_lt13(vyy300, vyy40, he, hf) → new_esEs20(new_compare30(vyy300, vyy40, he, hf))
new_compare19(vyy300, vyy40, ty_Bool) → new_compare8(vyy300, vyy40)
new_compare19(vyy300, vyy40, ty_Float) → new_compare14(vyy300, vyy40)
new_esEs22(vyy782, vyy792, ty_Bool) → new_esEs11(vyy782, vyy792)
new_compare11(vyy300, vyy40, False, he, hf) → GT
new_primCmpInt(Pos(Succ(vyy3000)), Neg(vyy40)) → GT
new_esEs6(Right(vyy780), Right(vyy790), bfh, ty_Bool) → new_esEs11(vyy780, vyy790)
new_esEs22(vyy782, vyy792, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs7(vyy782, vyy792, cdf, cdg, cdh)
new_esEs22(vyy782, vyy792, ty_Char) → new_esEs18(vyy782, vyy792)
new_lt6(vyy301, vyy41, ty_Int) → new_lt16(vyy301, vyy41)
new_primMulInt(Pos(vyy3010), Pos(vyy410)) → Pos(new_primMulNat0(vyy3010, vyy410))
new_lt20(vyy300, vyy40, ty_Integer) → new_lt10(vyy300, vyy40)
new_esEs29(vyy780, vyy790, ty_Integer) → new_esEs14(vyy780, vyy790)
new_ltEs9(vyy302, vyy42, ty_Char) → new_ltEs7(vyy302, vyy42)
new_esEs27(vyy780, vyy790, ty_Bool) → new_esEs11(vyy780, vyy790)
new_ltEs9(vyy302, vyy42, ty_Bool) → new_ltEs16(vyy302, vyy42)
new_compare29(vyy300, vyy40, hd) → new_compare210(vyy300, vyy40, new_esEs5(vyy300, vyy40, hd), hd)
new_esEs22(vyy782, vyy792, ty_Int) → new_esEs10(vyy782, vyy792)
new_esEs27(vyy780, vyy790, app(app(ty_FiniteMap, ddc), ddd)) → new_esEs13(vyy780, vyy790, ddc, ddd)
new_ltEs9(vyy302, vyy42, app(ty_[], fg)) → new_ltEs13(vyy302, vyy42, fg)
new_primMulInt(Neg(vyy3010), Neg(vyy410)) → Pos(new_primMulNat0(vyy3010, vyy410))
new_compare110(vyy300, vyy40, True) → LT
new_ltEs5(Right(vyy300), Right(vyy40), dd, app(ty_[], ec)) → new_ltEs13(vyy300, vyy40, ec)
new_ltEs19(vyy301, vyy41, app(app(ty_Either, bca), bcb)) → new_ltEs5(vyy301, vyy41, bca, bcb)
new_primEqNat0(Zero, Succ(vyy7900)) → False
new_primEqNat0(Succ(vyy7800), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_esEs6(Right(vyy780), Right(vyy790), bfh, ty_Double) → new_esEs12(vyy780, vyy790)
new_ltEs9(vyy302, vyy42, ty_Float) → new_ltEs12(vyy302, vyy42)
new_compare110(vyy300, vyy40, False) → GT
new_ltEs19(vyy301, vyy41, ty_Char) → new_ltEs7(vyy301, vyy41)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare23(vyy300, vyy40, False, bac, bad) → new_compare10(vyy300, vyy40, new_ltEs4(vyy300, vyy40, bac, bad), bac, bad)
new_esEs22(vyy782, vyy792, app(ty_Ratio, cde)) → new_esEs15(vyy782, vyy792, cde)
new_ltEs9(vyy302, vyy42, ty_Integer) → new_ltEs6(vyy302, vyy42)
new_ltEs19(vyy301, vyy41, app(app(app(ty_@3, bcc), bcd), bce)) → new_ltEs8(vyy301, vyy41, bcc, bcd, bce)
new_compare14(Float(vyy300, vyy301), Float(vyy40, vyy41)) → new_compare13(new_sr(vyy300, vyy40), new_sr(vyy301, vyy41))
new_ltEs14(vyy30, vyy4) → new_not(new_compare12(vyy30, vyy4))
new_esEs22(vyy782, vyy792, app(ty_[], ceb)) → new_esEs17(vyy782, vyy792, ceb)
new_sizeFM(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), bhg, bhh) → vyy792
new_lt20(vyy300, vyy40, ty_Bool) → new_lt18(vyy300, vyy40)
new_lt7(vyy300, vyy40, ty_@0) → new_lt8(vyy300, vyy40)
new_pePe(True, vyy78, vyy79, vyy97, bhf) → True
new_esEs26(vyy781, vyy791, app(ty_Maybe, dda)) → new_esEs5(vyy781, vyy791, dda)
new_primPlusNat1(Succ(vyy1260), vyy4100) → Succ(Succ(new_primPlusNat0(vyy1260, vyy4100)))
new_compare16(vyy300, vyy40, True, hg, hh, baa) → LT
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), bhg, bhh) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, bhg, bhh), vyy793, bhg, bhh)
new_lt19(vyy300, vyy40) → new_esEs20(new_compare17(vyy300, vyy40))
new_ltEs7(vyy30, vyy4) → new_not(new_compare9(vyy30, vyy4))
new_primCmpInt(Neg(Zero), Neg(Succ(vyy400))) → new_primCmpNat0(Succ(vyy400), Zero)
new_compare23(vyy300, vyy40, True, bac, bad) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vyy400))) → GT
new_esEs11(True, False) → False
new_esEs11(False, True) → False
new_esEs25(vyy780, vyy790, ty_Ordering) → new_esEs19(vyy780, vyy790)
new_esEs25(vyy780, vyy790, ty_Integer) → new_esEs14(vyy780, vyy790)
new_esEs23(vyy781, vyy791, app(app(ty_@2, cee), cef)) → new_esEs8(vyy781, vyy791, cee, cef)
new_compare19(vyy300, vyy40, ty_Char) → new_compare9(vyy300, vyy40)
new_lt20(vyy300, vyy40, app(ty_Maybe, bda)) → new_lt9(vyy300, vyy40, bda)
new_esEs24(vyy780, vyy790, app(app(ty_FiniteMap, cfg), cfh)) → new_esEs13(vyy780, vyy790, cfg, cfh)
new_ltEs5(Right(vyy300), Right(vyy40), dd, ty_@0) → new_ltEs10(vyy300, vyy40)
new_ltEs5(Left(vyy300), Left(vyy40), ty_@0, cb) → new_ltEs10(vyy300, vyy40)
new_esEs19(LT, LT) → True
new_compare19(vyy300, vyy40, ty_Int) → new_compare13(vyy300, vyy40)
new_esEs20(GT) → False
new_esEs19(GT, EQ) → False
new_esEs19(EQ, GT) → False
new_esEs21(vyy78, vyy79, ty_Bool) → new_esEs11(vyy78, vyy79)
new_esEs23(vyy781, vyy791, app(ty_Ratio, cfa)) → new_esEs15(vyy781, vyy791, cfa)
new_ltEs11(Just(vyy300), Just(vyy40), app(app(ty_Either, ba), bb)) → new_ltEs5(vyy300, vyy40, ba, bb)
new_esEs6(Left(vyy780), Left(vyy790), ty_Ordering, bec) → new_esEs19(vyy780, vyy790)
new_lt6(vyy301, vyy41, app(app(app(ty_@3, gf), gg), gh)) → new_lt14(vyy301, vyy41, gf, gg, gh)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt20(vyy300, vyy40, app(ty_[], bdh)) → new_lt15(vyy300, vyy40, bdh)
new_esEs24(vyy780, vyy790, app(app(app(ty_@3, cgf), cgg), cgh)) → new_esEs7(vyy780, vyy790, cgf, cgg, cgh)
new_lt6(vyy301, vyy41, app(ty_Maybe, gb)) → new_lt9(vyy301, vyy41, gb)
new_esEs6(Left(vyy780), Left(vyy790), ty_Double, bec) → new_esEs12(vyy780, vyy790)
new_esEs24(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_esEs24(vyy780, vyy790, ty_Double) → new_esEs12(vyy780, vyy790)
new_ltEs11(Just(vyy300), Just(vyy40), app(app(ty_@2, bg), bh)) → new_ltEs4(vyy300, vyy40, bg, bh)
new_asAs(False, vyy106) → False
new_esEs22(vyy782, vyy792, ty_Double) → new_esEs12(vyy782, vyy792)
new_ltEs10(vyy30, vyy4) → new_not(new_compare28(vyy30, vyy4))
new_primMulInt(Neg(vyy3010), Pos(vyy410)) → Neg(new_primMulNat0(vyy3010, vyy410))
new_primMulInt(Pos(vyy3010), Neg(vyy410)) → Neg(new_primMulNat0(vyy3010, vyy410))
new_ltEs5(Right(vyy300), Right(vyy40), dd, ty_Bool) → new_ltEs16(vyy300, vyy40)
new_primMulNat0(Zero, Succ(vyy4100)) → Zero
new_primMulNat0(Succ(vyy30100), Zero) → Zero
new_esEs25(vyy780, vyy790, ty_@0) → new_esEs16(vyy780, vyy790)
new_pePe(False, vyy78, vyy79, vyy97, bhf) → new_asAs(new_esEs21(vyy78, vyy79, bhf), vyy97)
new_compare13(vyy30, vyy4) → new_primCmpInt(vyy30, vyy4)
new_ltEs13(vyy30, vyy4, bae) → new_not(new_compare0(vyy30, vyy4, bae))
new_ltEs19(vyy301, vyy41, ty_@0) → new_ltEs10(vyy301, vyy41)
new_not(EQ) → new_not0
new_ltEs5(Right(vyy300), Right(vyy40), dd, ty_Char) → new_ltEs7(vyy300, vyy40)
new_lt11(vyy300, vyy40) → new_esEs20(new_compare9(vyy300, vyy40))
new_ltEs11(Just(vyy300), Just(vyy40), ty_Integer) → new_ltEs6(vyy300, vyy40)
new_esEs11(True, True) → True
new_esEs25(vyy780, vyy790, app(ty_[], dbf)) → new_esEs17(vyy780, vyy790, dbf)
new_esEs5(Just(vyy780), Just(vyy790), ty_@0) → new_esEs16(vyy780, vyy790)
new_esEs23(vyy781, vyy791, app(ty_Maybe, cfe)) → new_esEs5(vyy781, vyy791, cfe)
new_esEs6(Right(vyy780), Right(vyy790), bfh, ty_Integer) → new_esEs14(vyy780, vyy790)
new_esEs6(Right(vyy780), Right(vyy790), bfh, ty_Int) → new_esEs10(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), app(ty_Maybe, bff), bec) → new_esEs5(vyy780, vyy790, bff)
new_compare19(vyy300, vyy40, ty_Ordering) → new_compare17(vyy300, vyy40)
new_esEs16(@0, @0) → True
new_compare19(vyy300, vyy40, app(ty_Ratio, chf)) → new_compare6(vyy300, vyy40, chf)
new_ltEs17(GT, GT) → True
new_compare27(vyy300, vyy40, True) → EQ
new_esEs20(LT) → True
new_compare111(vyy300, vyy40, False, hd) → GT
new_ltEs5(Left(vyy300), Left(vyy40), ty_Bool, cb) → new_ltEs16(vyy300, vyy40)
new_ltEs17(GT, EQ) → False
new_esEs5(Just(vyy780), Nothing, cag) → False
new_esEs5(Nothing, Just(vyy790), cag) → False
new_compare19(vyy300, vyy40, ty_@0) → new_compare28(vyy300, vyy40)
new_esEs24(vyy780, vyy790, ty_Integer) → new_esEs14(vyy780, vyy790)
new_ltEs5(Left(vyy300), Left(vyy40), ty_Char, cb) → new_ltEs7(vyy300, vyy40)
new_esEs25(vyy780, vyy790, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs7(vyy780, vyy790, dbb, dbc, dbd)
new_compare19(vyy300, vyy40, app(ty_Maybe, baf)) → new_compare29(vyy300, vyy40, baf)
new_esEs5(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, cba), cbb)) → new_esEs13(vyy780, vyy790, cba, cbb)
new_ltEs11(Just(vyy300), Just(vyy40), ty_Ordering) → new_ltEs17(vyy300, vyy40)
new_ltEs19(vyy301, vyy41, ty_Int) → new_ltEs15(vyy301, vyy41)
new_ltEs12(vyy30, vyy4) → new_not(new_compare14(vyy30, vyy4))
new_esEs5(Just(vyy780), Just(vyy790), app(app(ty_Either, cbe), cbf)) → new_esEs6(vyy780, vyy790, cbe, cbf)
new_esEs27(vyy780, vyy790, ty_Float) → new_esEs9(vyy780, vyy790)
new_not(LT) → new_not0
new_compare7(Integer(vyy300), Integer(vyy40)) → new_primCmpInt(vyy300, vyy40)
new_esEs5(Nothing, Nothing, cag) → True
new_esEs22(vyy782, vyy792, app(app(ty_Either, cdc), cdd)) → new_esEs6(vyy782, vyy792, cdc, cdd)
new_esEs5(Just(vyy780), Just(vyy790), app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs7(vyy780, vyy790, cbh, cca, ccb)
new_esEs21(vyy78, vyy79, ty_Double) → new_esEs12(vyy78, vyy79)
new_esEs28(vyy781, vyy791, ty_Int) → new_esEs10(vyy781, vyy791)
new_lt4(vyy300, vyy40, bhe) → new_esEs20(new_compare6(vyy300, vyy40, bhe))
new_compare8(vyy300, vyy40) → new_compare25(vyy300, vyy40, new_esEs11(vyy300, vyy40))
new_esEs26(vyy781, vyy791, ty_Char) → new_esEs18(vyy781, vyy791)
new_compare27(vyy300, vyy40, False) → new_compare110(vyy300, vyy40, new_ltEs17(vyy300, vyy40))
new_esEs23(vyy781, vyy791, ty_Double) → new_esEs12(vyy781, vyy791)
new_compare26(vyy300, vyy40, True, hg, hh, baa) → EQ
new_primPlusNat0(Succ(vyy12600), Succ(vyy41000)) → Succ(Succ(new_primPlusNat0(vyy12600, vyy41000)))
new_esEs22(vyy782, vyy792, app(ty_Maybe, cea)) → new_esEs5(vyy782, vyy792, cea)
new_compare31(vyy300, vyy40, bac, bad) → new_compare23(vyy300, vyy40, new_esEs8(vyy300, vyy40, bac, bad), bac, bad)
new_esEs21(vyy78, vyy79, app(ty_Maybe, cag)) → new_esEs5(vyy78, vyy79, cag)
new_lt7(vyy300, vyy40, ty_Char) → new_lt11(vyy300, vyy40)
new_esEs26(vyy781, vyy791, app(app(ty_Either, dcc), dcd)) → new_esEs6(vyy781, vyy791, dcc, dcd)
new_compare0([], :(vyy40, vyy41), bae) → LT
new_esEs27(vyy780, vyy790, ty_Integer) → new_esEs14(vyy780, vyy790)
new_asAs(True, vyy106) → vyy106
new_ltEs17(LT, EQ) → True
new_lt6(vyy301, vyy41, ty_Ordering) → new_lt19(vyy301, vyy41)
new_ltEs11(Nothing, Nothing, daa) → True
new_esEs22(vyy782, vyy792, app(app(ty_@2, cda), cdb)) → new_esEs8(vyy782, vyy792, cda, cdb)
new_ltEs19(vyy301, vyy41, ty_Float) → new_ltEs12(vyy301, vyy41)
new_esEs27(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_ltEs16(False, False) → True
new_esEs23(vyy781, vyy791, ty_Int) → new_esEs10(vyy781, vyy791)
new_esEs22(vyy782, vyy792, ty_Float) → new_esEs9(vyy782, vyy792)
new_esEs21(vyy78, vyy79, ty_Int) → new_esEs10(vyy78, vyy79)
new_ltEs5(Right(vyy300), Right(vyy40), dd, app(app(app(ty_@3, dh), ea), eb)) → new_ltEs8(vyy300, vyy40, dh, ea, eb)
new_esEs17([], [], cah) → True
new_esEs17([], :(vyy790, vyy791), cah) → False
new_esEs17(:(vyy780, vyy781), [], cah) → False
new_fmToList(vyy79, bhg, bhh) → new_foldFM2(vyy79, bhg, bhh)
new_compare24(vyy300, vyy40, False, he, hf) → new_compare11(vyy300, vyy40, new_ltEs5(vyy300, vyy40, he, hf), he, hf)
new_esEs5(Just(vyy780), Just(vyy790), ty_Float) → new_esEs9(vyy780, vyy790)
new_esEs24(vyy780, vyy790, app(app(ty_@2, cga), cgb)) → new_esEs8(vyy780, vyy790, cga, cgb)
new_ltEs9(vyy302, vyy42, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs8(vyy302, vyy42, fc, fd, ff)
new_esEs27(vyy780, vyy790, ty_Char) → new_esEs18(vyy780, vyy790)
new_esEs9(Float(vyy780, vyy781), Float(vyy790, vyy791)) → new_esEs10(new_sr(vyy780, vyy790), new_sr(vyy781, vyy791))
new_compare210(vyy300, vyy40, False, hd) → new_compare111(vyy300, vyy40, new_ltEs11(vyy300, vyy40, hd), hd)
new_lt12(vyy300, vyy40) → new_esEs20(new_compare14(vyy300, vyy40))
new_lt14(vyy300, vyy40, hg, hh, baa) → new_esEs20(new_compare18(vyy300, vyy40, hg, hh, baa))
new_ltEs17(EQ, GT) → True
new_primCompAux00(vyy111, GT) → GT
new_esEs10(vyy78, vyy79) → new_primEqInt(vyy78, vyy79)
new_esEs28(vyy781, vyy791, ty_Integer) → new_esEs14(vyy781, vyy791)
new_esEs24(vyy780, vyy790, ty_Bool) → new_esEs11(vyy780, vyy790)
new_ltEs5(Left(vyy300), Left(vyy40), app(ty_Maybe, ca), cb) → new_ltEs11(vyy300, vyy40, ca)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs21(vyy78, vyy79, app(app(ty_FiniteMap, bhg), bhh)) → new_esEs13(vyy78, vyy79, bhg, bhh)
new_esEs24(vyy780, vyy790, ty_Char) → new_esEs18(vyy780, vyy790)
new_lt7(vyy300, vyy40, ty_Bool) → new_lt18(vyy300, vyy40)
new_compare28(@0, @0) → EQ
new_ltEs19(vyy301, vyy41, app(ty_[], bcf)) → new_ltEs13(vyy301, vyy41, bcf)
new_esEs25(vyy780, vyy790, ty_Float) → new_esEs9(vyy780, vyy790)
new_ltEs11(Just(vyy300), Nothing, daa) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vyy3000)), Pos(vyy40)) → LT
new_esEs6(Left(vyy780), Left(vyy790), ty_Int, bec) → new_esEs10(vyy780, vyy790)
new_ltEs5(Right(vyy300), Right(vyy40), dd, app(ty_Ratio, chh)) → new_ltEs18(vyy300, vyy40, chh)

The set Q consists of the following terms:

new_ltEs11(Nothing, Nothing, x0)
new_compare18(x0, x1, x2, x3, x4)
new_lt19(x0, x1)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare19(x0, x1, app(ty_Ratio, x2))
new_ltEs16(True, True)
new_esEs28(x0, x1, ty_Int)
new_ltEs18(x0, x1, x2)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs13(x0, x1, x2)
new_esEs11(True, True)
new_esEs23(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(Just(x0), Just(x1), ty_Bool)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_ltEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs25(x0, x1, ty_Char)
new_lt7(x0, x1, ty_Double)
new_lt20(x0, x1, ty_@0)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt9(x0, x1, x2)
new_lt6(x0, x1, ty_Int)
new_lt7(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(EQ, GT)
new_ltEs17(GT, EQ)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_@0)
new_ltEs12(x0, x1)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(Just(x0), Just(x1), ty_Char)
new_asAs(True, x0)
new_ltEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, ty_Bool)
new_primMulNat0(Succ(x0), Zero)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Pos(x0), Pos(x1))
new_asAs(False, x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1)
new_ltEs11(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(False, True)
new_esEs11(True, False)
new_compare8(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_lt7(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Ordering)
new_compare15(x0, x1, True)
new_ltEs11(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare19(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Integer)
new_lt7(x0, x1, ty_Float)
new_ltEs8(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs16(@0, @0)
new_esEs5(Nothing, Nothing, x0)
new_esEs20(LT)
new_compare15(x0, x1, False)
new_ltEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_compare19(x0, x1, ty_Integer)
new_esEs14(Integer(x0), Integer(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_primCompAux00(x0, GT)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare12(Double(x0, x1), Double(x2, x3))
new_ltEs9(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs6(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_ltEs11(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Zero)
new_ltEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs17([], [], x0)
new_compare19(x0, x1, ty_Double)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs9(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt6(x0, x1, ty_Float)
new_esEs24(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs9(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Char)
new_compare110(x0, x1, False)
new_compare28(@0, @0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_foldFM2(EmptyFM, x0, x1)
new_esEs5(Nothing, Just(x0), x1)
new_primMulNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Integer)
new_lt6(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Double)
new_compare210(x0, x1, True, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare19(x0, x1, ty_Int)
new_ltEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs21(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, app(ty_[], x2))
new_lt12(x0, x1)
new_esEs19(LT, LT)
new_esEs21(x0, x1, ty_Int)
new_compare19(x0, x1, app(ty_[], x2))
new_esEs19(EQ, GT)
new_esEs19(GT, EQ)
new_primMulNat0(Zero, Succ(x0))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs25(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_compare23(x0, x1, False, x2, x3)
new_ltEs9(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1)
new_compare0([], :(x0, x1), x2)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, ty_Int)
new_ltEs11(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_ltEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpNat0(Zero, Succ(x0))
new_lt7(x0, x1, ty_Int)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs11(False, False)
new_ltEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs23(x0, x1, ty_Ordering)
new_primMulInt(Neg(x0), Neg(x1))
new_compare19(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(Just(x0), Just(x1), ty_Double)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_sr(x0, x1)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False, x2, x3)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare25(x0, x1, False)
new_esEs27(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_compare29(x0, x1, x2)
new_esEs22(x0, x1, ty_Double)
new_compare6(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_compare23(x0, x1, True, x2, x3)
new_ltEs5(Right(x0), Right(x1), x2, ty_@0)
new_not0
new_esEs18(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(ty_[], x2))
new_primPlusNat0(Zero, Zero)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1)
new_compare16(x0, x1, True, x2, x3, x4)
new_compare6(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_lt18(x0, x1)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Int)
new_compare24(x0, x1, True, x2, x3)
new_lt17(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Integer)
new_lt7(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2, x3)
new_ltEs11(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_compare16(x0, x1, False, x2, x3, x4)
new_esEs21(x0, x1, ty_Bool)
new_sizeFM(EmptyFM, x0, x1)
new_esEs17([], :(x0, x1), x2)
new_not(GT)
new_pePe(True, x0, x1, x2, x3)
new_lt7(x0, x1, ty_Char)
new_ltEs17(GT, GT)
new_lt6(x0, x1, ty_Ordering)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs7(x0, x1)
new_compare27(x0, x1, False)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare13(x0, x1)
new_ltEs5(Left(x0), Right(x1), x2, x3)
new_ltEs5(Right(x0), Left(x1), x2, x3)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primPlusNat1(Succ(x0), x1)
new_esEs13(x0, x1, x2, x3)
new_compare7(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, app(ty_Ratio, x2))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_primCompAux00(x0, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Bool)
new_lt10(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_compare210(x0, x1, False, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, True)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_pePe(False, x0, x1, x2, x3)
new_lt8(x0, x1)
new_compare11(x0, x1, False, x2, x3)
new_lt11(x0, x1)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs27(x0, x1, ty_Integer)
new_ltEs11(Nothing, Just(x0), x1)
new_ltEs11(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Char)
new_ltEs9(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs9(x0, x1, ty_Ordering)
new_ltEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_primCompAux00(x0, EQ)
new_compare31(x0, x1, x2, x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare9(Char(x0), Char(x1))
new_esEs25(x0, x1, ty_Float)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_compare19(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(True, False)
new_ltEs16(False, True)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_fmToList(x0, x1, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, ty_Float)
new_ltEs9(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Bool)
new_ltEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs12(Double(x0, x1), Double(x2, x3))
new_ltEs11(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs29(x0, x1, ty_Int)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs17(LT, GT)
new_ltEs17(GT, LT)
new_ltEs11(Just(x0), Just(x1), ty_Ordering)
new_lt15(x0, x1, x2)
new_ltEs9(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Integer)
new_esEs19(GT, GT)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs5(Left(x0), Left(x1), ty_Int, x2)
new_lt20(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Ordering)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt6(x0, x1, ty_Char)
new_lt14(x0, x1, x2, x3, x4)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs11(Just(x0), Just(x1), ty_Float)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_esEs19(EQ, EQ)
new_esEs27(x0, x1, ty_Bool)
new_ltEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_compare30(x0, x1, x2, x3)
new_esEs20(EQ)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, ty_Double)
new_esEs19(EQ, LT)
new_esEs19(LT, EQ)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs5(Right(x0), Right(x1), x2, ty_Float)
new_ltEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Zero, Succ(x0))
new_esEs19(LT, GT)
new_esEs19(GT, LT)
new_esEs25(x0, x1, ty_Double)
new_not(EQ)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Bool)
new_ltEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs15(:%(x0, x1), :%(x2, x3), x4)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Bool)
new_primPlusNat1(Zero, x0)
new_lt20(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_lt16(x0, x1)
new_sr0(Integer(x0), Integer(x1))
new_esEs20(GT)
new_esEs24(x0, x1, ty_Double)
new_ltEs11(Just(x0), Just(x1), ty_Integer)
new_primCmpNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Float)
new_esEs5(Just(x0), Nothing, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs24(x0, x1, ty_Integer)
new_lt13(x0, x1, x2, x3)
new_lt6(x0, x1, ty_Double)
new_compare11(x0, x1, True, x2, x3)
new_ltEs10(x0, x1)
new_esEs27(x0, x1, ty_Int)
new_compare111(x0, x1, False, x2)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, x1, x2, x3)
new_compare111(x0, x1, True, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs17(:(x0, x1), [], x2)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs17(LT, EQ)
new_ltEs17(EQ, LT)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs22(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt7(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Int)
new_compare19(x0, x1, app(ty_Maybe, x2))
new_ltEs11(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(Just(x0), Nothing, x1)
new_primPlusNat0(Succ(x0), Zero)
new_lt7(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Char)
new_ltEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs9(Float(x0, x1), Float(x2, x3))
new_ltEs9(x0, x1, app(ty_[], x2))
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs23(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primEqNat0(Succ(x0), Succ(x1))
new_compare26(x0, x1, True, x2, x3, x4)
new_lt6(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare27(x0, x1, True)
new_compare110(x0, x1, True)
new_ltEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs15(x0, x1)
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs17(EQ, EQ)
new_compare19(x0, x1, ty_Bool)
new_compare0([], [], x0)
new_ltEs17(LT, LT)
new_ltEs14(x0, x1)
new_ltEs16(False, False)
new_not(LT)
new_ltEs19(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Char)
new_compare0(:(x0, x1), [], x2)
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, x2)
new_esEs25(x0, x1, ty_Int)

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_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, h), h, ba)
new_foldFM_LE2(vyy63, vyy64, vyy96, vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, h, ba) → new_foldFM_LE1(new_keysFM_LE0(vyy63, vyy64, vyy96, h, ba), vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, new_ltEs21(vyy670, vyy62, h), 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_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, h), 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_lt6(vyy301, vyy41, ty_Char) → new_lt11(vyy301, vyy41)
new_ltEs18(vyy30, vyy4, bhc) → new_not(new_compare6(vyy30, vyy4, bhc))
new_esEs18(Char(vyy780), Char(vyy790)) → new_primEqNat0(vyy780, vyy790)
new_lt20(vyy300, vyy40, ty_Int) → new_lt16(vyy300, vyy40)
new_esEs24(vyy780, vyy790, app(ty_Ratio, bdd)) → new_esEs15(vyy780, vyy790, bdd)
new_compare9(Char(vyy300), Char(vyy40)) → new_primCmpNat0(vyy300, vyy40)
new_ltEs17(LT, LT) → True
new_lt7(vyy300, vyy40, app(ty_[], dcb)) → new_lt15(vyy300, vyy40, dcb)
new_compare30(vyy300, vyy40, cd, ce) → new_compare24(vyy300, vyy40, new_esEs6(vyy300, vyy40, cd, ce), cd, ce)
new_lt6(vyy301, vyy41, ty_@0) → new_lt8(vyy301, vyy41)
new_esEs26(vyy781, vyy791, app(ty_Ratio, cde)) → new_esEs15(vyy781, vyy791, cde)
new_ltEs5(Right(vyy300), Right(vyy40), deh, ty_Float) → new_ltEs12(vyy300, vyy40)
new_lt20(vyy300, vyy40, ty_Char) → new_lt11(vyy300, vyy40)
new_compare10(vyy300, vyy40, True, bhd, bhe) → LT
new_ltEs21(vyy670, vyy62, app(ty_Ratio, cc)) → new_ltEs18(vyy670, vyy62, cc)
new_compare26(vyy300, vyy40, False, beb, bec, bed) → new_compare16(vyy300, vyy40, new_ltEs8(vyy300, vyy40, beb, bec, bed), beb, bec, bed)
new_compare16(vyy300, vyy40, False, beb, bec, bed) → GT
new_esEs27(vyy780, vyy790, ty_Ordering) → new_esEs19(vyy780, vyy790)
new_ltEs19(vyy301, vyy41, app(ty_Maybe, beg)) → new_ltEs11(vyy301, vyy41, beg)
new_esEs23(vyy781, vyy791, app(ty_[], bce)) → new_esEs17(vyy781, vyy791, bce)
new_esEs13(vyy78, vyy79, gd, ge) → new_asAs(new_esEs10(new_sizeFM(vyy78, gd, ge), new_sizeFM(vyy79, gd, ge)), new_esEs17(new_fmToList(vyy78, gd, ge), new_fmToList(vyy79, gd, ge), app(app(ty_@2, gd), ge)))
new_esEs6(Left(vyy780), Left(vyy790), app(ty_Ratio, df), cf) → new_esEs15(vyy780, vyy790, df)
new_ltEs11(Just(vyy300), Just(vyy40), ty_Bool) → new_ltEs16(vyy300, vyy40)
new_primMulNat0(Zero, Zero) → Zero
new_esEs25(vyy780, vyy790, ty_Double) → new_esEs12(vyy780, vyy790)
new_ltEs9(vyy302, vyy42, ty_Int) → new_ltEs15(vyy302, vyy42)
new_lt7(vyy300, vyy40, app(app(ty_Either, cd), ce)) → new_lt13(vyy300, vyy40, cd, ce)
new_esEs6(Left(vyy780), Left(vyy790), app(app(app(ty_@3, dg), dh), ea), cf) → new_esEs7(vyy780, vyy790, dg, dh, ea)
new_compare19(vyy300, vyy40, app(app(ty_@2, ddb), ddc)) → new_compare31(vyy300, vyy40, ddb, ddc)
new_ltEs20(vyy660, vyy62, ty_Float) → new_ltEs12(vyy660, vyy62)
new_compare19(vyy300, vyy40, app(app(app(ty_@3, dcf), dcg), dch)) → new_compare18(vyy300, vyy40, dcf, dcg, dch)
new_esEs25(vyy780, vyy790, app(app(ty_Either, cbf), cbg)) → new_esEs6(vyy780, vyy790, cbf, cbg)
new_lt20(vyy300, vyy40, app(app(ty_Either, bgb), bgc)) → new_lt13(vyy300, vyy40, bgb, bgc)
new_lt7(vyy300, vyy40, app(app(app(ty_@3, beb), bec), bed)) → new_lt14(vyy300, vyy40, beb, bec, bed)
new_esEs20(EQ) → False
new_lt20(vyy300, vyy40, ty_@0) → new_lt8(vyy300, vyy40)
new_ltEs16(False, True) → True
new_esEs15(:%(vyy780, vyy781), :%(vyy790, vyy791), gh) → new_asAs(new_esEs29(vyy780, vyy790, gh), new_esEs28(vyy781, vyy791, gh))
new_not(GT) → False
new_ltEs16(True, False) → False
new_esEs26(vyy781, vyy791, ty_Float) → new_esEs9(vyy781, vyy791)
new_esEs27(vyy780, vyy790, app(app(ty_@2, cee), cef)) → new_esEs8(vyy780, vyy790, cee, cef)
new_ltEs19(vyy301, vyy41, ty_Bool) → new_ltEs16(vyy301, vyy41)
new_esEs6(Left(vyy780), Left(vyy790), ty_Bool, cf) → new_esEs11(vyy780, vyy790)
new_ltEs9(vyy302, vyy42, ty_@0) → new_ltEs10(vyy302, vyy42)
new_ltEs6(vyy30, vyy4) → new_not(new_compare7(vyy30, vyy4))
new_esEs6(Right(vyy780), Right(vyy790), ed, app(ty_Ratio, fc)) → new_esEs15(vyy780, vyy790, fc)
new_compare19(vyy300, vyy40, app(ty_[], dda)) → new_compare0(vyy300, vyy40, dda)
new_primCompAux0(vyy300, vyy40, vyy107, bhf) → new_primCompAux00(vyy107, new_compare19(vyy300, vyy40, bhf))
new_ltEs5(Left(vyy300), Right(vyy40), deh, dde) → True
new_compare0(:(vyy300, vyy301), :(vyy40, vyy41), bhf) → new_primCompAux0(vyy300, vyy40, new_compare0(vyy301, vyy41, bhf), bhf)
new_esEs21(vyy78, vyy79, app(app(app(ty_@3, ha), hb), hc)) → new_esEs7(vyy78, vyy79, ha, hb, hc)
new_ltEs9(vyy302, vyy42, ty_Ordering) → new_ltEs17(vyy302, vyy42)
new_esEs5(Just(vyy780), Just(vyy790), app(ty_Maybe, cha)) → new_esEs5(vyy780, vyy790, cha)
new_ltEs5(Right(vyy300), Right(vyy40), deh, app(app(ty_@2, dfh), dga)) → new_ltEs4(vyy300, vyy40, dfh, dga)
new_ltEs5(Right(vyy300), Right(vyy40), deh, app(app(ty_Either, dfb), dfc)) → new_ltEs5(vyy300, vyy40, dfb, dfc)
new_esEs12(Double(vyy780, vyy781), Double(vyy790, vyy791)) → new_esEs10(new_sr(vyy780, vyy790), new_sr(vyy781, vyy791))
new_lt20(vyy300, vyy40, ty_Float) → new_lt12(vyy300, vyy40)
new_esEs21(vyy78, vyy79, app(app(ty_Either, ed), cf)) → new_esEs6(vyy78, vyy79, ed, cf)
new_ltEs21(vyy670, vyy62, app(app(ty_@2, ca), cb)) → new_ltEs4(vyy670, vyy62, ca, cb)
new_ltEs20(vyy660, vyy62, app(ty_Maybe, bb)) → new_ltEs11(vyy660, vyy62, bb)
new_esEs26(vyy781, vyy791, ty_Integer) → new_esEs14(vyy781, vyy791)
new_compare15(vyy300, vyy40, False) → GT
new_ltEs11(Just(vyy300), Just(vyy40), app(app(app(ty_@3, cac), cad), cae)) → new_ltEs8(vyy300, vyy40, cac, cad, cae)
new_lt7(vyy300, vyy40, ty_Integer) → new_lt10(vyy300, vyy40)
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, gd, ge) → :(@2(vyy790, vyy791), vyy125)
new_ltEs11(Just(vyy300), Just(vyy40), ty_Double) → new_ltEs14(vyy300, vyy40)
new_ltEs5(Right(vyy300), Left(vyy40), deh, dde) → False
new_ltEs21(vyy670, vyy62, ty_Ordering) → new_ltEs17(vyy670, vyy62)
new_ltEs16(True, True) → True
new_esEs21(vyy78, vyy79, app(app(ty_@2, gf), gg)) → new_esEs8(vyy78, vyy79, gf, gg)
new_ltEs17(EQ, LT) → False
new_lt6(vyy301, vyy41, ty_Bool) → new_lt18(vyy301, vyy41)
new_esEs19(GT, GT) → True
new_esEs26(vyy781, vyy791, app(app(ty_@2, cda), cdb)) → new_esEs8(vyy781, vyy791, cda, cdb)
new_esEs27(vyy780, vyy790, ty_@0) → new_esEs16(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), ty_Char, cf) → new_esEs18(vyy780, vyy790)
new_ltEs19(vyy301, vyy41, app(app(ty_@2, bff), bfg)) → new_ltEs4(vyy301, vyy41, bff, bfg)
new_esEs6(Right(vyy780), Right(vyy790), ed, app(app(ty_FiniteMap, ee), ef)) → new_esEs13(vyy780, vyy790, ee, ef)
new_ltEs20(vyy660, vyy62, ty_@0) → new_ltEs10(vyy660, vyy62)
new_ltEs19(vyy301, vyy41, ty_Integer) → new_ltEs6(vyy301, vyy41)
new_lt20(vyy300, vyy40, app(app(ty_@2, bgh), bha)) → new_lt17(vyy300, vyy40, bgh, bha)
new_compare15(vyy300, vyy40, True) → LT
new_ltEs5(Left(vyy300), Left(vyy40), ty_Float, dde) → new_ltEs12(vyy300, vyy40)
new_ltEs20(vyy660, vyy62, app(ty_[], bh)) → new_ltEs13(vyy660, vyy62, bh)
new_esEs5(Just(vyy780), Just(vyy790), ty_Ordering) → new_esEs19(vyy780, vyy790)
new_esEs27(vyy780, vyy790, app(ty_[], cff)) → new_esEs17(vyy780, vyy790, cff)
new_ltEs21(vyy670, vyy62, app(app(app(ty_@3, be), bf), bg)) → new_ltEs8(vyy670, vyy62, be, bf, bg)
new_ltEs5(Left(vyy300), Left(vyy40), app(app(app(ty_@3, dea), deb), dec), dde) → new_ltEs8(vyy300, vyy40, dea, deb, dec)
new_ltEs19(vyy301, vyy41, app(ty_Ratio, bfh)) → new_ltEs18(vyy301, vyy41, bfh)
new_esEs14(Integer(vyy780), Integer(vyy790)) → new_primEqInt(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), ty_Integer, cf) → new_esEs14(vyy780, vyy790)
new_lt6(vyy301, vyy41, app(ty_Ratio, dca)) → new_lt4(vyy301, vyy41, dca)
new_ltEs20(vyy660, vyy62, app(app(ty_@2, ca), cb)) → new_ltEs4(vyy660, vyy62, ca, cb)
new_esEs23(vyy781, vyy791, app(app(app(ty_@3, bca), bcb), bcc)) → new_esEs7(vyy781, vyy791, bca, bcb, bcc)
new_primCmpNat0(Zero, Succ(vyy400)) → LT
new_esEs27(vyy780, vyy790, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs7(vyy780, vyy790, cfb, cfc, cfd)
new_ltEs9(vyy302, vyy42, app(ty_Maybe, chf)) → new_ltEs11(vyy302, vyy42, chf)
new_ltEs20(vyy660, vyy62, ty_Double) → new_ltEs14(vyy660, vyy62)
new_esEs26(vyy781, vyy791, ty_Double) → new_esEs12(vyy781, vyy791)
new_esEs8(@2(vyy780, vyy781), @2(vyy790, vyy791), gf, gg) → new_asAs(new_esEs27(vyy780, vyy790, gf), new_esEs26(vyy781, vyy791, gg))
new_lt20(vyy300, vyy40, app(app(app(ty_@3, bgd), bge), bgf)) → new_lt14(vyy300, vyy40, bgd, bge, bgf)
new_esEs26(vyy781, vyy791, ty_Bool) → new_esEs11(vyy781, vyy791)
new_esEs6(Right(vyy780), Left(vyy790), ed, cf) → False
new_esEs6(Left(vyy780), Right(vyy790), ed, cf) → False
new_ltEs5(Right(vyy300), Right(vyy40), deh, ty_Integer) → new_ltEs6(vyy300, vyy40)
new_keysFM_LE0(vyy63, vyy64, vyy95, h, ba) → :(vyy63, vyy95)
new_compare19(vyy300, vyy40, app(app(ty_Either, dcd), dce)) → new_compare30(vyy300, vyy40, dcd, dce)
new_esEs23(vyy781, vyy791, ty_Char) → new_esEs18(vyy781, vyy791)
new_esEs5(Just(vyy780), Just(vyy790), app(ty_[], chb)) → new_esEs17(vyy780, vyy790, chb)
new_compare0([], [], bhf) → EQ
new_esEs23(vyy781, vyy791, ty_@0) → new_esEs16(vyy781, vyy791)
new_primEqNat0(Zero, Zero) → True
new_ltEs21(vyy670, vyy62, ty_@0) → new_ltEs10(vyy670, vyy62)
new_ltEs20(vyy660, vyy62, app(ty_Ratio, cc)) → new_ltEs18(vyy660, vyy62, cc)
new_compare6(:%(vyy300, vyy301), :%(vyy40, vyy41), ty_Integer) → new_compare7(new_sr0(vyy300, vyy41), new_sr0(vyy40, vyy301))
new_ltEs11(Nothing, Just(vyy40), bhg) → True
new_ltEs11(Just(vyy300), Just(vyy40), app(ty_Maybe, bhh)) → new_ltEs11(vyy300, vyy40, bhh)
new_esEs23(vyy781, vyy791, app(app(ty_Either, bbf), bbg)) → new_esEs6(vyy781, vyy791, bbf, bbg)
new_primMulNat0(Succ(vyy30100), Succ(vyy4100)) → new_primPlusNat1(new_primMulNat0(vyy30100, Succ(vyy4100)), vyy4100)
new_lt7(vyy300, vyy40, app(ty_Ratio, gb)) → new_lt4(vyy300, vyy40, gb)
new_esEs6(Right(vyy780), Right(vyy790), ed, ty_@0) → new_esEs16(vyy780, vyy790)
new_compare18(vyy300, vyy40, beb, bec, bed) → new_compare26(vyy300, vyy40, new_esEs7(vyy300, vyy40, beb, bec, bed), beb, bec, bed)
new_esEs26(vyy781, vyy791, ty_@0) → new_esEs16(vyy781, vyy791)
new_ltEs5(Left(vyy300), Left(vyy40), ty_Int, dde) → new_ltEs15(vyy300, vyy40)
new_esEs6(Right(vyy780), Right(vyy790), ed, app(app(ty_Either, fa), fb)) → new_esEs6(vyy780, vyy790, fa, fb)
new_ltEs15(vyy30, vyy4) → new_not(new_compare13(vyy30, vyy4))
new_esEs6(Right(vyy780), Right(vyy790), ed, ty_Char) → new_esEs18(vyy780, vyy790)
new_compare19(vyy300, vyy40, ty_Integer) → new_compare7(vyy300, vyy40)
new_esEs5(Just(vyy780), Just(vyy790), app(ty_Ratio, cge)) → new_esEs15(vyy780, vyy790, cge)
new_ltEs17(GT, LT) → False
new_sr(vyy301, vyy41) → new_primMulInt(vyy301, vyy41)
new_esEs5(Just(vyy780), Just(vyy790), ty_Integer) → new_esEs14(vyy780, vyy790)
new_lt7(vyy300, vyy40, ty_Int) → new_lt16(vyy300, vyy40)
new_esEs26(vyy781, vyy791, ty_Ordering) → new_esEs19(vyy781, vyy791)
new_ltEs5(Left(vyy300), Left(vyy40), app(ty_[], ded), dde) → new_ltEs13(vyy300, vyy40, ded)
new_esEs5(Just(vyy780), Just(vyy790), ty_Char) → new_esEs18(vyy780, vyy790)
new_ltEs21(vyy670, vyy62, ty_Bool) → new_ltEs16(vyy670, vyy62)
new_esEs21(vyy78, vyy79, ty_Float) → new_esEs9(vyy78, vyy79)
new_esEs23(vyy781, vyy791, ty_Float) → new_esEs9(vyy781, vyy791)
new_ltEs11(Just(vyy300), Just(vyy40), ty_Float) → new_ltEs12(vyy300, vyy40)
new_esEs21(vyy78, vyy79, ty_Ordering) → new_esEs19(vyy78, vyy79)
new_ltEs20(vyy660, vyy62, ty_Bool) → new_ltEs16(vyy660, vyy62)
new_esEs5(Just(vyy780), Just(vyy790), ty_Double) → new_esEs12(vyy780, vyy790)
new_ltEs20(vyy660, vyy62, ty_Int) → new_ltEs15(vyy660, vyy62)
new_compare25(vyy300, vyy40, False) → new_compare15(vyy300, vyy40, new_ltEs16(vyy300, vyy40))
new_lt6(vyy301, vyy41, app(app(ty_Either, dba), dbb)) → new_lt13(vyy301, vyy41, dba, dbb)
new_ltEs5(Left(vyy300), Left(vyy40), app(app(ty_@2, dee), def), dde) → new_ltEs4(vyy300, vyy40, dee, def)
new_esEs6(Left(vyy780), Left(vyy790), ty_Float, cf) → new_esEs9(vyy780, vyy790)
new_primEqInt(Neg(Succ(vyy7800)), Neg(Succ(vyy7900))) → new_primEqNat0(vyy7800, vyy7900)
new_compare25(vyy300, vyy40, True) → EQ
new_ltEs5(Left(vyy300), Left(vyy40), ty_Ordering, dde) → new_ltEs17(vyy300, vyy40)
new_esEs25(vyy780, vyy790, ty_Bool) → new_esEs11(vyy780, vyy790)
new_esEs25(vyy780, vyy790, app(app(ty_@2, cbd), cbe)) → new_esEs8(vyy780, vyy790, cbd, cbe)
new_esEs6(Right(vyy780), Right(vyy790), ed, app(app(app(ty_@3, fd), ff), fg)) → new_esEs7(vyy780, vyy790, fd, ff, fg)
new_esEs19(EQ, EQ) → True
new_ltEs17(LT, GT) → True
new_esEs22(vyy782, vyy792, ty_Ordering) → new_esEs19(vyy782, vyy792)
new_ltEs5(Right(vyy300), Right(vyy40), deh, ty_Double) → new_ltEs14(vyy300, vyy40)
new_esEs21(vyy78, vyy79, ty_@0) → new_esEs16(vyy78, vyy79)
new_ltEs5(Right(vyy300), Right(vyy40), deh, ty_Ordering) → new_ltEs17(vyy300, vyy40)
new_ltEs9(vyy302, vyy42, ty_Double) → new_ltEs14(vyy302, vyy42)
new_esEs6(Right(vyy780), Right(vyy790), ed, app(app(ty_@2, eg), eh)) → new_esEs8(vyy780, vyy790, eg, eh)
new_lt7(vyy300, vyy40, ty_Ordering) → new_lt19(vyy300, vyy40)
new_esEs26(vyy781, vyy791, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs7(vyy781, vyy791, cdf, cdg, cdh)
new_esEs25(vyy780, vyy790, ty_Char) → new_esEs18(vyy780, vyy790)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Just(vyy780), Just(vyy790), ty_Int) → new_esEs10(vyy780, vyy790)
new_ltEs21(vyy670, vyy62, app(ty_Maybe, bb)) → new_ltEs11(vyy670, vyy62, bb)
new_compare19(vyy300, vyy40, ty_Double) → new_compare12(vyy300, vyy40)
new_esEs25(vyy780, vyy790, app(ty_Ratio, cbh)) → new_esEs15(vyy780, vyy790, cbh)
new_ltEs11(Just(vyy300), Just(vyy40), ty_Int) → new_ltEs15(vyy300, vyy40)
new_primEqInt(Neg(Succ(vyy7800)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy7900))) → False
new_primPlusNat1(Zero, vyy4100) → Succ(vyy4100)
new_lt7(vyy300, vyy40, ty_Float) → new_lt12(vyy300, vyy40)
new_ltEs5(Left(vyy300), Left(vyy40), ty_Integer, dde) → new_ltEs6(vyy300, vyy40)
new_compare111(vyy300, vyy40, True, ccf) → LT
new_esEs6(Right(vyy780), Right(vyy790), ed, app(ty_[], ga)) → new_esEs17(vyy780, vyy790, ga)
new_ltEs4(@2(vyy300, vyy301), @2(vyy40, vyy41), bee, bef) → new_pePe(new_lt20(vyy300, vyy40, bee), vyy300, vyy40, new_ltEs19(vyy301, vyy41, bef), bee)
new_compare24(vyy300, vyy40, True, cd, ce) → EQ
new_esEs23(vyy781, vyy791, ty_Ordering) → new_esEs19(vyy781, vyy791)
new_lt6(vyy301, vyy41, ty_Float) → new_lt12(vyy301, vyy41)
new_ltEs11(Just(vyy300), Just(vyy40), ty_Char) → new_ltEs7(vyy300, vyy40)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), gd, ge) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, gd, ge), vyy7933, gd, ge)
new_lt9(vyy300, vyy40, ccf) → new_esEs20(new_compare29(vyy300, vyy40, ccf))
new_ltEs17(EQ, EQ) → True
new_ltEs19(vyy301, vyy41, ty_Ordering) → new_ltEs17(vyy301, vyy41)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs23(vyy781, vyy791, ty_Integer) → new_esEs14(vyy781, vyy791)
new_lt6(vyy301, vyy41, ty_Double) → new_lt5(vyy301, vyy41)
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, cg), da), cf) → new_esEs13(vyy780, vyy790, cg, da)
new_esEs19(EQ, LT) → False
new_esEs19(LT, EQ) → False
new_primCmpNat0(Succ(vyy3000), Succ(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_sizeFM(EmptyFM, gd, ge) → Pos(Zero)
new_lt15(vyy300, vyy40, dcb) → new_esEs20(new_compare0(vyy300, vyy40, dcb))
new_esEs11(False, False) → True
new_esEs25(vyy780, vyy790, app(app(ty_FiniteMap, cbb), cbc)) → new_esEs13(vyy780, vyy790, cbb, cbc)
new_primEqInt(Pos(Succ(vyy7800)), Pos(Succ(vyy7900))) → new_primEqNat0(vyy7800, vyy7900)
new_compare10(vyy300, vyy40, False, bhd, bhe) → GT
new_ltEs5(Left(vyy300), Left(vyy40), app(app(ty_Either, ddg), ddh), dde) → new_ltEs5(vyy300, vyy40, ddg, ddh)
new_esEs25(vyy780, vyy790, app(ty_Maybe, ccd)) → new_esEs5(vyy780, vyy790, ccd)
new_lt20(vyy300, vyy40, ty_Ordering) → new_lt19(vyy300, vyy40)
new_ltEs5(Right(vyy300), Right(vyy40), deh, app(ty_Maybe, dfa)) → new_ltEs11(vyy300, vyy40, dfa)
new_esEs5(Just(vyy780), Just(vyy790), ty_Bool) → new_esEs11(vyy780, vyy790)
new_esEs26(vyy781, vyy791, app(app(ty_FiniteMap, ccg), cch)) → new_esEs13(vyy781, vyy791, ccg, cch)
new_esEs6(Left(vyy780), Left(vyy790), ty_@0, cf) → new_esEs16(vyy780, vyy790)
new_primEqNat0(Succ(vyy7800), Succ(vyy7900)) → new_primEqNat0(vyy7800, vyy7900)
new_esEs17(:(vyy780, vyy781), :(vyy790, vyy791), he) → new_asAs(new_esEs25(vyy780, vyy790, he), new_esEs17(vyy781, vyy791, he))
new_esEs24(vyy780, vyy790, ty_@0) → new_esEs16(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), app(ty_[], ec), cf) → new_esEs17(vyy780, vyy790, ec)
new_lt7(vyy300, vyy40, app(app(ty_@2, bhd), bhe)) → new_lt17(vyy300, vyy40, bhd, bhe)
new_ltEs9(vyy302, vyy42, app(app(ty_@2, dae), daf)) → new_ltEs4(vyy302, vyy42, dae, daf)
new_ltEs19(vyy301, vyy41, ty_Double) → new_ltEs14(vyy301, vyy41)
new_esEs29(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_primCompAux00(vyy111, LT) → LT
new_esEs27(vyy780, vyy790, app(ty_Ratio, cfa)) → new_esEs15(vyy780, vyy790, cfa)
new_lt16(vyy300, vyy40) → new_esEs20(new_compare13(vyy300, vyy40))
new_compare12(Double(vyy300, vyy301), Double(vyy40, vyy41)) → new_compare13(new_sr(vyy300, vyy40), new_sr(vyy301, vyy41))
new_primCmpInt(Neg(Succ(vyy3000)), Neg(vyy40)) → new_primCmpNat0(vyy40, Succ(vyy3000))
new_esEs24(vyy780, vyy790, ty_Float) → new_esEs9(vyy780, vyy790)
new_esEs6(Right(vyy780), Right(vyy790), ed, app(ty_Maybe, fh)) → new_esEs5(vyy780, vyy790, fh)
new_esEs6(Right(vyy780), Right(vyy790), ed, ty_Float) → new_esEs9(vyy780, vyy790)
new_primEqInt(Pos(Zero), Pos(Succ(vyy7900))) → False
new_primEqInt(Pos(Succ(vyy7800)), Pos(Zero)) → False
new_ltEs8(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), chc, chd, che) → new_pePe(new_lt7(vyy300, vyy40, chc), vyy300, vyy40, new_pePe(new_lt6(vyy301, vyy41, chd), vyy301, vyy41, new_ltEs9(vyy302, vyy42, che), chd), chc)
new_primPlusNat0(Zero, Succ(vyy41000)) → Succ(vyy41000)
new_primPlusNat0(Succ(vyy12600), Zero) → Succ(vyy12600)
new_primCmpNat0(Zero, Zero) → EQ
new_lt6(vyy301, vyy41, ty_Integer) → new_lt10(vyy301, vyy41)
new_ltEs21(vyy670, vyy62, ty_Double) → new_ltEs14(vyy670, vyy62)
new_primCmpNat0(Succ(vyy3000), Zero) → GT
new_lt18(vyy300, vyy40) → new_esEs20(new_compare8(vyy300, vyy40))
new_esEs22(vyy782, vyy792, ty_Integer) → new_esEs14(vyy782, vyy792)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy400))) → LT
new_compare11(vyy300, vyy40, True, cd, ce) → LT
new_ltEs11(Just(vyy300), Just(vyy40), app(ty_[], caf)) → new_ltEs13(vyy300, vyy40, caf)
new_sr0(Integer(vyy400), Integer(vyy3010)) → Integer(new_primMulInt(vyy400, vyy3010))
new_ltEs20(vyy660, vyy62, ty_Integer) → new_ltEs6(vyy660, vyy62)
new_primEqInt(Pos(Succ(vyy7800)), Neg(vyy790)) → False
new_primEqInt(Neg(Succ(vyy7800)), Pos(vyy790)) → False
new_esEs25(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_ltEs5(Right(vyy300), Right(vyy40), deh, ty_Int) → new_ltEs15(vyy300, vyy40)
new_compare6(:%(vyy300, vyy301), :%(vyy40, vyy41), ty_Int) → new_compare13(new_sr(vyy300, vyy41), new_sr(vyy40, vyy301))
new_compare210(vyy300, vyy40, True, ccf) → EQ
new_esEs27(vyy780, vyy790, app(ty_Maybe, cfe)) → new_esEs5(vyy780, vyy790, cfe)
new_foldFM2(EmptyFM, gd, ge) → []
new_esEs6(Right(vyy780), Right(vyy790), ed, ty_Ordering) → new_esEs19(vyy780, vyy790)
new_ltEs5(Left(vyy300), Left(vyy40), ty_Double, dde) → new_ltEs14(vyy300, vyy40)
new_ltEs9(vyy302, vyy42, app(app(ty_Either, chg), chh)) → new_ltEs5(vyy302, vyy42, chg, chh)
new_esEs27(vyy780, vyy790, ty_Double) → new_esEs12(vyy780, vyy790)
new_foldFM_LE10(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, vyy67, False, h, ba) → new_foldFM_LE0(vyy61, vyy62, vyy66, h, ba)
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_@2, db), dc), cf) → new_esEs8(vyy780, vyy790, db, dc)
new_lt5(vyy300, vyy40) → new_esEs20(new_compare12(vyy300, vyy40))
new_esEs26(vyy781, vyy791, ty_Int) → new_esEs10(vyy781, vyy791)
new_primEqInt(Pos(Zero), Neg(Succ(vyy7900))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy7900))) → False
new_esEs26(vyy781, vyy791, app(ty_[], ceb)) → new_esEs17(vyy781, vyy791, ceb)
new_foldFM_LE20(vyy63, vyy64, vyy96, vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, h, ba) → new_foldFM_LE10(new_keysFM_LE0(vyy63, vyy64, vyy96, h, ba), vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, new_ltEs21(vyy670, vyy62, h), h, ba)
new_primCompAux00(vyy111, EQ) → vyy111
new_primCmpInt(Pos(Zero), Pos(Succ(vyy400))) → new_primCmpNat0(Zero, Succ(vyy400))
new_esEs22(vyy782, vyy792, app(app(ty_FiniteMap, hf), hg)) → new_esEs13(vyy782, vyy792, hf, hg)
new_esEs23(vyy781, vyy791, ty_Bool) → new_esEs11(vyy781, vyy791)
new_lt7(vyy300, vyy40, app(ty_Maybe, ccf)) → new_lt9(vyy300, vyy40, ccf)
new_esEs22(vyy782, vyy792, ty_@0) → new_esEs16(vyy782, vyy792)
new_lt20(vyy300, vyy40, app(ty_Ratio, bhb)) → new_lt4(vyy300, vyy40, bhb)
new_ltEs5(Left(vyy300), Left(vyy40), app(ty_Ratio, deg), dde) → new_ltEs18(vyy300, vyy40, deg)
new_esEs7(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), ha, hb, hc) → new_asAs(new_esEs24(vyy780, vyy790, ha), new_asAs(new_esEs23(vyy781, vyy791, hb), new_esEs22(vyy782, vyy792, hc)))
new_esEs21(vyy78, vyy79, app(ty_[], he)) → new_esEs17(vyy78, vyy79, he)
new_ltEs11(Just(vyy300), Just(vyy40), ty_@0) → new_ltEs10(vyy300, vyy40)
new_esEs21(vyy78, vyy79, ty_Char) → new_esEs18(vyy78, vyy79)
new_ltEs11(Just(vyy300), Just(vyy40), app(ty_Ratio, cba)) → new_ltEs18(vyy300, vyy40, cba)
new_lt6(vyy301, vyy41, app(app(ty_@2, dbg), dbh)) → new_lt17(vyy301, vyy41, dbg, dbh)
new_lt20(vyy300, vyy40, ty_Double) → new_lt5(vyy300, vyy40)
new_esEs21(vyy78, vyy79, ty_Integer) → new_esEs14(vyy78, vyy79)
new_compare17(vyy300, vyy40) → new_compare27(vyy300, vyy40, new_esEs19(vyy300, vyy40))
new_lt17(vyy300, vyy40, bhd, bhe) → new_esEs20(new_compare31(vyy300, vyy40, bhd, bhe))
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_Either, dd), de), cf) → new_esEs6(vyy780, vyy790, dd, de)
new_esEs23(vyy781, vyy791, app(app(ty_FiniteMap, bbb), bbc)) → new_esEs13(vyy781, vyy791, bbb, bbc)
new_lt10(vyy300, vyy40) → new_esEs20(new_compare7(vyy300, vyy40))
new_primCmpInt(Pos(Succ(vyy3000)), Pos(vyy40)) → new_primCmpNat0(Succ(vyy3000), vyy40)
new_esEs24(vyy780, vyy790, app(app(ty_Either, bdb), bdc)) → new_esEs6(vyy780, vyy790, bdb, bdc)
new_lt8(vyy300, vyy40) → new_esEs20(new_compare28(vyy300, vyy40))
new_esEs24(vyy780, vyy790, ty_Ordering) → new_esEs19(vyy780, vyy790)
new_lt7(vyy300, vyy40, ty_Double) → new_lt5(vyy300, vyy40)
new_not0True
new_compare0(:(vyy300, vyy301), [], bhf) → GT
new_esEs24(vyy780, vyy790, app(ty_[], bea)) → new_esEs17(vyy780, vyy790, bea)
new_ltEs9(vyy302, vyy42, app(ty_Ratio, dag)) → new_ltEs18(vyy302, vyy42, dag)
new_esEs21(vyy78, vyy79, app(ty_Ratio, gh)) → new_esEs15(vyy78, vyy79, gh)
new_esEs27(vyy780, vyy790, app(app(ty_Either, ceg), ceh)) → new_esEs6(vyy780, vyy790, ceg, ceh)
new_esEs24(vyy780, vyy790, app(ty_Maybe, bdh)) → new_esEs5(vyy780, vyy790, bdh)
new_lt6(vyy301, vyy41, app(ty_[], dbf)) → new_lt15(vyy301, vyy41, dbf)
new_esEs5(Just(vyy780), Just(vyy790), app(app(ty_@2, cga), cgb)) → new_esEs8(vyy780, vyy790, cga, cgb)
new_esEs19(GT, LT) → False
new_esEs19(LT, GT) → False
new_ltEs20(vyy660, vyy62, app(app(app(ty_@3, be), bf), bg)) → new_ltEs8(vyy660, vyy62, be, bf, bg)
new_lt13(vyy300, vyy40, cd, ce) → new_esEs20(new_compare30(vyy300, vyy40, cd, ce))
new_compare19(vyy300, vyy40, ty_Float) → new_compare14(vyy300, vyy40)
new_compare19(vyy300, vyy40, ty_Bool) → new_compare8(vyy300, vyy40)
new_esEs22(vyy782, vyy792, ty_Bool) → new_esEs11(vyy782, vyy792)
new_compare11(vyy300, vyy40, False, cd, ce) → GT
new_esEs6(Right(vyy780), Right(vyy790), ed, ty_Bool) → new_esEs11(vyy780, vyy790)
new_esEs22(vyy782, vyy792, app(app(app(ty_@3, bae), baf), bag)) → new_esEs7(vyy782, vyy792, bae, baf, bag)
new_esEs22(vyy782, vyy792, ty_Char) → new_esEs18(vyy782, vyy792)
new_primCmpInt(Pos(Succ(vyy3000)), Neg(vyy40)) → GT
new_lt6(vyy301, vyy41, ty_Int) → new_lt16(vyy301, vyy41)
new_esEs29(vyy780, vyy790, ty_Integer) → new_esEs14(vyy780, vyy790)
new_primMulInt(Pos(vyy3010), Pos(vyy410)) → Pos(new_primMulNat0(vyy3010, vyy410))
new_lt20(vyy300, vyy40, ty_Integer) → new_lt10(vyy300, vyy40)
new_ltEs9(vyy302, vyy42, ty_Char) → new_ltEs7(vyy302, vyy42)
new_esEs27(vyy780, vyy790, ty_Bool) → new_esEs11(vyy780, vyy790)
new_ltEs9(vyy302, vyy42, ty_Bool) → new_ltEs16(vyy302, vyy42)
new_compare29(vyy300, vyy40, ccf) → new_compare210(vyy300, vyy40, new_esEs5(vyy300, vyy40, ccf), ccf)
new_esEs27(vyy780, vyy790, app(app(ty_FiniteMap, cec), ced)) → new_esEs13(vyy780, vyy790, cec, ced)
new_ltEs21(vyy670, vyy62, app(app(ty_Either, bc), bd)) → new_ltEs5(vyy670, vyy62, bc, bd)
new_esEs22(vyy782, vyy792, ty_Int) → new_esEs10(vyy782, vyy792)
new_ltEs9(vyy302, vyy42, app(ty_[], dad)) → new_ltEs13(vyy302, vyy42, dad)
new_primMulInt(Neg(vyy3010), Neg(vyy410)) → Pos(new_primMulNat0(vyy3010, vyy410))
new_compare110(vyy300, vyy40, True) → LT
new_ltEs5(Right(vyy300), Right(vyy40), deh, app(ty_[], dfg)) → new_ltEs13(vyy300, vyy40, dfg)
new_ltEs19(vyy301, vyy41, app(app(ty_Either, beh), bfa)) → new_ltEs5(vyy301, vyy41, beh, bfa)
new_primEqNat0(Zero, Succ(vyy7900)) → False
new_primEqNat0(Succ(vyy7800), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs9(vyy302, vyy42, ty_Float) → new_ltEs12(vyy302, vyy42)
new_esEs6(Right(vyy780), Right(vyy790), ed, ty_Double) → new_esEs12(vyy780, vyy790)
new_compare110(vyy300, vyy40, False) → GT
new_compare23(vyy300, vyy40, False, bhd, bhe) → new_compare10(vyy300, vyy40, new_ltEs4(vyy300, vyy40, bhd, bhe), bhd, bhe)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs19(vyy301, vyy41, ty_Char) → new_ltEs7(vyy301, vyy41)
new_esEs22(vyy782, vyy792, app(ty_Ratio, bad)) → new_esEs15(vyy782, vyy792, bad)
new_ltEs9(vyy302, vyy42, ty_Integer) → new_ltEs6(vyy302, vyy42)
new_ltEs19(vyy301, vyy41, app(app(app(ty_@3, bfb), bfc), bfd)) → new_ltEs8(vyy301, vyy41, bfb, bfc, bfd)
new_ltEs14(vyy30, vyy4) → new_not(new_compare12(vyy30, vyy4))
new_compare14(Float(vyy300, vyy301), Float(vyy40, vyy41)) → new_compare13(new_sr(vyy300, vyy40), new_sr(vyy301, vyy41))
new_esEs22(vyy782, vyy792, app(ty_[], bba)) → new_esEs17(vyy782, vyy792, bba)
new_sizeFM(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), gd, ge) → vyy792
new_lt20(vyy300, vyy40, ty_Bool) → new_lt18(vyy300, vyy40)
new_lt7(vyy300, vyy40, ty_@0) → new_lt8(vyy300, vyy40)
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_esEs26(vyy781, vyy791, app(ty_Maybe, cea)) → new_esEs5(vyy781, vyy791, cea)
new_pePe(True, vyy78, vyy79, vyy97, gc) → True
new_primPlusNat1(Succ(vyy1260), vyy4100) → Succ(Succ(new_primPlusNat0(vyy1260, vyy4100)))
new_compare16(vyy300, vyy40, True, beb, bec, bed) → LT
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), gd, ge) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, gd, ge), vyy793, gd, ge)
new_lt19(vyy300, vyy40) → new_esEs20(new_compare17(vyy300, vyy40))
new_ltEs7(vyy30, vyy4) → new_not(new_compare9(vyy30, vyy4))
new_compare23(vyy300, vyy40, True, bhd, bhe) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(vyy400))) → new_primCmpNat0(Succ(vyy400), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy400))) → GT
new_esEs11(True, False) → False
new_esEs11(False, True) → False
new_esEs25(vyy780, vyy790, ty_Ordering) → new_esEs19(vyy780, vyy790)
new_esEs25(vyy780, vyy790, ty_Integer) → new_esEs14(vyy780, vyy790)
new_esEs23(vyy781, vyy791, app(app(ty_@2, bbd), bbe)) → new_esEs8(vyy781, vyy791, bbd, bbe)
new_lt20(vyy300, vyy40, app(ty_Maybe, bga)) → new_lt9(vyy300, vyy40, bga)
new_compare19(vyy300, vyy40, ty_Char) → new_compare9(vyy300, vyy40)
new_esEs24(vyy780, vyy790, app(app(ty_FiniteMap, bcf), bcg)) → new_esEs13(vyy780, vyy790, bcf, bcg)
new_ltEs21(vyy670, vyy62, ty_Integer) → new_ltEs6(vyy670, vyy62)
new_ltEs5(Left(vyy300), Left(vyy40), ty_@0, dde) → new_ltEs10(vyy300, vyy40)
new_ltEs5(Right(vyy300), Right(vyy40), deh, ty_@0) → new_ltEs10(vyy300, vyy40)
new_esEs19(LT, LT) → True
new_compare19(vyy300, vyy40, ty_Int) → new_compare13(vyy300, vyy40)
new_esEs20(GT) → False
new_esEs19(GT, EQ) → False
new_esEs19(EQ, GT) → False
new_ltEs20(vyy660, vyy62, ty_Ordering) → new_ltEs17(vyy660, vyy62)
new_esEs21(vyy78, vyy79, ty_Bool) → new_esEs11(vyy78, vyy79)
new_esEs23(vyy781, vyy791, app(ty_Ratio, bbh)) → new_esEs15(vyy781, vyy791, bbh)
new_ltEs11(Just(vyy300), Just(vyy40), app(app(ty_Either, caa), cab)) → new_ltEs5(vyy300, vyy40, caa, cab)
new_lt6(vyy301, vyy41, app(app(app(ty_@3, dbc), dbd), dbe)) → new_lt14(vyy301, vyy41, dbc, dbd, dbe)
new_esEs6(Left(vyy780), Left(vyy790), ty_Ordering, cf) → new_esEs19(vyy780, vyy790)
new_esEs24(vyy780, vyy790, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs7(vyy780, vyy790, bde, bdf, bdg)
new_lt20(vyy300, vyy40, app(ty_[], bgg)) → new_lt15(vyy300, vyy40, bgg)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt6(vyy301, vyy41, app(ty_Maybe, dah)) → new_lt9(vyy301, vyy41, dah)
new_esEs6(Left(vyy780), Left(vyy790), ty_Double, cf) → new_esEs12(vyy780, vyy790)
new_esEs24(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_esEs24(vyy780, vyy790, ty_Double) → new_esEs12(vyy780, vyy790)
new_ltEs11(Just(vyy300), Just(vyy40), app(app(ty_@2, cag), cah)) → new_ltEs4(vyy300, vyy40, cag, cah)
new_asAs(False, vyy106) → False
new_esEs22(vyy782, vyy792, ty_Double) → new_esEs12(vyy782, vyy792)
new_ltEs10(vyy30, vyy4) → new_not(new_compare28(vyy30, vyy4))
new_primMulInt(Neg(vyy3010), Pos(vyy410)) → Neg(new_primMulNat0(vyy3010, vyy410))
new_primMulInt(Pos(vyy3010), Neg(vyy410)) → Neg(new_primMulNat0(vyy3010, vyy410))
new_ltEs5(Right(vyy300), Right(vyy40), deh, ty_Bool) → new_ltEs16(vyy300, vyy40)
new_primMulNat0(Succ(vyy30100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy4100)) → Zero
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, h), h, ba)
new_esEs25(vyy780, vyy790, ty_@0) → new_esEs16(vyy780, vyy790)
new_pePe(False, vyy78, vyy79, vyy97, gc) → new_asAs(new_esEs21(vyy78, vyy79, gc), vyy97)
new_compare13(vyy30, vyy4) → new_primCmpInt(vyy30, vyy4)
new_ltEs13(vyy30, vyy4, bhf) → new_not(new_compare0(vyy30, vyy4, bhf))
new_ltEs19(vyy301, vyy41, ty_@0) → new_ltEs10(vyy301, vyy41)
new_not(EQ) → new_not0
new_ltEs5(Right(vyy300), Right(vyy40), deh, ty_Char) → new_ltEs7(vyy300, vyy40)
new_lt11(vyy300, vyy40) → new_esEs20(new_compare9(vyy300, vyy40))
new_ltEs11(Just(vyy300), Just(vyy40), ty_Integer) → new_ltEs6(vyy300, vyy40)
new_esEs11(True, True) → True
new_esEs25(vyy780, vyy790, app(ty_[], cce)) → new_esEs17(vyy780, vyy790, cce)
new_esEs5(Just(vyy780), Just(vyy790), ty_@0) → new_esEs16(vyy780, vyy790)
new_esEs23(vyy781, vyy791, app(ty_Maybe, bcd)) → new_esEs5(vyy781, vyy791, bcd)
new_esEs6(Right(vyy780), Right(vyy790), ed, ty_Integer) → new_esEs14(vyy780, vyy790)
new_esEs6(Right(vyy780), Right(vyy790), ed, ty_Int) → new_esEs10(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), app(ty_Maybe, eb), cf) → new_esEs5(vyy780, vyy790, eb)
new_compare19(vyy300, vyy40, ty_Ordering) → new_compare17(vyy300, vyy40)
new_esEs16(@0, @0) → True
new_compare19(vyy300, vyy40, app(ty_Ratio, ddd)) → new_compare6(vyy300, vyy40, ddd)
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_ltEs17(GT, GT) → True
new_esEs20(LT) → True
new_compare27(vyy300, vyy40, True) → EQ
new_compare111(vyy300, vyy40, False, ccf) → GT
new_ltEs5(Left(vyy300), Left(vyy40), ty_Bool, dde) → new_ltEs16(vyy300, vyy40)
new_ltEs17(GT, EQ) → False
new_esEs5(Just(vyy780), Nothing, hd) → False
new_esEs5(Nothing, Just(vyy790), hd) → False
new_ltEs21(vyy670, vyy62, ty_Char) → new_ltEs7(vyy670, vyy62)
new_compare19(vyy300, vyy40, ty_@0) → new_compare28(vyy300, vyy40)
new_esEs24(vyy780, vyy790, ty_Integer) → new_esEs14(vyy780, vyy790)
new_ltEs5(Left(vyy300), Left(vyy40), ty_Char, dde) → new_ltEs7(vyy300, vyy40)
new_esEs25(vyy780, vyy790, app(app(app(ty_@3, cca), ccb), ccc)) → new_esEs7(vyy780, vyy790, cca, ccb, ccc)
new_esEs5(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, cfg), cfh)) → new_esEs13(vyy780, vyy790, cfg, cfh)
new_compare19(vyy300, vyy40, app(ty_Maybe, dcc)) → new_compare29(vyy300, vyy40, dcc)
new_ltEs11(Just(vyy300), Just(vyy40), ty_Ordering) → new_ltEs17(vyy300, vyy40)
new_ltEs19(vyy301, vyy41, ty_Int) → new_ltEs15(vyy301, vyy41)
new_foldFM_LE3(vyy63, vyy64, vyy95, vyy62, h, ba) → new_keysFM_LE0(vyy63, vyy64, vyy95, h, ba)
new_esEs5(Just(vyy780), Just(vyy790), app(app(ty_Either, cgc), cgd)) → new_esEs6(vyy780, vyy790, cgc, cgd)
new_ltEs12(vyy30, vyy4) → new_not(new_compare14(vyy30, vyy4))
new_esEs27(vyy780, vyy790, ty_Float) → new_esEs9(vyy780, vyy790)
new_not(LT) → new_not0
new_compare7(Integer(vyy300), Integer(vyy40)) → new_primCmpInt(vyy300, vyy40)
new_esEs5(Nothing, Nothing, hd) → True
new_esEs22(vyy782, vyy792, app(app(ty_Either, bab), bac)) → new_esEs6(vyy782, vyy792, bab, bac)
new_esEs5(Just(vyy780), Just(vyy790), app(app(app(ty_@3, cgf), cgg), cgh)) → new_esEs7(vyy780, vyy790, cgf, cgg, cgh)
new_esEs21(vyy78, vyy79, ty_Double) → new_esEs12(vyy78, vyy79)
new_esEs28(vyy781, vyy791, ty_Int) → new_esEs10(vyy781, vyy791)
new_lt4(vyy300, vyy40, gb) → new_esEs20(new_compare6(vyy300, vyy40, gb))
new_compare8(vyy300, vyy40) → new_compare25(vyy300, vyy40, new_esEs11(vyy300, vyy40))
new_esEs26(vyy781, vyy791, ty_Char) → new_esEs18(vyy781, vyy791)
new_compare27(vyy300, vyy40, False) → new_compare110(vyy300, vyy40, new_ltEs17(vyy300, vyy40))
new_ltEs21(vyy670, vyy62, ty_Float) → new_ltEs12(vyy670, vyy62)
new_esEs23(vyy781, vyy791, ty_Double) → new_esEs12(vyy781, vyy791)
new_primPlusNat0(Succ(vyy12600), Succ(vyy41000)) → Succ(Succ(new_primPlusNat0(vyy12600, vyy41000)))
new_esEs22(vyy782, vyy792, app(ty_Maybe, bah)) → new_esEs5(vyy782, vyy792, bah)
new_compare26(vyy300, vyy40, True, beb, bec, bed) → EQ
new_compare31(vyy300, vyy40, bhd, bhe) → new_compare23(vyy300, vyy40, new_esEs8(vyy300, vyy40, bhd, bhe), bhd, bhe)
new_esEs21(vyy78, vyy79, app(ty_Maybe, hd)) → new_esEs5(vyy78, vyy79, hd)
new_lt7(vyy300, vyy40, ty_Char) → new_lt11(vyy300, vyy40)
new_esEs26(vyy781, vyy791, app(app(ty_Either, cdc), cdd)) → new_esEs6(vyy781, vyy791, cdc, cdd)
new_compare0([], :(vyy40, vyy41), bhf) → LT
new_esEs27(vyy780, vyy790, ty_Integer) → new_esEs14(vyy780, vyy790)
new_asAs(True, vyy106) → vyy106
new_lt6(vyy301, vyy41, ty_Ordering) → new_lt19(vyy301, vyy41)
new_ltEs17(LT, EQ) → True
new_ltEs11(Nothing, Nothing, bhg) → True
new_esEs22(vyy782, vyy792, app(app(ty_@2, hh), baa)) → new_esEs8(vyy782, vyy792, hh, baa)
new_ltEs19(vyy301, vyy41, ty_Float) → new_ltEs12(vyy301, vyy41)
new_esEs27(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_ltEs16(False, False) → True
new_esEs23(vyy781, vyy791, ty_Int) → new_esEs10(vyy781, vyy791)
new_esEs22(vyy782, vyy792, ty_Float) → new_esEs9(vyy782, vyy792)
new_esEs21(vyy78, vyy79, ty_Int) → new_esEs10(vyy78, vyy79)
new_ltEs5(Right(vyy300), Right(vyy40), deh, app(app(app(ty_@3, dfd), dfe), dff)) → new_ltEs8(vyy300, vyy40, dfd, dfe, dff)
new_esEs17([], [], he) → True
new_esEs17([], :(vyy790, vyy791), he) → False
new_esEs17(:(vyy780, vyy781), [], he) → False
new_compare24(vyy300, vyy40, False, cd, ce) → new_compare11(vyy300, vyy40, new_ltEs5(vyy300, vyy40, cd, ce), cd, ce)
new_fmToList(vyy79, gd, ge) → new_foldFM2(vyy79, gd, ge)
new_esEs5(Just(vyy780), Just(vyy790), ty_Float) → new_esEs9(vyy780, vyy790)
new_ltEs21(vyy670, vyy62, ty_Int) → new_ltEs15(vyy670, vyy62)
new_esEs24(vyy780, vyy790, app(app(ty_@2, bch), bda)) → new_esEs8(vyy780, vyy790, bch, bda)
new_ltEs9(vyy302, vyy42, app(app(app(ty_@3, daa), dab), dac)) → new_ltEs8(vyy302, vyy42, daa, dab, dac)
new_esEs27(vyy780, vyy790, ty_Char) → new_esEs18(vyy780, vyy790)
new_esEs9(Float(vyy780, vyy781), Float(vyy790, vyy791)) → new_esEs10(new_sr(vyy780, vyy790), new_sr(vyy781, vyy791))
new_compare210(vyy300, vyy40, False, ccf) → new_compare111(vyy300, vyy40, new_ltEs11(vyy300, vyy40, ccf), ccf)
new_lt12(vyy300, vyy40) → new_esEs20(new_compare14(vyy300, vyy40))
new_lt14(vyy300, vyy40, beb, bec, bed) → new_esEs20(new_compare18(vyy300, vyy40, beb, bec, bed))
new_ltEs17(EQ, GT) → True
new_esEs28(vyy781, vyy791, ty_Integer) → new_esEs14(vyy781, vyy791)
new_esEs10(vyy78, vyy79) → new_primEqInt(vyy78, vyy79)
new_primCompAux00(vyy111, GT) → GT
new_esEs24(vyy780, vyy790, ty_Bool) → new_esEs11(vyy780, vyy790)
new_ltEs5(Left(vyy300), Left(vyy40), app(ty_Maybe, ddf), dde) → new_ltEs11(vyy300, vyy40, ddf)
new_ltEs21(vyy670, vyy62, app(ty_[], bh)) → new_ltEs13(vyy670, vyy62, bh)
new_esEs21(vyy78, vyy79, app(app(ty_FiniteMap, gd), ge)) → new_esEs13(vyy78, vyy79, gd, ge)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs20(vyy660, vyy62, ty_Char) → new_ltEs7(vyy660, vyy62)
new_ltEs20(vyy660, vyy62, app(app(ty_Either, bc), bd)) → new_ltEs5(vyy660, vyy62, bc, bd)
new_compare28(@0, @0) → EQ
new_esEs24(vyy780, vyy790, ty_Char) → new_esEs18(vyy780, vyy790)
new_lt7(vyy300, vyy40, ty_Bool) → new_lt18(vyy300, vyy40)
new_esEs25(vyy780, vyy790, ty_Float) → new_esEs9(vyy780, vyy790)
new_ltEs19(vyy301, vyy41, app(ty_[], bfe)) → new_ltEs13(vyy301, vyy41, bfe)
new_ltEs11(Just(vyy300), Nothing, bhg) → False
new_foldFM_LE0(vyy61, vyy62, EmptyFM, h, ba) → vyy61
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(vyy3000)), Pos(vyy40)) → LT
new_esEs6(Left(vyy780), Left(vyy790), ty_Int, cf) → new_esEs10(vyy780, vyy790)
new_ltEs5(Right(vyy300), Right(vyy40), deh, app(ty_Ratio, dgb)) → new_ltEs18(vyy300, vyy40, dgb)

The set Q consists of the following terms:

new_ltEs5(Right(x0), Right(x1), x2, ty_Bool)
new_lt19(x0, x1)
new_esEs5(Nothing, Just(x0), x1)
new_ltEs16(True, True)
new_esEs28(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3, x4)
new_esEs11(True, True)
new_esEs23(x0, x1, ty_Double)
new_ltEs5(Left(x0), Right(x1), x2, x3)
new_ltEs5(Right(x0), Left(x1), x2, x3)
new_foldFM_LE0(x0, x1, EmptyFM, x2, x3)
new_ltEs20(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_ltEs11(Just(x0), Just(x1), ty_Bool)
new_fmToList(x0, x1, x2)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_lt7(x0, x1, ty_Double)
new_lt20(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt6(x0, x1, ty_Int)
new_lt7(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False, x2)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Char)
new_ltEs9(x0, x1, ty_Float)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs17(EQ, GT)
new_ltEs17(GT, EQ)
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(x0, x1)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(Just(x0), Just(x1), ty_Char)
new_asAs(True, x0)
new_esEs22(x0, x1, ty_Int)
new_compare24(x0, x1, True, x2, x3)
new_compare19(x0, x1, app(ty_[], x2))
new_ltEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, ty_Bool)
new_primMulInt(Pos(x0), Pos(x1))
new_asAs(False, x0)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt5(x0, x1)
new_esEs11(False, True)
new_esEs11(True, False)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare8(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt7(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Ordering)
new_compare15(x0, x1, True)
new_ltEs11(Just(x0), Just(x1), ty_@0)
new_ltEs5(Right(x0), Right(x1), x2, ty_Double)
new_compare19(x0, x1, ty_@0)
new_foldFM_LE3(x0, x1, x2, x3, x4, x5)
new_esEs22(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2)
new_esEs22(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Integer)
new_lt7(x0, x1, ty_Float)
new_ltEs18(x0, x1, x2)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs28(x0, x1, ty_Integer)
new_esEs15(:%(x0, x1), :%(x2, x3), x4)
new_esEs16(@0, @0)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs20(LT)
new_compare15(x0, x1, False)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs17([], [], x0)
new_esEs21(x0, x1, ty_@0)
new_compare19(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs14(Integer(x0), Integer(x1))
new_primCompAux00(x0, GT)
new_compare12(Double(x0, x1), Double(x2, x3))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_ltEs9(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs27(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Zero, Zero)
new_compare19(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare16(x0, x1, False, x2, x3, x4)
new_ltEs11(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(x0, x1, ty_Int)
new_compare19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Float)
new_esEs24(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs9(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Char)
new_compare110(x0, x1, False)
new_compare28(@0, @0)
new_ltEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs22(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primMulNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_lt6(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt20(x0, x1, ty_Double)
new_ltEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs9(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Char)
new_compare19(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_compare19(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs21(x0, x1, ty_Char)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1)
new_esEs19(LT, LT)
new_esEs21(x0, x1, ty_Int)
new_esEs19(EQ, GT)
new_esEs19(GT, EQ)
new_primMulNat0(Zero, Succ(x0))
new_lt14(x0, x1, x2, x3, x4)
new_esEs25(x0, x1, ty_Bool)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_sizeFM(EmptyFM, x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_compare16(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(ty_[], x2))
new_compare17(x0, x1)
new_esEs24(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, True, x2, x3)
new_esEs26(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_compare31(x0, x1, x2, x3)
new_lt7(x0, x1, ty_Int)
new_esEs11(False, False)
new_lt9(x0, x1, x2)
new_esEs23(x0, x1, ty_Ordering)
new_primMulInt(Neg(x0), Neg(x1))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare19(x0, x1, ty_Char)
new_esEs5(Just(x0), Nothing, x1)
new_ltEs11(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_foldFM2(EmptyFM, x0, x1)
new_lt4(x0, x1, x2)
new_sr(x0, x1)
new_ltEs11(Just(x0), Nothing, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare25(x0, x1, False)
new_esEs27(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs22(x0, x1, ty_Double)
new_ltEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare6(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_@0)
new_not0
new_esEs18(Char(x0), Char(x1))
new_lt17(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Ordering)
new_primPlusNat0(Zero, Zero)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs8(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(True, x0, x1, x2, x3)
new_esEs10(x0, x1)
new_compare6(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, EmptyFM, True, x6, x7)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt18(x0, x1)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Int)
new_ltEs5(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs5(Left(x0), Left(x1), ty_Char, x2)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Integer)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Zero)
new_ltEs11(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_esEs21(x0, x1, ty_Bool)
new_not(GT)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Char)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs17(GT, GT)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt6(x0, x1, ty_Ordering)
new_ltEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs13(x0, x1, x2, x3)
new_ltEs7(x0, x1)
new_compare27(x0, x1, False)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare13(x0, x1)
new_primPlusNat1(Succ(x0), x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare7(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare11(x0, x1, False, x2, x3)
new_compare23(x0, x1, False, x2, x3)
new_primCompAux00(x0, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs20(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_[], x2))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs17(:(x0, x1), [], x2)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Bool)
new_lt10(x0, x1)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs9(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs21(x0, x1, app(ty_[], x2))
new_compare25(x0, x1, True)
new_lt8(x0, x1)
new_ltEs11(Nothing, Nothing, x0)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), True, x11, x12)
new_lt11(x0, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs9(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs9(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Float)
new_primCompAux00(x0, EQ)
new_compare9(Char(x0), Char(x1))
new_esEs25(x0, x1, ty_Float)
new_compare29(x0, x1, x2)
new_compare19(x0, x1, ty_Float)
new_compare24(x0, x1, False, x2, x3)
new_ltEs5(Right(x0), Right(x1), x2, ty_@0)
new_ltEs16(True, False)
new_ltEs16(False, True)
new_compare30(x0, x1, x2, x3)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare19(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Int)
new_compare0([], [], x0)
new_compare19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_ltEs9(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_primCmpNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Bool)
new_ltEs11(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare11(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, ty_@0)
new_esEs12(Double(x0, x1), Double(x2, x3))
new_ltEs13(x0, x1, x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Int)
new_pePe(False, x0, x1, x2, x3)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Right(x0), Right(x1), x2, ty_Float)
new_ltEs17(LT, GT)
new_ltEs17(GT, LT)
new_ltEs11(Just(x0), Just(x1), ty_Ordering)
new_ltEs9(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Integer)
new_ltEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(GT, GT)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, ty_Integer)
new_esEs5(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_Ordering)
new_ltEs5(Left(x0), Left(x1), ty_Double, x2)
new_ltEs21(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_lt6(x0, x1, ty_Char)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs11(Just(x0), Just(x1), ty_Float)
new_ltEs21(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Integer)
new_compare18(x0, x1, x2, x3, x4)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(EQ, EQ)
new_esEs27(x0, x1, ty_Bool)
new_esEs20(EQ)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_ltEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs19(LT, EQ)
new_esEs19(EQ, LT)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare111(x0, x1, False, x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_keysFM_LE0(x0, x1, x2, x3, x4)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Zero, Succ(x0))
new_esEs19(LT, GT)
new_esEs19(GT, LT)
new_esEs25(x0, x1, ty_Double)
new_not(EQ)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt6(x0, x1, ty_Bool)
new_primPlusNat1(Zero, x0)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, ty_Float)
new_ltEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs21(x0, x1, ty_Double)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_lt16(x0, x1)
new_sr0(Integer(x0), Integer(x1))
new_esEs20(GT)
new_esEs24(x0, x1, ty_Double)
new_ltEs11(Just(x0), Just(x1), ty_Integer)
new_primCmpNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Float)
new_lt15(x0, x1, x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, x2, x3)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs24(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt6(x0, x1, ty_Double)
new_ltEs11(Nothing, Just(x0), x1)
new_ltEs10(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True, x2, x3)
new_esEs27(x0, x1, ty_Int)
new_ltEs5(Left(x0), Left(x1), ty_Integer, x2)
new_foldFM_LE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare10(x0, x1, False, x2, x3)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs17(LT, EQ)
new_ltEs17(EQ, LT)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs22(x0, x1, ty_@0)
new_ltEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Int)
new_ltEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs11(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), Zero)
new_compare210(x0, x1, True, x2)
new_lt7(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs9(Float(x0, x1), Float(x2, x3))
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Int)
new_ltEs21(x0, x1, ty_Float)
new_ltEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs11(Just(x0), Just(x1), app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs11(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt6(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare27(x0, x1, True)
new_compare110(x0, x1, True)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare14(Float(x0, x1), Float(x2, x3))
new_ltEs17(EQ, EQ)
new_compare19(x0, x1, ty_Bool)
new_ltEs17(LT, LT)
new_ltEs14(x0, x1)
new_esEs17([], :(x0, x1), x2)
new_ltEs16(False, False)
new_foldFM_LE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8)
new_not(LT)
new_compare19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)

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: