YES 9.122 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_GE :: (Ord a, Ord b) => FiniteMap (Either b a) c  ->  Either b a  ->  [Either b a]) :: (Ord a, Ord b) => FiniteMap (Either b a) c  ->  Either b a  ->  [Either b a])

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap 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 (\key elt rest ->(key,elt) : rest) [] fm

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Lambda Reductions:
The following Lambda expression
\keyeltrest→key : rest

is transformed to
keysFM_GE0 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_GE :: (Ord b, Ord a) => FiniteMap (Either a b) c  ->  Either a b  ->  [Either a b]) :: (Ord a, Ord b) => FiniteMap (Either a b) c  ->  Either a b  ->  [Either a b])

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) 
  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
fmToList0 key elt rest = (key,elt) : rest

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

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

  keysFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 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_GE :: (Ord c, Ord a) => FiniteMap (Either c a) b  ->  Either c a  ->  [Either c a]) :: (Ord c, Ord a) => FiniteMap (Either c a) b  ->  Either c a  ->  [Either c a])

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) 
  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
fmToList0 key elt rest = (key,elt) : rest

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

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

  keysFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 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_GE :: (Ord b, Ord a) => FiniteMap (Either a b) c  ->  Either a b  ->  [Either a b]) :: (Ord a, Ord b) => FiniteMap (Either a b) c  ->  Either a b  ->  [Either a b])

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) 
  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
fmToList0 key elt rest = (key,elt) : rest

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

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

  keysFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

mainModule FiniteMap
  ((keysFM_GE :: (Ord b, Ord a) => FiniteMap (Either a b) c  ->  Either a b  ->  [Either a b]) :: (Ord b, Ord a) => FiniteMap (Either a b) c  ->  Either a b  ->  [Either a b])

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) 
  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
fmToList0 key elt rest = (key,elt) : rest

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

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

  keysFM_GE :: Ord b => FiniteMap b a  ->  b  ->  [b]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Cond Reductions:
The following Function with conditions
foldFM_GE k z fr EmptyFM = z
foldFM_GE k z fr (Branch key elt wv fm_l fm_r)
 | key >= fr
 = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
 | otherwise
 = foldFM_GE k z fr fm_r

is transformed to
foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM
foldFM_GE k z fr (Branch key elt wv fm_l fm_r) = foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r)

foldFM_GE1 k z fr key elt wv fm_l fm_r True = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
foldFM_GE1 k z fr key elt wv fm_l fm_r False = foldFM_GE0 k z fr key elt wv fm_l fm_r otherwise

foldFM_GE0 k z fr key elt wv fm_l fm_r True = foldFM_GE k z fr fm_r

foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r) = foldFM_GE1 k z fr key elt wv fm_l fm_r (key >= fr)

foldFM_GE3 k z fr EmptyFM = z
foldFM_GE3 vvu vvv vvw vvx = foldFM_GE2 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

compare0 x y True = GT

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

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

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

absReal0 x True = `negate` x

absReal1 x True = x
absReal1 x False = absReal0 x otherwise

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_GE :: (Ord c, Ord b) => FiniteMap (Either c b) a  ->  Either c b  ->  [Either c b]) :: (Ord b, Ord c) => FiniteMap (Either c b) a  ->  Either c b  ->  [Either c b])

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) 
  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
fmToList0 key elt rest = (key,elt) : rest

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

  foldFM_GE :: Ord a => (a  ->  c  ->  b  ->  b)  ->  b  ->  a  ->  FiniteMap a c  ->  b
foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM
foldFM_GE k z fr (Branch key elt wv fm_l fm_r) = foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r)

  
foldFM_GE0 k z fr key elt wv fm_l fm_r True = foldFM_GE k z fr fm_r

  
foldFM_GE1 k z fr key elt wv fm_l fm_r True = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
foldFM_GE1 k z fr key elt wv fm_l fm_r False = foldFM_GE0 k z fr key elt wv fm_l fm_r otherwise

  
foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r) = foldFM_GE1 k z fr key elt wv fm_l fm_r (key >= fr)

  
foldFM_GE3 k z fr EmptyFM = z
foldFM_GE3 vvu vvv vvw vvx = foldFM_GE2 vvu vvv vvw vvx

  keysFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Let/Where Reductions:
The bindings of the following Let/Where expression
reduce1 x y (y == 0)
where 
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'0 x y = gcd0Gcd' y (x `rem` y)

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

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



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

mainModule FiniteMap
  ((keysFM_GE :: (Ord c, Ord a) => FiniteMap (Either c a) b  ->  Either c a  ->  [Either c a]) :: (Ord c, Ord a) => FiniteMap (Either c a) b  ->  Either c a  ->  [Either c a])

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) 
  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
fmToList0 key elt rest = (key,elt) : rest

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

  foldFM_GE :: Ord a => (a  ->  b  ->  c  ->  c)  ->  c  ->  a  ->  FiniteMap a b  ->  c
foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM
foldFM_GE k z fr (Branch key elt wv fm_l fm_r) = foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r)

  
foldFM_GE0 k z fr key elt wv fm_l fm_r True = foldFM_GE k z fr fm_r

  
foldFM_GE1 k z fr key elt wv fm_l fm_r True = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
foldFM_GE1 k z fr key elt wv fm_l fm_r False = foldFM_GE0 k z fr key elt wv fm_l fm_r otherwise

  
foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r) = foldFM_GE1 k z fr key elt wv fm_l fm_r (key >= fr)

  
foldFM_GE3 k z fr EmptyFM = z
foldFM_GE3 vvu vvv vvw vvx = foldFM_GE2 vvu vvv vvw vvx

  keysFM_GE :: Ord b => FiniteMap b a  ->  b  ->  [b]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

mainModule FiniteMap
  (keysFM_GE :: (Ord b, Ord a) => FiniteMap (Either a b) c  ->  Either a b  ->  [Either a b])

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap 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_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l

  foldFM_GE :: Ord c => (c  ->  b  ->  a  ->  a)  ->  a  ->  c  ->  FiniteMap c b  ->  a
foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM
foldFM_GE k z fr (Branch key elt wv fm_l fm_r) = foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r)

  
foldFM_GE0 k z fr key elt wv fm_l fm_r True = foldFM_GE k z fr fm_r

  
foldFM_GE1 k z fr key elt wv fm_l fm_r True = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
foldFM_GE1 k z fr key elt wv fm_l fm_r False = foldFM_GE0 k z fr key elt wv fm_l fm_r otherwise

  
foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r) = foldFM_GE1 k z fr key elt wv fm_l fm_r (key >= fr)

  
foldFM_GE3 k z fr EmptyFM = z
foldFM_GE3 vvu vvv vvw vvx = foldFM_GE2 vvu vvv vvw vvx

  keysFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Haskell To QDPs


↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primEqNat(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat(vyy30000, vyy4000)

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

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



↳ 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

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

new_primPlusNat(Succ(vyy15400), Succ(vyy400000)) → new_primPlusNat(vyy15400, vyy400000)

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

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



↳ 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

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

new_primMulNat(Succ(vyy300000), Succ(vyy40000)) → new_primMulNat(vyy300000, Succ(vyy40000))

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

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



↳ 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

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

new_primCmpNat(Succ(vyy10000), Succ(vyy10100)) → new_primCmpNat(vyy10000, vyy10100)

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

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

new_esEs1(Left(vyy3000), Left(vyy400), app(app(ty_@2, ha), hb), gd) → new_esEs3(vyy3000, vyy400, ha, hb)
new_esEs1(Right(vyy3000), Right(vyy400), hc, app(ty_Maybe, hg)) → new_esEs0(vyy3000, vyy400, hg)
new_esEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(ty_[], bcf)) → new_esEs2(vyy3001, vyy401, bcf)
new_esEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_Either, bdf), bdg), bdd) → new_esEs1(vyy3000, vyy400, bdf, bdg)
new_esEs1(Left(vyy3000), Left(vyy400), app(ty_[], gh), gd) → new_esEs2(vyy3000, vyy400, gh)
new_esEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(app(ty_@3, bda), bdb), bdc), bdd) → new_esEs(vyy3000, vyy400, bda, bdb, bdc)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_Maybe, ea), ba, cf) → new_esEs0(vyy3000, vyy400, ea)
new_esEs0(Just(vyy3000), Just(vyy400), app(ty_Maybe, fb)) → new_esEs0(vyy3000, vyy400, fb)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), h, app(app(ty_Either, da), db), cf) → new_esEs1(vyy3001, vyy401, da, db)
new_esEs1(Left(vyy3000), Left(vyy400), app(app(ty_Either, gf), gg), gd) → new_esEs1(vyy3000, vyy400, gf, gg)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(app(ty_@3, df), dg), dh), ba, cf) → new_esEs(vyy3000, vyy400, df, dg, dh)
new_esEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_[], bdh), bdd) → new_esEs2(vyy3000, vyy400, bdh)
new_esEs1(Right(vyy3000), Right(vyy400), hc, app(app(ty_Either, hh), baa)) → new_esEs1(vyy3000, vyy400, hh, baa)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_Either, eb), ec), ba, cf) → new_esEs1(vyy3000, vyy400, eb, ec)
new_esEs1(Right(vyy3000), Right(vyy400), hc, app(app(app(ty_@3, hd), he), hf)) → new_esEs(vyy3000, vyy400, hd, he, hf)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), h, ba, app(app(ty_@2, ca), cb)) → new_esEs3(vyy3002, vyy402, ca, cb)
new_esEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs(vyy3001, vyy401, bbh, bca, bcb)
new_esEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_Maybe, bba)) → new_esEs0(vyy3000, vyy400, bba)
new_esEs1(Left(vyy3000), Left(vyy400), app(ty_Maybe, ge), gd) → new_esEs0(vyy3000, vyy400, ge)
new_esEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(ty_@2, bcg), bch)) → new_esEs3(vyy3001, vyy401, bcg, bch)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), h, app(ty_Maybe, cg), cf) → new_esEs0(vyy3001, vyy401, cg)
new_esEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(app(ty_@3, baf), bag), bah)) → new_esEs(vyy3000, vyy400, baf, bag, bah)
new_esEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_Maybe, bde), bdd) → new_esEs0(vyy3000, vyy400, bde)
new_esEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(ty_Either, bcd), bce)) → new_esEs1(vyy3001, vyy401, bcd, bce)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_@2, ee), ef), ba, cf) → new_esEs3(vyy3000, vyy400, ee, ef)
new_esEs0(Just(vyy3000), Just(vyy400), app(app(ty_Either, fc), fd)) → new_esEs1(vyy3000, vyy400, fc, fd)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), h, ba, app(ty_Maybe, be)) → new_esEs0(vyy3002, vyy402, be)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), h, app(app(app(ty_@3, cc), cd), ce), cf) → new_esEs(vyy3001, vyy401, cc, cd, ce)
new_esEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_@2, bbe), bbf)) → new_esEs3(vyy3000, vyy400, bbe, bbf)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), h, ba, app(app(ty_Either, bf), bg)) → new_esEs1(vyy3002, vyy402, bf, bg)
new_esEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_Either, bbb), bbc)) → new_esEs1(vyy3000, vyy400, bbb, bbc)
new_esEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), bae) → new_esEs2(vyy3001, vyy401, bae)
new_esEs0(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, eg), eh), fa)) → new_esEs(vyy3000, vyy400, eg, eh, fa)
new_esEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_@2, bea), beb), bdd) → new_esEs3(vyy3000, vyy400, bea, beb)
new_esEs1(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, ga), gb), gc), gd) → new_esEs(vyy3000, vyy400, ga, gb, gc)
new_esEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(ty_Maybe, bcc)) → new_esEs0(vyy3001, vyy401, bcc)
new_esEs2(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_[], bbd)) → new_esEs2(vyy3000, vyy400, bbd)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_[], ed), ba, cf) → new_esEs2(vyy3000, vyy400, ed)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), h, app(ty_[], dc), cf) → new_esEs2(vyy3001, vyy401, dc)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), h, ba, app(ty_[], bh)) → new_esEs2(vyy3002, vyy402, bh)
new_esEs1(Right(vyy3000), Right(vyy400), hc, app(app(ty_@2, bac), bad)) → new_esEs3(vyy3000, vyy400, bac, bad)
new_esEs1(Right(vyy3000), Right(vyy400), hc, app(ty_[], bab)) → new_esEs2(vyy3000, vyy400, bab)
new_esEs0(Just(vyy3000), Just(vyy400), app(app(ty_@2, fg), fh)) → new_esEs3(vyy3000, vyy400, fg, fh)
new_esEs0(Just(vyy3000), Just(vyy400), app(ty_[], ff)) → new_esEs2(vyy3000, vyy400, ff)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), h, ba, app(app(app(ty_@3, bb), bc), bd)) → new_esEs(vyy3002, vyy402, bb, bc, bd)
new_esEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), h, app(app(ty_@2, dd), de), cf) → new_esEs3(vyy3001, vyy401, dd, de)

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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP

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

new_compare0(vyy1000, vyy1010, ef) → new_compare2(vyy1000, vyy1010, new_esEs4(vyy1000, vyy1010, ef), ef)
new_compare20(Left(vyy10000), Left(vyy10100), False, app(app(ty_Either, cc), cd), cb) → new_ltEs0(vyy10000, vyy10100, cc, cd)
new_ltEs0(Left(vyy10000), Left(vyy10100), app(ty_[], dc), cb) → new_ltEs3(vyy10000, vyy10100, dc)
new_ltEs1(@2(vyy1000, vyy1001), @2(vyy1010, vyy1011), fg, app(app(ty_@2, gc), gd)) → new_ltEs1(vyy1001, vyy1011, gc, gd)
new_ltEs0(Left(vyy10000), Left(vyy10100), app(app(ty_@2, ce), cf), cb) → new_ltEs1(vyy10000, vyy10100, ce, cf)
new_ltEs0(Left(vyy10000), Left(vyy10100), app(app(app(ty_@3, cg), da), db), cb) → new_ltEs2(vyy10000, vyy10100, cg, da, db)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), bad, hb, app(app(app(ty_@3, bcc), bcd), bce)) → new_ltEs2(vyy1002, vyy1012, bcc, bcd, bce)
new_ltEs1(@2(vyy1000, vyy1001), @2(vyy1010, vyy1011), app(ty_Maybe, ef), eg) → new_compare2(vyy1000, vyy1010, new_esEs4(vyy1000, vyy1010, ef), ef)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), app(app(ty_@2, hf), hg), hb, hc) → new_lt1(vyy1000, vyy1010, hf, hg)
new_primCompAux(vyy1000, vyy1010, vyy169, app(app(ty_@2, bdc), bdd)) → new_compare3(vyy1000, vyy1010, bdc, bdd)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), app(ty_[], bac), hb, hc) → new_lt3(vyy1000, vyy1010, bac)
new_ltEs(Just(vyy1000), Just(vyy1010), app(app(ty_Either, ba), bb)) → new_ltEs0(vyy1000, vyy1010, ba, bb)
new_compare20(Left(vyy10000), Left(vyy10100), False, app(app(app(ty_@3, cg), da), db), cb) → new_ltEs2(vyy10000, vyy10100, cg, da, db)
new_compare20(Left(vyy10000), Left(vyy10100), False, app(app(ty_@2, ce), cf), cb) → new_ltEs1(vyy10000, vyy10100, ce, cf)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), bad, app(app(app(ty_@3, bbb), bbc), bbd), hc) → new_lt2(vyy1001, vyy1011, bbb, bbc, bbd)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), bad, app(ty_[], bbe), hc) → new_lt3(vyy1001, vyy1011, bbe)
new_ltEs1(@2(vyy1000, vyy1001), @2(vyy1010, vyy1011), app(app(ty_@2, eh), fa), eg) → new_compare21(vyy1000, vyy1010, new_esEs6(vyy1000, vyy1010, eh, fa), eh, fa)
new_ltEs0(Right(vyy10000), Right(vyy10100), dd, app(app(ty_@2, dh), ea)) → new_ltEs1(vyy10000, vyy10100, dh, ea)
new_compare20(Right(vyy10000), Right(vyy10100), False, dd, app(ty_[], ee)) → new_ltEs3(vyy10000, vyy10100, ee)
new_ltEs1(@2(vyy1000, vyy1001), @2(vyy1010, vyy1011), fg, app(ty_[], gh)) → new_ltEs3(vyy1001, vyy1011, gh)
new_compare20(Right(vyy10000), Right(vyy10100), False, dd, app(ty_Maybe, de)) → new_ltEs(vyy10000, vyy10100, de)
new_ltEs0(Left(vyy10000), Left(vyy10100), app(app(ty_Either, cc), cd), cb) → new_ltEs0(vyy10000, vyy10100, cc, cd)
new_ltEs(Just(vyy1000), Just(vyy1010), app(ty_Maybe, h)) → new_ltEs(vyy1000, vyy1010, h)
new_primCompAux(vyy1000, vyy1010, vyy169, app(ty_[], bdh)) → new_compare(vyy1000, vyy1010, bdh)
new_ltEs3(:(vyy1000, vyy1001), :(vyy1010, vyy1011), bcg) → new_compare(vyy1001, vyy1011, bcg)
new_lt(vyy1000, vyy1010, ef) → new_compare2(vyy1000, vyy1010, new_esEs4(vyy1000, vyy1010, ef), ef)
new_compare20(Right(vyy10000), Right(vyy10100), False, dd, app(app(ty_Either, df), dg)) → new_ltEs0(vyy10000, vyy10100, df, dg)
new_compare20(Left(vyy10000), Left(vyy10100), False, app(ty_Maybe, ca), cb) → new_ltEs(vyy10000, vyy10100, ca)
new_compare3(vyy1000, vyy1010, eh, fa) → new_compare21(vyy1000, vyy1010, new_esEs6(vyy1000, vyy1010, eh, fa), eh, fa)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), bad, hb, app(ty_Maybe, bbf)) → new_ltEs(vyy1002, vyy1012, bbf)
new_lt0(vyy1000, vyy1010, dd, cb) → new_compare20(vyy1000, vyy1010, new_esEs5(vyy1000, vyy1010, dd, cb), dd, cb)
new_ltEs(Just(vyy1000), Just(vyy1010), app(ty_[], bh)) → new_ltEs3(vyy1000, vyy1010, bh)
new_compare(:(vyy1000, vyy1001), :(vyy1010, vyy1011), bcg) → new_primCompAux(vyy1000, vyy1010, new_compare5(vyy1001, vyy1011, bcg), bcg)
new_ltEs1(@2(vyy1000, vyy1001), @2(vyy1010, vyy1011), fg, app(ty_Maybe, fh)) → new_ltEs(vyy1001, vyy1011, fh)
new_compare21(vyy1000, vyy1010, False, eh, fa) → new_ltEs1(vyy1000, vyy1010, eh, fa)
new_ltEs3(:(vyy1000, vyy1001), :(vyy1010, vyy1011), bcg) → new_primCompAux(vyy1000, vyy1010, new_compare5(vyy1001, vyy1011, bcg), bcg)
new_ltEs1(@2(vyy1000, vyy1001), @2(vyy1010, vyy1011), app(ty_[], ff), eg) → new_compare(vyy1000, vyy1010, ff)
new_primCompAux(vyy1000, vyy1010, vyy169, app(app(ty_Either, bda), bdb)) → new_compare1(vyy1000, vyy1010, bda, bdb)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), bad, hb, app(ty_[], bcf)) → new_ltEs3(vyy1002, vyy1012, bcf)
new_ltEs1(@2(vyy1000, vyy1001), @2(vyy1010, vyy1011), app(app(app(ty_@3, fb), fc), fd), eg) → new_compare22(vyy1000, vyy1010, new_esEs7(vyy1000, vyy1010, fb, fc, fd), fb, fc, fd)
new_lt1(vyy1000, vyy1010, eh, fa) → new_compare21(vyy1000, vyy1010, new_esEs6(vyy1000, vyy1010, eh, fa), eh, fa)
new_ltEs0(Left(vyy10000), Left(vyy10100), app(ty_Maybe, ca), cb) → new_ltEs(vyy10000, vyy10100, ca)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), bad, app(app(ty_@2, bah), bba), hc) → new_lt1(vyy1001, vyy1011, bah, bba)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), bad, hb, app(app(ty_@2, bca), bcb)) → new_ltEs1(vyy1002, vyy1012, bca, bcb)
new_ltEs1(@2(vyy1000, vyy1001), @2(vyy1010, vyy1011), app(app(ty_Either, dd), cb), eg) → new_compare20(vyy1000, vyy1010, new_esEs5(vyy1000, vyy1010, dd, cb), dd, cb)
new_ltEs(Just(vyy1000), Just(vyy1010), app(app(ty_@2, bc), bd)) → new_ltEs1(vyy1000, vyy1010, bc, bd)
new_ltEs0(Right(vyy10000), Right(vyy10100), dd, app(app(ty_Either, df), dg)) → new_ltEs0(vyy10000, vyy10100, df, dg)
new_ltEs0(Right(vyy10000), Right(vyy10100), dd, app(ty_[], ee)) → new_ltEs3(vyy10000, vyy10100, ee)
new_ltEs0(Right(vyy10000), Right(vyy10100), dd, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs2(vyy10000, vyy10100, eb, ec, ed)
new_compare2(vyy1000, vyy1010, False, ef) → new_ltEs(vyy1000, vyy1010, ef)
new_ltEs1(@2(vyy1000, vyy1001), @2(vyy1010, vyy1011), fg, app(app(app(ty_@3, ge), gf), gg)) → new_ltEs2(vyy1001, vyy1011, ge, gf, gg)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), app(app(ty_Either, hd), he), hb, hc) → new_lt0(vyy1000, vyy1010, hd, he)
new_ltEs(Just(vyy1000), Just(vyy1010), app(app(app(ty_@3, be), bf), bg)) → new_ltEs2(vyy1000, vyy1010, be, bf, bg)
new_ltEs0(Right(vyy10000), Right(vyy10100), dd, app(ty_Maybe, de)) → new_ltEs(vyy10000, vyy10100, de)
new_compare(:(vyy1000, vyy1001), :(vyy1010, vyy1011), bcg) → new_compare(vyy1001, vyy1011, bcg)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), app(ty_Maybe, ha), hb, hc) → new_lt(vyy1000, vyy1010, ha)
new_compare20(Left(vyy10000), Left(vyy10100), False, app(ty_[], dc), cb) → new_ltEs3(vyy10000, vyy10100, dc)
new_lt3(vyy1000, vyy1010, ff) → new_compare(vyy1000, vyy1010, ff)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), bad, app(ty_Maybe, bae), hc) → new_lt(vyy1001, vyy1011, bae)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), app(app(app(ty_@3, hh), baa), bab), hb, hc) → new_lt2(vyy1000, vyy1010, hh, baa, bab)
new_compare4(vyy1000, vyy1010, fb, fc, fd) → new_compare22(vyy1000, vyy1010, new_esEs7(vyy1000, vyy1010, fb, fc, fd), fb, fc, fd)
new_ltEs1(@2(vyy1000, vyy1001), @2(vyy1010, vyy1011), fg, app(app(ty_Either, ga), gb)) → new_ltEs0(vyy1001, vyy1011, ga, gb)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), bad, hb, app(app(ty_Either, bbg), bbh)) → new_ltEs0(vyy1002, vyy1012, bbg, bbh)
new_compare1(vyy1000, vyy1010, dd, cb) → new_compare20(vyy1000, vyy1010, new_esEs5(vyy1000, vyy1010, dd, cb), dd, cb)
new_compare20(Right(vyy10000), Right(vyy10100), False, dd, app(app(ty_@2, dh), ea)) → new_ltEs1(vyy10000, vyy10100, dh, ea)
new_lt2(vyy1000, vyy1010, fb, fc, fd) → new_compare22(vyy1000, vyy1010, new_esEs7(vyy1000, vyy1010, fb, fc, fd), fb, fc, fd)
new_compare20(Right(vyy10000), Right(vyy10100), False, dd, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs2(vyy10000, vyy10100, eb, ec, ed)
new_compare22(vyy1000, vyy1010, False, fb, fc, fd) → new_ltEs2(vyy1000, vyy1010, fb, fc, fd)
new_ltEs2(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), bad, app(app(ty_Either, baf), bag), hc) → new_lt0(vyy1001, vyy1011, baf, bag)
new_primCompAux(vyy1000, vyy1010, vyy169, app(ty_Maybe, bch)) → new_compare0(vyy1000, vyy1010, bch)
new_primCompAux(vyy1000, vyy1010, vyy169, app(app(app(ty_@3, bde), bdf), bdg)) → new_compare4(vyy1000, vyy1010, bde, bdf, bdg)

The TRS R consists of the following rules:

new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, bee)) → new_esEs4(vyy3000, vyy400, bee)
new_ltEs19(vyy1002, vyy1012, ty_Integer) → new_ltEs16(vyy1002, vyy1012)
new_esEs24(vyy1001, vyy1011, app(app(ty_Either, baf), bag)) → new_esEs5(vyy1001, vyy1011, baf, bag)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Integer, cb) → new_ltEs16(vyy10000, vyy10100)
new_lt19(vyy1000, vyy1010, ty_Char) → new_lt7(vyy1000, vyy1010)
new_esEs21(vyy3000, vyy400, app(app(ty_@2, cbh), cca)) → new_esEs6(vyy3000, vyy400, cbh, cca)
new_ltEs18(vyy1001, vyy1011, ty_Float) → new_ltEs8(vyy1001, vyy1011)
new_esEs24(vyy1001, vyy1011, app(ty_Ratio, cfb)) → new_esEs15(vyy1001, vyy1011, cfb)
new_ltEs4(EQ, GT) → True
new_esEs5(Left(vyy3000), Left(vyy400), ty_@0, bfd) → new_esEs14(vyy3000, vyy400)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Double) → new_ltEs17(vyy1000, vyy1010)
new_esEs26(vyy3002, vyy402, app(ty_Ratio, chb)) → new_esEs15(vyy3002, vyy402, chb)
new_ltEs6(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), bad, hb, hc) → new_pePe(new_lt19(vyy1000, vyy1010, bad), new_asAs(new_esEs25(vyy1000, vyy1010, bad), new_pePe(new_lt20(vyy1001, vyy1011, hb), new_asAs(new_esEs24(vyy1001, vyy1011, hb), new_ltEs19(vyy1002, vyy1012, hc)))))
new_esEs18(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_lt6(vyy1000, vyy1010, ty_Char) → new_lt7(vyy1000, vyy1010)
new_compare110(vyy1000, vyy1010, True, eh, fa) → LT
new_esEs23(vyy3000, vyy400, app(app(ty_Either, cec), ced)) → new_esEs5(vyy3000, vyy400, cec, ced)
new_ltEs8(vyy100, vyy101) → new_not(new_esEs9(new_compare6(vyy100, vyy101), GT))
new_esEs24(vyy1001, vyy1011, app(ty_Maybe, bae)) → new_esEs4(vyy1001, vyy1011, bae)
new_esEs4(Nothing, Just(vyy400), bea) → False
new_esEs4(Just(vyy3000), Nothing, bea) → False
new_lt20(vyy1001, vyy1011, ty_Float) → new_lt14(vyy1001, vyy1011)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dbf)) → new_esEs15(vyy3000, vyy400, dbf)
new_ltEs9(Nothing, Just(vyy1010), cac) → True
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs14(vyy3000, vyy400)
new_lt19(vyy1000, vyy1010, ty_Double) → new_lt15(vyy1000, vyy1010)
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, ty_Double) → new_ltEs17(vyy10000, vyy10100)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Integer) → new_ltEs16(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, ty_Ordering) → new_esEs9(vyy3001, vyy401)
new_lt10(vyy1000, vyy1010) → new_esEs9(new_compare17(vyy1000, vyy1010), LT)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(ty_Ratio, cad)) → new_ltEs13(vyy1000, vyy1010, cad)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_lt18(vyy1000, vyy1010) → new_esEs9(new_compare12(vyy1000, vyy1010), LT)
new_esEs21(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_primMulNat0(Zero, Zero) → Zero
new_compare15(vyy1000, vyy1010, ty_Double) → new_compare19(vyy1000, vyy1010)
new_ltEs18(vyy1001, vyy1011, ty_Integer) → new_ltEs16(vyy1001, vyy1011)
new_esEs20(vyy1000, vyy1010, app(ty_Maybe, ef)) → new_esEs4(vyy1000, vyy1010, ef)
new_lt19(vyy1000, vyy1010, app(ty_Maybe, ha)) → new_lt9(vyy1000, vyy1010, ha)
new_esEs21(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs21(vyy3000, vyy400, app(ty_[], cbg)) → new_esEs10(vyy3000, vyy400, cbg)
new_esEs25(vyy1000, vyy1010, ty_Bool) → new_esEs17(vyy1000, vyy1010)
new_esEs24(vyy1001, vyy1011, ty_@0) → new_esEs14(vyy1001, vyy1011)
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, app(ty_[], ee)) → new_ltEs7(vyy10000, vyy10100, ee)
new_esEs23(vyy3000, vyy400, app(ty_Maybe, ceb)) → new_esEs4(vyy3000, vyy400, ceb)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(app(ty_@2, bc), bd)) → new_ltEs15(vyy1000, vyy1010, bc, bd)
new_esEs17(True, True) → True
new_esEs26(vyy3002, vyy402, app(ty_[], cgg)) → new_esEs10(vyy3002, vyy402, cgg)
new_lt6(vyy1000, vyy1010, ty_@0) → new_lt10(vyy1000, vyy1010)
new_lt6(vyy1000, vyy1010, app(ty_[], ff)) → new_lt5(vyy1000, vyy1010, ff)
new_esEs21(vyy3000, vyy400, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs7(vyy3000, vyy400, cba, cbb, cbc)
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs6(vyy10000, vyy10100, eb, ec, ed)
new_esEs23(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Char, bfd) → new_esEs11(vyy3000, vyy400)
new_esEs20(vyy1000, vyy1010, app(app(ty_@2, eh), fa)) → new_esEs6(vyy1000, vyy1010, eh, fa)
new_esEs26(vyy3002, vyy402, app(ty_Maybe, cgd)) → new_esEs4(vyy3002, vyy402, cgd)
new_ltEs18(vyy1001, vyy1011, app(ty_[], gh)) → new_ltEs7(vyy1001, vyy1011, gh)
new_esEs20(vyy1000, vyy1010, ty_@0) → new_esEs14(vyy1000, vyy1010)
new_esEs5(Right(vyy3000), Right(vyy400), bgg, ty_@0) → new_esEs14(vyy3000, vyy400)
new_esEs25(vyy1000, vyy1010, app(ty_[], bac)) → new_esEs10(vyy1000, vyy1010, bac)
new_pePe(False, vyy168) → vyy168
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs12(vyy3000, vyy400)
new_esEs25(vyy1000, vyy1010, ty_Char) → new_esEs11(vyy1000, vyy1010)
new_ltEs17(vyy100, vyy101) → new_not(new_esEs9(new_compare19(vyy100, vyy101), GT))
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Int, cb) → new_ltEs5(vyy10000, vyy10100)
new_compare23(vyy1000, vyy1010, False, ef) → new_compare113(vyy1000, vyy1010, new_ltEs9(vyy1000, vyy1010, ef), ef)
new_esEs25(vyy1000, vyy1010, ty_Float) → new_esEs8(vyy1000, vyy1010)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs9(vyy3001, vyy401)
new_compare11(vyy1000, vyy1010, False, fb, fc, fd) → GT
new_ltEs18(vyy1001, vyy1011, app(app(ty_Either, ga), gb)) → new_ltEs14(vyy1001, vyy1011, ga, gb)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_ltEs11(False, True) → True
new_lt17(vyy1000, vyy1010) → new_esEs9(new_compare7(vyy1000, vyy1010), LT)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_@2, bgd), bge), bfd) → new_esEs6(vyy3000, vyy400, bgd, bge)
new_compare111(vyy1000, vyy1010, False) → GT
new_compare111(vyy1000, vyy1010, True) → LT
new_ltEs19(vyy1002, vyy1012, ty_Double) → new_ltEs17(vyy1002, vyy1012)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Maybe, bfh), bfd) → new_esEs4(vyy3000, vyy400, bfh)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Float, cb) → new_ltEs8(vyy10000, vyy10100)
new_compare15(vyy1000, vyy1010, app(app(app(ty_@3, bde), bdf), bdg)) → new_compare29(vyy1000, vyy1010, bde, bdf, bdg)
new_compare13(vyy1000, vyy1010) → new_compare27(vyy1000, vyy1010, new_esEs17(vyy1000, vyy1010))
new_esEs23(vyy3000, vyy400, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs7(vyy3000, vyy400, cdg, cdh, cea)
new_primCmpNat0(Zero, Succ(vyy10100)) → LT
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, chc), chd), che)) → new_esEs7(vyy3001, vyy401, chc, chd, che)
new_compare113(vyy1000, vyy1010, True, ef) → LT
new_esEs25(vyy1000, vyy1010, app(app(ty_Either, hd), he)) → new_esEs5(vyy1000, vyy1010, hd, he)
new_esEs25(vyy1000, vyy1010, app(app(ty_@2, hf), hg)) → new_esEs6(vyy1000, vyy1010, hf, hg)
new_compare6(Float(vyy1000, vyy1001), Float(vyy1010, vyy1011)) → new_compare7(new_sr(vyy1000, vyy1010), new_sr(vyy1001, vyy1011))
new_compare25(vyy1000, vyy1010, True, fb, fc, fd) → EQ
new_ltEs13(vyy100, vyy101, dbg) → new_not(new_esEs9(new_compare18(vyy100, vyy101, dbg), GT))
new_lt6(vyy1000, vyy1010, app(app(ty_Either, dd), cb)) → new_lt4(vyy1000, vyy1010, dd, cb)
new_esEs24(vyy1001, vyy1011, ty_Int) → new_esEs12(vyy1001, vyy1011)
new_ltEs10(vyy100, vyy101) → new_not(new_esEs9(new_compare16(vyy100, vyy101), GT))
new_compare18(:%(vyy1000, vyy1001), :%(vyy1010, vyy1011), ty_Int) → new_compare7(new_sr(vyy1000, vyy1011), new_sr(vyy1010, vyy1001))
new_esEs5(Right(vyy3000), Right(vyy400), bgg, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs24(vyy1001, vyy1011, app(app(ty_@2, bah), bba)) → new_esEs6(vyy1001, vyy1011, bah, bba)
new_pePe(True, vyy168) → True
new_primEqNat0(Zero, Zero) → True
new_compare26(vyy1000, vyy1010, True) → EQ
new_ltEs18(vyy1001, vyy1011, ty_Double) → new_ltEs17(vyy1001, vyy1011)
new_esEs5(Right(vyy3000), Right(vyy400), bgg, app(app(ty_@2, bhg), bhh)) → new_esEs6(vyy3000, vyy400, bhg, bhh)
new_compare12(vyy1000, vyy1010) → new_compare26(vyy1000, vyy1010, new_esEs9(vyy1000, vyy1010))
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Ordering, cb) → new_ltEs4(vyy10000, vyy10100)
new_esEs14(@0, @0) → True
new_compare17(@0, @0) → EQ
new_esEs5(Right(vyy3000), Right(vyy400), bgg, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs11(vyy3000, vyy400)
new_esEs20(vyy1000, vyy1010, app(ty_Ratio, cae)) → new_esEs15(vyy1000, vyy1010, cae)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Ordering, bfd) → new_esEs9(vyy3000, vyy400)
new_ltEs5(vyy100, vyy101) → new_not(new_esEs9(new_compare7(vyy100, vyy101), GT))
new_esEs5(Right(vyy3000), Right(vyy400), bgg, app(ty_[], bhf)) → new_esEs10(vyy3000, vyy400, bhf)
new_esEs19(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy1002, vyy1012, ty_Float) → new_ltEs8(vyy1002, vyy1012)
new_lt4(vyy1000, vyy1010, dd, cb) → new_esEs9(new_compare8(vyy1000, vyy1010, dd, cb), LT)
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_compare110(vyy1000, vyy1010, False, eh, fa) → GT
new_compare25(vyy1000, vyy1010, False, fb, fc, fd) → new_compare11(vyy1000, vyy1010, new_ltEs6(vyy1000, vyy1010, fb, fc, fd), fb, fc, fd)
new_ltEs18(vyy1001, vyy1011, ty_Int) → new_ltEs5(vyy1001, vyy1011)
new_ltEs18(vyy1001, vyy1011, ty_Char) → new_ltEs10(vyy1001, vyy1011)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], beh)) → new_esEs10(vyy3000, vyy400, beh)
new_sr(vyy3000, vyy400) → new_primMulInt(vyy3000, vyy400)
new_esEs24(vyy1001, vyy1011, ty_Bool) → new_esEs17(vyy1001, vyy1011)
new_compare7(vyy100, vyy101) → new_primCmpInt(vyy100, vyy101)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(ty_Maybe, ca), cb) → new_ltEs9(vyy10000, vyy10100, ca)
new_ltEs19(vyy1002, vyy1012, ty_@0) → new_ltEs12(vyy1002, vyy1012)
new_compare18(:%(vyy1000, vyy1001), :%(vyy1010, vyy1011), ty_Integer) → new_compare14(new_sr0(vyy1000, vyy1011), new_sr0(vyy1010, vyy1001))
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs19(vyy1002, vyy1012, ty_Char) → new_ltEs10(vyy1002, vyy1012)
new_esEs26(vyy3002, vyy402, ty_Int) → new_esEs12(vyy3002, vyy402)
new_compare113(vyy1000, vyy1010, False, ef) → GT
new_primPlusNat0(Succ(vyy1540), vyy40000) → Succ(Succ(new_primPlusNat1(vyy1540, vyy40000)))
new_esEs22(vyy3001, vyy401, ty_Float) → new_esEs8(vyy3001, vyy401)
new_compare15(vyy1000, vyy1010, app(ty_[], bdh)) → new_compare5(vyy1000, vyy1010, bdh)
new_lt19(vyy1000, vyy1010, app(ty_Ratio, cfa)) → new_lt11(vyy1000, vyy1010, cfa)
new_esEs20(vyy1000, vyy1010, app(app(app(ty_@3, fb), fc), fd)) → new_esEs7(vyy1000, vyy1010, fb, fc, fd)
new_esEs20(vyy1000, vyy1010, ty_Bool) → new_esEs17(vyy1000, vyy1010)
new_ltEs19(vyy1002, vyy1012, app(ty_Maybe, bbf)) → new_ltEs9(vyy1002, vyy1012, bbf)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_esEs21(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Double, cb) → new_ltEs17(vyy10000, vyy10100)
new_esEs9(EQ, EQ) → True
new_lt19(vyy1000, vyy1010, ty_Bool) → new_lt8(vyy1000, vyy1010)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Integer, bfd) → new_esEs16(vyy3000, vyy400)
new_lt20(vyy1001, vyy1011, app(ty_Ratio, cfb)) → new_lt11(vyy1001, vyy1011, cfb)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs8(vyy3000, vyy400)
new_primPlusNat1(Zero, Succ(vyy400000)) → Succ(vyy400000)
new_primPlusNat1(Succ(vyy15400), Zero) → Succ(vyy15400)
new_esEs26(vyy3002, vyy402, app(app(app(ty_@3, cga), cgb), cgc)) → new_esEs7(vyy3002, vyy402, cga, cgb, cgc)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dah)) → new_esEs4(vyy3000, vyy400, dah)
new_compare19(Double(vyy1000, vyy1001), Double(vyy1010, vyy1011)) → new_compare7(new_sr(vyy1000, vyy1010), new_sr(vyy1001, vyy1011))
new_ltEs14(Right(vyy10000), Left(vyy10100), dd, cb) → False
new_lt20(vyy1001, vyy1011, app(app(ty_Either, baf), bag)) → new_lt4(vyy1001, vyy1011, baf, bag)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs7(vyy3000, vyy400, bfe, bff, bfg)
new_compare27(vyy1000, vyy1010, False) → new_compare111(vyy1000, vyy1010, new_ltEs11(vyy1000, vyy1010))
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_esEs23(vyy3000, vyy400, ty_Char) → new_esEs11(vyy3000, vyy400)
new_compare11(vyy1000, vyy1010, True, fb, fc, fd) → LT
new_ltEs19(vyy1002, vyy1012, ty_Ordering) → new_ltEs4(vyy1002, vyy1012)
new_lt6(vyy1000, vyy1010, app(ty_Ratio, cae)) → new_lt11(vyy1000, vyy1010, cae)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, app(app(ty_Either, chg), chh)) → new_esEs5(vyy3001, vyy401, chg, chh)
new_esEs5(Right(vyy3000), Right(vyy400), bgg, ty_Float) → new_esEs8(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(app(ty_@2, ce), cf), cb) → new_ltEs15(vyy10000, vyy10100, ce, cf)
new_esEs25(vyy1000, vyy1010, app(ty_Ratio, cfa)) → new_esEs15(vyy1000, vyy1010, cfa)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_esEs25(vyy1000, vyy1010, ty_Ordering) → new_esEs9(vyy1000, vyy1010)
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_lt20(vyy1001, vyy1011, ty_@0) → new_lt10(vyy1001, vyy1011)
new_esEs20(vyy1000, vyy1010, ty_Integer) → new_esEs16(vyy1000, vyy1010)
new_ltEs7(vyy100, vyy101, bcg) → new_not(new_esEs9(new_compare5(vyy100, vyy101, bcg), GT))
new_compare24(vyy1000, vyy1010, True, eh, fa) → EQ
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_@0, cb) → new_ltEs12(vyy10000, vyy10100)
new_esEs24(vyy1001, vyy1011, ty_Float) → new_esEs8(vyy1001, vyy1011)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs18(vyy1001, vyy1011, ty_Ordering) → new_ltEs4(vyy1001, vyy1011)
new_ltEs4(EQ, LT) → False
new_esEs10([], :(vyy400, vyy401), cah) → False
new_esEs10(:(vyy3000, vyy3001), [], cah) → False
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, app(app(ty_@2, dh), ea)) → new_ltEs15(vyy10000, vyy10100, dh, ea)
new_lt20(vyy1001, vyy1011, ty_Integer) → new_lt13(vyy1001, vyy1011)
new_primCmpNat0(Succ(vyy10000), Succ(vyy10100)) → new_primCmpNat0(vyy10000, vyy10100)
new_esEs22(vyy3001, vyy401, app(ty_Maybe, cch)) → new_esEs4(vyy3001, vyy401, cch)
new_compare5(:(vyy1000, vyy1001), [], bcg) → GT
new_esEs26(vyy3002, vyy402, ty_Integer) → new_esEs16(vyy3002, vyy402)
new_esEs25(vyy1000, vyy1010, app(ty_Maybe, ha)) → new_esEs4(vyy1000, vyy1010, ha)
new_compare112(vyy1000, vyy1010, True) → LT
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_[], bgc), bfd) → new_esEs10(vyy3000, vyy400, bgc)
new_compare15(vyy1000, vyy1010, ty_Bool) → new_compare13(vyy1000, vyy1010)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_lt19(vyy1000, vyy1010, app(app(ty_@2, hf), hg)) → new_lt12(vyy1000, vyy1010, hf, hg)
new_esEs13(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs12(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs18(vyy1001, vyy1011, app(ty_Maybe, fh)) → new_ltEs9(vyy1001, vyy1011, fh)
new_ltEs11(True, False) → False
new_esEs10([], [], cah) → True
new_esEs5(Right(vyy3000), Right(vyy400), bgg, app(app(ty_Either, bhd), bhe)) → new_esEs5(vyy3000, vyy400, bhd, bhe)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_compare14(Integer(vyy1000), Integer(vyy1010)) → new_primCmpInt(vyy1000, vyy1010)
new_compare15(vyy1000, vyy1010, app(ty_Ratio, cag)) → new_compare18(vyy1000, vyy1010, cag)
new_ltEs18(vyy1001, vyy1011, ty_@0) → new_ltEs12(vyy1001, vyy1011)
new_lt8(vyy1000, vyy1010) → new_esEs9(new_compare13(vyy1000, vyy1010), LT)
new_compare8(vyy1000, vyy1010, dd, cb) → new_compare28(vyy1000, vyy1010, new_esEs5(vyy1000, vyy1010, dd, cb), dd, cb)
new_compare5(:(vyy1000, vyy1001), :(vyy1010, vyy1011), bcg) → new_primCompAux0(vyy1000, vyy1010, new_compare5(vyy1001, vyy1011, bcg), bcg)
new_ltEs4(GT, EQ) → False
new_primCompAux00(vyy178, LT) → LT
new_esEs27(vyy3001, vyy401, app(ty_Ratio, dad)) → new_esEs15(vyy3001, vyy401, dad)
new_compare114(vyy1000, vyy1010, True, dd, cb) → LT
new_primCmpInt(Neg(Succ(vyy10000)), Neg(vyy1010)) → new_primCmpNat0(vyy1010, Succ(vyy10000))
new_lt6(vyy1000, vyy1010, ty_Int) → new_lt17(vyy1000, vyy1010)
new_ltEs18(vyy1001, vyy1011, ty_Bool) → new_ltEs11(vyy1001, vyy1011)
new_primCompAux0(vyy1000, vyy1010, vyy169, bcg) → new_primCompAux00(vyy169, new_compare15(vyy1000, vyy1010, bcg))
new_lt14(vyy1000, vyy1010) → new_esEs9(new_compare6(vyy1000, vyy1010), LT)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(app(app(ty_@3, be), bf), bg)) → new_ltEs6(vyy1000, vyy1010, be, bf, bg)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_lt20(vyy1001, vyy1011, ty_Int) → new_lt17(vyy1001, vyy1011)
new_lt12(vyy1000, vyy1010, eh, fa) → new_esEs9(new_compare10(vyy1000, vyy1010, eh, fa), LT)
new_lt6(vyy1000, vyy1010, app(app(app(ty_@3, fb), fc), fd)) → new_lt16(vyy1000, vyy1010, fb, fc, fd)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Char) → new_ltEs10(vyy1000, vyy1010)
new_ltEs4(EQ, EQ) → True
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy10000), Zero) → GT
new_lt7(vyy1000, vyy1010) → new_esEs9(new_compare16(vyy1000, vyy1010), LT)
new_ltEs19(vyy1002, vyy1012, app(ty_Ratio, cfc)) → new_ltEs13(vyy1002, vyy1012, cfc)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(ty_Maybe, h)) → new_ltEs9(vyy1000, vyy1010, h)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(ty_[], dc), cb) → new_ltEs7(vyy10000, vyy10100, dc)
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, ty_Bool) → new_ltEs11(vyy10000, vyy10100)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy10100))) → LT
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, bef), beg)) → new_esEs5(vyy3000, vyy400, bef, beg)
new_esEs20(vyy1000, vyy1010, app(app(ty_Either, dd), cb)) → new_esEs5(vyy1000, vyy1010, dd, cb)
new_ltEs4(GT, LT) → False
new_ltEs14(Left(vyy10000), Left(vyy10100), app(ty_Ratio, cfd), cb) → new_ltEs13(vyy10000, vyy10100, cfd)
new_esEs21(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Bool) → new_ltEs11(vyy1000, vyy1010)
new_sr0(Integer(vyy10000), Integer(vyy10110)) → Integer(new_primMulInt(vyy10000, vyy10110))
new_primPlusNat1(Succ(vyy15400), Succ(vyy400000)) → Succ(Succ(new_primPlusNat1(vyy15400, vyy400000)))
new_ltEs18(vyy1001, vyy1011, app(app(ty_@2, gc), gd)) → new_ltEs15(vyy1001, vyy1011, gc, gd)
new_compare28(vyy1000, vyy1010, True, dd, cb) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dba), dbb)) → new_esEs5(vyy3000, vyy400, dba, dbb)
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, ty_Int) → new_ltEs5(vyy10000, vyy10100)
new_esEs26(vyy3002, vyy402, ty_Double) → new_esEs13(vyy3002, vyy402)
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, ty_Char) → new_ltEs10(vyy10000, vyy10100)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, bfa), bfb)) → new_esEs6(vyy3000, vyy400, bfa, bfb)
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, ty_Integer) → new_ltEs16(vyy10000, vyy10100)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs11(vyy3000, vyy400)
new_compare15(vyy1000, vyy1010, ty_Integer) → new_compare14(vyy1000, vyy1010)
new_lt6(vyy1000, vyy1010, ty_Double) → new_lt15(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, app(app(ty_@2, cdd), cde)) → new_esEs6(vyy3001, vyy401, cdd, cde)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_ltEs9(Just(vyy1000), Nothing, cac) → False
new_esEs21(vyy3000, vyy400, ty_Char) → new_esEs11(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy10100))) → new_primCmpNat0(Zero, Succ(vyy10100))
new_primCompAux00(vyy178, EQ) → vyy178
new_esEs25(vyy1000, vyy1010, ty_@0) → new_esEs14(vyy1000, vyy1010)
new_ltEs15(@2(vyy1000, vyy1001), @2(vyy1010, vyy1011), fg, eg) → new_pePe(new_lt6(vyy1000, vyy1010, fg), new_asAs(new_esEs20(vyy1000, vyy1010, fg), new_ltEs18(vyy1001, vyy1011, eg)))
new_lt19(vyy1000, vyy1010, app(ty_[], bac)) → new_lt5(vyy1000, vyy1010, bac)
new_esEs5(Right(vyy3000), Right(vyy400), bgg, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_lt6(vyy1000, vyy1010, ty_Integer) → new_lt13(vyy1000, vyy1010)
new_esEs26(vyy3002, vyy402, ty_Char) → new_esEs11(vyy3002, vyy402)
new_esEs20(vyy1000, vyy1010, ty_Double) → new_esEs13(vyy1000, vyy1010)
new_compare114(vyy1000, vyy1010, False, dd, cb) → GT
new_not(False) → True
new_esEs10(:(vyy3000, vyy3001), :(vyy400, vyy401), cah) → new_asAs(new_esEs21(vyy3000, vyy400, cah), new_esEs10(vyy3001, vyy401, cah))
new_lt20(vyy1001, vyy1011, ty_Bool) → new_lt8(vyy1001, vyy1011)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, bfc)) → new_esEs15(vyy3000, vyy400, bfc)
new_primPlusNat0(Zero, vyy40000) → Succ(vyy40000)
new_primCmpInt(Pos(Succ(vyy10000)), Pos(vyy1010)) → new_primCmpNat0(Succ(vyy10000), vyy1010)
new_ltEs18(vyy1001, vyy1011, app(ty_Ratio, caf)) → new_ltEs13(vyy1001, vyy1011, caf)
new_esEs23(vyy3000, vyy400, app(app(ty_@2, cef), ceg)) → new_esEs6(vyy3000, vyy400, cef, ceg)
new_esEs25(vyy1000, vyy1010, ty_Double) → new_esEs13(vyy1000, vyy1010)
new_ltEs9(Nothing, Nothing, cac) → True
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Ordering) → new_ltEs4(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_esEs9(GT, GT) → True
new_ltEs18(vyy1001, vyy1011, app(app(app(ty_@3, ge), gf), gg)) → new_ltEs6(vyy1001, vyy1011, ge, gf, gg)
new_lt5(vyy1000, vyy1010, ff) → new_esEs9(new_compare5(vyy1000, vyy1010, ff), LT)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs14(vyy3001, vyy401)
new_ltEs19(vyy1002, vyy1012, app(app(app(ty_@3, bcc), bcd), bce)) → new_ltEs6(vyy1002, vyy1012, bcc, bcd, bce)
new_esEs23(vyy3000, vyy400, app(ty_[], cee)) → new_esEs10(vyy3000, vyy400, cee)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Double, bfd) → new_esEs13(vyy3000, vyy400)
new_compare29(vyy1000, vyy1010, fb, fc, fd) → new_compare25(vyy1000, vyy1010, new_esEs7(vyy1000, vyy1010, fb, fc, fd), fb, fc, fd)
new_ltEs11(False, False) → True
new_lt20(vyy1001, vyy1011, ty_Ordering) → new_lt18(vyy1001, vyy1011)
new_esEs21(vyy3000, vyy400, app(ty_Ratio, ccb)) → new_esEs15(vyy3000, vyy400, ccb)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Int, bfd) → new_esEs12(vyy3000, vyy400)
new_esEs26(vyy3002, vyy402, app(app(ty_Either, cge), cgf)) → new_esEs5(vyy3002, vyy402, cge, cgf)
new_lt19(vyy1000, vyy1010, ty_Float) → new_lt14(vyy1000, vyy1010)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_lt19(vyy1000, vyy1010, app(app(app(ty_@3, hh), baa), bab)) → new_lt16(vyy1000, vyy1010, hh, baa, bab)
new_compare16(Char(vyy1000), Char(vyy1010)) → new_primCmpNat0(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, app(app(app(ty_@3, cce), ccf), ccg)) → new_esEs7(vyy3001, vyy401, cce, ccf, ccg)
new_primCmpInt(Pos(Succ(vyy10000)), Neg(vyy1010)) → GT
new_esEs22(vyy3001, vyy401, ty_Char) → new_esEs11(vyy3001, vyy401)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(app(app(ty_@3, cg), da), db), cb) → new_ltEs6(vyy10000, vyy10100, cg, da, db)
new_esEs21(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs20(vyy1000, vyy1010, ty_Float) → new_esEs8(vyy1000, vyy1010)
new_lt20(vyy1001, vyy1011, ty_Double) → new_lt15(vyy1001, vyy1011)
new_primMulInt(Pos(vyy30000), Pos(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_esEs24(vyy1001, vyy1011, ty_Integer) → new_esEs16(vyy1001, vyy1011)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, dae), daf), dag)) → new_esEs7(vyy3000, vyy400, dae, daf, dag)
new_esEs15(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cab) → new_asAs(new_esEs19(vyy3000, vyy400, cab), new_esEs18(vyy3001, vyy401, cab))
new_lt6(vyy1000, vyy1010, ty_Ordering) → new_lt18(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, ty_Double) → new_esEs13(vyy3001, vyy401)
new_esEs20(vyy1000, vyy1010, ty_Char) → new_esEs11(vyy1000, vyy1010)
new_compare15(vyy1000, vyy1010, app(app(ty_@2, bdc), bdd)) → new_compare10(vyy1000, vyy1010, bdc, bdd)
new_esEs23(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Left(vyy400), bgg, bfd) → False
new_esEs5(Left(vyy3000), Right(vyy400), bgg, bfd) → False
new_esEs27(vyy3001, vyy401, app(app(ty_@2, dab), dac)) → new_esEs6(vyy3001, vyy401, dab, dac)
new_primMulInt(Neg(vyy30000), Neg(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_ltEs19(vyy1002, vyy1012, ty_Int) → new_ltEs5(vyy1002, vyy1012)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_@0) → new_ltEs12(vyy1000, vyy1010)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Bool, cb) → new_ltEs11(vyy10000, vyy10100)
new_lt20(vyy1001, vyy1011, app(app(ty_@2, bah), bba)) → new_lt12(vyy1001, vyy1011, bah, bba)
new_esEs18(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_esEs20(vyy1000, vyy1010, app(ty_[], ff)) → new_esEs10(vyy1000, vyy1010, ff)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, bea) → True
new_esEs22(vyy3001, vyy401, app(ty_Ratio, cdf)) → new_esEs15(vyy3001, vyy401, cdf)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(app(ty_Either, ba), bb)) → new_ltEs14(vyy1000, vyy1010, ba, bb)
new_esEs25(vyy1000, vyy1010, ty_Int) → new_esEs12(vyy1000, vyy1010)
new_compare15(vyy1000, vyy1010, ty_Float) → new_compare6(vyy1000, vyy1010)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_esEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), ccc, ccd) → new_asAs(new_esEs23(vyy3000, vyy400, ccc), new_esEs22(vyy3001, vyy401, ccd))
new_esEs27(vyy3001, vyy401, app(ty_Maybe, chf)) → new_esEs4(vyy3001, vyy401, chf)
new_ltEs4(LT, GT) → True
new_compare15(vyy1000, vyy1010, ty_Int) → new_compare7(vyy1000, vyy1010)
new_lt13(vyy1000, vyy1010) → new_esEs9(new_compare14(vyy1000, vyy1010), LT)
new_esEs25(vyy1000, vyy1010, ty_Integer) → new_esEs16(vyy1000, vyy1010)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy10100))) → new_primCmpNat0(Succ(vyy10100), Zero)
new_esEs23(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy10100))) → GT
new_lt16(vyy1000, vyy1010, fb, fc, fd) → new_esEs9(new_compare29(vyy1000, vyy1010, fb, fc, fd), LT)
new_esEs12(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_lt20(vyy1001, vyy1011, ty_Char) → new_lt7(vyy1001, vyy1011)
new_ltEs19(vyy1002, vyy1012, app(ty_[], bcf)) → new_ltEs7(vyy1002, vyy1012, bcf)
new_lt20(vyy1001, vyy1011, app(ty_Maybe, bae)) → new_lt9(vyy1001, vyy1011, bae)
new_esEs5(Right(vyy3000), Right(vyy400), bgg, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs7(vyy3000, vyy400, bgh, bha, bhb)
new_compare23(vyy1000, vyy1010, True, ef) → EQ
new_esEs26(vyy3002, vyy402, ty_@0) → new_esEs14(vyy3002, vyy402)
new_lt11(vyy1000, vyy1010, cae) → new_esEs9(new_compare18(vyy1000, vyy1010, cae), LT)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dbd), dbe)) → new_esEs6(vyy3000, vyy400, dbd, dbe)
new_compare15(vyy1000, vyy1010, app(app(ty_Either, bda), bdb)) → new_compare8(vyy1000, vyy1010, bda, bdb)
new_esEs11(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_lt19(vyy1000, vyy1010, app(app(ty_Either, hd), he)) → new_lt4(vyy1000, vyy1010, hd, he)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Float, bfd) → new_esEs8(vyy3000, vyy400)
new_compare5([], :(vyy1010, vyy1011), bcg) → LT
new_lt6(vyy1000, vyy1010, ty_Float) → new_lt14(vyy1000, vyy1010)
new_esEs16(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs12(vyy100, vyy101) → new_not(new_esEs9(new_compare17(vyy100, vyy101), GT))
new_esEs24(vyy1001, vyy1011, app(ty_[], bbe)) → new_esEs10(vyy1001, vyy1011, bbe)
new_esEs21(vyy3000, vyy400, app(ty_Maybe, cbd)) → new_esEs4(vyy3000, vyy400, cbd)
new_esEs23(vyy3000, vyy400, app(ty_Ratio, ceh)) → new_esEs15(vyy3000, vyy400, ceh)
new_esEs23(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_compare24(vyy1000, vyy1010, False, eh, fa) → new_compare110(vyy1000, vyy1010, new_ltEs15(vyy1000, vyy1010, eh, fa), eh, fa)
new_esEs24(vyy1001, vyy1011, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs7(vyy1001, vyy1011, bbb, bbc, bbd)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs4(LT, EQ) → True
new_esEs21(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_lt6(vyy1000, vyy1010, app(ty_Maybe, ef)) → new_lt9(vyy1000, vyy1010, ef)
new_lt15(vyy1000, vyy1010) → new_esEs9(new_compare19(vyy1000, vyy1010), LT)
new_esEs24(vyy1001, vyy1011, ty_Char) → new_esEs11(vyy1001, vyy1011)
new_ltEs14(Left(vyy10000), Right(vyy10100), dd, cb) → True
new_asAs(False, vyy144) → False
new_ltEs11(True, True) → True
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs16(vyy3000, vyy400)
new_ltEs19(vyy1002, vyy1012, app(app(ty_Either, bbg), bbh)) → new_ltEs14(vyy1002, vyy1012, bbg, bbh)
new_primMulInt(Pos(vyy30000), Neg(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulInt(Neg(vyy30000), Pos(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_esEs26(vyy3002, vyy402, ty_Float) → new_esEs8(vyy3002, vyy402)
new_primMulNat0(Zero, Succ(vyy40000)) → Zero
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs13(vyy3001, vyy401)
new_esEs24(vyy1001, vyy1011, ty_Double) → new_esEs13(vyy1001, vyy1011)
new_esEs21(vyy3000, vyy400, app(app(ty_Either, cbe), cbf)) → new_esEs5(vyy3000, vyy400, cbe, cbf)
new_lt19(vyy1000, vyy1010, ty_Ordering) → new_lt18(vyy1000, vyy1010)
new_esEs28(vyy3000, vyy400, app(ty_[], dbc)) → new_esEs10(vyy3000, vyy400, dbc)
new_esEs22(vyy3001, vyy401, app(ty_[], cdc)) → new_esEs10(vyy3001, vyy401, cdc)
new_compare15(vyy1000, vyy1010, ty_Char) → new_compare16(vyy1000, vyy1010)
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, app(app(ty_Either, df), dg)) → new_ltEs14(vyy10000, vyy10100, df, dg)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs13(vyy3000, vyy400)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Int) → new_ltEs5(vyy1000, vyy1010)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs8(vyy3000, vyy400)
new_compare27(vyy1000, vyy1010, True) → EQ
new_esEs27(vyy3001, vyy401, app(ty_[], daa)) → new_esEs10(vyy3001, vyy401, daa)
new_esEs20(vyy1000, vyy1010, ty_Ordering) → new_esEs9(vyy1000, vyy1010)
new_esEs19(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(ty_[], bh)) → new_ltEs7(vyy1000, vyy1010, bh)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(app(ty_Either, cc), cd), cb) → new_ltEs14(vyy10000, vyy10100, cc, cd)
new_esEs25(vyy1000, vyy1010, app(app(app(ty_@3, hh), baa), bab)) → new_esEs7(vyy1000, vyy1010, hh, baa, bab)
new_lt20(vyy1001, vyy1011, app(app(app(ty_@3, bbb), bbc), bbd)) → new_lt16(vyy1001, vyy1011, bbb, bbc, bbd)
new_lt19(vyy1000, vyy1010, ty_Integer) → new_lt13(vyy1000, vyy1010)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Bool, bfd) → new_esEs17(vyy3000, vyy400)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Float) → new_ltEs8(vyy1000, vyy1010)
new_esEs5(Right(vyy3000), Right(vyy400), bgg, app(ty_Maybe, bhc)) → new_esEs4(vyy3000, vyy400, bhc)
new_compare10(vyy1000, vyy1010, eh, fa) → new_compare24(vyy1000, vyy1010, new_esEs6(vyy1000, vyy1010, eh, fa), eh, fa)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), bgg, ty_Int) → new_esEs12(vyy3000, vyy400)
new_ltEs4(LT, LT) → True
new_esEs5(Right(vyy3000), Right(vyy400), bgg, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_esEs20(vyy1000, vyy1010, ty_Int) → new_esEs12(vyy1000, vyy1010)
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, ty_@0) → new_ltEs12(vyy10000, vyy10100)
new_esEs26(vyy3002, vyy402, ty_Bool) → new_esEs17(vyy3002, vyy402)
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_ltEs19(vyy1002, vyy1012, app(app(ty_@2, bca), bcb)) → new_ltEs15(vyy1002, vyy1012, bca, bcb)
new_esEs22(vyy3001, vyy401, ty_@0) → new_esEs14(vyy3001, vyy401)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_Either, bga), bgb), bfd) → new_esEs5(vyy3000, vyy400, bga, bgb)
new_compare15(vyy1000, vyy1010, ty_@0) → new_compare17(vyy1000, vyy1010)
new_compare112(vyy1000, vyy1010, False) → GT
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, ty_Float) → new_ltEs8(vyy10000, vyy10100)
new_esEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cff, cfg, cfh) → new_asAs(new_esEs28(vyy3000, vyy400, cff), new_asAs(new_esEs27(vyy3001, vyy401, cfg), new_esEs26(vyy3002, vyy402, cfh)))
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Ratio, bgf), bfd) → new_esEs15(vyy3000, vyy400, bgf)
new_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, app(ty_Ratio, cfe)) → new_ltEs13(vyy10000, vyy10100, cfe)
new_compare26(vyy1000, vyy1010, False) → new_compare112(vyy1000, vyy1010, new_ltEs4(vyy1000, vyy1010))
new_esEs24(vyy1001, vyy1011, ty_Ordering) → new_esEs9(vyy1001, vyy1011)
new_lt19(vyy1000, vyy1010, ty_@0) → new_lt10(vyy1000, vyy1010)
new_esEs21(vyy3000, vyy400, ty_Float) → new_esEs8(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, ty_Float) → new_esEs8(vyy3000, vyy400)
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, ty_Ordering) → new_ltEs4(vyy10000, vyy10100)
new_lt9(vyy1000, vyy1010, ef) → new_esEs9(new_compare9(vyy1000, vyy1010, ef), LT)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(vyy3002, vyy402, ty_Ordering) → new_esEs9(vyy3002, vyy402)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Char, cb) → new_ltEs10(vyy10000, vyy10100)
new_esEs5(Right(vyy3000), Right(vyy400), bgg, ty_Char) → new_esEs11(vyy3000, vyy400)
new_asAs(True, vyy144) → vyy144
new_ltEs16(vyy100, vyy101) → new_not(new_esEs9(new_compare14(vyy100, vyy101), GT))
new_primMulNat0(Succ(vyy300000), Succ(vyy40000)) → new_primPlusNat0(new_primMulNat0(vyy300000, Succ(vyy40000)), vyy40000)
new_compare28(vyy1000, vyy1010, False, dd, cb) → new_compare114(vyy1000, vyy1010, new_ltEs14(vyy1000, vyy1010, dd, cb), dd, cb)
new_compare15(vyy1000, vyy1010, app(ty_Maybe, bch)) → new_compare9(vyy1000, vyy1010, bch)
new_lt19(vyy1000, vyy1010, ty_Int) → new_lt17(vyy1000, vyy1010)
new_esEs26(vyy3002, vyy402, app(app(ty_@2, cgh), cha)) → new_esEs6(vyy3002, vyy402, cgh, cha)
new_lt20(vyy1001, vyy1011, app(ty_[], bbe)) → new_lt5(vyy1001, vyy1011, bbe)
new_compare5([], [], bcg) → EQ
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, beb), bec), bed)) → new_esEs7(vyy3000, vyy400, beb, bec, bed)
new_ltEs4(GT, GT) → True
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs11(vyy3001, vyy401)
new_lt6(vyy1000, vyy1010, ty_Bool) → new_lt8(vyy1000, vyy1010)
new_esEs9(LT, LT) → True
new_esEs22(vyy3001, vyy401, app(app(ty_Either, cda), cdb)) → new_esEs5(vyy3001, vyy401, cda, cdb)
new_primCompAux00(vyy178, GT) → GT
new_esEs5(Right(vyy3000), Right(vyy400), bgg, app(ty_Ratio, caa)) → new_esEs15(vyy3000, vyy400, caa)
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs8(vyy3001, vyy401)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(vyy1000, vyy1010, app(app(ty_@2, eh), fa)) → new_lt12(vyy1000, vyy1010, eh, fa)
new_ltEs14(Right(vyy10000), Right(vyy10100), dd, app(ty_Maybe, de)) → new_ltEs9(vyy10000, vyy10100, de)
new_compare9(vyy1000, vyy1010, ef) → new_compare23(vyy1000, vyy1010, new_esEs4(vyy1000, vyy1010, ef), ef)
new_esEs8(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs12(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(vyy1002, vyy1012, ty_Bool) → new_ltEs11(vyy1002, vyy1012)
new_primCmpInt(Neg(Succ(vyy10000)), Pos(vyy1010)) → LT
new_compare15(vyy1000, vyy1010, ty_Ordering) → new_compare12(vyy1000, vyy1010)
new_not(True) → False

The set Q consists of the following terms:

new_compare15(x0, x1, app(ty_Ratio, x2))
new_compare113(x0, x1, False, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs10([], [], x0)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_compare15(x0, x1, app(ty_Maybe, x2))
new_compare18(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_lt6(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Bool)
new_compare11(x0, x1, True, x2, x3, x4)
new_esEs20(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(False, x0)
new_esEs28(x0, x1, ty_Int)
new_compare10(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_compare114(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs4(Just(x0), Nothing, x1)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs16(Integer(x0), Integer(x1))
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs23(x0, x1, ty_Double)
new_lt18(x0, x1)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_@0)
new_compare17(@0, @0)
new_compare12(x0, x1)
new_primCompAux0(x0, x1, x2, x3)
new_esEs21(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Ordering)
new_esEs17(False, False)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare14(Integer(x0), Integer(x1))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare16(Char(x0), Char(x1))
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_compare8(x0, x1, x2, x3)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_compare113(x0, x1, True, x2)
new_esEs23(x0, x1, ty_Int)
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(ty_[], x2))
new_lt16(x0, x1, x2, x3, x4)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Integer)
new_primEqNat0(Zero, Zero)
new_esEs20(x0, x1, ty_Bool)
new_compare110(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs11(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs16(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_compare26(x0, x1, True)
new_lt19(x0, x1, ty_Double)
new_compare5(:(x0, x1), [], x2)
new_lt9(x0, x1, x2)
new_lt6(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare15(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1, x2)
new_compare28(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare24(x0, x1, True, x2, x3)
new_primCompAux00(x0, EQ)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(GT, GT)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs10(:(x0, x1), :(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs25(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primPlusNat0(Succ(x0), x1)
new_esEs25(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs4(Nothing, Nothing, x0)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1, True)
new_compare13(x0, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primPlusNat0(Zero, x0)
new_esEs14(@0, @0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_lt15(x0, x1)
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(True, x0)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt6(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Ordering)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt12(x0, x1, x2, x3)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_ltEs17(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare23(x0, x1, False, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt6(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_lt14(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Double)
new_ltEs9(Nothing, Just(x0), x1)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare110(x0, x1, False, x2, x3)
new_lt6(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare23(x0, x1, True, x2)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs4(EQ, EQ)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_lt17(x0, x1)
new_ltEs4(EQ, LT)
new_esEs27(x0, x1, ty_Int)
new_ltEs4(LT, EQ)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Pos(x0), Pos(x1))
new_compare28(x0, x1, False, x2, x3)
new_compare15(x0, x1, ty_Integer)
new_esEs9(GT, GT)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_compare112(x0, x1, False)
new_compare15(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_compare27(x0, x1, False)
new_compare15(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare15(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Integer)
new_lt11(x0, x1, x2)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs19(x0, x1, ty_Integer)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False, x2, x3, x4)
new_ltEs11(False, False)
new_esEs22(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_compare6(Float(x0, x1), Float(x2, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs15(:%(x0, x1), :%(x2, x3), x4)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs9(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs19(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs19(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs11(False, True)
new_ltEs11(True, False)
new_lt19(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Int)
new_ltEs4(LT, LT)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_ltEs18(x0, x1, ty_Float)
new_primPlusNat1(Zero, Succ(x0))
new_lt20(x0, x1, ty_Ordering)
new_esEs4(Nothing, Just(x0), x1)
new_lt5(x0, x1, x2)
new_compare15(x0, x1, ty_Int)
new_compare9(x0, x1, x2)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Bool)
new_compare5([], :(x0, x1), x2)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Double)
new_lt20(x0, x1, ty_@0)
new_ltEs12(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs18(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Float)
new_compare5(:(x0, x1), :(x2, x3), x4)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(Double(x0, x1), Double(x2, x3))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Float(x0, x1), Float(x2, x3))
new_compare15(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs28(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_lt13(x0, x1)
new_esEs24(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs21(x0, x1, ty_Bool)
new_compare111(x0, x1, False)
new_lt19(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs27(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs5(x0, x1)
new_esEs22(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare15(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_[], x2))
new_lt7(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_sr0(Integer(x0), Integer(x1))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Int)
new_compare24(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_ltEs9(Nothing, Nothing, x0)
new_esEs18(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt6(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, GT)
new_primCompAux00(x0, LT)
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_esEs28(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs28(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs20(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_lt8(x0, x1)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_asAs(True, x0)
new_esEs28(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, x2, x3)
new_primPlusNat1(Succ(x0), Zero)
new_esEs27(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs10([], :(x0, x1), x2)
new_lt6(x0, x1, ty_Char)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_sr(x0, x1)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs10(:(x0, x1), [], x2)
new_ltEs19(x0, x1, ty_Integer)
new_compare7(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_primMulNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs8(x0, x1)
new_pePe(False, x0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Ordering)
new_compare5([], [], x0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs17(True, False)
new_esEs17(False, True)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs13(x0, x1, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs24(x0, x1, ty_Double)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_compare29(x0, x1, x2, x3, x4)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs20(x0, x1, ty_Float)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_@0)
new_ltEs10(x0, x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare114(x0, x1, True, x2, x3)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_compare111(x0, x1, True)
new_esEs23(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Integer)
new_lt10(x0, x1)
new_ltEs11(True, True)
new_esEs9(LT, LT)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, ty_Double)
new_compare26(x0, x1, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare15(x0, x1, app(app(app(ty_@3, x2), x3), x4))

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

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



↳ 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

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

new_foldFM_GE1(vyy89, vyy40, vyy330, vyy331, vyy332, vyy333, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), False, h, ba, bb) → new_foldFM_GE1(vyy89, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h, ba), h, ba, bb)
new_foldFM_GE(vyy89, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba, bb) → new_foldFM_GE1(vyy89, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h, ba), h, ba, bb)
new_foldFM_GE2(vyy330, vyy331, vyy113, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb) → new_foldFM_GE1(new_keysFM_GE0(vyy330, vyy331, vyy113, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, h, ba), h, ba, bb)
new_foldFM_GE1(vyy89, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba, bb) → new_foldFM_GE(vyy89, vyy40, vyy334, h, ba, bb)
new_foldFM_GE1(vyy89, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba, bb) → new_foldFM_GE(vyy89, vyy40, vyy334, h, ba, bb)
new_foldFM_GE1(vyy89, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba, bb) → new_foldFM_GE2(vyy330, vyy331, new_foldFM_GE0(vyy89, vyy40, vyy334, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb)

The TRS R consists of the following rules:

new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, bg)) → new_esEs4(vyy3000, vyy400, bg)
new_ltEs19(vyy1002, vyy1012, ty_Integer) → new_ltEs16(vyy1002, vyy1012)
new_esEs24(vyy1001, vyy1011, app(app(ty_Either, cbf), cbg)) → new_esEs5(vyy1001, vyy1011, cbf, cbg)
new_lt19(vyy1000, vyy1010, ty_Char) → new_lt7(vyy1000, vyy1010)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Integer, cg) → new_ltEs16(vyy10000, vyy10100)
new_esEs21(vyy3000, vyy400, app(app(ty_@2, bef), beg)) → new_esEs6(vyy3000, vyy400, bef, beg)
new_ltEs18(vyy1001, vyy1011, ty_Float) → new_ltEs8(vyy1001, vyy1011)
new_esEs24(vyy1001, vyy1011, app(ty_Ratio, cbe)) → new_esEs15(vyy1001, vyy1011, cbe)
new_ltEs4(EQ, GT) → True
new_esEs5(Left(vyy3000), Left(vyy400), ty_@0, ea) → new_esEs14(vyy3000, vyy400)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Double) → new_ltEs17(vyy1000, vyy1010)
new_esEs26(vyy3002, vyy402, app(ty_Ratio, chh)) → new_esEs15(vyy3002, vyy402, chh)
new_ltEs6(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), bhg, bhh, caa) → new_pePe(new_lt19(vyy1000, vyy1010, bhg), new_asAs(new_esEs25(vyy1000, vyy1010, bhg), new_pePe(new_lt20(vyy1001, vyy1011, bhh), new_asAs(new_esEs24(vyy1001, vyy1011, bhh), new_ltEs19(vyy1002, vyy1012, caa)))))
new_esEs18(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_lt6(vyy1000, vyy1010, ty_Char) → new_lt7(vyy1000, vyy1010)
new_compare110(vyy1000, vyy1010, True, dd, de) → LT
new_esEs23(vyy3000, vyy400, app(app(ty_Either, bha), bhb)) → new_esEs5(vyy3000, vyy400, bha, bhb)
new_ltEs8(vyy100, vyy101) → new_not(new_esEs9(new_compare6(vyy100, vyy101), GT))
new_esEs24(vyy1001, vyy1011, app(ty_Maybe, cbd)) → new_esEs4(vyy1001, vyy1011, cbd)
new_esEs4(Nothing, Just(vyy400), bc) → False
new_esEs4(Just(vyy3000), Nothing, bc) → False
new_lt20(vyy1001, vyy1011, ty_Float) → new_lt14(vyy1001, vyy1011)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dcd)) → new_esEs15(vyy3000, vyy400, dcd)
new_ltEs9(Nothing, Just(vyy1010), ha) → True
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs14(vyy3000, vyy400)
new_lt19(vyy1000, vyy1010, ty_Double) → new_lt15(vyy1000, vyy1010)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Double) → new_ltEs17(vyy10000, vyy10100)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Integer) → new_ltEs16(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, ty_Ordering) → new_esEs9(vyy3001, vyy401)
new_lt10(vyy1000, vyy1010) → new_esEs9(new_compare17(vyy1000, vyy1010), LT)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(ty_Ratio, hc)) → new_ltEs13(vyy1000, vyy1010, hc)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_lt18(vyy1000, vyy1010) → new_esEs9(new_compare12(vyy1000, vyy1010), LT)
new_esEs21(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_primMulNat0(Zero, Zero) → Zero
new_compare15(vyy1000, vyy1010, ty_Double) → new_compare19(vyy1000, vyy1010)
new_ltEs18(vyy1001, vyy1011, ty_Integer) → new_ltEs16(vyy1001, vyy1011)
new_esEs20(vyy1000, vyy1010, app(ty_Maybe, db)) → new_esEs4(vyy1000, vyy1010, db)
new_lt19(vyy1000, vyy1010, app(ty_Maybe, cab)) → new_lt9(vyy1000, vyy1010, cab)
new_esEs21(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs21(vyy3000, vyy400, app(ty_[], bee)) → new_esEs10(vyy3000, vyy400, bee)
new_esEs25(vyy1000, vyy1010, ty_Bool) → new_esEs17(vyy1000, vyy1010)
new_esEs24(vyy1001, vyy1011, ty_@0) → new_esEs14(vyy1001, vyy1011)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, app(ty_[], cgc)) → new_ltEs7(vyy10000, vyy10100, cgc)
new_esEs23(vyy3000, vyy400, app(ty_Maybe, bgh)) → new_esEs4(vyy3000, vyy400, bgh)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(app(ty_@2, hf), hg)) → new_ltEs15(vyy1000, vyy1010, hf, hg)
new_esEs17(True, True) → True
new_foldFM_GE3(vyy330, vyy331, vyy112, vyy40, h, ba, bb) → new_keysFM_GE0(vyy330, vyy331, vyy112, h, ba, bb)
new_esEs26(vyy3002, vyy402, app(ty_[], che)) → new_esEs10(vyy3002, vyy402, che)
new_lt6(vyy1000, vyy1010, ty_@0) → new_lt10(vyy1000, vyy1010)
new_lt6(vyy1000, vyy1010, app(ty_[], da)) → new_lt5(vyy1000, vyy1010, da)
new_esEs21(vyy3000, vyy400, app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs7(vyy3000, vyy400, bdg, bdh, bea)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs6(vyy10000, vyy10100, cfh, cga, cgb)
new_esEs23(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Char, ea) → new_esEs11(vyy3000, vyy400)
new_esEs20(vyy1000, vyy1010, app(app(ty_@2, dd), de)) → new_esEs6(vyy1000, vyy1010, dd, de)
new_esEs26(vyy3002, vyy402, app(ty_Maybe, chb)) → new_esEs4(vyy3002, vyy402, chb)
new_ltEs18(vyy1001, vyy1011, app(ty_[], bbh)) → new_ltEs7(vyy1001, vyy1011, bbh)
new_esEs20(vyy1000, vyy1010, ty_@0) → new_esEs14(vyy1000, vyy1010)
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_@0) → new_esEs14(vyy3000, vyy400)
new_esEs25(vyy1000, vyy1010, app(ty_[], cbc)) → new_esEs10(vyy1000, vyy1010, cbc)
new_pePe(False, vyy168) → vyy168
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs12(vyy3000, vyy400)
new_esEs25(vyy1000, vyy1010, ty_Char) → new_esEs11(vyy1000, vyy1010)
new_ltEs17(vyy100, vyy101) → new_not(new_esEs9(new_compare19(vyy100, vyy101), GT))
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Int, cg) → new_ltEs5(vyy10000, vyy10100)
new_compare23(vyy1000, vyy1010, False, db) → new_compare113(vyy1000, vyy1010, new_ltEs9(vyy1000, vyy1010, db), db)
new_esEs25(vyy1000, vyy1010, ty_Float) → new_esEs8(vyy1000, vyy1010)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs9(vyy3001, vyy401)
new_compare11(vyy1000, vyy1010, False, df, dg, dh) → GT
new_ltEs18(vyy1001, vyy1011, app(app(ty_Either, bba), bbb)) → new_ltEs14(vyy1001, vyy1011, bba, bbb)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_ltEs11(False, True) → True
new_lt17(vyy1000, vyy1010) → new_esEs9(new_compare7(vyy1000, vyy1010), LT)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_@2, fa), fb), ea) → new_esEs6(vyy3000, vyy400, fa, fb)
new_compare111(vyy1000, vyy1010, False) → GT
new_keysFM_GE0(vyy170, vyy171, vyy110, bdc, bdd, bde) → :(vyy170, vyy110)
new_compare111(vyy1000, vyy1010, True) → LT
new_ltEs19(vyy1002, vyy1012, ty_Double) → new_ltEs17(vyy1002, vyy1012)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Maybe, ee), ea) → new_esEs4(vyy3000, vyy400, ee)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Float, cg) → new_ltEs8(vyy10000, vyy10100)
new_compare15(vyy1000, vyy1010, app(app(app(ty_@3, bcg), bch), bda)) → new_compare29(vyy1000, vyy1010, bcg, bch, bda)
new_compare13(vyy1000, vyy1010) → new_compare27(vyy1000, vyy1010, new_esEs17(vyy1000, vyy1010))
new_esEs23(vyy3000, vyy400, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs7(vyy3000, vyy400, bge, bgf, bgg)
new_primCmpNat0(Zero, Succ(vyy10100)) → LT
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, daa), dab), dac)) → new_esEs7(vyy3001, vyy401, daa, dab, dac)
new_compare113(vyy1000, vyy1010, True, db) → LT
new_esEs25(vyy1000, vyy1010, app(app(ty_Either, cad), cae)) → new_esEs5(vyy1000, vyy1010, cad, cae)
new_esEs25(vyy1000, vyy1010, app(app(ty_@2, caf), cag)) → new_esEs6(vyy1000, vyy1010, caf, cag)
new_compare6(Float(vyy1000, vyy1001), Float(vyy1010, vyy1011)) → new_compare7(new_sr(vyy1000, vyy1010), new_sr(vyy1001, vyy1011))
new_compare25(vyy1000, vyy1010, True, df, dg, dh) → EQ
new_ltEs13(vyy100, vyy101, dce) → new_not(new_esEs9(new_compare18(vyy100, vyy101, dce), GT))
new_lt6(vyy1000, vyy1010, app(app(ty_Either, cf), cg)) → new_lt4(vyy1000, vyy1010, cf, cg)
new_esEs24(vyy1001, vyy1011, ty_Int) → new_esEs12(vyy1001, vyy1011)
new_ltEs10(vyy100, vyy101) → new_not(new_esEs9(new_compare16(vyy100, vyy101), GT))
new_compare18(:%(vyy1000, vyy1001), :%(vyy1010, vyy1011), ty_Int) → new_compare7(new_sr(vyy1000, vyy1011), new_sr(vyy1010, vyy1001))
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_foldFM_GE0(vyy89, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba, bb) → new_foldFM_GE10(vyy89, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h, ba), h, ba, bb)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs24(vyy1001, vyy1011, app(app(ty_@2, cbh), cca)) → new_esEs6(vyy1001, vyy1011, cbh, cca)
new_pePe(True, vyy168) → True
new_primEqNat0(Zero, Zero) → True
new_compare26(vyy1000, vyy1010, True) → EQ
new_ltEs18(vyy1001, vyy1011, ty_Double) → new_ltEs17(vyy1001, vyy1011)
new_esEs5(Right(vyy3000), Right(vyy400), fd, app(app(ty_@2, ge), gf)) → new_esEs6(vyy3000, vyy400, ge, gf)
new_compare12(vyy1000, vyy1010) → new_compare26(vyy1000, vyy1010, new_esEs9(vyy1000, vyy1010))
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Ordering, cg) → new_ltEs4(vyy10000, vyy10100)
new_esEs14(@0, @0) → True
new_compare17(@0, @0) → EQ
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs11(vyy3000, vyy400)
new_esEs20(vyy1000, vyy1010, app(ty_Ratio, baf)) → new_esEs15(vyy1000, vyy1010, baf)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Ordering, ea) → new_esEs9(vyy3000, vyy400)
new_gtEs(vyy3330, vyy40, h, ba) → new_not(new_esEs9(new_compare28(vyy3330, Right(vyy40), new_esEs5(vyy3330, Right(vyy40), h, ba), h, ba), LT))
new_ltEs5(vyy100, vyy101) → new_not(new_esEs9(new_compare7(vyy100, vyy101), GT))
new_esEs5(Right(vyy3000), Right(vyy400), fd, app(ty_[], gd)) → new_esEs10(vyy3000, vyy400, gd)
new_esEs19(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy1002, vyy1012, ty_Float) → new_ltEs8(vyy1002, vyy1012)
new_foldFM_GE10(vyy89, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba, bb) → new_foldFM_GE3(vyy330, vyy331, new_foldFM_GE0(vyy89, vyy40, vyy334, h, ba, bb), vyy40, h, ba, bb)
new_lt4(vyy1000, vyy1010, cf, cg) → new_esEs9(new_compare8(vyy1000, vyy1010, cf, cg), LT)
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_compare110(vyy1000, vyy1010, False, dd, de) → GT
new_compare25(vyy1000, vyy1010, False, df, dg, dh) → new_compare11(vyy1000, vyy1010, new_ltEs6(vyy1000, vyy1010, df, dg, dh), df, dg, dh)
new_ltEs18(vyy1001, vyy1011, ty_Int) → new_ltEs5(vyy1001, vyy1011)
new_ltEs18(vyy1001, vyy1011, ty_Char) → new_ltEs10(vyy1001, vyy1011)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], cb)) → new_esEs10(vyy3000, vyy400, cb)
new_sr(vyy3000, vyy400) → new_primMulInt(vyy3000, vyy400)
new_esEs24(vyy1001, vyy1011, ty_Bool) → new_esEs17(vyy1001, vyy1011)
new_compare7(vyy100, vyy101) → new_primCmpInt(vyy100, vyy101)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(ty_Maybe, cdh), cg) → new_ltEs9(vyy10000, vyy10100, cdh)
new_ltEs19(vyy1002, vyy1012, ty_@0) → new_ltEs12(vyy1002, vyy1012)
new_compare18(:%(vyy1000, vyy1001), :%(vyy1010, vyy1011), ty_Integer) → new_compare14(new_sr0(vyy1000, vyy1011), new_sr0(vyy1010, vyy1001))
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs19(vyy1002, vyy1012, ty_Char) → new_ltEs10(vyy1002, vyy1012)
new_esEs26(vyy3002, vyy402, ty_Int) → new_esEs12(vyy3002, vyy402)
new_compare113(vyy1000, vyy1010, False, db) → GT
new_primPlusNat0(Succ(vyy1540), vyy40000) → Succ(Succ(new_primPlusNat1(vyy1540, vyy40000)))
new_esEs22(vyy3001, vyy401, ty_Float) → new_esEs8(vyy3001, vyy401)
new_compare15(vyy1000, vyy1010, app(ty_[], bdb)) → new_compare5(vyy1000, vyy1010, bdb)
new_lt19(vyy1000, vyy1010, app(ty_Ratio, cac)) → new_lt11(vyy1000, vyy1010, cac)
new_esEs20(vyy1000, vyy1010, app(app(app(ty_@3, df), dg), dh)) → new_esEs7(vyy1000, vyy1010, df, dg, dh)
new_esEs20(vyy1000, vyy1010, ty_Bool) → new_esEs17(vyy1000, vyy1010)
new_ltEs19(vyy1002, vyy1012, app(ty_Maybe, ccf)) → new_ltEs9(vyy1002, vyy1012, ccf)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_esEs21(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Double, cg) → new_ltEs17(vyy10000, vyy10100)
new_esEs9(EQ, EQ) → True
new_lt19(vyy1000, vyy1010, ty_Bool) → new_lt8(vyy1000, vyy1010)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Integer, ea) → new_esEs16(vyy3000, vyy400)
new_lt20(vyy1001, vyy1011, app(ty_Ratio, cbe)) → new_lt11(vyy1001, vyy1011, cbe)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs8(vyy3000, vyy400)
new_primPlusNat1(Zero, Succ(vyy400000)) → Succ(vyy400000)
new_primPlusNat1(Succ(vyy15400), Zero) → Succ(vyy15400)
new_esEs26(vyy3002, vyy402, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs7(vyy3002, vyy402, cgg, cgh, cha)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dbf)) → new_esEs4(vyy3000, vyy400, dbf)
new_compare19(Double(vyy1000, vyy1001), Double(vyy1010, vyy1011)) → new_compare7(new_sr(vyy1000, vyy1010), new_sr(vyy1001, vyy1011))
new_ltEs14(Right(vyy10000), Left(vyy10100), cf, cg) → False
new_foldFM_GE10(vyy89, vyy40, vyy330, vyy331, vyy332, vyy333, vyy334, False, h, ba, bb) → new_foldFM_GE0(vyy89, vyy40, vyy334, h, ba, bb)
new_lt20(vyy1001, vyy1011, app(app(ty_Either, cbf), cbg)) → new_lt4(vyy1001, vyy1011, cbf, cbg)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, eb), ec), ed), ea) → new_esEs7(vyy3000, vyy400, eb, ec, ed)
new_compare27(vyy1000, vyy1010, False) → new_compare111(vyy1000, vyy1010, new_ltEs11(vyy1000, vyy1010))
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_esEs23(vyy3000, vyy400, ty_Char) → new_esEs11(vyy3000, vyy400)
new_compare11(vyy1000, vyy1010, True, df, dg, dh) → LT
new_ltEs19(vyy1002, vyy1012, ty_Ordering) → new_ltEs4(vyy1002, vyy1012)
new_lt6(vyy1000, vyy1010, app(ty_Ratio, baf)) → new_lt11(vyy1000, vyy1010, baf)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, app(app(ty_Either, dae), daf)) → new_esEs5(vyy3001, vyy401, dae, daf)
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Float) → new_esEs8(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(app(ty_@2, ced), cee), cg) → new_ltEs15(vyy10000, vyy10100, ced, cee)
new_esEs25(vyy1000, vyy1010, app(ty_Ratio, cac)) → new_esEs15(vyy1000, vyy1010, cac)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_esEs25(vyy1000, vyy1010, ty_Ordering) → new_esEs9(vyy1000, vyy1010)
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_lt20(vyy1001, vyy1011, ty_@0) → new_lt10(vyy1001, vyy1011)
new_esEs20(vyy1000, vyy1010, ty_Integer) → new_esEs16(vyy1000, vyy1010)
new_compare24(vyy1000, vyy1010, True, dd, de) → EQ
new_ltEs7(vyy100, vyy101, dc) → new_not(new_esEs9(new_compare5(vyy100, vyy101, dc), GT))
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_@0, cg) → new_ltEs12(vyy10000, vyy10100)
new_esEs24(vyy1001, vyy1011, ty_Float) → new_esEs8(vyy1001, vyy1011)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs18(vyy1001, vyy1011, ty_Ordering) → new_ltEs4(vyy1001, vyy1011)
new_ltEs4(EQ, LT) → False
new_esEs10([], :(vyy400, vyy401), bdf) → False
new_esEs10(:(vyy3000, vyy3001), [], bdf) → False
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, app(app(ty_@2, cff), cfg)) → new_ltEs15(vyy10000, vyy10100, cff, cfg)
new_lt20(vyy1001, vyy1011, ty_Integer) → new_lt13(vyy1001, vyy1011)
new_primCmpNat0(Succ(vyy10000), Succ(vyy10100)) → new_primCmpNat0(vyy10000, vyy10100)
new_esEs22(vyy3001, vyy401, app(ty_Maybe, bff)) → new_esEs4(vyy3001, vyy401, bff)
new_compare5(:(vyy1000, vyy1001), [], dc) → GT
new_esEs26(vyy3002, vyy402, ty_Integer) → new_esEs16(vyy3002, vyy402)
new_esEs25(vyy1000, vyy1010, app(ty_Maybe, cab)) → new_esEs4(vyy1000, vyy1010, cab)
new_compare112(vyy1000, vyy1010, True) → LT
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_[], eh), ea) → new_esEs10(vyy3000, vyy400, eh)
new_compare15(vyy1000, vyy1010, ty_Bool) → new_compare13(vyy1000, vyy1010)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_lt19(vyy1000, vyy1010, app(app(ty_@2, caf), cag)) → new_lt12(vyy1000, vyy1010, caf, cag)
new_esEs13(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs12(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs18(vyy1001, vyy1011, app(ty_Maybe, bag)) → new_ltEs9(vyy1001, vyy1011, bag)
new_ltEs11(True, False) → False
new_esEs10([], [], bdf) → True
new_esEs5(Right(vyy3000), Right(vyy400), fd, app(app(ty_Either, gb), gc)) → new_esEs5(vyy3000, vyy400, gb, gc)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_compare14(Integer(vyy1000), Integer(vyy1010)) → new_primCmpInt(vyy1000, vyy1010)
new_compare15(vyy1000, vyy1010, app(ty_Ratio, bcb)) → new_compare18(vyy1000, vyy1010, bcb)
new_ltEs18(vyy1001, vyy1011, ty_@0) → new_ltEs12(vyy1001, vyy1011)
new_lt8(vyy1000, vyy1010) → new_esEs9(new_compare13(vyy1000, vyy1010), LT)
new_compare8(vyy1000, vyy1010, cf, cg) → new_compare28(vyy1000, vyy1010, new_esEs5(vyy1000, vyy1010, cf, cg), cf, cg)
new_compare5(:(vyy1000, vyy1001), :(vyy1010, vyy1011), dc) → new_primCompAux0(vyy1000, vyy1010, new_compare5(vyy1001, vyy1011, dc), dc)
new_ltEs4(GT, EQ) → False
new_primCompAux00(vyy178, LT) → LT
new_esEs27(vyy3001, vyy401, app(ty_Ratio, dbb)) → new_esEs15(vyy3001, vyy401, dbb)
new_compare114(vyy1000, vyy1010, True, cf, cg) → LT
new_primCmpInt(Neg(Succ(vyy10000)), Neg(vyy1010)) → new_primCmpNat0(vyy1010, Succ(vyy10000))
new_lt6(vyy1000, vyy1010, ty_Int) → new_lt17(vyy1000, vyy1010)
new_ltEs18(vyy1001, vyy1011, ty_Bool) → new_ltEs11(vyy1001, vyy1011)
new_primCompAux0(vyy1000, vyy1010, vyy169, dc) → new_primCompAux00(vyy169, new_compare15(vyy1000, vyy1010, dc))
new_lt14(vyy1000, vyy1010) → new_esEs9(new_compare6(vyy1000, vyy1010), LT)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(app(app(ty_@3, hh), baa), bab)) → new_ltEs6(vyy1000, vyy1010, hh, baa, bab)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_lt20(vyy1001, vyy1011, ty_Int) → new_lt17(vyy1001, vyy1011)
new_lt12(vyy1000, vyy1010, dd, de) → new_esEs9(new_compare10(vyy1000, vyy1010, dd, de), LT)
new_lt6(vyy1000, vyy1010, app(app(app(ty_@3, df), dg), dh)) → new_lt16(vyy1000, vyy1010, df, dg, dh)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Char) → new_ltEs10(vyy1000, vyy1010)
new_ltEs4(EQ, EQ) → True
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy10000), Zero) → GT
new_lt7(vyy1000, vyy1010) → new_esEs9(new_compare16(vyy1000, vyy1010), LT)
new_ltEs19(vyy1002, vyy1012, app(ty_Ratio, ccg)) → new_ltEs13(vyy1002, vyy1012, ccg)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(ty_Maybe, hb)) → new_ltEs9(vyy1000, vyy1010, hb)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(ty_[], cfa), cg) → new_ltEs7(vyy10000, vyy10100, cfa)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Bool) → new_ltEs11(vyy10000, vyy10100)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy10100))) → LT
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, bh), ca)) → new_esEs5(vyy3000, vyy400, bh, ca)
new_esEs20(vyy1000, vyy1010, app(app(ty_Either, cf), cg)) → new_esEs5(vyy1000, vyy1010, cf, cg)
new_ltEs4(GT, LT) → False
new_esEs21(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(ty_Ratio, cea), cg) → new_ltEs13(vyy10000, vyy10100, cea)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Bool) → new_ltEs11(vyy1000, vyy1010)
new_sr0(Integer(vyy10000), Integer(vyy10110)) → Integer(new_primMulInt(vyy10000, vyy10110))
new_primPlusNat1(Succ(vyy15400), Succ(vyy400000)) → Succ(Succ(new_primPlusNat1(vyy15400, vyy400000)))
new_ltEs18(vyy1001, vyy1011, app(app(ty_@2, bbc), bbd)) → new_ltEs15(vyy1001, vyy1011, bbc, bbd)
new_compare28(vyy1000, vyy1010, True, cf, cg) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dbg), dbh)) → new_esEs5(vyy3000, vyy400, dbg, dbh)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Int) → new_ltEs5(vyy10000, vyy10100)
new_esEs26(vyy3002, vyy402, ty_Double) → new_esEs13(vyy3002, vyy402)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Char) → new_ltEs10(vyy10000, vyy10100)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, cc), cd)) → new_esEs6(vyy3000, vyy400, cc, cd)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Integer) → new_ltEs16(vyy10000, vyy10100)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs11(vyy3000, vyy400)
new_compare15(vyy1000, vyy1010, ty_Integer) → new_compare14(vyy1000, vyy1010)
new_lt6(vyy1000, vyy1010, ty_Double) → new_lt15(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, app(app(ty_@2, bgb), bgc)) → new_esEs6(vyy3001, vyy401, bgb, bgc)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_ltEs9(Just(vyy1000), Nothing, ha) → False
new_esEs21(vyy3000, vyy400, ty_Char) → new_esEs11(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy10100))) → new_primCmpNat0(Zero, Succ(vyy10100))
new_primCompAux00(vyy178, EQ) → vyy178
new_esEs25(vyy1000, vyy1010, ty_@0) → new_esEs14(vyy1000, vyy1010)
new_ltEs15(@2(vyy1000, vyy1001), @2(vyy1010, vyy1011), bad, bae) → new_pePe(new_lt6(vyy1000, vyy1010, bad), new_asAs(new_esEs20(vyy1000, vyy1010, bad), new_ltEs18(vyy1001, vyy1011, bae)))
new_foldFM_GE10(vyy89, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba, bb) → new_foldFM_GE20(vyy330, vyy331, new_foldFM_GE0(vyy89, vyy40, vyy334, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb)
new_lt19(vyy1000, vyy1010, app(ty_[], cbc)) → new_lt5(vyy1000, vyy1010, cbc)
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_lt6(vyy1000, vyy1010, ty_Integer) → new_lt13(vyy1000, vyy1010)
new_esEs26(vyy3002, vyy402, ty_Char) → new_esEs11(vyy3002, vyy402)
new_esEs20(vyy1000, vyy1010, ty_Double) → new_esEs13(vyy1000, vyy1010)
new_compare114(vyy1000, vyy1010, False, cf, cg) → GT
new_not(False) → True
new_esEs10(:(vyy3000, vyy3001), :(vyy400, vyy401), bdf) → new_asAs(new_esEs21(vyy3000, vyy400, bdf), new_esEs10(vyy3001, vyy401, bdf))
new_lt20(vyy1001, vyy1011, ty_Bool) → new_lt8(vyy1001, vyy1011)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, ce)) → new_esEs15(vyy3000, vyy400, ce)
new_primPlusNat0(Zero, vyy40000) → Succ(vyy40000)
new_primCmpInt(Pos(Succ(vyy10000)), Pos(vyy1010)) → new_primCmpNat0(Succ(vyy10000), vyy1010)
new_ltEs18(vyy1001, vyy1011, app(ty_Ratio, bah)) → new_ltEs13(vyy1001, vyy1011, bah)
new_esEs23(vyy3000, vyy400, app(app(ty_@2, bhd), bhe)) → new_esEs6(vyy3000, vyy400, bhd, bhe)
new_esEs25(vyy1000, vyy1010, ty_Double) → new_esEs13(vyy1000, vyy1010)
new_ltEs9(Nothing, Nothing, ha) → True
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Ordering) → new_ltEs4(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_esEs9(GT, GT) → True
new_ltEs18(vyy1001, vyy1011, app(app(app(ty_@3, bbe), bbf), bbg)) → new_ltEs6(vyy1001, vyy1011, bbe, bbf, bbg)
new_lt5(vyy1000, vyy1010, da) → new_esEs9(new_compare5(vyy1000, vyy1010, da), LT)
new_foldFM_GE20(vyy330, vyy331, vyy113, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb) → new_foldFM_GE10(new_keysFM_GE0(vyy330, vyy331, vyy113, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, h, ba), h, ba, bb)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs14(vyy3001, vyy401)
new_ltEs19(vyy1002, vyy1012, app(app(app(ty_@3, cdd), cde), cdf)) → new_ltEs6(vyy1002, vyy1012, cdd, cde, cdf)
new_esEs23(vyy3000, vyy400, app(ty_[], bhc)) → new_esEs10(vyy3000, vyy400, bhc)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Double, ea) → new_esEs13(vyy3000, vyy400)
new_compare29(vyy1000, vyy1010, df, dg, dh) → new_compare25(vyy1000, vyy1010, new_esEs7(vyy1000, vyy1010, df, dg, dh), df, dg, dh)
new_ltEs11(False, False) → True
new_lt20(vyy1001, vyy1011, ty_Ordering) → new_lt18(vyy1001, vyy1011)
new_esEs21(vyy3000, vyy400, app(ty_Ratio, beh)) → new_esEs15(vyy3000, vyy400, beh)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Int, ea) → new_esEs12(vyy3000, vyy400)
new_esEs26(vyy3002, vyy402, app(app(ty_Either, chc), chd)) → new_esEs5(vyy3002, vyy402, chc, chd)
new_lt19(vyy1000, vyy1010, ty_Float) → new_lt14(vyy1000, vyy1010)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_lt19(vyy1000, vyy1010, app(app(app(ty_@3, cah), cba), cbb)) → new_lt16(vyy1000, vyy1010, cah, cba, cbb)
new_compare16(Char(vyy1000), Char(vyy1010)) → new_primCmpNat0(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs7(vyy3001, vyy401, bfc, bfd, bfe)
new_primCmpInt(Pos(Succ(vyy10000)), Neg(vyy1010)) → GT
new_esEs22(vyy3001, vyy401, ty_Char) → new_esEs11(vyy3001, vyy401)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(app(app(ty_@3, cef), ceg), ceh), cg) → new_ltEs6(vyy10000, vyy10100, cef, ceg, ceh)
new_esEs21(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs20(vyy1000, vyy1010, ty_Float) → new_esEs8(vyy1000, vyy1010)
new_lt20(vyy1001, vyy1011, ty_Double) → new_lt15(vyy1001, vyy1011)
new_primMulInt(Pos(vyy30000), Pos(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_esEs24(vyy1001, vyy1011, ty_Integer) → new_esEs16(vyy1001, vyy1011)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs7(vyy3000, vyy400, dbc, dbd, dbe)
new_esEs15(:%(vyy3000, vyy3001), :%(vyy400, vyy401), gh) → new_asAs(new_esEs19(vyy3000, vyy400, gh), new_esEs18(vyy3001, vyy401, gh))
new_lt6(vyy1000, vyy1010, ty_Ordering) → new_lt18(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, ty_Double) → new_esEs13(vyy3001, vyy401)
new_esEs20(vyy1000, vyy1010, ty_Char) → new_esEs11(vyy1000, vyy1010)
new_compare15(vyy1000, vyy1010, app(app(ty_@2, bce), bcf)) → new_compare10(vyy1000, vyy1010, bce, bcf)
new_esEs23(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Left(vyy400), fd, ea) → False
new_esEs5(Left(vyy3000), Right(vyy400), fd, ea) → False
new_esEs27(vyy3001, vyy401, app(app(ty_@2, dah), dba)) → new_esEs6(vyy3001, vyy401, dah, dba)
new_primMulInt(Neg(vyy30000), Neg(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_ltEs19(vyy1002, vyy1012, ty_Int) → new_ltEs5(vyy1002, vyy1012)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_@0) → new_ltEs12(vyy1000, vyy1010)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Bool, cg) → new_ltEs11(vyy10000, vyy10100)
new_lt20(vyy1001, vyy1011, app(app(ty_@2, cbh), cca)) → new_lt12(vyy1001, vyy1011, cbh, cca)
new_esEs18(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_esEs20(vyy1000, vyy1010, app(ty_[], da)) → new_esEs10(vyy1000, vyy1010, da)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, bc) → True
new_esEs22(vyy3001, vyy401, app(ty_Ratio, bgd)) → new_esEs15(vyy3001, vyy401, bgd)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(app(ty_Either, hd), he)) → new_ltEs14(vyy1000, vyy1010, hd, he)
new_esEs25(vyy1000, vyy1010, ty_Int) → new_esEs12(vyy1000, vyy1010)
new_compare15(vyy1000, vyy1010, ty_Float) → new_compare6(vyy1000, vyy1010)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_esEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bfa, bfb) → new_asAs(new_esEs23(vyy3000, vyy400, bfa), new_esEs22(vyy3001, vyy401, bfb))
new_esEs27(vyy3001, vyy401, app(ty_Maybe, dad)) → new_esEs4(vyy3001, vyy401, dad)
new_ltEs4(LT, GT) → True
new_compare15(vyy1000, vyy1010, ty_Int) → new_compare7(vyy1000, vyy1010)
new_lt13(vyy1000, vyy1010) → new_esEs9(new_compare14(vyy1000, vyy1010), LT)
new_esEs25(vyy1000, vyy1010, ty_Integer) → new_esEs16(vyy1000, vyy1010)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy10100))) → new_primCmpNat0(Succ(vyy10100), Zero)
new_esEs23(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy10100))) → GT
new_lt16(vyy1000, vyy1010, df, dg, dh) → new_esEs9(new_compare29(vyy1000, vyy1010, df, dg, dh), LT)
new_esEs12(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_lt20(vyy1001, vyy1011, ty_Char) → new_lt7(vyy1001, vyy1011)
new_ltEs19(vyy1002, vyy1012, app(ty_[], cdg)) → new_ltEs7(vyy1002, vyy1012, cdg)
new_lt20(vyy1001, vyy1011, app(ty_Maybe, cbd)) → new_lt9(vyy1001, vyy1011, cbd)
new_esEs5(Right(vyy3000), Right(vyy400), fd, app(app(app(ty_@3, ff), fg), fh)) → new_esEs7(vyy3000, vyy400, ff, fg, fh)
new_compare23(vyy1000, vyy1010, True, db) → EQ
new_esEs26(vyy3002, vyy402, ty_@0) → new_esEs14(vyy3002, vyy402)
new_lt11(vyy1000, vyy1010, baf) → new_esEs9(new_compare18(vyy1000, vyy1010, baf), LT)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dcb), dcc)) → new_esEs6(vyy3000, vyy400, dcb, dcc)
new_compare15(vyy1000, vyy1010, app(app(ty_Either, bcc), bcd)) → new_compare8(vyy1000, vyy1010, bcc, bcd)
new_esEs11(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_lt19(vyy1000, vyy1010, app(app(ty_Either, cad), cae)) → new_lt4(vyy1000, vyy1010, cad, cae)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Float, ea) → new_esEs8(vyy3000, vyy400)
new_compare5([], :(vyy1010, vyy1011), dc) → LT
new_lt6(vyy1000, vyy1010, ty_Float) → new_lt14(vyy1000, vyy1010)
new_esEs16(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs12(vyy100, vyy101) → new_not(new_esEs9(new_compare17(vyy100, vyy101), GT))
new_esEs24(vyy1001, vyy1011, app(ty_[], cce)) → new_esEs10(vyy1001, vyy1011, cce)
new_esEs21(vyy3000, vyy400, app(ty_Maybe, beb)) → new_esEs4(vyy3000, vyy400, beb)
new_esEs23(vyy3000, vyy400, app(ty_Ratio, bhf)) → new_esEs15(vyy3000, vyy400, bhf)
new_esEs23(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_compare24(vyy1000, vyy1010, False, dd, de) → new_compare110(vyy1000, vyy1010, new_ltEs15(vyy1000, vyy1010, dd, de), dd, de)
new_esEs24(vyy1001, vyy1011, app(app(app(ty_@3, ccb), ccc), ccd)) → new_esEs7(vyy1001, vyy1011, ccb, ccc, ccd)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs4(LT, EQ) → True
new_esEs21(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_lt6(vyy1000, vyy1010, app(ty_Maybe, db)) → new_lt9(vyy1000, vyy1010, db)
new_lt15(vyy1000, vyy1010) → new_esEs9(new_compare19(vyy1000, vyy1010), LT)
new_esEs24(vyy1001, vyy1011, ty_Char) → new_esEs11(vyy1001, vyy1011)
new_ltEs14(Left(vyy10000), Right(vyy10100), cf, cg) → True
new_asAs(False, vyy144) → False
new_ltEs11(True, True) → True
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs16(vyy3000, vyy400)
new_ltEs19(vyy1002, vyy1012, app(app(ty_Either, cch), cda)) → new_ltEs14(vyy1002, vyy1012, cch, cda)
new_primMulInt(Pos(vyy30000), Neg(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulInt(Neg(vyy30000), Pos(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_esEs26(vyy3002, vyy402, ty_Float) → new_esEs8(vyy3002, vyy402)
new_primMulNat0(Zero, Succ(vyy40000)) → Zero
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs13(vyy3001, vyy401)
new_esEs24(vyy1001, vyy1011, ty_Double) → new_esEs13(vyy1001, vyy1011)
new_esEs21(vyy3000, vyy400, app(app(ty_Either, bec), bed)) → new_esEs5(vyy3000, vyy400, bec, bed)
new_lt19(vyy1000, vyy1010, ty_Ordering) → new_lt18(vyy1000, vyy1010)
new_esEs28(vyy3000, vyy400, app(ty_[], dca)) → new_esEs10(vyy3000, vyy400, dca)
new_esEs22(vyy3001, vyy401, app(ty_[], bga)) → new_esEs10(vyy3001, vyy401, bga)
new_compare15(vyy1000, vyy1010, ty_Char) → new_compare16(vyy1000, vyy1010)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, app(app(ty_Either, cfd), cfe)) → new_ltEs14(vyy10000, vyy10100, cfd, cfe)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs13(vyy3000, vyy400)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Int) → new_ltEs5(vyy1000, vyy1010)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs8(vyy3000, vyy400)
new_compare27(vyy1000, vyy1010, True) → EQ
new_esEs27(vyy3001, vyy401, app(ty_[], dag)) → new_esEs10(vyy3001, vyy401, dag)
new_esEs20(vyy1000, vyy1010, ty_Ordering) → new_esEs9(vyy1000, vyy1010)
new_esEs19(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(ty_[], bac)) → new_ltEs7(vyy1000, vyy1010, bac)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(app(ty_Either, ceb), cec), cg) → new_ltEs14(vyy10000, vyy10100, ceb, cec)
new_esEs25(vyy1000, vyy1010, app(app(app(ty_@3, cah), cba), cbb)) → new_esEs7(vyy1000, vyy1010, cah, cba, cbb)
new_lt20(vyy1001, vyy1011, app(app(app(ty_@3, ccb), ccc), ccd)) → new_lt16(vyy1001, vyy1011, ccb, ccc, ccd)
new_lt19(vyy1000, vyy1010, ty_Integer) → new_lt13(vyy1000, vyy1010)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Bool, ea) → new_esEs17(vyy3000, vyy400)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Float) → new_ltEs8(vyy1000, vyy1010)
new_esEs5(Right(vyy3000), Right(vyy400), fd, app(ty_Maybe, ga)) → new_esEs4(vyy3000, vyy400, ga)
new_compare10(vyy1000, vyy1010, dd, de) → new_compare24(vyy1000, vyy1010, new_esEs6(vyy1000, vyy1010, dd, de), dd, de)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Int) → new_esEs12(vyy3000, vyy400)
new_ltEs4(LT, LT) → True
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_esEs20(vyy1000, vyy1010, ty_Int) → new_esEs12(vyy1000, vyy1010)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_@0) → new_ltEs12(vyy10000, vyy10100)
new_esEs26(vyy3002, vyy402, ty_Bool) → new_esEs17(vyy3002, vyy402)
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_ltEs19(vyy1002, vyy1012, app(app(ty_@2, cdb), cdc)) → new_ltEs15(vyy1002, vyy1012, cdb, cdc)
new_esEs22(vyy3001, vyy401, ty_@0) → new_esEs14(vyy3001, vyy401)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_Either, ef), eg), ea) → new_esEs5(vyy3000, vyy400, ef, eg)
new_compare15(vyy1000, vyy1010, ty_@0) → new_compare17(vyy1000, vyy1010)
new_compare112(vyy1000, vyy1010, False) → GT
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Float) → new_ltEs8(vyy10000, vyy10100)
new_esEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cgd, cge, cgf) → new_asAs(new_esEs28(vyy3000, vyy400, cgd), new_asAs(new_esEs27(vyy3001, vyy401, cge), new_esEs26(vyy3002, vyy402, cgf)))
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Ratio, fc), ea) → new_esEs15(vyy3000, vyy400, fc)
new_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, app(ty_Ratio, cfc)) → new_ltEs13(vyy10000, vyy10100, cfc)
new_compare26(vyy1000, vyy1010, False) → new_compare112(vyy1000, vyy1010, new_ltEs4(vyy1000, vyy1010))
new_esEs24(vyy1001, vyy1011, ty_Ordering) → new_esEs9(vyy1001, vyy1011)
new_lt19(vyy1000, vyy1010, ty_@0) → new_lt10(vyy1000, vyy1010)
new_esEs21(vyy3000, vyy400, ty_Float) → new_esEs8(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, ty_Float) → new_esEs8(vyy3000, vyy400)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Ordering) → new_ltEs4(vyy10000, vyy10100)
new_lt9(vyy1000, vyy1010, db) → new_esEs9(new_compare9(vyy1000, vyy1010, db), LT)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(vyy3002, vyy402, ty_Ordering) → new_esEs9(vyy3002, vyy402)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Char, cg) → new_ltEs10(vyy10000, vyy10100)
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Char) → new_esEs11(vyy3000, vyy400)
new_asAs(True, vyy144) → vyy144
new_ltEs16(vyy100, vyy101) → new_not(new_esEs9(new_compare14(vyy100, vyy101), GT))
new_primMulNat0(Succ(vyy300000), Succ(vyy40000)) → new_primPlusNat0(new_primMulNat0(vyy300000, Succ(vyy40000)), vyy40000)
new_compare28(vyy1000, vyy1010, False, cf, cg) → new_compare114(vyy1000, vyy1010, new_ltEs14(vyy1000, vyy1010, cf, cg), cf, cg)
new_compare15(vyy1000, vyy1010, app(ty_Maybe, bca)) → new_compare9(vyy1000, vyy1010, bca)
new_lt19(vyy1000, vyy1010, ty_Int) → new_lt17(vyy1000, vyy1010)
new_esEs26(vyy3002, vyy402, app(app(ty_@2, chf), chg)) → new_esEs6(vyy3002, vyy402, chf, chg)
new_lt20(vyy1001, vyy1011, app(ty_[], cce)) → new_lt5(vyy1001, vyy1011, cce)
new_compare5([], [], dc) → EQ
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bd), be), bf)) → new_esEs7(vyy3000, vyy400, bd, be, bf)
new_ltEs4(GT, GT) → True
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs11(vyy3001, vyy401)
new_lt6(vyy1000, vyy1010, ty_Bool) → new_lt8(vyy1000, vyy1010)
new_esEs9(LT, LT) → True
new_esEs22(vyy3001, vyy401, app(app(ty_Either, bfg), bfh)) → new_esEs5(vyy3001, vyy401, bfg, bfh)
new_primCompAux00(vyy178, GT) → GT
new_esEs5(Right(vyy3000), Right(vyy400), fd, app(ty_Ratio, gg)) → new_esEs15(vyy3000, vyy400, gg)
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs8(vyy3001, vyy401)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(vyy1000, vyy1010, app(app(ty_@2, dd), de)) → new_lt12(vyy1000, vyy1010, dd, de)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, app(ty_Maybe, cfb)) → new_ltEs9(vyy10000, vyy10100, cfb)
new_compare9(vyy1000, vyy1010, db) → new_compare23(vyy1000, vyy1010, new_esEs4(vyy1000, vyy1010, db), db)
new_foldFM_GE0(vyy89, vyy40, EmptyFM, h, ba, bb) → vyy89
new_esEs8(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs12(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(vyy1002, vyy1012, ty_Bool) → new_ltEs11(vyy1002, vyy1012)
new_primCmpInt(Neg(Succ(vyy10000)), Pos(vyy1010)) → LT
new_compare15(vyy1000, vyy1010, ty_Ordering) → new_compare12(vyy1000, vyy1010)
new_not(True) → False

The set Q consists of the following terms:

new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_compare15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_lt6(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Bool)
new_compare15(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(x0, x1, x2)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Bool)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs18(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(Integer(x0), Integer(x1))
new_gtEs(x0, x1, x2, x3)
new_compare15(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_compare9(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare15(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs23(x0, x1, ty_Double)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1)
new_esEs23(x0, x1, ty_@0)
new_compare17(@0, @0)
new_compare12(x0, x1)
new_esEs21(x0, x1, ty_Double)
new_compare15(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt16(x0, x1, x2, x3, x4)
new_esEs17(False, False)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primMulNat0(Zero, Succ(x0))
new_compare14(Integer(x0), Integer(x1))
new_compare16(Char(x0), Char(x1))
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_compare112(x0, x1, True)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Nothing, x1)
new_esEs23(x0, x1, ty_Int)
new_compare28(x0, x1, True, x2, x3)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_primEqNat0(Zero, Zero)
new_esEs20(x0, x1, ty_Bool)
new_esEs11(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_esEs21(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs16(x0, x1)
new_foldFM_GE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_compare26(x0, x1, True)
new_lt19(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Zero)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_compare15(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_primCompAux00(x0, EQ)
new_ltEs4(GT, GT)
new_compare24(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs4(Nothing, Just(x0), x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primPlusNat0(Succ(x0), x1)
new_esEs25(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_compare27(x0, x1, True)
new_compare13(x0, x1)
new_compare15(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primPlusNat0(Zero, x0)
new_esEs14(@0, @0)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare114(x0, x1, False, x2, x3)
new_lt15(x0, x1)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_pePe(True, x0)
new_lt6(x0, x1, ty_Bool)
new_lt5(x0, x1, x2)
new_keysFM_GE0(x0, x1, x2, x3, x4, x5)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_compare113(x0, x1, False, x2)
new_foldFM_GE0(x0, x1, EmptyFM, x2, x3, x4)
new_esEs27(x0, x1, ty_Bool)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_ltEs17(x0, x1)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_Double)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, ty_@0)
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Char)
new_compare15(x0, x1, app(ty_Maybe, x2))
new_lt14(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs10(:(x0, x1), [], x2)
new_compare23(x0, x1, False, x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_lt6(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs10([], :(x0, x1), x2)
new_ltEs4(EQ, EQ)
new_esEs26(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs9(Nothing, Nothing, x0)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_lt17(x0, x1)
new_esEs27(x0, x1, ty_Int)
new_ltEs4(EQ, LT)
new_ltEs4(LT, EQ)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_foldFM_GE10(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, True, x11, x12, x13)
new_foldFM_GE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare15(x0, x1, ty_Integer)
new_esEs9(GT, GT)
new_compare10(x0, x1, x2, x3)
new_foldFM_GE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_compare112(x0, x1, False)
new_ltEs18(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_compare11(x0, x1, True, x2, x3, x4)
new_compare27(x0, x1, False)
new_compare15(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs9(Nothing, Just(x0), x1)
new_ltEs11(False, False)
new_esEs22(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare6(Float(x0, x1), Float(x2, x3))
new_esEs10(:(x0, x1), :(x2, x3), x4)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_ltEs11(False, True)
new_ltEs11(True, False)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(LT, LT)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(x0, x1, ty_Float)
new_compare24(x0, x1, False, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_lt20(x0, x1, ty_Ordering)
new_compare15(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs22(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs28(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Double)
new_lt20(x0, x1, ty_@0)
new_ltEs12(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare5(:(x0, x1), :(x2, x3), x4)
new_esEs4(Nothing, Nothing, x0)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primEqNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare19(Double(x0, x1), Double(x2, x3))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3, x4)
new_esEs8(Float(x0, x1), Float(x2, x3))
new_compare15(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs28(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs24(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs21(x0, x1, ty_Bool)
new_compare113(x0, x1, True, x2)
new_compare111(x0, x1, False)
new_lt19(x0, x1, ty_Bool)
new_esEs15(:%(x0, x1), :%(x2, x3), x4)
new_compare5([], [], x0)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt6(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs27(x0, x1, ty_Double)
new_compare5(:(x0, x1), [], x2)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs5(x0, x1)
new_esEs22(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, ty_@0)
new_compare29(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Char)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare15(x0, x1, ty_Float)
new_primCompAux0(x0, x1, x2, x3)
new_lt9(x0, x1, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_sr0(Integer(x0), Integer(x1))
new_ltEs18(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, False, x2, x3, x4)
new_primCompAux00(x0, GT)
new_primCompAux00(x0, LT)
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_lt11(x0, x1, x2)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs20(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_foldFM_GE10(x0, x1, x2, x3, x4, EmptyFM, x5, True, x6, x7, x8)
new_lt8(x0, x1)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_asAs(True, x0)
new_esEs28(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primPlusNat1(Succ(x0), Zero)
new_esEs27(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10([], [], x0)
new_lt6(x0, x1, ty_Char)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Integer)
new_compare7(x0, x1)
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs23(x0, x1, ty_Char)
new_primMulNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_foldFM_GE3(x0, x1, x2, x3, x4, x5, x6)
new_ltEs8(x0, x1)
new_pePe(False, x0)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs17(True, False)
new_esEs17(False, True)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs19(x0, x1, ty_@0)
new_compare23(x0, x1, True, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, x2, x3)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare114(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqNat0(Succ(x0), Zero)
new_esEs24(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(x0, x1)
new_lt6(x0, x1, ty_@0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_compare111(x0, x1, True)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_ltEs11(True, True)
new_lt10(x0, x1)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(LT, LT)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, ty_Double)
new_compare26(x0, x1, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_compare5([], :(x0, x1), x2)
new_compare8(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))

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

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

new_foldFM_GE11(vyy88, vyy13, vyy170, vyy171, vyy172, Branch(vyy1730, vyy1731, vyy1732, vyy1733, vyy1734), vyy174, True, h, ba, bb) → new_foldFM_GE4(vyy88, vyy13, vyy174, h, ba, bb)
new_foldFM_GE11(vyy88, vyy13, vyy170, vyy171, vyy172, Branch(vyy1730, vyy1731, vyy1732, vyy1733, vyy1734), vyy174, True, h, ba, bb) → new_foldFM_GE21(vyy170, vyy171, new_foldFM_GE5(vyy88, vyy13, vyy174, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb)
new_foldFM_GE21(vyy170, vyy171, vyy111, vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb) → new_foldFM_GE11(new_keysFM_GE0(vyy170, vyy171, vyy111, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, new_gtEs0(vyy1730, vyy13, h, ba), h, ba, bb)
new_foldFM_GE4(vyy88, vyy13, Branch(vyy1740, vyy1741, vyy1742, vyy1743, vyy1744), h, ba, bb) → new_foldFM_GE11(vyy88, vyy13, vyy1740, vyy1741, vyy1742, vyy1743, vyy1744, new_gtEs0(vyy1740, vyy13, h, ba), h, ba, bb)
new_foldFM_GE11(vyy88, vyy13, vyy170, vyy171, vyy172, vyy173, Branch(vyy1740, vyy1741, vyy1742, vyy1743, vyy1744), False, h, ba, bb) → new_foldFM_GE11(vyy88, vyy13, vyy1740, vyy1741, vyy1742, vyy1743, vyy1744, new_gtEs0(vyy1740, vyy13, h, ba), h, ba, bb)
new_foldFM_GE11(vyy88, vyy13, vyy170, vyy171, vyy172, EmptyFM, vyy174, True, h, ba, bb) → new_foldFM_GE4(vyy88, vyy13, vyy174, h, ba, bb)

The TRS R consists of the following rules:

new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, bg)) → new_esEs4(vyy3000, vyy400, bg)
new_ltEs19(vyy1002, vyy1012, ty_Integer) → new_ltEs16(vyy1002, vyy1012)
new_esEs24(vyy1001, vyy1011, app(app(ty_Either, cbc), cbd)) → new_esEs5(vyy1001, vyy1011, cbc, cbd)
new_lt19(vyy1000, vyy1010, ty_Char) → new_lt7(vyy1000, vyy1010)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Integer, cg) → new_ltEs16(vyy10000, vyy10100)
new_esEs21(vyy3000, vyy400, app(app(ty_@2, bec), bed)) → new_esEs6(vyy3000, vyy400, bec, bed)
new_ltEs18(vyy1001, vyy1011, ty_Float) → new_ltEs8(vyy1001, vyy1011)
new_esEs24(vyy1001, vyy1011, app(ty_Ratio, cbb)) → new_esEs15(vyy1001, vyy1011, cbb)
new_ltEs4(EQ, GT) → True
new_esEs5(Left(vyy3000), Left(vyy400), ty_@0, ea) → new_esEs14(vyy3000, vyy400)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Double) → new_ltEs17(vyy1000, vyy1010)
new_esEs26(vyy3002, vyy402, app(ty_Ratio, che)) → new_esEs15(vyy3002, vyy402, che)
new_ltEs6(@3(vyy1000, vyy1001, vyy1002), @3(vyy1010, vyy1011, vyy1012), bhd, bhe, bhf) → new_pePe(new_lt19(vyy1000, vyy1010, bhd), new_asAs(new_esEs25(vyy1000, vyy1010, bhd), new_pePe(new_lt20(vyy1001, vyy1011, bhe), new_asAs(new_esEs24(vyy1001, vyy1011, bhe), new_ltEs19(vyy1002, vyy1012, bhf)))))
new_esEs18(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_lt6(vyy1000, vyy1010, ty_Char) → new_lt7(vyy1000, vyy1010)
new_compare110(vyy1000, vyy1010, True, dd, de) → LT
new_esEs23(vyy3000, vyy400, app(app(ty_Either, bgf), bgg)) → new_esEs5(vyy3000, vyy400, bgf, bgg)
new_ltEs8(vyy100, vyy101) → new_not(new_esEs9(new_compare6(vyy100, vyy101), GT))
new_esEs24(vyy1001, vyy1011, app(ty_Maybe, cba)) → new_esEs4(vyy1001, vyy1011, cba)
new_esEs4(Nothing, Just(vyy400), bc) → False
new_esEs4(Just(vyy3000), Nothing, bc) → False
new_lt20(vyy1001, vyy1011, ty_Float) → new_lt14(vyy1001, vyy1011)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dca)) → new_esEs15(vyy3000, vyy400, dca)
new_ltEs9(Nothing, Just(vyy1010), ha) → True
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs14(vyy3000, vyy400)
new_lt19(vyy1000, vyy1010, ty_Double) → new_lt15(vyy1000, vyy1010)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Double) → new_ltEs17(vyy10000, vyy10100)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Integer) → new_ltEs16(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, ty_Ordering) → new_esEs9(vyy3001, vyy401)
new_lt10(vyy1000, vyy1010) → new_esEs9(new_compare17(vyy1000, vyy1010), LT)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(ty_Ratio, hc)) → new_ltEs13(vyy1000, vyy1010, hc)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_lt18(vyy1000, vyy1010) → new_esEs9(new_compare12(vyy1000, vyy1010), LT)
new_foldFM_GE12(vyy88, vyy13, vyy170, vyy171, vyy172, Branch(vyy1730, vyy1731, vyy1732, vyy1733, vyy1734), vyy174, True, h, ba, bb) → new_foldFM_GE22(vyy170, vyy171, new_foldFM_GE5(vyy88, vyy13, vyy174, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb)
new_esEs21(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_primMulNat0(Zero, Zero) → Zero
new_compare15(vyy1000, vyy1010, ty_Double) → new_compare19(vyy1000, vyy1010)
new_ltEs18(vyy1001, vyy1011, ty_Integer) → new_ltEs16(vyy1001, vyy1011)
new_esEs20(vyy1000, vyy1010, app(ty_Maybe, db)) → new_esEs4(vyy1000, vyy1010, db)
new_lt19(vyy1000, vyy1010, app(ty_Maybe, bhg)) → new_lt9(vyy1000, vyy1010, bhg)
new_esEs21(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs21(vyy3000, vyy400, app(ty_[], beb)) → new_esEs10(vyy3000, vyy400, beb)
new_esEs25(vyy1000, vyy1010, ty_Bool) → new_esEs17(vyy1000, vyy1010)
new_esEs24(vyy1001, vyy1011, ty_@0) → new_esEs14(vyy1001, vyy1011)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, app(ty_[], cfh)) → new_ltEs7(vyy10000, vyy10100, cfh)
new_esEs23(vyy3000, vyy400, app(ty_Maybe, bge)) → new_esEs4(vyy3000, vyy400, bge)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(app(ty_@2, hf), hg)) → new_ltEs15(vyy1000, vyy1010, hf, hg)
new_esEs17(True, True) → True
new_esEs26(vyy3002, vyy402, app(ty_[], chb)) → new_esEs10(vyy3002, vyy402, chb)
new_lt6(vyy1000, vyy1010, ty_@0) → new_lt10(vyy1000, vyy1010)
new_lt6(vyy1000, vyy1010, app(ty_[], da)) → new_lt5(vyy1000, vyy1010, da)
new_esEs21(vyy3000, vyy400, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs7(vyy3000, vyy400, bdd, bde, bdf)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, app(app(app(ty_@3, cfe), cff), cfg)) → new_ltEs6(vyy10000, vyy10100, cfe, cff, cfg)
new_esEs23(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Char, ea) → new_esEs11(vyy3000, vyy400)
new_esEs20(vyy1000, vyy1010, app(app(ty_@2, dd), de)) → new_esEs6(vyy1000, vyy1010, dd, de)
new_esEs26(vyy3002, vyy402, app(ty_Maybe, cgg)) → new_esEs4(vyy3002, vyy402, cgg)
new_ltEs18(vyy1001, vyy1011, app(ty_[], bbh)) → new_ltEs7(vyy1001, vyy1011, bbh)
new_esEs20(vyy1000, vyy1010, ty_@0) → new_esEs14(vyy1000, vyy1010)
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_@0) → new_esEs14(vyy3000, vyy400)
new_esEs25(vyy1000, vyy1010, app(ty_[], cah)) → new_esEs10(vyy1000, vyy1010, cah)
new_pePe(False, vyy168) → vyy168
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs12(vyy3000, vyy400)
new_esEs25(vyy1000, vyy1010, ty_Char) → new_esEs11(vyy1000, vyy1010)
new_ltEs17(vyy100, vyy101) → new_not(new_esEs9(new_compare19(vyy100, vyy101), GT))
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Int, cg) → new_ltEs5(vyy10000, vyy10100)
new_compare23(vyy1000, vyy1010, False, db) → new_compare113(vyy1000, vyy1010, new_ltEs9(vyy1000, vyy1010, db), db)
new_esEs25(vyy1000, vyy1010, ty_Float) → new_esEs8(vyy1000, vyy1010)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs9(vyy3001, vyy401)
new_compare11(vyy1000, vyy1010, False, df, dg, dh) → GT
new_ltEs18(vyy1001, vyy1011, app(app(ty_Either, bba), bbb)) → new_ltEs14(vyy1001, vyy1011, bba, bbb)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_ltEs11(False, True) → True
new_lt17(vyy1000, vyy1010) → new_esEs9(new_compare7(vyy1000, vyy1010), LT)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_@2, fa), fb), ea) → new_esEs6(vyy3000, vyy400, fa, fb)
new_compare111(vyy1000, vyy1010, False) → GT
new_keysFM_GE0(vyy170, vyy171, vyy110, h, ba, bb) → :(vyy170, vyy110)
new_compare111(vyy1000, vyy1010, True) → LT
new_ltEs19(vyy1002, vyy1012, ty_Double) → new_ltEs17(vyy1002, vyy1012)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Maybe, ee), ea) → new_esEs4(vyy3000, vyy400, ee)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Float, cg) → new_ltEs8(vyy10000, vyy10100)
new_compare15(vyy1000, vyy1010, app(app(app(ty_@3, bcg), bch), bda)) → new_compare29(vyy1000, vyy1010, bcg, bch, bda)
new_compare13(vyy1000, vyy1010) → new_compare27(vyy1000, vyy1010, new_esEs17(vyy1000, vyy1010))
new_esEs23(vyy3000, vyy400, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs7(vyy3000, vyy400, bgb, bgc, bgd)
new_primCmpNat0(Zero, Succ(vyy10100)) → LT
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, chf), chg), chh)) → new_esEs7(vyy3001, vyy401, chf, chg, chh)
new_compare113(vyy1000, vyy1010, True, db) → LT
new_esEs25(vyy1000, vyy1010, app(app(ty_Either, caa), cab)) → new_esEs5(vyy1000, vyy1010, caa, cab)
new_esEs25(vyy1000, vyy1010, app(app(ty_@2, cac), cad)) → new_esEs6(vyy1000, vyy1010, cac, cad)
new_compare6(Float(vyy1000, vyy1001), Float(vyy1010, vyy1011)) → new_compare7(new_sr(vyy1000, vyy1010), new_sr(vyy1001, vyy1011))
new_compare25(vyy1000, vyy1010, True, df, dg, dh) → EQ
new_ltEs13(vyy100, vyy101, dcb) → new_not(new_esEs9(new_compare18(vyy100, vyy101, dcb), GT))
new_lt6(vyy1000, vyy1010, app(app(ty_Either, cf), cg)) → new_lt4(vyy1000, vyy1010, cf, cg)
new_esEs24(vyy1001, vyy1011, ty_Int) → new_esEs12(vyy1001, vyy1011)
new_ltEs10(vyy100, vyy101) → new_not(new_esEs9(new_compare16(vyy100, vyy101), GT))
new_compare18(:%(vyy1000, vyy1001), :%(vyy1010, vyy1011), ty_Int) → new_compare7(new_sr(vyy1000, vyy1011), new_sr(vyy1010, vyy1001))
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs24(vyy1001, vyy1011, app(app(ty_@2, cbe), cbf)) → new_esEs6(vyy1001, vyy1011, cbe, cbf)
new_pePe(True, vyy168) → True
new_primEqNat0(Zero, Zero) → True
new_compare26(vyy1000, vyy1010, True) → EQ
new_ltEs18(vyy1001, vyy1011, ty_Double) → new_ltEs17(vyy1001, vyy1011)
new_esEs5(Right(vyy3000), Right(vyy400), fd, app(app(ty_@2, ge), gf)) → new_esEs6(vyy3000, vyy400, ge, gf)
new_compare12(vyy1000, vyy1010) → new_compare26(vyy1000, vyy1010, new_esEs9(vyy1000, vyy1010))
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Ordering, cg) → new_ltEs4(vyy10000, vyy10100)
new_esEs14(@0, @0) → True
new_compare17(@0, @0) → EQ
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs11(vyy3000, vyy400)
new_esEs20(vyy1000, vyy1010, app(ty_Ratio, baf)) → new_esEs15(vyy1000, vyy1010, baf)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Ordering, ea) → new_esEs9(vyy3000, vyy400)
new_ltEs5(vyy100, vyy101) → new_not(new_esEs9(new_compare7(vyy100, vyy101), GT))
new_esEs5(Right(vyy3000), Right(vyy400), fd, app(ty_[], gd)) → new_esEs10(vyy3000, vyy400, gd)
new_esEs19(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy1002, vyy1012, ty_Float) → new_ltEs8(vyy1002, vyy1012)
new_lt4(vyy1000, vyy1010, cf, cg) → new_esEs9(new_compare8(vyy1000, vyy1010, cf, cg), LT)
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_foldFM_GE12(vyy88, vyy13, vyy170, vyy171, vyy172, EmptyFM, vyy174, True, h, ba, bb) → new_foldFM_GE30(vyy170, vyy171, new_foldFM_GE5(vyy88, vyy13, vyy174, h, ba, bb), vyy13, h, ba, bb)
new_compare110(vyy1000, vyy1010, False, dd, de) → GT
new_compare25(vyy1000, vyy1010, False, df, dg, dh) → new_compare11(vyy1000, vyy1010, new_ltEs6(vyy1000, vyy1010, df, dg, dh), df, dg, dh)
new_ltEs18(vyy1001, vyy1011, ty_Int) → new_ltEs5(vyy1001, vyy1011)
new_ltEs18(vyy1001, vyy1011, ty_Char) → new_ltEs10(vyy1001, vyy1011)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], cb)) → new_esEs10(vyy3000, vyy400, cb)
new_sr(vyy3000, vyy400) → new_primMulInt(vyy3000, vyy400)
new_esEs24(vyy1001, vyy1011, ty_Bool) → new_esEs17(vyy1001, vyy1011)
new_compare7(vyy100, vyy101) → new_primCmpInt(vyy100, vyy101)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(ty_Maybe, cde), cg) → new_ltEs9(vyy10000, vyy10100, cde)
new_ltEs19(vyy1002, vyy1012, ty_@0) → new_ltEs12(vyy1002, vyy1012)
new_compare18(:%(vyy1000, vyy1001), :%(vyy1010, vyy1011), ty_Integer) → new_compare14(new_sr0(vyy1000, vyy1011), new_sr0(vyy1010, vyy1001))
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs19(vyy1002, vyy1012, ty_Char) → new_ltEs10(vyy1002, vyy1012)
new_esEs26(vyy3002, vyy402, ty_Int) → new_esEs12(vyy3002, vyy402)
new_compare113(vyy1000, vyy1010, False, db) → GT
new_primPlusNat0(Succ(vyy1540), vyy40000) → Succ(Succ(new_primPlusNat1(vyy1540, vyy40000)))
new_esEs22(vyy3001, vyy401, ty_Float) → new_esEs8(vyy3001, vyy401)
new_compare15(vyy1000, vyy1010, app(ty_[], bdb)) → new_compare5(vyy1000, vyy1010, bdb)
new_lt19(vyy1000, vyy1010, app(ty_Ratio, bhh)) → new_lt11(vyy1000, vyy1010, bhh)
new_esEs20(vyy1000, vyy1010, app(app(app(ty_@3, df), dg), dh)) → new_esEs7(vyy1000, vyy1010, df, dg, dh)
new_esEs20(vyy1000, vyy1010, ty_Bool) → new_esEs17(vyy1000, vyy1010)
new_ltEs19(vyy1002, vyy1012, app(ty_Maybe, ccc)) → new_ltEs9(vyy1002, vyy1012, ccc)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_esEs21(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Double, cg) → new_ltEs17(vyy10000, vyy10100)
new_esEs9(EQ, EQ) → True
new_lt19(vyy1000, vyy1010, ty_Bool) → new_lt8(vyy1000, vyy1010)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Integer, ea) → new_esEs16(vyy3000, vyy400)
new_lt20(vyy1001, vyy1011, app(ty_Ratio, cbb)) → new_lt11(vyy1001, vyy1011, cbb)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs8(vyy3000, vyy400)
new_primPlusNat1(Zero, Succ(vyy400000)) → Succ(vyy400000)
new_primPlusNat1(Succ(vyy15400), Zero) → Succ(vyy15400)
new_esEs26(vyy3002, vyy402, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs7(vyy3002, vyy402, cgd, cge, cgf)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dbc)) → new_esEs4(vyy3000, vyy400, dbc)
new_compare19(Double(vyy1000, vyy1001), Double(vyy1010, vyy1011)) → new_compare7(new_sr(vyy1000, vyy1010), new_sr(vyy1001, vyy1011))
new_ltEs14(Right(vyy10000), Left(vyy10100), cf, cg) → False
new_lt20(vyy1001, vyy1011, app(app(ty_Either, cbc), cbd)) → new_lt4(vyy1001, vyy1011, cbc, cbd)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, eb), ec), ed), ea) → new_esEs7(vyy3000, vyy400, eb, ec, ed)
new_compare27(vyy1000, vyy1010, False) → new_compare111(vyy1000, vyy1010, new_ltEs11(vyy1000, vyy1010))
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_esEs23(vyy3000, vyy400, ty_Char) → new_esEs11(vyy3000, vyy400)
new_compare11(vyy1000, vyy1010, True, df, dg, dh) → LT
new_ltEs19(vyy1002, vyy1012, ty_Ordering) → new_ltEs4(vyy1002, vyy1012)
new_lt6(vyy1000, vyy1010, app(ty_Ratio, baf)) → new_lt11(vyy1000, vyy1010, baf)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, app(app(ty_Either, dab), dac)) → new_esEs5(vyy3001, vyy401, dab, dac)
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Float) → new_esEs8(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(app(ty_@2, cea), ceb), cg) → new_ltEs15(vyy10000, vyy10100, cea, ceb)
new_esEs25(vyy1000, vyy1010, app(ty_Ratio, bhh)) → new_esEs15(vyy1000, vyy1010, bhh)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_esEs25(vyy1000, vyy1010, ty_Ordering) → new_esEs9(vyy1000, vyy1010)
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_lt20(vyy1001, vyy1011, ty_@0) → new_lt10(vyy1001, vyy1011)
new_esEs20(vyy1000, vyy1010, ty_Integer) → new_esEs16(vyy1000, vyy1010)
new_compare24(vyy1000, vyy1010, True, dd, de) → EQ
new_ltEs7(vyy100, vyy101, dc) → new_not(new_esEs9(new_compare5(vyy100, vyy101, dc), GT))
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_@0, cg) → new_ltEs12(vyy10000, vyy10100)
new_esEs24(vyy1001, vyy1011, ty_Float) → new_esEs8(vyy1001, vyy1011)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs18(vyy1001, vyy1011, ty_Ordering) → new_ltEs4(vyy1001, vyy1011)
new_ltEs4(EQ, LT) → False
new_esEs10([], :(vyy400, vyy401), bdc) → False
new_esEs10(:(vyy3000, vyy3001), [], bdc) → False
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, app(app(ty_@2, cfc), cfd)) → new_ltEs15(vyy10000, vyy10100, cfc, cfd)
new_lt20(vyy1001, vyy1011, ty_Integer) → new_lt13(vyy1001, vyy1011)
new_primCmpNat0(Succ(vyy10000), Succ(vyy10100)) → new_primCmpNat0(vyy10000, vyy10100)
new_esEs22(vyy3001, vyy401, app(ty_Maybe, bfc)) → new_esEs4(vyy3001, vyy401, bfc)
new_compare5(:(vyy1000, vyy1001), [], dc) → GT
new_esEs26(vyy3002, vyy402, ty_Integer) → new_esEs16(vyy3002, vyy402)
new_esEs25(vyy1000, vyy1010, app(ty_Maybe, bhg)) → new_esEs4(vyy1000, vyy1010, bhg)
new_compare112(vyy1000, vyy1010, True) → LT
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_[], eh), ea) → new_esEs10(vyy3000, vyy400, eh)
new_compare15(vyy1000, vyy1010, ty_Bool) → new_compare13(vyy1000, vyy1010)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_lt19(vyy1000, vyy1010, app(app(ty_@2, cac), cad)) → new_lt12(vyy1000, vyy1010, cac, cad)
new_esEs13(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs12(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs18(vyy1001, vyy1011, app(ty_Maybe, bag)) → new_ltEs9(vyy1001, vyy1011, bag)
new_ltEs11(True, False) → False
new_esEs10([], [], bdc) → True
new_esEs5(Right(vyy3000), Right(vyy400), fd, app(app(ty_Either, gb), gc)) → new_esEs5(vyy3000, vyy400, gb, gc)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_compare14(Integer(vyy1000), Integer(vyy1010)) → new_primCmpInt(vyy1000, vyy1010)
new_compare15(vyy1000, vyy1010, app(ty_Ratio, bcb)) → new_compare18(vyy1000, vyy1010, bcb)
new_ltEs18(vyy1001, vyy1011, ty_@0) → new_ltEs12(vyy1001, vyy1011)
new_lt8(vyy1000, vyy1010) → new_esEs9(new_compare13(vyy1000, vyy1010), LT)
new_compare8(vyy1000, vyy1010, cf, cg) → new_compare28(vyy1000, vyy1010, new_esEs5(vyy1000, vyy1010, cf, cg), cf, cg)
new_compare5(:(vyy1000, vyy1001), :(vyy1010, vyy1011), dc) → new_primCompAux0(vyy1000, vyy1010, new_compare5(vyy1001, vyy1011, dc), dc)
new_ltEs4(GT, EQ) → False
new_primCompAux00(vyy178, LT) → LT
new_esEs27(vyy3001, vyy401, app(ty_Ratio, dag)) → new_esEs15(vyy3001, vyy401, dag)
new_compare114(vyy1000, vyy1010, True, cf, cg) → LT
new_primCmpInt(Neg(Succ(vyy10000)), Neg(vyy1010)) → new_primCmpNat0(vyy1010, Succ(vyy10000))
new_lt6(vyy1000, vyy1010, ty_Int) → new_lt17(vyy1000, vyy1010)
new_ltEs18(vyy1001, vyy1011, ty_Bool) → new_ltEs11(vyy1001, vyy1011)
new_primCompAux0(vyy1000, vyy1010, vyy169, dc) → new_primCompAux00(vyy169, new_compare15(vyy1000, vyy1010, dc))
new_foldFM_GE30(vyy170, vyy171, vyy110, vyy13, h, ba, bb) → new_keysFM_GE0(vyy170, vyy171, vyy110, h, ba, bb)
new_lt14(vyy1000, vyy1010) → new_esEs9(new_compare6(vyy1000, vyy1010), LT)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(app(app(ty_@3, hh), baa), bab)) → new_ltEs6(vyy1000, vyy1010, hh, baa, bab)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_lt20(vyy1001, vyy1011, ty_Int) → new_lt17(vyy1001, vyy1011)
new_lt12(vyy1000, vyy1010, dd, de) → new_esEs9(new_compare10(vyy1000, vyy1010, dd, de), LT)
new_lt6(vyy1000, vyy1010, app(app(app(ty_@3, df), dg), dh)) → new_lt16(vyy1000, vyy1010, df, dg, dh)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Char) → new_ltEs10(vyy1000, vyy1010)
new_ltEs4(EQ, EQ) → True
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy10000), Zero) → GT
new_lt7(vyy1000, vyy1010) → new_esEs9(new_compare16(vyy1000, vyy1010), LT)
new_ltEs19(vyy1002, vyy1012, app(ty_Ratio, ccd)) → new_ltEs13(vyy1002, vyy1012, ccd)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(ty_Maybe, hb)) → new_ltEs9(vyy1000, vyy1010, hb)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(ty_[], cef), cg) → new_ltEs7(vyy10000, vyy10100, cef)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Bool) → new_ltEs11(vyy10000, vyy10100)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy10100))) → LT
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, bh), ca)) → new_esEs5(vyy3000, vyy400, bh, ca)
new_esEs20(vyy1000, vyy1010, app(app(ty_Either, cf), cg)) → new_esEs5(vyy1000, vyy1010, cf, cg)
new_ltEs4(GT, LT) → False
new_esEs21(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(ty_Ratio, cdf), cg) → new_ltEs13(vyy10000, vyy10100, cdf)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Bool) → new_ltEs11(vyy1000, vyy1010)
new_sr0(Integer(vyy10000), Integer(vyy10110)) → Integer(new_primMulInt(vyy10000, vyy10110))
new_primPlusNat1(Succ(vyy15400), Succ(vyy400000)) → Succ(Succ(new_primPlusNat1(vyy15400, vyy400000)))
new_ltEs18(vyy1001, vyy1011, app(app(ty_@2, bbc), bbd)) → new_ltEs15(vyy1001, vyy1011, bbc, bbd)
new_compare28(vyy1000, vyy1010, True, cf, cg) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dbd), dbe)) → new_esEs5(vyy3000, vyy400, dbd, dbe)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Int) → new_ltEs5(vyy10000, vyy10100)
new_esEs26(vyy3002, vyy402, ty_Double) → new_esEs13(vyy3002, vyy402)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Char) → new_ltEs10(vyy10000, vyy10100)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, cc), cd)) → new_esEs6(vyy3000, vyy400, cc, cd)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Integer) → new_ltEs16(vyy10000, vyy10100)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs11(vyy3000, vyy400)
new_compare15(vyy1000, vyy1010, ty_Integer) → new_compare14(vyy1000, vyy1010)
new_lt6(vyy1000, vyy1010, ty_Double) → new_lt15(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, app(app(ty_@2, bfg), bfh)) → new_esEs6(vyy3001, vyy401, bfg, bfh)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_ltEs9(Just(vyy1000), Nothing, ha) → False
new_esEs21(vyy3000, vyy400, ty_Char) → new_esEs11(vyy3000, vyy400)
new_foldFM_GE12(vyy88, vyy13, vyy170, vyy171, vyy172, vyy173, vyy174, False, h, ba, bb) → new_foldFM_GE5(vyy88, vyy13, vyy174, h, ba, bb)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy10100))) → new_primCmpNat0(Zero, Succ(vyy10100))
new_primCompAux00(vyy178, EQ) → vyy178
new_esEs25(vyy1000, vyy1010, ty_@0) → new_esEs14(vyy1000, vyy1010)
new_ltEs15(@2(vyy1000, vyy1001), @2(vyy1010, vyy1011), bad, bae) → new_pePe(new_lt6(vyy1000, vyy1010, bad), new_asAs(new_esEs20(vyy1000, vyy1010, bad), new_ltEs18(vyy1001, vyy1011, bae)))
new_lt19(vyy1000, vyy1010, app(ty_[], cah)) → new_lt5(vyy1000, vyy1010, cah)
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_lt6(vyy1000, vyy1010, ty_Integer) → new_lt13(vyy1000, vyy1010)
new_esEs26(vyy3002, vyy402, ty_Char) → new_esEs11(vyy3002, vyy402)
new_esEs20(vyy1000, vyy1010, ty_Double) → new_esEs13(vyy1000, vyy1010)
new_compare114(vyy1000, vyy1010, False, cf, cg) → GT
new_not(False) → True
new_esEs10(:(vyy3000, vyy3001), :(vyy400, vyy401), bdc) → new_asAs(new_esEs21(vyy3000, vyy400, bdc), new_esEs10(vyy3001, vyy401, bdc))
new_lt20(vyy1001, vyy1011, ty_Bool) → new_lt8(vyy1001, vyy1011)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, ce)) → new_esEs15(vyy3000, vyy400, ce)
new_primPlusNat0(Zero, vyy40000) → Succ(vyy40000)
new_primCmpInt(Pos(Succ(vyy10000)), Pos(vyy1010)) → new_primCmpNat0(Succ(vyy10000), vyy1010)
new_ltEs18(vyy1001, vyy1011, app(ty_Ratio, bah)) → new_ltEs13(vyy1001, vyy1011, bah)
new_esEs23(vyy3000, vyy400, app(app(ty_@2, bha), bhb)) → new_esEs6(vyy3000, vyy400, bha, bhb)
new_esEs25(vyy1000, vyy1010, ty_Double) → new_esEs13(vyy1000, vyy1010)
new_ltEs9(Nothing, Nothing, ha) → True
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Ordering) → new_ltEs4(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_esEs9(GT, GT) → True
new_ltEs18(vyy1001, vyy1011, app(app(app(ty_@3, bbe), bbf), bbg)) → new_ltEs6(vyy1001, vyy1011, bbe, bbf, bbg)
new_lt5(vyy1000, vyy1010, da) → new_esEs9(new_compare5(vyy1000, vyy1010, da), LT)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs14(vyy3001, vyy401)
new_ltEs19(vyy1002, vyy1012, app(app(app(ty_@3, cda), cdb), cdc)) → new_ltEs6(vyy1002, vyy1012, cda, cdb, cdc)
new_esEs23(vyy3000, vyy400, app(ty_[], bgh)) → new_esEs10(vyy3000, vyy400, bgh)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Double, ea) → new_esEs13(vyy3000, vyy400)
new_compare29(vyy1000, vyy1010, df, dg, dh) → new_compare25(vyy1000, vyy1010, new_esEs7(vyy1000, vyy1010, df, dg, dh), df, dg, dh)
new_ltEs11(False, False) → True
new_lt20(vyy1001, vyy1011, ty_Ordering) → new_lt18(vyy1001, vyy1011)
new_esEs21(vyy3000, vyy400, app(ty_Ratio, bee)) → new_esEs15(vyy3000, vyy400, bee)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Int, ea) → new_esEs12(vyy3000, vyy400)
new_esEs26(vyy3002, vyy402, app(app(ty_Either, cgh), cha)) → new_esEs5(vyy3002, vyy402, cgh, cha)
new_lt19(vyy1000, vyy1010, ty_Float) → new_lt14(vyy1000, vyy1010)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_lt19(vyy1000, vyy1010, app(app(app(ty_@3, cae), caf), cag)) → new_lt16(vyy1000, vyy1010, cae, caf, cag)
new_compare16(Char(vyy1000), Char(vyy1010)) → new_primCmpNat0(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs7(vyy3001, vyy401, beh, bfa, bfb)
new_primCmpInt(Pos(Succ(vyy10000)), Neg(vyy1010)) → GT
new_esEs22(vyy3001, vyy401, ty_Char) → new_esEs11(vyy3001, vyy401)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(app(app(ty_@3, cec), ced), cee), cg) → new_ltEs6(vyy10000, vyy10100, cec, ced, cee)
new_esEs21(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs20(vyy1000, vyy1010, ty_Float) → new_esEs8(vyy1000, vyy1010)
new_lt20(vyy1001, vyy1011, ty_Double) → new_lt15(vyy1001, vyy1011)
new_primMulInt(Pos(vyy30000), Pos(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_esEs24(vyy1001, vyy1011, ty_Integer) → new_esEs16(vyy1001, vyy1011)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs7(vyy3000, vyy400, dah, dba, dbb)
new_esEs15(:%(vyy3000, vyy3001), :%(vyy400, vyy401), gh) → new_asAs(new_esEs19(vyy3000, vyy400, gh), new_esEs18(vyy3001, vyy401, gh))
new_lt6(vyy1000, vyy1010, ty_Ordering) → new_lt18(vyy1000, vyy1010)
new_esEs22(vyy3001, vyy401, ty_Double) → new_esEs13(vyy3001, vyy401)
new_esEs20(vyy1000, vyy1010, ty_Char) → new_esEs11(vyy1000, vyy1010)
new_compare15(vyy1000, vyy1010, app(app(ty_@2, bce), bcf)) → new_compare10(vyy1000, vyy1010, bce, bcf)
new_esEs23(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Left(vyy400), fd, ea) → False
new_esEs5(Left(vyy3000), Right(vyy400), fd, ea) → False
new_esEs27(vyy3001, vyy401, app(app(ty_@2, dae), daf)) → new_esEs6(vyy3001, vyy401, dae, daf)
new_primMulInt(Neg(vyy30000), Neg(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_ltEs19(vyy1002, vyy1012, ty_Int) → new_ltEs5(vyy1002, vyy1012)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_@0) → new_ltEs12(vyy1000, vyy1010)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Bool, cg) → new_ltEs11(vyy10000, vyy10100)
new_lt20(vyy1001, vyy1011, app(app(ty_@2, cbe), cbf)) → new_lt12(vyy1001, vyy1011, cbe, cbf)
new_esEs18(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_esEs20(vyy1000, vyy1010, app(ty_[], da)) → new_esEs10(vyy1000, vyy1010, da)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, bc) → True
new_esEs22(vyy3001, vyy401, app(ty_Ratio, bga)) → new_esEs15(vyy3001, vyy401, bga)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(app(ty_Either, hd), he)) → new_ltEs14(vyy1000, vyy1010, hd, he)
new_esEs25(vyy1000, vyy1010, ty_Int) → new_esEs12(vyy1000, vyy1010)
new_compare15(vyy1000, vyy1010, ty_Float) → new_compare6(vyy1000, vyy1010)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_esEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bef, beg) → new_asAs(new_esEs23(vyy3000, vyy400, bef), new_esEs22(vyy3001, vyy401, beg))
new_esEs27(vyy3001, vyy401, app(ty_Maybe, daa)) → new_esEs4(vyy3001, vyy401, daa)
new_ltEs4(LT, GT) → True
new_compare15(vyy1000, vyy1010, ty_Int) → new_compare7(vyy1000, vyy1010)
new_lt13(vyy1000, vyy1010) → new_esEs9(new_compare14(vyy1000, vyy1010), LT)
new_esEs25(vyy1000, vyy1010, ty_Integer) → new_esEs16(vyy1000, vyy1010)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy10100))) → new_primCmpNat0(Succ(vyy10100), Zero)
new_esEs23(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy10100))) → GT
new_lt16(vyy1000, vyy1010, df, dg, dh) → new_esEs9(new_compare29(vyy1000, vyy1010, df, dg, dh), LT)
new_esEs12(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_lt20(vyy1001, vyy1011, ty_Char) → new_lt7(vyy1001, vyy1011)
new_ltEs19(vyy1002, vyy1012, app(ty_[], cdd)) → new_ltEs7(vyy1002, vyy1012, cdd)
new_lt20(vyy1001, vyy1011, app(ty_Maybe, cba)) → new_lt9(vyy1001, vyy1011, cba)
new_esEs5(Right(vyy3000), Right(vyy400), fd, app(app(app(ty_@3, ff), fg), fh)) → new_esEs7(vyy3000, vyy400, ff, fg, fh)
new_compare23(vyy1000, vyy1010, True, db) → EQ
new_esEs26(vyy3002, vyy402, ty_@0) → new_esEs14(vyy3002, vyy402)
new_lt11(vyy1000, vyy1010, baf) → new_esEs9(new_compare18(vyy1000, vyy1010, baf), LT)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dbg), dbh)) → new_esEs6(vyy3000, vyy400, dbg, dbh)
new_compare15(vyy1000, vyy1010, app(app(ty_Either, bcc), bcd)) → new_compare8(vyy1000, vyy1010, bcc, bcd)
new_esEs11(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_lt19(vyy1000, vyy1010, app(app(ty_Either, caa), cab)) → new_lt4(vyy1000, vyy1010, caa, cab)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Float, ea) → new_esEs8(vyy3000, vyy400)
new_compare5([], :(vyy1010, vyy1011), dc) → LT
new_lt6(vyy1000, vyy1010, ty_Float) → new_lt14(vyy1000, vyy1010)
new_esEs16(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs12(vyy100, vyy101) → new_not(new_esEs9(new_compare17(vyy100, vyy101), GT))
new_esEs24(vyy1001, vyy1011, app(ty_[], ccb)) → new_esEs10(vyy1001, vyy1011, ccb)
new_esEs21(vyy3000, vyy400, app(ty_Maybe, bdg)) → new_esEs4(vyy3000, vyy400, bdg)
new_esEs23(vyy3000, vyy400, app(ty_Ratio, bhc)) → new_esEs15(vyy3000, vyy400, bhc)
new_esEs23(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_compare24(vyy1000, vyy1010, False, dd, de) → new_compare110(vyy1000, vyy1010, new_ltEs15(vyy1000, vyy1010, dd, de), dd, de)
new_esEs24(vyy1001, vyy1011, app(app(app(ty_@3, cbg), cbh), cca)) → new_esEs7(vyy1001, vyy1011, cbg, cbh, cca)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs4(LT, EQ) → True
new_esEs21(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_lt6(vyy1000, vyy1010, app(ty_Maybe, db)) → new_lt9(vyy1000, vyy1010, db)
new_lt15(vyy1000, vyy1010) → new_esEs9(new_compare19(vyy1000, vyy1010), LT)
new_esEs24(vyy1001, vyy1011, ty_Char) → new_esEs11(vyy1001, vyy1011)
new_ltEs14(Left(vyy10000), Right(vyy10100), cf, cg) → True
new_asAs(False, vyy144) → False
new_ltEs11(True, True) → True
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs16(vyy3000, vyy400)
new_ltEs19(vyy1002, vyy1012, app(app(ty_Either, cce), ccf)) → new_ltEs14(vyy1002, vyy1012, cce, ccf)
new_primMulInt(Pos(vyy30000), Neg(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulInt(Neg(vyy30000), Pos(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_esEs26(vyy3002, vyy402, ty_Float) → new_esEs8(vyy3002, vyy402)
new_primMulNat0(Zero, Succ(vyy40000)) → Zero
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs13(vyy3001, vyy401)
new_esEs24(vyy1001, vyy1011, ty_Double) → new_esEs13(vyy1001, vyy1011)
new_esEs21(vyy3000, vyy400, app(app(ty_Either, bdh), bea)) → new_esEs5(vyy3000, vyy400, bdh, bea)
new_lt19(vyy1000, vyy1010, ty_Ordering) → new_lt18(vyy1000, vyy1010)
new_esEs28(vyy3000, vyy400, app(ty_[], dbf)) → new_esEs10(vyy3000, vyy400, dbf)
new_esEs22(vyy3001, vyy401, app(ty_[], bff)) → new_esEs10(vyy3001, vyy401, bff)
new_compare15(vyy1000, vyy1010, ty_Char) → new_compare16(vyy1000, vyy1010)
new_foldFM_GE5(vyy88, vyy13, Branch(vyy1740, vyy1741, vyy1742, vyy1743, vyy1744), h, ba, bb) → new_foldFM_GE12(vyy88, vyy13, vyy1740, vyy1741, vyy1742, vyy1743, vyy1744, new_gtEs0(vyy1740, vyy13, h, ba), h, ba, bb)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, app(app(ty_Either, cfa), cfb)) → new_ltEs14(vyy10000, vyy10100, cfa, cfb)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs13(vyy3000, vyy400)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Int) → new_ltEs5(vyy1000, vyy1010)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs8(vyy3000, vyy400)
new_compare27(vyy1000, vyy1010, True) → EQ
new_esEs27(vyy3001, vyy401, app(ty_[], dad)) → new_esEs10(vyy3001, vyy401, dad)
new_esEs20(vyy1000, vyy1010, ty_Ordering) → new_esEs9(vyy1000, vyy1010)
new_esEs19(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_ltEs9(Just(vyy1000), Just(vyy1010), app(ty_[], bac)) → new_ltEs7(vyy1000, vyy1010, bac)
new_ltEs14(Left(vyy10000), Left(vyy10100), app(app(ty_Either, cdg), cdh), cg) → new_ltEs14(vyy10000, vyy10100, cdg, cdh)
new_esEs25(vyy1000, vyy1010, app(app(app(ty_@3, cae), caf), cag)) → new_esEs7(vyy1000, vyy1010, cae, caf, cag)
new_lt20(vyy1001, vyy1011, app(app(app(ty_@3, cbg), cbh), cca)) → new_lt16(vyy1001, vyy1011, cbg, cbh, cca)
new_lt19(vyy1000, vyy1010, ty_Integer) → new_lt13(vyy1000, vyy1010)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Bool, ea) → new_esEs17(vyy3000, vyy400)
new_ltEs9(Just(vyy1000), Just(vyy1010), ty_Float) → new_ltEs8(vyy1000, vyy1010)
new_esEs5(Right(vyy3000), Right(vyy400), fd, app(ty_Maybe, ga)) → new_esEs4(vyy3000, vyy400, ga)
new_compare10(vyy1000, vyy1010, dd, de) → new_compare24(vyy1000, vyy1010, new_esEs6(vyy1000, vyy1010, dd, de), dd, de)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Int) → new_esEs12(vyy3000, vyy400)
new_ltEs4(LT, LT) → True
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_esEs20(vyy1000, vyy1010, ty_Int) → new_esEs12(vyy1000, vyy1010)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_@0) → new_ltEs12(vyy10000, vyy10100)
new_esEs26(vyy3002, vyy402, ty_Bool) → new_esEs17(vyy3002, vyy402)
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_ltEs19(vyy1002, vyy1012, app(app(ty_@2, ccg), cch)) → new_ltEs15(vyy1002, vyy1012, ccg, cch)
new_foldFM_GE22(vyy170, vyy171, vyy111, vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb) → new_foldFM_GE12(new_keysFM_GE0(vyy170, vyy171, vyy111, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, new_gtEs0(vyy1730, vyy13, h, ba), h, ba, bb)
new_esEs22(vyy3001, vyy401, ty_@0) → new_esEs14(vyy3001, vyy401)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_Either, ef), eg), ea) → new_esEs5(vyy3000, vyy400, ef, eg)
new_compare15(vyy1000, vyy1010, ty_@0) → new_compare17(vyy1000, vyy1010)
new_compare112(vyy1000, vyy1010, False) → GT
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Float) → new_ltEs8(vyy10000, vyy10100)
new_esEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cga, cgb, cgc) → new_asAs(new_esEs28(vyy3000, vyy400, cga), new_asAs(new_esEs27(vyy3001, vyy401, cgb), new_esEs26(vyy3002, vyy402, cgc)))
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Ratio, fc), ea) → new_esEs15(vyy3000, vyy400, fc)
new_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, app(ty_Ratio, ceh)) → new_ltEs13(vyy10000, vyy10100, ceh)
new_compare26(vyy1000, vyy1010, False) → new_compare112(vyy1000, vyy1010, new_ltEs4(vyy1000, vyy1010))
new_esEs24(vyy1001, vyy1011, ty_Ordering) → new_esEs9(vyy1001, vyy1011)
new_lt19(vyy1000, vyy1010, ty_@0) → new_lt10(vyy1000, vyy1010)
new_esEs21(vyy3000, vyy400, ty_Float) → new_esEs8(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, ty_Float) → new_esEs8(vyy3000, vyy400)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, ty_Ordering) → new_ltEs4(vyy10000, vyy10100)
new_lt9(vyy1000, vyy1010, db) → new_esEs9(new_compare9(vyy1000, vyy1010, db), LT)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(vyy3002, vyy402, ty_Ordering) → new_esEs9(vyy3002, vyy402)
new_ltEs14(Left(vyy10000), Left(vyy10100), ty_Char, cg) → new_ltEs10(vyy10000, vyy10100)
new_esEs5(Right(vyy3000), Right(vyy400), fd, ty_Char) → new_esEs11(vyy3000, vyy400)
new_asAs(True, vyy144) → vyy144
new_ltEs16(vyy100, vyy101) → new_not(new_esEs9(new_compare14(vyy100, vyy101), GT))
new_primMulNat0(Succ(vyy300000), Succ(vyy40000)) → new_primPlusNat0(new_primMulNat0(vyy300000, Succ(vyy40000)), vyy40000)
new_compare28(vyy1000, vyy1010, False, cf, cg) → new_compare114(vyy1000, vyy1010, new_ltEs14(vyy1000, vyy1010, cf, cg), cf, cg)
new_compare15(vyy1000, vyy1010, app(ty_Maybe, bca)) → new_compare9(vyy1000, vyy1010, bca)
new_lt19(vyy1000, vyy1010, ty_Int) → new_lt17(vyy1000, vyy1010)
new_esEs26(vyy3002, vyy402, app(app(ty_@2, chc), chd)) → new_esEs6(vyy3002, vyy402, chc, chd)
new_lt20(vyy1001, vyy1011, app(ty_[], ccb)) → new_lt5(vyy1001, vyy1011, ccb)
new_compare5([], [], dc) → EQ
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bd), be), bf)) → new_esEs7(vyy3000, vyy400, bd, be, bf)
new_gtEs0(vyy1730, vyy13, h, ba) → new_not(new_esEs9(new_compare28(vyy1730, Left(vyy13), new_esEs5(vyy1730, Left(vyy13), h, ba), h, ba), LT))
new_ltEs4(GT, GT) → True
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs11(vyy3001, vyy401)
new_lt6(vyy1000, vyy1010, ty_Bool) → new_lt8(vyy1000, vyy1010)
new_foldFM_GE5(vyy88, vyy13, EmptyFM, h, ba, bb) → vyy88
new_esEs9(LT, LT) → True
new_esEs22(vyy3001, vyy401, app(app(ty_Either, bfd), bfe)) → new_esEs5(vyy3001, vyy401, bfd, bfe)
new_primCompAux00(vyy178, GT) → GT
new_esEs5(Right(vyy3000), Right(vyy400), fd, app(ty_Ratio, gg)) → new_esEs15(vyy3000, vyy400, gg)
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs8(vyy3001, vyy401)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(vyy1000, vyy1010, app(app(ty_@2, dd), de)) → new_lt12(vyy1000, vyy1010, dd, de)
new_ltEs14(Right(vyy10000), Right(vyy10100), cf, app(ty_Maybe, ceg)) → new_ltEs9(vyy10000, vyy10100, ceg)
new_compare9(vyy1000, vyy1010, db) → new_compare23(vyy1000, vyy1010, new_esEs4(vyy1000, vyy1010, db), db)
new_esEs8(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs12(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(vyy1002, vyy1012, ty_Bool) → new_ltEs11(vyy1002, vyy1012)
new_primCmpInt(Neg(Succ(vyy10000)), Pos(vyy1010)) → LT
new_compare15(vyy1000, vyy1010, ty_Ordering) → new_compare12(vyy1000, vyy1010)
new_not(True) → False

The set Q consists of the following terms:

new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs10([], :(x0, x1), x2)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_lt6(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Bool)
new_compare15(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Bool)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs18(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_foldFM_GE5(x0, x1, EmptyFM, x2, x3, x4)
new_esEs28(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(Integer(x0), Integer(x1))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare15(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_compare28(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, x2)
new_compare15(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs23(x0, x1, ty_Double)
new_lt18(x0, x1)
new_esEs23(x0, x1, ty_@0)
new_compare17(@0, @0)
new_compare12(x0, x1)
new_esEs21(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt16(x0, x1, x2, x3, x4)
new_esEs17(False, False)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primMulNat0(Zero, Succ(x0))
new_compare14(Integer(x0), Integer(x1))
new_compare16(Char(x0), Char(x1))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_compare112(x0, x1, True)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Nothing, x1)
new_esEs23(x0, x1, ty_Int)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(x0, x1, True, x2, x3)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Integer)
new_primEqNat0(Zero, Zero)
new_esEs20(x0, x1, ty_Bool)
new_esEs11(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(x0, x1)
new_compare26(x0, x1, True)
new_lt19(x0, x1, ty_Double)
new_lt6(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primMulNat0(Zero, Zero)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_compare15(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Integer)
new_foldFM_GE12(x0, x1, x2, x3, x4, EmptyFM, x5, True, x6, x7, x8)
new_lt20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_primCompAux00(x0, EQ)
new_ltEs4(GT, GT)
new_compare24(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs4(Nothing, Just(x0), x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primPlusNat0(Succ(x0), x1)
new_esEs25(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_compare27(x0, x1, True)
new_compare13(x0, x1)
new_compare15(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_foldFM_GE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primPlusNat0(Zero, x0)
new_esEs14(@0, @0)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare114(x0, x1, False, x2, x3)
new_lt15(x0, x1)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(True, x0)
new_lt6(x0, x1, ty_Bool)
new_lt5(x0, x1, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Ordering)
new_compare113(x0, x1, False, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs27(x0, x1, ty_Bool)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs10(:(x0, x1), :(x2, x3), x4)
new_ltEs17(x0, x1)
new_lt6(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Char)
new_compare15(x0, x1, app(ty_Maybe, x2))
new_lt14(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Double)
new_compare15(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare23(x0, x1, False, x2)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_lt6(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs4(EQ, EQ)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs9(Nothing, Nothing, x0)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs22(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_foldFM_GE12(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_esEs22(x0, x1, ty_@0)
new_lt17(x0, x1)
new_ltEs4(EQ, LT)
new_esEs27(x0, x1, ty_Int)
new_ltEs4(LT, EQ)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare15(x0, x1, ty_Integer)
new_esEs9(GT, GT)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare10(x0, x1, x2, x3)
new_compare112(x0, x1, False)
new_ltEs18(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True, x2, x3, x4)
new_compare27(x0, x1, False)
new_compare15(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs19(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Bool)
new_ltEs9(Nothing, Just(x0), x1)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs11(False, False)
new_esEs22(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs12(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare6(Float(x0, x1), Float(x2, x3))
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_ltEs11(False, True)
new_ltEs11(True, False)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(LT, LT)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs18(x0, x1, ty_Float)
new_compare24(x0, x1, False, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_lt20(x0, x1, ty_Ordering)
new_compare15(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs22(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs28(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Double)
new_lt20(x0, x1, ty_@0)
new_ltEs12(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare5(:(x0, x1), :(x2, x3), x4)
new_esEs4(Nothing, Nothing, x0)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Succ(x0))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs18(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare19(Double(x0, x1), Double(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3, x4)
new_esEs8(Float(x0, x1), Float(x2, x3))
new_compare15(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs28(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_lt13(x0, x1)
new_esEs24(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Bool)
new_compare113(x0, x1, True, x2)
new_compare111(x0, x1, False)
new_lt19(x0, x1, ty_Bool)
new_esEs15(:%(x0, x1), :%(x2, x3), x4)
new_compare5([], [], x0)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt6(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs27(x0, x1, ty_Double)
new_compare5(:(x0, x1), [], x2)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs5(x0, x1)
new_esEs22(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_@0)
new_compare29(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Char)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare15(x0, x1, ty_Float)
new_primCompAux0(x0, x1, x2, x3)
new_lt9(x0, x1, x2)
new_lt7(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_foldFM_GE30(x0, x1, x2, x3, x4, x5, x6)
new_sr0(Integer(x0), Integer(x1))
new_ltEs18(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_not(True)
new_esEs18(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, False, x2, x3, x4)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux00(x0, GT)
new_primCompAux00(x0, LT)
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_gtEs0(x0, x1, x2, x3)
new_lt11(x0, x1, x2)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs20(x0, x1, ty_Int)
new_esEs10(:(x0, x1), [], x2)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_lt8(x0, x1)
new_primMulInt(Neg(x0), Neg(x1))
new_foldFM_GE12(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, True, x11, x12, x13)
new_asAs(True, x0)
new_esEs28(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs13(x0, x1, x2)
new_esEs27(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1, x2)
new_esEs10([], [], x0)
new_lt6(x0, x1, ty_Char)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Integer)
new_keysFM_GE0(x0, x1, x2, x3, x4, x5)
new_compare7(x0, x1)
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs23(x0, x1, ty_Char)
new_primMulNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_ltEs8(x0, x1)
new_pePe(False, x0)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs17(True, False)
new_esEs17(False, True)
new_ltEs19(x0, x1, ty_@0)
new_compare23(x0, x1, True, x2)
new_lt4(x0, x1, x2, x3)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare114(x0, x1, True, x2, x3)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqNat0(Succ(x0), Zero)
new_esEs24(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3)
new_esEs27(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs20(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Bool)
new_ltEs10(x0, x1)
new_lt6(x0, x1, ty_@0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_compare111(x0, x1, True)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_ltEs11(True, True)
new_lt10(x0, x1)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(LT, LT)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, ty_Double)
new_compare26(x0, x1, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_compare5([], :(x0, x1), x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(x0, x1, x2, x3)
new_foldFM_GE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))

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: