YES 8.744 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
  ((fmToList_GE :: (Ord c, Ord a) => FiniteMap (Either c a) b  ->  Either c a  ->  [(Either c a,b)]) :: (Ord a, Ord c) => FiniteMap (Either c a) b  ->  Either c a  ->  [(Either c a,b)])

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

is transformed to
fmToList_GE0 key elt rest = (key,elt) : 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
  ((fmToList_GE :: (Ord b, Ord a) => FiniteMap (Either a b) c  ->  Either a b  ->  [(Either a b,c)]) :: (Ord b, Ord a) => FiniteMap (Either a b) c  ->  Either a b  ->  [(Either a b,c)])

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

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

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

  fmToList_GE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 key elt rest = (key,elt) : rest

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

  foldFM_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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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



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

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

  fmToList_GE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 key elt rest = (key,elt) : rest

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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



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

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

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

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

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

  fmToList_GE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 key elt rest = (key,elt) : rest

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

  foldFM_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

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

  fmToList_GE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 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 = 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

  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

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

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

compare3 x y = compare2 x y (x == y)

The following Function with conditions
gcd' x 0 = x
gcd' x y = gcd' y (x `rem` y)

is transformed to
gcd' x vvy = gcd'2 x vvy
gcd' x y = gcd'0 x y

gcd'0 x y = gcd' y (x `rem` y)

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

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

The following Function with conditions
gcd 0 0 = error []
gcd x y = 
gcd' (abs x) (abs y)
where 
gcd' x 0 = x
gcd' x y = gcd' y (x `rem` y)

is transformed to
gcd vwy vwz = gcd3 vwy vwz
gcd x y = gcd0 x y

gcd0 x y = 
gcd' (abs x) (abs y)
where 
gcd' x vvy = gcd'2 x vvy
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x vvy = x
gcd'1 vvz vwu vwv = gcd'0 vwu vwv
gcd'2 x vvy = gcd'1 (vvy == 0) x vvy
gcd'2 vww vwx = gcd'0 vww vwx

gcd1 True vwy vwz = error []
gcd1 vxu vxv vxw = gcd0 vxv vxw

gcd2 True vwy vwz = gcd1 (vwz == 0) vwy vwz
gcd2 vxx vxy vxz = gcd0 vxy vxz

gcd3 vwy vwz = gcd2 (vwy == 0) vwy vwz
gcd3 vyu vyv = gcd0 vyu vyv

The following Function with conditions
absReal x
 | x >= 0
 = x
 | otherwise
 = `negate` x

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

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

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

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

  fmToList_GE :: Ord b => FiniteMap b a  ->  b  ->  [(b,a)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 key elt rest = (key,elt) : rest

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

  foldFM_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

  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

reduce2D vyw vyx = gcd vyw vyx

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

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

are unpacked to the following functions on top level
gcd0Gcd'1 True x vvy = x
gcd0Gcd'1 vvz vwu vwv = gcd0Gcd'0 vwu vwv

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

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

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

  fmToList_GE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 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 c => (c  ->  a  ->  b  ->  b)  ->  b  ->  c  ->  FiniteMap c a  ->  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

  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


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

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

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

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

  fmToList_GE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 key elt rest = (key,elt) : rest

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

  foldFM_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

  sizeFM :: FiniteMap a b  ->  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(vyy13400), Succ(vyy401000)) → new_primPlusNat(vyy13400, vyy401000)

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(vyy300100), Succ(vyy40100)) → new_primMulNat(vyy300100, Succ(vyy40100))

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(vyy9000), Succ(vyy9100)) → new_primCmpNat(vyy9000, vyy9100)

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

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_ltEs0(@2(vyy900, vyy901), @2(vyy910, vyy911), app(app(ty_@2, gf), gg), ge) → new_lt0(vyy900, vyy910, gf, gg)
new_lt3(vyy900, vyy910, ef) → new_compare22(vyy900, vyy910, new_esEs7(vyy900, vyy910, ef), ef)
new_ltEs1(:(vyy900, vyy901), :(vyy910, vyy911), hd) → new_compare(vyy901, vyy911, hd)
new_primCompAux(vyy900, vyy910, vyy151, app(app(app(ty_@3, he), hf), hg)) → new_compare1(vyy900, vyy910, he, hf, hg)
new_compare21(Left(vyy9000), Left(vyy9100), False, app(ty_Maybe, bbf), ee) → new_ltEs3(vyy9000, vyy9100, bbf)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), h, app(app(ty_@2, cg), da), cf) → new_lt0(vyy901, vyy911, cg, da)
new_primCompAux(vyy900, vyy910, vyy151, app(app(ty_@2, hh), baa)) → new_compare3(vyy900, vyy910, hh, baa)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), app(app(ty_@2, ea), eb), ba, cf) → new_compare20(vyy900, vyy910, new_esEs5(vyy900, vyy910, ea, eb), ea, eb)
new_ltEs0(@2(vyy900, vyy901), @2(vyy910, vyy911), app(ty_Maybe, hc), ge) → new_lt3(vyy900, vyy910, hc)
new_ltEs2(Left(vyy9000), Left(vyy9100), app(app(ty_Either, bbd), bbe), ee) → new_ltEs2(vyy9000, vyy9100, bbd, bbe)
new_compare21(Right(vyy9000), Right(vyy9100), False, ed, app(ty_Maybe, bcg)) → new_ltEs3(vyy9000, vyy9100, bcg)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), h, app(app(ty_Either, dc), dd), cf) → new_lt2(vyy901, vyy911, dc, dd)
new_compare3(vyy900, vyy910, ea, eb) → new_compare20(vyy900, vyy910, new_esEs5(vyy900, vyy910, ea, eb), ea, eb)
new_compare21(Left(vyy9000), Left(vyy9100), False, app(app(ty_Either, bbd), bbe), ee) → new_ltEs2(vyy9000, vyy9100, bbd, bbe)
new_ltEs0(@2(vyy900, vyy901), @2(vyy910, vyy911), eg, app(app(app(ty_@3, eh), fa), fb)) → new_ltEs(vyy901, vyy911, eh, fa, fb)
new_ltEs2(Left(vyy9000), Left(vyy9100), app(app(ty_@2, bba), bbb), ee) → new_ltEs0(vyy9000, vyy9100, bba, bbb)
new_compare5(vyy900, vyy910, ef) → new_compare22(vyy900, vyy910, new_esEs7(vyy900, vyy910, ef), ef)
new_ltEs2(Left(vyy9000), Left(vyy9100), app(ty_Maybe, bbf), ee) → new_ltEs3(vyy9000, vyy9100, bbf)
new_primCompAux(vyy900, vyy910, vyy151, app(ty_[], bab)) → new_compare(vyy900, vyy910, bab)
new_compare22(vyy900, vyy910, False, ef) → new_ltEs3(vyy900, vyy910, ef)
new_ltEs3(Just(vyy900), Just(vyy910), app(app(ty_Either, bdf), bdg)) → new_ltEs2(vyy900, vyy910, bdf, bdg)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), h, ba, app(app(ty_Either, bh), ca)) → new_ltEs2(vyy902, vyy912, bh, ca)
new_lt0(vyy900, vyy910, ea, eb) → new_compare20(vyy900, vyy910, new_esEs5(vyy900, vyy910, ea, eb), ea, eb)
new_lt(vyy900, vyy910, df, dg, dh) → new_compare2(vyy900, vyy910, new_esEs4(vyy900, vyy910, df, dg, dh), df, dg, dh)
new_compare21(Right(vyy9000), Right(vyy9100), False, ed, app(app(app(ty_@3, bbg), bbh), bca)) → new_ltEs(vyy9000, vyy9100, bbg, bbh, bca)
new_compare21(Right(vyy9000), Right(vyy9100), False, ed, app(app(ty_@2, bcb), bcc)) → new_ltEs0(vyy9000, vyy9100, bcb, bcc)
new_compare20(vyy900, vyy910, False, ea, eb) → new_ltEs0(vyy900, vyy910, ea, eb)
new_compare1(vyy900, vyy910, df, dg, dh) → new_compare2(vyy900, vyy910, new_esEs4(vyy900, vyy910, df, dg, dh), df, dg, dh)
new_ltEs2(Right(vyy9000), Right(vyy9100), ed, app(ty_[], bcd)) → new_ltEs1(vyy9000, vyy9100, bcd)
new_ltEs2(Right(vyy9000), Right(vyy9100), ed, app(app(app(ty_@3, bbg), bbh), bca)) → new_ltEs(vyy9000, vyy9100, bbg, bbh, bca)
new_ltEs2(Left(vyy9000), Left(vyy9100), app(app(app(ty_@3, baf), bag), bah), ee) → new_ltEs(vyy9000, vyy9100, baf, bag, bah)
new_compare21(Left(vyy9000), Left(vyy9100), False, app(app(ty_@2, bba), bbb), ee) → new_ltEs0(vyy9000, vyy9100, bba, bbb)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), app(ty_Maybe, ef), ba, cf) → new_compare22(vyy900, vyy910, new_esEs7(vyy900, vyy910, ef), ef)
new_primCompAux(vyy900, vyy910, vyy151, app(app(ty_Either, bac), bad)) → new_compare4(vyy900, vyy910, bac, bad)
new_ltEs3(Just(vyy900), Just(vyy910), app(app(app(ty_@3, bch), bda), bdb)) → new_ltEs(vyy900, vyy910, bch, bda, bdb)
new_compare21(Left(vyy9000), Left(vyy9100), False, app(app(app(ty_@3, baf), bag), bah), ee) → new_ltEs(vyy9000, vyy9100, baf, bag, bah)
new_ltEs2(Right(vyy9000), Right(vyy9100), ed, app(app(ty_Either, bce), bcf)) → new_ltEs2(vyy9000, vyy9100, bce, bcf)
new_ltEs0(@2(vyy900, vyy901), @2(vyy910, vyy911), eg, app(ty_[], ff)) → new_ltEs1(vyy901, vyy911, ff)
new_ltEs0(@2(vyy900, vyy901), @2(vyy910, vyy911), eg, app(app(ty_@2, fc), fd)) → new_ltEs0(vyy901, vyy911, fc, fd)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), app(app(ty_Either, ed), ee), ba, cf) → new_compare21(vyy900, vyy910, new_esEs6(vyy900, vyy910, ed, ee), ed, ee)
new_lt1(vyy900, vyy910, ec) → new_compare(vyy900, vyy910, ec)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), h, app(app(app(ty_@3, cc), cd), ce), cf) → new_lt(vyy901, vyy911, cc, cd, ce)
new_lt2(vyy900, vyy910, ed, ee) → new_compare21(vyy900, vyy910, new_esEs6(vyy900, vyy910, ed, ee), ed, ee)
new_ltEs0(@2(vyy900, vyy901), @2(vyy910, vyy911), eg, app(ty_Maybe, ga)) → new_ltEs3(vyy901, vyy911, ga)
new_ltEs0(@2(vyy900, vyy901), @2(vyy910, vyy911), app(ty_[], gh), ge) → new_lt1(vyy900, vyy910, gh)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), h, ba, app(ty_Maybe, cb)) → new_ltEs3(vyy902, vyy912, cb)
new_ltEs3(Just(vyy900), Just(vyy910), app(app(ty_@2, bdc), bdd)) → new_ltEs0(vyy900, vyy910, bdc, bdd)
new_ltEs0(@2(vyy900, vyy901), @2(vyy910, vyy911), eg, app(app(ty_Either, fg), fh)) → new_ltEs2(vyy901, vyy911, fg, fh)
new_compare(:(vyy900, vyy901), :(vyy910, vyy911), hd) → new_compare(vyy901, vyy911, hd)
new_compare2(vyy900, vyy910, False, df, dg, dh) → new_ltEs(vyy900, vyy910, df, dg, dh)
new_compare(:(vyy900, vyy901), :(vyy910, vyy911), hd) → new_primCompAux(vyy900, vyy910, new_compare0(vyy901, vyy911, hd), hd)
new_compare21(Right(vyy9000), Right(vyy9100), False, ed, app(ty_[], bcd)) → new_ltEs1(vyy9000, vyy9100, bcd)
new_primCompAux(vyy900, vyy910, vyy151, app(ty_Maybe, bae)) → new_compare5(vyy900, vyy910, bae)
new_ltEs2(Right(vyy9000), Right(vyy9100), ed, app(app(ty_@2, bcb), bcc)) → new_ltEs0(vyy9000, vyy9100, bcb, bcc)
new_ltEs0(@2(vyy900, vyy901), @2(vyy910, vyy911), app(app(app(ty_@3, gb), gc), gd), ge) → new_lt(vyy900, vyy910, gb, gc, gd)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), app(ty_[], ec), ba, cf) → new_compare(vyy900, vyy910, ec)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), app(app(app(ty_@3, df), dg), dh), ba, cf) → new_compare2(vyy900, vyy910, new_esEs4(vyy900, vyy910, df, dg, dh), df, dg, dh)
new_ltEs2(Right(vyy9000), Right(vyy9100), ed, app(ty_Maybe, bcg)) → new_ltEs3(vyy9000, vyy9100, bcg)
new_ltEs1(:(vyy900, vyy901), :(vyy910, vyy911), hd) → new_primCompAux(vyy900, vyy910, new_compare0(vyy901, vyy911, hd), hd)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), h, app(ty_[], db), cf) → new_lt1(vyy901, vyy911, db)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), h, ba, app(app(app(ty_@3, bb), bc), bd)) → new_ltEs(vyy902, vyy912, bb, bc, bd)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), h, app(ty_Maybe, de), cf) → new_lt3(vyy901, vyy911, de)
new_compare21(Left(vyy9000), Left(vyy9100), False, app(ty_[], bbc), ee) → new_ltEs1(vyy9000, vyy9100, bbc)
new_ltEs0(@2(vyy900, vyy901), @2(vyy910, vyy911), app(app(ty_Either, ha), hb), ge) → new_lt2(vyy900, vyy910, ha, hb)
new_compare4(vyy900, vyy910, ed, ee) → new_compare21(vyy900, vyy910, new_esEs6(vyy900, vyy910, ed, ee), ed, ee)
new_ltEs3(Just(vyy900), Just(vyy910), app(ty_Maybe, bdh)) → new_ltEs3(vyy900, vyy910, bdh)
new_compare21(Right(vyy9000), Right(vyy9100), False, ed, app(app(ty_Either, bce), bcf)) → new_ltEs2(vyy9000, vyy9100, bce, bcf)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), h, ba, app(app(ty_@2, be), bf)) → new_ltEs0(vyy902, vyy912, be, bf)
new_ltEs2(Left(vyy9000), Left(vyy9100), app(ty_[], bbc), ee) → new_ltEs1(vyy9000, vyy9100, bbc)
new_ltEs3(Just(vyy900), Just(vyy910), app(ty_[], bde)) → new_ltEs1(vyy900, vyy910, bde)
new_ltEs(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), h, ba, app(ty_[], bg)) → new_ltEs1(vyy902, vyy912, bg)

The TRS R consists of the following rules:

new_esEs10(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, cab)) → new_esEs7(vyy3000, vyy400, cab)
new_esEs28(vyy900, vyy910, ty_Char) → new_esEs21(vyy900, vyy910)
new_lt20(vyy900, vyy910, app(app(app(ty_@3, df), dg), dh)) → new_lt12(vyy900, vyy910, df, dg, dh)
new_esEs22(vyy3002, vyy402, app(ty_Ratio, cba)) → new_esEs9(vyy3002, vyy402, cba)
new_esEs25(vyy900, vyy910, ty_Integer) → new_esEs12(vyy900, vyy910)
new_esEs23(vyy3001, vyy401, ty_Float) → new_esEs20(vyy3001, vyy401)
new_ltEs19(vyy902, vyy912, app(ty_Ratio, dbf)) → new_ltEs16(vyy902, vyy912, dbf)
new_compare15(vyy900, vyy910, True, ea, eb) → LT
new_compare8(Double(vyy900, vyy901), Double(vyy910, vyy911)) → new_compare9(new_sr0(vyy900, vyy910), new_sr0(vyy901, vyy911))
new_esEs15(vyy3000, vyy400, ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), cgh, ty_Int) → new_esEs13(vyy3000, vyy400)
new_ltEs18(vyy90, vyy91) → new_not(new_esEs8(new_compare17(vyy90, vyy91), GT))
new_compare13(vyy900, vyy910) → new_compare24(vyy900, vyy910, new_esEs19(vyy900, vyy910))
new_esEs27(vyy901, vyy911, app(ty_Maybe, de)) → new_esEs7(vyy901, vyy911, de)
new_lt19(vyy901, vyy911, app(ty_Ratio, dbg)) → new_lt9(vyy901, vyy911, dbg)
new_lt11(vyy900, vyy910, ty_Float) → new_lt8(vyy900, vyy910)
new_ltEs11(vyy901, vyy911, ty_Float) → new_ltEs12(vyy901, vyy911)
new_lt5(vyy900, vyy910, ea, eb) → new_esEs8(new_compare7(vyy900, vyy910, ea, eb), LT)
new_esEs23(vyy3001, vyy401, app(ty_[], ccb)) → new_esEs17(vyy3001, vyy401, ccb)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, bha), bhb)) → new_esEs6(vyy3000, vyy400, bha, bhb)
new_primMulNat0(Zero, Zero) → Zero
new_esEs28(vyy900, vyy910, ty_Bool) → new_esEs19(vyy900, vyy910)
new_ltEs4(Just(vyy900), Just(vyy910), app(app(ty_@2, bdc), bdd)) → new_ltEs7(vyy900, vyy910, bdc, bdd)
new_ltEs7(@2(vyy900, vyy901), @2(vyy910, vyy911), eg, ge) → new_pePe(new_lt11(vyy900, vyy910, eg), new_asAs(new_esEs25(vyy900, vyy910, eg), new_ltEs11(vyy901, vyy911, ge)))
new_esEs17(:(vyy3000, vyy3001), :(vyy400, vyy401), dac) → new_asAs(new_esEs26(vyy3000, vyy400, dac), new_esEs17(vyy3001, vyy401, dac))
new_esEs27(vyy901, vyy911, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(vyy901, vyy911, cc, cd, ce)
new_compare27(vyy900, vyy910, app(app(ty_@2, hh), baa)) → new_compare7(vyy900, vyy910, hh, baa)
new_esEs6(Right(vyy3000), Right(vyy400), cgh, app(ty_Ratio, chd)) → new_esEs9(vyy3000, vyy400, chd)
new_sr(Integer(vyy9000), Integer(vyy9110)) → Integer(new_primMulInt(vyy9000, vyy9110))
new_esEs25(vyy900, vyy910, app(app(ty_Either, ha), hb)) → new_esEs6(vyy900, vyy910, ha, hb)
new_lt20(vyy900, vyy910, ty_Integer) → new_lt4(vyy900, vyy910)
new_lt19(vyy901, vyy911, app(app(ty_Either, dc), dd)) → new_lt15(vyy901, vyy911, dc, dd)
new_ltEs19(vyy902, vyy912, ty_Integer) → new_ltEs14(vyy902, vyy912)
new_lt20(vyy900, vyy910, app(app(ty_@2, ea), eb)) → new_lt5(vyy900, vyy910, ea, eb)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, cgd), cge), cgf), cfg) → new_esEs4(vyy3000, vyy400, cgd, cge, cgf)
new_ltEs16(vyy90, vyy91, cfa) → new_not(new_esEs8(new_compare16(vyy90, vyy91, cfa), GT))
new_ltEs4(Just(vyy900), Just(vyy910), ty_Bool) → new_ltEs5(vyy900, vyy910)
new_esEs27(vyy901, vyy911, ty_Integer) → new_esEs12(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, cfg) → new_esEs18(vyy3000, vyy400)
new_esEs25(vyy900, vyy910, ty_Double) → new_esEs16(vyy900, vyy910)
new_ltEs19(vyy902, vyy912, ty_Double) → new_ltEs6(vyy902, vyy912)
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, ty_Int) → new_ltEs10(vyy9000, vyy9100)
new_esEs27(vyy901, vyy911, app(ty_Ratio, dbg)) → new_esEs9(vyy901, vyy911, dbg)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs20(vyy3000, vyy400)
new_ltEs9(vyy90, vyy91) → new_not(new_esEs8(new_compare18(vyy90, vyy91), GT))
new_esEs22(vyy3002, vyy402, app(app(ty_@2, cbb), cbc)) → new_esEs5(vyy3002, vyy402, cbb, cbc)
new_compare0(:(vyy900, vyy901), :(vyy910, vyy911), hd) → new_primCompAux0(vyy900, vyy910, new_compare0(vyy901, vyy911, hd), hd)
new_ltEs19(vyy902, vyy912, ty_Int) → new_ltEs10(vyy902, vyy912)
new_esEs24(vyy3000, vyy400, app(app(ty_@2, cdf), cdg)) → new_esEs5(vyy3000, vyy400, cdf, cdg)
new_lt11(vyy900, vyy910, ty_Int) → new_lt7(vyy900, vyy910)
new_compare12(Float(vyy900, vyy901), Float(vyy910, vyy911)) → new_compare9(new_sr0(vyy900, vyy910), new_sr0(vyy901, vyy911))
new_ltEs8(EQ, EQ) → True
new_lt12(vyy900, vyy910, df, dg, dh) → new_esEs8(new_compare28(vyy900, vyy910, df, dg, dh), LT)
new_ltEs12(vyy90, vyy91) → new_not(new_esEs8(new_compare12(vyy90, vyy91), GT))
new_esEs23(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, ty_Ordering) → new_ltEs8(vyy9000, vyy9100)
new_esEs14(vyy3001, vyy401, ty_Int) → new_esEs13(vyy3001, vyy401)
new_esEs12(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs19(vyy902, vyy912, app(ty_Maybe, cb)) → new_ltEs4(vyy902, vyy912, cb)
new_esEs28(vyy900, vyy910, ty_Integer) → new_esEs12(vyy900, vyy910)
new_esEs22(vyy3002, vyy402, ty_Float) → new_esEs20(vyy3002, vyy402)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, bhd)) → new_esEs9(vyy3000, vyy400, bhd)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, cfg) → new_esEs12(vyy3000, vyy400)
new_pePe(False, vyy150) → vyy150
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Bool, ee) → new_ltEs5(vyy9000, vyy9100)
new_esEs11(vyy3000, vyy400, ty_Int) → new_esEs13(vyy3000, vyy400)
new_lt11(vyy900, vyy910, app(app(app(ty_@3, gb), gc), gd)) → new_lt12(vyy900, vyy910, gb, gc, gd)
new_lt6(vyy900, vyy910) → new_esEs8(new_compare8(vyy900, vyy910), LT)
new_esEs6(Right(vyy3000), Right(vyy400), cgh, ty_Double) → new_esEs16(vyy3000, vyy400)
new_compare29(vyy900, vyy910) → new_compare211(vyy900, vyy910, new_esEs8(vyy900, vyy910))
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, ty_Double) → new_ltEs6(vyy9000, vyy9100)
new_esEs24(vyy3000, vyy400, app(ty_Maybe, cec)) → new_esEs7(vyy3000, vyy400, cec)
new_ltEs4(Nothing, Just(vyy910), ceg) → True
new_esEs28(vyy900, vyy910, app(app(app(ty_@3, df), dg), dh)) → new_esEs4(vyy900, vyy910, df, dg, dh)
new_esEs22(vyy3002, vyy402, ty_Integer) → new_esEs12(vyy3002, vyy402)
new_ltEs11(vyy901, vyy911, ty_Ordering) → new_ltEs8(vyy901, vyy911)
new_esEs23(vyy3001, vyy401, app(ty_Maybe, cda)) → new_esEs7(vyy3001, vyy401, cda)
new_compare9(vyy90, vyy91) → new_primCmpInt(vyy90, vyy91)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, cfg) → new_esEs16(vyy3000, vyy400)
new_ltEs10(vyy90, vyy91) → new_not(new_esEs8(new_compare9(vyy90, vyy91), GT))
new_lt8(vyy900, vyy910) → new_esEs8(new_compare12(vyy900, vyy910), LT)
new_esEs27(vyy901, vyy911, ty_Float) → new_esEs20(vyy901, vyy911)
new_esEs27(vyy901, vyy911, app(ty_[], db)) → new_esEs17(vyy901, vyy911, db)
new_esEs22(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_ltEs8(EQ, GT) → True
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, app(ty_Maybe, bcg)) → new_ltEs4(vyy9000, vyy9100, bcg)
new_ltEs8(GT, GT) → True
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, ty_Float) → new_ltEs12(vyy9000, vyy9100)
new_compare10(vyy900, vyy910, True, ef) → LT
new_lt20(vyy900, vyy910, app(ty_Maybe, ef)) → new_lt16(vyy900, vyy910, ef)
new_esEs14(vyy3001, vyy401, app(ty_[], bef)) → new_esEs17(vyy3001, vyy401, bef)
new_primCmpNat0(Zero, Succ(vyy9100)) → LT
new_esEs23(vyy3001, vyy401, ty_Char) → new_esEs21(vyy3001, vyy401)
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, ty_Integer) → new_ltEs14(vyy9000, vyy9100)
new_lt19(vyy901, vyy911, app(app(ty_@2, cg), da)) → new_lt5(vyy901, vyy911, cg, da)
new_esEs6(Right(vyy3000), Left(vyy400), cgh, cfg) → False
new_esEs6(Left(vyy3000), Right(vyy400), cgh, cfg) → False
new_esEs8(LT, LT) → True
new_esEs6(Right(vyy3000), Right(vyy400), cgh, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, cfg) → new_esEs20(vyy3000, vyy400)
new_esEs28(vyy900, vyy910, ty_Double) → new_esEs16(vyy900, vyy910)
new_ltEs8(LT, EQ) → True
new_lt20(vyy900, vyy910, app(ty_Ratio, ced)) → new_lt9(vyy900, vyy910, ced)
new_esEs25(vyy900, vyy910, ty_Ordering) → new_esEs8(vyy900, vyy910)
new_compare10(vyy900, vyy910, False, ef) → GT
new_compare27(vyy900, vyy910, ty_Double) → new_compare8(vyy900, vyy910)
new_ltEs5(True, False) → False
new_pePe(True, vyy150) → True
new_compare0([], [], hd) → EQ
new_esEs27(vyy901, vyy911, ty_@0) → new_esEs18(vyy901, vyy911)
new_primEqNat0(Zero, Zero) → True
new_esEs23(vyy3001, vyy401, app(app(ty_Either, cbh), cca)) → new_esEs6(vyy3001, vyy401, cbh, cca)
new_compare17(@0, @0) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), cgh, app(app(app(ty_@3, chg), chh), daa)) → new_esEs4(vyy3000, vyy400, chg, chh, daa)
new_primCompAux0(vyy900, vyy910, vyy151, hd) → new_primCompAux00(vyy151, new_compare27(vyy900, vyy910, hd))
new_esEs6(Right(vyy3000), Right(vyy400), cgh, app(app(ty_Either, cha), chb)) → new_esEs6(vyy3000, vyy400, cha, chb)
new_ltEs5(True, True) → True
new_ltEs17(Right(vyy9000), Left(vyy9100), ed, ee) → False
new_esEs19(True, True) → True
new_ltEs17(Left(vyy9000), Left(vyy9100), app(ty_[], bbc), ee) → new_ltEs15(vyy9000, vyy9100, bbc)
new_ltEs8(GT, EQ) → False
new_ltEs8(EQ, LT) → False
new_ltEs17(Left(vyy9000), Left(vyy9100), app(app(ty_@2, bba), bbb), ee) → new_ltEs7(vyy9000, vyy9100, bba, bbb)
new_compare16(:%(vyy900, vyy901), :%(vyy910, vyy911), ty_Integer) → new_compare6(new_sr(vyy900, vyy911), new_sr(vyy910, vyy901))
new_ltEs11(vyy901, vyy911, ty_Char) → new_ltEs9(vyy901, vyy911)
new_esEs25(vyy900, vyy910, ty_Int) → new_esEs13(vyy900, vyy910)
new_esEs6(Right(vyy3000), Right(vyy400), cgh, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_esEs28(vyy900, vyy910, app(app(ty_Either, ed), ee)) → new_esEs6(vyy900, vyy910, ed, ee)
new_esEs22(vyy3002, vyy402, ty_Char) → new_esEs21(vyy3002, vyy402)
new_esEs24(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt11(vyy900, vyy910, ty_@0) → new_lt10(vyy900, vyy910)
new_esEs8(GT, GT) → True
new_esEs13(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_primPlusNat0(Succ(vyy1340), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1340, vyy40100)))
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs4(vyy3000, vyy400, dbb, dbc, dbd)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_lt20(vyy900, vyy910, ty_Char) → new_lt17(vyy900, vyy910)
new_esEs14(vyy3001, vyy401, app(app(ty_Either, bed), bee)) → new_esEs6(vyy3001, vyy401, bed, bee)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs21(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs15(vyy3000, vyy400, app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs4(vyy3000, vyy400, bgd, bge, bgf)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs19(vyy902, vyy912, ty_Ordering) → new_ltEs8(vyy902, vyy912)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Double, ee) → new_ltEs6(vyy9000, vyy9100)
new_esEs15(vyy3000, vyy400, ty_Char) → new_esEs21(vyy3000, vyy400)
new_ltEs5(False, False) → True
new_esEs23(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy13400), Zero) → Succ(vyy13400)
new_esEs24(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_compare27(vyy900, vyy910, ty_Integer) → new_compare6(vyy900, vyy910)
new_ltEs4(Nothing, Nothing, ceg) → True
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs17(Left(vyy9000), Left(vyy9100), app(app(app(ty_@3, baf), bag), bah), ee) → new_ltEs13(vyy9000, vyy9100, baf, bag, bah)
new_esEs28(vyy900, vyy910, ty_Float) → new_esEs20(vyy900, vyy910)
new_esEs19(False, False) → True
new_esEs22(vyy3002, vyy402, ty_@0) → new_esEs18(vyy3002, vyy402)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs11(vyy901, vyy911, app(ty_[], ff)) → new_ltEs15(vyy901, vyy911, ff)
new_esEs15(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_compare112(vyy900, vyy910, False, ed, ee) → GT
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_esEs8(EQ, EQ) → True
new_ltEs17(Left(vyy9000), Left(vyy9100), app(ty_Maybe, bbf), ee) → new_ltEs4(vyy9000, vyy9100, bbf)
new_compare26(vyy900, vyy910, True, ed, ee) → EQ
new_lt20(vyy900, vyy910, ty_@0) → new_lt10(vyy900, vyy910)
new_esEs6(Right(vyy3000), Right(vyy400), cgh, app(ty_[], chc)) → new_esEs17(vyy3000, vyy400, chc)
new_lt20(vyy900, vyy910, ty_Ordering) → new_lt13(vyy900, vyy910)
new_esEs23(vyy3001, vyy401, app(app(app(ty_@3, ccf), ccg), cch)) → new_esEs4(vyy3001, vyy401, ccf, ccg, cch)
new_esEs14(vyy3001, vyy401, app(ty_Ratio, beg)) → new_esEs9(vyy3001, vyy401, beg)
new_esEs28(vyy900, vyy910, ty_Int) → new_esEs13(vyy900, vyy910)
new_lt9(vyy900, vyy910, ced) → new_esEs8(new_compare16(vyy900, vyy910, ced), LT)
new_lt18(vyy900, vyy910) → new_esEs8(new_compare13(vyy900, vyy910), LT)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs28(vyy900, vyy910, ty_@0) → new_esEs18(vyy900, vyy910)
new_esEs14(vyy3001, vyy401, app(ty_Maybe, bfe)) → new_esEs7(vyy3001, vyy401, bfe)
new_esEs15(vyy3000, vyy400, app(ty_Ratio, bga)) → new_esEs9(vyy3000, vyy400, bga)
new_primCmpNat0(Succ(vyy9000), Succ(vyy9100)) → new_primCmpNat0(vyy9000, vyy9100)
new_compare7(vyy900, vyy910, ea, eb) → new_compare25(vyy900, vyy910, new_esEs5(vyy900, vyy910, ea, eb), ea, eb)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_lt20(vyy900, vyy910, ty_Int) → new_lt7(vyy900, vyy910)
new_esEs14(vyy3001, vyy401, ty_Float) → new_esEs20(vyy3001, vyy401)
new_lt10(vyy900, vyy910) → new_esEs8(new_compare17(vyy900, vyy910), LT)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs13(vyy3000, vyy400)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_esEs27(vyy901, vyy911, ty_Ordering) → new_esEs8(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], cfh), cfg) → new_esEs17(vyy3000, vyy400, cfh)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, cga), cfg) → new_esEs9(vyy3000, vyy400, cga)
new_esEs6(Right(vyy3000), Right(vyy400), cgh, app(app(ty_@2, che), chf)) → new_esEs5(vyy3000, vyy400, che, chf)
new_compare111(vyy900, vyy910, True, df, dg, dh) → LT
new_esEs22(vyy3002, vyy402, ty_Int) → new_esEs13(vyy3002, vyy402)
new_primCompAux00(vyy160, LT) → LT
new_ltEs4(Just(vyy900), Just(vyy910), ty_Int) → new_ltEs10(vyy900, vyy910)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs13(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy9000)), Neg(vyy910)) → new_primCmpNat0(vyy910, Succ(vyy9000))
new_esEs24(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt7(vyy900, vyy910) → new_esEs8(new_compare9(vyy900, vyy910), LT)
new_esEs7(Nothing, Nothing, bgh) → True
new_esEs28(vyy900, vyy910, ty_Ordering) → new_esEs8(vyy900, vyy910)
new_compare27(vyy900, vyy910, app(ty_Maybe, bae)) → new_compare14(vyy900, vyy910, bae)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_lt4(vyy900, vyy910) → new_esEs8(new_compare6(vyy900, vyy910), LT)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs21(vyy3000, vyy400)
new_ltEs19(vyy902, vyy912, app(app(ty_Either, bh), ca)) → new_ltEs17(vyy902, vyy912, bh, ca)
new_primCmpNat0(Zero, Zero) → EQ
new_compare28(vyy900, vyy910, df, dg, dh) → new_compare210(vyy900, vyy910, new_esEs4(vyy900, vyy910, df, dg, dh), df, dg, dh)
new_esEs6(Right(vyy3000), Right(vyy400), cgh, app(ty_Maybe, dab)) → new_esEs7(vyy3000, vyy400, dab)
new_esEs23(vyy3001, vyy401, ty_@0) → new_esEs18(vyy3001, vyy401)
new_primCmpNat0(Succ(vyy9000), Zero) → GT
new_esEs23(vyy3001, vyy401, app(app(ty_@2, ccd), cce)) → new_esEs5(vyy3001, vyy401, ccd, cce)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy9100))) → LT
new_esEs19(True, False) → False
new_esEs19(False, True) → False
new_compare210(vyy900, vyy910, True, df, dg, dh) → EQ
new_compare27(vyy900, vyy910, app(ty_[], bab)) → new_compare0(vyy900, vyy910, bab)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bhg), bhh), caa)) → new_esEs4(vyy3000, vyy400, bhg, bhh, caa)
new_primPlusNat1(Succ(vyy13400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy13400, vyy401000)))
new_compare6(Integer(vyy900), Integer(vyy910)) → new_primCmpInt(vyy900, vyy910)
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_esEs25(vyy900, vyy910, ty_Bool) → new_esEs19(vyy900, vyy910)
new_esEs7(Just(vyy3000), Nothing, bgh) → False
new_esEs7(Nothing, Just(vyy400), bgh) → False
new_esEs15(vyy3000, vyy400, app(app(ty_@2, bgb), bgc)) → new_esEs5(vyy3000, vyy400, bgb, bgc)
new_ltEs5(False, True) → True
new_lt11(vyy900, vyy910, app(ty_Ratio, cef)) → new_lt9(vyy900, vyy910, cef)
new_lt19(vyy901, vyy911, app(ty_Maybe, de)) → new_lt16(vyy901, vyy911, de)
new_compare26(vyy900, vyy910, False, ed, ee) → new_compare112(vyy900, vyy910, new_ltEs17(vyy900, vyy910, ed, ee), ed, ee)
new_ltEs11(vyy901, vyy911, app(app(app(ty_@3, eh), fa), fb)) → new_ltEs13(vyy901, vyy911, eh, fa, fb)
new_lt19(vyy901, vyy911, ty_Int) → new_lt7(vyy901, vyy911)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_esEs14(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, app(ty_[], daf)) → new_esEs17(vyy3000, vyy400, daf)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy9100))) → new_primCmpNat0(Zero, Succ(vyy9100))
new_compare27(vyy900, vyy910, app(app(app(ty_@3, he), hf), hg)) → new_compare28(vyy900, vyy910, he, hf, hg)
new_primCompAux00(vyy160, EQ) → vyy160
new_compare24(vyy900, vyy910, True) → EQ
new_compare27(vyy900, vyy910, ty_Float) → new_compare12(vyy900, vyy910)
new_esEs27(vyy901, vyy911, ty_Int) → new_esEs13(vyy901, vyy911)
new_esEs23(vyy3001, vyy401, ty_Bool) → new_esEs19(vyy3001, vyy401)
new_esEs22(vyy3002, vyy402, ty_Bool) → new_esEs19(vyy3002, vyy402)
new_ltEs8(GT, LT) → False
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs27(vyy901, vyy911, ty_Double) → new_esEs16(vyy901, vyy911)
new_esEs15(vyy3000, vyy400, app(ty_Maybe, bgg)) → new_esEs7(vyy3000, vyy400, bgg)
new_ltEs19(vyy902, vyy912, app(app(app(ty_@3, bb), bc), bd)) → new_ltEs13(vyy902, vyy912, bb, bc, bd)
new_ltEs11(vyy901, vyy911, ty_@0) → new_ltEs18(vyy901, vyy911)
new_compare27(vyy900, vyy910, ty_Int) → new_compare9(vyy900, vyy910)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, dah), dba)) → new_esEs5(vyy3000, vyy400, dah, dba)
new_ltEs15(vyy90, vyy91, hd) → new_not(new_esEs8(new_compare0(vyy90, vyy91, hd), GT))
new_ltEs11(vyy901, vyy911, ty_Double) → new_ltEs6(vyy901, vyy911)
new_not(False) → True
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, cfe), cff), cfg) → new_esEs6(vyy3000, vyy400, cfe, cff)
new_compare211(vyy900, vyy910, False) → new_compare110(vyy900, vyy910, new_ltEs8(vyy900, vyy910))
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, ty_@0) → new_ltEs18(vyy9000, vyy9100)
new_esEs24(vyy3000, vyy400, ty_Int) → new_esEs13(vyy3000, vyy400)
new_esEs25(vyy900, vyy910, ty_Float) → new_esEs20(vyy900, vyy910)
new_primCmpInt(Pos(Succ(vyy9000)), Pos(vyy910)) → new_primCmpNat0(Succ(vyy9000), vyy910)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs14(vyy3001, vyy401, app(app(ty_@2, beh), bfa)) → new_esEs5(vyy3001, vyy401, beh, bfa)
new_ltEs4(Just(vyy900), Just(vyy910), app(app(app(ty_@3, bch), bda), bdb)) → new_ltEs13(vyy900, vyy910, bch, bda, bdb)
new_esEs6(Right(vyy3000), Right(vyy400), cgh, ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs15(vyy3000, vyy400, app(ty_[], bfh)) → new_esEs17(vyy3000, vyy400, bfh)
new_esEs24(vyy3000, vyy400, app(app(ty_Either, cdb), cdc)) → new_esEs6(vyy3000, vyy400, cdb, cdc)
new_esEs20(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs13(new_sr0(vyy3000, vyy400), new_sr0(vyy3001, vyy401))
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, app(app(ty_Either, bce), bcf)) → new_ltEs17(vyy9000, vyy9100, bce, bcf)
new_lt11(vyy900, vyy910, ty_Ordering) → new_lt13(vyy900, vyy910)
new_esEs25(vyy900, vyy910, app(app(app(ty_@3, gb), gc), gd)) → new_esEs4(vyy900, vyy910, gb, gc, gd)
new_esEs24(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs28(vyy900, vyy910, app(app(ty_@2, ea), eb)) → new_esEs5(vyy900, vyy910, ea, eb)
new_compare0(:(vyy900, vyy901), [], hd) → GT
new_lt11(vyy900, vyy910, ty_Integer) → new_lt4(vyy900, vyy910)
new_ltEs19(vyy902, vyy912, ty_@0) → new_ltEs18(vyy902, vyy912)
new_ltEs4(Just(vyy900), Just(vyy910), ty_Ordering) → new_ltEs8(vyy900, vyy910)
new_esEs24(vyy3000, vyy400, app(ty_[], cdd)) → new_esEs17(vyy3000, vyy400, cdd)
new_lt19(vyy901, vyy911, app(app(app(ty_@3, cc), cd), ce)) → new_lt12(vyy901, vyy911, cc, cd, ce)
new_lt19(vyy901, vyy911, ty_Integer) → new_lt4(vyy901, vyy911)
new_esEs22(vyy3002, vyy402, app(app(app(ty_@3, cbd), cbe), cbf)) → new_esEs4(vyy3002, vyy402, cbd, cbe, cbf)
new_esEs27(vyy901, vyy911, app(app(ty_Either, dc), dd)) → new_esEs6(vyy901, vyy911, dc, dd)
new_lt20(vyy900, vyy910, ty_Double) → new_lt6(vyy900, vyy910)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, cfg) → new_esEs21(vyy3000, vyy400)
new_ltEs19(vyy902, vyy912, app(ty_[], bg)) → new_ltEs15(vyy902, vyy912, bg)
new_esEs15(vyy3000, vyy400, app(app(ty_Either, bff), bfg)) → new_esEs6(vyy3000, vyy400, bff, bfg)
new_ltEs11(vyy901, vyy911, app(app(ty_Either, fg), fh)) → new_ltEs17(vyy901, vyy911, fg, fh)
new_lt11(vyy900, vyy910, ty_Char) → new_lt17(vyy900, vyy910)
new_primCmpInt(Pos(Succ(vyy9000)), Neg(vyy910)) → GT
new_compare27(vyy900, vyy910, ty_@0) → new_compare17(vyy900, vyy910)
new_esEs28(vyy900, vyy910, app(ty_Maybe, ef)) → new_esEs7(vyy900, vyy910, ef)
new_ltEs4(Just(vyy900), Just(vyy910), ty_@0) → new_ltEs18(vyy900, vyy910)
new_lt19(vyy901, vyy911, ty_Char) → new_lt17(vyy901, vyy911)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs14(vyy3001, vyy401, ty_Double) → new_esEs16(vyy3001, vyy401)
new_ltEs17(Left(vyy9000), Left(vyy9100), app(app(ty_Either, bbd), bbe), ee) → new_ltEs17(vyy9000, vyy9100, bbd, bbe)
new_ltEs17(Left(vyy9000), Left(vyy9100), app(ty_Ratio, cfc), ee) → new_ltEs16(vyy9000, vyy9100, cfc)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, cgb), cgc), cfg) → new_esEs5(vyy3000, vyy400, cgb, cgc)
new_lt11(vyy900, vyy910, app(ty_[], gh)) → new_lt14(vyy900, vyy910, gh)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare27(vyy900, vyy910, ty_Char) → new_compare18(vyy900, vyy910)
new_compare110(vyy900, vyy910, True) → LT
new_esEs28(vyy900, vyy910, app(ty_Ratio, ced)) → new_esEs9(vyy900, vyy910, ced)
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_compare25(vyy900, vyy910, True, ea, eb) → EQ
new_esEs14(vyy3001, vyy401, ty_Char) → new_esEs21(vyy3001, vyy401)
new_compare110(vyy900, vyy910, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs4(Just(vyy900), Just(vyy910), ty_Double) → new_ltEs6(vyy900, vyy910)
new_esEs24(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_compare111(vyy900, vyy910, False, df, dg, dh) → GT
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs19(vyy3000, vyy400)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Int, ee) → new_ltEs10(vyy9000, vyy9100)
new_esEs5(@2(vyy3000, vyy3001), @2(vyy400, vyy401), beb, bec) → new_asAs(new_esEs15(vyy3000, vyy400, beb), new_esEs14(vyy3001, vyy401, bec))
new_esEs27(vyy901, vyy911, app(app(ty_@2, cg), da)) → new_esEs5(vyy901, vyy911, cg, da)
new_ltEs11(vyy901, vyy911, app(ty_Maybe, ga)) → new_ltEs4(vyy901, vyy911, ga)
new_ltEs4(Just(vyy900), Just(vyy910), app(ty_[], bde)) → new_ltEs15(vyy900, vyy910, bde)
new_esEs22(vyy3002, vyy402, app(ty_[], cah)) → new_esEs17(vyy3002, vyy402, cah)
new_lt20(vyy900, vyy910, ty_Bool) → new_lt18(vyy900, vyy910)
new_ltEs19(vyy902, vyy912, ty_Char) → new_ltEs9(vyy902, vyy912)
new_compare25(vyy900, vyy910, False, ea, eb) → new_compare15(vyy900, vyy910, new_ltEs7(vyy900, vyy910, ea, eb), ea, eb)
new_ltEs11(vyy901, vyy911, ty_Int) → new_ltEs10(vyy901, vyy911)
new_lt19(vyy901, vyy911, ty_Bool) → new_lt18(vyy901, vyy911)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy9100))) → new_primCmpNat0(Succ(vyy9100), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy9100))) → GT
new_esEs24(vyy3000, vyy400, ty_Char) → new_esEs21(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, cgg), cfg) → new_esEs7(vyy3000, vyy400, cgg)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, cfg) → new_esEs8(vyy3000, vyy400)
new_ltEs11(vyy901, vyy911, app(ty_Ratio, cee)) → new_ltEs16(vyy901, vyy911, cee)
new_ltEs11(vyy901, vyy911, ty_Bool) → new_ltEs5(vyy901, vyy911)
new_ltEs4(Just(vyy900), Just(vyy910), app(app(ty_Either, bdf), bdg)) → new_ltEs17(vyy900, vyy910, bdf, bdg)
new_sr0(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_compare23(vyy900, vyy910, True, ef) → EQ
new_compare15(vyy900, vyy910, False, ea, eb) → GT
new_compare27(vyy900, vyy910, app(ty_Ratio, cfb)) → new_compare16(vyy900, vyy910, cfb)
new_ltEs17(Left(vyy9000), Right(vyy9100), ed, ee) → True
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, app(app(ty_@2, bcb), bcc)) → new_ltEs7(vyy9000, vyy9100, bcb, bcc)
new_compare210(vyy900, vyy910, False, df, dg, dh) → new_compare111(vyy900, vyy910, new_ltEs13(vyy900, vyy910, df, dg, dh), df, dg, dh)
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Int) → new_esEs13(vyy3001, vyy401)
new_esEs25(vyy900, vyy910, app(ty_Maybe, hc)) → new_esEs7(vyy900, vyy910, hc)
new_ltEs4(Just(vyy900), Just(vyy910), app(ty_Maybe, bdh)) → new_ltEs4(vyy900, vyy910, bdh)
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, app(app(app(ty_@3, bbg), bbh), bca)) → new_ltEs13(vyy9000, vyy9100, bbg, bbh, bca)
new_ltEs4(Just(vyy900), Just(vyy910), ty_Float) → new_ltEs12(vyy900, vyy910)
new_compare16(:%(vyy900, vyy901), :%(vyy910, vyy911), ty_Int) → new_compare9(new_sr0(vyy900, vyy911), new_sr0(vyy910, vyy901))
new_ltEs14(vyy90, vyy91) → new_not(new_esEs8(new_compare6(vyy90, vyy91), GT))
new_esEs6(Right(vyy3000), Right(vyy400), cgh, ty_Float) → new_esEs20(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs16(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs13(new_sr0(vyy3000, vyy400), new_sr0(vyy3001, vyy401))
new_lt19(vyy901, vyy911, ty_Ordering) → new_lt13(vyy901, vyy911)
new_esEs6(Right(vyy3000), Right(vyy400), cgh, ty_Char) → new_esEs21(vyy3000, vyy400)
new_asAs(False, vyy123) → False
new_ltEs19(vyy902, vyy912, app(app(ty_@2, be), bf)) → new_ltEs7(vyy902, vyy912, be, bf)
new_compare24(vyy900, vyy910, False) → new_compare11(vyy900, vyy910, new_ltEs5(vyy900, vyy910))
new_esEs25(vyy900, vyy910, app(ty_Ratio, cef)) → new_esEs9(vyy900, vyy910, cef)
new_lt15(vyy900, vyy910, ed, ee) → new_esEs8(new_compare19(vyy900, vyy910, ed, ee), LT)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_lt20(vyy900, vyy910, app(ty_[], ec)) → new_lt14(vyy900, vyy910, ec)
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, app(ty_Ratio, cfd)) → new_ltEs16(vyy9000, vyy9100, cfd)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, dbe)) → new_esEs7(vyy3000, vyy400, dbe)
new_esEs14(vyy3001, vyy401, app(app(app(ty_@3, bfb), bfc), bfd)) → new_esEs4(vyy3001, vyy401, bfb, bfc, bfd)
new_lt19(vyy901, vyy911, ty_Float) → new_lt8(vyy901, vyy911)
new_ltEs4(Just(vyy900), Just(vyy910), ty_Integer) → new_ltEs14(vyy900, vyy910)
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, ty_Char) → new_ltEs9(vyy9000, vyy9100)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Ordering, ee) → new_ltEs8(vyy9000, vyy9100)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, dag)) → new_esEs9(vyy3000, vyy400, dag)
new_lt20(vyy900, vyy910, ty_Float) → new_lt8(vyy900, vyy910)
new_lt11(vyy900, vyy910, app(app(ty_@2, gf), gg)) → new_lt5(vyy900, vyy910, gf, gg)
new_esEs4(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cac, cad, cae) → new_asAs(new_esEs24(vyy3000, vyy400, cac), new_asAs(new_esEs23(vyy3001, vyy401, cad), new_esEs22(vyy3002, vyy402, cae)))
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs25(vyy900, vyy910, app(ty_[], gh)) → new_esEs17(vyy900, vyy910, gh)
new_compare27(vyy900, vyy910, app(app(ty_Either, bac), bad)) → new_compare19(vyy900, vyy910, bac, bad)
new_esEs23(vyy3001, vyy401, ty_Double) → new_esEs16(vyy3001, vyy401)
new_esEs25(vyy900, vyy910, ty_@0) → new_esEs18(vyy900, vyy910)
new_ltEs4(Just(vyy900), Just(vyy910), app(ty_Ratio, ceh)) → new_ltEs16(vyy900, vyy910, ceh)
new_ltEs6(vyy90, vyy91) → new_not(new_esEs8(new_compare8(vyy90, vyy91), GT))
new_lt19(vyy901, vyy911, app(ty_[], db)) → new_lt14(vyy901, vyy911, db)
new_ltEs11(vyy901, vyy911, app(app(ty_@2, fc), fd)) → new_ltEs7(vyy901, vyy911, fc, fd)
new_ltEs8(LT, GT) → True
new_ltEs13(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), h, ba, cf) → new_pePe(new_lt20(vyy900, vyy910, h), new_asAs(new_esEs28(vyy900, vyy910, h), new_pePe(new_lt19(vyy901, vyy911, ba), new_asAs(new_esEs27(vyy901, vyy911, ba), new_ltEs19(vyy902, vyy912, cf)))))
new_compare19(vyy900, vyy910, ed, ee) → new_compare26(vyy900, vyy910, new_esEs6(vyy900, vyy910, ed, ee), ed, ee)
new_esEs25(vyy900, vyy910, ty_Char) → new_esEs21(vyy900, vyy910)
new_compare23(vyy900, vyy910, False, ef) → new_compare10(vyy900, vyy910, new_ltEs4(vyy900, vyy910, ef), ef)
new_ltEs19(vyy902, vyy912, ty_Bool) → new_ltEs5(vyy902, vyy912)
new_compare27(vyy900, vyy910, ty_Ordering) → new_compare29(vyy900, vyy910)
new_esEs28(vyy900, vyy910, app(ty_[], ec)) → new_esEs17(vyy900, vyy910, ec)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], bhc)) → new_esEs17(vyy3000, vyy400, bhc)
new_esEs14(vyy3001, vyy401, ty_Bool) → new_esEs19(vyy3001, vyy401)
new_esEs27(vyy901, vyy911, ty_Char) → new_esEs21(vyy901, vyy911)
new_esEs15(vyy3000, vyy400, ty_Int) → new_esEs13(vyy3000, vyy400)
new_esEs11(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_lt11(vyy900, vyy910, app(app(ty_Either, ha), hb)) → new_lt15(vyy900, vyy910, ha, hb)
new_compare11(vyy900, vyy910, False) → GT
new_esEs9(:%(vyy3000, vyy3001), :%(vyy400, vyy401), bea) → new_asAs(new_esEs11(vyy3000, vyy400, bea), new_esEs10(vyy3001, vyy401, bea))
new_esEs14(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_ltEs4(Just(vyy900), Just(vyy910), ty_Char) → new_ltEs9(vyy900, vyy910)
new_esEs25(vyy900, vyy910, app(app(ty_@2, gf), gg)) → new_esEs5(vyy900, vyy910, gf, gg)
new_lt16(vyy900, vyy910, ef) → new_esEs8(new_compare14(vyy900, vyy910, ef), LT)
new_lt20(vyy900, vyy910, app(app(ty_Either, ed), ee)) → new_lt15(vyy900, vyy910, ed, ee)
new_compare11(vyy900, vyy910, True) → LT
new_lt11(vyy900, vyy910, ty_Bool) → new_lt18(vyy900, vyy910)
new_compare18(Char(vyy900), Char(vyy910)) → new_primCmpNat0(vyy900, vyy910)
new_esEs23(vyy3001, vyy401, app(ty_Ratio, ccc)) → new_esEs9(vyy3001, vyy401, ccc)
new_esEs22(vyy3002, vyy402, app(app(ty_Either, caf), cag)) → new_esEs6(vyy3002, vyy402, caf, cag)
new_lt17(vyy900, vyy910) → new_esEs8(new_compare18(vyy900, vyy910), LT)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, cfg) → new_esEs13(vyy3000, vyy400)
new_lt19(vyy901, vyy911, ty_Double) → new_lt6(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, cfg) → new_esEs19(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, bhe), bhf)) → new_esEs5(vyy3000, vyy400, bhe, bhf)
new_esEs10(vyy3001, vyy401, ty_Int) → new_esEs13(vyy3001, vyy401)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Char, ee) → new_ltEs9(vyy9000, vyy9100)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_@0, ee) → new_ltEs18(vyy9000, vyy9100)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_esEs24(vyy3000, vyy400, ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs15(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_esEs22(vyy3002, vyy402, ty_Double) → new_esEs16(vyy3002, vyy402)
new_lt19(vyy901, vyy911, ty_@0) → new_lt10(vyy901, vyy911)
new_ltEs8(LT, LT) → True
new_compare27(vyy900, vyy910, ty_Bool) → new_compare13(vyy900, vyy910)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs21(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, dad), dae)) → new_esEs6(vyy3000, vyy400, dad, dae)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vyy910, vyy911), hd) → LT
new_esEs15(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_ltEs11(vyy901, vyy911, ty_Integer) → new_ltEs14(vyy901, vyy911)
new_asAs(True, vyy123) → vyy123
new_ltEs4(Just(vyy900), Nothing, ceg) → False
new_compare112(vyy900, vyy910, True, ed, ee) → LT
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Float, ee) → new_ltEs12(vyy9000, vyy9100)
new_ltEs19(vyy902, vyy912, ty_Float) → new_ltEs12(vyy902, vyy912)
new_esEs18(@0, @0) → True
new_esEs17([], [], dac) → True
new_compare211(vyy900, vyy910, True) → EQ
new_esEs17([], :(vyy400, vyy401), dac) → False
new_esEs17(:(vyy3000, vyy3001), [], dac) → False
new_compare14(vyy900, vyy910, ef) → new_compare23(vyy900, vyy910, new_esEs7(vyy900, vyy910, ef), ef)
new_esEs14(vyy3001, vyy401, ty_@0) → new_esEs18(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)
new_lt14(vyy900, vyy910, ec) → new_esEs8(new_compare0(vyy900, vyy910, ec), LT)
new_lt11(vyy900, vyy910, ty_Double) → new_lt6(vyy900, vyy910)
new_esEs15(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs24(vyy3000, vyy400, app(app(app(ty_@3, cdh), cea), ceb)) → new_esEs4(vyy3000, vyy400, cdh, cea, ceb)
new_lt11(vyy900, vyy910, app(ty_Maybe, hc)) → new_lt16(vyy900, vyy910, hc)
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, ty_Bool) → new_ltEs5(vyy9000, vyy9100)
new_primCompAux00(vyy160, GT) → GT
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Integer, ee) → new_ltEs14(vyy9000, vyy9100)
new_esEs6(Right(vyy3000), Right(vyy400), cgh, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(vyy3000, vyy400, app(ty_Ratio, cde)) → new_esEs9(vyy3000, vyy400, cde)
new_esEs27(vyy901, vyy911, ty_Bool) → new_esEs19(vyy901, vyy911)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs16(vyy3000, vyy400)
new_ltEs17(Right(vyy9000), Right(vyy9100), ed, app(ty_[], bcd)) → new_ltEs15(vyy9000, vyy9100, bcd)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_lt13(vyy900, vyy910) → new_esEs8(new_compare29(vyy900, vyy910), LT)
new_esEs22(vyy3002, vyy402, app(ty_Maybe, cbg)) → new_esEs7(vyy3002, vyy402, cbg)
new_primCmpInt(Neg(Succ(vyy9000)), Pos(vyy910)) → LT
new_not(True) → False
new_esEs15(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)

The set Q consists of the following terms:

new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Float)
new_compare18(Char(x0), Char(x1))
new_compare27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs18(@0, @0)
new_lt19(x0, x1, ty_Double)
new_compare10(x0, x1, True, x2)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs14(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs14(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_esEs15(x0, x1, ty_Int)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_asAs(True, x0)
new_ltEs9(x0, x1)
new_ltEs8(EQ, EQ)
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs15(x0, x1, ty_Double)
new_lt5(x0, x1, x2, x3)
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Bool)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_primCompAux0(x0, x1, x2, x3)
new_primMulNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Bool)
new_compare0([], [], x0)
new_compare211(x0, x1, False)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_compare111(x0, x1, False, x2, x3, x4)
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Double)
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_Ordering)
new_lt11(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_lt11(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, x2, x3, x4)
new_lt9(x0, x1, x2)
new_lt16(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs17(Right(x0), Right(x1), x2, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_compare17(@0, @0)
new_compare15(x0, x1, True, x2, x3)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs8(LT, LT)
new_esEs15(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_ltEs11(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Char)
new_ltEs5(False, False)
new_ltEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare210(x0, x1, True, x2, x3, x4)
new_lt11(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, ty_Ordering)
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs17(Left(x0), Left(x1), ty_Integer, x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Integer)
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_esEs19(True, True)
new_compare19(x0, x1, x2, x3)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs28(x0, x1, ty_Float)
new_ltEs17(Left(x0), Left(x1), ty_@0, x2)
new_ltEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs11(x0, x1, ty_Integer)
new_lt14(x0, x1, x2)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare8(Double(x0, x1), Double(x2, x3))
new_lt20(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Succ(x1))
new_asAs(False, x0)
new_esEs27(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_ltEs17(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, False)
new_primEqNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs17(Left(x0), Left(x1), ty_Char, x2)
new_ltEs16(x0, x1, x2)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare24(x0, x1, False)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, ty_Float)
new_compare29(x0, x1)
new_esEs22(x0, x1, ty_Float)
new_primPlusNat1(Zero, Succ(x0))
new_esEs17(:(x0, x1), [], x2)
new_esEs14(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Zero)
new_esEs25(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Pos(x1))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare10(x0, x1, False, x2)
new_esEs14(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Int)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs19(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1, x2, x3)
new_esEs11(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_compare27(x0, x1, ty_Bool)
new_compare27(x0, x1, ty_Double)
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs6(x0, x1)
new_compare23(x0, x1, True, x2)
new_lt13(x0, x1)
new_ltEs15(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs11(x0, x1, ty_Double)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs17(Right(x0), Left(x1), x2, x3)
new_ltEs17(Left(x0), Right(x1), x2, x3)
new_ltEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, ty_Char)
new_ltEs11(x0, x1, ty_Bool)
new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, ty_Float)
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_lt11(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Double)
new_ltEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs10(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_@0)
new_esEs14(x0, x1, ty_Float)
new_esEs15(x0, x1, ty_Bool)
new_sr0(x0, x1)
new_esEs25(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, ty_Double)
new_compare210(x0, x1, False, x2, x3, x4)
new_ltEs4(Nothing, Nothing, x0)
new_esEs19(False, True)
new_esEs19(True, False)
new_esEs22(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpNat0(Zero, Succ(x0))
new_compare112(x0, x1, False, x2, x3)
new_ltEs17(Left(x0), Left(x1), ty_Double, x2)
new_ltEs17(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs7(Nothing, Just(x0), x1)
new_esEs15(x0, x1, ty_Float)
new_ltEs11(x0, x1, ty_@0)
new_esEs14(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs17(Right(x0), Right(x1), x2, ty_@0)
new_ltEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs25(x0, x1, ty_Integer)
new_compare13(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primCompAux00(x0, LT)
new_esEs11(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Ordering)
new_esEs14(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, ty_Int)
new_ltEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs14(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt19(x0, x1, ty_Integer)
new_compare25(x0, x1, True, x2, x3)
new_compare0([], :(x0, x1), x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare11(x0, x1, True)
new_compare27(x0, x1, ty_Int)
new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_lt18(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_esEs24(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(False, False)
new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Ordering)
new_compare25(x0, x1, False, x2, x3)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Integer)
new_ltEs11(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_compare28(x0, x1, x2, x3, x4)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_compare16(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs14(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs17(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare110(x0, x1, False)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs15(x0, x1, ty_@0)
new_esEs17([], :(x0, x1), x2)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Char)
new_compare27(x0, x1, app(ty_Maybe, x2))
new_compare27(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs17(Right(x0), Right(x1), x2, ty_Char)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_lt11(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs14(x0, x1, ty_Double)
new_esEs15(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Double)
new_primPlusNat0(Zero, x0)
new_ltEs8(LT, LT)
new_esEs7(Just(x0), Nothing, x1)
new_esEs7(Nothing, Nothing, x0)
new_esEs23(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs17(Right(x0), Right(x1), x2, ty_Double)
new_primCmpNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_compare26(x0, x1, False, x2, x3)
new_esEs25(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs22(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Double)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, ty_Int)
new_ltEs8(GT, GT)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(Integer(x0), Integer(x1))
new_lt4(x0, x1)
new_lt17(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, ty_Float)
new_ltEs4(Just(x0), Nothing, x1)
new_esEs22(x0, x1, ty_Double)
new_pePe(False, x0)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_compare12(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCompAux00(x0, GT)
new_esEs22(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare9(x0, x1)
new_esEs20(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare211(x0, x1, True)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs15(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1, ty_Bool)
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Ordering)
new_compare23(x0, x1, False, x2)
new_esEs28(x0, x1, ty_@0)
new_sr(Integer(x0), Integer(x1))
new_ltEs11(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primCompAux00(x0, EQ)
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(:(x0, x1), [], x2)
new_compare24(x0, x1, True)
new_esEs23(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs5(True, True)
new_lt11(x0, x1, ty_Int)
new_not(True)
new_lt11(x0, x1, ty_Char)
new_lt6(x0, x1)
new_esEs14(x0, x1, ty_Ordering)
new_esEs15(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1, ty_Ordering)
new_lt11(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Float)
new_lt7(x0, x1)
new_ltEs17(Left(x0), Left(x1), ty_Int, x2)
new_not(False)
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare15(x0, x1, False, x2, x3)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare16(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Int)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Integer)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs10(x0, x1)
new_esEs14(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Int)
new_esEs17([], [], x0)
new_compare112(x0, x1, True, x2, x3)
new_esEs28(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(x0, x1)
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Integer)
new_lt11(x0, x1, ty_Integer)
new_compare26(x0, x1, True, x2, x3)
new_compare27(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs13(x0, x1)
new_esEs28(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_ltEs4(Nothing, Just(x0), x1)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs10(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs17(Right(x0), Right(x1), x2, ty_Int)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_compare14(x0, x1, x2)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(x0, x1)
new_esEs28(x0, x1, ty_Double)
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs14(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(True, False)
new_ltEs5(False, True)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primMulInt(Neg(x0), Neg(x1))
new_lt8(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare7(x0, x1, x2, x3)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)

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

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



↳ 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_GE2(vyy330, vyy331, vyy103, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb) → new_foldFM_GE1(new_fmToList_GE0(vyy330, vyy331, vyy103, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, h, ba), h, ba, bb)
new_foldFM_GE1(vyy78, vyy40, vyy330, vyy331, vyy332, vyy333, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), False, h, ba, bb) → new_foldFM_GE1(vyy78, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h, ba), h, ba, bb)
new_foldFM_GE(vyy78, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba, bb) → new_foldFM_GE1(vyy78, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h, ba), h, ba, bb)
new_foldFM_GE1(vyy78, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba, bb) → new_foldFM_GE(vyy78, vyy40, vyy334, h, ba, bb)
new_foldFM_GE1(vyy78, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba, bb) → new_foldFM_GE(vyy78, vyy40, vyy334, h, ba, bb)
new_foldFM_GE1(vyy78, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba, bb) → new_foldFM_GE2(vyy330, vyy331, new_foldFM_GE0(vyy78, vyy40, vyy334, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb)

The TRS R consists of the following rules:

new_esEs10(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, gb)) → new_esEs7(vyy3000, vyy400, gb)
new_esEs28(vyy900, vyy910, ty_Char) → new_esEs21(vyy900, vyy910)
new_lt20(vyy900, vyy910, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt12(vyy900, vyy910, bfh, bga, bgb)
new_esEs22(vyy3002, vyy402, app(ty_Ratio, ha)) → new_esEs9(vyy3002, vyy402, ha)
new_esEs25(vyy900, vyy910, ty_Integer) → new_esEs12(vyy900, vyy910)
new_esEs23(vyy3001, vyy401, ty_Float) → new_esEs20(vyy3001, vyy401)
new_ltEs19(vyy902, vyy912, app(ty_Ratio, dah)) → new_ltEs16(vyy902, vyy912, dah)
new_compare15(vyy900, vyy910, True, bc, bd) → LT
new_compare8(Double(vyy900, vyy901), Double(vyy910, vyy911)) → new_compare9(new_sr0(vyy900, vyy910), new_sr0(vyy901, vyy911))
new_esEs15(vyy3000, vyy400, ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), cfa, ty_Int) → new_esEs13(vyy3000, vyy400)
new_ltEs18(vyy90, vyy91) → new_not(new_esEs8(new_compare17(vyy90, vyy91), GT))
new_compare13(vyy900, vyy910) → new_compare24(vyy900, vyy910, new_esEs19(vyy900, vyy910))
new_esEs27(vyy901, vyy911, app(ty_Maybe, dce)) → new_esEs7(vyy901, vyy911, dce)
new_lt19(vyy901, vyy911, app(ty_Ratio, dcb)) → new_lt9(vyy901, vyy911, dcb)
new_lt11(vyy900, vyy910, ty_Float) → new_lt8(vyy900, vyy910)
new_ltEs11(vyy901, vyy911, ty_Float) → new_ltEs12(vyy901, vyy911)
new_lt5(vyy900, vyy910, bc, bd) → new_esEs8(new_compare7(vyy900, vyy910, bc, bd), LT)
new_esEs23(vyy3001, vyy401, app(ty_[], bab)) → new_esEs17(vyy3001, vyy401, bab)
new_fmToList_GE0(vyy170, vyy171, vyy100, bce, bcf, bcg) → :(@2(vyy170, vyy171), vyy100)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, eh), fa)) → new_esEs6(vyy3000, vyy400, eh, fa)
new_primMulNat0(Zero, Zero) → Zero
new_esEs28(vyy900, vyy910, ty_Bool) → new_esEs19(vyy900, vyy910)
new_ltEs4(Just(vyy900), Just(vyy910), app(app(ty_@2, bgg), bgh)) → new_ltEs7(vyy900, vyy910, bgg, bgh)
new_ltEs7(@2(vyy900, vyy901), @2(vyy910, vyy911), bch, bda) → new_pePe(new_lt11(vyy900, vyy910, bch), new_asAs(new_esEs25(vyy900, vyy910, bch), new_ltEs11(vyy901, vyy911, bda)))
new_esEs17(:(vyy3000, vyy3001), :(vyy400, vyy401), cgd) → new_asAs(new_esEs26(vyy3000, vyy400, cgd), new_esEs17(vyy3001, vyy401, cgd))
new_esEs27(vyy901, vyy911, app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs4(vyy901, vyy911, dbd, dbe, dbf)
new_compare27(vyy900, vyy910, app(app(ty_@2, cac), cad)) → new_compare7(vyy900, vyy910, cac, cad)
new_esEs6(Right(vyy3000), Right(vyy400), cfa, app(ty_Ratio, cfe)) → new_esEs9(vyy3000, vyy400, cfe)
new_sr(Integer(vyy9000), Integer(vyy9110)) → Integer(new_primMulInt(vyy9000, vyy9110))
new_esEs25(vyy900, vyy910, app(app(ty_Either, bfc), bfd)) → new_esEs6(vyy900, vyy910, bfc, bfd)
new_lt20(vyy900, vyy910, ty_Integer) → new_lt4(vyy900, vyy910)
new_lt19(vyy901, vyy911, app(app(ty_Either, dcc), dcd)) → new_lt15(vyy901, vyy911, dcc, dcd)
new_ltEs19(vyy902, vyy912, ty_Integer) → new_ltEs14(vyy902, vyy912)
new_lt20(vyy900, vyy910, app(app(ty_@2, bc), bd)) → new_lt5(vyy900, vyy910, bc, bd)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, cee), cef), ceg), cdh) → new_esEs4(vyy3000, vyy400, cee, cef, ceg)
new_ltEs16(vyy90, vyy91, bhg) → new_not(new_esEs8(new_compare16(vyy90, vyy91, bhg), GT))
new_ltEs4(Just(vyy900), Just(vyy910), ty_Bool) → new_ltEs5(vyy900, vyy910)
new_esEs27(vyy901, vyy911, ty_Integer) → new_esEs12(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, cdh) → new_esEs18(vyy3000, vyy400)
new_esEs25(vyy900, vyy910, ty_Double) → new_esEs16(vyy900, vyy910)
new_ltEs19(vyy902, vyy912, ty_Double) → new_ltEs6(vyy902, vyy912)
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, ty_Int) → new_ltEs10(vyy9000, vyy9100)
new_esEs27(vyy901, vyy911, app(ty_Ratio, dcb)) → new_esEs9(vyy901, vyy911, dcb)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs20(vyy3000, vyy400)
new_ltEs9(vyy90, vyy91) → new_not(new_esEs8(new_compare18(vyy90, vyy91), GT))
new_esEs22(vyy3002, vyy402, app(app(ty_@2, hb), hc)) → new_esEs5(vyy3002, vyy402, hb, hc)
new_compare0(:(vyy900, vyy901), :(vyy910, vyy911), bg) → new_primCompAux0(vyy900, vyy910, new_compare0(vyy901, vyy911, bg), bg)
new_ltEs19(vyy902, vyy912, ty_Int) → new_ltEs10(vyy902, vyy912)
new_esEs24(vyy3000, vyy400, app(app(ty_@2, bbf), bbg)) → new_esEs5(vyy3000, vyy400, bbf, bbg)
new_lt11(vyy900, vyy910, ty_Int) → new_lt7(vyy900, vyy910)
new_compare12(Float(vyy900, vyy901), Float(vyy910, vyy911)) → new_compare9(new_sr0(vyy900, vyy910), new_sr0(vyy901, vyy911))
new_ltEs8(EQ, EQ) → True
new_lt12(vyy900, vyy910, bfh, bga, bgb) → new_esEs8(new_compare28(vyy900, vyy910, bfh, bga, bgb), LT)
new_ltEs12(vyy90, vyy91) → new_not(new_esEs8(new_compare12(vyy90, vyy91), GT))
new_esEs23(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, ty_Ordering) → new_ltEs8(vyy9000, vyy9100)
new_esEs14(vyy3001, vyy401, ty_Int) → new_esEs13(vyy3001, vyy401)
new_esEs12(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs19(vyy902, vyy912, app(ty_Maybe, dbc)) → new_ltEs4(vyy902, vyy912, dbc)
new_esEs28(vyy900, vyy910, ty_Integer) → new_esEs12(vyy900, vyy910)
new_esEs22(vyy3002, vyy402, ty_Float) → new_esEs20(vyy3002, vyy402)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, fc)) → new_esEs9(vyy3000, vyy400, fc)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, cdh) → new_esEs12(vyy3000, vyy400)
new_pePe(False, vyy150) → vyy150
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Bool, bfg) → new_ltEs5(vyy9000, vyy9100)
new_esEs11(vyy3000, vyy400, ty_Int) → new_esEs13(vyy3000, vyy400)
new_lt11(vyy900, vyy910, app(app(app(ty_@3, bed), bee), bef)) → new_lt12(vyy900, vyy910, bed, bee, bef)
new_lt6(vyy900, vyy910) → new_esEs8(new_compare8(vyy900, vyy910), LT)
new_esEs6(Right(vyy3000), Right(vyy400), cfa, ty_Double) → new_esEs16(vyy3000, vyy400)
new_compare29(vyy900, vyy910) → new_compare211(vyy900, vyy910, new_esEs8(vyy900, vyy910))
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, ty_Double) → new_ltEs6(vyy9000, vyy9100)
new_esEs24(vyy3000, vyy400, app(ty_Maybe, bcc)) → new_esEs7(vyy3000, vyy400, bcc)
new_ltEs4(Nothing, Just(vyy910), bgc) → True
new_esEs28(vyy900, vyy910, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs4(vyy900, vyy910, bfh, bga, bgb)
new_esEs22(vyy3002, vyy402, ty_Integer) → new_esEs12(vyy3002, vyy402)
new_ltEs11(vyy901, vyy911, ty_Ordering) → new_ltEs8(vyy901, vyy911)
new_esEs23(vyy3001, vyy401, app(ty_Maybe, bba)) → new_esEs7(vyy3001, vyy401, bba)
new_compare9(vyy90, vyy91) → new_primCmpInt(vyy90, vyy91)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, cdh) → new_esEs16(vyy3000, vyy400)
new_ltEs10(vyy90, vyy91) → new_not(new_esEs8(new_compare9(vyy90, vyy91), GT))
new_lt8(vyy900, vyy910) → new_esEs8(new_compare12(vyy900, vyy910), LT)
new_esEs27(vyy901, vyy911, ty_Float) → new_esEs20(vyy901, vyy911)
new_esEs27(vyy901, vyy911, app(ty_[], dca)) → new_esEs17(vyy901, vyy911, dca)
new_esEs22(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_ltEs8(EQ, GT) → True
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, app(ty_Maybe, cde)) → new_ltEs4(vyy9000, vyy9100, cde)
new_ltEs8(GT, GT) → True
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, ty_Float) → new_ltEs12(vyy9000, vyy9100)
new_compare10(vyy900, vyy910, True, be) → LT
new_lt20(vyy900, vyy910, app(ty_Maybe, be)) → new_lt16(vyy900, vyy910, be)
new_esEs14(vyy3001, vyy401, app(ty_[], cd)) → new_esEs17(vyy3001, vyy401, cd)
new_primCmpNat0(Zero, Succ(vyy9100)) → LT
new_esEs23(vyy3001, vyy401, ty_Char) → new_esEs21(vyy3001, vyy401)
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, ty_Integer) → new_ltEs14(vyy9000, vyy9100)
new_lt19(vyy901, vyy911, app(app(ty_@2, dbg), dbh)) → new_lt5(vyy901, vyy911, dbg, dbh)
new_esEs6(Right(vyy3000), Left(vyy400), cfa, cdh) → False
new_esEs6(Left(vyy3000), Right(vyy400), cfa, cdh) → False
new_esEs8(LT, LT) → True
new_esEs6(Right(vyy3000), Right(vyy400), cfa, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, cdh) → new_esEs20(vyy3000, vyy400)
new_esEs28(vyy900, vyy910, ty_Double) → new_esEs16(vyy900, vyy910)
new_ltEs8(LT, EQ) → True
new_lt20(vyy900, vyy910, app(ty_Ratio, bcd)) → new_lt9(vyy900, vyy910, bcd)
new_esEs25(vyy900, vyy910, ty_Ordering) → new_esEs8(vyy900, vyy910)
new_compare10(vyy900, vyy910, False, be) → GT
new_foldFM_GE0(vyy78, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba, bb) → new_foldFM_GE10(vyy78, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h, ba), h, ba, bb)
new_compare27(vyy900, vyy910, ty_Double) → new_compare8(vyy900, vyy910)
new_ltEs5(True, False) → False
new_pePe(True, vyy150) → True
new_compare0([], [], bg) → EQ
new_esEs27(vyy901, vyy911, ty_@0) → new_esEs18(vyy901, vyy911)
new_primEqNat0(Zero, Zero) → True
new_esEs23(vyy3001, vyy401, app(app(ty_Either, hh), baa)) → new_esEs6(vyy3001, vyy401, hh, baa)
new_compare17(@0, @0) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), cfa, app(app(app(ty_@3, cfh), cga), cgb)) → new_esEs4(vyy3000, vyy400, cfh, cga, cgb)
new_primCompAux0(vyy900, vyy910, vyy151, bg) → new_primCompAux00(vyy151, new_compare27(vyy900, vyy910, bg))
new_esEs6(Right(vyy3000), Right(vyy400), cfa, app(app(ty_Either, cfb), cfc)) → new_esEs6(vyy3000, vyy400, cfb, cfc)
new_foldFM_GE10(vyy78, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba, bb) → new_foldFM_GE3(vyy330, vyy331, new_foldFM_GE0(vyy78, vyy40, vyy334, h, ba, bb), vyy40, h, ba, bb)
new_ltEs5(True, True) → True
new_ltEs17(Right(vyy9000), Left(vyy9100), bff, bfg) → False
new_esEs19(True, True) → True
new_ltEs17(Left(vyy9000), Left(vyy9100), app(ty_[], cbg), bfg) → new_ltEs15(vyy9000, vyy9100, cbg)
new_ltEs8(GT, EQ) → False
new_ltEs8(EQ, LT) → False
new_ltEs17(Left(vyy9000), Left(vyy9100), app(app(ty_@2, cbe), cbf), bfg) → new_ltEs7(vyy9000, vyy9100, cbe, cbf)
new_compare16(:%(vyy900, vyy901), :%(vyy910, vyy911), ty_Integer) → new_compare6(new_sr(vyy900, vyy911), new_sr(vyy910, vyy901))
new_ltEs11(vyy901, vyy911, ty_Char) → new_ltEs9(vyy901, vyy911)
new_esEs25(vyy900, vyy910, ty_Int) → new_esEs13(vyy900, vyy910)
new_esEs6(Right(vyy3000), Right(vyy400), cfa, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_esEs28(vyy900, vyy910, app(app(ty_Either, bff), bfg)) → new_esEs6(vyy900, vyy910, bff, bfg)
new_esEs22(vyy3002, vyy402, ty_Char) → new_esEs21(vyy3002, vyy402)
new_esEs24(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt11(vyy900, vyy910, ty_@0) → new_lt10(vyy900, vyy910)
new_esEs8(GT, GT) → True
new_esEs13(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_primPlusNat0(Succ(vyy1340), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1340, vyy40100)))
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, chc), chd), che)) → new_esEs4(vyy3000, vyy400, chc, chd, che)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_lt20(vyy900, vyy910, ty_Char) → new_lt17(vyy900, vyy910)
new_esEs14(vyy3001, vyy401, app(app(ty_Either, cb), cc)) → new_esEs6(vyy3001, vyy401, cb, cc)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs21(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs15(vyy3000, vyy400, app(app(app(ty_@3, ec), ed), ee)) → new_esEs4(vyy3000, vyy400, ec, ed, ee)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs19(vyy902, vyy912, ty_Ordering) → new_ltEs8(vyy902, vyy912)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Double, bfg) → new_ltEs6(vyy9000, vyy9100)
new_esEs15(vyy3000, vyy400, ty_Char) → new_esEs21(vyy3000, vyy400)
new_ltEs5(False, False) → True
new_esEs23(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy13400), Zero) → Succ(vyy13400)
new_esEs24(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_compare27(vyy900, vyy910, ty_Integer) → new_compare6(vyy900, vyy910)
new_ltEs4(Nothing, Nothing, bgc) → True
new_foldFM_GE10(vyy78, vyy40, vyy330, vyy331, vyy332, vyy333, vyy334, False, h, ba, bb) → new_foldFM_GE0(vyy78, vyy40, vyy334, h, ba, bb)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs17(Left(vyy9000), Left(vyy9100), app(app(app(ty_@3, cbb), cbc), cbd), bfg) → new_ltEs13(vyy9000, vyy9100, cbb, cbc, cbd)
new_esEs28(vyy900, vyy910, ty_Float) → new_esEs20(vyy900, vyy910)
new_esEs19(False, False) → True
new_esEs22(vyy3002, vyy402, ty_@0) → new_esEs18(vyy3002, vyy402)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs11(vyy901, vyy911, app(ty_[], bdg)) → new_ltEs15(vyy901, vyy911, bdg)
new_esEs15(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_compare112(vyy900, vyy910, False, bff, bfg) → GT
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_esEs8(EQ, EQ) → True
new_ltEs17(Left(vyy9000), Left(vyy9100), app(ty_Maybe, ccc), bfg) → new_ltEs4(vyy9000, vyy9100, ccc)
new_compare26(vyy900, vyy910, True, bff, bfg) → EQ
new_lt20(vyy900, vyy910, ty_@0) → new_lt10(vyy900, vyy910)
new_esEs6(Right(vyy3000), Right(vyy400), cfa, app(ty_[], cfd)) → new_esEs17(vyy3000, vyy400, cfd)
new_lt20(vyy900, vyy910, ty_Ordering) → new_lt13(vyy900, vyy910)
new_esEs23(vyy3001, vyy401, app(app(app(ty_@3, baf), bag), bah)) → new_esEs4(vyy3001, vyy401, baf, bag, bah)
new_esEs14(vyy3001, vyy401, app(ty_Ratio, ce)) → new_esEs9(vyy3001, vyy401, ce)
new_esEs28(vyy900, vyy910, ty_Int) → new_esEs13(vyy900, vyy910)
new_lt9(vyy900, vyy910, bcd) → new_esEs8(new_compare16(vyy900, vyy910, bcd), LT)
new_lt18(vyy900, vyy910) → new_esEs8(new_compare13(vyy900, vyy910), LT)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs28(vyy900, vyy910, ty_@0) → new_esEs18(vyy900, vyy910)
new_esEs14(vyy3001, vyy401, app(ty_Maybe, dd)) → new_esEs7(vyy3001, vyy401, dd)
new_esEs15(vyy3000, vyy400, app(ty_Ratio, dh)) → new_esEs9(vyy3000, vyy400, dh)
new_primCmpNat0(Succ(vyy9000), Succ(vyy9100)) → new_primCmpNat0(vyy9000, vyy9100)
new_compare7(vyy900, vyy910, bc, bd) → new_compare25(vyy900, vyy910, new_esEs5(vyy900, vyy910, bc, bd), bc, bd)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_lt20(vyy900, vyy910, ty_Int) → new_lt7(vyy900, vyy910)
new_esEs14(vyy3001, vyy401, ty_Float) → new_esEs20(vyy3001, vyy401)
new_lt10(vyy900, vyy910) → new_esEs8(new_compare17(vyy900, vyy910), LT)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs13(vyy3000, vyy400)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_esEs27(vyy901, vyy911, ty_Ordering) → new_esEs8(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], cea), cdh) → new_esEs17(vyy3000, vyy400, cea)
new_gtEs(vyy3330, vyy40, h, ba) → new_not(new_esEs8(new_compare26(vyy3330, Right(vyy40), new_esEs6(vyy3330, Right(vyy40), h, ba), h, ba), LT))
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, ceb), cdh) → new_esEs9(vyy3000, vyy400, ceb)
new_esEs6(Right(vyy3000), Right(vyy400), cfa, app(app(ty_@2, cff), cfg)) → new_esEs5(vyy3000, vyy400, cff, cfg)
new_compare111(vyy900, vyy910, True, bfh, bga, bgb) → LT
new_esEs22(vyy3002, vyy402, ty_Int) → new_esEs13(vyy3002, vyy402)
new_primCompAux00(vyy160, LT) → LT
new_ltEs4(Just(vyy900), Just(vyy910), ty_Int) → new_ltEs10(vyy900, vyy910)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs13(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy9000)), Neg(vyy910)) → new_primCmpNat0(vyy910, Succ(vyy9000))
new_esEs24(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt7(vyy900, vyy910) → new_esEs8(new_compare9(vyy900, vyy910), LT)
new_esEs7(Nothing, Nothing, eg) → True
new_esEs28(vyy900, vyy910, ty_Ordering) → new_esEs8(vyy900, vyy910)
new_compare27(vyy900, vyy910, app(ty_Maybe, cba)) → new_compare14(vyy900, vyy910, cba)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_lt4(vyy900, vyy910) → new_esEs8(new_compare6(vyy900, vyy910), LT)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs21(vyy3000, vyy400)
new_ltEs19(vyy902, vyy912, app(app(ty_Either, dba), dbb)) → new_ltEs17(vyy902, vyy912, dba, dbb)
new_primCmpNat0(Zero, Zero) → EQ
new_compare28(vyy900, vyy910, bfh, bga, bgb) → new_compare210(vyy900, vyy910, new_esEs4(vyy900, vyy910, bfh, bga, bgb), bfh, bga, bgb)
new_esEs6(Right(vyy3000), Right(vyy400), cfa, app(ty_Maybe, cgc)) → new_esEs7(vyy3000, vyy400, cgc)
new_esEs23(vyy3001, vyy401, ty_@0) → new_esEs18(vyy3001, vyy401)
new_primCmpNat0(Succ(vyy9000), Zero) → GT
new_esEs23(vyy3001, vyy401, app(app(ty_@2, bad), bae)) → new_esEs5(vyy3001, vyy401, bad, bae)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy9100))) → LT
new_esEs19(True, False) → False
new_esEs19(False, True) → False
new_compare210(vyy900, vyy910, True, bfh, bga, bgb) → EQ
new_compare27(vyy900, vyy910, app(ty_[], cae)) → new_compare0(vyy900, vyy910, cae)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, fg), fh), ga)) → new_esEs4(vyy3000, vyy400, fg, fh, ga)
new_primPlusNat1(Succ(vyy13400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy13400, vyy401000)))
new_compare6(Integer(vyy900), Integer(vyy910)) → new_primCmpInt(vyy900, vyy910)
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_esEs25(vyy900, vyy910, ty_Bool) → new_esEs19(vyy900, vyy910)
new_esEs7(Just(vyy3000), Nothing, eg) → False
new_esEs7(Nothing, Just(vyy400), eg) → False
new_esEs15(vyy3000, vyy400, app(app(ty_@2, ea), eb)) → new_esEs5(vyy3000, vyy400, ea, eb)
new_ltEs5(False, True) → True
new_lt11(vyy900, vyy910, app(ty_Ratio, bfb)) → new_lt9(vyy900, vyy910, bfb)
new_lt19(vyy901, vyy911, app(ty_Maybe, dce)) → new_lt16(vyy901, vyy911, dce)
new_compare26(vyy900, vyy910, False, bff, bfg) → new_compare112(vyy900, vyy910, new_ltEs17(vyy900, vyy910, bff, bfg), bff, bfg)
new_ltEs11(vyy901, vyy911, app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs13(vyy901, vyy911, bdb, bdc, bdd)
new_lt19(vyy901, vyy911, ty_Int) → new_lt7(vyy901, vyy911)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_esEs14(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, app(ty_[], cgg)) → new_esEs17(vyy3000, vyy400, cgg)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy9100))) → new_primCmpNat0(Zero, Succ(vyy9100))
new_compare27(vyy900, vyy910, app(app(app(ty_@3, bhh), caa), cab)) → new_compare28(vyy900, vyy910, bhh, caa, cab)
new_primCompAux00(vyy160, EQ) → vyy160
new_compare24(vyy900, vyy910, True) → EQ
new_compare27(vyy900, vyy910, ty_Float) → new_compare12(vyy900, vyy910)
new_esEs27(vyy901, vyy911, ty_Int) → new_esEs13(vyy901, vyy911)
new_foldFM_GE10(vyy78, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba, bb) → new_foldFM_GE20(vyy330, vyy331, new_foldFM_GE0(vyy78, vyy40, vyy334, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb)
new_esEs23(vyy3001, vyy401, ty_Bool) → new_esEs19(vyy3001, vyy401)
new_esEs22(vyy3002, vyy402, ty_Bool) → new_esEs19(vyy3002, vyy402)
new_ltEs8(GT, LT) → False
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs27(vyy901, vyy911, ty_Double) → new_esEs16(vyy901, vyy911)
new_esEs15(vyy3000, vyy400, app(ty_Maybe, ef)) → new_esEs7(vyy3000, vyy400, ef)
new_ltEs19(vyy902, vyy912, app(app(app(ty_@3, dab), dac), dad)) → new_ltEs13(vyy902, vyy912, dab, dac, dad)
new_ltEs11(vyy901, vyy911, ty_@0) → new_ltEs18(vyy901, vyy911)
new_compare27(vyy900, vyy910, ty_Int) → new_compare9(vyy900, vyy910)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, cha), chb)) → new_esEs5(vyy3000, vyy400, cha, chb)
new_ltEs15(vyy90, vyy91, bg) → new_not(new_esEs8(new_compare0(vyy90, vyy91, bg), GT))
new_ltEs11(vyy901, vyy911, ty_Double) → new_ltEs6(vyy901, vyy911)
new_not(False) → True
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, cdf), cdg), cdh) → new_esEs6(vyy3000, vyy400, cdf, cdg)
new_compare211(vyy900, vyy910, False) → new_compare110(vyy900, vyy910, new_ltEs8(vyy900, vyy910))
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, ty_@0) → new_ltEs18(vyy9000, vyy9100)
new_esEs24(vyy3000, vyy400, ty_Int) → new_esEs13(vyy3000, vyy400)
new_esEs25(vyy900, vyy910, ty_Float) → new_esEs20(vyy900, vyy910)
new_primCmpInt(Pos(Succ(vyy9000)), Pos(vyy910)) → new_primCmpNat0(Succ(vyy9000), vyy910)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs14(vyy3001, vyy401, app(app(ty_@2, cf), cg)) → new_esEs5(vyy3001, vyy401, cf, cg)
new_ltEs4(Just(vyy900), Just(vyy910), app(app(app(ty_@3, bgd), bge), bgf)) → new_ltEs13(vyy900, vyy910, bgd, bge, bgf)
new_esEs6(Right(vyy3000), Right(vyy400), cfa, ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs15(vyy3000, vyy400, app(ty_[], dg)) → new_esEs17(vyy3000, vyy400, dg)
new_esEs24(vyy3000, vyy400, app(app(ty_Either, bbb), bbc)) → new_esEs6(vyy3000, vyy400, bbb, bbc)
new_esEs20(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs13(new_sr0(vyy3000, vyy400), new_sr0(vyy3001, vyy401))
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, app(app(ty_Either, cdc), cdd)) → new_ltEs17(vyy9000, vyy9100, cdc, cdd)
new_lt11(vyy900, vyy910, ty_Ordering) → new_lt13(vyy900, vyy910)
new_esEs25(vyy900, vyy910, app(app(app(ty_@3, bed), bee), bef)) → new_esEs4(vyy900, vyy910, bed, bee, bef)
new_esEs24(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs28(vyy900, vyy910, app(app(ty_@2, bc), bd)) → new_esEs5(vyy900, vyy910, bc, bd)
new_compare0(:(vyy900, vyy901), [], bg) → GT
new_lt11(vyy900, vyy910, ty_Integer) → new_lt4(vyy900, vyy910)
new_ltEs19(vyy902, vyy912, ty_@0) → new_ltEs18(vyy902, vyy912)
new_ltEs4(Just(vyy900), Just(vyy910), ty_Ordering) → new_ltEs8(vyy900, vyy910)
new_esEs24(vyy3000, vyy400, app(ty_[], bbd)) → new_esEs17(vyy3000, vyy400, bbd)
new_lt19(vyy901, vyy911, app(app(app(ty_@3, dbd), dbe), dbf)) → new_lt12(vyy901, vyy911, dbd, dbe, dbf)
new_lt19(vyy901, vyy911, ty_Integer) → new_lt4(vyy901, vyy911)
new_esEs22(vyy3002, vyy402, app(app(app(ty_@3, hd), he), hf)) → new_esEs4(vyy3002, vyy402, hd, he, hf)
new_esEs27(vyy901, vyy911, app(app(ty_Either, dcc), dcd)) → new_esEs6(vyy901, vyy911, dcc, dcd)
new_lt20(vyy900, vyy910, ty_Double) → new_lt6(vyy900, vyy910)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, cdh) → new_esEs21(vyy3000, vyy400)
new_ltEs19(vyy902, vyy912, app(ty_[], dag)) → new_ltEs15(vyy902, vyy912, dag)
new_esEs15(vyy3000, vyy400, app(app(ty_Either, de), df)) → new_esEs6(vyy3000, vyy400, de, df)
new_ltEs11(vyy901, vyy911, app(app(ty_Either, bea), beb)) → new_ltEs17(vyy901, vyy911, bea, beb)
new_lt11(vyy900, vyy910, ty_Char) → new_lt17(vyy900, vyy910)
new_primCmpInt(Pos(Succ(vyy9000)), Neg(vyy910)) → GT
new_compare27(vyy900, vyy910, ty_@0) → new_compare17(vyy900, vyy910)
new_esEs28(vyy900, vyy910, app(ty_Maybe, be)) → new_esEs7(vyy900, vyy910, be)
new_ltEs4(Just(vyy900), Just(vyy910), ty_@0) → new_ltEs18(vyy900, vyy910)
new_lt19(vyy901, vyy911, ty_Char) → new_lt17(vyy901, vyy911)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs14(vyy3001, vyy401, ty_Double) → new_esEs16(vyy3001, vyy401)
new_ltEs17(Left(vyy9000), Left(vyy9100), app(app(ty_Either, cca), ccb), bfg) → new_ltEs17(vyy9000, vyy9100, cca, ccb)
new_ltEs17(Left(vyy9000), Left(vyy9100), app(ty_Ratio, cbh), bfg) → new_ltEs16(vyy9000, vyy9100, cbh)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, cec), ced), cdh) → new_esEs5(vyy3000, vyy400, cec, ced)
new_lt11(vyy900, vyy910, app(ty_[], bfa)) → new_lt14(vyy900, vyy910, bfa)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare27(vyy900, vyy910, ty_Char) → new_compare18(vyy900, vyy910)
new_compare110(vyy900, vyy910, True) → LT
new_esEs28(vyy900, vyy910, app(ty_Ratio, bcd)) → new_esEs9(vyy900, vyy910, bcd)
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_compare25(vyy900, vyy910, True, bc, bd) → EQ
new_esEs14(vyy3001, vyy401, ty_Char) → new_esEs21(vyy3001, vyy401)
new_compare110(vyy900, vyy910, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs4(Just(vyy900), Just(vyy910), ty_Double) → new_ltEs6(vyy900, vyy910)
new_esEs24(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_compare111(vyy900, vyy910, False, bfh, bga, bgb) → GT
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs19(vyy3000, vyy400)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Int, bfg) → new_ltEs10(vyy9000, vyy9100)
new_esEs5(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bh, ca) → new_asAs(new_esEs15(vyy3000, vyy400, bh), new_esEs14(vyy3001, vyy401, ca))
new_esEs27(vyy901, vyy911, app(app(ty_@2, dbg), dbh)) → new_esEs5(vyy901, vyy911, dbg, dbh)
new_ltEs11(vyy901, vyy911, app(ty_Maybe, bec)) → new_ltEs4(vyy901, vyy911, bec)
new_ltEs4(Just(vyy900), Just(vyy910), app(ty_[], bha)) → new_ltEs15(vyy900, vyy910, bha)
new_esEs22(vyy3002, vyy402, app(ty_[], gh)) → new_esEs17(vyy3002, vyy402, gh)
new_lt20(vyy900, vyy910, ty_Bool) → new_lt18(vyy900, vyy910)
new_ltEs19(vyy902, vyy912, ty_Char) → new_ltEs9(vyy902, vyy912)
new_compare25(vyy900, vyy910, False, bc, bd) → new_compare15(vyy900, vyy910, new_ltEs7(vyy900, vyy910, bc, bd), bc, bd)
new_ltEs11(vyy901, vyy911, ty_Int) → new_ltEs10(vyy901, vyy911)
new_lt19(vyy901, vyy911, ty_Bool) → new_lt18(vyy901, vyy911)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy9100))) → new_primCmpNat0(Succ(vyy9100), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy9100))) → GT
new_esEs24(vyy3000, vyy400, ty_Char) → new_esEs21(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, ceh), cdh) → new_esEs7(vyy3000, vyy400, ceh)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, cdh) → new_esEs8(vyy3000, vyy400)
new_ltEs11(vyy901, vyy911, app(ty_Ratio, bdh)) → new_ltEs16(vyy901, vyy911, bdh)
new_ltEs11(vyy901, vyy911, ty_Bool) → new_ltEs5(vyy901, vyy911)
new_ltEs4(Just(vyy900), Just(vyy910), app(app(ty_Either, bhc), bhd)) → new_ltEs17(vyy900, vyy910, bhc, bhd)
new_sr0(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_compare23(vyy900, vyy910, True, be) → EQ
new_compare15(vyy900, vyy910, False, bc, bd) → GT
new_compare27(vyy900, vyy910, app(ty_Ratio, caf)) → new_compare16(vyy900, vyy910, caf)
new_ltEs17(Left(vyy9000), Right(vyy9100), bff, bfg) → True
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, app(app(ty_@2, ccg), cch)) → new_ltEs7(vyy9000, vyy9100, ccg, cch)
new_compare210(vyy900, vyy910, False, bfh, bga, bgb) → new_compare111(vyy900, vyy910, new_ltEs13(vyy900, vyy910, bfh, bga, bgb), bfh, bga, bgb)
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Int) → new_esEs13(vyy3001, vyy401)
new_esEs25(vyy900, vyy910, app(ty_Maybe, bfe)) → new_esEs7(vyy900, vyy910, bfe)
new_ltEs4(Just(vyy900), Just(vyy910), app(ty_Maybe, bhe)) → new_ltEs4(vyy900, vyy910, bhe)
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, app(app(app(ty_@3, ccd), cce), ccf)) → new_ltEs13(vyy9000, vyy9100, ccd, cce, ccf)
new_ltEs4(Just(vyy900), Just(vyy910), ty_Float) → new_ltEs12(vyy900, vyy910)
new_compare16(:%(vyy900, vyy901), :%(vyy910, vyy911), ty_Int) → new_compare9(new_sr0(vyy900, vyy911), new_sr0(vyy910, vyy901))
new_ltEs14(vyy90, vyy91) → new_not(new_esEs8(new_compare6(vyy90, vyy91), GT))
new_esEs6(Right(vyy3000), Right(vyy400), cfa, ty_Float) → new_esEs20(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs16(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs13(new_sr0(vyy3000, vyy400), new_sr0(vyy3001, vyy401))
new_lt19(vyy901, vyy911, ty_Ordering) → new_lt13(vyy901, vyy911)
new_foldFM_GE20(vyy330, vyy331, vyy103, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb) → new_foldFM_GE10(new_fmToList_GE0(vyy330, vyy331, vyy103, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, h, ba), h, ba, bb)
new_esEs6(Right(vyy3000), Right(vyy400), cfa, ty_Char) → new_esEs21(vyy3000, vyy400)
new_asAs(False, vyy123) → False
new_ltEs19(vyy902, vyy912, app(app(ty_@2, dae), daf)) → new_ltEs7(vyy902, vyy912, dae, daf)
new_compare24(vyy900, vyy910, False) → new_compare11(vyy900, vyy910, new_ltEs5(vyy900, vyy910))
new_esEs25(vyy900, vyy910, app(ty_Ratio, bfb)) → new_esEs9(vyy900, vyy910, bfb)
new_lt15(vyy900, vyy910, bff, bfg) → new_esEs8(new_compare19(vyy900, vyy910, bff, bfg), LT)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_lt20(vyy900, vyy910, app(ty_[], bhf)) → new_lt14(vyy900, vyy910, bhf)
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, app(ty_Ratio, cdb)) → new_ltEs16(vyy9000, vyy9100, cdb)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, chf)) → new_esEs7(vyy3000, vyy400, chf)
new_esEs14(vyy3001, vyy401, app(app(app(ty_@3, da), db), dc)) → new_esEs4(vyy3001, vyy401, da, db, dc)
new_lt19(vyy901, vyy911, ty_Float) → new_lt8(vyy901, vyy911)
new_ltEs4(Just(vyy900), Just(vyy910), ty_Integer) → new_ltEs14(vyy900, vyy910)
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, ty_Char) → new_ltEs9(vyy9000, vyy9100)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Ordering, bfg) → new_ltEs8(vyy9000, vyy9100)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, cgh)) → new_esEs9(vyy3000, vyy400, cgh)
new_lt20(vyy900, vyy910, ty_Float) → new_lt8(vyy900, vyy910)
new_lt11(vyy900, vyy910, app(app(ty_@2, beg), beh)) → new_lt5(vyy900, vyy910, beg, beh)
new_esEs4(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), gc, gd, ge) → new_asAs(new_esEs24(vyy3000, vyy400, gc), new_asAs(new_esEs23(vyy3001, vyy401, gd), new_esEs22(vyy3002, vyy402, ge)))
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs25(vyy900, vyy910, app(ty_[], bfa)) → new_esEs17(vyy900, vyy910, bfa)
new_compare27(vyy900, vyy910, app(app(ty_Either, cag), cah)) → new_compare19(vyy900, vyy910, cag, cah)
new_foldFM_GE3(vyy330, vyy331, vyy102, vyy40, h, ba, bb) → new_fmToList_GE0(vyy330, vyy331, vyy102, h, ba, bb)
new_esEs23(vyy3001, vyy401, ty_Double) → new_esEs16(vyy3001, vyy401)
new_esEs25(vyy900, vyy910, ty_@0) → new_esEs18(vyy900, vyy910)
new_ltEs4(Just(vyy900), Just(vyy910), app(ty_Ratio, bhb)) → new_ltEs16(vyy900, vyy910, bhb)
new_ltEs6(vyy90, vyy91) → new_not(new_esEs8(new_compare8(vyy90, vyy91), GT))
new_lt19(vyy901, vyy911, app(ty_[], dca)) → new_lt14(vyy901, vyy911, dca)
new_ltEs11(vyy901, vyy911, app(app(ty_@2, bde), bdf)) → new_ltEs7(vyy901, vyy911, bde, bdf)
new_ltEs8(LT, GT) → True
new_compare19(vyy900, vyy910, bff, bfg) → new_compare26(vyy900, vyy910, new_esEs6(vyy900, vyy910, bff, bfg), bff, bfg)
new_ltEs13(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), chg, chh, daa) → new_pePe(new_lt20(vyy900, vyy910, chg), new_asAs(new_esEs28(vyy900, vyy910, chg), new_pePe(new_lt19(vyy901, vyy911, chh), new_asAs(new_esEs27(vyy901, vyy911, chh), new_ltEs19(vyy902, vyy912, daa)))))
new_esEs25(vyy900, vyy910, ty_Char) → new_esEs21(vyy900, vyy910)
new_compare23(vyy900, vyy910, False, be) → new_compare10(vyy900, vyy910, new_ltEs4(vyy900, vyy910, be), be)
new_ltEs19(vyy902, vyy912, ty_Bool) → new_ltEs5(vyy902, vyy912)
new_compare27(vyy900, vyy910, ty_Ordering) → new_compare29(vyy900, vyy910)
new_esEs28(vyy900, vyy910, app(ty_[], bhf)) → new_esEs17(vyy900, vyy910, bhf)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], fb)) → new_esEs17(vyy3000, vyy400, fb)
new_esEs14(vyy3001, vyy401, ty_Bool) → new_esEs19(vyy3001, vyy401)
new_esEs27(vyy901, vyy911, ty_Char) → new_esEs21(vyy901, vyy911)
new_esEs15(vyy3000, vyy400, ty_Int) → new_esEs13(vyy3000, vyy400)
new_esEs11(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_lt11(vyy900, vyy910, app(app(ty_Either, bfc), bfd)) → new_lt15(vyy900, vyy910, bfc, bfd)
new_compare11(vyy900, vyy910, False) → GT
new_esEs9(:%(vyy3000, vyy3001), :%(vyy400, vyy401), bf) → new_asAs(new_esEs11(vyy3000, vyy400, bf), new_esEs10(vyy3001, vyy401, bf))
new_esEs14(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_ltEs4(Just(vyy900), Just(vyy910), ty_Char) → new_ltEs9(vyy900, vyy910)
new_esEs25(vyy900, vyy910, app(app(ty_@2, beg), beh)) → new_esEs5(vyy900, vyy910, beg, beh)
new_lt16(vyy900, vyy910, be) → new_esEs8(new_compare14(vyy900, vyy910, be), LT)
new_lt20(vyy900, vyy910, app(app(ty_Either, bff), bfg)) → new_lt15(vyy900, vyy910, bff, bfg)
new_compare11(vyy900, vyy910, True) → LT
new_lt11(vyy900, vyy910, ty_Bool) → new_lt18(vyy900, vyy910)
new_compare18(Char(vyy900), Char(vyy910)) → new_primCmpNat0(vyy900, vyy910)
new_esEs22(vyy3002, vyy402, app(app(ty_Either, gf), gg)) → new_esEs6(vyy3002, vyy402, gf, gg)
new_esEs23(vyy3001, vyy401, app(ty_Ratio, bac)) → new_esEs9(vyy3001, vyy401, bac)
new_lt17(vyy900, vyy910) → new_esEs8(new_compare18(vyy900, vyy910), LT)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, cdh) → new_esEs13(vyy3000, vyy400)
new_lt19(vyy901, vyy911, ty_Double) → new_lt6(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, cdh) → new_esEs19(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, fd), ff)) → new_esEs5(vyy3000, vyy400, fd, ff)
new_esEs10(vyy3001, vyy401, ty_Int) → new_esEs13(vyy3001, vyy401)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Char, bfg) → new_ltEs9(vyy9000, vyy9100)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_@0, bfg) → new_ltEs18(vyy9000, vyy9100)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_esEs24(vyy3000, vyy400, ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs15(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_esEs22(vyy3002, vyy402, ty_Double) → new_esEs16(vyy3002, vyy402)
new_lt19(vyy901, vyy911, ty_@0) → new_lt10(vyy901, vyy911)
new_ltEs8(LT, LT) → True
new_compare27(vyy900, vyy910, ty_Bool) → new_compare13(vyy900, vyy910)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs21(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, cge), cgf)) → new_esEs6(vyy3000, vyy400, cge, cgf)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs15(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_compare0([], :(vyy910, vyy911), bg) → LT
new_ltEs11(vyy901, vyy911, ty_Integer) → new_ltEs14(vyy901, vyy911)
new_asAs(True, vyy123) → vyy123
new_ltEs4(Just(vyy900), Nothing, bgc) → False
new_compare112(vyy900, vyy910, True, bff, bfg) → LT
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Float, bfg) → new_ltEs12(vyy9000, vyy9100)
new_ltEs19(vyy902, vyy912, ty_Float) → new_ltEs12(vyy902, vyy912)
new_esEs18(@0, @0) → True
new_esEs17([], [], cgd) → True
new_compare211(vyy900, vyy910, True) → EQ
new_esEs17([], :(vyy400, vyy401), cgd) → False
new_esEs17(:(vyy3000, vyy3001), [], cgd) → False
new_compare14(vyy900, vyy910, be) → new_compare23(vyy900, vyy910, new_esEs7(vyy900, vyy910, be), be)
new_esEs14(vyy3001, vyy401, ty_@0) → new_esEs18(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)
new_lt14(vyy900, vyy910, bhf) → new_esEs8(new_compare0(vyy900, vyy910, bhf), LT)
new_lt11(vyy900, vyy910, ty_Double) → new_lt6(vyy900, vyy910)
new_esEs15(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs24(vyy3000, vyy400, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs4(vyy3000, vyy400, bbh, bca, bcb)
new_lt11(vyy900, vyy910, app(ty_Maybe, bfe)) → new_lt16(vyy900, vyy910, bfe)
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, ty_Bool) → new_ltEs5(vyy9000, vyy9100)
new_primCompAux00(vyy160, GT) → GT
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Integer, bfg) → new_ltEs14(vyy9000, vyy9100)
new_esEs6(Right(vyy3000), Right(vyy400), cfa, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(vyy3000, vyy400, app(ty_Ratio, bbe)) → new_esEs9(vyy3000, vyy400, bbe)
new_foldFM_GE0(vyy78, vyy40, EmptyFM, h, ba, bb) → vyy78
new_esEs27(vyy901, vyy911, ty_Bool) → new_esEs19(vyy901, vyy911)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs16(vyy3000, vyy400)
new_ltEs17(Right(vyy9000), Right(vyy9100), bff, app(ty_[], cda)) → new_ltEs15(vyy9000, vyy9100, cda)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_lt13(vyy900, vyy910) → new_esEs8(new_compare29(vyy900, vyy910), LT)
new_esEs22(vyy3002, vyy402, app(ty_Maybe, hg)) → new_esEs7(vyy3002, vyy402, hg)
new_primCmpInt(Neg(Succ(vyy9000)), Pos(vyy910)) → LT
new_not(True) → False
new_esEs15(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)

The set Q consists of the following terms:

new_esEs23(x0, x1, ty_Float)
new_compare18(Char(x0), Char(x1))
new_esEs26(x0, x1, ty_Ordering)
new_ltEs17(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs18(@0, @0)
new_lt19(x0, x1, ty_Double)
new_esEs14(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_compare23(x0, x1, False, x2)
new_compare27(x0, x1, app(ty_Maybe, x2))
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_esEs15(x0, x1, ty_Int)
new_asAs(True, x0)
new_ltEs9(x0, x1)
new_esEs17([], [], x0)
new_ltEs8(EQ, EQ)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs14(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_esEs27(x0, x1, ty_Char)
new_esEs14(x0, x1, app(ty_Maybe, x2))
new_compare0([], [], x0)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs15(x0, x1, ty_Double)
new_esEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs25(x0, x1, ty_Ordering)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primMulNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_compare211(x0, x1, False)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_esEs27(x0, x1, ty_@0)
new_gtEs(x0, x1, x2, x3)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs19(x0, x1, ty_Double)
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, True, x2)
new_lt19(x0, x1, ty_@0)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Char)
new_foldFM_GE0(x0, x1, EmptyFM, x2, x3, x4)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs15(x0, x1, x2)
new_compare17(@0, @0)
new_esEs8(LT, LT)
new_esEs15(x0, x1, ty_Integer)
new_compare111(x0, x1, False, x2, x3, x4)
new_ltEs11(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, ty_Char)
new_ltEs17(Right(x0), Right(x1), x2, ty_Float)
new_esEs15(x0, x1, app(ty_Maybe, x2))
new_ltEs5(False, False)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, ty_Ordering)
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_compare26(x0, x1, False, x2, x3)
new_compare27(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Integer)
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_esEs19(True, True)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_lt11(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Float)
new_ltEs11(x0, x1, ty_Integer)
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_compare8(Double(x0, x1), Double(x2, x3))
new_lt20(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_asAs(False, x0)
new_esEs27(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_lt16(x0, x1, x2)
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_compare11(x0, x1, False)
new_compare27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Char)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs7(Nothing, Nothing, x0)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, False)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs17(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_compare29(x0, x1)
new_ltEs17(Right(x0), Left(x1), x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs22(x0, x1, ty_Float)
new_ltEs17(Left(x0), Right(x1), x2, x3)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs17(Right(x0), Right(x1), x2, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Right(x0), Right(x1), x2, ty_Integer)
new_esEs11(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1, ty_Bool)
new_compare27(x0, x1, ty_Double)
new_compare0(:(x0, x1), [], x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs17(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt13(x0, x1)
new_ltEs11(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1, ty_Double)
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_primCmpNat0(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare27(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs18(x0, x1)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt11(x0, x1, app(ty_[], x2))
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, ty_Char)
new_compare25(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, ty_Bool)
new_compare27(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_lt11(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Double)
new_ltEs17(Left(x0), Left(x1), ty_Int, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_esEs14(x0, x1, ty_Float)
new_esEs15(x0, x1, ty_Bool)
new_sr0(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare27(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs19(False, True)
new_esEs19(True, False)
new_esEs22(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt11(x0, x1, app(ty_Ratio, x2))
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs17(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primPlusNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpNat0(Zero, Succ(x0))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(x0, x1, app(ty_[], x2))
new_ltEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs15(x0, x1, ty_Float)
new_ltEs11(x0, x1, ty_@0)
new_ltEs17(Left(x0), Left(x1), ty_Integer, x2)
new_compare15(x0, x1, False, x2, x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Integer)
new_compare13(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux00(x0, LT)
new_esEs11(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Ordering)
new_esEs14(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_compare0([], :(x0, x1), x2)
new_ltEs19(x0, x1, ty_Int)
new_compare7(x0, x1, x2, x3)
new_compare10(x0, x1, False, x2)
new_compare112(x0, x1, True, x2, x3)
new_compare15(x0, x1, True, x2, x3)
new_esEs22(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_lt19(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_@0)
new_esEs17(:(x0, x1), [], x2)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare11(x0, x1, True)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, ty_Int)
new_compare28(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_lt18(x0, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_compare14(x0, x1, x2)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(False, False)
new_ltEs11(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs15(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Float)
new_lt20(x0, x1, ty_@0)
new_compare16(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs14(x0, x1, ty_Int)
new_compare110(x0, x1, False)
new_foldFM_GE10(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, True, x11, x12, x13)
new_esEs15(x0, x1, ty_@0)
new_ltEs17(Left(x0), Left(x1), ty_@0, x2)
new_esEs25(x0, x1, ty_Char)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Left(x0), Left(x1), ty_Double, x2)
new_foldFM_GE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_lt20(x0, x1, ty_Float)
new_compare27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs27(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primEqNat0(Zero, Succ(x0))
new_foldFM_GE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_esEs28(x0, x1, ty_Ordering)
new_lt11(x0, x1, ty_Float)
new_esEs17([], :(x0, x1), x2)
new_compare10(x0, x1, True, x2)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs14(x0, x1, ty_Double)
new_esEs15(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Char)
new_fmToList_GE0(x0, x1, x2, x3, x4, x5)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_compare25(x0, x1, True, x2, x3)
new_primPlusNat0(Zero, x0)
new_esEs14(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs8(LT, LT)
new_esEs23(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Zero, Zero)
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Double)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Int)
new_ltEs8(GT, GT)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
new_compare6(Integer(x0), Integer(x1))
new_lt4(x0, x1)
new_lt17(x0, x1)
new_esEs22(x0, x1, ty_Double)
new_ltEs4(Nothing, Nothing, x0)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_compare12(Float(x0, x1), Float(x2, x3))
new_compare112(x0, x1, False, x2, x3)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCompAux00(x0, GT)
new_esEs22(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2, x3)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs4(Nothing, Just(x0), x1)
new_compare9(x0, x1)
new_esEs20(Float(x0, x1), Float(x2, x3))
new_ltEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare211(x0, x1, True)
new_lt11(x0, x1, ty_Bool)
new_ltEs8(LT, GT)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs8(GT, LT)
new_esEs24(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_ltEs17(Right(x0), Right(x1), x2, ty_Char)
new_sr(Integer(x0), Integer(x1))
new_ltEs11(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1, x2, x3)
new_primCompAux00(x0, EQ)
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare24(x0, x1, True)
new_esEs23(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(True, True)
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt11(x0, x1, ty_Int)
new_lt15(x0, x1, x2, x3)
new_lt14(x0, x1, x2)
new_not(True)
new_lt11(x0, x1, ty_Char)
new_lt6(x0, x1)
new_esEs14(x0, x1, ty_Ordering)
new_ltEs11(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(ty_[], x2))
new_lt11(x0, x1, ty_Ordering)
new_ltEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Float)
new_lt7(x0, x1)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_not(False)
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM_GE3(x0, x1, x2, x3, x4, x5, x6)
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare16(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt20(x0, x1, ty_Int)
new_esEs14(x0, x1, app(ty_Ratio, x2))
new_esEs15(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Integer)
new_ltEs17(Right(x0), Right(x1), x2, ty_@0)
new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt9(x0, x1, x2)
new_esEs21(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs10(x0, x1)
new_ltEs17(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Float)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_lt19(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_ltEs12(x0, x1)
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_foldFM_GE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_ltEs4(Just(x0), Nothing, x1)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Integer)
new_lt11(x0, x1, ty_Integer)
new_compare27(x0, x1, ty_Integer)
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs13(x0, x1)
new_esEs28(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs15(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs10(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare26(x0, x1, True, x2, x3)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1)
new_ltEs17(Left(x0), Left(x1), ty_Char, x2)
new_ltEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs28(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs14(x0, x1, ty_Integer)
new_ltEs16(x0, x1, x2)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primMulInt(Neg(x0), Neg(x1))
new_lt8(x0, x1)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt12(x0, x1, x2, x3, x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs26(x0, x1, ty_Integer)
new_foldFM_GE10(x0, x1, x2, x3, x4, EmptyFM, x5, True, x6, x7, x8)
new_lt19(x0, x1, ty_Bool)
new_lt10(x0, x1)

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_GE21(vyy170, vyy171, vyy101, vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb) → new_foldFM_GE11(new_fmToList_GE0(vyy170, vyy171, vyy101, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, new_gtEs0(vyy1730, vyy13, h, ba), h, ba, bb)
new_foldFM_GE11(vyy77, vyy13, vyy170, vyy171, vyy172, Branch(vyy1730, vyy1731, vyy1732, vyy1733, vyy1734), vyy174, True, h, ba, bb) → new_foldFM_GE4(vyy77, vyy13, vyy174, h, ba, bb)
new_foldFM_GE11(vyy77, vyy13, vyy170, vyy171, vyy172, Branch(vyy1730, vyy1731, vyy1732, vyy1733, vyy1734), vyy174, True, h, ba, bb) → new_foldFM_GE21(vyy170, vyy171, new_foldFM_GE5(vyy77, vyy13, vyy174, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb)
new_foldFM_GE4(vyy77, vyy13, Branch(vyy1740, vyy1741, vyy1742, vyy1743, vyy1744), h, ba, bb) → new_foldFM_GE11(vyy77, vyy13, vyy1740, vyy1741, vyy1742, vyy1743, vyy1744, new_gtEs0(vyy1740, vyy13, h, ba), h, ba, bb)
new_foldFM_GE11(vyy77, vyy13, vyy170, vyy171, vyy172, vyy173, Branch(vyy1740, vyy1741, vyy1742, vyy1743, vyy1744), False, h, ba, bb) → new_foldFM_GE11(vyy77, vyy13, vyy1740, vyy1741, vyy1742, vyy1743, vyy1744, new_gtEs0(vyy1740, vyy13, h, ba), h, ba, bb)
new_foldFM_GE11(vyy77, vyy13, vyy170, vyy171, vyy172, EmptyFM, vyy174, True, h, ba, bb) → new_foldFM_GE4(vyy77, vyy13, vyy174, h, ba, bb)

The TRS R consists of the following rules:

new_esEs10(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, gb)) → new_esEs7(vyy3000, vyy400, gb)
new_esEs28(vyy900, vyy910, ty_Char) → new_esEs21(vyy900, vyy910)
new_lt20(vyy900, vyy910, app(app(app(ty_@3, bfe), bff), bfg)) → new_lt12(vyy900, vyy910, bfe, bff, bfg)
new_esEs22(vyy3002, vyy402, app(ty_Ratio, ha)) → new_esEs9(vyy3002, vyy402, ha)
new_esEs25(vyy900, vyy910, ty_Integer) → new_esEs12(vyy900, vyy910)
new_esEs23(vyy3001, vyy401, ty_Float) → new_esEs20(vyy3001, vyy401)
new_ltEs19(vyy902, vyy912, app(ty_Ratio, dae)) → new_ltEs16(vyy902, vyy912, dae)
new_compare15(vyy900, vyy910, True, bc, bd) → LT
new_compare8(Double(vyy900, vyy901), Double(vyy910, vyy911)) → new_compare9(new_sr0(vyy900, vyy910), new_sr0(vyy901, vyy911))
new_esEs15(vyy3000, vyy400, ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), cef, ty_Int) → new_esEs13(vyy3000, vyy400)
new_ltEs18(vyy90, vyy91) → new_not(new_esEs8(new_compare17(vyy90, vyy91), GT))
new_compare13(vyy900, vyy910) → new_compare24(vyy900, vyy910, new_esEs19(vyy900, vyy910))
new_esEs27(vyy901, vyy911, app(ty_Maybe, dcb)) → new_esEs7(vyy901, vyy911, dcb)
new_lt19(vyy901, vyy911, app(ty_Ratio, dbg)) → new_lt9(vyy901, vyy911, dbg)
new_lt11(vyy900, vyy910, ty_Float) → new_lt8(vyy900, vyy910)
new_ltEs11(vyy901, vyy911, ty_Float) → new_ltEs12(vyy901, vyy911)
new_lt5(vyy900, vyy910, bc, bd) → new_esEs8(new_compare7(vyy900, vyy910, bc, bd), LT)
new_esEs23(vyy3001, vyy401, app(ty_[], bab)) → new_esEs17(vyy3001, vyy401, bab)
new_fmToList_GE0(vyy170, vyy171, vyy100, h, ba, bb) → :(@2(vyy170, vyy171), vyy100)
new_foldFM_GE12(vyy77, vyy13, vyy170, vyy171, vyy172, Branch(vyy1730, vyy1731, vyy1732, vyy1733, vyy1734), vyy174, True, h, ba, bb) → new_foldFM_GE22(vyy170, vyy171, new_foldFM_GE5(vyy77, vyy13, vyy174, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, eh), fa)) → new_esEs6(vyy3000, vyy400, eh, fa)
new_primMulNat0(Zero, Zero) → Zero
new_esEs28(vyy900, vyy910, ty_Bool) → new_esEs19(vyy900, vyy910)
new_ltEs4(Just(vyy900), Just(vyy910), app(app(ty_@2, bgd), bge)) → new_ltEs7(vyy900, vyy910, bgd, bge)
new_ltEs7(@2(vyy900, vyy901), @2(vyy910, vyy911), bce, bcf) → new_pePe(new_lt11(vyy900, vyy910, bce), new_asAs(new_esEs25(vyy900, vyy910, bce), new_ltEs11(vyy901, vyy911, bcf)))
new_esEs17(:(vyy3000, vyy3001), :(vyy400, vyy401), cga) → new_asAs(new_esEs26(vyy3000, vyy400, cga), new_esEs17(vyy3001, vyy401, cga))
new_esEs27(vyy901, vyy911, app(app(app(ty_@3, dba), dbb), dbc)) → new_esEs4(vyy901, vyy911, dba, dbb, dbc)
new_compare27(vyy900, vyy910, app(app(ty_@2, bhh), caa)) → new_compare7(vyy900, vyy910, bhh, caa)
new_esEs6(Right(vyy3000), Right(vyy400), cef, app(ty_Ratio, cfb)) → new_esEs9(vyy3000, vyy400, cfb)
new_sr(Integer(vyy9000), Integer(vyy9110)) → Integer(new_primMulInt(vyy9000, vyy9110))
new_esEs25(vyy900, vyy910, app(app(ty_Either, beh), bfa)) → new_esEs6(vyy900, vyy910, beh, bfa)
new_lt20(vyy900, vyy910, ty_Integer) → new_lt4(vyy900, vyy910)
new_lt19(vyy901, vyy911, app(app(ty_Either, dbh), dca)) → new_lt15(vyy901, vyy911, dbh, dca)
new_ltEs19(vyy902, vyy912, ty_Integer) → new_ltEs14(vyy902, vyy912)
new_lt20(vyy900, vyy910, app(app(ty_@2, bc), bd)) → new_lt5(vyy900, vyy910, bc, bd)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, ceb), cec), ced), cde) → new_esEs4(vyy3000, vyy400, ceb, cec, ced)
new_ltEs16(vyy90, vyy91, bhd) → new_not(new_esEs8(new_compare16(vyy90, vyy91, bhd), GT))
new_ltEs4(Just(vyy900), Just(vyy910), ty_Bool) → new_ltEs5(vyy900, vyy910)
new_esEs27(vyy901, vyy911, ty_Integer) → new_esEs12(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, cde) → new_esEs18(vyy3000, vyy400)
new_esEs25(vyy900, vyy910, ty_Double) → new_esEs16(vyy900, vyy910)
new_ltEs19(vyy902, vyy912, ty_Double) → new_ltEs6(vyy902, vyy912)
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, ty_Int) → new_ltEs10(vyy9000, vyy9100)
new_esEs27(vyy901, vyy911, app(ty_Ratio, dbg)) → new_esEs9(vyy901, vyy911, dbg)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs20(vyy3000, vyy400)
new_foldFM_GE22(vyy170, vyy171, vyy101, vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb) → new_foldFM_GE12(new_fmToList_GE0(vyy170, vyy171, vyy101, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, new_gtEs0(vyy1730, vyy13, h, ba), h, ba, bb)
new_ltEs9(vyy90, vyy91) → new_not(new_esEs8(new_compare18(vyy90, vyy91), GT))
new_esEs22(vyy3002, vyy402, app(app(ty_@2, hb), hc)) → new_esEs5(vyy3002, vyy402, hb, hc)
new_compare0(:(vyy900, vyy901), :(vyy910, vyy911), bg) → new_primCompAux0(vyy900, vyy910, new_compare0(vyy901, vyy911, bg), bg)
new_ltEs19(vyy902, vyy912, ty_Int) → new_ltEs10(vyy902, vyy912)
new_esEs24(vyy3000, vyy400, app(app(ty_@2, bbf), bbg)) → new_esEs5(vyy3000, vyy400, bbf, bbg)
new_lt11(vyy900, vyy910, ty_Int) → new_lt7(vyy900, vyy910)
new_compare12(Float(vyy900, vyy901), Float(vyy910, vyy911)) → new_compare9(new_sr0(vyy900, vyy910), new_sr0(vyy901, vyy911))
new_ltEs8(EQ, EQ) → True
new_lt12(vyy900, vyy910, bfe, bff, bfg) → new_esEs8(new_compare28(vyy900, vyy910, bfe, bff, bfg), LT)
new_ltEs12(vyy90, vyy91) → new_not(new_esEs8(new_compare12(vyy90, vyy91), GT))
new_esEs23(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, ty_Ordering) → new_ltEs8(vyy9000, vyy9100)
new_esEs14(vyy3001, vyy401, ty_Int) → new_esEs13(vyy3001, vyy401)
new_esEs12(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs19(vyy902, vyy912, app(ty_Maybe, dah)) → new_ltEs4(vyy902, vyy912, dah)
new_esEs28(vyy900, vyy910, ty_Integer) → new_esEs12(vyy900, vyy910)
new_esEs22(vyy3002, vyy402, ty_Float) → new_esEs20(vyy3002, vyy402)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, fc)) → new_esEs9(vyy3000, vyy400, fc)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, cde) → new_esEs12(vyy3000, vyy400)
new_pePe(False, vyy150) → vyy150
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Bool, bfd) → new_ltEs5(vyy9000, vyy9100)
new_esEs11(vyy3000, vyy400, ty_Int) → new_esEs13(vyy3000, vyy400)
new_lt11(vyy900, vyy910, app(app(app(ty_@3, bea), beb), bec)) → new_lt12(vyy900, vyy910, bea, beb, bec)
new_lt6(vyy900, vyy910) → new_esEs8(new_compare8(vyy900, vyy910), LT)
new_esEs6(Right(vyy3000), Right(vyy400), cef, ty_Double) → new_esEs16(vyy3000, vyy400)
new_compare29(vyy900, vyy910) → new_compare211(vyy900, vyy910, new_esEs8(vyy900, vyy910))
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, ty_Double) → new_ltEs6(vyy9000, vyy9100)
new_esEs24(vyy3000, vyy400, app(ty_Maybe, bcc)) → new_esEs7(vyy3000, vyy400, bcc)
new_ltEs4(Nothing, Just(vyy910), bfh) → True
new_esEs28(vyy900, vyy910, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs4(vyy900, vyy910, bfe, bff, bfg)
new_esEs22(vyy3002, vyy402, ty_Integer) → new_esEs12(vyy3002, vyy402)
new_ltEs11(vyy901, vyy911, ty_Ordering) → new_ltEs8(vyy901, vyy911)
new_esEs23(vyy3001, vyy401, app(ty_Maybe, bba)) → new_esEs7(vyy3001, vyy401, bba)
new_compare9(vyy90, vyy91) → new_primCmpInt(vyy90, vyy91)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, cde) → new_esEs16(vyy3000, vyy400)
new_ltEs10(vyy90, vyy91) → new_not(new_esEs8(new_compare9(vyy90, vyy91), GT))
new_lt8(vyy900, vyy910) → new_esEs8(new_compare12(vyy900, vyy910), LT)
new_esEs27(vyy901, vyy911, ty_Float) → new_esEs20(vyy901, vyy911)
new_esEs27(vyy901, vyy911, app(ty_[], dbf)) → new_esEs17(vyy901, vyy911, dbf)
new_esEs22(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_ltEs8(EQ, GT) → True
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, app(ty_Maybe, cdb)) → new_ltEs4(vyy9000, vyy9100, cdb)
new_ltEs8(GT, GT) → True
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, ty_Float) → new_ltEs12(vyy9000, vyy9100)
new_compare10(vyy900, vyy910, True, be) → LT
new_lt20(vyy900, vyy910, app(ty_Maybe, be)) → new_lt16(vyy900, vyy910, be)
new_esEs14(vyy3001, vyy401, app(ty_[], cd)) → new_esEs17(vyy3001, vyy401, cd)
new_primCmpNat0(Zero, Succ(vyy9100)) → LT
new_esEs23(vyy3001, vyy401, ty_Char) → new_esEs21(vyy3001, vyy401)
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, ty_Integer) → new_ltEs14(vyy9000, vyy9100)
new_lt19(vyy901, vyy911, app(app(ty_@2, dbd), dbe)) → new_lt5(vyy901, vyy911, dbd, dbe)
new_esEs6(Right(vyy3000), Left(vyy400), cef, cde) → False
new_esEs6(Left(vyy3000), Right(vyy400), cef, cde) → False
new_esEs8(LT, LT) → True
new_esEs6(Right(vyy3000), Right(vyy400), cef, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, cde) → new_esEs20(vyy3000, vyy400)
new_esEs28(vyy900, vyy910, ty_Double) → new_esEs16(vyy900, vyy910)
new_ltEs8(LT, EQ) → True
new_lt20(vyy900, vyy910, app(ty_Ratio, bcd)) → new_lt9(vyy900, vyy910, bcd)
new_esEs25(vyy900, vyy910, ty_Ordering) → new_esEs8(vyy900, vyy910)
new_compare10(vyy900, vyy910, False, be) → GT
new_compare27(vyy900, vyy910, ty_Double) → new_compare8(vyy900, vyy910)
new_ltEs5(True, False) → False
new_pePe(True, vyy150) → True
new_compare0([], [], bg) → EQ
new_esEs27(vyy901, vyy911, ty_@0) → new_esEs18(vyy901, vyy911)
new_primEqNat0(Zero, Zero) → True
new_esEs23(vyy3001, vyy401, app(app(ty_Either, hh), baa)) → new_esEs6(vyy3001, vyy401, hh, baa)
new_compare17(@0, @0) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), cef, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs4(vyy3000, vyy400, cfe, cff, cfg)
new_primCompAux0(vyy900, vyy910, vyy151, bg) → new_primCompAux00(vyy151, new_compare27(vyy900, vyy910, bg))
new_esEs6(Right(vyy3000), Right(vyy400), cef, app(app(ty_Either, ceg), ceh)) → new_esEs6(vyy3000, vyy400, ceg, ceh)
new_ltEs5(True, True) → True
new_ltEs17(Right(vyy9000), Left(vyy9100), bfc, bfd) → False
new_esEs19(True, True) → True
new_ltEs17(Left(vyy9000), Left(vyy9100), app(ty_[], cbd), bfd) → new_ltEs15(vyy9000, vyy9100, cbd)
new_ltEs8(GT, EQ) → False
new_ltEs8(EQ, LT) → False
new_foldFM_GE12(vyy77, vyy13, vyy170, vyy171, vyy172, EmptyFM, vyy174, True, h, ba, bb) → new_foldFM_GE30(vyy170, vyy171, new_foldFM_GE5(vyy77, vyy13, vyy174, h, ba, bb), vyy13, h, ba, bb)
new_ltEs17(Left(vyy9000), Left(vyy9100), app(app(ty_@2, cbb), cbc), bfd) → new_ltEs7(vyy9000, vyy9100, cbb, cbc)
new_compare16(:%(vyy900, vyy901), :%(vyy910, vyy911), ty_Integer) → new_compare6(new_sr(vyy900, vyy911), new_sr(vyy910, vyy901))
new_ltEs11(vyy901, vyy911, ty_Char) → new_ltEs9(vyy901, vyy911)
new_esEs25(vyy900, vyy910, ty_Int) → new_esEs13(vyy900, vyy910)
new_esEs6(Right(vyy3000), Right(vyy400), cef, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_esEs28(vyy900, vyy910, app(app(ty_Either, bfc), bfd)) → new_esEs6(vyy900, vyy910, bfc, bfd)
new_esEs22(vyy3002, vyy402, ty_Char) → new_esEs21(vyy3002, vyy402)
new_esEs24(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt11(vyy900, vyy910, ty_@0) → new_lt10(vyy900, vyy910)
new_esEs8(GT, GT) → True
new_esEs13(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_primPlusNat0(Succ(vyy1340), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1340, vyy40100)))
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, cgh), cha), chb)) → new_esEs4(vyy3000, vyy400, cgh, cha, chb)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_lt20(vyy900, vyy910, ty_Char) → new_lt17(vyy900, vyy910)
new_esEs14(vyy3001, vyy401, app(app(ty_Either, cb), cc)) → new_esEs6(vyy3001, vyy401, cb, cc)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs21(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs15(vyy3000, vyy400, app(app(app(ty_@3, ec), ed), ee)) → new_esEs4(vyy3000, vyy400, ec, ed, ee)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs19(vyy902, vyy912, ty_Ordering) → new_ltEs8(vyy902, vyy912)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Double, bfd) → new_ltEs6(vyy9000, vyy9100)
new_esEs15(vyy3000, vyy400, ty_Char) → new_esEs21(vyy3000, vyy400)
new_ltEs5(False, False) → True
new_esEs23(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy13400), Zero) → Succ(vyy13400)
new_esEs24(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_compare27(vyy900, vyy910, ty_Integer) → new_compare6(vyy900, vyy910)
new_ltEs4(Nothing, Nothing, bfh) → True
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs17(Left(vyy9000), Left(vyy9100), app(app(app(ty_@3, cag), cah), cba), bfd) → new_ltEs13(vyy9000, vyy9100, cag, cah, cba)
new_esEs28(vyy900, vyy910, ty_Float) → new_esEs20(vyy900, vyy910)
new_esEs19(False, False) → True
new_esEs22(vyy3002, vyy402, ty_@0) → new_esEs18(vyy3002, vyy402)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs11(vyy901, vyy911, app(ty_[], bdd)) → new_ltEs15(vyy901, vyy911, bdd)
new_esEs15(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_compare112(vyy900, vyy910, False, bfc, bfd) → GT
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_esEs8(EQ, EQ) → True
new_ltEs17(Left(vyy9000), Left(vyy9100), app(ty_Maybe, cbh), bfd) → new_ltEs4(vyy9000, vyy9100, cbh)
new_compare26(vyy900, vyy910, True, bfc, bfd) → EQ
new_lt20(vyy900, vyy910, ty_@0) → new_lt10(vyy900, vyy910)
new_esEs6(Right(vyy3000), Right(vyy400), cef, app(ty_[], cfa)) → new_esEs17(vyy3000, vyy400, cfa)
new_lt20(vyy900, vyy910, ty_Ordering) → new_lt13(vyy900, vyy910)
new_esEs23(vyy3001, vyy401, app(app(app(ty_@3, baf), bag), bah)) → new_esEs4(vyy3001, vyy401, baf, bag, bah)
new_esEs14(vyy3001, vyy401, app(ty_Ratio, ce)) → new_esEs9(vyy3001, vyy401, ce)
new_esEs28(vyy900, vyy910, ty_Int) → new_esEs13(vyy900, vyy910)
new_lt9(vyy900, vyy910, bcd) → new_esEs8(new_compare16(vyy900, vyy910, bcd), LT)
new_lt18(vyy900, vyy910) → new_esEs8(new_compare13(vyy900, vyy910), LT)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs28(vyy900, vyy910, ty_@0) → new_esEs18(vyy900, vyy910)
new_esEs14(vyy3001, vyy401, app(ty_Maybe, dd)) → new_esEs7(vyy3001, vyy401, dd)
new_esEs15(vyy3000, vyy400, app(ty_Ratio, dh)) → new_esEs9(vyy3000, vyy400, dh)
new_primCmpNat0(Succ(vyy9000), Succ(vyy9100)) → new_primCmpNat0(vyy9000, vyy9100)
new_compare7(vyy900, vyy910, bc, bd) → new_compare25(vyy900, vyy910, new_esEs5(vyy900, vyy910, bc, bd), bc, bd)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_lt20(vyy900, vyy910, ty_Int) → new_lt7(vyy900, vyy910)
new_esEs14(vyy3001, vyy401, ty_Float) → new_esEs20(vyy3001, vyy401)
new_lt10(vyy900, vyy910) → new_esEs8(new_compare17(vyy900, vyy910), LT)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs13(vyy3000, vyy400)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_esEs27(vyy901, vyy911, ty_Ordering) → new_esEs8(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], cdf), cde) → new_esEs17(vyy3000, vyy400, cdf)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, cdg), cde) → new_esEs9(vyy3000, vyy400, cdg)
new_esEs6(Right(vyy3000), Right(vyy400), cef, app(app(ty_@2, cfc), cfd)) → new_esEs5(vyy3000, vyy400, cfc, cfd)
new_compare111(vyy900, vyy910, True, bfe, bff, bfg) → LT
new_esEs22(vyy3002, vyy402, ty_Int) → new_esEs13(vyy3002, vyy402)
new_primCompAux00(vyy160, LT) → LT
new_ltEs4(Just(vyy900), Just(vyy910), ty_Int) → new_ltEs10(vyy900, vyy910)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs13(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy9000)), Neg(vyy910)) → new_primCmpNat0(vyy910, Succ(vyy9000))
new_esEs24(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt7(vyy900, vyy910) → new_esEs8(new_compare9(vyy900, vyy910), LT)
new_esEs7(Nothing, Nothing, eg) → True
new_esEs28(vyy900, vyy910, ty_Ordering) → new_esEs8(vyy900, vyy910)
new_compare27(vyy900, vyy910, app(ty_Maybe, caf)) → new_compare14(vyy900, vyy910, caf)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_lt4(vyy900, vyy910) → new_esEs8(new_compare6(vyy900, vyy910), LT)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs21(vyy3000, vyy400)
new_ltEs19(vyy902, vyy912, app(app(ty_Either, daf), dag)) → new_ltEs17(vyy902, vyy912, daf, dag)
new_primCmpNat0(Zero, Zero) → EQ
new_compare28(vyy900, vyy910, bfe, bff, bfg) → new_compare210(vyy900, vyy910, new_esEs4(vyy900, vyy910, bfe, bff, bfg), bfe, bff, bfg)
new_esEs6(Right(vyy3000), Right(vyy400), cef, app(ty_Maybe, cfh)) → new_esEs7(vyy3000, vyy400, cfh)
new_esEs23(vyy3001, vyy401, ty_@0) → new_esEs18(vyy3001, vyy401)
new_primCmpNat0(Succ(vyy9000), Zero) → GT
new_esEs23(vyy3001, vyy401, app(app(ty_@2, bad), bae)) → new_esEs5(vyy3001, vyy401, bad, bae)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy9100))) → LT
new_esEs19(True, False) → False
new_esEs19(False, True) → False
new_compare210(vyy900, vyy910, True, bfe, bff, bfg) → EQ
new_compare27(vyy900, vyy910, app(ty_[], cab)) → new_compare0(vyy900, vyy910, cab)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, fg), fh), ga)) → new_esEs4(vyy3000, vyy400, fg, fh, ga)
new_primPlusNat1(Succ(vyy13400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy13400, vyy401000)))
new_compare6(Integer(vyy900), Integer(vyy910)) → new_primCmpInt(vyy900, vyy910)
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_esEs25(vyy900, vyy910, ty_Bool) → new_esEs19(vyy900, vyy910)
new_esEs7(Just(vyy3000), Nothing, eg) → False
new_esEs7(Nothing, Just(vyy400), eg) → False
new_esEs15(vyy3000, vyy400, app(app(ty_@2, ea), eb)) → new_esEs5(vyy3000, vyy400, ea, eb)
new_ltEs5(False, True) → True
new_lt11(vyy900, vyy910, app(ty_Ratio, beg)) → new_lt9(vyy900, vyy910, beg)
new_lt19(vyy901, vyy911, app(ty_Maybe, dcb)) → new_lt16(vyy901, vyy911, dcb)
new_compare26(vyy900, vyy910, False, bfc, bfd) → new_compare112(vyy900, vyy910, new_ltEs17(vyy900, vyy910, bfc, bfd), bfc, bfd)
new_ltEs11(vyy901, vyy911, app(app(app(ty_@3, bcg), bch), bda)) → new_ltEs13(vyy901, vyy911, bcg, bch, bda)
new_lt19(vyy901, vyy911, ty_Int) → new_lt7(vyy901, vyy911)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_esEs14(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, app(ty_[], cgd)) → new_esEs17(vyy3000, vyy400, cgd)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy9100))) → new_primCmpNat0(Zero, Succ(vyy9100))
new_compare27(vyy900, vyy910, app(app(app(ty_@3, bhe), bhf), bhg)) → new_compare28(vyy900, vyy910, bhe, bhf, bhg)
new_primCompAux00(vyy160, EQ) → vyy160
new_foldFM_GE12(vyy77, vyy13, vyy170, vyy171, vyy172, vyy173, vyy174, False, h, ba, bb) → new_foldFM_GE5(vyy77, vyy13, vyy174, h, ba, bb)
new_compare24(vyy900, vyy910, True) → EQ
new_compare27(vyy900, vyy910, ty_Float) → new_compare12(vyy900, vyy910)
new_esEs27(vyy901, vyy911, ty_Int) → new_esEs13(vyy901, vyy911)
new_esEs23(vyy3001, vyy401, ty_Bool) → new_esEs19(vyy3001, vyy401)
new_esEs22(vyy3002, vyy402, ty_Bool) → new_esEs19(vyy3002, vyy402)
new_ltEs8(GT, LT) → False
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs27(vyy901, vyy911, ty_Double) → new_esEs16(vyy901, vyy911)
new_esEs15(vyy3000, vyy400, app(ty_Maybe, ef)) → new_esEs7(vyy3000, vyy400, ef)
new_ltEs19(vyy902, vyy912, app(app(app(ty_@3, chg), chh), daa)) → new_ltEs13(vyy902, vyy912, chg, chh, daa)
new_ltEs11(vyy901, vyy911, ty_@0) → new_ltEs18(vyy901, vyy911)
new_compare27(vyy900, vyy910, ty_Int) → new_compare9(vyy900, vyy910)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, cgf), cgg)) → new_esEs5(vyy3000, vyy400, cgf, cgg)
new_ltEs15(vyy90, vyy91, bg) → new_not(new_esEs8(new_compare0(vyy90, vyy91, bg), GT))
new_ltEs11(vyy901, vyy911, ty_Double) → new_ltEs6(vyy901, vyy911)
new_not(False) → True
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, cdc), cdd), cde) → new_esEs6(vyy3000, vyy400, cdc, cdd)
new_compare211(vyy900, vyy910, False) → new_compare110(vyy900, vyy910, new_ltEs8(vyy900, vyy910))
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, ty_@0) → new_ltEs18(vyy9000, vyy9100)
new_esEs24(vyy3000, vyy400, ty_Int) → new_esEs13(vyy3000, vyy400)
new_esEs25(vyy900, vyy910, ty_Float) → new_esEs20(vyy900, vyy910)
new_primCmpInt(Pos(Succ(vyy9000)), Pos(vyy910)) → new_primCmpNat0(Succ(vyy9000), vyy910)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs14(vyy3001, vyy401, app(app(ty_@2, cf), cg)) → new_esEs5(vyy3001, vyy401, cf, cg)
new_ltEs4(Just(vyy900), Just(vyy910), app(app(app(ty_@3, bga), bgb), bgc)) → new_ltEs13(vyy900, vyy910, bga, bgb, bgc)
new_esEs6(Right(vyy3000), Right(vyy400), cef, ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs15(vyy3000, vyy400, app(ty_[], dg)) → new_esEs17(vyy3000, vyy400, dg)
new_esEs24(vyy3000, vyy400, app(app(ty_Either, bbb), bbc)) → new_esEs6(vyy3000, vyy400, bbb, bbc)
new_esEs20(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs13(new_sr0(vyy3000, vyy400), new_sr0(vyy3001, vyy401))
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, app(app(ty_Either, cch), cda)) → new_ltEs17(vyy9000, vyy9100, cch, cda)
new_lt11(vyy900, vyy910, ty_Ordering) → new_lt13(vyy900, vyy910)
new_esEs25(vyy900, vyy910, app(app(app(ty_@3, bea), beb), bec)) → new_esEs4(vyy900, vyy910, bea, beb, bec)
new_esEs24(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs28(vyy900, vyy910, app(app(ty_@2, bc), bd)) → new_esEs5(vyy900, vyy910, bc, bd)
new_compare0(:(vyy900, vyy901), [], bg) → GT
new_lt11(vyy900, vyy910, ty_Integer) → new_lt4(vyy900, vyy910)
new_ltEs19(vyy902, vyy912, ty_@0) → new_ltEs18(vyy902, vyy912)
new_ltEs4(Just(vyy900), Just(vyy910), ty_Ordering) → new_ltEs8(vyy900, vyy910)
new_esEs24(vyy3000, vyy400, app(ty_[], bbd)) → new_esEs17(vyy3000, vyy400, bbd)
new_lt19(vyy901, vyy911, app(app(app(ty_@3, dba), dbb), dbc)) → new_lt12(vyy901, vyy911, dba, dbb, dbc)
new_lt19(vyy901, vyy911, ty_Integer) → new_lt4(vyy901, vyy911)
new_esEs22(vyy3002, vyy402, app(app(app(ty_@3, hd), he), hf)) → new_esEs4(vyy3002, vyy402, hd, he, hf)
new_esEs27(vyy901, vyy911, app(app(ty_Either, dbh), dca)) → new_esEs6(vyy901, vyy911, dbh, dca)
new_lt20(vyy900, vyy910, ty_Double) → new_lt6(vyy900, vyy910)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, cde) → new_esEs21(vyy3000, vyy400)
new_ltEs19(vyy902, vyy912, app(ty_[], dad)) → new_ltEs15(vyy902, vyy912, dad)
new_esEs15(vyy3000, vyy400, app(app(ty_Either, de), df)) → new_esEs6(vyy3000, vyy400, de, df)
new_ltEs11(vyy901, vyy911, app(app(ty_Either, bdf), bdg)) → new_ltEs17(vyy901, vyy911, bdf, bdg)
new_lt11(vyy900, vyy910, ty_Char) → new_lt17(vyy900, vyy910)
new_primCmpInt(Pos(Succ(vyy9000)), Neg(vyy910)) → GT
new_compare27(vyy900, vyy910, ty_@0) → new_compare17(vyy900, vyy910)
new_esEs28(vyy900, vyy910, app(ty_Maybe, be)) → new_esEs7(vyy900, vyy910, be)
new_ltEs4(Just(vyy900), Just(vyy910), ty_@0) → new_ltEs18(vyy900, vyy910)
new_lt19(vyy901, vyy911, ty_Char) → new_lt17(vyy901, vyy911)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs14(vyy3001, vyy401, ty_Double) → new_esEs16(vyy3001, vyy401)
new_ltEs17(Left(vyy9000), Left(vyy9100), app(app(ty_Either, cbf), cbg), bfd) → new_ltEs17(vyy9000, vyy9100, cbf, cbg)
new_ltEs17(Left(vyy9000), Left(vyy9100), app(ty_Ratio, cbe), bfd) → new_ltEs16(vyy9000, vyy9100, cbe)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, cdh), cea), cde) → new_esEs5(vyy3000, vyy400, cdh, cea)
new_lt11(vyy900, vyy910, app(ty_[], bef)) → new_lt14(vyy900, vyy910, bef)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare27(vyy900, vyy910, ty_Char) → new_compare18(vyy900, vyy910)
new_compare110(vyy900, vyy910, True) → LT
new_esEs28(vyy900, vyy910, app(ty_Ratio, bcd)) → new_esEs9(vyy900, vyy910, bcd)
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_compare25(vyy900, vyy910, True, bc, bd) → EQ
new_esEs14(vyy3001, vyy401, ty_Char) → new_esEs21(vyy3001, vyy401)
new_compare110(vyy900, vyy910, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs4(Just(vyy900), Just(vyy910), ty_Double) → new_ltEs6(vyy900, vyy910)
new_esEs24(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_compare111(vyy900, vyy910, False, bfe, bff, bfg) → GT
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs19(vyy3000, vyy400)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Int, bfd) → new_ltEs10(vyy9000, vyy9100)
new_esEs5(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bh, ca) → new_asAs(new_esEs15(vyy3000, vyy400, bh), new_esEs14(vyy3001, vyy401, ca))
new_esEs27(vyy901, vyy911, app(app(ty_@2, dbd), dbe)) → new_esEs5(vyy901, vyy911, dbd, dbe)
new_ltEs11(vyy901, vyy911, app(ty_Maybe, bdh)) → new_ltEs4(vyy901, vyy911, bdh)
new_ltEs4(Just(vyy900), Just(vyy910), app(ty_[], bgf)) → new_ltEs15(vyy900, vyy910, bgf)
new_esEs22(vyy3002, vyy402, app(ty_[], gh)) → new_esEs17(vyy3002, vyy402, gh)
new_lt20(vyy900, vyy910, ty_Bool) → new_lt18(vyy900, vyy910)
new_ltEs19(vyy902, vyy912, ty_Char) → new_ltEs9(vyy902, vyy912)
new_compare25(vyy900, vyy910, False, bc, bd) → new_compare15(vyy900, vyy910, new_ltEs7(vyy900, vyy910, bc, bd), bc, bd)
new_ltEs11(vyy901, vyy911, ty_Int) → new_ltEs10(vyy901, vyy911)
new_lt19(vyy901, vyy911, ty_Bool) → new_lt18(vyy901, vyy911)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy9100))) → new_primCmpNat0(Succ(vyy9100), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy9100))) → GT
new_esEs24(vyy3000, vyy400, ty_Char) → new_esEs21(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, cee), cde) → new_esEs7(vyy3000, vyy400, cee)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, cde) → new_esEs8(vyy3000, vyy400)
new_ltEs11(vyy901, vyy911, app(ty_Ratio, bde)) → new_ltEs16(vyy901, vyy911, bde)
new_ltEs11(vyy901, vyy911, ty_Bool) → new_ltEs5(vyy901, vyy911)
new_ltEs4(Just(vyy900), Just(vyy910), app(app(ty_Either, bgh), bha)) → new_ltEs17(vyy900, vyy910, bgh, bha)
new_sr0(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_compare23(vyy900, vyy910, True, be) → EQ
new_compare15(vyy900, vyy910, False, bc, bd) → GT
new_compare27(vyy900, vyy910, app(ty_Ratio, cac)) → new_compare16(vyy900, vyy910, cac)
new_ltEs17(Left(vyy9000), Right(vyy9100), bfc, bfd) → True
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, app(app(ty_@2, ccd), cce)) → new_ltEs7(vyy9000, vyy9100, ccd, cce)
new_compare210(vyy900, vyy910, False, bfe, bff, bfg) → new_compare111(vyy900, vyy910, new_ltEs13(vyy900, vyy910, bfe, bff, bfg), bfe, bff, bfg)
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Int) → new_esEs13(vyy3001, vyy401)
new_esEs25(vyy900, vyy910, app(ty_Maybe, bfb)) → new_esEs7(vyy900, vyy910, bfb)
new_ltEs4(Just(vyy900), Just(vyy910), app(ty_Maybe, bhb)) → new_ltEs4(vyy900, vyy910, bhb)
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, app(app(app(ty_@3, cca), ccb), ccc)) → new_ltEs13(vyy9000, vyy9100, cca, ccb, ccc)
new_ltEs4(Just(vyy900), Just(vyy910), ty_Float) → new_ltEs12(vyy900, vyy910)
new_compare16(:%(vyy900, vyy901), :%(vyy910, vyy911), ty_Int) → new_compare9(new_sr0(vyy900, vyy911), new_sr0(vyy910, vyy901))
new_ltEs14(vyy90, vyy91) → new_not(new_esEs8(new_compare6(vyy90, vyy91), GT))
new_esEs6(Right(vyy3000), Right(vyy400), cef, ty_Float) → new_esEs20(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs16(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs13(new_sr0(vyy3000, vyy400), new_sr0(vyy3001, vyy401))
new_lt19(vyy901, vyy911, ty_Ordering) → new_lt13(vyy901, vyy911)
new_esEs6(Right(vyy3000), Right(vyy400), cef, ty_Char) → new_esEs21(vyy3000, vyy400)
new_asAs(False, vyy123) → False
new_ltEs19(vyy902, vyy912, app(app(ty_@2, dab), dac)) → new_ltEs7(vyy902, vyy912, dab, dac)
new_compare24(vyy900, vyy910, False) → new_compare11(vyy900, vyy910, new_ltEs5(vyy900, vyy910))
new_esEs25(vyy900, vyy910, app(ty_Ratio, beg)) → new_esEs9(vyy900, vyy910, beg)
new_lt15(vyy900, vyy910, bfc, bfd) → new_esEs8(new_compare19(vyy900, vyy910, bfc, bfd), LT)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_lt20(vyy900, vyy910, app(ty_[], bhc)) → new_lt14(vyy900, vyy910, bhc)
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, app(ty_Ratio, ccg)) → new_ltEs16(vyy9000, vyy9100, ccg)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, chc)) → new_esEs7(vyy3000, vyy400, chc)
new_esEs14(vyy3001, vyy401, app(app(app(ty_@3, da), db), dc)) → new_esEs4(vyy3001, vyy401, da, db, dc)
new_lt19(vyy901, vyy911, ty_Float) → new_lt8(vyy901, vyy911)
new_ltEs4(Just(vyy900), Just(vyy910), ty_Integer) → new_ltEs14(vyy900, vyy910)
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, ty_Char) → new_ltEs9(vyy9000, vyy9100)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Ordering, bfd) → new_ltEs8(vyy9000, vyy9100)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, cge)) → new_esEs9(vyy3000, vyy400, cge)
new_lt20(vyy900, vyy910, ty_Float) → new_lt8(vyy900, vyy910)
new_lt11(vyy900, vyy910, app(app(ty_@2, bed), bee)) → new_lt5(vyy900, vyy910, bed, bee)
new_esEs4(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), gc, gd, ge) → new_asAs(new_esEs24(vyy3000, vyy400, gc), new_asAs(new_esEs23(vyy3001, vyy401, gd), new_esEs22(vyy3002, vyy402, ge)))
new_foldFM_GE5(vyy77, vyy13, Branch(vyy1740, vyy1741, vyy1742, vyy1743, vyy1744), h, ba, bb) → new_foldFM_GE12(vyy77, vyy13, vyy1740, vyy1741, vyy1742, vyy1743, vyy1744, new_gtEs0(vyy1740, vyy13, h, ba), h, ba, bb)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs25(vyy900, vyy910, app(ty_[], bef)) → new_esEs17(vyy900, vyy910, bef)
new_compare27(vyy900, vyy910, app(app(ty_Either, cad), cae)) → new_compare19(vyy900, vyy910, cad, cae)
new_esEs23(vyy3001, vyy401, ty_Double) → new_esEs16(vyy3001, vyy401)
new_esEs25(vyy900, vyy910, ty_@0) → new_esEs18(vyy900, vyy910)
new_ltEs4(Just(vyy900), Just(vyy910), app(ty_Ratio, bgg)) → new_ltEs16(vyy900, vyy910, bgg)
new_ltEs6(vyy90, vyy91) → new_not(new_esEs8(new_compare8(vyy90, vyy91), GT))
new_lt19(vyy901, vyy911, app(ty_[], dbf)) → new_lt14(vyy901, vyy911, dbf)
new_ltEs11(vyy901, vyy911, app(app(ty_@2, bdb), bdc)) → new_ltEs7(vyy901, vyy911, bdb, bdc)
new_ltEs8(LT, GT) → True
new_compare19(vyy900, vyy910, bfc, bfd) → new_compare26(vyy900, vyy910, new_esEs6(vyy900, vyy910, bfc, bfd), bfc, bfd)
new_ltEs13(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), chd, che, chf) → new_pePe(new_lt20(vyy900, vyy910, chd), new_asAs(new_esEs28(vyy900, vyy910, chd), new_pePe(new_lt19(vyy901, vyy911, che), new_asAs(new_esEs27(vyy901, vyy911, che), new_ltEs19(vyy902, vyy912, chf)))))
new_esEs25(vyy900, vyy910, ty_Char) → new_esEs21(vyy900, vyy910)
new_compare23(vyy900, vyy910, False, be) → new_compare10(vyy900, vyy910, new_ltEs4(vyy900, vyy910, be), be)
new_ltEs19(vyy902, vyy912, ty_Bool) → new_ltEs5(vyy902, vyy912)
new_compare27(vyy900, vyy910, ty_Ordering) → new_compare29(vyy900, vyy910)
new_esEs28(vyy900, vyy910, app(ty_[], bhc)) → new_esEs17(vyy900, vyy910, bhc)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], fb)) → new_esEs17(vyy3000, vyy400, fb)
new_esEs14(vyy3001, vyy401, ty_Bool) → new_esEs19(vyy3001, vyy401)
new_esEs27(vyy901, vyy911, ty_Char) → new_esEs21(vyy901, vyy911)
new_esEs15(vyy3000, vyy400, ty_Int) → new_esEs13(vyy3000, vyy400)
new_esEs11(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_lt11(vyy900, vyy910, app(app(ty_Either, beh), bfa)) → new_lt15(vyy900, vyy910, beh, bfa)
new_compare11(vyy900, vyy910, False) → GT
new_esEs9(:%(vyy3000, vyy3001), :%(vyy400, vyy401), bf) → new_asAs(new_esEs11(vyy3000, vyy400, bf), new_esEs10(vyy3001, vyy401, bf))
new_esEs14(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_ltEs4(Just(vyy900), Just(vyy910), ty_Char) → new_ltEs9(vyy900, vyy910)
new_esEs25(vyy900, vyy910, app(app(ty_@2, bed), bee)) → new_esEs5(vyy900, vyy910, bed, bee)
new_lt16(vyy900, vyy910, be) → new_esEs8(new_compare14(vyy900, vyy910, be), LT)
new_lt20(vyy900, vyy910, app(app(ty_Either, bfc), bfd)) → new_lt15(vyy900, vyy910, bfc, bfd)
new_compare11(vyy900, vyy910, True) → LT
new_lt11(vyy900, vyy910, ty_Bool) → new_lt18(vyy900, vyy910)
new_compare18(Char(vyy900), Char(vyy910)) → new_primCmpNat0(vyy900, vyy910)
new_esEs22(vyy3002, vyy402, app(app(ty_Either, gf), gg)) → new_esEs6(vyy3002, vyy402, gf, gg)
new_esEs23(vyy3001, vyy401, app(ty_Ratio, bac)) → new_esEs9(vyy3001, vyy401, bac)
new_lt17(vyy900, vyy910) → new_esEs8(new_compare18(vyy900, vyy910), LT)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, cde) → new_esEs13(vyy3000, vyy400)
new_lt19(vyy901, vyy911, ty_Double) → new_lt6(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, cde) → new_esEs19(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, fd), ff)) → new_esEs5(vyy3000, vyy400, fd, ff)
new_esEs10(vyy3001, vyy401, ty_Int) → new_esEs13(vyy3001, vyy401)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Char, bfd) → new_ltEs9(vyy9000, vyy9100)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_@0, bfd) → new_ltEs18(vyy9000, vyy9100)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_esEs24(vyy3000, vyy400, ty_@0) → new_esEs18(vyy3000, vyy400)
new_esEs15(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_esEs22(vyy3002, vyy402, ty_Double) → new_esEs16(vyy3002, vyy402)
new_lt19(vyy901, vyy911, ty_@0) → new_lt10(vyy901, vyy911)
new_ltEs8(LT, LT) → True
new_compare27(vyy900, vyy910, ty_Bool) → new_compare13(vyy900, vyy910)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs21(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, cgb), cgc)) → new_esEs6(vyy3000, vyy400, cgb, cgc)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vyy910, vyy911), bg) → LT
new_esEs15(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_foldFM_GE30(vyy170, vyy171, vyy100, vyy13, h, ba, bb) → new_fmToList_GE0(vyy170, vyy171, vyy100, h, ba, bb)
new_ltEs11(vyy901, vyy911, ty_Integer) → new_ltEs14(vyy901, vyy911)
new_asAs(True, vyy123) → vyy123
new_ltEs4(Just(vyy900), Nothing, bfh) → False
new_compare112(vyy900, vyy910, True, bfc, bfd) → LT
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Float, bfd) → new_ltEs12(vyy9000, vyy9100)
new_ltEs19(vyy902, vyy912, ty_Float) → new_ltEs12(vyy902, vyy912)
new_esEs18(@0, @0) → True
new_esEs17([], [], cga) → True
new_compare211(vyy900, vyy910, True) → EQ
new_esEs17([], :(vyy400, vyy401), cga) → False
new_esEs17(:(vyy3000, vyy3001), [], cga) → False
new_compare14(vyy900, vyy910, be) → new_compare23(vyy900, vyy910, new_esEs7(vyy900, vyy910, be), be)
new_esEs14(vyy3001, vyy401, ty_@0) → new_esEs18(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)
new_lt14(vyy900, vyy910, bhc) → new_esEs8(new_compare0(vyy900, vyy910, bhc), LT)
new_lt11(vyy900, vyy910, ty_Double) → new_lt6(vyy900, vyy910)
new_gtEs0(vyy1730, vyy13, h, ba) → new_not(new_esEs8(new_compare26(vyy1730, Left(vyy13), new_esEs6(vyy1730, Left(vyy13), h, ba), h, ba), LT))
new_esEs15(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_foldFM_GE5(vyy77, vyy13, EmptyFM, h, ba, bb) → vyy77
new_esEs24(vyy3000, vyy400, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs4(vyy3000, vyy400, bbh, bca, bcb)
new_lt11(vyy900, vyy910, app(ty_Maybe, bfb)) → new_lt16(vyy900, vyy910, bfb)
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, ty_Bool) → new_ltEs5(vyy9000, vyy9100)
new_primCompAux00(vyy160, GT) → GT
new_ltEs17(Left(vyy9000), Left(vyy9100), ty_Integer, bfd) → new_ltEs14(vyy9000, vyy9100)
new_esEs6(Right(vyy3000), Right(vyy400), cef, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(vyy3000, vyy400, app(ty_Ratio, bbe)) → new_esEs9(vyy3000, vyy400, bbe)
new_esEs27(vyy901, vyy911, ty_Bool) → new_esEs19(vyy901, vyy911)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs16(vyy3000, vyy400)
new_ltEs17(Right(vyy9000), Right(vyy9100), bfc, app(ty_[], ccf)) → new_ltEs15(vyy9000, vyy9100, ccf)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_lt13(vyy900, vyy910) → new_esEs8(new_compare29(vyy900, vyy910), LT)
new_esEs22(vyy3002, vyy402, app(ty_Maybe, hg)) → new_esEs7(vyy3002, vyy402, hg)
new_primCmpInt(Neg(Succ(vyy9000)), Pos(vyy910)) → LT
new_not(True) → False
new_esEs15(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)

The set Q consists of the following terms:

new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_GE12(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, True, x11, x12, x13)
new_esEs23(x0, x1, ty_Float)
new_compare18(Char(x0), Char(x1))
new_ltEs16(x0, x1, x2)
new_esEs26(x0, x1, ty_Ordering)
new_esEs18(@0, @0)
new_lt19(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs14(x0, x1, ty_Bool)
new_compare111(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_compare23(x0, x1, False, x2)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_compare27(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_esEs15(x0, x1, ty_Int)
new_asAs(True, x0)
new_ltEs9(x0, x1)
new_fmToList_GE0(x0, x1, x2, x3, x4, x5)
new_ltEs8(EQ, EQ)
new_esEs14(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_esEs27(x0, x1, ty_Char)
new_esEs14(x0, x1, app(ty_Maybe, x2))
new_compare0([], [], x0)
new_esEs15(x0, x1, ty_Double)
new_esEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Bool)
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs25(x0, x1, ty_Ordering)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Bool)
new_compare211(x0, x1, False)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_esEs27(x0, x1, ty_@0)
new_ltEs17(Right(x0), Left(x1), x2, x3)
new_compare27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Left(x0), Right(x1), x2, x3)
new_foldFM_GE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_@0)
new_esEs17([], :(x0, x1), x2)
new_pePe(True, x0)
new_ltEs19(x0, x1, ty_Double)
new_esEs8(GT, GT)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare112(x0, x1, True, x2, x3)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare23(x0, x1, True, x2)
new_lt19(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Char)
new_ltEs15(x0, x1, x2)
new_compare17(@0, @0)
new_esEs8(LT, LT)
new_esEs15(x0, x1, ty_Integer)
new_ltEs11(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Char)
new_ltEs17(Right(x0), Right(x1), x2, ty_Float)
new_esEs15(x0, x1, app(ty_Maybe, x2))
new_ltEs5(False, False)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, ty_Ordering)
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_compare27(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Integer)
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_esEs19(True, True)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs28(x0, x1, ty_Float)
new_ltEs11(x0, x1, ty_Integer)
new_ltEs17(Left(x0), Left(x1), ty_Char, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare8(Double(x0, x1), Double(x2, x3))
new_lt20(x0, x1, ty_Bool)
new_ltEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqNat0(Succ(x0), Succ(x1))
new_asAs(False, x0)
new_esEs27(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_lt16(x0, x1, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare11(x0, x1, False)
new_primEqNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Char)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Nothing, Nothing, x0)
new_lt15(x0, x1, x2, x3)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare26(x0, x1, False, x2, x3)
new_compare24(x0, x1, False)
new_esEs26(x0, x1, ty_Float)
new_compare29(x0, x1)
new_esEs22(x0, x1, ty_Float)
new_compare28(x0, x1, x2, x3, x4)
new_ltEs17(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_foldFM_GE12(x0, x1, x2, x3, x4, EmptyFM, x5, True, x6, x7, x8)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Int)
new_ltEs17(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs4(Just(x0), Nothing, x1)
new_ltEs17(Left(x0), Left(x1), ty_Double, x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare27(x0, x1, ty_Double)
new_compare112(x0, x1, False, x2, x3)
new_compare0(:(x0, x1), [], x2)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs11(x0, x1, ty_Double)
new_primCmpNat0(Succ(x0), Zero)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs18(x0, x1)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_compare111(x0, x1, True, x2, x3, x4)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Int)
new_compare27(x0, x1, ty_Char)
new_compare25(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, ty_Bool)
new_compare27(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_lt11(x0, x1, ty_@0)
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_esEs14(x0, x1, ty_Float)
new_esEs15(x0, x1, ty_Bool)
new_sr0(x0, x1)
new_esEs25(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs19(False, True)
new_esEs19(True, False)
new_esEs22(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare27(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Zero)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_primMulNat0(Succ(x0), Zero)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpNat0(Zero, Succ(x0))
new_ltEs17(Right(x0), Right(x1), x2, ty_Double)
new_esEs14(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, x2, x3, x4)
new_esEs15(x0, x1, ty_Float)
new_foldFM_GE30(x0, x1, x2, x3, x4, x5, x6)
new_ltEs11(x0, x1, ty_@0)
new_compare15(x0, x1, False, x2, x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(Just(x0), Nothing, x1)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, ty_Integer)
new_compare13(x0, x1)
new_primCompAux00(x0, LT)
new_esEs11(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs14(x0, x1, ty_@0)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_primCompAux0(x0, x1, x2, x3)
new_compare0([], :(x0, x1), x2)
new_ltEs19(x0, x1, ty_Int)
new_compare7(x0, x1, x2, x3)
new_compare10(x0, x1, False, x2)
new_ltEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare15(x0, x1, True, x2, x3)
new_esEs17(:(x0, x1), [], x2)
new_esEs22(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt19(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare11(x0, x1, True)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_compare14(x0, x1, x2)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(False, False)
new_foldFM_GE12(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_ltEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs11(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs15(x0, x1, app(ty_[], x2))
new_ltEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt19(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, ty_@0)
new_compare16(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs17(Right(x0), Right(x1), x2, ty_@0)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs14(x0, x1, ty_Int)
new_esEs17([], [], x0)
new_compare110(x0, x1, False)
new_esEs15(x0, x1, ty_@0)
new_ltEs17(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, ty_Char)
new_compare26(x0, x1, True, x2, x3)
new_lt20(x0, x1, ty_Float)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs17(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Zero, Succ(x0))
new_esEs28(x0, x1, ty_Ordering)
new_lt11(x0, x1, ty_Float)
new_compare10(x0, x1, True, x2)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs14(x0, x1, ty_Double)
new_esEs15(x0, x1, ty_Ordering)
new_lt14(x0, x1, x2)
new_ltEs19(x0, x1, ty_Char)
new_lt11(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Double)
new_foldFM_GE5(x0, x1, EmptyFM, x2, x3, x4)
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare25(x0, x1, True, x2, x3)
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(LT, LT)
new_esEs23(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Zero, Zero)
new_lt11(x0, x1, app(ty_[], x2))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_ltEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs25(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Double)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_ltEs8(GT, GT)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
new_compare6(Integer(x0), Integer(x1))
new_lt4(x0, x1)
new_lt17(x0, x1)
new_esEs22(x0, x1, ty_Double)
new_pePe(False, x0)
new_ltEs4(Nothing, Just(x0), x1)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_compare12(Float(x0, x1), Float(x2, x3))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Left(x0), Left(x1), ty_Int, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCompAux00(x0, GT)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(ty_[], x2))
new_foldFM_GE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare9(x0, x1)
new_esEs20(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare211(x0, x1, True)
new_lt11(x0, x1, ty_Bool)
new_ltEs8(LT, GT)
new_ltEs17(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs8(GT, LT)
new_esEs24(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_sr(Integer(x0), Integer(x1))
new_ltEs11(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_lt5(x0, x1, x2, x3)
new_primCompAux00(x0, EQ)
new_compare24(x0, x1, True)
new_esEs23(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(True, True)
new_lt11(x0, x1, ty_Int)
new_not(True)
new_lt11(x0, x1, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1)
new_esEs14(x0, x1, ty_Ordering)
new_ltEs11(x0, x1, ty_Ordering)
new_lt11(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_gtEs0(x0, x1, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Float)
new_lt7(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_not(False)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1, app(ty_[], x2))
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare16(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt20(x0, x1, ty_Int)
new_esEs14(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Integer)
new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_lt9(x0, x1, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs21(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs10(x0, x1)
new_esEs14(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Float)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_compare19(x0, x1, x2, x3)
new_lt19(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_ltEs12(x0, x1)
new_esEs24(x0, x1, ty_Double)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_ltEs17(Left(x0), Left(x1), ty_Bool, x2)
new_lt19(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_lt11(x0, x1, ty_Integer)
new_compare27(x0, x1, ty_Integer)
new_ltEs4(Nothing, Nothing, x0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_esEs13(x0, x1)
new_esEs28(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs15(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Integer)
new_ltEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1)
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare27(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs14(x0, x1, ty_Integer)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primMulInt(Neg(x0), Neg(x1))
new_lt8(x0, x1)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Integer)
new_ltEs17(Left(x0), Left(x1), ty_Ordering, x2)
new_lt19(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt10(x0, x1)

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: