YES 7.105 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ LR

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

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

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

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

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

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

  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 : rest

is transformed to
keysFM_LE0 key elt rest = key : rest

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

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

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

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

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

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

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

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

  
keysFM_LE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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



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

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

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

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

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

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

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

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

  
keysFM_LE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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



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

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

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

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

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

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

  
keysFM_LE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

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

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

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

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

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

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

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

  
keysFM_LE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Cond Reductions:
The following Function with conditions
foldFM_LE k z fr EmptyFM = z
foldFM_LE k z fr (Branch key elt vx fm_l fm_r)
 | key <= fr
 = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r
 | otherwise
 = foldFM_LE k z fr fm_l

is transformed to
foldFM_LE k z fr EmptyFM = foldFM_LE3 k z fr EmptyFM
foldFM_LE k z fr (Branch key elt vx fm_l fm_r) = foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r)

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

foldFM_LE0 k z fr key elt vx fm_l fm_r True = foldFM_LE k z fr fm_l

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

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

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

is transformed to
compare x y = compare3 x y

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

compare0 x y True = GT

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

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

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

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

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

  foldFM_LE :: Ord a => (a  ->  c  ->  b  ->  b)  ->  b  ->  a  ->  FiniteMap a c  ->  b
foldFM_LE k z fr EmptyFM = foldFM_LE3 k z fr EmptyFM
foldFM_LE k z fr (Branch key elt vx fm_l fm_r) = foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r)

  
foldFM_LE0 k z fr key elt vx fm_l fm_r True = foldFM_LE k z fr fm_l

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

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

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

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

  
keysFM_LE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Let/Where Reductions:
The bindings of the following Let/Where expression
reduce1 x y (y == 0)
where 
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
reduce2Reduce0 vyw vyx x y True = x `quot` reduce2D vyw vyx :% (y `quot` reduce2D vyw vyx)

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

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

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

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

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



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

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

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

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

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

  foldFM :: (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_LE :: Ord c => (c  ->  a  ->  b  ->  b)  ->  b  ->  c  ->  FiniteMap c a  ->  b
foldFM_LE k z fr EmptyFM = foldFM_LE3 k z fr EmptyFM
foldFM_LE k z fr (Branch key elt vx fm_l fm_r) = foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r)

  
foldFM_LE0 k z fr key elt vx fm_l fm_r True = foldFM_LE k z fr fm_l

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

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

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

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

  
keysFM_LE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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

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

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

  foldFM_LE :: Ord b => (b  ->  a  ->  c  ->  c)  ->  c  ->  b  ->  FiniteMap b a  ->  c
foldFM_LE k z fr EmptyFM = foldFM_LE3 k z fr EmptyFM
foldFM_LE k z fr (Branch key elt vx fm_l fm_r) = foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r)

  
foldFM_LE0 k z fr key elt vx fm_l fm_r True = foldFM_LE k z fr fm_l

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

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

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

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

  
keysFM_LE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Haskell To QDPs


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

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

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

new_primPlusNat(Succ(vyy17300), Succ(vyy401000)) → new_primPlusNat(vyy17300, 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

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

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

new_primCmpNat(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat(vyy30000, vyy4000)

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

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



↳ 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

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

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

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
                                    ↳ DependencyGraphProof
                                  ↳ QDP

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

new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(ty_Maybe, bcf)) → new_ltEs(vyy3010, vyy410, bcf)
new_compare22(vyy300, vyy40, False, bgc, bgd) → new_ltEs3(vyy300, vyy40, bgc, bgd)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(app(app(ty_@3, ha), hb), hc), fd) → new_lt1(vyy3011, vyy411, ha, hb, hc)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(app(ty_@3, beb), bec), bed), bdh) → new_lt1(vyy950, vyy960, beb, bec, bed)
new_primCompAux0(vyy163, vyy164, EQ, app(app(app(ty_@3, dh), ea), eb)) → new_compare4(vyy163, vyy164, dh, ea, eb)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_[], ff), fc, fd) → new_lt0(vyy3010, vyy410, ff)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(app(ty_@2, bag), bah)) → new_ltEs3(vyy3012, vyy412, bag, bah)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_Either, bee), bef), bdh) → new_lt2(vyy950, vyy960, bee, bef)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(app(app(ty_@3, bfd), bfe), bff)) → new_ltEs1(vyy951, vyy961, bfd, bfe, bff)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(ty_Maybe, cd)) → new_compare3(vyy3000, vyy400, cd)
new_ltEs2(Left(vyy3010), Left(vyy410), app(app(ty_Either, bca), bcb), bbd) → new_ltEs2(vyy3010, vyy410, bca, bcb)
new_ltEs(Just(vyy3010), Just(vyy410), app(ty_[], bb)) → new_ltEs0(vyy3010, vyy410, bb)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_Either, db), dc)) → new_compare31(vyy3000, vyy400, db, dc)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_Maybe, fb), fc, fd) → new_lt(vyy3010, vyy410, fb)
new_compare1(vyy3000, vyy400, cd) → new_compare3(vyy3000, vyy400, cd)
new_ltEs2(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bbd) → new_ltEs(vyy3010, vyy410, bbc)
new_compare(:(vyy3010, vyy3011), :(vyy410, vyy411), cb) → new_primCompAux(vyy3010, vyy410, vyy3011, vyy411, cb)
new_compare31(vyy300, vyy40, bba, bbb) → new_compare21(vyy300, vyy40, new_esEs6(vyy300, vyy40, bba, bbb), bba, bbb)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(app(ty_@2, hf), hg), fd) → new_lt3(vyy3011, vyy411, hf, hg)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, cc) → new_primCompAux0(vyy3001, vyy401, new_compare0(vyy3000, vyy400, cc), app(ty_[], cc))
new_ltEs(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bc), bd), be)) → new_ltEs1(vyy3010, vyy410, bc, bd, be)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(ty_[], gh), fd) → new_lt0(vyy3011, vyy411, gh)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_@2, dd), de)) → new_compare32(vyy3000, vyy400, dd, de)
new_lt3(vyy300, vyy40, bgc, bgd) → new_compare22(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgc, bgd), bgc, bgd)
new_lt(vyy300, vyy40, h) → new_compare2(vyy300, vyy40, new_esEs4(vyy300, vyy40, h), h)
new_ltEs(Just(vyy3010), Just(vyy410), app(ty_Maybe, ba)) → new_ltEs(vyy3010, vyy410, ba)
new_ltEs2(Left(vyy3010), Left(vyy410), app(app(ty_@2, bcc), bcd), bbd) → new_ltEs3(vyy3010, vyy410, bcc, bcd)
new_ltEs2(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, bbf), bbg), bbh), bbd) → new_ltEs1(vyy3010, vyy410, bbf, bbg, bbh)
new_primCompAux0(vyy163, vyy164, EQ, app(ty_Maybe, df)) → new_compare1(vyy163, vyy164, df)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(ty_Maybe, bfb)) → new_ltEs(vyy951, vyy961, bfb)
new_compare4(vyy3000, vyy400, cf, cg, da) → new_compare30(vyy3000, vyy400, cf, cg, da)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(ty_@2, dd), de)) → new_compare32(vyy3000, vyy400, dd, de)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_@2, gd), ge), fc, fd) → new_lt3(vyy3010, vyy410, gd, ge)
new_compare5(vyy3000, vyy400, db, dc) → new_compare31(vyy3000, vyy400, db, dc)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(app(ty_@2, bga), bgb)) → new_ltEs3(vyy951, vyy961, bga, bgb)
new_compare3(vyy300, vyy40, h) → new_compare2(vyy300, vyy40, new_esEs4(vyy300, vyy40, h), h)
new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(app(app(ty_@3, bch), bda), bdb)) → new_ltEs1(vyy3010, vyy410, bch, bda, bdb)
new_compare30(vyy300, vyy40, eg, eh, fa) → new_compare20(vyy300, vyy40, new_esEs5(vyy300, vyy40, eg, eh, fa), eg, eh, fa)
new_compare32(vyy300, vyy40, bgc, bgd) → new_compare22(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgc, bgd), bgc, bgd)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(app(ty_@3, cf), cg), da)) → new_compare30(vyy3000, vyy400, cf, cg, da)
new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(app(ty_@2, bde), bdf)) → new_ltEs3(vyy3010, vyy410, bde, bdf)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(app(ty_Either, hd), he), fd) → new_lt2(vyy3011, vyy411, hd, he)
new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(app(ty_Either, bdc), bdd)) → new_ltEs2(vyy3010, vyy410, bdc, bdd)
new_compare21(vyy300, vyy40, False, bba, bbb) → new_ltEs2(vyy300, vyy40, bba, bbb)
new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(ty_[], bcg)) → new_ltEs0(vyy3010, vyy410, bcg)
new_ltEs(Just(vyy3010), Just(vyy410), app(app(ty_Either, bf), bg)) → new_ltEs2(vyy3010, vyy410, bf, bg)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(ty_[], ce)) → new_compare(vyy3000, vyy400, ce)
new_primCompAux0(vyy163, vyy164, EQ, app(ty_[], dg)) → new_compare(vyy163, vyy164, dg)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_Either, gb), gc), fc, fd) → new_lt2(vyy3010, vyy410, gb, gc)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(app(ty_@3, cf), cg), da)) → new_compare30(vyy3000, vyy400, cf, cg, da)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_@2, beg), beh), bdh) → new_lt3(vyy950, vyy960, beg, beh)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(ty_Maybe, gg), fd) → new_lt(vyy3011, vyy411, gg)
new_compare2(vyy300, vyy40, False, h) → new_ltEs(vyy300, vyy40, h)
new_lt2(vyy300, vyy40, bba, bbb) → new_compare21(vyy300, vyy40, new_esEs6(vyy300, vyy40, bba, bbb), bba, bbb)
new_ltEs(Just(vyy3010), Just(vyy410), app(app(ty_@2, bh), ca)) → new_ltEs3(vyy3010, vyy410, bh, ca)
new_primCompAux0(vyy163, vyy164, EQ, app(app(ty_Either, ec), ed)) → new_compare5(vyy163, vyy164, ec, ed)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), cc) → new_primCompAux0(vyy3001, vyy401, new_compare0(vyy3000, vyy400, cc), app(ty_[], cc))
new_compare6(vyy3000, vyy400, dd, de) → new_compare32(vyy3000, vyy400, dd, de)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(ty_Maybe, hh)) → new_ltEs(vyy3012, vyy412, hh)
new_ltEs0(:(vyy3010, vyy3011), :(vyy410, vyy411), cb) → new_primCompAux(vyy3010, vyy410, vyy3011, vyy411, cb)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs1(vyy3012, vyy412, bab, bac, bad)
new_lt1(vyy300, vyy40, eg, eh, fa) → new_compare20(vyy300, vyy40, new_esEs5(vyy300, vyy40, eg, eh, fa), eg, eh, fa)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(ty_Either, db), dc)) → new_compare31(vyy3000, vyy400, db, dc)
new_primCompAux0(vyy163, vyy164, EQ, app(app(ty_@2, ee), ef)) → new_compare6(vyy163, vyy164, ee, ef)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(ty_[], baa)) → new_ltEs0(vyy3012, vyy412, baa)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_Maybe, bdg), bdh) → new_lt(vyy950, vyy960, bdg)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_Maybe, cd)) → new_compare3(vyy3000, vyy400, cd)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(app(ty_Either, bfg), bfh)) → new_ltEs2(vyy951, vyy961, bfg, bfh)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_[], ce)) → new_compare(vyy3000, vyy400, ce)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(ty_[], bfc)) → new_ltEs0(vyy951, vyy961, bfc)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(app(ty_Either, bae), baf)) → new_ltEs2(vyy3012, vyy412, bae, baf)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, fg), fh), ga), fc, fd) → new_lt1(vyy3010, vyy410, fg, fh, ga)
new_compare20(vyy300, vyy40, False, eg, eh, fa) → new_ltEs1(vyy300, vyy40, eg, eh, fa)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_[], bea), bdh) → new_lt0(vyy950, vyy960, bea)
new_ltEs2(Left(vyy3010), Left(vyy410), app(ty_[], bbe), bbd) → new_ltEs0(vyy3010, vyy410, bbe)

The TRS R consists of the following rules:

new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, bge)) → new_esEs4(vyy3000, vyy400, bge)
new_lt12(vyy300, vyy40) → new_esEs8(new_primCmpFloat(vyy300, vyy40), LT)
new_esEs28(vyy3000, vyy400, app(ty_[], dbg)) → new_esEs13(vyy3000, vyy400, dbg)
new_esEs11(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare35(vyy300, vyy40) → new_compare27(vyy300, vyy40, new_esEs12(vyy300, vyy40))
new_lt15(vyy3010, vyy410, ty_Bool) → new_lt5(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_[], bcg)) → new_ltEs6(vyy3010, vyy410, bcg)
new_esEs18(vyy3002, vyy402, ty_Int) → new_esEs14(vyy3002, vyy402)
new_ltEs18(vyy3012, vyy412, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs16(vyy3012, vyy412, bab, bac, bad)
new_esEs13([], [], cc) → True
new_esEs20(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(ty_[], ce)) → new_compare8(vyy3000, vyy400, ce)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Char) → new_ltEs12(vyy3010, vyy410)
new_esEs4(Nothing, Just(vyy400), h) → False
new_esEs4(Just(vyy3000), Nothing, h) → False
new_ltEs5(EQ, GT) → True
new_ltEs19(vyy951, vyy961, ty_Float) → new_ltEs11(vyy951, vyy961)
new_lt15(vyy3010, vyy410, app(ty_[], ff)) → new_lt4(vyy3010, vyy410, ff)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Char) → new_ltEs12(vyy3010, vyy410)
new_ltEs6(vyy301, vyy41, cb) → new_not(new_esEs8(new_compare8(vyy301, vyy41, cb), GT))
new_esEs21(vyy3011, vyy411, ty_Int) → new_esEs14(vyy3011, vyy411)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Integer, bbd) → new_ltEs4(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, ty_Char) → new_lt19(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Double) → new_ltEs15(vyy3010, vyy410)
new_esEs21(vyy3011, vyy411, ty_@0) → new_esEs17(vyy3011, vyy411)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(vyy3000, vyy400, app(ty_[], cgd)) → new_esEs13(vyy3000, vyy400, cgd)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(app(ty_@2, ccc), ccd)) → new_esEs7(vyy3000, vyy400, ccc, ccd)
new_esEs12(True, True) → True
new_esEs20(vyy3000, vyy400, app(ty_Ratio, cge)) → new_esEs16(vyy3000, vyy400, cge)
new_esEs20(vyy3000, vyy400, app(ty_Maybe, cff)) → new_esEs4(vyy3000, vyy400, cff)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, cbd), bbb) → new_esEs16(vyy3000, vyy400, cbd)
new_esEs18(vyy3002, vyy402, ty_Double) → new_esEs9(vyy3002, vyy402)
new_ltEs13(Nothing, Just(vyy410), cgh) → True
new_lt20(vyy950, vyy960, ty_Integer) → new_lt18(vyy950, vyy960)
new_esEs23(vyy950, vyy960, ty_Double) → new_esEs9(vyy950, vyy960)
new_compare8([], [], cb) → EQ
new_ltEs11(vyy301, vyy41) → new_not(new_esEs8(new_compare14(vyy301, vyy41), GT))
new_lt9(vyy300, vyy40, bgc, bgd) → new_esEs8(new_compare34(vyy300, vyy40, bgc, bgd), LT)
new_compare14(vyy301, vyy41) → new_primCmpFloat(vyy301, vyy41)
new_lt20(vyy950, vyy960, app(ty_Maybe, bdg)) → new_lt13(vyy950, vyy960, bdg)
new_esEs23(vyy950, vyy960, ty_Bool) → new_esEs12(vyy950, vyy960)
new_esEs22(vyy3010, vyy410, ty_@0) → new_esEs17(vyy3010, vyy410)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_ltEs7(True, True) → True
new_lt19(vyy300, vyy40) → new_esEs8(new_primCmpChar(vyy300, vyy40), LT)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Bool) → new_ltEs7(vyy3010, vyy410)
new_esEs23(vyy950, vyy960, app(ty_Maybe, bdg)) → new_esEs4(vyy950, vyy960, bdg)
new_esEs23(vyy950, vyy960, ty_Char) → new_esEs15(vyy950, vyy960)
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Float) → new_esEs11(vyy3000, vyy400)
new_compare9(vyy301, vyy41) → new_primCmpChar(vyy301, vyy41)
new_lt20(vyy950, vyy960, ty_Double) → new_lt14(vyy950, vyy960)
new_esEs20(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs15(vyy3001, vyy401)
new_lt15(vyy3010, vyy410, ty_Float) → new_lt12(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, app(ty_Maybe, fb)) → new_lt13(vyy3010, vyy410, fb)
new_esEs13(:(vyy3000, vyy3001), :(vyy400, vyy401), cc) → new_asAs(new_esEs26(vyy3000, vyy400, cc), new_esEs13(vyy3001, vyy401, cc))
new_compare8(:(vyy3010, vyy3011), :(vyy410, vyy411), cb) → new_primCompAux1(vyy3010, vyy410, vyy3011, vyy411, cb)
new_compare25(vyy3000, vyy400, db, dc) → new_compare33(vyy3000, vyy400, db, dc)
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_Ratio, cha)) → new_ltEs14(vyy3010, vyy410, cha)
new_lt15(vyy3010, vyy410, ty_@0) → new_lt10(vyy3010, vyy410)
new_lt20(vyy950, vyy960, app(app(ty_@2, beg), beh)) → new_lt9(vyy950, vyy960, beg, beh)
new_ltEs5(EQ, LT) → False
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Char, bbd) → new_ltEs12(vyy3010, vyy410)
new_esEs23(vyy950, vyy960, ty_Integer) → new_esEs10(vyy950, vyy960)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, bbb) → new_esEs14(vyy3000, vyy400)
new_lt20(vyy950, vyy960, ty_Float) → new_lt12(vyy950, vyy960)
new_esEs21(vyy3011, vyy411, app(app(ty_Either, hd), he)) → new_esEs6(vyy3011, vyy411, hd, he)
new_esEs18(vyy3002, vyy402, ty_Float) → new_esEs11(vyy3002, vyy402)
new_lt15(vyy3010, vyy410, ty_Integer) → new_lt18(vyy3010, vyy410)
new_esEs19(vyy3001, vyy401, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs5(vyy3001, vyy401, cee, cef, ceg)
new_compare0(vyy3000, vyy400, app(app(ty_Either, db), dc)) → new_compare25(vyy3000, vyy400, db, dc)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, cd)) → new_esEs4(vyy3000, vyy400, cd)
new_lt7(vyy300, vyy40, bba, bbb) → new_esEs8(new_compare33(vyy300, vyy40, bba, bbb), LT)
new_compare211(vyy300, vyy40, False, h) → new_compare113(vyy300, vyy40, new_ltEs13(vyy300, vyy40, h), h)
new_esEs22(vyy3010, vyy410, ty_Integer) → new_esEs10(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs5(vyy3000, vyy400, dbb, dbc, dbd)
new_esEs18(vyy3002, vyy402, ty_Integer) → new_esEs10(vyy3002, vyy402)
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Int) → new_compare11(new_sr(vyy3010, vyy411), new_sr(vyy410, vyy3011))
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, bbb) → new_esEs11(vyy3000, vyy400)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(ty_@2, bde), bdf)) → new_ltEs17(vyy3010, vyy410, bde, bdf)
new_esEs17(@0, @0) → True
new_ltEs7(True, False) → False
new_pePe(False, vyy139) → vyy139
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Double) → new_ltEs15(vyy3010, vyy410)
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_esEs18(vyy3002, vyy402, app(app(ty_@2, cdf), cdg)) → new_esEs7(vyy3002, vyy402, cdf, cdg)
new_lt18(Integer(vyy3000), Integer(vyy400)) → new_esEs8(new_primCmpInt(vyy3000, vyy400), LT)
new_ltEs7(False, True) → True
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Int) → new_ltEs9(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(ty_@2, bcc), bcd), bbd) → new_ltEs17(vyy3010, vyy410, bcc, bcd)
new_lt16(vyy3011, vyy411, ty_Bool) → new_lt5(vyy3011, vyy411)
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs22(vyy3010, vyy410, ty_Ordering) → new_esEs8(vyy3010, vyy410)
new_esEs18(vyy3002, vyy402, ty_Bool) → new_esEs12(vyy3002, vyy402)
new_compare8(:(vyy3010, vyy3011), [], cb) → GT
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dbh)) → new_esEs16(vyy3000, vyy400, dbh)
new_lt4(:(vyy3000, vyy3001), :(vyy400, vyy401), cc) → new_esEs8(new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, cc), LT)
new_lt15(vyy3010, vyy410, app(app(ty_Either, gb), gc)) → new_lt7(vyy3010, vyy410, gb, gc)
new_lt20(vyy950, vyy960, app(app(ty_Either, bee), bef)) → new_lt7(vyy950, vyy960, bee, bef)
new_esEs18(vyy3002, vyy402, app(app(ty_Either, ceb), cec)) → new_esEs6(vyy3002, vyy402, ceb, cec)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Int, bbd) → new_ltEs9(vyy3010, vyy410)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Int) → new_esEs14(vyy3000, vyy400)
new_compare113(vyy300, vyy40, True, h) → LT
new_ltEs13(Nothing, Nothing, cgh) → True
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Integer) → new_ltEs4(vyy3010, vyy410)
new_compare16(vyy3000, vyy400, cd) → new_compare36(vyy3000, vyy400, cd)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bbd) → new_ltEs13(vyy3010, vyy410, bbc)
new_lt10(@0, @0) → new_esEs8(EQ, LT)
new_esEs8(LT, LT) → True
new_esEs6(Left(vyy3000), Right(vyy400), bba, bbb) → False
new_esEs6(Right(vyy3000), Left(vyy400), bba, bbb) → False
new_esEs19(vyy3001, vyy401, app(ty_Maybe, ced)) → new_esEs4(vyy3001, vyy401, ced)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_@0) → new_ltEs10(vyy3010, vyy410)
new_lt20(vyy950, vyy960, ty_Char) → new_lt19(vyy950, vyy960)
new_compare29(vyy3000, vyy400, vyy3001, vyy401) → new_primCmpInt(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs18(vyy3012, vyy412, ty_Integer) → new_ltEs4(vyy3012, vyy412)
new_esEs19(vyy3001, vyy401, ty_Bool) → new_esEs12(vyy3001, vyy401)
new_esEs18(vyy3002, vyy402, app(ty_[], cdh)) → new_esEs13(vyy3002, vyy402, cdh)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs11(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, EQ, app(ty_[], dg)) → new_compare8(vyy163, vyy164, dg)
new_esEs23(vyy950, vyy960, ty_Int) → new_esEs14(vyy950, vyy960)
new_esEs18(vyy3002, vyy402, app(ty_Ratio, cea)) → new_esEs16(vyy3002, vyy402, cea)
new_pePe(True, vyy139) → True
new_primEqNat0(Zero, Zero) → True
new_esEs23(vyy950, vyy960, app(app(ty_Either, bee), bef)) → new_esEs6(vyy950, vyy960, bee, bef)
new_compare111(vyy300, vyy40, False, bgc, bgd) → GT
new_ltEs19(vyy951, vyy961, app(app(ty_Either, bfg), bfh)) → new_ltEs8(vyy951, vyy961, bfg, bfh)
new_primCompAux00(vyy163, vyy164, EQ, ty_@0) → new_compare12(vyy163, vyy164)
new_esEs22(vyy3010, vyy410, app(app(ty_@2, gd), ge)) → new_esEs7(vyy3010, vyy410, gd, ge)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(app(ty_Either, ccg), cch)) → new_esEs6(vyy3000, vyy400, ccg, cch)
new_esEs15(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs20(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, EQ, ty_Ordering) → new_compare13(vyy163, vyy164)
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dca), dcb)) → new_esEs6(vyy3000, vyy400, dca, dcb)
new_esEs18(vyy3002, vyy402, app(app(app(ty_@3, cdc), cdd), cde)) → new_esEs5(vyy3002, vyy402, cdc, cdd, cde)
new_esEs22(vyy3010, vyy410, ty_Double) → new_esEs9(vyy3010, vyy410)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, bbb) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs8(GT, GT) → True
new_compare39(vyy300, vyy40, eg, eh, fa) → new_compare210(vyy300, vyy40, new_esEs5(vyy300, vyy40, eg, eh, fa), eg, eh, fa)
new_compare113(vyy300, vyy40, False, h) → GT
new_primPlusNat0(Succ(vyy1730), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1730, vyy40100)))
new_ltEs15(vyy301, vyy41) → new_not(new_esEs8(new_compare18(vyy301, vyy41), GT))
new_compare0(vyy3000, vyy400, ty_@0) → new_compare12(vyy3000, vyy400)
new_lt16(vyy3011, vyy411, ty_Int) → new_lt17(vyy3011, vyy411)
new_esEs12(False, False) → True
new_ltEs5(LT, LT) → True
new_ltEs19(vyy951, vyy961, app(ty_Ratio, chf)) → new_ltEs14(vyy951, vyy961, chf)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs10(vyy301, vyy41) → new_not(new_esEs8(new_compare12(vyy301, vyy41), GT))
new_compare211(vyy300, vyy40, True, h) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, bbf), bbg), bbh), bbd) → new_ltEs16(vyy3010, vyy410, bbf, bbg, bbh)
new_ltEs19(vyy951, vyy961, app(app(ty_@2, bga), bgb)) → new_ltEs17(vyy951, vyy961, bga, bgb)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Bool) → new_ltEs7(vyy3010, vyy410)
new_esEs20(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs23(vyy950, vyy960, ty_Ordering) → new_esEs8(vyy950, vyy960)
new_esEs26(vyy3000, vyy400, app(ty_[], ce)) → new_esEs13(vyy3000, vyy400, ce)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy17300), Zero) → Succ(vyy17300)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(app(app(ty_@3, cf), cg), da)) → new_compare19(vyy3000, vyy400, cf, cg, da)
new_esEs21(vyy3011, vyy411, ty_Char) → new_esEs15(vyy3011, vyy411)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Float) → new_ltEs11(vyy3010, vyy410)
new_lt13(vyy300, vyy40, h) → new_esEs8(new_compare36(vyy300, vyy40, h), LT)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dba)) → new_esEs4(vyy3000, vyy400, dba)
new_lt15(vyy3010, vyy410, app(app(ty_@2, gd), ge)) → new_lt9(vyy3010, vyy410, gd, ge)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primCompAux00(vyy163, vyy164, EQ, ty_Float) → new_compare14(vyy163, vyy164)
new_esEs21(vyy3011, vyy411, app(app(ty_@2, hf), hg)) → new_esEs7(vyy3011, vyy411, hf, hg)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_ltEs19(vyy951, vyy961, ty_Integer) → new_ltEs4(vyy951, vyy961)
new_compare19(vyy3000, vyy400, cf, cg, da) → new_compare39(vyy3000, vyy400, cf, cg, da)
new_ltEs19(vyy951, vyy961, ty_Char) → new_ltEs12(vyy951, vyy961)
new_esEs8(EQ, EQ) → True
new_lt20(vyy950, vyy960, ty_@0) → new_lt10(vyy950, vyy960)
new_lt15(vyy3010, vyy410, app(app(app(ty_@3, fg), fh), ga)) → new_lt11(vyy3010, vyy410, fg, fh, ga)
new_lt20(vyy950, vyy960, ty_Ordering) → new_lt8(vyy950, vyy960)
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(ty_@2, bh), ca)) → new_ltEs17(vyy3010, vyy410, bh, ca)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_@0) → new_ltEs10(vyy3010, vyy410)
new_esEs20(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs22(vyy3010, vyy410, app(app(app(ty_@3, fg), fh), ga)) → new_esEs5(vyy3010, vyy410, fg, fh, ga)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_lt14(vyy300, vyy40) → new_esEs8(new_primCmpDouble(vyy300, vyy40), LT)
new_compare23(vyy300, vyy40, False, bba, bbb) → new_compare114(vyy300, vyy40, new_ltEs8(vyy300, vyy40, bba, bbb), bba, bbb)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dbe), dbf)) → new_esEs7(vyy3000, vyy400, dbe, dbf)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_esEs22(vyy3010, vyy410, app(ty_Maybe, fb)) → new_esEs4(vyy3010, vyy410, fb)
new_ltEs5(EQ, EQ) → True
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, bhe), bhf)) → new_esEs6(vyy3000, vyy400, bhe, bhf)
new_ltEs18(vyy3012, vyy412, ty_@0) → new_ltEs10(vyy3012, vyy412)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, caf), cag), cah), bbb) → new_esEs5(vyy3000, vyy400, caf, cag, cah)
new_esEs19(vyy3001, vyy401, app(app(ty_Either, cfd), cfe)) → new_esEs6(vyy3001, vyy401, cfd, cfe)
new_esEs7(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bgc, bgd) → new_asAs(new_esEs28(vyy3000, vyy400, bgc), new_esEs27(vyy3001, vyy401, bgd))
new_lt16(vyy3011, vyy411, app(ty_Ratio, chc)) → new_lt6(vyy3011, vyy411, chc)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(ty_Maybe, cbg)) → new_esEs4(vyy3000, vyy400, cbg)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Int) → new_ltEs9(vyy3010, vyy410)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_Maybe, bcf)) → new_ltEs13(vyy3010, vyy410, bcf)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs5(vyy3000, vyy400, bgf, bgg, bgh)
new_lt16(vyy3011, vyy411, ty_Double) → new_lt14(vyy3011, vyy411)
new_esEs22(vyy3010, vyy410, ty_Bool) → new_esEs12(vyy3010, vyy410)
new_lt5(vyy300, vyy40) → new_esEs8(new_compare35(vyy300, vyy40), LT)
new_lt16(vyy3011, vyy411, ty_Float) → new_lt12(vyy3011, vyy411)
new_lt15(vyy3010, vyy410, app(ty_Ratio, chb)) → new_lt6(vyy3010, vyy410, chb)
new_compare114(vyy300, vyy40, True, bba, bbb) → LT
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bc), bd), be)) → new_ltEs16(vyy3010, vyy410, bc, bd, be)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Integer) → new_ltEs4(vyy3010, vyy410)
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, chh), daa), dab)) → new_esEs5(vyy3001, vyy401, chh, daa, dab)
new_esEs22(vyy3010, vyy410, ty_Char) → new_esEs15(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_lt20(vyy950, vyy960, ty_Int) → new_lt17(vyy950, vyy960)
new_ltEs18(vyy3012, vyy412, ty_Float) → new_ltEs11(vyy3012, vyy412)
new_ltEs5(GT, LT) → False
new_esEs23(vyy950, vyy960, ty_@0) → new_esEs17(vyy950, vyy960)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, bbb) → new_esEs17(vyy3000, vyy400)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, bbb) → new_esEs12(vyy3000, vyy400)
new_lt20(vyy950, vyy960, ty_Bool) → new_lt5(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(ty_Ratio, che)) → new_lt6(vyy950, vyy960, che)
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Integer) → new_compare7(new_sr0(vyy3010, vyy411), new_sr0(vyy410, vyy3011))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_lt4(:(vyy3000, vyy3001), [], cc) → new_esEs8(GT, LT)
new_compare210(vyy300, vyy40, True, eg, eh, fa) → EQ
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs9(vyy3001, vyy401)
new_compare28(vyy300, vyy40, False, bgc, bgd) → new_compare111(vyy300, vyy40, new_ltEs17(vyy300, vyy40, bgc, bgd), bgc, bgd)
new_compare0(vyy3000, vyy400, ty_Char) → new_compare9(vyy3000, vyy400)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Bool, bbd) → new_ltEs7(vyy3010, vyy410)
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_primPlusNat1(Succ(vyy17300), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy17300, vyy401000)))
new_compare28(vyy300, vyy40, True, bgc, bgd) → EQ
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_compare33(vyy300, vyy40, bba, bbb) → new_compare23(vyy300, vyy40, new_esEs6(vyy300, vyy40, bba, bbb), bba, bbb)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_Ratio, cac)) → new_ltEs14(vyy3010, vyy410, cac)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_lt15(vyy3010, vyy410, ty_Double) → new_lt14(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Float) → new_ltEs11(vyy3010, vyy410)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, bhg)) → new_esEs16(vyy3000, vyy400, bhg)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, cae), bbb) → new_esEs4(vyy3000, vyy400, cae)
new_esEs21(vyy3011, vyy411, app(ty_[], gh)) → new_esEs13(vyy3011, vyy411, gh)
new_compare0(vyy3000, vyy400, ty_Bool) → new_compare15(vyy3000, vyy400)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_ltEs18(vyy3012, vyy412, ty_Int) → new_ltEs9(vyy3012, vyy412)
new_compare24(vyy300, vyy40, True) → EQ
new_esEs27(vyy3001, vyy401, app(app(ty_@2, dac), dad)) → new_esEs7(vyy3001, vyy401, dac, dad)
new_lt16(vyy3011, vyy411, app(app(ty_@2, hf), hg)) → new_lt9(vyy3011, vyy411, hf, hg)
new_ltEs16(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, fd) → new_pePe(new_lt15(vyy3010, vyy410, gf), new_asAs(new_esEs22(vyy3010, vyy410, gf), new_pePe(new_lt16(vyy3011, vyy411, fc), new_asAs(new_esEs21(vyy3011, vyy411, fc), new_ltEs18(vyy3012, vyy412, fd)))))
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs19(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_lt6(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cad) → new_esEs8(new_compare38(vyy3000, vyy401, vyy400, vyy3001, cad), LT)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, app(ty_Ratio, daf)) → new_esEs16(vyy3001, vyy401, daf)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, cba), cbb), bbb) → new_esEs7(vyy3000, vyy400, cba, cbb)
new_esEs23(vyy950, vyy960, ty_Float) → new_esEs11(vyy950, vyy960)
new_compare114(vyy300, vyy40, False, bba, bbb) → GT
new_not(False) → True
new_compare12(@0, @0) → EQ
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(ty_Either, bdc), bdd)) → new_ltEs8(vyy3010, vyy410, bdc, bdd)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, cbe), cbf), bbb) → new_esEs6(vyy3000, vyy400, cbe, cbf)
new_ltEs18(vyy3012, vyy412, app(ty_Ratio, chd)) → new_ltEs14(vyy3012, vyy412, chd)
new_lt15(vyy3010, vyy410, ty_Int) → new_lt17(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(app(ty_Either, bae), baf)) → new_ltEs8(vyy3012, vyy412, bae, baf)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs22(vyy3010, vyy410, ty_Float) → new_esEs11(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(ty_Either, bf), bg)) → new_ltEs8(vyy3010, vyy410, bf, bg)
new_esEs19(vyy3001, vyy401, app(app(ty_@2, ceh), cfa)) → new_esEs7(vyy3001, vyy401, ceh, cfa)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_Ratio, cab), bbd) → new_ltEs14(vyy3010, vyy410, cab)
new_primCompAux00(vyy163, vyy164, EQ, app(app(app(ty_@3, dh), ea), eb)) → new_compare19(vyy163, vyy164, dh, ea, eb)
new_lt11(vyy300, vyy40, eg, eh, fa) → new_esEs8(new_compare39(vyy300, vyy40, eg, eh, fa), LT)
new_esEs20(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(app(ty_@3, bch), bda), bdb)) → new_ltEs16(vyy3010, vyy410, bch, bda, bdb)
new_compare26(vyy3000, vyy400, dd, de) → new_compare34(vyy3000, vyy400, dd, de)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs18(vyy3002, vyy402, app(ty_Maybe, cdb)) → new_esEs4(vyy3002, vyy402, cdb)
new_lt4([], :(vyy400, vyy401), cc) → new_esEs8(LT, LT)
new_esEs27(vyy3001, vyy401, app(app(ty_Either, dag), dah)) → new_esEs6(vyy3001, vyy401, dag, dah)
new_esEs22(vyy3010, vyy410, app(ty_[], ff)) → new_esEs13(vyy3010, vyy410, ff)
new_lt16(vyy3011, vyy411, ty_Integer) → new_lt18(vyy3011, vyy411)
new_esEs20(vyy3000, vyy400, app(app(app(ty_@3, cfg), cfh), cga)) → new_esEs5(vyy3000, vyy400, cfg, cfh, cga)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_ltEs19(vyy951, vyy961, ty_Int) → new_ltEs9(vyy951, vyy961)
new_ltEs4(vyy301, vyy41) → new_not(new_esEs8(new_compare7(vyy301, vyy41), GT))
new_esEs21(vyy3011, vyy411, app(app(app(ty_@3, ha), hb), hc)) → new_esEs5(vyy3011, vyy411, ha, hb, hc)
new_compare0(vyy3000, vyy400, app(app(ty_@2, dd), de)) → new_compare26(vyy3000, vyy400, dd, de)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_compare24(vyy300, vyy40, False) → new_compare10(vyy300, vyy40, new_ltEs5(vyy300, vyy40))
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs5(LT, GT) → True
new_ltEs14(vyy301, vyy41, cda) → new_not(new_esEs8(new_compare17(vyy301, vyy41, cda), GT))
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare110(vyy300, vyy40, True) → LT
new_lt20(vyy950, vyy960, app(app(app(ty_@3, beb), bec), bed)) → new_lt11(vyy950, vyy960, beb, bec, bed)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(ty_Either, bca), bcb), bbd) → new_ltEs8(vyy3010, vyy410, bca, bcb)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, dd), de)) → new_esEs7(vyy3000, vyy400, dd, de)
new_compare110(vyy300, vyy40, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs21(vyy3011, vyy411, ty_Integer) → new_esEs10(vyy3011, vyy411)
new_esEs4(Nothing, Nothing, h) → True
new_esEs10(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, bhd)) → new_esEs16(vyy3000, vyy400, bhd)
new_lt16(vyy3011, vyy411, ty_@0) → new_lt10(vyy3011, vyy411)
new_esEs20(vyy3000, vyy400, app(app(ty_Either, cgf), cgg)) → new_esEs6(vyy3000, vyy400, cgf, cgg)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_@0, bbd) → new_ltEs10(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(app(ty_@2, bag), bah)) → new_ltEs17(vyy3012, vyy412, bag, bah)
new_esEs18(vyy3002, vyy402, ty_@0) → new_esEs17(vyy3002, vyy402)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Float, bbd) → new_ltEs11(vyy3010, vyy410)
new_lt16(vyy3011, vyy411, app(ty_[], gh)) → new_lt4(vyy3011, vyy411, gh)
new_esEs27(vyy3001, vyy401, app(ty_Maybe, chg)) → new_esEs4(vyy3001, vyy401, chg)
new_compare0(vyy3000, vyy400, app(ty_Ratio, bhg)) → new_compare17(vyy3000, vyy400, bhg)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], bhc)) → new_esEs13(vyy3000, vyy400, bhc)
new_ltEs19(vyy951, vyy961, ty_Bool) → new_ltEs7(vyy951, vyy961)
new_compare15(vyy3000, vyy400) → new_compare35(vyy3000, vyy400)
new_compare112(vyy300, vyy40, True, eg, eh, fa) → LT
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_compare23(vyy300, vyy40, True, bba, bbb) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, bbb) → new_esEs8(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs17(vyy3001, vyy401)
new_primCompAux00(vyy163, vyy164, EQ, ty_Char) → new_compare9(vyy163, vyy164)
new_compare0(vyy3000, vyy400, ty_Ordering) → new_compare13(vyy3000, vyy400)
new_esEs19(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, bbb) → new_esEs9(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_ltEs18(vyy3012, vyy412, app(ty_[], baa)) → new_ltEs6(vyy3012, vyy412, baa)
new_esEs21(vyy3011, vyy411, app(ty_Maybe, gg)) → new_esEs4(vyy3011, vyy411, gg)
new_esEs23(vyy950, vyy960, app(ty_Ratio, che)) → new_esEs16(vyy950, vyy960, che)
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_Maybe, ba)) → new_ltEs13(vyy3010, vyy410, ba)
new_esEs22(vyy3010, vyy410, app(ty_Ratio, chb)) → new_esEs16(vyy3010, vyy410, chb)
new_primCmpFloat(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs21(vyy3011, vyy411, ty_Double) → new_esEs9(vyy3011, vyy411)
new_ltEs13(Just(vyy3010), Nothing, cgh) → False
new_esEs19(vyy3001, vyy401, app(ty_Ratio, cfc)) → new_esEs16(vyy3001, vyy401, cfc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Char) → new_esEs15(vyy3000, vyy400)
new_lt16(vyy3011, vyy411, ty_Ordering) → new_lt8(vyy3011, vyy411)
new_ltEs12(vyy301, vyy41) → new_not(new_esEs8(new_compare9(vyy301, vyy41), GT))
new_compare8([], :(vyy410, vyy411), cb) → LT
new_esEs19(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(ty_[], cce)) → new_esEs13(vyy3000, vyy400, cce)
new_asAs(False, vyy158) → False
new_ltEs18(vyy3012, vyy412, ty_Double) → new_ltEs15(vyy3012, vyy412)
new_lt8(vyy300, vyy40) → new_esEs8(new_compare37(vyy300, vyy40), LT)
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, EQ, app(app(ty_Either, ec), ed)) → new_compare25(vyy163, vyy164, ec, ed)
new_lt16(vyy3011, vyy411, ty_Char) → new_lt19(vyy3011, vyy411)
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_esEs13(:(vyy3000, vyy3001), [], cc) → False
new_esEs13([], :(vyy400, vyy401), cc) → False
new_lt16(vyy3011, vyy411, app(app(app(ty_@3, ha), hb), hc)) → new_lt11(vyy3011, vyy411, ha, hb, hc)
new_primCompAux00(vyy163, vyy164, EQ, ty_Bool) → new_compare15(vyy163, vyy164)
new_ltEs18(vyy3012, vyy412, ty_Ordering) → new_ltEs5(vyy3012, vyy412)
new_esEs21(vyy3011, vyy411, ty_Ordering) → new_esEs8(vyy3011, vyy411)
new_compare38(Integer(vyy30000), Integer(vyy4010), vyy400, vyy3001, ty_Integer) → new_compare7(Integer(new_primMulInt(vyy30000, vyy4010)), new_sr0(vyy400, vyy3001))
new_ltEs5(LT, EQ) → True
new_primCompAux00(vyy163, vyy164, EQ, app(ty_Ratio, caa)) → new_compare17(vyy163, vyy164, caa)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(ty_Ratio, ccf)) → new_esEs16(vyy3000, vyy400, ccf)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, bbb) → new_esEs15(vyy3000, vyy400)
new_esEs23(vyy950, vyy960, app(app(ty_@2, beg), beh)) → new_esEs7(vyy950, vyy960, beg, beh)
new_ltEs19(vyy951, vyy961, ty_@0) → new_ltEs10(vyy951, vyy961)
new_compare0(vyy3000, vyy400, ty_Float) → new_compare14(vyy3000, vyy400)
new_lt20(vyy950, vyy960, app(ty_[], bea)) → new_lt4(vyy950, vyy960, bea)
new_lt16(vyy3011, vyy411, app(app(ty_Either, hd), he)) → new_lt7(vyy3011, vyy411, hd, he)
new_primCompAux00(vyy163, vyy164, EQ, app(ty_Maybe, df)) → new_compare16(vyy163, vyy164, df)
new_ltEs8(Right(vyy3010), Left(vyy410), bce, bbd) → False
new_compare34(vyy300, vyy40, bgc, bgd) → new_compare28(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgc, bgd), bgc, bgd)
new_esEs18(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_esEs19(vyy3001, vyy401, ty_Double) → new_esEs9(vyy3001, vyy401)
new_esEs18(vyy3002, vyy402, ty_Char) → new_esEs15(vyy3002, vyy402)
new_primCompAux00(vyy163, vyy164, LT, bhh) → LT
new_compare0(vyy3000, vyy400, app(ty_Maybe, cd)) → new_compare16(vyy3000, vyy400, cd)
new_primCompAux00(vyy163, vyy164, GT, bhh) → GT
new_ltEs18(vyy3012, vyy412, ty_Char) → new_ltEs12(vyy3012, vyy412)
new_esEs16(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cad) → new_asAs(new_esEs25(vyy3000, vyy400, cad), new_esEs24(vyy3001, vyy401, cad))
new_compare13(vyy3000, vyy400) → new_compare37(vyy3000, vyy400)
new_ltEs18(vyy3012, vyy412, app(ty_Maybe, hh)) → new_ltEs13(vyy3012, vyy412, hh)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Double, bbd) → new_ltEs15(vyy3010, vyy410)
new_compare112(vyy300, vyy40, False, eg, eh, fa) → GT
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_compare27(vyy300, vyy40, True) → EQ
new_esEs21(vyy3011, vyy411, app(ty_Ratio, chc)) → new_esEs16(vyy3011, vyy411, chc)
new_esEs12(True, False) → False
new_esEs12(False, True) → False
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Double) → new_esEs9(vyy3000, vyy400)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Ordering, bbd) → new_ltEs5(vyy3010, vyy410)
new_lt16(vyy3011, vyy411, app(ty_Maybe, gg)) → new_lt13(vyy3011, vyy411, gg)
new_compare0(vyy3000, vyy400, ty_Integer) → new_compare7(vyy3000, vyy400)
new_compare11(vyy301, vyy41) → new_primCmpInt(vyy301, vyy41)
new_compare0(vyy3000, vyy400, ty_Double) → new_compare18(vyy3000, vyy400)
new_esEs14(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs12(vyy3001, vyy401)
new_compare37(vyy300, vyy40) → new_compare24(vyy300, vyy40, new_esEs8(vyy300, vyy40))
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_@0) → new_esEs17(vyy3000, vyy400)
new_lt4([], [], cc) → new_esEs8(EQ, LT)
new_compare27(vyy300, vyy40, False) → new_compare110(vyy300, vyy40, new_ltEs7(vyy300, vyy40))
new_ltEs9(vyy301, vyy41) → new_not(new_esEs8(new_compare11(vyy301, vyy41), GT))
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_[], bb)) → new_ltEs6(vyy3010, vyy410, bb)
new_ltEs19(vyy951, vyy961, app(ty_Maybe, bfb)) → new_ltEs13(vyy951, vyy961, bfb)
new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, cc) → new_primCompAux00(vyy3001, vyy401, new_compare0(vyy3000, vyy400, cc), app(ty_[], cc))
new_esEs9(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs19(vyy3001, vyy401, ty_Char) → new_esEs15(vyy3001, vyy401)
new_esEs20(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_compare7(Integer(vyy3010), Integer(vyy410)) → new_primCmpInt(vyy3010, vyy410)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], cbc), bbb) → new_esEs13(vyy3000, vyy400, cbc)
new_esEs22(vyy3010, vyy410, app(app(ty_Either, gb), gc)) → new_esEs6(vyy3010, vyy410, gb, gc)
new_ltEs19(vyy951, vyy961, app(ty_[], bfc)) → new_ltEs6(vyy951, vyy961, bfc)
new_ltEs19(vyy951, vyy961, app(app(app(ty_@3, bfd), bfe), bff)) → new_ltEs16(vyy951, vyy961, bfd, bfe, bff)
new_compare36(vyy300, vyy40, h) → new_compare211(vyy300, vyy40, new_esEs4(vyy300, vyy40, h), h)
new_compare210(vyy300, vyy40, False, eg, eh, fa) → new_compare112(vyy300, vyy40, new_ltEs16(vyy300, vyy40, eg, eh, fa), eg, eh, fa)
new_ltEs7(False, False) → True
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, bha), bhb)) → new_esEs7(vyy3000, vyy400, bha, bhb)
new_lt15(vyy3010, vyy410, ty_Ordering) → new_lt8(vyy3010, vyy410)
new_primCmpDouble(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_esEs21(vyy3011, vyy411, ty_Float) → new_esEs11(vyy3011, vyy411)
new_ltEs19(vyy951, vyy961, ty_Double) → new_ltEs15(vyy951, vyy961)
new_esEs22(vyy3010, vyy410, ty_Int) → new_esEs14(vyy3010, vyy410)
new_primCompAux00(vyy163, vyy164, EQ, ty_Int) → new_compare11(vyy163, vyy164)
new_esEs20(vyy3000, vyy400, app(app(ty_@2, cgb), cgc)) → new_esEs7(vyy3000, vyy400, cgb, cgc)
new_ltEs19(vyy951, vyy961, ty_Ordering) → new_ltEs5(vyy951, vyy961)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, db), dc)) → new_esEs6(vyy3000, vyy400, db, dc)
new_primPlusNat1(Zero, Zero) → Zero
new_compare111(vyy300, vyy40, True, bgc, bgd) → LT
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), eg, eh, fa) → new_asAs(new_esEs20(vyy3000, vyy400, eg), new_asAs(new_esEs19(vyy3001, vyy401, eh), new_esEs18(vyy3002, vyy402, fa)))
new_esEs19(vyy3001, vyy401, ty_@0) → new_esEs17(vyy3001, vyy401)
new_asAs(True, vyy158) → vyy158
new_primCmpChar(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, cf), cg), da)) → new_esEs5(vyy3000, vyy400, cf, cg, da)
new_esEs27(vyy3001, vyy401, app(ty_[], dae)) → new_esEs13(vyy3001, vyy401, dae)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Ordering) → new_ltEs5(vyy3010, vyy410)
new_ltEs5(GT, GT) → True
new_primCompAux00(vyy163, vyy164, EQ, ty_Integer) → new_compare7(vyy163, vyy164)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_[], bbe), bbd) → new_ltEs6(vyy3010, vyy410, bbe)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs14(vyy3000, vyy400)
new_compare38(vyy3000, vyy401, vyy400, vyy3001, ty_Int) → new_compare29(vyy3000, vyy401, vyy400, vyy3001)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs15(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, EQ, app(app(ty_@2, ee), ef)) → new_compare26(vyy163, vyy164, ee, ef)
new_ltEs18(vyy3012, vyy412, ty_Bool) → new_ltEs7(vyy3012, vyy412)
new_ltEs17(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, bdh) → new_pePe(new_lt20(vyy950, vyy960, bfa), new_asAs(new_esEs23(vyy950, vyy960, bfa), new_ltEs19(vyy951, vyy961, bdh)))
new_esEs23(vyy950, vyy960, app(app(app(ty_@3, beb), bec), bed)) → new_esEs5(vyy950, vyy960, beb, bec, bed)
new_esEs19(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs8(Left(vyy3010), Right(vyy410), bce, bbd) → True
new_compare18(vyy301, vyy41) → new_primCmpDouble(vyy301, vyy41)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs9(vyy3000, vyy400)
new_compare10(vyy300, vyy40, True) → LT
new_primCompAux00(vyy163, vyy164, EQ, ty_Double) → new_compare18(vyy163, vyy164)
new_lt17(vyy300, vyy40) → new_esEs8(new_primCmpInt(vyy300, vyy40), LT)
new_esEs19(vyy3001, vyy401, app(ty_[], cfb)) → new_esEs13(vyy3001, vyy401, cfb)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs21(vyy3011, vyy411, ty_Bool) → new_esEs12(vyy3011, vyy411)
new_compare10(vyy300, vyy40, False) → GT
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Ordering) → new_ltEs5(vyy3010, vyy410)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs5(vyy3000, vyy400, cbh, cca, ccb)
new_compare0(vyy3000, vyy400, ty_Int) → new_compare11(vyy3000, vyy400)
new_ltEs5(GT, EQ) → False
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs23(vyy950, vyy960, app(ty_[], bea)) → new_esEs13(vyy950, vyy960, bea)
new_not(True) → False

The set Q consists of the following terms:

new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_ltEs18(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Float)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt19(x0, x1)
new_asAs(True, x0)
new_esEs26(x0, x1, ty_Ordering)
new_lt14(x0, x1)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs13(:(x0, x1), [], x2)
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Nothing, Just(x0), x1)
new_compare34(x0, x1, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs18(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_compare7(Integer(x0), Integer(x1))
new_lt16(x0, x1, ty_@0)
new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_compare39(x0, x1, x2, x3, x4)
new_lt16(x0, x1, ty_Char)
new_esEs12(False, False)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Float)
new_compare26(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare8(:(x0, x1), :(x2, x3), x4)
new_esEs10(Integer(x0), Integer(x1))
new_primMulNat0(Zero, Succ(x0))
new_esEs13([], [], x0)
new_compare0(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1)
new_esEs27(x0, x1, ty_Integer)
new_ltEs13(Nothing, Just(x0), x1)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, ty_Float)
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_@0)
new_esEs8(GT, GT)
new_esEs24(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_lt16(x0, x1, ty_Int)
new_lt16(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs8(LT, LT)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs7(True, True)
new_esEs19(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_sr(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs22(x0, x1, ty_Double)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs7(True, False)
new_ltEs7(False, True)
new_esEs23(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs5(LT, EQ)
new_ltEs5(EQ, LT)
new_compare16(x0, x1, x2)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_asAs(False, x0)
new_primEqNat0(Zero, Zero)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Char)
new_lt15(x0, x1, ty_Ordering)
new_compare211(x0, x1, False, x2)
new_compare211(x0, x1, True, x2)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare33(x0, x1, x2, x3)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt15(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs15(Char(x0), Char(x1))
new_lt15(x0, x1, ty_Integer)
new_compare12(@0, @0)
new_compare18(x0, x1)
new_compare37(x0, x1)
new_esEs26(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_compare110(x0, x1, False)
new_primPlusNat0(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs19(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare0(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Integer)
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt16(x0, x1, ty_Bool)
new_compare0(x0, x1, ty_@0)
new_ltEs9(x0, x1)
new_esEs14(x0, x1)
new_primCompAux00(x0, x1, LT, x2)
new_lt15(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1)
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulNat0(Succ(x0), Succ(x1))
new_compare19(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_compare24(x0, x1, False)
new_ltEs18(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Double)
new_compare14(x0, x1)
new_lt15(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Int)
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Nothing, Nothing, x0)
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_@0)
new_compare0(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare36(x0, x1, x2)
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, ty_Char)
new_primCmpChar(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_Bool)
new_lt4([], :(x0, x1), x2)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare9(x0, x1)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_@0)
new_ltEs13(Nothing, Nothing, x0)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Zero, Zero)
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs13(Just(x0), Nothing, x1)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_primMulNat0(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt7(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare23(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs12(x0, x1)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_compare11(x0, x1)
new_esEs17(@0, @0)
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, ty_Int)
new_lt16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt16(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Ordering)
new_compare23(x0, x1, True, x2, x3)
new_esEs20(x0, x1, ty_Bool)
new_ltEs10(x0, x1)
new_compare8([], :(x0, x1), x2)
new_lt18(Integer(x0), Integer(x1))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Bool)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs12(True, True)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, x1, EQ, ty_Double)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_lt17(x0, x1)
new_compare27(x0, x1, False)
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Int)
new_compare113(x0, x1, False, x2)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, ty_Ordering)
new_compare28(x0, x1, False, x2, x3)
new_lt10(@0, @0)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCompAux00(x0, x1, EQ, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs13([], :(x0, x1), x2)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Int)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt4([], [], x0)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare210(x0, x1, True, x2, x3, x4)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, ty_Integer)
new_lt15(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt15(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare38(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, True, x2, x3)
new_primCompAux00(x0, x1, GT, x2)
new_lt8(x0, x1)
new_esEs19(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Char)
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_compare35(x0, x1)
new_pePe(True, x0)
new_ltEs4(x0, x1)
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_compare0(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_pePe(False, x0)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs22(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, x2, x3)
new_primEqNat0(Zero, Succ(x0))
new_esEs20(x0, x1, ty_Int)
new_compare10(x0, x1, False)
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_compare112(x0, x1, False, x2, x3, x4)
new_compare114(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(x0, x1, ty_Integer)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs21(x0, x1, ty_Ordering)
new_lt15(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_lt20(x0, x1, ty_Integer)
new_lt13(x0, x1, x2)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_Float)
new_lt6(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_compare0(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt16(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs27(x0, x1, ty_Double)
new_esEs18(x0, x1, app(ty_[], x2))
new_lt15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(GT, GT)
new_esEs12(True, False)
new_esEs12(False, True)
new_esEs22(x0, x1, ty_@0)
new_lt16(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare28(x0, x1, True, x2, x3)
new_esEs22(x0, x1, ty_Ordering)
new_lt15(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_Char)
new_compare15(x0, x1)
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_not(True)
new_compare25(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Float)
new_lt16(x0, x1, app(ty_[], x2))
new_lt4(:(x0, x1), [], x2)
new_esEs20(x0, x1, ty_Integer)
new_compare38(x0, x1, x2, x3, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_lt4(:(x0, x1), :(x2, x3), x4)
new_lt15(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, x1, EQ, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_compare114(x0, x1, True, x2, x3)
new_not(False)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare0(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare0(x0, x1, ty_Int)
new_lt16(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_ltEs5(EQ, EQ)
new_compare8([], [], x0)
new_esEs27(x0, x1, ty_Char)
new_primCompAux1(x0, x1, x2, x3, x4)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt15(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Bool)
new_lt16(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs21(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Int)
new_compare24(x0, x1, True)
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_ltEs14(x0, x1, x2)
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Char)
new_compare8(:(x0, x1), [], x2)
new_compare10(x0, x1, True)
new_compare210(x0, x1, False, x2, x3, x4)
new_compare112(x0, x1, True, x2, x3, x4)
new_ltEs6(x0, x1, x2)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare113(x0, x1, True, x2)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, x2, x3, x4)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_@0)
new_sr0(Integer(x0), Integer(x1))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_lt15(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_compare0(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs19(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, True)
new_compare110(x0, x1, True)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_esEs19(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Float)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare111(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Double)
new_ltEs5(LT, LT)
new_esEs26(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(False, False)
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Double)
new_compare13(x0, x1)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 8 less nodes.

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

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

new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(ty_Maybe, bcf)) → new_ltEs(vyy3010, vyy410, bcf)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(app(app(ty_@3, ha), hb), hc), fd) → new_lt1(vyy3011, vyy411, ha, hb, hc)
new_compare22(vyy300, vyy40, False, bgc, bgd) → new_ltEs3(vyy300, vyy40, bgc, bgd)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(app(ty_@3, beb), bec), bed), bdh) → new_lt1(vyy950, vyy960, beb, bec, bed)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_[], ff), fc, fd) → new_lt0(vyy3010, vyy410, ff)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(app(ty_@2, bag), bah)) → new_ltEs3(vyy3012, vyy412, bag, bah)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_Either, bee), bef), bdh) → new_lt2(vyy950, vyy960, bee, bef)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(app(app(ty_@3, bfd), bfe), bff)) → new_ltEs1(vyy951, vyy961, bfd, bfe, bff)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(ty_Maybe, cd)) → new_compare3(vyy3000, vyy400, cd)
new_ltEs2(Left(vyy3010), Left(vyy410), app(app(ty_Either, bca), bcb), bbd) → new_ltEs2(vyy3010, vyy410, bca, bcb)
new_ltEs(Just(vyy3010), Just(vyy410), app(ty_[], bb)) → new_ltEs0(vyy3010, vyy410, bb)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_Either, db), dc)) → new_compare31(vyy3000, vyy400, db, dc)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_Maybe, fb), fc, fd) → new_lt(vyy3010, vyy410, fb)
new_ltEs2(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bbd) → new_ltEs(vyy3010, vyy410, bbc)
new_compare(:(vyy3010, vyy3011), :(vyy410, vyy411), cb) → new_primCompAux(vyy3010, vyy410, vyy3011, vyy411, cb)
new_compare31(vyy300, vyy40, bba, bbb) → new_compare21(vyy300, vyy40, new_esEs6(vyy300, vyy40, bba, bbb), bba, bbb)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(app(ty_@2, hf), hg), fd) → new_lt3(vyy3011, vyy411, hf, hg)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, cc) → new_primCompAux0(vyy3001, vyy401, new_compare0(vyy3000, vyy400, cc), app(ty_[], cc))
new_ltEs(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bc), bd), be)) → new_ltEs1(vyy3010, vyy410, bc, bd, be)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(ty_[], gh), fd) → new_lt0(vyy3011, vyy411, gh)
new_lt3(vyy300, vyy40, bgc, bgd) → new_compare22(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgc, bgd), bgc, bgd)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_@2, dd), de)) → new_compare32(vyy3000, vyy400, dd, de)
new_ltEs(Just(vyy3010), Just(vyy410), app(ty_Maybe, ba)) → new_ltEs(vyy3010, vyy410, ba)
new_lt(vyy300, vyy40, h) → new_compare2(vyy300, vyy40, new_esEs4(vyy300, vyy40, h), h)
new_ltEs2(Left(vyy3010), Left(vyy410), app(app(ty_@2, bcc), bcd), bbd) → new_ltEs3(vyy3010, vyy410, bcc, bcd)
new_ltEs2(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, bbf), bbg), bbh), bbd) → new_ltEs1(vyy3010, vyy410, bbf, bbg, bbh)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(ty_Maybe, bfb)) → new_ltEs(vyy951, vyy961, bfb)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(ty_@2, dd), de)) → new_compare32(vyy3000, vyy400, dd, de)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_@2, gd), ge), fc, fd) → new_lt3(vyy3010, vyy410, gd, ge)
new_compare3(vyy300, vyy40, h) → new_compare2(vyy300, vyy40, new_esEs4(vyy300, vyy40, h), h)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(app(ty_@2, bga), bgb)) → new_ltEs3(vyy951, vyy961, bga, bgb)
new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(app(app(ty_@3, bch), bda), bdb)) → new_ltEs1(vyy3010, vyy410, bch, bda, bdb)
new_compare30(vyy300, vyy40, eg, eh, fa) → new_compare20(vyy300, vyy40, new_esEs5(vyy300, vyy40, eg, eh, fa), eg, eh, fa)
new_compare32(vyy300, vyy40, bgc, bgd) → new_compare22(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgc, bgd), bgc, bgd)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(app(ty_@3, cf), cg), da)) → new_compare30(vyy3000, vyy400, cf, cg, da)
new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(app(ty_@2, bde), bdf)) → new_ltEs3(vyy3010, vyy410, bde, bdf)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(app(ty_Either, hd), he), fd) → new_lt2(vyy3011, vyy411, hd, he)
new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(app(ty_Either, bdc), bdd)) → new_ltEs2(vyy3010, vyy410, bdc, bdd)
new_compare21(vyy300, vyy40, False, bba, bbb) → new_ltEs2(vyy300, vyy40, bba, bbb)
new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(ty_[], bcg)) → new_ltEs0(vyy3010, vyy410, bcg)
new_ltEs(Just(vyy3010), Just(vyy410), app(app(ty_Either, bf), bg)) → new_ltEs2(vyy3010, vyy410, bf, bg)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(ty_[], ce)) → new_compare(vyy3000, vyy400, ce)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_Either, gb), gc), fc, fd) → new_lt2(vyy3010, vyy410, gb, gc)
new_primCompAux0(vyy163, vyy164, EQ, app(ty_[], dg)) → new_compare(vyy163, vyy164, dg)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(app(ty_@3, cf), cg), da)) → new_compare30(vyy3000, vyy400, cf, cg, da)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_@2, beg), beh), bdh) → new_lt3(vyy950, vyy960, beg, beh)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(ty_Maybe, gg), fd) → new_lt(vyy3011, vyy411, gg)
new_compare2(vyy300, vyy40, False, h) → new_ltEs(vyy300, vyy40, h)
new_lt2(vyy300, vyy40, bba, bbb) → new_compare21(vyy300, vyy40, new_esEs6(vyy300, vyy40, bba, bbb), bba, bbb)
new_ltEs(Just(vyy3010), Just(vyy410), app(app(ty_@2, bh), ca)) → new_ltEs3(vyy3010, vyy410, bh, ca)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), cc) → new_primCompAux0(vyy3001, vyy401, new_compare0(vyy3000, vyy400, cc), app(ty_[], cc))
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(ty_Maybe, hh)) → new_ltEs(vyy3012, vyy412, hh)
new_ltEs0(:(vyy3010, vyy3011), :(vyy410, vyy411), cb) → new_primCompAux(vyy3010, vyy410, vyy3011, vyy411, cb)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs1(vyy3012, vyy412, bab, bac, bad)
new_lt1(vyy300, vyy40, eg, eh, fa) → new_compare20(vyy300, vyy40, new_esEs5(vyy300, vyy40, eg, eh, fa), eg, eh, fa)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(ty_Either, db), dc)) → new_compare31(vyy3000, vyy400, db, dc)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(ty_[], baa)) → new_ltEs0(vyy3012, vyy412, baa)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_Maybe, bdg), bdh) → new_lt(vyy950, vyy960, bdg)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(app(ty_Either, bfg), bfh)) → new_ltEs2(vyy951, vyy961, bfg, bfh)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_Maybe, cd)) → new_compare3(vyy3000, vyy400, cd)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_[], ce)) → new_compare(vyy3000, vyy400, ce)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(ty_[], bfc)) → new_ltEs0(vyy951, vyy961, bfc)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(app(ty_Either, bae), baf)) → new_ltEs2(vyy3012, vyy412, bae, baf)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, fg), fh), ga), fc, fd) → new_lt1(vyy3010, vyy410, fg, fh, ga)
new_compare20(vyy300, vyy40, False, eg, eh, fa) → new_ltEs1(vyy300, vyy40, eg, eh, fa)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_[], bea), bdh) → new_lt0(vyy950, vyy960, bea)
new_ltEs2(Left(vyy3010), Left(vyy410), app(ty_[], bbe), bbd) → new_ltEs0(vyy3010, vyy410, bbe)

The TRS R consists of the following rules:

new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, bge)) → new_esEs4(vyy3000, vyy400, bge)
new_lt12(vyy300, vyy40) → new_esEs8(new_primCmpFloat(vyy300, vyy40), LT)
new_esEs28(vyy3000, vyy400, app(ty_[], dbg)) → new_esEs13(vyy3000, vyy400, dbg)
new_esEs11(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare35(vyy300, vyy40) → new_compare27(vyy300, vyy40, new_esEs12(vyy300, vyy40))
new_lt15(vyy3010, vyy410, ty_Bool) → new_lt5(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_[], bcg)) → new_ltEs6(vyy3010, vyy410, bcg)
new_esEs18(vyy3002, vyy402, ty_Int) → new_esEs14(vyy3002, vyy402)
new_ltEs18(vyy3012, vyy412, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs16(vyy3012, vyy412, bab, bac, bad)
new_esEs13([], [], cc) → True
new_esEs20(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(ty_[], ce)) → new_compare8(vyy3000, vyy400, ce)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Char) → new_ltEs12(vyy3010, vyy410)
new_esEs4(Nothing, Just(vyy400), h) → False
new_esEs4(Just(vyy3000), Nothing, h) → False
new_ltEs5(EQ, GT) → True
new_ltEs19(vyy951, vyy961, ty_Float) → new_ltEs11(vyy951, vyy961)
new_lt15(vyy3010, vyy410, app(ty_[], ff)) → new_lt4(vyy3010, vyy410, ff)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Char) → new_ltEs12(vyy3010, vyy410)
new_ltEs6(vyy301, vyy41, cb) → new_not(new_esEs8(new_compare8(vyy301, vyy41, cb), GT))
new_esEs21(vyy3011, vyy411, ty_Int) → new_esEs14(vyy3011, vyy411)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Integer, bbd) → new_ltEs4(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, ty_Char) → new_lt19(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Double) → new_ltEs15(vyy3010, vyy410)
new_esEs21(vyy3011, vyy411, ty_@0) → new_esEs17(vyy3011, vyy411)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(vyy3000, vyy400, app(ty_[], cgd)) → new_esEs13(vyy3000, vyy400, cgd)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(app(ty_@2, ccc), ccd)) → new_esEs7(vyy3000, vyy400, ccc, ccd)
new_esEs12(True, True) → True
new_esEs20(vyy3000, vyy400, app(ty_Ratio, cge)) → new_esEs16(vyy3000, vyy400, cge)
new_esEs20(vyy3000, vyy400, app(ty_Maybe, cff)) → new_esEs4(vyy3000, vyy400, cff)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, cbd), bbb) → new_esEs16(vyy3000, vyy400, cbd)
new_esEs18(vyy3002, vyy402, ty_Double) → new_esEs9(vyy3002, vyy402)
new_ltEs13(Nothing, Just(vyy410), cgh) → True
new_lt20(vyy950, vyy960, ty_Integer) → new_lt18(vyy950, vyy960)
new_esEs23(vyy950, vyy960, ty_Double) → new_esEs9(vyy950, vyy960)
new_compare8([], [], cb) → EQ
new_ltEs11(vyy301, vyy41) → new_not(new_esEs8(new_compare14(vyy301, vyy41), GT))
new_lt9(vyy300, vyy40, bgc, bgd) → new_esEs8(new_compare34(vyy300, vyy40, bgc, bgd), LT)
new_compare14(vyy301, vyy41) → new_primCmpFloat(vyy301, vyy41)
new_lt20(vyy950, vyy960, app(ty_Maybe, bdg)) → new_lt13(vyy950, vyy960, bdg)
new_esEs23(vyy950, vyy960, ty_Bool) → new_esEs12(vyy950, vyy960)
new_esEs22(vyy3010, vyy410, ty_@0) → new_esEs17(vyy3010, vyy410)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_ltEs7(True, True) → True
new_lt19(vyy300, vyy40) → new_esEs8(new_primCmpChar(vyy300, vyy40), LT)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Bool) → new_ltEs7(vyy3010, vyy410)
new_esEs23(vyy950, vyy960, app(ty_Maybe, bdg)) → new_esEs4(vyy950, vyy960, bdg)
new_esEs23(vyy950, vyy960, ty_Char) → new_esEs15(vyy950, vyy960)
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Float) → new_esEs11(vyy3000, vyy400)
new_compare9(vyy301, vyy41) → new_primCmpChar(vyy301, vyy41)
new_lt20(vyy950, vyy960, ty_Double) → new_lt14(vyy950, vyy960)
new_esEs20(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs15(vyy3001, vyy401)
new_lt15(vyy3010, vyy410, ty_Float) → new_lt12(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, app(ty_Maybe, fb)) → new_lt13(vyy3010, vyy410, fb)
new_esEs13(:(vyy3000, vyy3001), :(vyy400, vyy401), cc) → new_asAs(new_esEs26(vyy3000, vyy400, cc), new_esEs13(vyy3001, vyy401, cc))
new_compare8(:(vyy3010, vyy3011), :(vyy410, vyy411), cb) → new_primCompAux1(vyy3010, vyy410, vyy3011, vyy411, cb)
new_compare25(vyy3000, vyy400, db, dc) → new_compare33(vyy3000, vyy400, db, dc)
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_Ratio, cha)) → new_ltEs14(vyy3010, vyy410, cha)
new_lt15(vyy3010, vyy410, ty_@0) → new_lt10(vyy3010, vyy410)
new_lt20(vyy950, vyy960, app(app(ty_@2, beg), beh)) → new_lt9(vyy950, vyy960, beg, beh)
new_ltEs5(EQ, LT) → False
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Char, bbd) → new_ltEs12(vyy3010, vyy410)
new_esEs23(vyy950, vyy960, ty_Integer) → new_esEs10(vyy950, vyy960)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, bbb) → new_esEs14(vyy3000, vyy400)
new_lt20(vyy950, vyy960, ty_Float) → new_lt12(vyy950, vyy960)
new_esEs21(vyy3011, vyy411, app(app(ty_Either, hd), he)) → new_esEs6(vyy3011, vyy411, hd, he)
new_esEs18(vyy3002, vyy402, ty_Float) → new_esEs11(vyy3002, vyy402)
new_lt15(vyy3010, vyy410, ty_Integer) → new_lt18(vyy3010, vyy410)
new_esEs19(vyy3001, vyy401, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs5(vyy3001, vyy401, cee, cef, ceg)
new_compare0(vyy3000, vyy400, app(app(ty_Either, db), dc)) → new_compare25(vyy3000, vyy400, db, dc)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, cd)) → new_esEs4(vyy3000, vyy400, cd)
new_lt7(vyy300, vyy40, bba, bbb) → new_esEs8(new_compare33(vyy300, vyy40, bba, bbb), LT)
new_compare211(vyy300, vyy40, False, h) → new_compare113(vyy300, vyy40, new_ltEs13(vyy300, vyy40, h), h)
new_esEs22(vyy3010, vyy410, ty_Integer) → new_esEs10(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs5(vyy3000, vyy400, dbb, dbc, dbd)
new_esEs18(vyy3002, vyy402, ty_Integer) → new_esEs10(vyy3002, vyy402)
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Int) → new_compare11(new_sr(vyy3010, vyy411), new_sr(vyy410, vyy3011))
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, bbb) → new_esEs11(vyy3000, vyy400)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(ty_@2, bde), bdf)) → new_ltEs17(vyy3010, vyy410, bde, bdf)
new_esEs17(@0, @0) → True
new_ltEs7(True, False) → False
new_pePe(False, vyy139) → vyy139
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Double) → new_ltEs15(vyy3010, vyy410)
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_esEs18(vyy3002, vyy402, app(app(ty_@2, cdf), cdg)) → new_esEs7(vyy3002, vyy402, cdf, cdg)
new_lt18(Integer(vyy3000), Integer(vyy400)) → new_esEs8(new_primCmpInt(vyy3000, vyy400), LT)
new_ltEs7(False, True) → True
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Int) → new_ltEs9(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(ty_@2, bcc), bcd), bbd) → new_ltEs17(vyy3010, vyy410, bcc, bcd)
new_lt16(vyy3011, vyy411, ty_Bool) → new_lt5(vyy3011, vyy411)
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs22(vyy3010, vyy410, ty_Ordering) → new_esEs8(vyy3010, vyy410)
new_esEs18(vyy3002, vyy402, ty_Bool) → new_esEs12(vyy3002, vyy402)
new_compare8(:(vyy3010, vyy3011), [], cb) → GT
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dbh)) → new_esEs16(vyy3000, vyy400, dbh)
new_lt4(:(vyy3000, vyy3001), :(vyy400, vyy401), cc) → new_esEs8(new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, cc), LT)
new_lt15(vyy3010, vyy410, app(app(ty_Either, gb), gc)) → new_lt7(vyy3010, vyy410, gb, gc)
new_lt20(vyy950, vyy960, app(app(ty_Either, bee), bef)) → new_lt7(vyy950, vyy960, bee, bef)
new_esEs18(vyy3002, vyy402, app(app(ty_Either, ceb), cec)) → new_esEs6(vyy3002, vyy402, ceb, cec)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Int, bbd) → new_ltEs9(vyy3010, vyy410)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Int) → new_esEs14(vyy3000, vyy400)
new_compare113(vyy300, vyy40, True, h) → LT
new_ltEs13(Nothing, Nothing, cgh) → True
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Integer) → new_ltEs4(vyy3010, vyy410)
new_compare16(vyy3000, vyy400, cd) → new_compare36(vyy3000, vyy400, cd)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bbd) → new_ltEs13(vyy3010, vyy410, bbc)
new_lt10(@0, @0) → new_esEs8(EQ, LT)
new_esEs8(LT, LT) → True
new_esEs6(Left(vyy3000), Right(vyy400), bba, bbb) → False
new_esEs6(Right(vyy3000), Left(vyy400), bba, bbb) → False
new_esEs19(vyy3001, vyy401, app(ty_Maybe, ced)) → new_esEs4(vyy3001, vyy401, ced)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_@0) → new_ltEs10(vyy3010, vyy410)
new_lt20(vyy950, vyy960, ty_Char) → new_lt19(vyy950, vyy960)
new_compare29(vyy3000, vyy400, vyy3001, vyy401) → new_primCmpInt(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs18(vyy3012, vyy412, ty_Integer) → new_ltEs4(vyy3012, vyy412)
new_esEs19(vyy3001, vyy401, ty_Bool) → new_esEs12(vyy3001, vyy401)
new_esEs18(vyy3002, vyy402, app(ty_[], cdh)) → new_esEs13(vyy3002, vyy402, cdh)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs11(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, EQ, app(ty_[], dg)) → new_compare8(vyy163, vyy164, dg)
new_esEs23(vyy950, vyy960, ty_Int) → new_esEs14(vyy950, vyy960)
new_esEs18(vyy3002, vyy402, app(ty_Ratio, cea)) → new_esEs16(vyy3002, vyy402, cea)
new_pePe(True, vyy139) → True
new_primEqNat0(Zero, Zero) → True
new_esEs23(vyy950, vyy960, app(app(ty_Either, bee), bef)) → new_esEs6(vyy950, vyy960, bee, bef)
new_compare111(vyy300, vyy40, False, bgc, bgd) → GT
new_ltEs19(vyy951, vyy961, app(app(ty_Either, bfg), bfh)) → new_ltEs8(vyy951, vyy961, bfg, bfh)
new_primCompAux00(vyy163, vyy164, EQ, ty_@0) → new_compare12(vyy163, vyy164)
new_esEs22(vyy3010, vyy410, app(app(ty_@2, gd), ge)) → new_esEs7(vyy3010, vyy410, gd, ge)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(app(ty_Either, ccg), cch)) → new_esEs6(vyy3000, vyy400, ccg, cch)
new_esEs15(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs20(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, EQ, ty_Ordering) → new_compare13(vyy163, vyy164)
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dca), dcb)) → new_esEs6(vyy3000, vyy400, dca, dcb)
new_esEs18(vyy3002, vyy402, app(app(app(ty_@3, cdc), cdd), cde)) → new_esEs5(vyy3002, vyy402, cdc, cdd, cde)
new_esEs22(vyy3010, vyy410, ty_Double) → new_esEs9(vyy3010, vyy410)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, bbb) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs8(GT, GT) → True
new_compare39(vyy300, vyy40, eg, eh, fa) → new_compare210(vyy300, vyy40, new_esEs5(vyy300, vyy40, eg, eh, fa), eg, eh, fa)
new_compare113(vyy300, vyy40, False, h) → GT
new_primPlusNat0(Succ(vyy1730), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1730, vyy40100)))
new_ltEs15(vyy301, vyy41) → new_not(new_esEs8(new_compare18(vyy301, vyy41), GT))
new_compare0(vyy3000, vyy400, ty_@0) → new_compare12(vyy3000, vyy400)
new_lt16(vyy3011, vyy411, ty_Int) → new_lt17(vyy3011, vyy411)
new_esEs12(False, False) → True
new_ltEs5(LT, LT) → True
new_ltEs19(vyy951, vyy961, app(ty_Ratio, chf)) → new_ltEs14(vyy951, vyy961, chf)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs10(vyy301, vyy41) → new_not(new_esEs8(new_compare12(vyy301, vyy41), GT))
new_compare211(vyy300, vyy40, True, h) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, bbf), bbg), bbh), bbd) → new_ltEs16(vyy3010, vyy410, bbf, bbg, bbh)
new_ltEs19(vyy951, vyy961, app(app(ty_@2, bga), bgb)) → new_ltEs17(vyy951, vyy961, bga, bgb)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Bool) → new_ltEs7(vyy3010, vyy410)
new_esEs20(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs23(vyy950, vyy960, ty_Ordering) → new_esEs8(vyy950, vyy960)
new_esEs26(vyy3000, vyy400, app(ty_[], ce)) → new_esEs13(vyy3000, vyy400, ce)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy17300), Zero) → Succ(vyy17300)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(app(app(ty_@3, cf), cg), da)) → new_compare19(vyy3000, vyy400, cf, cg, da)
new_esEs21(vyy3011, vyy411, ty_Char) → new_esEs15(vyy3011, vyy411)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Float) → new_ltEs11(vyy3010, vyy410)
new_lt13(vyy300, vyy40, h) → new_esEs8(new_compare36(vyy300, vyy40, h), LT)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dba)) → new_esEs4(vyy3000, vyy400, dba)
new_lt15(vyy3010, vyy410, app(app(ty_@2, gd), ge)) → new_lt9(vyy3010, vyy410, gd, ge)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primCompAux00(vyy163, vyy164, EQ, ty_Float) → new_compare14(vyy163, vyy164)
new_esEs21(vyy3011, vyy411, app(app(ty_@2, hf), hg)) → new_esEs7(vyy3011, vyy411, hf, hg)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_ltEs19(vyy951, vyy961, ty_Integer) → new_ltEs4(vyy951, vyy961)
new_compare19(vyy3000, vyy400, cf, cg, da) → new_compare39(vyy3000, vyy400, cf, cg, da)
new_ltEs19(vyy951, vyy961, ty_Char) → new_ltEs12(vyy951, vyy961)
new_esEs8(EQ, EQ) → True
new_lt20(vyy950, vyy960, ty_@0) → new_lt10(vyy950, vyy960)
new_lt15(vyy3010, vyy410, app(app(app(ty_@3, fg), fh), ga)) → new_lt11(vyy3010, vyy410, fg, fh, ga)
new_lt20(vyy950, vyy960, ty_Ordering) → new_lt8(vyy950, vyy960)
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(ty_@2, bh), ca)) → new_ltEs17(vyy3010, vyy410, bh, ca)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_@0) → new_ltEs10(vyy3010, vyy410)
new_esEs20(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs22(vyy3010, vyy410, app(app(app(ty_@3, fg), fh), ga)) → new_esEs5(vyy3010, vyy410, fg, fh, ga)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_lt14(vyy300, vyy40) → new_esEs8(new_primCmpDouble(vyy300, vyy40), LT)
new_compare23(vyy300, vyy40, False, bba, bbb) → new_compare114(vyy300, vyy40, new_ltEs8(vyy300, vyy40, bba, bbb), bba, bbb)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dbe), dbf)) → new_esEs7(vyy3000, vyy400, dbe, dbf)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_esEs22(vyy3010, vyy410, app(ty_Maybe, fb)) → new_esEs4(vyy3010, vyy410, fb)
new_ltEs5(EQ, EQ) → True
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, bhe), bhf)) → new_esEs6(vyy3000, vyy400, bhe, bhf)
new_ltEs18(vyy3012, vyy412, ty_@0) → new_ltEs10(vyy3012, vyy412)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, caf), cag), cah), bbb) → new_esEs5(vyy3000, vyy400, caf, cag, cah)
new_esEs19(vyy3001, vyy401, app(app(ty_Either, cfd), cfe)) → new_esEs6(vyy3001, vyy401, cfd, cfe)
new_esEs7(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bgc, bgd) → new_asAs(new_esEs28(vyy3000, vyy400, bgc), new_esEs27(vyy3001, vyy401, bgd))
new_lt16(vyy3011, vyy411, app(ty_Ratio, chc)) → new_lt6(vyy3011, vyy411, chc)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(ty_Maybe, cbg)) → new_esEs4(vyy3000, vyy400, cbg)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Int) → new_ltEs9(vyy3010, vyy410)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_Maybe, bcf)) → new_ltEs13(vyy3010, vyy410, bcf)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs5(vyy3000, vyy400, bgf, bgg, bgh)
new_lt16(vyy3011, vyy411, ty_Double) → new_lt14(vyy3011, vyy411)
new_esEs22(vyy3010, vyy410, ty_Bool) → new_esEs12(vyy3010, vyy410)
new_lt5(vyy300, vyy40) → new_esEs8(new_compare35(vyy300, vyy40), LT)
new_lt16(vyy3011, vyy411, ty_Float) → new_lt12(vyy3011, vyy411)
new_lt15(vyy3010, vyy410, app(ty_Ratio, chb)) → new_lt6(vyy3010, vyy410, chb)
new_compare114(vyy300, vyy40, True, bba, bbb) → LT
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bc), bd), be)) → new_ltEs16(vyy3010, vyy410, bc, bd, be)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Integer) → new_ltEs4(vyy3010, vyy410)
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, chh), daa), dab)) → new_esEs5(vyy3001, vyy401, chh, daa, dab)
new_esEs22(vyy3010, vyy410, ty_Char) → new_esEs15(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_lt20(vyy950, vyy960, ty_Int) → new_lt17(vyy950, vyy960)
new_ltEs18(vyy3012, vyy412, ty_Float) → new_ltEs11(vyy3012, vyy412)
new_ltEs5(GT, LT) → False
new_esEs23(vyy950, vyy960, ty_@0) → new_esEs17(vyy950, vyy960)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, bbb) → new_esEs17(vyy3000, vyy400)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, bbb) → new_esEs12(vyy3000, vyy400)
new_lt20(vyy950, vyy960, ty_Bool) → new_lt5(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(ty_Ratio, che)) → new_lt6(vyy950, vyy960, che)
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Integer) → new_compare7(new_sr0(vyy3010, vyy411), new_sr0(vyy410, vyy3011))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_lt4(:(vyy3000, vyy3001), [], cc) → new_esEs8(GT, LT)
new_compare210(vyy300, vyy40, True, eg, eh, fa) → EQ
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs9(vyy3001, vyy401)
new_compare28(vyy300, vyy40, False, bgc, bgd) → new_compare111(vyy300, vyy40, new_ltEs17(vyy300, vyy40, bgc, bgd), bgc, bgd)
new_compare0(vyy3000, vyy400, ty_Char) → new_compare9(vyy3000, vyy400)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Bool, bbd) → new_ltEs7(vyy3010, vyy410)
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_primPlusNat1(Succ(vyy17300), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy17300, vyy401000)))
new_compare28(vyy300, vyy40, True, bgc, bgd) → EQ
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_compare33(vyy300, vyy40, bba, bbb) → new_compare23(vyy300, vyy40, new_esEs6(vyy300, vyy40, bba, bbb), bba, bbb)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_Ratio, cac)) → new_ltEs14(vyy3010, vyy410, cac)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_lt15(vyy3010, vyy410, ty_Double) → new_lt14(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Float) → new_ltEs11(vyy3010, vyy410)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, bhg)) → new_esEs16(vyy3000, vyy400, bhg)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, cae), bbb) → new_esEs4(vyy3000, vyy400, cae)
new_esEs21(vyy3011, vyy411, app(ty_[], gh)) → new_esEs13(vyy3011, vyy411, gh)
new_compare0(vyy3000, vyy400, ty_Bool) → new_compare15(vyy3000, vyy400)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_ltEs18(vyy3012, vyy412, ty_Int) → new_ltEs9(vyy3012, vyy412)
new_compare24(vyy300, vyy40, True) → EQ
new_esEs27(vyy3001, vyy401, app(app(ty_@2, dac), dad)) → new_esEs7(vyy3001, vyy401, dac, dad)
new_lt16(vyy3011, vyy411, app(app(ty_@2, hf), hg)) → new_lt9(vyy3011, vyy411, hf, hg)
new_ltEs16(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, fd) → new_pePe(new_lt15(vyy3010, vyy410, gf), new_asAs(new_esEs22(vyy3010, vyy410, gf), new_pePe(new_lt16(vyy3011, vyy411, fc), new_asAs(new_esEs21(vyy3011, vyy411, fc), new_ltEs18(vyy3012, vyy412, fd)))))
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs19(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_lt6(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cad) → new_esEs8(new_compare38(vyy3000, vyy401, vyy400, vyy3001, cad), LT)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, app(ty_Ratio, daf)) → new_esEs16(vyy3001, vyy401, daf)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, cba), cbb), bbb) → new_esEs7(vyy3000, vyy400, cba, cbb)
new_esEs23(vyy950, vyy960, ty_Float) → new_esEs11(vyy950, vyy960)
new_compare114(vyy300, vyy40, False, bba, bbb) → GT
new_not(False) → True
new_compare12(@0, @0) → EQ
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(ty_Either, bdc), bdd)) → new_ltEs8(vyy3010, vyy410, bdc, bdd)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, cbe), cbf), bbb) → new_esEs6(vyy3000, vyy400, cbe, cbf)
new_ltEs18(vyy3012, vyy412, app(ty_Ratio, chd)) → new_ltEs14(vyy3012, vyy412, chd)
new_lt15(vyy3010, vyy410, ty_Int) → new_lt17(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(app(ty_Either, bae), baf)) → new_ltEs8(vyy3012, vyy412, bae, baf)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs22(vyy3010, vyy410, ty_Float) → new_esEs11(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(ty_Either, bf), bg)) → new_ltEs8(vyy3010, vyy410, bf, bg)
new_esEs19(vyy3001, vyy401, app(app(ty_@2, ceh), cfa)) → new_esEs7(vyy3001, vyy401, ceh, cfa)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_Ratio, cab), bbd) → new_ltEs14(vyy3010, vyy410, cab)
new_primCompAux00(vyy163, vyy164, EQ, app(app(app(ty_@3, dh), ea), eb)) → new_compare19(vyy163, vyy164, dh, ea, eb)
new_lt11(vyy300, vyy40, eg, eh, fa) → new_esEs8(new_compare39(vyy300, vyy40, eg, eh, fa), LT)
new_esEs20(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(app(ty_@3, bch), bda), bdb)) → new_ltEs16(vyy3010, vyy410, bch, bda, bdb)
new_compare26(vyy3000, vyy400, dd, de) → new_compare34(vyy3000, vyy400, dd, de)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs18(vyy3002, vyy402, app(ty_Maybe, cdb)) → new_esEs4(vyy3002, vyy402, cdb)
new_lt4([], :(vyy400, vyy401), cc) → new_esEs8(LT, LT)
new_esEs27(vyy3001, vyy401, app(app(ty_Either, dag), dah)) → new_esEs6(vyy3001, vyy401, dag, dah)
new_esEs22(vyy3010, vyy410, app(ty_[], ff)) → new_esEs13(vyy3010, vyy410, ff)
new_lt16(vyy3011, vyy411, ty_Integer) → new_lt18(vyy3011, vyy411)
new_esEs20(vyy3000, vyy400, app(app(app(ty_@3, cfg), cfh), cga)) → new_esEs5(vyy3000, vyy400, cfg, cfh, cga)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_ltEs19(vyy951, vyy961, ty_Int) → new_ltEs9(vyy951, vyy961)
new_ltEs4(vyy301, vyy41) → new_not(new_esEs8(new_compare7(vyy301, vyy41), GT))
new_esEs21(vyy3011, vyy411, app(app(app(ty_@3, ha), hb), hc)) → new_esEs5(vyy3011, vyy411, ha, hb, hc)
new_compare0(vyy3000, vyy400, app(app(ty_@2, dd), de)) → new_compare26(vyy3000, vyy400, dd, de)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_compare24(vyy300, vyy40, False) → new_compare10(vyy300, vyy40, new_ltEs5(vyy300, vyy40))
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs5(LT, GT) → True
new_ltEs14(vyy301, vyy41, cda) → new_not(new_esEs8(new_compare17(vyy301, vyy41, cda), GT))
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare110(vyy300, vyy40, True) → LT
new_lt20(vyy950, vyy960, app(app(app(ty_@3, beb), bec), bed)) → new_lt11(vyy950, vyy960, beb, bec, bed)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(ty_Either, bca), bcb), bbd) → new_ltEs8(vyy3010, vyy410, bca, bcb)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, dd), de)) → new_esEs7(vyy3000, vyy400, dd, de)
new_compare110(vyy300, vyy40, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs21(vyy3011, vyy411, ty_Integer) → new_esEs10(vyy3011, vyy411)
new_esEs4(Nothing, Nothing, h) → True
new_esEs10(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, bhd)) → new_esEs16(vyy3000, vyy400, bhd)
new_lt16(vyy3011, vyy411, ty_@0) → new_lt10(vyy3011, vyy411)
new_esEs20(vyy3000, vyy400, app(app(ty_Either, cgf), cgg)) → new_esEs6(vyy3000, vyy400, cgf, cgg)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_@0, bbd) → new_ltEs10(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(app(ty_@2, bag), bah)) → new_ltEs17(vyy3012, vyy412, bag, bah)
new_esEs18(vyy3002, vyy402, ty_@0) → new_esEs17(vyy3002, vyy402)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Float, bbd) → new_ltEs11(vyy3010, vyy410)
new_lt16(vyy3011, vyy411, app(ty_[], gh)) → new_lt4(vyy3011, vyy411, gh)
new_esEs27(vyy3001, vyy401, app(ty_Maybe, chg)) → new_esEs4(vyy3001, vyy401, chg)
new_compare0(vyy3000, vyy400, app(ty_Ratio, bhg)) → new_compare17(vyy3000, vyy400, bhg)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], bhc)) → new_esEs13(vyy3000, vyy400, bhc)
new_ltEs19(vyy951, vyy961, ty_Bool) → new_ltEs7(vyy951, vyy961)
new_compare15(vyy3000, vyy400) → new_compare35(vyy3000, vyy400)
new_compare112(vyy300, vyy40, True, eg, eh, fa) → LT
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_compare23(vyy300, vyy40, True, bba, bbb) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, bbb) → new_esEs8(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs17(vyy3001, vyy401)
new_primCompAux00(vyy163, vyy164, EQ, ty_Char) → new_compare9(vyy163, vyy164)
new_compare0(vyy3000, vyy400, ty_Ordering) → new_compare13(vyy3000, vyy400)
new_esEs19(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, bbb) → new_esEs9(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_ltEs18(vyy3012, vyy412, app(ty_[], baa)) → new_ltEs6(vyy3012, vyy412, baa)
new_esEs21(vyy3011, vyy411, app(ty_Maybe, gg)) → new_esEs4(vyy3011, vyy411, gg)
new_esEs23(vyy950, vyy960, app(ty_Ratio, che)) → new_esEs16(vyy950, vyy960, che)
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_Maybe, ba)) → new_ltEs13(vyy3010, vyy410, ba)
new_esEs22(vyy3010, vyy410, app(ty_Ratio, chb)) → new_esEs16(vyy3010, vyy410, chb)
new_primCmpFloat(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs21(vyy3011, vyy411, ty_Double) → new_esEs9(vyy3011, vyy411)
new_ltEs13(Just(vyy3010), Nothing, cgh) → False
new_esEs19(vyy3001, vyy401, app(ty_Ratio, cfc)) → new_esEs16(vyy3001, vyy401, cfc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Char) → new_esEs15(vyy3000, vyy400)
new_lt16(vyy3011, vyy411, ty_Ordering) → new_lt8(vyy3011, vyy411)
new_ltEs12(vyy301, vyy41) → new_not(new_esEs8(new_compare9(vyy301, vyy41), GT))
new_compare8([], :(vyy410, vyy411), cb) → LT
new_esEs19(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(ty_[], cce)) → new_esEs13(vyy3000, vyy400, cce)
new_asAs(False, vyy158) → False
new_ltEs18(vyy3012, vyy412, ty_Double) → new_ltEs15(vyy3012, vyy412)
new_lt8(vyy300, vyy40) → new_esEs8(new_compare37(vyy300, vyy40), LT)
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, EQ, app(app(ty_Either, ec), ed)) → new_compare25(vyy163, vyy164, ec, ed)
new_lt16(vyy3011, vyy411, ty_Char) → new_lt19(vyy3011, vyy411)
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_esEs13(:(vyy3000, vyy3001), [], cc) → False
new_esEs13([], :(vyy400, vyy401), cc) → False
new_lt16(vyy3011, vyy411, app(app(app(ty_@3, ha), hb), hc)) → new_lt11(vyy3011, vyy411, ha, hb, hc)
new_primCompAux00(vyy163, vyy164, EQ, ty_Bool) → new_compare15(vyy163, vyy164)
new_ltEs18(vyy3012, vyy412, ty_Ordering) → new_ltEs5(vyy3012, vyy412)
new_esEs21(vyy3011, vyy411, ty_Ordering) → new_esEs8(vyy3011, vyy411)
new_compare38(Integer(vyy30000), Integer(vyy4010), vyy400, vyy3001, ty_Integer) → new_compare7(Integer(new_primMulInt(vyy30000, vyy4010)), new_sr0(vyy400, vyy3001))
new_ltEs5(LT, EQ) → True
new_primCompAux00(vyy163, vyy164, EQ, app(ty_Ratio, caa)) → new_compare17(vyy163, vyy164, caa)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(ty_Ratio, ccf)) → new_esEs16(vyy3000, vyy400, ccf)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, bbb) → new_esEs15(vyy3000, vyy400)
new_esEs23(vyy950, vyy960, app(app(ty_@2, beg), beh)) → new_esEs7(vyy950, vyy960, beg, beh)
new_ltEs19(vyy951, vyy961, ty_@0) → new_ltEs10(vyy951, vyy961)
new_compare0(vyy3000, vyy400, ty_Float) → new_compare14(vyy3000, vyy400)
new_lt20(vyy950, vyy960, app(ty_[], bea)) → new_lt4(vyy950, vyy960, bea)
new_lt16(vyy3011, vyy411, app(app(ty_Either, hd), he)) → new_lt7(vyy3011, vyy411, hd, he)
new_primCompAux00(vyy163, vyy164, EQ, app(ty_Maybe, df)) → new_compare16(vyy163, vyy164, df)
new_ltEs8(Right(vyy3010), Left(vyy410), bce, bbd) → False
new_compare34(vyy300, vyy40, bgc, bgd) → new_compare28(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgc, bgd), bgc, bgd)
new_esEs18(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_esEs19(vyy3001, vyy401, ty_Double) → new_esEs9(vyy3001, vyy401)
new_esEs18(vyy3002, vyy402, ty_Char) → new_esEs15(vyy3002, vyy402)
new_primCompAux00(vyy163, vyy164, LT, bhh) → LT
new_compare0(vyy3000, vyy400, app(ty_Maybe, cd)) → new_compare16(vyy3000, vyy400, cd)
new_primCompAux00(vyy163, vyy164, GT, bhh) → GT
new_ltEs18(vyy3012, vyy412, ty_Char) → new_ltEs12(vyy3012, vyy412)
new_esEs16(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cad) → new_asAs(new_esEs25(vyy3000, vyy400, cad), new_esEs24(vyy3001, vyy401, cad))
new_compare13(vyy3000, vyy400) → new_compare37(vyy3000, vyy400)
new_ltEs18(vyy3012, vyy412, app(ty_Maybe, hh)) → new_ltEs13(vyy3012, vyy412, hh)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Double, bbd) → new_ltEs15(vyy3010, vyy410)
new_compare112(vyy300, vyy40, False, eg, eh, fa) → GT
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_compare27(vyy300, vyy40, True) → EQ
new_esEs21(vyy3011, vyy411, app(ty_Ratio, chc)) → new_esEs16(vyy3011, vyy411, chc)
new_esEs12(True, False) → False
new_esEs12(False, True) → False
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Double) → new_esEs9(vyy3000, vyy400)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Ordering, bbd) → new_ltEs5(vyy3010, vyy410)
new_lt16(vyy3011, vyy411, app(ty_Maybe, gg)) → new_lt13(vyy3011, vyy411, gg)
new_compare0(vyy3000, vyy400, ty_Integer) → new_compare7(vyy3000, vyy400)
new_compare11(vyy301, vyy41) → new_primCmpInt(vyy301, vyy41)
new_compare0(vyy3000, vyy400, ty_Double) → new_compare18(vyy3000, vyy400)
new_esEs14(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs12(vyy3001, vyy401)
new_compare37(vyy300, vyy40) → new_compare24(vyy300, vyy40, new_esEs8(vyy300, vyy40))
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_@0) → new_esEs17(vyy3000, vyy400)
new_lt4([], [], cc) → new_esEs8(EQ, LT)
new_compare27(vyy300, vyy40, False) → new_compare110(vyy300, vyy40, new_ltEs7(vyy300, vyy40))
new_ltEs9(vyy301, vyy41) → new_not(new_esEs8(new_compare11(vyy301, vyy41), GT))
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_[], bb)) → new_ltEs6(vyy3010, vyy410, bb)
new_ltEs19(vyy951, vyy961, app(ty_Maybe, bfb)) → new_ltEs13(vyy951, vyy961, bfb)
new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, cc) → new_primCompAux00(vyy3001, vyy401, new_compare0(vyy3000, vyy400, cc), app(ty_[], cc))
new_esEs9(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs19(vyy3001, vyy401, ty_Char) → new_esEs15(vyy3001, vyy401)
new_esEs20(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_compare7(Integer(vyy3010), Integer(vyy410)) → new_primCmpInt(vyy3010, vyy410)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], cbc), bbb) → new_esEs13(vyy3000, vyy400, cbc)
new_esEs22(vyy3010, vyy410, app(app(ty_Either, gb), gc)) → new_esEs6(vyy3010, vyy410, gb, gc)
new_ltEs19(vyy951, vyy961, app(ty_[], bfc)) → new_ltEs6(vyy951, vyy961, bfc)
new_ltEs19(vyy951, vyy961, app(app(app(ty_@3, bfd), bfe), bff)) → new_ltEs16(vyy951, vyy961, bfd, bfe, bff)
new_compare36(vyy300, vyy40, h) → new_compare211(vyy300, vyy40, new_esEs4(vyy300, vyy40, h), h)
new_compare210(vyy300, vyy40, False, eg, eh, fa) → new_compare112(vyy300, vyy40, new_ltEs16(vyy300, vyy40, eg, eh, fa), eg, eh, fa)
new_ltEs7(False, False) → True
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, bha), bhb)) → new_esEs7(vyy3000, vyy400, bha, bhb)
new_lt15(vyy3010, vyy410, ty_Ordering) → new_lt8(vyy3010, vyy410)
new_primCmpDouble(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_esEs21(vyy3011, vyy411, ty_Float) → new_esEs11(vyy3011, vyy411)
new_ltEs19(vyy951, vyy961, ty_Double) → new_ltEs15(vyy951, vyy961)
new_esEs22(vyy3010, vyy410, ty_Int) → new_esEs14(vyy3010, vyy410)
new_primCompAux00(vyy163, vyy164, EQ, ty_Int) → new_compare11(vyy163, vyy164)
new_esEs20(vyy3000, vyy400, app(app(ty_@2, cgb), cgc)) → new_esEs7(vyy3000, vyy400, cgb, cgc)
new_ltEs19(vyy951, vyy961, ty_Ordering) → new_ltEs5(vyy951, vyy961)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, db), dc)) → new_esEs6(vyy3000, vyy400, db, dc)
new_primPlusNat1(Zero, Zero) → Zero
new_compare111(vyy300, vyy40, True, bgc, bgd) → LT
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), eg, eh, fa) → new_asAs(new_esEs20(vyy3000, vyy400, eg), new_asAs(new_esEs19(vyy3001, vyy401, eh), new_esEs18(vyy3002, vyy402, fa)))
new_esEs19(vyy3001, vyy401, ty_@0) → new_esEs17(vyy3001, vyy401)
new_asAs(True, vyy158) → vyy158
new_primCmpChar(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, cf), cg), da)) → new_esEs5(vyy3000, vyy400, cf, cg, da)
new_esEs27(vyy3001, vyy401, app(ty_[], dae)) → new_esEs13(vyy3001, vyy401, dae)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Ordering) → new_ltEs5(vyy3010, vyy410)
new_ltEs5(GT, GT) → True
new_primCompAux00(vyy163, vyy164, EQ, ty_Integer) → new_compare7(vyy163, vyy164)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_[], bbe), bbd) → new_ltEs6(vyy3010, vyy410, bbe)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs14(vyy3000, vyy400)
new_compare38(vyy3000, vyy401, vyy400, vyy3001, ty_Int) → new_compare29(vyy3000, vyy401, vyy400, vyy3001)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs15(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, EQ, app(app(ty_@2, ee), ef)) → new_compare26(vyy163, vyy164, ee, ef)
new_ltEs18(vyy3012, vyy412, ty_Bool) → new_ltEs7(vyy3012, vyy412)
new_ltEs17(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, bdh) → new_pePe(new_lt20(vyy950, vyy960, bfa), new_asAs(new_esEs23(vyy950, vyy960, bfa), new_ltEs19(vyy951, vyy961, bdh)))
new_esEs23(vyy950, vyy960, app(app(app(ty_@3, beb), bec), bed)) → new_esEs5(vyy950, vyy960, beb, bec, bed)
new_esEs19(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs8(Left(vyy3010), Right(vyy410), bce, bbd) → True
new_compare18(vyy301, vyy41) → new_primCmpDouble(vyy301, vyy41)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs9(vyy3000, vyy400)
new_compare10(vyy300, vyy40, True) → LT
new_primCompAux00(vyy163, vyy164, EQ, ty_Double) → new_compare18(vyy163, vyy164)
new_lt17(vyy300, vyy40) → new_esEs8(new_primCmpInt(vyy300, vyy40), LT)
new_esEs19(vyy3001, vyy401, app(ty_[], cfb)) → new_esEs13(vyy3001, vyy401, cfb)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs21(vyy3011, vyy411, ty_Bool) → new_esEs12(vyy3011, vyy411)
new_compare10(vyy300, vyy40, False) → GT
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Ordering) → new_ltEs5(vyy3010, vyy410)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs5(vyy3000, vyy400, cbh, cca, ccb)
new_compare0(vyy3000, vyy400, ty_Int) → new_compare11(vyy3000, vyy400)
new_ltEs5(GT, EQ) → False
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs23(vyy950, vyy960, app(ty_[], bea)) → new_esEs13(vyy950, vyy960, bea)
new_not(True) → False

The set Q consists of the following terms:

new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_ltEs18(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Float)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt19(x0, x1)
new_asAs(True, x0)
new_esEs26(x0, x1, ty_Ordering)
new_lt14(x0, x1)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs13(:(x0, x1), [], x2)
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Nothing, Just(x0), x1)
new_compare34(x0, x1, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs18(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_compare7(Integer(x0), Integer(x1))
new_lt16(x0, x1, ty_@0)
new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_compare39(x0, x1, x2, x3, x4)
new_lt16(x0, x1, ty_Char)
new_esEs12(False, False)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Float)
new_compare26(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare8(:(x0, x1), :(x2, x3), x4)
new_esEs10(Integer(x0), Integer(x1))
new_primMulNat0(Zero, Succ(x0))
new_esEs13([], [], x0)
new_compare0(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1)
new_esEs27(x0, x1, ty_Integer)
new_ltEs13(Nothing, Just(x0), x1)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, ty_Float)
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_@0)
new_esEs8(GT, GT)
new_esEs24(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_lt16(x0, x1, ty_Int)
new_lt16(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs8(LT, LT)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs7(True, True)
new_esEs19(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_sr(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs22(x0, x1, ty_Double)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs7(True, False)
new_ltEs7(False, True)
new_esEs23(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs5(LT, EQ)
new_ltEs5(EQ, LT)
new_compare16(x0, x1, x2)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_asAs(False, x0)
new_primEqNat0(Zero, Zero)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Char)
new_lt15(x0, x1, ty_Ordering)
new_compare211(x0, x1, False, x2)
new_compare211(x0, x1, True, x2)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare33(x0, x1, x2, x3)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt15(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs15(Char(x0), Char(x1))
new_lt15(x0, x1, ty_Integer)
new_compare12(@0, @0)
new_compare18(x0, x1)
new_compare37(x0, x1)
new_esEs26(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_compare110(x0, x1, False)
new_primPlusNat0(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs19(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare0(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Integer)
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt16(x0, x1, ty_Bool)
new_compare0(x0, x1, ty_@0)
new_ltEs9(x0, x1)
new_esEs14(x0, x1)
new_primCompAux00(x0, x1, LT, x2)
new_lt15(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1)
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulNat0(Succ(x0), Succ(x1))
new_compare19(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_compare24(x0, x1, False)
new_ltEs18(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Double)
new_compare14(x0, x1)
new_lt15(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Int)
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Nothing, Nothing, x0)
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_@0)
new_compare0(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare36(x0, x1, x2)
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, ty_Char)
new_primCmpChar(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_Bool)
new_lt4([], :(x0, x1), x2)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare9(x0, x1)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_@0)
new_ltEs13(Nothing, Nothing, x0)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Zero, Zero)
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs13(Just(x0), Nothing, x1)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_primMulNat0(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt7(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare23(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs12(x0, x1)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_compare11(x0, x1)
new_esEs17(@0, @0)
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, ty_Int)
new_lt16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt16(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Ordering)
new_compare23(x0, x1, True, x2, x3)
new_esEs20(x0, x1, ty_Bool)
new_ltEs10(x0, x1)
new_compare8([], :(x0, x1), x2)
new_lt18(Integer(x0), Integer(x1))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Bool)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs12(True, True)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, x1, EQ, ty_Double)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_lt17(x0, x1)
new_compare27(x0, x1, False)
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Int)
new_compare113(x0, x1, False, x2)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, ty_Ordering)
new_compare28(x0, x1, False, x2, x3)
new_lt10(@0, @0)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCompAux00(x0, x1, EQ, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs13([], :(x0, x1), x2)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Int)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt4([], [], x0)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare210(x0, x1, True, x2, x3, x4)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, ty_Integer)
new_lt15(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt15(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare38(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, True, x2, x3)
new_primCompAux00(x0, x1, GT, x2)
new_lt8(x0, x1)
new_esEs19(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Char)
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_compare35(x0, x1)
new_pePe(True, x0)
new_ltEs4(x0, x1)
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_compare0(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_pePe(False, x0)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs22(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, x2, x3)
new_primEqNat0(Zero, Succ(x0))
new_esEs20(x0, x1, ty_Int)
new_compare10(x0, x1, False)
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_compare112(x0, x1, False, x2, x3, x4)
new_compare114(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(x0, x1, ty_Integer)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs21(x0, x1, ty_Ordering)
new_lt15(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_lt20(x0, x1, ty_Integer)
new_lt13(x0, x1, x2)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_Float)
new_lt6(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_compare0(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt16(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs27(x0, x1, ty_Double)
new_esEs18(x0, x1, app(ty_[], x2))
new_lt15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(GT, GT)
new_esEs12(True, False)
new_esEs12(False, True)
new_esEs22(x0, x1, ty_@0)
new_lt16(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare28(x0, x1, True, x2, x3)
new_esEs22(x0, x1, ty_Ordering)
new_lt15(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_Char)
new_compare15(x0, x1)
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_not(True)
new_compare25(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Float)
new_lt16(x0, x1, app(ty_[], x2))
new_lt4(:(x0, x1), [], x2)
new_esEs20(x0, x1, ty_Integer)
new_compare38(x0, x1, x2, x3, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_lt4(:(x0, x1), :(x2, x3), x4)
new_lt15(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, x1, EQ, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_compare114(x0, x1, True, x2, x3)
new_not(False)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare0(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare0(x0, x1, ty_Int)
new_lt16(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_ltEs5(EQ, EQ)
new_compare8([], [], x0)
new_esEs27(x0, x1, ty_Char)
new_primCompAux1(x0, x1, x2, x3, x4)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt15(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Bool)
new_lt16(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs21(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Int)
new_compare24(x0, x1, True)
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_ltEs14(x0, x1, x2)
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Char)
new_compare8(:(x0, x1), [], x2)
new_compare10(x0, x1, True)
new_compare210(x0, x1, False, x2, x3, x4)
new_compare112(x0, x1, True, x2, x3, x4)
new_ltEs6(x0, x1, x2)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare113(x0, x1, True, x2)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, x2, x3, x4)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_@0)
new_sr0(Integer(x0), Integer(x1))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_lt15(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_compare0(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs19(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, True)
new_compare110(x0, x1, True)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_esEs19(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Float)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare111(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Double)
new_ltEs5(LT, LT)
new_esEs26(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(False, False)
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Double)
new_compare13(x0, x1)

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

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

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

new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(ty_Maybe, bcf)) → new_ltEs(vyy3010, vyy410, bcf)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(app(app(ty_@3, ha), hb), hc), fd) → new_lt1(vyy3011, vyy411, ha, hb, hc)
new_compare22(vyy300, vyy40, False, bgc, bgd) → new_ltEs3(vyy300, vyy40, bgc, bgd)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(app(ty_@3, beb), bec), bed), bdh) → new_lt1(vyy950, vyy960, beb, bec, bed)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_[], ff), fc, fd) → new_lt0(vyy3010, vyy410, ff)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(app(ty_@2, bag), bah)) → new_ltEs3(vyy3012, vyy412, bag, bah)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_Either, bee), bef), bdh) → new_lt2(vyy950, vyy960, bee, bef)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(app(app(ty_@3, bfd), bfe), bff)) → new_ltEs1(vyy951, vyy961, bfd, bfe, bff)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(ty_Maybe, cd)) → new_compare3(vyy3000, vyy400, cd)
new_ltEs2(Left(vyy3010), Left(vyy410), app(app(ty_Either, bca), bcb), bbd) → new_ltEs2(vyy3010, vyy410, bca, bcb)
new_ltEs(Just(vyy3010), Just(vyy410), app(ty_[], bb)) → new_ltEs0(vyy3010, vyy410, bb)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_Either, db), dc)) → new_compare31(vyy3000, vyy400, db, dc)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_Maybe, fb), fc, fd) → new_lt(vyy3010, vyy410, fb)
new_ltEs2(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bbd) → new_ltEs(vyy3010, vyy410, bbc)
new_compare(:(vyy3010, vyy3011), :(vyy410, vyy411), cb) → new_primCompAux(vyy3010, vyy410, vyy3011, vyy411, cb)
new_compare31(vyy300, vyy40, bba, bbb) → new_compare21(vyy300, vyy40, new_esEs6(vyy300, vyy40, bba, bbb), bba, bbb)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(app(ty_@2, hf), hg), fd) → new_lt3(vyy3011, vyy411, hf, hg)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, cc) → new_primCompAux0(vyy3001, vyy401, new_compare0(vyy3000, vyy400, cc), app(ty_[], cc))
new_ltEs(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bc), bd), be)) → new_ltEs1(vyy3010, vyy410, bc, bd, be)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(ty_[], gh), fd) → new_lt0(vyy3011, vyy411, gh)
new_lt3(vyy300, vyy40, bgc, bgd) → new_compare22(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgc, bgd), bgc, bgd)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_@2, dd), de)) → new_compare32(vyy3000, vyy400, dd, de)
new_ltEs(Just(vyy3010), Just(vyy410), app(ty_Maybe, ba)) → new_ltEs(vyy3010, vyy410, ba)
new_lt(vyy300, vyy40, h) → new_compare2(vyy300, vyy40, new_esEs4(vyy300, vyy40, h), h)
new_ltEs2(Left(vyy3010), Left(vyy410), app(app(ty_@2, bcc), bcd), bbd) → new_ltEs3(vyy3010, vyy410, bcc, bcd)
new_ltEs2(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, bbf), bbg), bbh), bbd) → new_ltEs1(vyy3010, vyy410, bbf, bbg, bbh)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(ty_Maybe, bfb)) → new_ltEs(vyy951, vyy961, bfb)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(ty_@2, dd), de)) → new_compare32(vyy3000, vyy400, dd, de)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_@2, gd), ge), fc, fd) → new_lt3(vyy3010, vyy410, gd, ge)
new_compare3(vyy300, vyy40, h) → new_compare2(vyy300, vyy40, new_esEs4(vyy300, vyy40, h), h)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(app(ty_@2, bga), bgb)) → new_ltEs3(vyy951, vyy961, bga, bgb)
new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(app(app(ty_@3, bch), bda), bdb)) → new_ltEs1(vyy3010, vyy410, bch, bda, bdb)
new_compare30(vyy300, vyy40, eg, eh, fa) → new_compare20(vyy300, vyy40, new_esEs5(vyy300, vyy40, eg, eh, fa), eg, eh, fa)
new_compare32(vyy300, vyy40, bgc, bgd) → new_compare22(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgc, bgd), bgc, bgd)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(app(ty_@3, cf), cg), da)) → new_compare30(vyy3000, vyy400, cf, cg, da)
new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(app(ty_@2, bde), bdf)) → new_ltEs3(vyy3010, vyy410, bde, bdf)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(app(ty_Either, hd), he), fd) → new_lt2(vyy3011, vyy411, hd, he)
new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(app(ty_Either, bdc), bdd)) → new_ltEs2(vyy3010, vyy410, bdc, bdd)
new_compare21(vyy300, vyy40, False, bba, bbb) → new_ltEs2(vyy300, vyy40, bba, bbb)
new_ltEs2(Right(vyy3010), Right(vyy410), bce, app(ty_[], bcg)) → new_ltEs0(vyy3010, vyy410, bcg)
new_ltEs(Just(vyy3010), Just(vyy410), app(app(ty_Either, bf), bg)) → new_ltEs2(vyy3010, vyy410, bf, bg)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(ty_[], ce)) → new_compare(vyy3000, vyy400, ce)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_Either, gb), gc), fc, fd) → new_lt2(vyy3010, vyy410, gb, gc)
new_primCompAux0(vyy163, vyy164, EQ, app(ty_[], dg)) → new_compare(vyy163, vyy164, dg)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(app(ty_@3, cf), cg), da)) → new_compare30(vyy3000, vyy400, cf, cg, da)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_@2, beg), beh), bdh) → new_lt3(vyy950, vyy960, beg, beh)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, app(ty_Maybe, gg), fd) → new_lt(vyy3011, vyy411, gg)
new_compare2(vyy300, vyy40, False, h) → new_ltEs(vyy300, vyy40, h)
new_lt2(vyy300, vyy40, bba, bbb) → new_compare21(vyy300, vyy40, new_esEs6(vyy300, vyy40, bba, bbb), bba, bbb)
new_ltEs(Just(vyy3010), Just(vyy410), app(app(ty_@2, bh), ca)) → new_ltEs3(vyy3010, vyy410, bh, ca)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), cc) → new_primCompAux0(vyy3001, vyy401, new_compare0(vyy3000, vyy400, cc), app(ty_[], cc))
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(ty_Maybe, hh)) → new_ltEs(vyy3012, vyy412, hh)
new_ltEs0(:(vyy3010, vyy3011), :(vyy410, vyy411), cb) → new_primCompAux(vyy3010, vyy410, vyy3011, vyy411, cb)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs1(vyy3012, vyy412, bab, bac, bad)
new_lt1(vyy300, vyy40, eg, eh, fa) → new_compare20(vyy300, vyy40, new_esEs5(vyy300, vyy40, eg, eh, fa), eg, eh, fa)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(ty_Either, db), dc)) → new_compare31(vyy3000, vyy400, db, dc)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(ty_[], baa)) → new_ltEs0(vyy3012, vyy412, baa)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_Maybe, bdg), bdh) → new_lt(vyy950, vyy960, bdg)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(app(ty_Either, bfg), bfh)) → new_ltEs2(vyy951, vyy961, bfg, bfh)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_Maybe, cd)) → new_compare3(vyy3000, vyy400, cd)
new_lt0(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_[], ce)) → new_compare(vyy3000, vyy400, ce)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, app(ty_[], bfc)) → new_ltEs0(vyy951, vyy961, bfc)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, app(app(ty_Either, bae), baf)) → new_ltEs2(vyy3012, vyy412, bae, baf)
new_ltEs1(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, fg), fh), ga), fc, fd) → new_lt1(vyy3010, vyy410, fg, fh, ga)
new_compare20(vyy300, vyy40, False, eg, eh, fa) → new_ltEs1(vyy300, vyy40, eg, eh, fa)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_[], bea), bdh) → new_lt0(vyy950, vyy960, bea)
new_ltEs2(Left(vyy3010), Left(vyy410), app(ty_[], bbe), bbd) → new_ltEs0(vyy3010, vyy410, bbe)

The TRS R consists of the following rules:

new_esEs6(Right(vyy3000), Right(vyy400), bba, app(app(ty_@2, ccc), ccd)) → new_esEs7(vyy3000, vyy400, ccc, ccd)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, cbd), bbb) → new_esEs16(vyy3000, vyy400, cbd)
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, bbb) → new_esEs14(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, bbb) → new_esEs11(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Right(vyy400), bba, bbb) → False
new_esEs6(Right(vyy3000), Left(vyy400), bba, bbb) → False
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, bhe), bhf)) → new_esEs6(vyy3000, vyy400, bhe, bhf)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, bge)) → new_esEs4(vyy3000, vyy400, bge)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, cae), bbb) → new_esEs4(vyy3000, vyy400, cae)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(ty_Maybe, cbg)) → new_esEs4(vyy3000, vyy400, cbg)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, cbe), cbf), bbb) → new_esEs6(vyy3000, vyy400, cbe, cbf)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(app(ty_Either, ccg), cch)) → new_esEs6(vyy3000, vyy400, ccg, cch)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, bbb) → new_esEs10(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, caf), cag), cah), bbb) → new_esEs5(vyy3000, vyy400, caf, cag, cah)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, bbb) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, bbb) → new_esEs12(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, cba), cbb), bbb) → new_esEs7(vyy3000, vyy400, cba, cbb)
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, bbb) → new_esEs8(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, bbb) → new_esEs9(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Char) → new_esEs15(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(ty_[], cce)) → new_esEs13(vyy3000, vyy400, cce)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(ty_Ratio, ccf)) → new_esEs16(vyy3000, vyy400, ccf)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, bbb) → new_esEs15(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Double) → new_esEs9(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], cbc), bbb) → new_esEs13(vyy3000, vyy400, cbc)
new_esEs6(Right(vyy3000), Right(vyy400), bba, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bba, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs5(vyy3000, vyy400, cbh, cca, ccb)
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), eg, eh, fa) → new_asAs(new_esEs20(vyy3000, vyy400, eg), new_asAs(new_esEs19(vyy3001, vyy401, eh), new_esEs18(vyy3002, vyy402, fa)))
new_esEs20(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, app(ty_[], cgd)) → new_esEs13(vyy3000, vyy400, cgd)
new_esEs20(vyy3000, vyy400, app(ty_Ratio, cge)) → new_esEs16(vyy3000, vyy400, cge)
new_esEs20(vyy3000, vyy400, app(ty_Maybe, cff)) → new_esEs4(vyy3000, vyy400, cff)
new_esEs20(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, app(app(app(ty_@3, cfg), cfh), cga)) → new_esEs5(vyy3000, vyy400, cfg, cfh, cga)
new_esEs20(vyy3000, vyy400, app(app(ty_Either, cgf), cgg)) → new_esEs6(vyy3000, vyy400, cgf, cgg)
new_esEs20(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, app(app(ty_@2, cgb), cgc)) → new_esEs7(vyy3000, vyy400, cgb, cgc)
new_esEs20(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_esEs19(vyy3001, vyy401, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs5(vyy3001, vyy401, cee, cef, ceg)
new_esEs19(vyy3001, vyy401, app(ty_Maybe, ced)) → new_esEs4(vyy3001, vyy401, ced)
new_esEs19(vyy3001, vyy401, ty_Bool) → new_esEs12(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, app(app(ty_Either, cfd), cfe)) → new_esEs6(vyy3001, vyy401, cfd, cfe)
new_esEs19(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, app(app(ty_@2, ceh), cfa)) → new_esEs7(vyy3001, vyy401, ceh, cfa)
new_esEs19(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, app(ty_Ratio, cfc)) → new_esEs16(vyy3001, vyy401, cfc)
new_esEs19(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, ty_Double) → new_esEs9(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, ty_Char) → new_esEs15(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, ty_@0) → new_esEs17(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, app(ty_[], cfb)) → new_esEs13(vyy3001, vyy401, cfb)
new_esEs18(vyy3002, vyy402, ty_Int) → new_esEs14(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, ty_Double) → new_esEs9(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, ty_Float) → new_esEs11(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, ty_Integer) → new_esEs10(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, app(app(ty_@2, cdf), cdg)) → new_esEs7(vyy3002, vyy402, cdf, cdg)
new_esEs18(vyy3002, vyy402, ty_Bool) → new_esEs12(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, app(app(ty_Either, ceb), cec)) → new_esEs6(vyy3002, vyy402, ceb, cec)
new_esEs18(vyy3002, vyy402, app(ty_[], cdh)) → new_esEs13(vyy3002, vyy402, cdh)
new_esEs18(vyy3002, vyy402, app(ty_Ratio, cea)) → new_esEs16(vyy3002, vyy402, cea)
new_esEs18(vyy3002, vyy402, app(app(app(ty_@3, cdc), cdd), cde)) → new_esEs5(vyy3002, vyy402, cdc, cdd, cde)
new_esEs18(vyy3002, vyy402, app(ty_Maybe, cdb)) → new_esEs4(vyy3002, vyy402, cdb)
new_esEs18(vyy3002, vyy402, ty_@0) → new_esEs17(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, ty_Char) → new_esEs15(vyy3002, vyy402)
new_asAs(False, vyy158) → False
new_asAs(True, vyy158) → vyy158
new_esEs15(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_esEs8(LT, LT) → True
new_esEs8(GT, GT) → True
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs8(EQ, EQ) → True
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs17(@0, @0) → True
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs4(Nothing, Just(vyy400), h) → False
new_esEs4(Just(vyy3000), Nothing, h) → False
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs5(vyy3000, vyy400, bgf, bgg, bgh)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs4(Nothing, Nothing, h) → True
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, bhd)) → new_esEs16(vyy3000, vyy400, bhd)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], bhc)) → new_esEs13(vyy3000, vyy400, bhc)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, bha), bhb)) → new_esEs7(vyy3000, vyy400, bha, bhb)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs15(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs9(vyy3000, vyy400)
new_esEs9(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs14(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_primPlusNat0(Succ(vyy1730), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1730, vyy40100)))
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy17300), Zero) → Succ(vyy17300)
new_primPlusNat1(Succ(vyy17300), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy17300, vyy401000)))
new_primPlusNat1(Zero, Zero) → Zero
new_esEs7(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bgc, bgd) → new_asAs(new_esEs28(vyy3000, vyy400, bgc), new_esEs27(vyy3001, vyy401, bgd))
new_esEs28(vyy3000, vyy400, app(ty_[], dbg)) → new_esEs13(vyy3000, vyy400, dbg)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs5(vyy3000, vyy400, dbb, dbc, dbd)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dbh)) → new_esEs16(vyy3000, vyy400, dbh)
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dca), dcb)) → new_esEs6(vyy3000, vyy400, dca, dcb)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dba)) → new_esEs4(vyy3000, vyy400, dba)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dbe), dbf)) → new_esEs7(vyy3000, vyy400, dbe, dbf)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs15(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, chh), daa), dab)) → new_esEs5(vyy3001, vyy401, chh, daa, dab)
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs9(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, app(app(ty_@2, dac), dad)) → new_esEs7(vyy3001, vyy401, dac, dad)
new_esEs27(vyy3001, vyy401, app(ty_Ratio, daf)) → new_esEs16(vyy3001, vyy401, daf)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, app(app(ty_Either, dag), dah)) → new_esEs6(vyy3001, vyy401, dag, dah)
new_esEs27(vyy3001, vyy401, app(ty_Maybe, chg)) → new_esEs4(vyy3001, vyy401, chg)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs17(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs12(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, app(ty_[], dae)) → new_esEs13(vyy3001, vyy401, dae)
new_esEs13([], [], cc) → True
new_esEs13(:(vyy3000, vyy3001), :(vyy400, vyy401), cc) → new_asAs(new_esEs26(vyy3000, vyy400, cc), new_esEs13(vyy3001, vyy401, cc))
new_esEs13(:(vyy3000, vyy3001), [], cc) → False
new_esEs13([], :(vyy400, vyy401), cc) → False
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, cd)) → new_esEs4(vyy3000, vyy400, cd)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_[], ce)) → new_esEs13(vyy3000, vyy400, ce)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, bhg)) → new_esEs16(vyy3000, vyy400, bhg)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, dd), de)) → new_esEs7(vyy3000, vyy400, dd, de)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, db), dc)) → new_esEs6(vyy3000, vyy400, db, dc)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, cf), cg), da)) → new_esEs5(vyy3000, vyy400, cf, cg, da)
new_esEs16(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cad) → new_asAs(new_esEs25(vyy3000, vyy400, cad), new_esEs24(vyy3001, vyy401, cad))
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_esEs10(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs11(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs12(True, True) → True
new_esEs12(False, False) → True
new_esEs12(True, False) → False
new_esEs12(False, True) → False
new_compare0(vyy3000, vyy400, app(ty_[], ce)) → new_compare8(vyy3000, vyy400, ce)
new_compare0(vyy3000, vyy400, app(app(ty_Either, db), dc)) → new_compare25(vyy3000, vyy400, db, dc)
new_compare0(vyy3000, vyy400, ty_@0) → new_compare12(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(app(app(ty_@3, cf), cg), da)) → new_compare19(vyy3000, vyy400, cf, cg, da)
new_compare0(vyy3000, vyy400, ty_Char) → new_compare9(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Bool) → new_compare15(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(app(ty_@2, dd), de)) → new_compare26(vyy3000, vyy400, dd, de)
new_compare0(vyy3000, vyy400, app(ty_Ratio, bhg)) → new_compare17(vyy3000, vyy400, bhg)
new_compare0(vyy3000, vyy400, ty_Ordering) → new_compare13(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Float) → new_compare14(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(ty_Maybe, cd)) → new_compare16(vyy3000, vyy400, cd)
new_compare0(vyy3000, vyy400, ty_Integer) → new_compare7(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Double) → new_compare18(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Int) → new_compare11(vyy3000, vyy400)
new_compare11(vyy301, vyy41) → new_primCmpInt(vyy301, vyy41)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_compare18(vyy301, vyy41) → new_primCmpDouble(vyy301, vyy41)
new_primCmpDouble(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_compare29(vyy3000, vyy400, vyy3001, vyy401) → new_primCmpInt(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare7(Integer(vyy3010), Integer(vyy410)) → new_primCmpInt(vyy3010, vyy410)
new_compare16(vyy3000, vyy400, cd) → new_compare36(vyy3000, vyy400, cd)
new_compare36(vyy300, vyy40, h) → new_compare211(vyy300, vyy40, new_esEs4(vyy300, vyy40, h), h)
new_compare211(vyy300, vyy40, False, h) → new_compare113(vyy300, vyy40, new_ltEs13(vyy300, vyy40, h), h)
new_compare211(vyy300, vyy40, True, h) → EQ
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Char) → new_ltEs12(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Double) → new_ltEs15(vyy3010, vyy410)
new_ltEs13(Nothing, Just(vyy410), cgh) → True
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_Ratio, cha)) → new_ltEs14(vyy3010, vyy410, cha)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Int) → new_ltEs9(vyy3010, vyy410)
new_ltEs13(Nothing, Nothing, cgh) → True
new_ltEs13(Just(vyy3010), Just(vyy410), ty_@0) → new_ltEs10(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Bool) → new_ltEs7(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Float) → new_ltEs11(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(ty_@2, bh), ca)) → new_ltEs17(vyy3010, vyy410, bh, ca)
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bc), bd), be)) → new_ltEs16(vyy3010, vyy410, bc, bd, be)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Integer) → new_ltEs4(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Nothing, cgh) → False
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_[], bb)) → new_ltEs6(vyy3010, vyy410, bb)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Ordering) → new_ltEs5(vyy3010, vyy410)
new_compare113(vyy300, vyy40, True, h) → LT
new_compare113(vyy300, vyy40, False, h) → GT
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(ty_Either, bca), bcb), bbd) → new_ltEs8(vyy3010, vyy410, bca, bcb)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bbd) → new_ltEs13(vyy3010, vyy410, bbc)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_Maybe, bcf)) → new_ltEs13(vyy3010, vyy410, bcf)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(ty_Either, bdc), bdd)) → new_ltEs8(vyy3010, vyy410, bdc, bdd)
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(ty_Either, bf), bg)) → new_ltEs8(vyy3010, vyy410, bf, bg)
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_Maybe, ba)) → new_ltEs13(vyy3010, vyy410, ba)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_[], bcg)) → new_ltEs6(vyy3010, vyy410, bcg)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Char) → new_ltEs12(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Integer, bbd) → new_ltEs4(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Bool) → new_ltEs7(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Char, bbd) → new_ltEs12(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(ty_@2, bde), bdf)) → new_ltEs17(vyy3010, vyy410, bde, bdf)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Double) → new_ltEs15(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(ty_@2, bcc), bcd), bbd) → new_ltEs17(vyy3010, vyy410, bcc, bcd)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Int, bbd) → new_ltEs9(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Integer) → new_ltEs4(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, bbf), bbg), bbh), bbd) → new_ltEs16(vyy3010, vyy410, bbf, bbg, bbh)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_@0) → new_ltEs10(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Int) → new_ltEs9(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Bool, bbd) → new_ltEs7(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_Ratio, cac)) → new_ltEs14(vyy3010, vyy410, cac)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Float) → new_ltEs11(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_Ratio, cab), bbd) → new_ltEs14(vyy3010, vyy410, cab)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(app(ty_@3, bch), bda), bdb)) → new_ltEs16(vyy3010, vyy410, bch, bda, bdb)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_@0, bbd) → new_ltEs10(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Float, bbd) → new_ltEs11(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Left(vyy410), bce, bbd) → False
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Double, bbd) → new_ltEs15(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Ordering, bbd) → new_ltEs5(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Ordering) → new_ltEs5(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_[], bbe), bbd) → new_ltEs6(vyy3010, vyy410, bbe)
new_ltEs8(Left(vyy3010), Right(vyy410), bce, bbd) → True
new_ltEs6(vyy301, vyy41, cb) → new_not(new_esEs8(new_compare8(vyy301, vyy41, cb), GT))
new_compare8([], [], cb) → EQ
new_compare8(:(vyy3010, vyy3011), :(vyy410, vyy411), cb) → new_primCompAux1(vyy3010, vyy410, vyy3011, vyy411, cb)
new_primCompAux00(vyy163, vyy164, EQ, app(ty_[], dg)) → new_compare8(vyy163, vyy164, dg)
new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, cc) → new_primCompAux00(vyy3001, vyy401, new_compare0(vyy3000, vyy400, cc), app(ty_[], cc))
new_compare8(:(vyy3010, vyy3011), [], cb) → GT
new_compare8([], :(vyy410, vyy411), cb) → LT
new_not(False) → True
new_not(True) → False
new_primCompAux00(vyy163, vyy164, LT, bhh) → LT
new_primCompAux00(vyy163, vyy164, GT, bhh) → GT
new_ltEs5(EQ, GT) → True
new_ltEs5(EQ, LT) → False
new_ltEs5(LT, LT) → True
new_ltEs5(EQ, EQ) → True
new_ltEs5(GT, LT) → False
new_ltEs5(LT, GT) → True
new_ltEs5(LT, EQ) → True
new_ltEs5(GT, GT) → True
new_ltEs5(GT, EQ) → False
new_ltEs15(vyy301, vyy41) → new_not(new_esEs8(new_compare18(vyy301, vyy41), GT))
new_ltEs11(vyy301, vyy41) → new_not(new_esEs8(new_compare14(vyy301, vyy41), GT))
new_compare14(vyy301, vyy41) → new_primCmpFloat(vyy301, vyy41)
new_primCmpFloat(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_ltEs10(vyy301, vyy41) → new_not(new_esEs8(new_compare12(vyy301, vyy41), GT))
new_compare12(@0, @0) → EQ
new_ltEs16(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), gf, fc, fd) → new_pePe(new_lt15(vyy3010, vyy410, gf), new_asAs(new_esEs22(vyy3010, vyy410, gf), new_pePe(new_lt16(vyy3011, vyy411, fc), new_asAs(new_esEs21(vyy3011, vyy411, fc), new_ltEs18(vyy3012, vyy412, fd)))))
new_lt15(vyy3010, vyy410, ty_Bool) → new_lt5(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, app(ty_[], ff)) → new_lt4(vyy3010, vyy410, ff)
new_lt15(vyy3010, vyy410, ty_Char) → new_lt19(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, ty_Float) → new_lt12(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, app(ty_Maybe, fb)) → new_lt13(vyy3010, vyy410, fb)
new_lt15(vyy3010, vyy410, ty_@0) → new_lt10(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, ty_Integer) → new_lt18(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, app(app(ty_Either, gb), gc)) → new_lt7(vyy3010, vyy410, gb, gc)
new_lt15(vyy3010, vyy410, app(app(ty_@2, gd), ge)) → new_lt9(vyy3010, vyy410, gd, ge)
new_lt15(vyy3010, vyy410, app(app(app(ty_@3, fg), fh), ga)) → new_lt11(vyy3010, vyy410, fg, fh, ga)
new_lt15(vyy3010, vyy410, app(ty_Ratio, chb)) → new_lt6(vyy3010, vyy410, chb)
new_lt15(vyy3010, vyy410, ty_Double) → new_lt14(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, ty_Int) → new_lt17(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, ty_Ordering) → new_lt8(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, ty_@0) → new_esEs17(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, ty_Integer) → new_esEs10(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, ty_Ordering) → new_esEs8(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, app(app(ty_@2, gd), ge)) → new_esEs7(vyy3010, vyy410, gd, ge)
new_esEs22(vyy3010, vyy410, ty_Double) → new_esEs9(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, app(app(app(ty_@3, fg), fh), ga)) → new_esEs5(vyy3010, vyy410, fg, fh, ga)
new_esEs22(vyy3010, vyy410, app(ty_Maybe, fb)) → new_esEs4(vyy3010, vyy410, fb)
new_esEs22(vyy3010, vyy410, ty_Bool) → new_esEs12(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, ty_Char) → new_esEs15(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, ty_Float) → new_esEs11(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, app(ty_[], ff)) → new_esEs13(vyy3010, vyy410, ff)
new_esEs22(vyy3010, vyy410, app(ty_Ratio, chb)) → new_esEs16(vyy3010, vyy410, chb)
new_esEs22(vyy3010, vyy410, app(app(ty_Either, gb), gc)) → new_esEs6(vyy3010, vyy410, gb, gc)
new_esEs22(vyy3010, vyy410, ty_Int) → new_esEs14(vyy3010, vyy410)
new_lt16(vyy3011, vyy411, ty_Bool) → new_lt5(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, ty_Int) → new_lt17(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, app(ty_Ratio, chc)) → new_lt6(vyy3011, vyy411, chc)
new_lt16(vyy3011, vyy411, ty_Double) → new_lt14(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, ty_Float) → new_lt12(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, app(app(ty_@2, hf), hg)) → new_lt9(vyy3011, vyy411, hf, hg)
new_lt16(vyy3011, vyy411, ty_Integer) → new_lt18(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, ty_@0) → new_lt10(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, app(ty_[], gh)) → new_lt4(vyy3011, vyy411, gh)
new_lt16(vyy3011, vyy411, ty_Ordering) → new_lt8(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, ty_Char) → new_lt19(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, app(app(app(ty_@3, ha), hb), hc)) → new_lt11(vyy3011, vyy411, ha, hb, hc)
new_lt16(vyy3011, vyy411, app(app(ty_Either, hd), he)) → new_lt7(vyy3011, vyy411, hd, he)
new_lt16(vyy3011, vyy411, app(ty_Maybe, gg)) → new_lt13(vyy3011, vyy411, gg)
new_esEs21(vyy3011, vyy411, ty_Int) → new_esEs14(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, ty_@0) → new_esEs17(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, app(app(ty_Either, hd), he)) → new_esEs6(vyy3011, vyy411, hd, he)
new_esEs21(vyy3011, vyy411, ty_Char) → new_esEs15(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, app(app(ty_@2, hf), hg)) → new_esEs7(vyy3011, vyy411, hf, hg)
new_esEs21(vyy3011, vyy411, app(ty_[], gh)) → new_esEs13(vyy3011, vyy411, gh)
new_esEs21(vyy3011, vyy411, app(app(app(ty_@3, ha), hb), hc)) → new_esEs5(vyy3011, vyy411, ha, hb, hc)
new_esEs21(vyy3011, vyy411, ty_Integer) → new_esEs10(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, app(ty_Maybe, gg)) → new_esEs4(vyy3011, vyy411, gg)
new_esEs21(vyy3011, vyy411, ty_Double) → new_esEs9(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, ty_Ordering) → new_esEs8(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, app(ty_Ratio, chc)) → new_esEs16(vyy3011, vyy411, chc)
new_esEs21(vyy3011, vyy411, ty_Float) → new_esEs11(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, ty_Bool) → new_esEs12(vyy3011, vyy411)
new_ltEs18(vyy3012, vyy412, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs16(vyy3012, vyy412, bab, bac, bad)
new_ltEs18(vyy3012, vyy412, ty_Integer) → new_ltEs4(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_@0) → new_ltEs10(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Float) → new_ltEs11(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Int) → new_ltEs9(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, app(ty_Ratio, chd)) → new_ltEs14(vyy3012, vyy412, chd)
new_ltEs18(vyy3012, vyy412, app(app(ty_Either, bae), baf)) → new_ltEs8(vyy3012, vyy412, bae, baf)
new_ltEs18(vyy3012, vyy412, app(app(ty_@2, bag), bah)) → new_ltEs17(vyy3012, vyy412, bag, bah)
new_ltEs18(vyy3012, vyy412, app(ty_[], baa)) → new_ltEs6(vyy3012, vyy412, baa)
new_ltEs18(vyy3012, vyy412, ty_Double) → new_ltEs15(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Ordering) → new_ltEs5(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Char) → new_ltEs12(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, app(ty_Maybe, hh)) → new_ltEs13(vyy3012, vyy412, hh)
new_ltEs18(vyy3012, vyy412, ty_Bool) → new_ltEs7(vyy3012, vyy412)
new_pePe(False, vyy139) → vyy139
new_pePe(True, vyy139) → True
new_ltEs7(True, True) → True
new_ltEs7(True, False) → False
new_ltEs7(False, True) → True
new_ltEs7(False, False) → True
new_ltEs12(vyy301, vyy41) → new_not(new_esEs8(new_compare9(vyy301, vyy41), GT))
new_compare9(vyy301, vyy41) → new_primCmpChar(vyy301, vyy41)
new_primCmpChar(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_ltEs17(@2(vyy950, vyy951), @2(vyy960, vyy961), bfa, bdh) → new_pePe(new_lt20(vyy950, vyy960, bfa), new_asAs(new_esEs23(vyy950, vyy960, bfa), new_ltEs19(vyy951, vyy961, bdh)))
new_lt20(vyy950, vyy960, ty_Integer) → new_lt18(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(ty_Maybe, bdg)) → new_lt13(vyy950, vyy960, bdg)
new_lt20(vyy950, vyy960, ty_Double) → new_lt14(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(app(ty_@2, beg), beh)) → new_lt9(vyy950, vyy960, beg, beh)
new_lt20(vyy950, vyy960, ty_Float) → new_lt12(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(app(ty_Either, bee), bef)) → new_lt7(vyy950, vyy960, bee, bef)
new_lt20(vyy950, vyy960, ty_Char) → new_lt19(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_@0) → new_lt10(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_Ordering) → new_lt8(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_Int) → new_lt17(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_Bool) → new_lt5(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(ty_Ratio, che)) → new_lt6(vyy950, vyy960, che)
new_lt20(vyy950, vyy960, app(app(app(ty_@3, beb), bec), bed)) → new_lt11(vyy950, vyy960, beb, bec, bed)
new_lt20(vyy950, vyy960, app(ty_[], bea)) → new_lt4(vyy950, vyy960, bea)
new_esEs23(vyy950, vyy960, ty_Double) → new_esEs9(vyy950, vyy960)
new_esEs23(vyy950, vyy960, ty_Bool) → new_esEs12(vyy950, vyy960)
new_esEs23(vyy950, vyy960, app(ty_Maybe, bdg)) → new_esEs4(vyy950, vyy960, bdg)
new_esEs23(vyy950, vyy960, ty_Char) → new_esEs15(vyy950, vyy960)
new_esEs23(vyy950, vyy960, ty_Integer) → new_esEs10(vyy950, vyy960)
new_esEs23(vyy950, vyy960, ty_Int) → new_esEs14(vyy950, vyy960)
new_esEs23(vyy950, vyy960, app(app(ty_Either, bee), bef)) → new_esEs6(vyy950, vyy960, bee, bef)
new_esEs23(vyy950, vyy960, ty_Ordering) → new_esEs8(vyy950, vyy960)
new_esEs23(vyy950, vyy960, ty_@0) → new_esEs17(vyy950, vyy960)
new_esEs23(vyy950, vyy960, ty_Float) → new_esEs11(vyy950, vyy960)
new_esEs23(vyy950, vyy960, app(ty_Ratio, che)) → new_esEs16(vyy950, vyy960, che)
new_esEs23(vyy950, vyy960, app(app(ty_@2, beg), beh)) → new_esEs7(vyy950, vyy960, beg, beh)
new_esEs23(vyy950, vyy960, app(app(app(ty_@3, beb), bec), bed)) → new_esEs5(vyy950, vyy960, beb, bec, bed)
new_esEs23(vyy950, vyy960, app(ty_[], bea)) → new_esEs13(vyy950, vyy960, bea)
new_ltEs19(vyy951, vyy961, ty_Float) → new_ltEs11(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, app(app(ty_Either, bfg), bfh)) → new_ltEs8(vyy951, vyy961, bfg, bfh)
new_ltEs19(vyy951, vyy961, app(ty_Ratio, chf)) → new_ltEs14(vyy951, vyy961, chf)
new_ltEs19(vyy951, vyy961, app(app(ty_@2, bga), bgb)) → new_ltEs17(vyy951, vyy961, bga, bgb)
new_ltEs19(vyy951, vyy961, ty_Integer) → new_ltEs4(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Char) → new_ltEs12(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Int) → new_ltEs9(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Bool) → new_ltEs7(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_@0) → new_ltEs10(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, app(ty_Maybe, bfb)) → new_ltEs13(vyy951, vyy961, bfb)
new_ltEs19(vyy951, vyy961, app(ty_[], bfc)) → new_ltEs6(vyy951, vyy961, bfc)
new_ltEs19(vyy951, vyy961, app(app(app(ty_@3, bfd), bfe), bff)) → new_ltEs16(vyy951, vyy961, bfd, bfe, bff)
new_ltEs19(vyy951, vyy961, ty_Double) → new_ltEs15(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Ordering) → new_ltEs5(vyy951, vyy961)
new_ltEs9(vyy301, vyy41) → new_not(new_esEs8(new_compare11(vyy301, vyy41), GT))
new_ltEs4(vyy301, vyy41) → new_not(new_esEs8(new_compare7(vyy301, vyy41), GT))
new_ltEs14(vyy301, vyy41, cda) → new_not(new_esEs8(new_compare17(vyy301, vyy41, cda), GT))
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Int) → new_compare11(new_sr(vyy3010, vyy411), new_sr(vyy410, vyy3011))
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Integer) → new_compare7(new_sr0(vyy3010, vyy411), new_sr0(vyy410, vyy3011))
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_lt4(:(vyy3000, vyy3001), :(vyy400, vyy401), cc) → new_esEs8(new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, cc), LT)
new_lt4(:(vyy3000, vyy3001), [], cc) → new_esEs8(GT, LT)
new_lt4([], :(vyy400, vyy401), cc) → new_esEs8(LT, LT)
new_lt4([], [], cc) → new_esEs8(EQ, LT)
new_lt11(vyy300, vyy40, eg, eh, fa) → new_esEs8(new_compare39(vyy300, vyy40, eg, eh, fa), LT)
new_compare39(vyy300, vyy40, eg, eh, fa) → new_compare210(vyy300, vyy40, new_esEs5(vyy300, vyy40, eg, eh, fa), eg, eh, fa)
new_compare210(vyy300, vyy40, True, eg, eh, fa) → EQ
new_compare210(vyy300, vyy40, False, eg, eh, fa) → new_compare112(vyy300, vyy40, new_ltEs16(vyy300, vyy40, eg, eh, fa), eg, eh, fa)
new_compare112(vyy300, vyy40, True, eg, eh, fa) → LT
new_compare112(vyy300, vyy40, False, eg, eh, fa) → GT
new_lt6(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cad) → new_esEs8(new_compare38(vyy3000, vyy401, vyy400, vyy3001, cad), LT)
new_compare38(Integer(vyy30000), Integer(vyy4010), vyy400, vyy3001, ty_Integer) → new_compare7(Integer(new_primMulInt(vyy30000, vyy4010)), new_sr0(vyy400, vyy3001))
new_compare38(vyy3000, vyy401, vyy400, vyy3001, ty_Int) → new_compare29(vyy3000, vyy401, vyy400, vyy3001)
new_lt5(vyy300, vyy40) → new_esEs8(new_compare35(vyy300, vyy40), LT)
new_compare35(vyy300, vyy40) → new_compare27(vyy300, vyy40, new_esEs12(vyy300, vyy40))
new_compare27(vyy300, vyy40, True) → EQ
new_compare27(vyy300, vyy40, False) → new_compare110(vyy300, vyy40, new_ltEs7(vyy300, vyy40))
new_compare110(vyy300, vyy40, True) → LT
new_compare110(vyy300, vyy40, False) → GT
new_lt17(vyy300, vyy40) → new_esEs8(new_primCmpInt(vyy300, vyy40), LT)
new_lt8(vyy300, vyy40) → new_esEs8(new_compare37(vyy300, vyy40), LT)
new_compare37(vyy300, vyy40) → new_compare24(vyy300, vyy40, new_esEs8(vyy300, vyy40))
new_compare24(vyy300, vyy40, True) → EQ
new_compare24(vyy300, vyy40, False) → new_compare10(vyy300, vyy40, new_ltEs5(vyy300, vyy40))
new_compare10(vyy300, vyy40, True) → LT
new_compare10(vyy300, vyy40, False) → GT
new_lt10(@0, @0) → new_esEs8(EQ, LT)
new_lt19(vyy300, vyy40) → new_esEs8(new_primCmpChar(vyy300, vyy40), LT)
new_lt7(vyy300, vyy40, bba, bbb) → new_esEs8(new_compare33(vyy300, vyy40, bba, bbb), LT)
new_compare33(vyy300, vyy40, bba, bbb) → new_compare23(vyy300, vyy40, new_esEs6(vyy300, vyy40, bba, bbb), bba, bbb)
new_compare23(vyy300, vyy40, False, bba, bbb) → new_compare114(vyy300, vyy40, new_ltEs8(vyy300, vyy40, bba, bbb), bba, bbb)
new_compare23(vyy300, vyy40, True, bba, bbb) → EQ
new_compare114(vyy300, vyy40, True, bba, bbb) → LT
new_compare114(vyy300, vyy40, False, bba, bbb) → GT
new_lt12(vyy300, vyy40) → new_esEs8(new_primCmpFloat(vyy300, vyy40), LT)
new_lt9(vyy300, vyy40, bgc, bgd) → new_esEs8(new_compare34(vyy300, vyy40, bgc, bgd), LT)
new_compare34(vyy300, vyy40, bgc, bgd) → new_compare28(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgc, bgd), bgc, bgd)
new_compare28(vyy300, vyy40, False, bgc, bgd) → new_compare111(vyy300, vyy40, new_ltEs17(vyy300, vyy40, bgc, bgd), bgc, bgd)
new_compare28(vyy300, vyy40, True, bgc, bgd) → EQ
new_compare111(vyy300, vyy40, False, bgc, bgd) → GT
new_compare111(vyy300, vyy40, True, bgc, bgd) → LT
new_lt14(vyy300, vyy40) → new_esEs8(new_primCmpDouble(vyy300, vyy40), LT)
new_lt13(vyy300, vyy40, h) → new_esEs8(new_compare36(vyy300, vyy40, h), LT)
new_lt18(Integer(vyy3000), Integer(vyy400)) → new_esEs8(new_primCmpInt(vyy3000, vyy400), LT)
new_compare13(vyy3000, vyy400) → new_compare37(vyy3000, vyy400)
new_compare26(vyy3000, vyy400, dd, de) → new_compare34(vyy3000, vyy400, dd, de)
new_compare15(vyy3000, vyy400) → new_compare35(vyy3000, vyy400)
new_compare19(vyy3000, vyy400, cf, cg, da) → new_compare39(vyy3000, vyy400, cf, cg, da)
new_compare25(vyy3000, vyy400, db, dc) → new_compare33(vyy3000, vyy400, db, dc)

The set Q consists of the following terms:

new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_ltEs18(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Float)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt19(x0, x1)
new_asAs(True, x0)
new_esEs26(x0, x1, ty_Ordering)
new_lt14(x0, x1)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs13(:(x0, x1), [], x2)
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Nothing, Just(x0), x1)
new_compare34(x0, x1, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs18(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_compare7(Integer(x0), Integer(x1))
new_lt16(x0, x1, ty_@0)
new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_compare39(x0, x1, x2, x3, x4)
new_lt16(x0, x1, ty_Char)
new_esEs12(False, False)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Float)
new_compare26(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare8(:(x0, x1), :(x2, x3), x4)
new_esEs10(Integer(x0), Integer(x1))
new_primMulNat0(Zero, Succ(x0))
new_esEs13([], [], x0)
new_compare0(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1)
new_esEs27(x0, x1, ty_Integer)
new_ltEs13(Nothing, Just(x0), x1)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, ty_Float)
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_@0)
new_esEs8(GT, GT)
new_esEs24(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_lt16(x0, x1, ty_Int)
new_lt16(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs8(LT, LT)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs7(True, True)
new_esEs19(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_sr(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs22(x0, x1, ty_Double)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs7(True, False)
new_ltEs7(False, True)
new_esEs23(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs5(LT, EQ)
new_ltEs5(EQ, LT)
new_compare16(x0, x1, x2)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_asAs(False, x0)
new_primEqNat0(Zero, Zero)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Char)
new_lt15(x0, x1, ty_Ordering)
new_compare211(x0, x1, False, x2)
new_compare211(x0, x1, True, x2)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare33(x0, x1, x2, x3)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt15(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs15(Char(x0), Char(x1))
new_lt15(x0, x1, ty_Integer)
new_compare12(@0, @0)
new_compare18(x0, x1)
new_compare37(x0, x1)
new_esEs26(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_compare110(x0, x1, False)
new_primPlusNat0(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs19(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare0(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Integer)
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt16(x0, x1, ty_Bool)
new_compare0(x0, x1, ty_@0)
new_ltEs9(x0, x1)
new_esEs14(x0, x1)
new_primCompAux00(x0, x1, LT, x2)
new_lt15(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1)
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulNat0(Succ(x0), Succ(x1))
new_compare19(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_compare24(x0, x1, False)
new_ltEs18(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Double)
new_compare14(x0, x1)
new_lt15(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Int)
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Nothing, Nothing, x0)
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_@0)
new_compare0(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare36(x0, x1, x2)
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, ty_Char)
new_primCmpChar(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_Bool)
new_lt4([], :(x0, x1), x2)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare9(x0, x1)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_@0)
new_ltEs13(Nothing, Nothing, x0)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Zero, Zero)
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs13(Just(x0), Nothing, x1)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_primMulNat0(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt7(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare23(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs12(x0, x1)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_compare11(x0, x1)
new_esEs17(@0, @0)
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, ty_Int)
new_lt16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt16(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Ordering)
new_compare23(x0, x1, True, x2, x3)
new_esEs20(x0, x1, ty_Bool)
new_ltEs10(x0, x1)
new_compare8([], :(x0, x1), x2)
new_lt18(Integer(x0), Integer(x1))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Bool)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs12(True, True)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, x1, EQ, ty_Double)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_lt17(x0, x1)
new_compare27(x0, x1, False)
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Int)
new_compare113(x0, x1, False, x2)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, ty_Ordering)
new_compare28(x0, x1, False, x2, x3)
new_lt10(@0, @0)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCompAux00(x0, x1, EQ, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs13([], :(x0, x1), x2)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Int)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt4([], [], x0)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare210(x0, x1, True, x2, x3, x4)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, ty_Integer)
new_lt15(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt15(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare38(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, True, x2, x3)
new_primCompAux00(x0, x1, GT, x2)
new_lt8(x0, x1)
new_esEs19(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Char)
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_compare35(x0, x1)
new_pePe(True, x0)
new_ltEs4(x0, x1)
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_compare0(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_pePe(False, x0)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs22(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, x2, x3)
new_primEqNat0(Zero, Succ(x0))
new_esEs20(x0, x1, ty_Int)
new_compare10(x0, x1, False)
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_compare112(x0, x1, False, x2, x3, x4)
new_compare114(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(x0, x1, ty_Integer)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs21(x0, x1, ty_Ordering)
new_lt15(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_lt20(x0, x1, ty_Integer)
new_lt13(x0, x1, x2)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_Float)
new_lt6(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_compare0(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt16(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs27(x0, x1, ty_Double)
new_esEs18(x0, x1, app(ty_[], x2))
new_lt15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(GT, GT)
new_esEs12(True, False)
new_esEs12(False, True)
new_esEs22(x0, x1, ty_@0)
new_lt16(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare28(x0, x1, True, x2, x3)
new_esEs22(x0, x1, ty_Ordering)
new_lt15(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_Char)
new_compare15(x0, x1)
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_not(True)
new_compare25(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Float)
new_lt16(x0, x1, app(ty_[], x2))
new_lt4(:(x0, x1), [], x2)
new_esEs20(x0, x1, ty_Integer)
new_compare38(x0, x1, x2, x3, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_lt4(:(x0, x1), :(x2, x3), x4)
new_lt15(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, x1, EQ, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_compare114(x0, x1, True, x2, x3)
new_not(False)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare0(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare0(x0, x1, ty_Int)
new_lt16(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_ltEs5(EQ, EQ)
new_compare8([], [], x0)
new_esEs27(x0, x1, ty_Char)
new_primCompAux1(x0, x1, x2, x3, x4)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt15(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Bool)
new_lt16(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs21(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Int)
new_compare24(x0, x1, True)
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_ltEs14(x0, x1, x2)
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Char)
new_compare8(:(x0, x1), [], x2)
new_compare10(x0, x1, True)
new_compare210(x0, x1, False, x2, x3, x4)
new_compare112(x0, x1, True, x2, x3, x4)
new_ltEs6(x0, x1, x2)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare113(x0, x1, True, x2)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, x2, x3, x4)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_@0)
new_sr0(Integer(x0), Integer(x1))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_lt15(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_compare0(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs19(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, True)
new_compare110(x0, x1, True)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_esEs19(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Float)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare111(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Double)
new_ltEs5(LT, LT)
new_esEs26(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(False, False)
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Double)
new_compare13(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
                                    ↳ UsableRulesProof

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

new_foldFM_LE1(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, Branch(vyy6130, vyy6131, vyy6132, vyy6133, vyy6134), vyy614, False, h, ba, bb) → new_foldFM_LE1(vyy84, vyy54, vyy55, vyy6130, vyy6131, vyy6132, vyy6133, vyy6134, new_ltEs17(vyy6130, @2(vyy54, vyy55), h, ba), h, ba, bb)
new_foldFM_LE1(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, Branch(vyy6140, vyy6141, vyy6142, vyy6143, vyy6144), True, h, ba, bb) → new_foldFM_LE(vyy84, vyy54, vyy55, vyy613, h, ba, bb)
new_foldFM_LE1(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, EmptyFM, True, h, ba, bb) → new_foldFM_LE(vyy84, vyy54, vyy55, vyy613, h, ba, bb)
new_foldFM_LE(vyy84, vyy54, vyy55, Branch(vyy6130, vyy6131, vyy6132, vyy6133, vyy6134), h, ba, bb) → new_foldFM_LE1(vyy84, vyy54, vyy55, vyy6130, vyy6131, vyy6132, vyy6133, vyy6134, new_ltEs17(vyy6130, @2(vyy54, vyy55), h, ba), h, ba, bb)
new_foldFM_LE2(vyy610, vyy611, vyy105, vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb) → new_foldFM_LE1(new_keysFM_LE0(vyy610, vyy611, vyy105, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, new_ltEs17(vyy6140, @2(vyy54, vyy55), h, ba), h, ba, bb)
new_foldFM_LE1(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, Branch(vyy6140, vyy6141, vyy6142, vyy6143, vyy6144), True, h, ba, bb) → new_foldFM_LE2(vyy610, vyy611, new_foldFM_LE0(vyy84, vyy54, vyy55, vyy613, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb)

The TRS R consists of the following rules:

new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, gd)) → new_esEs4(vyy3000, vyy400, gd)
new_lt12(vyy300, vyy40) → new_esEs8(new_primCmpFloat(vyy300, vyy40), LT)
new_esEs28(vyy3000, vyy400, app(ty_[], dcb)) → new_esEs13(vyy3000, vyy400, dcb)
new_esEs11(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare35(vyy300, vyy40) → new_compare27(vyy300, vyy40, new_esEs12(vyy300, vyy40))
new_lt15(vyy3010, vyy410, ty_Bool) → new_lt5(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_[], bcg)) → new_ltEs6(vyy3010, vyy410, bcg)
new_esEs18(vyy3002, vyy402, ty_Int) → new_esEs14(vyy3002, vyy402)
new_ltEs18(vyy3012, vyy412, app(app(app(ty_@3, cee), cef), ceg)) → new_ltEs16(vyy3012, vyy412, cee, cef, ceg)
new_esEs13([], [], bc) → True
new_esEs20(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(ty_[], be)) → new_compare8(vyy3000, vyy400, be)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Char) → new_ltEs12(vyy3010, vyy410)
new_esEs4(Nothing, Just(vyy400), gb) → False
new_esEs4(Just(vyy3000), Nothing, gb) → False
new_keysFM_LE0(vyy610, vyy611, vyy104, h, ba, bb) → :(vyy610, vyy104)
new_ltEs5(EQ, GT) → True
new_ltEs19(vyy951, vyy961, ty_Float) → new_ltEs11(vyy951, vyy961)
new_lt15(vyy3010, vyy410, app(ty_[], cbg)) → new_lt4(vyy3010, vyy410, cbg)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Char) → new_ltEs12(vyy3010, vyy410)
new_ltEs6(vyy301, vyy41, hf) → new_not(new_esEs8(new_compare8(vyy301, vyy41, hf), GT))
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Integer, bbb) → new_ltEs4(vyy3010, vyy410)
new_esEs21(vyy3011, vyy411, ty_Int) → new_esEs14(vyy3011, vyy411)
new_lt15(vyy3010, vyy410, ty_Char) → new_lt19(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Double) → new_ltEs15(vyy3010, vyy410)
new_esEs21(vyy3011, vyy411, ty_@0) → new_esEs17(vyy3011, vyy411)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(vyy3000, vyy400, app(ty_[], bhd)) → new_esEs13(vyy3000, vyy400, bhd)
new_esEs6(Right(vyy3000), Right(vyy400), ec, app(app(ty_@2, eh), fa)) → new_esEs7(vyy3000, vyy400, eh, fa)
new_esEs12(True, True) → True
new_esEs20(vyy3000, vyy400, app(ty_Ratio, bhe)) → new_esEs16(vyy3000, vyy400, bhe)
new_esEs20(vyy3000, vyy400, app(ty_Maybe, bgf)) → new_esEs4(vyy3000, vyy400, bgf)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, dh), da) → new_esEs16(vyy3000, vyy400, dh)
new_esEs18(vyy3002, vyy402, ty_Double) → new_esEs9(vyy3002, vyy402)
new_ltEs13(Nothing, Just(vyy410), bhh) → True
new_lt20(vyy950, vyy960, ty_Integer) → new_lt18(vyy950, vyy960)
new_esEs23(vyy950, vyy960, ty_Double) → new_esEs9(vyy950, vyy960)
new_compare8([], [], hf) → EQ
new_ltEs11(vyy301, vyy41) → new_not(new_esEs8(new_compare14(vyy301, vyy41), GT))
new_lt9(vyy300, vyy40, bdh, bea) → new_esEs8(new_compare34(vyy300, vyy40, bdh, bea), LT)
new_compare14(vyy301, vyy41) → new_primCmpFloat(vyy301, vyy41)
new_lt20(vyy950, vyy960, app(ty_Maybe, cff)) → new_lt13(vyy950, vyy960, cff)
new_esEs23(vyy950, vyy960, ty_Bool) → new_esEs12(vyy950, vyy960)
new_esEs22(vyy3010, vyy410, ty_@0) → new_esEs17(vyy3010, vyy410)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_lt19(vyy300, vyy40) → new_esEs8(new_primCmpChar(vyy300, vyy40), LT)
new_ltEs7(True, True) → True
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Bool) → new_ltEs7(vyy3010, vyy410)
new_esEs23(vyy950, vyy960, app(ty_Maybe, cff)) → new_esEs4(vyy950, vyy960, cff)
new_esEs23(vyy950, vyy960, ty_Char) → new_esEs15(vyy950, vyy960)
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Float) → new_esEs11(vyy3000, vyy400)
new_compare9(vyy301, vyy41) → new_primCmpChar(vyy301, vyy41)
new_lt20(vyy950, vyy960, ty_Double) → new_lt14(vyy950, vyy960)
new_esEs20(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs15(vyy3001, vyy401)
new_lt15(vyy3010, vyy410, ty_Float) → new_lt12(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, app(ty_Maybe, cbf)) → new_lt13(vyy3010, vyy410, cbf)
new_esEs13(:(vyy3000, vyy3001), :(vyy400, vyy401), bc) → new_asAs(new_esEs26(vyy3000, vyy400, bc), new_esEs13(vyy3001, vyy401, bc))
new_compare8(:(vyy3010, vyy3011), :(vyy410, vyy411), hf) → new_primCompAux1(vyy3010, vyy410, vyy3011, vyy411, hf)
new_compare25(vyy3000, vyy400, cb, cc) → new_compare33(vyy3000, vyy400, cb, cc)
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_Ratio, cac)) → new_ltEs14(vyy3010, vyy410, cac)
new_lt15(vyy3010, vyy410, ty_@0) → new_lt10(vyy3010, vyy410)
new_lt20(vyy950, vyy960, app(app(ty_@2, cgf), cgg)) → new_lt9(vyy950, vyy960, cgf, cgg)
new_ltEs5(EQ, LT) → False
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Char, bbb) → new_ltEs12(vyy3010, vyy410)
new_esEs23(vyy950, vyy960, ty_Integer) → new_esEs10(vyy950, vyy960)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, da) → new_esEs14(vyy3000, vyy400)
new_lt20(vyy950, vyy960, ty_Float) → new_lt12(vyy950, vyy960)
new_esEs21(vyy3011, vyy411, app(app(ty_Either, cdf), cdg)) → new_esEs6(vyy3011, vyy411, cdf, cdg)
new_esEs18(vyy3002, vyy402, ty_Float) → new_esEs11(vyy3002, vyy402)
new_lt15(vyy3010, vyy410, ty_Integer) → new_lt18(vyy3010, vyy410)
new_esEs19(vyy3001, vyy401, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs5(vyy3001, vyy401, bfe, bff, bfg)
new_compare0(vyy3000, vyy400, app(app(ty_Either, cb), cc)) → new_compare25(vyy3000, vyy400, cb, cc)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, bd)) → new_esEs4(vyy3000, vyy400, bd)
new_lt7(vyy300, vyy40, ec, da) → new_esEs8(new_compare33(vyy300, vyy40, ec, da), LT)
new_compare211(vyy300, vyy40, False, gb) → new_compare113(vyy300, vyy40, new_ltEs13(vyy300, vyy40, gb), gb)
new_esEs22(vyy3010, vyy410, ty_Integer) → new_esEs10(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs5(vyy3000, vyy400, dbe, dbf, dbg)
new_esEs18(vyy3002, vyy402, ty_Integer) → new_esEs10(vyy3002, vyy402)
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Int) → new_compare11(new_sr(vyy3010, vyy411), new_sr(vyy410, vyy3011))
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, da) → new_esEs11(vyy3000, vyy400)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(ty_@2, bdf), bdg)) → new_ltEs17(vyy3010, vyy410, bdf, bdg)
new_esEs17(@0, @0) → True
new_ltEs7(True, False) → False
new_pePe(False, vyy139) → vyy139
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Double) → new_ltEs15(vyy3010, vyy410)
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_esEs18(vyy3002, vyy402, app(app(ty_@2, bef), beg)) → new_esEs7(vyy3002, vyy402, bef, beg)
new_lt18(Integer(vyy3000), Integer(vyy400)) → new_esEs8(new_primCmpInt(vyy3000, vyy400), LT)
new_ltEs7(False, True) → True
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Int) → new_ltEs9(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(ty_@2, bcc), bcd), bbb) → new_ltEs17(vyy3010, vyy410, bcc, bcd)
new_lt16(vyy3011, vyy411, ty_Bool) → new_lt5(vyy3011, vyy411)
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_foldFM_LE10(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, Branch(vyy6140, vyy6141, vyy6142, vyy6143, vyy6144), True, h, ba, bb) → new_foldFM_LE20(vyy610, vyy611, new_foldFM_LE0(vyy84, vyy54, vyy55, vyy613, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb)
new_esEs22(vyy3010, vyy410, ty_Ordering) → new_esEs8(vyy3010, vyy410)
new_esEs18(vyy3002, vyy402, ty_Bool) → new_esEs12(vyy3002, vyy402)
new_compare8(:(vyy3010, vyy3011), [], hf) → GT
new_foldFM_LE10(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, vyy614, False, h, ba, bb) → new_foldFM_LE0(vyy84, vyy54, vyy55, vyy613, h, ba, bb)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dcc)) → new_esEs16(vyy3000, vyy400, dcc)
new_lt4(:(vyy3000, vyy3001), :(vyy400, vyy401), bc) → new_esEs8(new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, bc), LT)
new_lt15(vyy3010, vyy410, app(app(ty_Either, ccd), cce)) → new_lt7(vyy3010, vyy410, ccd, cce)
new_lt20(vyy950, vyy960, app(app(ty_Either, cgd), cge)) → new_lt7(vyy950, vyy960, cgd, cge)
new_esEs18(vyy3002, vyy402, app(app(ty_Either, bfb), bfc)) → new_esEs6(vyy3002, vyy402, bfb, bfc)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Int, bbb) → new_ltEs9(vyy3010, vyy410)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Int) → new_esEs14(vyy3000, vyy400)
new_compare113(vyy300, vyy40, True, gb) → LT
new_ltEs13(Nothing, Nothing, bhh) → True
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Integer) → new_ltEs4(vyy3010, vyy410)
new_compare16(vyy3000, vyy400, bd) → new_compare36(vyy3000, vyy400, bd)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bbb) → new_ltEs13(vyy3010, vyy410, bbc)
new_lt10(@0, @0) → new_esEs8(EQ, LT)
new_esEs8(LT, LT) → True
new_esEs6(Right(vyy3000), Left(vyy400), ec, da) → False
new_esEs6(Left(vyy3000), Right(vyy400), ec, da) → False
new_esEs19(vyy3001, vyy401, app(ty_Maybe, bfd)) → new_esEs4(vyy3001, vyy401, bfd)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_@0) → new_ltEs10(vyy3010, vyy410)
new_lt20(vyy950, vyy960, ty_Char) → new_lt19(vyy950, vyy960)
new_compare29(vyy3000, vyy400, vyy3001, vyy401) → new_primCmpInt(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs18(vyy3012, vyy412, ty_Integer) → new_ltEs4(vyy3012, vyy412)
new_esEs19(vyy3001, vyy401, ty_Bool) → new_esEs12(vyy3001, vyy401)
new_esEs18(vyy3002, vyy402, app(ty_[], beh)) → new_esEs13(vyy3002, vyy402, beh)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs11(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, EQ, app(ty_[], baa)) → new_compare8(vyy163, vyy164, baa)
new_esEs23(vyy950, vyy960, ty_Int) → new_esEs14(vyy950, vyy960)
new_esEs18(vyy3002, vyy402, app(ty_Ratio, bfa)) → new_esEs16(vyy3002, vyy402, bfa)
new_foldFM_LE20(vyy610, vyy611, vyy105, vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb) → new_foldFM_LE10(new_keysFM_LE0(vyy610, vyy611, vyy105, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, new_ltEs17(vyy6140, @2(vyy54, vyy55), h, ba), h, ba, bb)
new_pePe(True, vyy139) → True
new_primEqNat0(Zero, Zero) → True
new_esEs23(vyy950, vyy960, app(app(ty_Either, cgd), cge)) → new_esEs6(vyy950, vyy960, cgd, cge)
new_compare111(vyy300, vyy40, False, bdh, bea) → GT
new_ltEs19(vyy951, vyy961, app(app(ty_Either, chf), chg)) → new_ltEs8(vyy951, vyy961, chf, chg)
new_primCompAux00(vyy163, vyy164, EQ, ty_@0) → new_compare12(vyy163, vyy164)
new_esEs22(vyy3010, vyy410, app(app(ty_@2, ccf), ccg)) → new_esEs7(vyy3010, vyy410, ccf, ccg)
new_esEs6(Right(vyy3000), Right(vyy400), ec, app(app(ty_Either, fd), ff)) → new_esEs6(vyy3000, vyy400, fd, ff)
new_esEs15(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs20(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, EQ, ty_Ordering) → new_compare13(vyy163, vyy164)
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dcd), dce)) → new_esEs6(vyy3000, vyy400, dcd, dce)
new_esEs18(vyy3002, vyy402, app(app(app(ty_@3, bec), bed), bee)) → new_esEs5(vyy3002, vyy402, bec, bed, bee)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, da) → new_esEs10(vyy3000, vyy400)
new_esEs22(vyy3010, vyy410, ty_Double) → new_esEs9(vyy3010, vyy410)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs8(GT, GT) → True
new_compare113(vyy300, vyy40, False, gb) → GT
new_compare39(vyy300, vyy40, fg, fh, ga) → new_compare210(vyy300, vyy40, new_esEs5(vyy300, vyy40, fg, fh, ga), fg, fh, ga)
new_primPlusNat0(Succ(vyy1730), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1730, vyy40100)))
new_ltEs15(vyy301, vyy41) → new_not(new_esEs8(new_compare18(vyy301, vyy41), GT))
new_compare0(vyy3000, vyy400, ty_@0) → new_compare12(vyy3000, vyy400)
new_lt16(vyy3011, vyy411, ty_Int) → new_lt17(vyy3011, vyy411)
new_esEs12(False, False) → True
new_ltEs5(LT, LT) → True
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_ltEs19(vyy951, vyy961, app(ty_Ratio, chb)) → new_ltEs14(vyy951, vyy961, chb)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs10(vyy301, vyy41) → new_not(new_esEs8(new_compare12(vyy301, vyy41), GT))
new_compare211(vyy300, vyy40, True, gb) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, bbf), bbg), bbh), bbb) → new_ltEs16(vyy3010, vyy410, bbf, bbg, bbh)
new_ltEs19(vyy951, vyy961, app(app(ty_@2, chh), daa)) → new_ltEs17(vyy951, vyy961, chh, daa)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Bool) → new_ltEs7(vyy3010, vyy410)
new_esEs20(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_[], be)) → new_esEs13(vyy3000, vyy400, be)
new_esEs23(vyy950, vyy960, ty_Ordering) → new_esEs8(vyy950, vyy960)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_primPlusNat1(Succ(vyy17300), Zero) → Succ(vyy17300)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(app(app(ty_@3, bg), bh), ca)) → new_compare19(vyy3000, vyy400, bg, bh, ca)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Float) → new_ltEs11(vyy3010, vyy410)
new_esEs21(vyy3011, vyy411, ty_Char) → new_esEs15(vyy3011, vyy411)
new_lt13(vyy300, vyy40, gb) → new_esEs8(new_compare36(vyy300, vyy40, gb), LT)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dbd)) → new_esEs4(vyy3000, vyy400, dbd)
new_lt15(vyy3010, vyy410, app(app(ty_@2, ccf), ccg)) → new_lt9(vyy3010, vyy410, ccf, ccg)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primCompAux00(vyy163, vyy164, EQ, ty_Float) → new_compare14(vyy163, vyy164)
new_esEs21(vyy3011, vyy411, app(app(ty_@2, cdh), cea)) → new_esEs7(vyy3011, vyy411, cdh, cea)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_ltEs19(vyy951, vyy961, ty_Integer) → new_ltEs4(vyy951, vyy961)
new_compare19(vyy3000, vyy400, bg, bh, ca) → new_compare39(vyy3000, vyy400, bg, bh, ca)
new_ltEs19(vyy951, vyy961, ty_Char) → new_ltEs12(vyy951, vyy961)
new_esEs8(EQ, EQ) → True
new_lt20(vyy950, vyy960, ty_@0) → new_lt10(vyy950, vyy960)
new_lt15(vyy3010, vyy410, app(app(app(ty_@3, cca), ccb), ccc)) → new_lt11(vyy3010, vyy410, cca, ccb, ccc)
new_lt20(vyy950, vyy960, ty_Ordering) → new_lt8(vyy950, vyy960)
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(ty_@2, cba), cbb)) → new_ltEs17(vyy3010, vyy410, cba, cbb)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_@0) → new_ltEs10(vyy3010, vyy410)
new_esEs20(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs22(vyy3010, vyy410, app(app(app(ty_@3, cca), ccb), ccc)) → new_esEs5(vyy3010, vyy410, cca, ccb, ccc)
new_foldFM_LE0(vyy84, vyy54, vyy55, Branch(vyy6130, vyy6131, vyy6132, vyy6133, vyy6134), h, ba, bb) → new_foldFM_LE10(vyy84, vyy54, vyy55, vyy6130, vyy6131, vyy6132, vyy6133, vyy6134, new_ltEs17(vyy6130, @2(vyy54, vyy55), h, ba), h, ba, bb)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_lt14(vyy300, vyy40) → new_esEs8(new_primCmpDouble(vyy300, vyy40), LT)
new_compare23(vyy300, vyy40, False, ec, da) → new_compare114(vyy300, vyy40, new_ltEs8(vyy300, vyy40, ec, da), ec, da)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dbh), dca)) → new_esEs7(vyy3000, vyy400, dbh, dca)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs5(EQ, EQ) → True
new_esEs22(vyy3010, vyy410, app(ty_Maybe, cbf)) → new_esEs4(vyy3010, vyy410, cbf)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, hd), he)) → new_esEs6(vyy3000, vyy400, hd, he)
new_ltEs18(vyy3012, vyy412, ty_@0) → new_ltEs10(vyy3012, vyy412)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, db), dc), dd), da) → new_esEs5(vyy3000, vyy400, db, dc, dd)
new_esEs19(vyy3001, vyy401, app(app(ty_Either, bgd), bge)) → new_esEs6(vyy3001, vyy401, bgd, bge)
new_esEs7(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bdh, bea) → new_asAs(new_esEs28(vyy3000, vyy400, bdh), new_esEs27(vyy3001, vyy401, bea))
new_lt16(vyy3011, vyy411, app(ty_Ratio, cdb)) → new_lt6(vyy3011, vyy411, cdb)
new_esEs6(Right(vyy3000), Right(vyy400), ec, app(ty_Maybe, ed)) → new_esEs4(vyy3000, vyy400, ed)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Int) → new_ltEs9(vyy3010, vyy410)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_Maybe, bcf)) → new_ltEs13(vyy3010, vyy410, bcf)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ge), gf), gg)) → new_esEs5(vyy3000, vyy400, ge, gf, gg)
new_lt16(vyy3011, vyy411, ty_Double) → new_lt14(vyy3011, vyy411)
new_esEs22(vyy3010, vyy410, ty_Bool) → new_esEs12(vyy3010, vyy410)
new_lt5(vyy300, vyy40) → new_esEs8(new_compare35(vyy300, vyy40), LT)
new_lt16(vyy3011, vyy411, ty_Float) → new_lt12(vyy3011, vyy411)
new_lt15(vyy3010, vyy410, app(ty_Ratio, cbh)) → new_lt6(vyy3010, vyy410, cbh)
new_compare114(vyy300, vyy40, True, ec, da) → LT
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, cad), cae), caf)) → new_ltEs16(vyy3010, vyy410, cad, cae, caf)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Integer) → new_ltEs4(vyy3010, vyy410)
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, dac), dad), dae)) → new_esEs5(vyy3001, vyy401, dac, dad, dae)
new_esEs22(vyy3010, vyy410, ty_Char) → new_esEs15(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
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_lt20(vyy950, vyy960, ty_Int) → new_lt17(vyy950, vyy960)
new_ltEs18(vyy3012, vyy412, ty_Float) → new_ltEs11(vyy3012, vyy412)
new_ltEs5(GT, LT) → False
new_esEs23(vyy950, vyy960, ty_@0) → new_esEs17(vyy950, vyy960)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, da) → new_esEs17(vyy3000, vyy400)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, da) → new_esEs12(vyy3000, vyy400)
new_lt20(vyy950, vyy960, ty_Bool) → new_lt5(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(ty_Ratio, cfh)) → new_lt6(vyy950, vyy960, cfh)
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Integer) → new_compare7(new_sr0(vyy3010, vyy411), new_sr0(vyy410, vyy3011))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_lt4(:(vyy3000, vyy3001), [], bc) → new_esEs8(GT, LT)
new_compare210(vyy300, vyy40, True, fg, fh, ga) → EQ
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs9(vyy3001, vyy401)
new_compare28(vyy300, vyy40, False, bdh, bea) → new_compare111(vyy300, vyy40, new_ltEs17(vyy300, vyy40, bdh, bea), bdh, bea)
new_compare0(vyy3000, vyy400, ty_Char) → new_compare9(vyy3000, vyy400)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Bool, bbb) → new_ltEs7(vyy3010, vyy410)
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_primPlusNat1(Succ(vyy17300), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy17300, vyy401000)))
new_compare28(vyy300, vyy40, True, bdh, bea) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_Ratio, bch)) → new_ltEs14(vyy3010, vyy410, bch)
new_compare33(vyy300, vyy40, ec, da) → new_compare23(vyy300, vyy40, new_esEs6(vyy300, vyy40, ec, da), ec, da)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_lt15(vyy3010, vyy410, ty_Double) → new_lt14(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Float) → new_ltEs11(vyy3010, vyy410)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, bf)) → new_esEs16(vyy3000, vyy400, bf)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, cg), da) → new_esEs4(vyy3000, vyy400, cg)
new_esEs21(vyy3011, vyy411, app(ty_[], cda)) → new_esEs13(vyy3011, vyy411, cda)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_compare0(vyy3000, vyy400, ty_Bool) → new_compare15(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_ltEs18(vyy3012, vyy412, ty_Int) → new_ltEs9(vyy3012, vyy412)
new_compare24(vyy300, vyy40, True) → EQ
new_esEs27(vyy3001, vyy401, app(app(ty_@2, daf), dag)) → new_esEs7(vyy3001, vyy401, daf, dag)
new_lt16(vyy3011, vyy411, app(app(ty_@2, cdh), cea)) → new_lt9(vyy3011, vyy411, cdh, cea)
new_ltEs16(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), cbc, cbd, cbe) → new_pePe(new_lt15(vyy3010, vyy410, cbc), new_asAs(new_esEs22(vyy3010, vyy410, cbc), new_pePe(new_lt16(vyy3011, vyy411, cbd), new_asAs(new_esEs21(vyy3011, vyy411, cbd), new_ltEs18(vyy3012, vyy412, cbe)))))
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs19(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_lt6(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cf) → new_esEs8(new_compare38(vyy3000, vyy401, vyy400, vyy3001, cf), LT)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, app(ty_Ratio, dba)) → new_esEs16(vyy3001, vyy401, dba)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, de), df), da) → new_esEs7(vyy3000, vyy400, de, df)
new_esEs23(vyy950, vyy960, ty_Float) → new_esEs11(vyy950, vyy960)
new_compare114(vyy300, vyy40, False, ec, da) → GT
new_not(False) → True
new_compare12(@0, @0) → EQ
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(ty_Either, bdd), bde)) → new_ltEs8(vyy3010, vyy410, bdd, bde)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, ea), eb), da) → new_esEs6(vyy3000, vyy400, ea, eb)
new_ltEs18(vyy3012, vyy412, app(ty_Ratio, ced)) → new_ltEs14(vyy3012, vyy412, ced)
new_lt15(vyy3010, vyy410, ty_Int) → new_lt17(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(app(ty_Either, ceh), cfa)) → new_ltEs8(vyy3012, vyy412, ceh, cfa)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(ty_Either, cag), cah)) → new_ltEs8(vyy3010, vyy410, cag, cah)
new_esEs19(vyy3001, vyy401, app(app(ty_@2, bfh), bga)) → new_esEs7(vyy3001, vyy401, bfh, bga)
new_esEs22(vyy3010, vyy410, ty_Float) → new_esEs11(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_Ratio, bbe), bbb) → new_ltEs14(vyy3010, vyy410, bbe)
new_primCompAux00(vyy163, vyy164, EQ, app(app(app(ty_@3, bac), bad), bae)) → new_compare19(vyy163, vyy164, bac, bad, bae)
new_lt11(vyy300, vyy40, fg, fh, ga) → new_esEs8(new_compare39(vyy300, vyy40, fg, fh, ga), LT)
new_esEs20(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(app(ty_@3, bda), bdb), bdc)) → new_ltEs16(vyy3010, vyy410, bda, bdb, bdc)
new_compare26(vyy3000, vyy400, cd, ce) → new_compare34(vyy3000, vyy400, cd, ce)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs18(vyy3002, vyy402, app(ty_Maybe, beb)) → new_esEs4(vyy3002, vyy402, beb)
new_lt4([], :(vyy400, vyy401), bc) → new_esEs8(LT, LT)
new_esEs27(vyy3001, vyy401, app(app(ty_Either, dbb), dbc)) → new_esEs6(vyy3001, vyy401, dbb, dbc)
new_esEs22(vyy3010, vyy410, app(ty_[], cbg)) → new_esEs13(vyy3010, vyy410, cbg)
new_lt16(vyy3011, vyy411, ty_Integer) → new_lt18(vyy3011, vyy411)
new_esEs20(vyy3000, vyy400, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs5(vyy3000, vyy400, bgg, bgh, bha)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_ltEs19(vyy951, vyy961, ty_Int) → new_ltEs9(vyy951, vyy961)
new_ltEs4(vyy301, vyy41) → new_not(new_esEs8(new_compare7(vyy301, vyy41), GT))
new_compare0(vyy3000, vyy400, app(app(ty_@2, cd), ce)) → new_compare26(vyy3000, vyy400, cd, ce)
new_esEs21(vyy3011, vyy411, app(app(app(ty_@3, cdc), cdd), cde)) → new_esEs5(vyy3011, vyy411, cdc, cdd, cde)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_compare24(vyy300, vyy40, False) → new_compare10(vyy300, vyy40, new_ltEs5(vyy300, vyy40))
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs5(LT, GT) → True
new_ltEs14(vyy301, vyy41, gc) → new_not(new_esEs8(new_compare17(vyy301, vyy41, gc), GT))
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare110(vyy300, vyy40, True) → LT
new_lt20(vyy950, vyy960, app(app(app(ty_@3, cga), cgb), cgc)) → new_lt11(vyy950, vyy960, cga, cgb, cgc)
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(ty_Either, bca), bcb), bbb) → new_ltEs8(vyy3010, vyy410, bca, bcb)
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_esEs26(vyy3000, vyy400, app(app(ty_@2, cd), ce)) → new_esEs7(vyy3000, vyy400, cd, ce)
new_compare110(vyy300, vyy40, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs21(vyy3011, vyy411, ty_Integer) → new_esEs10(vyy3011, vyy411)
new_esEs10(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs4(Nothing, Nothing, gb) → True
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, hc)) → new_esEs16(vyy3000, vyy400, hc)
new_lt16(vyy3011, vyy411, ty_@0) → new_lt10(vyy3011, vyy411)
new_esEs20(vyy3000, vyy400, app(app(ty_Either, bhf), bhg)) → new_esEs6(vyy3000, vyy400, bhf, bhg)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_@0, bbb) → new_ltEs10(vyy3010, vyy410)
new_esEs18(vyy3002, vyy402, ty_@0) → new_esEs17(vyy3002, vyy402)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Float, bbb) → new_ltEs11(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(app(ty_@2, cfb), cfc)) → new_ltEs17(vyy3012, vyy412, cfb, cfc)
new_lt16(vyy3011, vyy411, app(ty_[], cda)) → new_lt4(vyy3011, vyy411, cda)
new_esEs27(vyy3001, vyy401, app(ty_Maybe, dab)) → new_esEs4(vyy3001, vyy401, dab)
new_compare0(vyy3000, vyy400, app(ty_Ratio, bf)) → new_compare17(vyy3000, vyy400, bf)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], hb)) → new_esEs13(vyy3000, vyy400, hb)
new_ltEs19(vyy951, vyy961, ty_Bool) → new_ltEs7(vyy951, vyy961)
new_compare15(vyy3000, vyy400) → new_compare35(vyy3000, vyy400)
new_compare112(vyy300, vyy40, True, fg, fh, ga) → LT
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_compare23(vyy300, vyy40, True, ec, da) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, da) → new_esEs8(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs17(vyy3001, vyy401)
new_primCompAux00(vyy163, vyy164, EQ, ty_Char) → new_compare9(vyy163, vyy164)
new_compare0(vyy3000, vyy400, ty_Ordering) → new_compare13(vyy3000, vyy400)
new_esEs19(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, da) → new_esEs9(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_ltEs18(vyy3012, vyy412, app(ty_[], cec)) → new_ltEs6(vyy3012, vyy412, cec)
new_esEs21(vyy3011, vyy411, app(ty_Maybe, cch)) → new_esEs4(vyy3011, vyy411, cch)
new_esEs23(vyy950, vyy960, app(ty_Ratio, cfh)) → new_esEs16(vyy950, vyy960, cfh)
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_Maybe, caa)) → new_ltEs13(vyy3010, vyy410, caa)
new_primCmpFloat(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_esEs22(vyy3010, vyy410, app(ty_Ratio, cbh)) → new_esEs16(vyy3010, vyy410, cbh)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs21(vyy3011, vyy411, ty_Double) → new_esEs9(vyy3011, vyy411)
new_ltEs13(Just(vyy3010), Nothing, bhh) → False
new_esEs19(vyy3001, vyy401, app(ty_Ratio, bgc)) → new_esEs16(vyy3001, vyy401, bgc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Char) → new_esEs15(vyy3000, vyy400)
new_lt16(vyy3011, vyy411, ty_Ordering) → new_lt8(vyy3011, vyy411)
new_ltEs12(vyy301, vyy41) → new_not(new_esEs8(new_compare9(vyy301, vyy41), GT))
new_compare8([], :(vyy410, vyy411), hf) → LT
new_esEs19(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), ec, app(ty_[], fb)) → new_esEs13(vyy3000, vyy400, fb)
new_asAs(False, vyy158) → False
new_lt8(vyy300, vyy40) → new_esEs8(new_compare37(vyy300, vyy40), LT)
new_ltEs18(vyy3012, vyy412, ty_Double) → new_ltEs15(vyy3012, vyy412)
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, EQ, app(app(ty_Either, baf), bag)) → new_compare25(vyy163, vyy164, baf, bag)
new_lt16(vyy3011, vyy411, ty_Char) → new_lt19(vyy3011, vyy411)
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_esEs13(:(vyy3000, vyy3001), [], bc) → False
new_esEs13([], :(vyy400, vyy401), bc) → False
new_lt16(vyy3011, vyy411, app(app(app(ty_@3, cdc), cdd), cde)) → new_lt11(vyy3011, vyy411, cdc, cdd, cde)
new_primCompAux00(vyy163, vyy164, EQ, ty_Bool) → new_compare15(vyy163, vyy164)
new_ltEs18(vyy3012, vyy412, ty_Ordering) → new_ltEs5(vyy3012, vyy412)
new_esEs21(vyy3011, vyy411, ty_Ordering) → new_esEs8(vyy3011, vyy411)
new_ltEs5(LT, EQ) → True
new_compare38(Integer(vyy30000), Integer(vyy4010), vyy400, vyy3001, ty_Integer) → new_compare7(Integer(new_primMulInt(vyy30000, vyy4010)), new_sr0(vyy400, vyy3001))
new_primCompAux00(vyy163, vyy164, EQ, app(ty_Ratio, bab)) → new_compare17(vyy163, vyy164, bab)
new_esEs6(Right(vyy3000), Right(vyy400), ec, app(ty_Ratio, fc)) → new_esEs16(vyy3000, vyy400, fc)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, da) → new_esEs15(vyy3000, vyy400)
new_esEs23(vyy950, vyy960, app(app(ty_@2, cgf), cgg)) → new_esEs7(vyy950, vyy960, cgf, cgg)
new_ltEs19(vyy951, vyy961, ty_@0) → new_ltEs10(vyy951, vyy961)
new_compare0(vyy3000, vyy400, ty_Float) → new_compare14(vyy3000, vyy400)
new_lt20(vyy950, vyy960, app(ty_[], cfg)) → new_lt4(vyy950, vyy960, cfg)
new_lt16(vyy3011, vyy411, app(app(ty_Either, cdf), cdg)) → new_lt7(vyy3011, vyy411, cdf, cdg)
new_primCompAux00(vyy163, vyy164, EQ, app(ty_Maybe, hh)) → new_compare16(vyy163, vyy164, hh)
new_ltEs8(Right(vyy3010), Left(vyy410), bce, bbb) → False
new_compare34(vyy300, vyy40, bdh, bea) → new_compare28(vyy300, vyy40, new_esEs7(vyy300, vyy40, bdh, bea), bdh, bea)
new_esEs18(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_esEs19(vyy3001, vyy401, ty_Double) → new_esEs9(vyy3001, vyy401)
new_esEs18(vyy3002, vyy402, ty_Char) → new_esEs15(vyy3002, vyy402)
new_compare0(vyy3000, vyy400, app(ty_Maybe, bd)) → new_compare16(vyy3000, vyy400, bd)
new_primCompAux00(vyy163, vyy164, LT, hg) → LT
new_primCompAux00(vyy163, vyy164, GT, hg) → GT
new_ltEs18(vyy3012, vyy412, ty_Char) → new_ltEs12(vyy3012, vyy412)
new_esEs16(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cf) → new_asAs(new_esEs25(vyy3000, vyy400, cf), new_esEs24(vyy3001, vyy401, cf))
new_compare13(vyy3000, vyy400) → new_compare37(vyy3000, vyy400)
new_ltEs18(vyy3012, vyy412, app(ty_Maybe, ceb)) → new_ltEs13(vyy3012, vyy412, ceb)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Double, bbb) → new_ltEs15(vyy3010, vyy410)
new_compare112(vyy300, vyy40, False, fg, fh, ga) → GT
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_compare27(vyy300, vyy40, True) → EQ
new_esEs21(vyy3011, vyy411, app(ty_Ratio, cdb)) → new_esEs16(vyy3011, vyy411, cdb)
new_esEs12(False, True) → False
new_esEs12(True, False) → False
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Double) → new_esEs9(vyy3000, vyy400)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Ordering, bbb) → new_ltEs5(vyy3010, vyy410)
new_lt16(vyy3011, vyy411, app(ty_Maybe, cch)) → new_lt13(vyy3011, vyy411, cch)
new_compare0(vyy3000, vyy400, ty_Integer) → new_compare7(vyy3000, vyy400)
new_compare11(vyy301, vyy41) → new_primCmpInt(vyy301, vyy41)
new_compare0(vyy3000, vyy400, ty_Double) → new_compare18(vyy3000, vyy400)
new_esEs14(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs12(vyy3001, vyy401)
new_compare37(vyy300, vyy40) → new_compare24(vyy300, vyy40, new_esEs8(vyy300, vyy40))
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_@0) → new_esEs17(vyy3000, vyy400)
new_lt4([], [], bc) → new_esEs8(EQ, LT)
new_foldFM_LE10(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, EmptyFM, True, h, ba, bb) → new_foldFM_LE3(vyy610, vyy611, new_foldFM_LE0(vyy84, vyy54, vyy55, vyy613, h, ba, bb), vyy54, vyy55, h, ba, bb)
new_compare27(vyy300, vyy40, False) → new_compare110(vyy300, vyy40, new_ltEs7(vyy300, vyy40))
new_ltEs9(vyy301, vyy41) → new_not(new_esEs8(new_compare11(vyy301, vyy41), GT))
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_[], cab)) → new_ltEs6(vyy3010, vyy410, cab)
new_ltEs19(vyy951, vyy961, app(ty_Maybe, cgh)) → new_ltEs13(vyy951, vyy961, cgh)
new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, bc) → new_primCompAux00(vyy3001, vyy401, new_compare0(vyy3000, vyy400, bc), app(ty_[], bc))
new_esEs9(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs19(vyy3001, vyy401, ty_Char) → new_esEs15(vyy3001, vyy401)
new_esEs20(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_compare7(Integer(vyy3010), Integer(vyy410)) → new_primCmpInt(vyy3010, vyy410)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], dg), da) → new_esEs13(vyy3000, vyy400, dg)
new_esEs22(vyy3010, vyy410, app(app(ty_Either, ccd), cce)) → new_esEs6(vyy3010, vyy410, ccd, cce)
new_ltEs19(vyy951, vyy961, app(ty_[], cha)) → new_ltEs6(vyy951, vyy961, cha)
new_ltEs19(vyy951, vyy961, app(app(app(ty_@3, chc), chd), che)) → new_ltEs16(vyy951, vyy961, chc, chd, che)
new_compare36(vyy300, vyy40, gb) → new_compare211(vyy300, vyy40, new_esEs4(vyy300, vyy40, gb), gb)
new_compare210(vyy300, vyy40, False, fg, fh, ga) → new_compare112(vyy300, vyy40, new_ltEs16(vyy300, vyy40, fg, fh, ga), fg, fh, ga)
new_ltEs7(False, False) → True
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, gh), ha)) → new_esEs7(vyy3000, vyy400, gh, ha)
new_lt15(vyy3010, vyy410, ty_Ordering) → new_lt8(vyy3010, vyy410)
new_primCmpDouble(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_esEs21(vyy3011, vyy411, ty_Float) → new_esEs11(vyy3011, vyy411)
new_ltEs19(vyy951, vyy961, ty_Double) → new_ltEs15(vyy951, vyy961)
new_primCompAux00(vyy163, vyy164, EQ, ty_Int) → new_compare11(vyy163, vyy164)
new_esEs22(vyy3010, vyy410, ty_Int) → new_esEs14(vyy3010, vyy410)
new_esEs20(vyy3000, vyy400, app(app(ty_@2, bhb), bhc)) → new_esEs7(vyy3000, vyy400, bhb, bhc)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, cb), cc)) → new_esEs6(vyy3000, vyy400, cb, cc)
new_ltEs19(vyy951, vyy961, ty_Ordering) → new_ltEs5(vyy951, vyy961)
new_primPlusNat1(Zero, Zero) → Zero
new_compare111(vyy300, vyy40, True, bdh, bea) → LT
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), fg, fh, ga) → new_asAs(new_esEs20(vyy3000, vyy400, fg), new_asAs(new_esEs19(vyy3001, vyy401, fh), new_esEs18(vyy3002, vyy402, ga)))
new_esEs19(vyy3001, vyy401, ty_@0) → new_esEs17(vyy3001, vyy401)
new_asAs(True, vyy158) → vyy158
new_primCmpChar(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, bg), bh), ca)) → new_esEs5(vyy3000, vyy400, bg, bh, ca)
new_esEs27(vyy3001, vyy401, app(ty_[], dah)) → new_esEs13(vyy3001, vyy401, dah)
new_ltEs5(GT, GT) → True
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Ordering) → new_ltEs5(vyy3010, vyy410)
new_primCompAux00(vyy163, vyy164, EQ, ty_Integer) → new_compare7(vyy163, vyy164)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_[], bbd), bbb) → new_ltEs6(vyy3010, vyy410, bbd)
new_compare38(vyy3000, vyy401, vyy400, vyy3001, ty_Int) → new_compare29(vyy3000, vyy401, vyy400, vyy3001)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs15(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, EQ, app(app(ty_@2, bah), bba)) → new_compare26(vyy163, vyy164, bah, bba)
new_ltEs18(vyy3012, vyy412, ty_Bool) → new_ltEs7(vyy3012, vyy412)
new_ltEs17(@2(vyy950, vyy951), @2(vyy960, vyy961), cfd, cfe) → new_pePe(new_lt20(vyy950, vyy960, cfd), new_asAs(new_esEs23(vyy950, vyy960, cfd), new_ltEs19(vyy951, vyy961, cfe)))
new_esEs23(vyy950, vyy960, app(app(app(ty_@3, cga), cgb), cgc)) → new_esEs5(vyy950, vyy960, cga, cgb, cgc)
new_esEs19(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs8(Left(vyy3010), Right(vyy410), bce, bbb) → True
new_compare18(vyy301, vyy41) → new_primCmpDouble(vyy301, vyy41)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs9(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, EQ, ty_Double) → new_compare18(vyy163, vyy164)
new_compare10(vyy300, vyy40, True) → LT
new_lt17(vyy300, vyy40) → new_esEs8(new_primCmpInt(vyy300, vyy40), LT)
new_esEs19(vyy3001, vyy401, app(ty_[], bgb)) → new_esEs13(vyy3001, vyy401, bgb)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs21(vyy3011, vyy411, ty_Bool) → new_esEs12(vyy3011, vyy411)
new_compare10(vyy300, vyy40, False) → GT
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Ordering) → new_ltEs5(vyy3010, vyy410)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), ec, app(app(app(ty_@3, ee), ef), eg)) → new_esEs5(vyy3000, vyy400, ee, ef, eg)
new_compare0(vyy3000, vyy400, ty_Int) → new_compare11(vyy3000, vyy400)
new_ltEs5(GT, EQ) → False
new_foldFM_LE3(vyy610, vyy611, vyy104, vyy54, vyy55, h, ba, bb) → new_keysFM_LE0(vyy610, vyy611, vyy104, h, ba, bb)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs23(vyy950, vyy960, app(ty_[], cfg)) → new_esEs13(vyy950, vyy960, cfg)
new_foldFM_LE0(vyy84, vyy54, vyy55, EmptyFM, h, ba, bb) → vyy84
new_not(True) → False

The set Q consists of the following terms:

new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_ltEs18(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt19(x0, x1)
new_asAs(True, x0)
new_esEs26(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt14(x0, x1)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare23(x0, x1, True, x2, x3)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_lt16(x0, x1, app(ty_[], x2))
new_compare8(:(x0, x1), [], x2)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Char)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs18(x0, x1, ty_Ordering)
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare7(Integer(x0), Integer(x1))
new_lt16(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, EmptyFM, True, x7, x8, x9)
new_compare112(x0, x1, False, x2, x3, x4)
new_lt16(x0, x1, ty_Char)
new_esEs12(False, False)
new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Integer)
new_compare211(x0, x1, True, x2)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primMulNat0(Zero, Succ(x0))
new_esEs10(Integer(x0), Integer(x1))
new_compare0(x0, x1, ty_Char)
new_compare0(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_lt13(x0, x1, x2)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_compare23(x0, x1, False, x2, x3)
new_foldFM_LE3(x0, x1, x2, x3, x4, x5, x6, x7)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_LE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_lt5(x0, x1)
new_esEs27(x0, x1, ty_Integer)
new_compare113(x0, x1, False, x2)
new_ltEs18(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Float)
new_lt4(:(x0, x1), [], x2)
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_@0)
new_esEs8(GT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_foldFM_LE0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10)
new_lt4([], [], x0)
new_lt20(x0, x1, ty_Bool)
new_lt16(x0, x1, ty_Int)
new_lt16(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs8(LT, LT)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(True, True)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs19(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt11(x0, x1, x2, x3, x4)
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_ltEs7(True, False)
new_ltEs7(False, True)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_ltEs5(LT, EQ)
new_ltEs5(EQ, LT)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs27(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_primEqNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Char)
new_lt15(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt15(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_compare114(x0, x1, False, x2, x3)
new_esEs25(x0, x1, ty_Int)
new_esEs15(Char(x0), Char(x1))
new_lt15(x0, x1, ty_Integer)
new_compare12(@0, @0)
new_compare18(x0, x1)
new_compare37(x0, x1)
new_compare8(:(x0, x1), :(x2, x3), x4)
new_esEs26(x0, x1, ty_Float)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_compare110(x0, x1, False)
new_primPlusNat0(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs19(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_primPlusNat1(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs18(x0, x1, ty_Integer)
new_lt16(x0, x1, ty_Bool)
new_compare0(x0, x1, ty_@0)
new_ltEs9(x0, x1)
new_esEs14(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt15(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Double)
new_lt6(:%(x0, x1), :%(x2, x3), x4)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt12(x0, x1)
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare112(x0, x1, True, x2, x3, x4)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_compare211(x0, x1, False, x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, False)
new_ltEs18(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Double)
new_compare14(x0, x1)
new_compare111(x0, x1, True, x2, x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs13([], :(x0, x1), x2)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs19(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs26(x0, x1, ty_@0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, ty_Char)
new_primCmpChar(Char(x0), Char(x1))
new_primCompAux1(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, ty_Bool)
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Just(x0), Nothing, x1)
new_esEs19(x0, x1, app(ty_[], x2))
new_compare9(x0, x1)
new_lt15(x0, x1, app(ty_Ratio, x2))
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_@0)
new_compare113(x0, x1, True, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, x2, x3)
new_primPlusNat1(Zero, Zero)
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Succ(x0), Zero)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs13([], [], x0)
new_lt15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_keysFM_LE0(x0, x1, x2, x3, x4, x5)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs12(x0, x1)
new_lt16(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Double)
new_compare11(x0, x1)
new_compare19(x0, x1, x2, x3, x4)
new_esEs17(@0, @0)
new_esEs22(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt16(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Bool)
new_compare33(x0, x1, x2, x3)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13(:(x0, x1), [], x2)
new_lt18(Integer(x0), Integer(x1))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Int)
new_compare36(x0, x1, x2)
new_esEs27(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Bool)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_lt15(x0, x1, app(ty_Maybe, x2))
new_esEs12(True, True)
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_lt15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, x1, EQ, ty_Double)
new_compare114(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, False, x2, x3)
new_lt17(x0, x1)
new_compare27(x0, x1, False)
new_ltEs19(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Ordering)
new_ltEs14(x0, x1, x2)
new_lt10(@0, @0)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, ty_@0)
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCompAux00(x0, x1, EQ, ty_Float)
new_lt4(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Int)
new_esEs4(Nothing, Just(x0), x1)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, True, x2, x3, x4)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt15(x0, x1, ty_Int)
new_compare38(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1)
new_esEs19(x0, x1, ty_Double)
new_compare39(x0, x1, x2, x3, x4)
new_esEs22(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare35(x0, x1)
new_pePe(True, x0)
new_ltEs4(x0, x1)
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_lt4([], :(x0, x1), x2)
new_pePe(False, x0)
new_esEs22(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(x0, x1, ty_Char)
new_compare29(x0, x1, x2, x3)
new_primEqNat0(Zero, Succ(x0))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Int)
new_compare10(x0, x1, False)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_compare0(x0, x1, ty_Integer)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs21(x0, x1, ty_Ordering)
new_compare28(x0, x1, True, x2, x3)
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primPlusNat0(Zero, x0)
new_lt16(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_ltEs13(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs26(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_Float)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_compare8([], [], x0)
new_compare0(x0, x1, ty_Float)
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_compare8([], :(x0, x1), x2)
new_esEs18(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs13(Nothing, Just(x0), x1)
new_compare25(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs5(GT, GT)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(False, True)
new_esEs12(True, False)
new_esEs22(x0, x1, ty_@0)
new_primCompAux00(x0, x1, GT, x2)
new_esEs22(x0, x1, ty_Ordering)
new_lt15(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_Char)
new_compare15(x0, x1)
new_ltEs18(x0, x1, app(ty_[], x2))
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_lt16(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, x2)
new_not(True)
new_lt20(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare38(x0, x1, x2, x3, ty_Int)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCompAux00(x0, x1, LT, x2)
new_lt15(x0, x1, ty_Double)
new_lt15(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, x1, EQ, ty_@0)
new_foldFM_LE0(x0, x1, x2, EmptyFM, x3, x4, x5)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_lt9(x0, x1, x2, x3)
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare34(x0, x1, x2, x3)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, x7, False, x8, x9, x10)
new_esEs28(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare0(x0, x1, ty_Int)
new_lt16(x0, x1, ty_Ordering)
new_ltEs5(EQ, EQ)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_Bool)
new_esEs18(x0, x1, ty_Char)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), True, x12, x13, x14)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs21(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Int)
new_compare24(x0, x1, True)
new_compare26(x0, x1, x2, x3)
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Char)
new_compare10(x0, x1, True)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt16(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_@0)
new_sr0(Integer(x0), Integer(x1))
new_primEqNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt15(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Ordering)
new_compare0(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs19(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, True)
new_compare110(x0, x1, True)
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Float)
new_esEs22(x0, x1, app(ty_[], x2))
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare16(x0, x1, x2)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_compare0(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs18(x0, x1, ty_Double)
new_ltEs5(LT, LT)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, ty_Integer)
new_compare28(x0, x1, False, x2, x3)
new_ltEs7(False, False)
new_esEs20(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, ty_Double)
new_compare13(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Nothing, x1)

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

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

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

new_foldFM_LE1(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, Branch(vyy6130, vyy6131, vyy6132, vyy6133, vyy6134), vyy614, False, h, ba, bb) → new_foldFM_LE1(vyy84, vyy54, vyy55, vyy6130, vyy6131, vyy6132, vyy6133, vyy6134, new_ltEs17(vyy6130, @2(vyy54, vyy55), h, ba), h, ba, bb)
new_foldFM_LE1(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, Branch(vyy6140, vyy6141, vyy6142, vyy6143, vyy6144), True, h, ba, bb) → new_foldFM_LE(vyy84, vyy54, vyy55, vyy613, h, ba, bb)
new_foldFM_LE1(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, EmptyFM, True, h, ba, bb) → new_foldFM_LE(vyy84, vyy54, vyy55, vyy613, h, ba, bb)
new_foldFM_LE(vyy84, vyy54, vyy55, Branch(vyy6130, vyy6131, vyy6132, vyy6133, vyy6134), h, ba, bb) → new_foldFM_LE1(vyy84, vyy54, vyy55, vyy6130, vyy6131, vyy6132, vyy6133, vyy6134, new_ltEs17(vyy6130, @2(vyy54, vyy55), h, ba), h, ba, bb)
new_foldFM_LE2(vyy610, vyy611, vyy105, vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb) → new_foldFM_LE1(new_keysFM_LE0(vyy610, vyy611, vyy105, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, new_ltEs17(vyy6140, @2(vyy54, vyy55), h, ba), h, ba, bb)
new_foldFM_LE1(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, Branch(vyy6140, vyy6141, vyy6142, vyy6143, vyy6144), True, h, ba, bb) → new_foldFM_LE2(vyy610, vyy611, new_foldFM_LE0(vyy84, vyy54, vyy55, vyy613, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb)

The TRS R consists of the following rules:

new_ltEs17(@2(vyy950, vyy951), @2(vyy960, vyy961), cfd, cfe) → new_pePe(new_lt20(vyy950, vyy960, cfd), new_asAs(new_esEs23(vyy950, vyy960, cfd), new_ltEs19(vyy951, vyy961, cfe)))
new_lt20(vyy950, vyy960, ty_Integer) → new_lt18(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(ty_Maybe, cff)) → new_lt13(vyy950, vyy960, cff)
new_lt20(vyy950, vyy960, ty_Double) → new_lt14(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(app(ty_@2, cgf), cgg)) → new_lt9(vyy950, vyy960, cgf, cgg)
new_lt20(vyy950, vyy960, ty_Float) → new_lt12(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(app(ty_Either, cgd), cge)) → new_lt7(vyy950, vyy960, cgd, cge)
new_lt20(vyy950, vyy960, ty_Char) → new_lt19(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_@0) → new_lt10(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_Ordering) → new_lt8(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_Int) → new_lt17(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_Bool) → new_lt5(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(ty_Ratio, cfh)) → new_lt6(vyy950, vyy960, cfh)
new_lt20(vyy950, vyy960, app(app(app(ty_@3, cga), cgb), cgc)) → new_lt11(vyy950, vyy960, cga, cgb, cgc)
new_lt20(vyy950, vyy960, app(ty_[], cfg)) → new_lt4(vyy950, vyy960, cfg)
new_esEs23(vyy950, vyy960, ty_Double) → new_esEs9(vyy950, vyy960)
new_esEs23(vyy950, vyy960, ty_Bool) → new_esEs12(vyy950, vyy960)
new_esEs23(vyy950, vyy960, app(ty_Maybe, cff)) → new_esEs4(vyy950, vyy960, cff)
new_esEs23(vyy950, vyy960, ty_Char) → new_esEs15(vyy950, vyy960)
new_esEs23(vyy950, vyy960, ty_Integer) → new_esEs10(vyy950, vyy960)
new_esEs23(vyy950, vyy960, ty_Int) → new_esEs14(vyy950, vyy960)
new_esEs23(vyy950, vyy960, app(app(ty_Either, cgd), cge)) → new_esEs6(vyy950, vyy960, cgd, cge)
new_esEs23(vyy950, vyy960, ty_Ordering) → new_esEs8(vyy950, vyy960)
new_esEs23(vyy950, vyy960, ty_@0) → new_esEs17(vyy950, vyy960)
new_esEs23(vyy950, vyy960, ty_Float) → new_esEs11(vyy950, vyy960)
new_esEs23(vyy950, vyy960, app(ty_Ratio, cfh)) → new_esEs16(vyy950, vyy960, cfh)
new_esEs23(vyy950, vyy960, app(app(ty_@2, cgf), cgg)) → new_esEs7(vyy950, vyy960, cgf, cgg)
new_esEs23(vyy950, vyy960, app(app(app(ty_@3, cga), cgb), cgc)) → new_esEs5(vyy950, vyy960, cga, cgb, cgc)
new_esEs23(vyy950, vyy960, app(ty_[], cfg)) → new_esEs13(vyy950, vyy960, cfg)
new_ltEs19(vyy951, vyy961, ty_Float) → new_ltEs11(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, app(app(ty_Either, chf), chg)) → new_ltEs8(vyy951, vyy961, chf, chg)
new_ltEs19(vyy951, vyy961, app(ty_Ratio, chb)) → new_ltEs14(vyy951, vyy961, chb)
new_ltEs19(vyy951, vyy961, app(app(ty_@2, chh), daa)) → new_ltEs17(vyy951, vyy961, chh, daa)
new_ltEs19(vyy951, vyy961, ty_Integer) → new_ltEs4(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Char) → new_ltEs12(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Int) → new_ltEs9(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Bool) → new_ltEs7(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_@0) → new_ltEs10(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, app(ty_Maybe, cgh)) → new_ltEs13(vyy951, vyy961, cgh)
new_ltEs19(vyy951, vyy961, app(ty_[], cha)) → new_ltEs6(vyy951, vyy961, cha)
new_ltEs19(vyy951, vyy961, app(app(app(ty_@3, chc), chd), che)) → new_ltEs16(vyy951, vyy961, chc, chd, che)
new_ltEs19(vyy951, vyy961, ty_Double) → new_ltEs15(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Ordering) → new_ltEs5(vyy951, vyy961)
new_asAs(False, vyy158) → False
new_asAs(True, vyy158) → vyy158
new_pePe(False, vyy139) → vyy139
new_pePe(True, vyy139) → True
new_ltEs5(EQ, GT) → True
new_ltEs5(EQ, LT) → False
new_ltEs5(LT, LT) → True
new_ltEs5(EQ, EQ) → True
new_ltEs5(GT, LT) → False
new_ltEs5(LT, GT) → True
new_ltEs5(LT, EQ) → True
new_ltEs5(GT, GT) → True
new_ltEs5(GT, EQ) → False
new_ltEs15(vyy301, vyy41) → new_not(new_esEs8(new_compare18(vyy301, vyy41), GT))
new_compare18(vyy301, vyy41) → new_primCmpDouble(vyy301, vyy41)
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_not(False) → True
new_not(True) → False
new_primCmpDouble(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_compare29(vyy3000, vyy400, vyy3001, vyy401) → new_primCmpInt(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_primPlusNat0(Succ(vyy1730), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1730, vyy40100)))
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_primPlusNat1(Succ(vyy17300), Zero) → Succ(vyy17300)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy17300), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy17300, vyy401000)))
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs16(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), cbc, cbd, cbe) → new_pePe(new_lt15(vyy3010, vyy410, cbc), new_asAs(new_esEs22(vyy3010, vyy410, cbc), new_pePe(new_lt16(vyy3011, vyy411, cbd), new_asAs(new_esEs21(vyy3011, vyy411, cbd), new_ltEs18(vyy3012, vyy412, cbe)))))
new_lt15(vyy3010, vyy410, ty_Bool) → new_lt5(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, app(ty_[], cbg)) → new_lt4(vyy3010, vyy410, cbg)
new_lt15(vyy3010, vyy410, ty_Char) → new_lt19(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, ty_Float) → new_lt12(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, app(ty_Maybe, cbf)) → new_lt13(vyy3010, vyy410, cbf)
new_lt15(vyy3010, vyy410, ty_@0) → new_lt10(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, ty_Integer) → new_lt18(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, app(app(ty_Either, ccd), cce)) → new_lt7(vyy3010, vyy410, ccd, cce)
new_lt15(vyy3010, vyy410, app(app(ty_@2, ccf), ccg)) → new_lt9(vyy3010, vyy410, ccf, ccg)
new_lt15(vyy3010, vyy410, app(app(app(ty_@3, cca), ccb), ccc)) → new_lt11(vyy3010, vyy410, cca, ccb, ccc)
new_lt15(vyy3010, vyy410, app(ty_Ratio, cbh)) → new_lt6(vyy3010, vyy410, cbh)
new_lt15(vyy3010, vyy410, ty_Double) → new_lt14(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, ty_Int) → new_lt17(vyy3010, vyy410)
new_lt15(vyy3010, vyy410, ty_Ordering) → new_lt8(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, ty_@0) → new_esEs17(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, ty_Integer) → new_esEs10(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, ty_Ordering) → new_esEs8(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, app(app(ty_@2, ccf), ccg)) → new_esEs7(vyy3010, vyy410, ccf, ccg)
new_esEs22(vyy3010, vyy410, ty_Double) → new_esEs9(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, app(app(app(ty_@3, cca), ccb), ccc)) → new_esEs5(vyy3010, vyy410, cca, ccb, ccc)
new_esEs22(vyy3010, vyy410, app(ty_Maybe, cbf)) → new_esEs4(vyy3010, vyy410, cbf)
new_esEs22(vyy3010, vyy410, ty_Bool) → new_esEs12(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, ty_Char) → new_esEs15(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, ty_Float) → new_esEs11(vyy3010, vyy410)
new_esEs22(vyy3010, vyy410, app(ty_[], cbg)) → new_esEs13(vyy3010, vyy410, cbg)
new_esEs22(vyy3010, vyy410, app(ty_Ratio, cbh)) → new_esEs16(vyy3010, vyy410, cbh)
new_esEs22(vyy3010, vyy410, app(app(ty_Either, ccd), cce)) → new_esEs6(vyy3010, vyy410, ccd, cce)
new_esEs22(vyy3010, vyy410, ty_Int) → new_esEs14(vyy3010, vyy410)
new_lt16(vyy3011, vyy411, ty_Bool) → new_lt5(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, ty_Int) → new_lt17(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, app(ty_Ratio, cdb)) → new_lt6(vyy3011, vyy411, cdb)
new_lt16(vyy3011, vyy411, ty_Double) → new_lt14(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, ty_Float) → new_lt12(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, app(app(ty_@2, cdh), cea)) → new_lt9(vyy3011, vyy411, cdh, cea)
new_lt16(vyy3011, vyy411, ty_Integer) → new_lt18(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, ty_@0) → new_lt10(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, app(ty_[], cda)) → new_lt4(vyy3011, vyy411, cda)
new_lt16(vyy3011, vyy411, ty_Ordering) → new_lt8(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, ty_Char) → new_lt19(vyy3011, vyy411)
new_lt16(vyy3011, vyy411, app(app(app(ty_@3, cdc), cdd), cde)) → new_lt11(vyy3011, vyy411, cdc, cdd, cde)
new_lt16(vyy3011, vyy411, app(app(ty_Either, cdf), cdg)) → new_lt7(vyy3011, vyy411, cdf, cdg)
new_lt16(vyy3011, vyy411, app(ty_Maybe, cch)) → new_lt13(vyy3011, vyy411, cch)
new_esEs21(vyy3011, vyy411, ty_Int) → new_esEs14(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, ty_@0) → new_esEs17(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, app(app(ty_Either, cdf), cdg)) → new_esEs6(vyy3011, vyy411, cdf, cdg)
new_esEs21(vyy3011, vyy411, ty_Char) → new_esEs15(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, app(app(ty_@2, cdh), cea)) → new_esEs7(vyy3011, vyy411, cdh, cea)
new_esEs21(vyy3011, vyy411, app(ty_[], cda)) → new_esEs13(vyy3011, vyy411, cda)
new_esEs21(vyy3011, vyy411, app(app(app(ty_@3, cdc), cdd), cde)) → new_esEs5(vyy3011, vyy411, cdc, cdd, cde)
new_esEs21(vyy3011, vyy411, ty_Integer) → new_esEs10(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, app(ty_Maybe, cch)) → new_esEs4(vyy3011, vyy411, cch)
new_esEs21(vyy3011, vyy411, ty_Double) → new_esEs9(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, ty_Ordering) → new_esEs8(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, app(ty_Ratio, cdb)) → new_esEs16(vyy3011, vyy411, cdb)
new_esEs21(vyy3011, vyy411, ty_Float) → new_esEs11(vyy3011, vyy411)
new_esEs21(vyy3011, vyy411, ty_Bool) → new_esEs12(vyy3011, vyy411)
new_ltEs18(vyy3012, vyy412, app(app(app(ty_@3, cee), cef), ceg)) → new_ltEs16(vyy3012, vyy412, cee, cef, ceg)
new_ltEs18(vyy3012, vyy412, ty_Integer) → new_ltEs4(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_@0) → new_ltEs10(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Float) → new_ltEs11(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Int) → new_ltEs9(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, app(ty_Ratio, ced)) → new_ltEs14(vyy3012, vyy412, ced)
new_ltEs18(vyy3012, vyy412, app(app(ty_Either, ceh), cfa)) → new_ltEs8(vyy3012, vyy412, ceh, cfa)
new_ltEs18(vyy3012, vyy412, app(app(ty_@2, cfb), cfc)) → new_ltEs17(vyy3012, vyy412, cfb, cfc)
new_ltEs18(vyy3012, vyy412, app(ty_[], cec)) → new_ltEs6(vyy3012, vyy412, cec)
new_ltEs18(vyy3012, vyy412, ty_Double) → new_ltEs15(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Ordering) → new_ltEs5(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Char) → new_ltEs12(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, app(ty_Maybe, ceb)) → new_ltEs13(vyy3012, vyy412, ceb)
new_ltEs18(vyy3012, vyy412, ty_Bool) → new_ltEs7(vyy3012, vyy412)
new_ltEs7(True, True) → True
new_ltEs7(True, False) → False
new_ltEs7(False, True) → True
new_ltEs7(False, False) → True
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Char) → new_ltEs12(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Double) → new_ltEs15(vyy3010, vyy410)
new_ltEs13(Nothing, Just(vyy410), bhh) → True
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_Ratio, cac)) → new_ltEs14(vyy3010, vyy410, cac)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Int) → new_ltEs9(vyy3010, vyy410)
new_ltEs13(Nothing, Nothing, bhh) → True
new_ltEs13(Just(vyy3010), Just(vyy410), ty_@0) → new_ltEs10(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Bool) → new_ltEs7(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Float) → new_ltEs11(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(ty_@2, cba), cbb)) → new_ltEs17(vyy3010, vyy410, cba, cbb)
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, cad), cae), caf)) → new_ltEs16(vyy3010, vyy410, cad, cae, caf)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Integer) → new_ltEs4(vyy3010, vyy410)
new_ltEs13(Just(vyy3010), Nothing, bhh) → False
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_[], cab)) → new_ltEs6(vyy3010, vyy410, cab)
new_ltEs13(Just(vyy3010), Just(vyy410), ty_Ordering) → new_ltEs5(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(ty_Either, bca), bcb), bbb) → new_ltEs8(vyy3010, vyy410, bca, bcb)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bbb) → new_ltEs13(vyy3010, vyy410, bbc)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_Maybe, bcf)) → new_ltEs13(vyy3010, vyy410, bcf)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(ty_Either, bdd), bde)) → new_ltEs8(vyy3010, vyy410, bdd, bde)
new_ltEs13(Just(vyy3010), Just(vyy410), app(app(ty_Either, cag), cah)) → new_ltEs8(vyy3010, vyy410, cag, cah)
new_ltEs13(Just(vyy3010), Just(vyy410), app(ty_Maybe, caa)) → new_ltEs13(vyy3010, vyy410, caa)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_[], bcg)) → new_ltEs6(vyy3010, vyy410, bcg)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Char) → new_ltEs12(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Integer, bbb) → new_ltEs4(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Bool) → new_ltEs7(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Char, bbb) → new_ltEs12(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(ty_@2, bdf), bdg)) → new_ltEs17(vyy3010, vyy410, bdf, bdg)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Double) → new_ltEs15(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(ty_@2, bcc), bcd), bbb) → new_ltEs17(vyy3010, vyy410, bcc, bcd)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Int, bbb) → new_ltEs9(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Integer) → new_ltEs4(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, bbf), bbg), bbh), bbb) → new_ltEs16(vyy3010, vyy410, bbf, bbg, bbh)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_@0) → new_ltEs10(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Int) → new_ltEs9(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Bool, bbb) → new_ltEs7(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(ty_Ratio, bch)) → new_ltEs14(vyy3010, vyy410, bch)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Float) → new_ltEs11(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_Ratio, bbe), bbb) → new_ltEs14(vyy3010, vyy410, bbe)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, app(app(app(ty_@3, bda), bdb), bdc)) → new_ltEs16(vyy3010, vyy410, bda, bdb, bdc)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_@0, bbb) → new_ltEs10(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Float, bbb) → new_ltEs11(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Left(vyy410), bce, bbb) → False
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Double, bbb) → new_ltEs15(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), ty_Ordering, bbb) → new_ltEs5(vyy3010, vyy410)
new_ltEs8(Right(vyy3010), Right(vyy410), bce, ty_Ordering) → new_ltEs5(vyy3010, vyy410)
new_ltEs8(Left(vyy3010), Left(vyy410), app(ty_[], bbd), bbb) → new_ltEs6(vyy3010, vyy410, bbd)
new_ltEs8(Left(vyy3010), Right(vyy410), bce, bbb) → True
new_ltEs6(vyy301, vyy41, hf) → new_not(new_esEs8(new_compare8(vyy301, vyy41, hf), GT))
new_compare8([], [], hf) → EQ
new_compare8(:(vyy3010, vyy3011), :(vyy410, vyy411), hf) → new_primCompAux1(vyy3010, vyy410, vyy3011, vyy411, hf)
new_primCompAux00(vyy163, vyy164, EQ, app(ty_[], baa)) → new_compare8(vyy163, vyy164, baa)
new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, bc) → new_primCompAux00(vyy3001, vyy401, new_compare0(vyy3000, vyy400, bc), app(ty_[], bc))
new_compare8(:(vyy3010, vyy3011), [], hf) → GT
new_compare8([], :(vyy410, vyy411), hf) → LT
new_compare0(vyy3000, vyy400, app(ty_[], be)) → new_compare8(vyy3000, vyy400, be)
new_compare0(vyy3000, vyy400, app(app(ty_Either, cb), cc)) → new_compare25(vyy3000, vyy400, cb, cc)
new_compare0(vyy3000, vyy400, ty_@0) → new_compare12(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(app(app(ty_@3, bg), bh), ca)) → new_compare19(vyy3000, vyy400, bg, bh, ca)
new_compare0(vyy3000, vyy400, ty_Char) → new_compare9(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Bool) → new_compare15(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(app(ty_@2, cd), ce)) → new_compare26(vyy3000, vyy400, cd, ce)
new_compare0(vyy3000, vyy400, app(ty_Ratio, bf)) → new_compare17(vyy3000, vyy400, bf)
new_compare0(vyy3000, vyy400, ty_Ordering) → new_compare13(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Float) → new_compare14(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(ty_Maybe, bd)) → new_compare16(vyy3000, vyy400, bd)
new_compare0(vyy3000, vyy400, ty_Integer) → new_compare7(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Double) → new_compare18(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Int) → new_compare11(vyy3000, vyy400)
new_primCompAux00(vyy163, vyy164, LT, hg) → LT
new_primCompAux00(vyy163, vyy164, GT, hg) → GT
new_compare11(vyy301, vyy41) → new_primCmpInt(vyy301, vyy41)
new_compare7(Integer(vyy3010), Integer(vyy410)) → new_primCmpInt(vyy3010, vyy410)
new_compare16(vyy3000, vyy400, bd) → new_compare36(vyy3000, vyy400, bd)
new_compare36(vyy300, vyy40, gb) → new_compare211(vyy300, vyy40, new_esEs4(vyy300, vyy40, gb), gb)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs4(Nothing, Just(vyy400), gb) → False
new_esEs4(Just(vyy3000), Nothing, gb) → False
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, hd), he)) → new_esEs6(vyy3000, vyy400, hd, he)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, gd)) → new_esEs4(vyy3000, vyy400, gd)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, cg), da) → new_esEs4(vyy3000, vyy400, cg)
new_esEs6(Right(vyy3000), Right(vyy400), ec, app(ty_Maybe, ed)) → new_esEs4(vyy3000, vyy400, ed)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, ea), eb), da) → new_esEs6(vyy3000, vyy400, ea, eb)
new_esEs6(Right(vyy3000), Right(vyy400), ec, app(app(ty_Either, fd), ff)) → new_esEs6(vyy3000, vyy400, fd, ff)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ge), gf), gg)) → new_esEs5(vyy3000, vyy400, ge, gf, gg)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs4(Nothing, Nothing, gb) → True
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, hc)) → new_esEs16(vyy3000, vyy400, hc)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], hb)) → new_esEs13(vyy3000, vyy400, hb)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, gh), ha)) → new_esEs7(vyy3000, vyy400, gh, ha)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs15(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs9(vyy3000, vyy400)
new_compare211(vyy300, vyy40, False, gb) → new_compare113(vyy300, vyy40, new_ltEs13(vyy300, vyy40, gb), gb)
new_compare211(vyy300, vyy40, True, gb) → EQ
new_compare113(vyy300, vyy40, True, gb) → LT
new_compare113(vyy300, vyy40, False, gb) → GT
new_esEs9(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs14(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_esEs15(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs7(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bdh, bea) → new_asAs(new_esEs28(vyy3000, vyy400, bdh), new_esEs27(vyy3001, vyy401, bea))
new_esEs28(vyy3000, vyy400, app(ty_[], dcb)) → new_esEs13(vyy3000, vyy400, dcb)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs5(vyy3000, vyy400, dbe, dbf, dbg)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dcc)) → new_esEs16(vyy3000, vyy400, dcc)
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dcd), dce)) → new_esEs6(vyy3000, vyy400, dcd, dce)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dbd)) → new_esEs4(vyy3000, vyy400, dbd)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dbh), dca)) → new_esEs7(vyy3000, vyy400, dbh, dca)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs15(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, dac), dad), dae)) → new_esEs5(vyy3001, vyy401, dac, dad, dae)
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs9(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, app(app(ty_@2, daf), dag)) → new_esEs7(vyy3001, vyy401, daf, dag)
new_esEs27(vyy3001, vyy401, app(ty_Ratio, dba)) → new_esEs16(vyy3001, vyy401, dba)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, app(app(ty_Either, dbb), dbc)) → new_esEs6(vyy3001, vyy401, dbb, dbc)
new_esEs27(vyy3001, vyy401, app(ty_Maybe, dab)) → new_esEs4(vyy3001, vyy401, dab)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs17(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs12(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, app(ty_[], dah)) → new_esEs13(vyy3001, vyy401, dah)
new_esEs13([], [], bc) → True
new_esEs13(:(vyy3000, vyy3001), :(vyy400, vyy401), bc) → new_asAs(new_esEs26(vyy3000, vyy400, bc), new_esEs13(vyy3001, vyy401, bc))
new_esEs13(:(vyy3000, vyy3001), [], bc) → False
new_esEs13([], :(vyy400, vyy401), bc) → False
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, bd)) → new_esEs4(vyy3000, vyy400, bd)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_[], be)) → new_esEs13(vyy3000, vyy400, be)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, bf)) → new_esEs16(vyy3000, vyy400, bf)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, cd), ce)) → new_esEs7(vyy3000, vyy400, cd, ce)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, cb), cc)) → new_esEs6(vyy3000, vyy400, cb, cc)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, bg), bh), ca)) → new_esEs5(vyy3000, vyy400, bg, bh, ca)
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), fg, fh, ga) → new_asAs(new_esEs20(vyy3000, vyy400, fg), new_asAs(new_esEs19(vyy3001, vyy401, fh), new_esEs18(vyy3002, vyy402, ga)))
new_esEs20(vyy3000, vyy400, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, app(ty_[], bhd)) → new_esEs13(vyy3000, vyy400, bhd)
new_esEs20(vyy3000, vyy400, app(ty_Ratio, bhe)) → new_esEs16(vyy3000, vyy400, bhe)
new_esEs20(vyy3000, vyy400, app(ty_Maybe, bgf)) → new_esEs4(vyy3000, vyy400, bgf)
new_esEs20(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, ty_Char) → new_esEs15(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs5(vyy3000, vyy400, bgg, bgh, bha)
new_esEs20(vyy3000, vyy400, app(app(ty_Either, bhf), bhg)) → new_esEs6(vyy3000, vyy400, bhf, bhg)
new_esEs20(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, app(app(ty_@2, bhb), bhc)) → new_esEs7(vyy3000, vyy400, bhb, bhc)
new_esEs20(vyy3000, vyy400, ty_Double) → new_esEs9(vyy3000, vyy400)
new_esEs19(vyy3001, vyy401, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs5(vyy3001, vyy401, bfe, bff, bfg)
new_esEs19(vyy3001, vyy401, app(ty_Maybe, bfd)) → new_esEs4(vyy3001, vyy401, bfd)
new_esEs19(vyy3001, vyy401, ty_Bool) → new_esEs12(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, app(app(ty_Either, bgd), bge)) → new_esEs6(vyy3001, vyy401, bgd, bge)
new_esEs19(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, app(app(ty_@2, bfh), bga)) → new_esEs7(vyy3001, vyy401, bfh, bga)
new_esEs19(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, app(ty_Ratio, bgc)) → new_esEs16(vyy3001, vyy401, bgc)
new_esEs19(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, ty_Double) → new_esEs9(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, ty_Char) → new_esEs15(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, ty_@0) → new_esEs17(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs19(vyy3001, vyy401, app(ty_[], bgb)) → new_esEs13(vyy3001, vyy401, bgb)
new_esEs18(vyy3002, vyy402, ty_Int) → new_esEs14(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, ty_Double) → new_esEs9(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, ty_Float) → new_esEs11(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, ty_Integer) → new_esEs10(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, app(app(ty_@2, bef), beg)) → new_esEs7(vyy3002, vyy402, bef, beg)
new_esEs18(vyy3002, vyy402, ty_Bool) → new_esEs12(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, app(app(ty_Either, bfb), bfc)) → new_esEs6(vyy3002, vyy402, bfb, bfc)
new_esEs18(vyy3002, vyy402, app(ty_[], beh)) → new_esEs13(vyy3002, vyy402, beh)
new_esEs18(vyy3002, vyy402, app(ty_Ratio, bfa)) → new_esEs16(vyy3002, vyy402, bfa)
new_esEs18(vyy3002, vyy402, app(app(app(ty_@3, bec), bed), bee)) → new_esEs5(vyy3002, vyy402, bec, bed, bee)
new_esEs18(vyy3002, vyy402, app(ty_Maybe, beb)) → new_esEs4(vyy3002, vyy402, beb)
new_esEs18(vyy3002, vyy402, ty_@0) → new_esEs17(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_esEs18(vyy3002, vyy402, ty_Char) → new_esEs15(vyy3002, vyy402)
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, EQ) → True
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs8(GT, EQ) → False
new_esEs17(@0, @0) → True
new_esEs16(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cf) → new_asAs(new_esEs25(vyy3000, vyy400, cf), new_esEs24(vyy3001, vyy401, cf))
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs10(vyy3001, vyy401)
new_esEs10(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), ec, app(app(ty_@2, eh), fa)) → new_esEs7(vyy3000, vyy400, eh, fa)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, dh), da) → new_esEs16(vyy3000, vyy400, dh)
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Integer) → new_esEs10(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, da) → new_esEs14(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, da) → new_esEs11(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Left(vyy400), ec, da) → False
new_esEs6(Left(vyy3000), Right(vyy400), ec, da) → False
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, da) → new_esEs10(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, db), dc), dd), da) → new_esEs5(vyy3000, vyy400, db, dc, dd)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, da) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, da) → new_esEs12(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, de), df), da) → new_esEs7(vyy3000, vyy400, de, df)
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Bool) → new_esEs12(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, da) → new_esEs8(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, da) → new_esEs9(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Char) → new_esEs15(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), ec, app(ty_[], fb)) → new_esEs13(vyy3000, vyy400, fb)
new_esEs6(Right(vyy3000), Right(vyy400), ec, app(ty_Ratio, fc)) → new_esEs16(vyy3000, vyy400, fc)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, da) → new_esEs15(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Double) → new_esEs9(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_@0) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], dg), da) → new_esEs13(vyy3000, vyy400, dg)
new_esEs6(Right(vyy3000), Right(vyy400), ec, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), ec, app(app(app(ty_@3, ee), ef), eg)) → new_esEs5(vyy3000, vyy400, ee, ef, eg)
new_esEs12(True, True) → True
new_esEs12(False, False) → True
new_esEs12(False, True) → False
new_esEs12(True, False) → False
new_esEs11(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare14(vyy301, vyy41) → new_primCmpFloat(vyy301, vyy41)
new_primCmpFloat(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_compare13(vyy3000, vyy400) → new_compare37(vyy3000, vyy400)
new_compare37(vyy300, vyy40) → new_compare24(vyy300, vyy40, new_esEs8(vyy300, vyy40))
new_compare24(vyy300, vyy40, True) → EQ
new_compare24(vyy300, vyy40, False) → new_compare10(vyy300, vyy40, new_ltEs5(vyy300, vyy40))
new_compare10(vyy300, vyy40, True) → LT
new_compare10(vyy300, vyy40, False) → GT
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Int) → new_compare11(new_sr(vyy3010, vyy411), new_sr(vyy410, vyy3011))
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Integer) → new_compare7(new_sr0(vyy3010, vyy411), new_sr0(vyy410, vyy3011))
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_compare26(vyy3000, vyy400, cd, ce) → new_compare34(vyy3000, vyy400, cd, ce)
new_compare34(vyy300, vyy40, bdh, bea) → new_compare28(vyy300, vyy40, new_esEs7(vyy300, vyy40, bdh, bea), bdh, bea)
new_compare28(vyy300, vyy40, False, bdh, bea) → new_compare111(vyy300, vyy40, new_ltEs17(vyy300, vyy40, bdh, bea), bdh, bea)
new_compare28(vyy300, vyy40, True, bdh, bea) → EQ
new_compare111(vyy300, vyy40, False, bdh, bea) → GT
new_compare111(vyy300, vyy40, True, bdh, bea) → LT
new_compare15(vyy3000, vyy400) → new_compare35(vyy3000, vyy400)
new_compare35(vyy300, vyy40) → new_compare27(vyy300, vyy40, new_esEs12(vyy300, vyy40))
new_compare27(vyy300, vyy40, True) → EQ
new_compare27(vyy300, vyy40, False) → new_compare110(vyy300, vyy40, new_ltEs7(vyy300, vyy40))
new_compare110(vyy300, vyy40, True) → LT
new_compare110(vyy300, vyy40, False) → GT
new_compare9(vyy301, vyy41) → new_primCmpChar(vyy301, vyy41)
new_primCmpChar(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_compare19(vyy3000, vyy400, bg, bh, ca) → new_compare39(vyy3000, vyy400, bg, bh, ca)
new_compare39(vyy300, vyy40, fg, fh, ga) → new_compare210(vyy300, vyy40, new_esEs5(vyy300, vyy40, fg, fh, ga), fg, fh, ga)
new_compare210(vyy300, vyy40, True, fg, fh, ga) → EQ
new_compare210(vyy300, vyy40, False, fg, fh, ga) → new_compare112(vyy300, vyy40, new_ltEs16(vyy300, vyy40, fg, fh, ga), fg, fh, ga)
new_compare112(vyy300, vyy40, True, fg, fh, ga) → LT
new_compare112(vyy300, vyy40, False, fg, fh, ga) → GT
new_compare12(@0, @0) → EQ
new_compare25(vyy3000, vyy400, cb, cc) → new_compare33(vyy3000, vyy400, cb, cc)
new_compare33(vyy300, vyy40, ec, da) → new_compare23(vyy300, vyy40, new_esEs6(vyy300, vyy40, ec, da), ec, da)
new_compare23(vyy300, vyy40, False, ec, da) → new_compare114(vyy300, vyy40, new_ltEs8(vyy300, vyy40, ec, da), ec, da)
new_compare23(vyy300, vyy40, True, ec, da) → EQ
new_compare114(vyy300, vyy40, True, ec, da) → LT
new_compare114(vyy300, vyy40, False, ec, da) → GT
new_ltEs11(vyy301, vyy41) → new_not(new_esEs8(new_compare14(vyy301, vyy41), GT))
new_ltEs10(vyy301, vyy41) → new_not(new_esEs8(new_compare12(vyy301, vyy41), GT))
new_ltEs14(vyy301, vyy41, gc) → new_not(new_esEs8(new_compare17(vyy301, vyy41, gc), GT))
new_ltEs9(vyy301, vyy41) → new_not(new_esEs8(new_compare11(vyy301, vyy41), GT))
new_ltEs4(vyy301, vyy41) → new_not(new_esEs8(new_compare7(vyy301, vyy41), GT))
new_ltEs12(vyy301, vyy41) → new_not(new_esEs8(new_compare9(vyy301, vyy41), GT))
new_lt13(vyy300, vyy40, gb) → new_esEs8(new_compare36(vyy300, vyy40, gb), LT)
new_lt7(vyy300, vyy40, ec, da) → new_esEs8(new_compare33(vyy300, vyy40, ec, da), LT)
new_lt11(vyy300, vyy40, fg, fh, ga) → new_esEs8(new_compare39(vyy300, vyy40, fg, fh, ga), LT)
new_lt19(vyy300, vyy40) → new_esEs8(new_primCmpChar(vyy300, vyy40), LT)
new_lt8(vyy300, vyy40) → new_esEs8(new_compare37(vyy300, vyy40), LT)
new_lt4(:(vyy3000, vyy3001), :(vyy400, vyy401), bc) → new_esEs8(new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, bc), LT)
new_lt4(:(vyy3000, vyy3001), [], bc) → new_esEs8(GT, LT)
new_lt4([], :(vyy400, vyy401), bc) → new_esEs8(LT, LT)
new_lt4([], [], bc) → new_esEs8(EQ, LT)
new_lt10(@0, @0) → new_esEs8(EQ, LT)
new_lt18(Integer(vyy3000), Integer(vyy400)) → new_esEs8(new_primCmpInt(vyy3000, vyy400), LT)
new_lt9(vyy300, vyy40, bdh, bea) → new_esEs8(new_compare34(vyy300, vyy40, bdh, bea), LT)
new_lt12(vyy300, vyy40) → new_esEs8(new_primCmpFloat(vyy300, vyy40), LT)
new_lt14(vyy300, vyy40) → new_esEs8(new_primCmpDouble(vyy300, vyy40), LT)
new_lt6(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cf) → new_esEs8(new_compare38(vyy3000, vyy401, vyy400, vyy3001, cf), LT)
new_compare38(Integer(vyy30000), Integer(vyy4010), vyy400, vyy3001, ty_Integer) → new_compare7(Integer(new_primMulInt(vyy30000, vyy4010)), new_sr0(vyy400, vyy3001))
new_compare38(vyy3000, vyy401, vyy400, vyy3001, ty_Int) → new_compare29(vyy3000, vyy401, vyy400, vyy3001)
new_lt17(vyy300, vyy40) → new_esEs8(new_primCmpInt(vyy300, vyy40), LT)
new_lt5(vyy300, vyy40) → new_esEs8(new_compare35(vyy300, vyy40), LT)
new_foldFM_LE0(vyy84, vyy54, vyy55, Branch(vyy6130, vyy6131, vyy6132, vyy6133, vyy6134), h, ba, bb) → new_foldFM_LE10(vyy84, vyy54, vyy55, vyy6130, vyy6131, vyy6132, vyy6133, vyy6134, new_ltEs17(vyy6130, @2(vyy54, vyy55), h, ba), h, ba, bb)
new_foldFM_LE10(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, vyy614, False, h, ba, bb) → new_foldFM_LE0(vyy84, vyy54, vyy55, vyy613, h, ba, bb)
new_foldFM_LE20(vyy610, vyy611, vyy105, vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb) → new_foldFM_LE10(new_keysFM_LE0(vyy610, vyy611, vyy105, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, new_ltEs17(vyy6140, @2(vyy54, vyy55), h, ba), h, ba, bb)
new_foldFM_LE10(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, Branch(vyy6140, vyy6141, vyy6142, vyy6143, vyy6144), True, h, ba, bb) → new_foldFM_LE20(vyy610, vyy611, new_foldFM_LE0(vyy84, vyy54, vyy55, vyy613, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb)
new_foldFM_LE0(vyy84, vyy54, vyy55, EmptyFM, h, ba, bb) → vyy84
new_keysFM_LE0(vyy610, vyy611, vyy104, h, ba, bb) → :(vyy610, vyy104)
new_foldFM_LE10(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, EmptyFM, True, h, ba, bb) → new_foldFM_LE3(vyy610, vyy611, new_foldFM_LE0(vyy84, vyy54, vyy55, vyy613, h, ba, bb), vyy54, vyy55, h, ba, bb)
new_foldFM_LE3(vyy610, vyy611, vyy104, vyy54, vyy55, h, ba, bb) → new_keysFM_LE0(vyy610, vyy611, vyy104, h, ba, bb)

The set Q consists of the following terms:

new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_ltEs18(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt19(x0, x1)
new_asAs(True, x0)
new_esEs26(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt14(x0, x1)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare23(x0, x1, True, x2, x3)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_lt16(x0, x1, app(ty_[], x2))
new_compare8(:(x0, x1), [], x2)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Char)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs18(x0, x1, ty_Ordering)
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare7(Integer(x0), Integer(x1))
new_lt16(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, EmptyFM, True, x7, x8, x9)
new_compare112(x0, x1, False, x2, x3, x4)
new_lt16(x0, x1, ty_Char)
new_esEs12(False, False)
new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Integer)
new_compare211(x0, x1, True, x2)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primMulNat0(Zero, Succ(x0))
new_esEs10(Integer(x0), Integer(x1))
new_compare0(x0, x1, ty_Char)
new_compare0(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_lt13(x0, x1, x2)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_compare23(x0, x1, False, x2, x3)
new_foldFM_LE3(x0, x1, x2, x3, x4, x5, x6, x7)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_LE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_lt5(x0, x1)
new_esEs27(x0, x1, ty_Integer)
new_compare113(x0, x1, False, x2)
new_ltEs18(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Float)
new_lt4(:(x0, x1), [], x2)
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_@0)
new_esEs8(GT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_foldFM_LE0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10)
new_lt4([], [], x0)
new_lt20(x0, x1, ty_Bool)
new_lt16(x0, x1, ty_Int)
new_lt16(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs8(LT, LT)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(True, True)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs19(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt11(x0, x1, x2, x3, x4)
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_ltEs7(True, False)
new_ltEs7(False, True)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_ltEs5(LT, EQ)
new_ltEs5(EQ, LT)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs27(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_primEqNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Char)
new_lt15(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt15(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_compare114(x0, x1, False, x2, x3)
new_esEs25(x0, x1, ty_Int)
new_esEs15(Char(x0), Char(x1))
new_lt15(x0, x1, ty_Integer)
new_compare12(@0, @0)
new_compare18(x0, x1)
new_compare37(x0, x1)
new_compare8(:(x0, x1), :(x2, x3), x4)
new_esEs26(x0, x1, ty_Float)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_compare110(x0, x1, False)
new_primPlusNat0(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs19(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_primPlusNat1(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs18(x0, x1, ty_Integer)
new_lt16(x0, x1, ty_Bool)
new_compare0(x0, x1, ty_@0)
new_ltEs9(x0, x1)
new_esEs14(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt15(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Double)
new_lt6(:%(x0, x1), :%(x2, x3), x4)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt12(x0, x1)
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare112(x0, x1, True, x2, x3, x4)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_compare211(x0, x1, False, x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, False)
new_ltEs18(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Double)
new_compare14(x0, x1)
new_compare111(x0, x1, True, x2, x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs13([], :(x0, x1), x2)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs19(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs26(x0, x1, ty_@0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, ty_Char)
new_primCmpChar(Char(x0), Char(x1))
new_primCompAux1(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, ty_Bool)
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Just(x0), Nothing, x1)
new_esEs19(x0, x1, app(ty_[], x2))
new_compare9(x0, x1)
new_lt15(x0, x1, app(ty_Ratio, x2))
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_@0)
new_compare113(x0, x1, True, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, x2, x3)
new_primPlusNat1(Zero, Zero)
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Succ(x0), Zero)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs13([], [], x0)
new_lt15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_keysFM_LE0(x0, x1, x2, x3, x4, x5)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs12(x0, x1)
new_lt16(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Double)
new_compare11(x0, x1)
new_compare19(x0, x1, x2, x3, x4)
new_esEs17(@0, @0)
new_esEs22(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt16(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Bool)
new_compare33(x0, x1, x2, x3)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13(:(x0, x1), [], x2)
new_lt18(Integer(x0), Integer(x1))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Int)
new_compare36(x0, x1, x2)
new_esEs27(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Bool)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_lt15(x0, x1, app(ty_Maybe, x2))
new_esEs12(True, True)
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_lt15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, x1, EQ, ty_Double)
new_compare114(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, False, x2, x3)
new_lt17(x0, x1)
new_compare27(x0, x1, False)
new_ltEs19(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Ordering)
new_ltEs14(x0, x1, x2)
new_lt10(@0, @0)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, ty_@0)
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCompAux00(x0, x1, EQ, ty_Float)
new_lt4(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Int)
new_esEs4(Nothing, Just(x0), x1)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, True, x2, x3, x4)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt15(x0, x1, ty_Int)
new_compare38(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1)
new_esEs19(x0, x1, ty_Double)
new_compare39(x0, x1, x2, x3, x4)
new_esEs22(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare35(x0, x1)
new_pePe(True, x0)
new_ltEs4(x0, x1)
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_lt4([], :(x0, x1), x2)
new_pePe(False, x0)
new_esEs22(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(x0, x1, ty_Char)
new_compare29(x0, x1, x2, x3)
new_primEqNat0(Zero, Succ(x0))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Int)
new_compare10(x0, x1, False)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_compare0(x0, x1, ty_Integer)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs21(x0, x1, ty_Ordering)
new_compare28(x0, x1, True, x2, x3)
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primPlusNat0(Zero, x0)
new_lt16(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_ltEs13(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs26(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_Float)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_compare8([], [], x0)
new_compare0(x0, x1, ty_Float)
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_compare8([], :(x0, x1), x2)
new_esEs18(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs13(Nothing, Just(x0), x1)
new_compare25(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs5(GT, GT)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(False, True)
new_esEs12(True, False)
new_esEs22(x0, x1, ty_@0)
new_primCompAux00(x0, x1, GT, x2)
new_esEs22(x0, x1, ty_Ordering)
new_lt15(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_Char)
new_compare15(x0, x1)
new_ltEs18(x0, x1, app(ty_[], x2))
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_lt16(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, x2)
new_not(True)
new_lt20(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare38(x0, x1, x2, x3, ty_Int)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCompAux00(x0, x1, LT, x2)
new_lt15(x0, x1, ty_Double)
new_lt15(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, x1, EQ, ty_@0)
new_foldFM_LE0(x0, x1, x2, EmptyFM, x3, x4, x5)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_lt9(x0, x1, x2, x3)
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare34(x0, x1, x2, x3)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, x7, False, x8, x9, x10)
new_esEs28(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare0(x0, x1, ty_Int)
new_lt16(x0, x1, ty_Ordering)
new_ltEs5(EQ, EQ)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_Bool)
new_esEs18(x0, x1, ty_Char)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), True, x12, x13, x14)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs21(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Int)
new_compare24(x0, x1, True)
new_compare26(x0, x1, x2, x3)
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Char)
new_compare10(x0, x1, True)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt16(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_@0)
new_sr0(Integer(x0), Integer(x1))
new_primEqNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt15(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Ordering)
new_compare0(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs19(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, True)
new_compare110(x0, x1, True)
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Float)
new_esEs22(x0, x1, app(ty_[], x2))
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare16(x0, x1, x2)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_compare0(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs18(x0, x1, ty_Double)
new_ltEs5(LT, LT)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, ty_Integer)
new_compare28(x0, x1, False, x2, x3)
new_ltEs7(False, False)
new_esEs20(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, ty_Double)
new_compare13(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Nothing, 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: