YES 8.672 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ LR

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

is transformed to
fmToList_GE0 key elt rest = (key,elt) : rest

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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



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

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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



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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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
reduce2D vyw vyx = gcd vyw vyx

reduce2Reduce1 vyw vyx x y True = error []
reduce2Reduce1 vyw vyx x y False = reduce2Reduce0 vyw vyx x y otherwise

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

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

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

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

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

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



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

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

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Haskell To QDPs


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

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

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

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

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



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

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

new_primPlusNat(Succ(vyy8900), Succ(vyy401000)) → new_primPlusNat(vyy8900, vyy401000)

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

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



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

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

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

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

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



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

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

new_primCmpNat(Succ(vyy5800), Succ(vyy5900)) → new_primCmpNat(vyy5800, vyy5900)

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

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



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

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

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

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

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



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

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

new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), he, app(app(ty_Either, hh), baa), ge) → new_lt0(vyy581, vyy591, hh, baa)
new_ltEs0(Left(vyy580), Left(vyy590), app(ty_[], ef), dg) → new_ltEs3(vyy580, vyy590, ef)
new_lt(vyy580, vyy590, h, ba) → new_compare2(vyy580, vyy590, new_esEs4(vyy580, vyy590, h, ba), h, ba)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), he, app(app(app(ty_@3, bab), bac), bad), ge) → new_lt1(vyy581, vyy591, bab, bac, bad)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), he, app(ty_Maybe, bae), ge) → new_lt2(vyy581, vyy591, bae)
new_compare2(vyy580, vyy590, False, h, ba) → new_ltEs(vyy580, vyy590, h, ba)
new_compare22(Just(vyy5800), Just(vyy5900), False, app(app(ty_@2, bbh), bca)) → new_ltEs(vyy5800, vyy5900, bbh, bca)
new_ltEs(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_Either, bc), bd), bb) → new_compare20(vyy580, vyy590, new_esEs5(vyy580, vyy590, bc, bd), bc, bd)
new_ltEs2(Just(vyy5800), Just(vyy5900), app(app(ty_Either, bcb), bcc)) → new_ltEs0(vyy5800, vyy5900, bcb, bcc)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), he, gd, app(ty_Maybe, bbf)) → new_ltEs2(vyy582, vyy592, bbf)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), he, gd, app(ty_[], bbg)) → new_ltEs3(vyy582, vyy592, bbg)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), he, app(app(ty_@2, hf), hg), ge) → new_lt(vyy581, vyy591, hf, hg)
new_ltEs(@2(vyy580, vyy581), @2(vyy590, vyy591), cb, app(ty_Maybe, dc)) → new_ltEs2(vyy581, vyy591, dc)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_Maybe, hc), gd, ge) → new_lt2(vyy580, vyy590, hc)
new_ltEs(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(app(ty_@3, be), bf), bg), bb) → new_compare21(vyy580, vyy590, new_esEs6(vyy580, vyy590, be, bf, bg), be, bf, bg)
new_compare21(vyy580, vyy590, False, be, bf, bg) → new_ltEs1(vyy580, vyy590, be, bf, bg)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_@2, gb), gc), gd, ge) → new_lt(vyy580, vyy590, gb, gc)
new_ltEs2(Just(vyy5800), Just(vyy5900), app(ty_[], bch)) → new_ltEs3(vyy5800, vyy5900, bch)
new_compare4(vyy580, vyy590, bh) → new_compare22(vyy580, vyy590, new_esEs7(vyy580, vyy590, bh), bh)
new_primCompAux(vyy580, vyy590, vyy115, app(app(ty_@2, bdb), bdc)) → new_compare0(vyy580, vyy590, bdb, bdc)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_[], hd), gd, ge) → new_lt3(vyy580, vyy590, hd)
new_ltEs0(Left(vyy580), Left(vyy590), app(app(ty_Either, dh), ea), dg) → new_ltEs0(vyy580, vyy590, dh, ea)
new_ltEs(@2(vyy580, vyy581), @2(vyy590, vyy591), cb, app(ty_[], dd)) → new_ltEs3(vyy581, vyy591, dd)
new_compare22(Just(vyy5800), Just(vyy5900), False, app(ty_[], bch)) → new_ltEs3(vyy5800, vyy5900, bch)
new_primCompAux(vyy580, vyy590, vyy115, app(ty_[], beb)) → new_compare(vyy580, vyy590, beb)
new_ltEs3(:(vyy580, vyy581), :(vyy590, vyy591), bda) → new_compare(vyy581, vyy591, bda)
new_ltEs(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_[], ca), bb) → new_compare(vyy580, vyy590, ca)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_Either, gf), gg), gd, ge) → new_lt0(vyy580, vyy590, gf, gg)
new_ltEs0(Right(vyy580), Right(vyy590), eg, app(app(ty_@2, eh), fa)) → new_ltEs(vyy580, vyy590, eh, fa)
new_ltEs2(Just(vyy5800), Just(vyy5900), app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs1(vyy5800, vyy5900, bcd, bce, bcf)
new_lt0(vyy580, vyy590, bc, bd) → new_compare20(vyy580, vyy590, new_esEs5(vyy580, vyy590, bc, bd), bc, bd)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), he, gd, app(app(ty_@2, bag), bah)) → new_ltEs(vyy582, vyy592, bag, bah)
new_compare22(Just(vyy5800), Just(vyy5900), False, app(app(ty_Either, bcb), bcc)) → new_ltEs0(vyy5800, vyy5900, bcb, bcc)
new_compare(:(vyy580, vyy581), :(vyy590, vyy591), bda) → new_primCompAux(vyy580, vyy590, new_compare5(vyy581, vyy591, bda), bda)
new_compare20(vyy580, vyy590, False, bc, bd) → new_ltEs0(vyy580, vyy590, bc, bd)
new_ltEs(@2(vyy580, vyy581), @2(vyy590, vyy591), cb, app(app(app(ty_@3, cg), da), db)) → new_ltEs1(vyy581, vyy591, cg, da, db)
new_ltEs0(Left(vyy580), Left(vyy590), app(app(ty_@2, de), df), dg) → new_ltEs(vyy580, vyy590, de, df)
new_ltEs3(:(vyy580, vyy581), :(vyy590, vyy591), bda) → new_primCompAux(vyy580, vyy590, new_compare5(vyy581, vyy591, bda), bda)
new_primCompAux(vyy580, vyy590, vyy115, app(app(ty_Either, bdd), bde)) → new_compare1(vyy580, vyy590, bdd, bde)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), he, gd, app(app(ty_Either, bba), bbb)) → new_ltEs0(vyy582, vyy592, bba, bbb)
new_lt2(vyy580, vyy590, bh) → new_compare22(vyy580, vyy590, new_esEs7(vyy580, vyy590, bh), bh)
new_compare3(vyy580, vyy590, be, bf, bg) → new_compare21(vyy580, vyy590, new_esEs6(vyy580, vyy590, be, bf, bg), be, bf, bg)
new_compare22(Just(vyy5800), Just(vyy5900), False, app(ty_Maybe, bcg)) → new_ltEs2(vyy5800, vyy5900, bcg)
new_ltEs0(Right(vyy580), Right(vyy590), eg, app(app(ty_Either, fb), fc)) → new_ltEs0(vyy580, vyy590, fb, fc)
new_ltEs0(Right(vyy580), Right(vyy590), eg, app(ty_Maybe, fh)) → new_ltEs2(vyy580, vyy590, fh)
new_ltEs2(Just(vyy5800), Just(vyy5900), app(app(ty_@2, bbh), bca)) → new_ltEs(vyy5800, vyy5900, bbh, bca)
new_ltEs0(Right(vyy580), Right(vyy590), eg, app(ty_[], ga)) → new_ltEs3(vyy580, vyy590, ga)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), he, app(ty_[], baf), ge) → new_lt3(vyy581, vyy591, baf)
new_ltEs2(Just(vyy5800), Just(vyy5900), app(ty_Maybe, bcg)) → new_ltEs2(vyy5800, vyy5900, bcg)
new_compare(:(vyy580, vyy581), :(vyy590, vyy591), bda) → new_compare(vyy581, vyy591, bda)
new_ltEs0(Left(vyy580), Left(vyy590), app(ty_Maybe, ee), dg) → new_ltEs2(vyy580, vyy590, ee)
new_primCompAux(vyy580, vyy590, vyy115, app(app(app(ty_@3, bdf), bdg), bdh)) → new_compare3(vyy580, vyy590, bdf, bdg, bdh)
new_lt3(vyy580, vyy590, ca) → new_compare(vyy580, vyy590, ca)
new_ltEs(@2(vyy580, vyy581), @2(vyy590, vyy591), cb, app(app(ty_@2, cc), cd)) → new_ltEs(vyy581, vyy591, cc, cd)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), he, gd, app(app(app(ty_@3, bbc), bbd), bbe)) → new_ltEs1(vyy582, vyy592, bbc, bbd, bbe)
new_compare22(Just(vyy5800), Just(vyy5900), False, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs1(vyy5800, vyy5900, bcd, bce, bcf)
new_lt1(vyy580, vyy590, be, bf, bg) → new_compare21(vyy580, vyy590, new_esEs6(vyy580, vyy590, be, bf, bg), be, bf, bg)
new_primCompAux(vyy580, vyy590, vyy115, app(ty_Maybe, bea)) → new_compare4(vyy580, vyy590, bea)
new_compare0(vyy580, vyy590, h, ba) → new_compare2(vyy580, vyy590, new_esEs4(vyy580, vyy590, h, ba), h, ba)
new_ltEs(@2(vyy580, vyy581), @2(vyy590, vyy591), cb, app(app(ty_Either, ce), cf)) → new_ltEs0(vyy581, vyy591, ce, cf)
new_compare1(vyy580, vyy590, bc, bd) → new_compare20(vyy580, vyy590, new_esEs5(vyy580, vyy590, bc, bd), bc, bd)
new_ltEs(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_@2, h), ba), bb) → new_compare2(vyy580, vyy590, new_esEs4(vyy580, vyy590, h, ba), h, ba)
new_ltEs0(Left(vyy580), Left(vyy590), app(app(app(ty_@3, eb), ec), ed), dg) → new_ltEs1(vyy580, vyy590, eb, ec, ed)
new_ltEs(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_Maybe, bh), bb) → new_compare22(vyy580, vyy590, new_esEs7(vyy580, vyy590, bh), bh)
new_ltEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(app(ty_@3, gh), ha), hb), gd, ge) → new_lt1(vyy580, vyy590, gh, ha, hb)
new_ltEs0(Right(vyy580), Right(vyy590), eg, app(app(app(ty_@3, fd), ff), fg)) → new_ltEs1(vyy580, vyy590, fd, ff, fg)

The TRS R consists of the following rules:

new_lt19(vyy580, vyy590, ty_Float) → new_lt6(vyy580, vyy590)
new_ltEs19(vyy582, vyy592, app(app(ty_@2, bag), bah)) → new_ltEs5(vyy582, vyy592, bag, bah)
new_compare25(vyy580, vyy590, False) → new_compare12(vyy580, vyy590, new_ltEs10(vyy580, vyy590))
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, daf)) → new_esEs7(vyy3000, vyy400, daf)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs15(vyy3000, vyy400)
new_esEs20(vyy3001, vyy401, app(ty_Maybe, cbd)) → new_esEs7(vyy3001, vyy401, cbd)
new_ltEs13(Just(vyy5800), Just(vyy5900), app(app(ty_Either, bcb), bcc)) → new_ltEs9(vyy5800, vyy5900, bcb, bcc)
new_ltEs7(vyy58, vyy59) → new_not(new_esEs8(new_compare14(vyy58, vyy59), GT))
new_esEs27(vyy3001, vyy401, app(ty_[], cgd)) → new_esEs16(vyy3001, vyy401, cgd)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_compare18(vyy580, vyy590, app(app(app(ty_@3, bdf), bdg), bdh)) → new_compare27(vyy580, vyy590, bdf, bdg, bdh)
new_compare8(Integer(vyy580), Integer(vyy590)) → new_primCmpInt(vyy580, vyy590)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_compare110(vyy580, vyy590, True, bc, bd) → LT
new_esEs23(vyy580, vyy590, app(app(ty_Either, gf), gg)) → new_esEs5(vyy580, vyy590, gf, gg)
new_esEs27(vyy3001, vyy401, app(ty_Ratio, chb)) → new_esEs18(vyy3001, vyy401, chb)
new_esEs23(vyy580, vyy590, app(app(ty_@2, gb), gc)) → new_esEs4(vyy580, vyy590, gb, gc)
new_esEs19(vyy3002, vyy402, app(ty_[], cae)) → new_esEs16(vyy3002, vyy402, cae)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_esEs19(vyy3002, vyy402, ty_Char) → new_esEs13(vyy3002, vyy402)
new_esEs27(vyy3001, vyy401, app(ty_Maybe, cga)) → new_esEs7(vyy3001, vyy401, cga)
new_primCompAux1(vyy580, vyy590, vyy115, bda) → new_primCompAux0(vyy115, new_compare18(vyy580, vyy590, bda))
new_compare18(vyy580, vyy590, app(ty_Ratio, bhd)) → new_compare7(vyy580, vyy590, bhd)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Double) → new_ltEs15(vyy5800, vyy5900)
new_esEs19(vyy3002, vyy402, app(ty_Ratio, cbc)) → new_esEs18(vyy3002, vyy402, cbc)
new_primMulNat0(Zero, Zero) → Zero
new_compare5(:(vyy580, vyy581), :(vyy590, vyy591), bda) → new_primCompAux1(vyy580, vyy590, new_compare5(vyy581, vyy591, bda), bda)
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs15(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_[], ceh)) → new_esEs16(vyy3000, vyy400, ceh)
new_lt12(vyy580, vyy590) → new_esEs8(new_compare8(vyy580, vyy590), LT)
new_compare16(vyy580, vyy590, h, ba) → new_compare26(vyy580, vyy590, new_esEs4(vyy580, vyy590, h, ba), h, ba)
new_esEs9(vyy580, vyy590, ty_@0) → new_esEs15(vyy580, vyy590)
new_ltEs13(Nothing, Just(vyy5900), bh) → True
new_esEs21(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_lt20(vyy581, vyy591, ty_Float) → new_lt6(vyy581, vyy591)
new_lt5(vyy580, vyy590, ty_Bool) → new_lt17(vyy580, vyy590)
new_lt20(vyy581, vyy591, app(ty_Maybe, bae)) → new_lt13(vyy581, vyy591, bae)
new_lt11(vyy580, vyy590, be, bf, bg) → new_esEs8(new_compare27(vyy580, vyy590, be, bf, bg), LT)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_ltEs19(vyy582, vyy592, ty_Bool) → new_ltEs18(vyy582, vyy592)
new_esEs17(True, True) → True
new_ltEs13(Just(vyy5800), Just(vyy5900), app(app(ty_@2, bbh), bca)) → new_ltEs5(vyy5800, vyy5900, bbh, bca)
new_lt19(vyy580, vyy590, ty_Bool) → new_lt17(vyy580, vyy590)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Integer, dg) → new_ltEs12(vyy580, vyy590)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs17(vyy3000, vyy400)
new_compare23(vyy580, vyy590, False) → new_compare10(vyy580, vyy590, new_ltEs18(vyy580, vyy590))
new_ltEs14(vyy58, vyy59) → new_not(new_esEs8(new_compare29(vyy58, vyy59), GT))
new_ltEs19(vyy582, vyy592, ty_Ordering) → new_ltEs10(vyy582, vyy592)
new_lt17(vyy580, vyy590) → new_esEs8(new_compare13(vyy580, vyy590), LT)
new_compare29(Char(vyy580), Char(vyy590)) → new_primCmpNat0(vyy580, vyy590)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_@0) → new_ltEs16(vyy5800, vyy5900)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, dbe), dbf)) → new_esEs4(vyy3000, vyy400, dbe, dbf)
new_ltEs10(EQ, GT) → True
new_compare7(:%(vyy580, vyy581), :%(vyy590, vyy591), ty_Integer) → new_compare8(new_sr0(vyy580, vyy591), new_sr0(vyy590, vyy581))
new_esEs23(vyy580, vyy590, ty_Integer) → new_esEs12(vyy580, vyy590)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs12(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_compare18(vyy580, vyy590, ty_Ordering) → new_compare19(vyy580, vyy590)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_ltEs16(vyy58, vyy59) → new_not(new_esEs8(new_compare30(vyy58, vyy59), GT))
new_esEs22(vyy581, vyy591, app(ty_Ratio, cea)) → new_esEs18(vyy581, vyy591, cea)
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_esEs19(vyy3002, vyy402, app(app(ty_Either, cac), cad)) → new_esEs5(vyy3002, vyy402, cac, cad)
new_esEs5(Right(vyy3000), Right(vyy400), bga, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs6(vyy3000, vyy400, bgf, bgg, bgh)
new_ltEs6(vyy581, vyy591, ty_@0) → new_ltEs16(vyy581, vyy591)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Float, dg) → new_ltEs7(vyy580, vyy590)
new_pePe(False, vyy114) → vyy114
new_ltEs9(Right(vyy580), Right(vyy590), eg, ty_Ordering) → new_ltEs10(vyy580, vyy590)
new_ltEs6(vyy581, vyy591, app(app(ty_Either, ce), cf)) → new_ltEs9(vyy581, vyy591, ce, cf)
new_compare18(vyy580, vyy590, app(app(ty_Either, bdd), bde)) → new_compare15(vyy580, vyy590, bdd, bde)
new_esEs19(vyy3002, vyy402, ty_@0) → new_esEs15(vyy3002, vyy402)
new_compare23(vyy580, vyy590, True) → EQ
new_lt19(vyy580, vyy590, app(ty_[], hd)) → new_lt16(vyy580, vyy590, hd)
new_lt5(vyy580, vyy590, app(ty_[], ca)) → new_lt16(vyy580, vyy590, ca)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs22(vyy581, vyy591, ty_@0) → new_esEs15(vyy581, vyy591)
new_esEs22(vyy581, vyy591, app(app(ty_@2, hf), hg)) → new_esEs4(vyy581, vyy591, hf, hg)
new_esEs22(vyy581, vyy591, ty_Int) → new_esEs11(vyy581, vyy591)
new_esEs22(vyy581, vyy591, ty_Integer) → new_esEs12(vyy581, vyy591)
new_esEs23(vyy580, vyy590, app(ty_Maybe, hc)) → new_esEs7(vyy580, vyy590, hc)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs15(vyy3000, vyy400)
new_compare9(vyy58, vyy59) → new_primCmpInt(vyy58, vyy59)
new_compare6(Double(vyy580, vyy581), Double(vyy590, vyy591)) → new_compare9(new_sr(vyy580, vyy590), new_sr(vyy581, vyy591))
new_lt19(vyy580, vyy590, app(app(ty_Either, gf), gg)) → new_lt9(vyy580, vyy590, gf, gg)
new_ltEs9(Right(vyy580), Right(vyy590), eg, ty_Char) → new_ltEs14(vyy580, vyy590)
new_esEs22(vyy581, vyy591, ty_Ordering) → new_esEs8(vyy581, vyy591)
new_lt7(vyy580, vyy590, h, ba) → new_esEs8(new_compare16(vyy580, vyy590, h, ba), LT)
new_esEs5(Right(vyy3000), Right(vyy400), bga, ty_@0) → new_esEs15(vyy3000, vyy400)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Int, bef) → new_esEs11(vyy3000, vyy400)
new_lt20(vyy581, vyy591, app(app(ty_@2, hf), hg)) → new_lt7(vyy581, vyy591, hf, hg)
new_lt16(vyy580, vyy590, ca) → new_esEs8(new_compare5(vyy580, vyy590, ca), LT)
new_esEs5(Right(vyy3000), Right(vyy400), bga, app(app(ty_@2, bha), bhb)) → new_esEs4(vyy3000, vyy400, bha, bhb)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Ordering, bef) → new_esEs8(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, dbg)) → new_esEs18(vyy3000, vyy400, dbg)
new_ltEs19(vyy582, vyy592, ty_Int) → new_ltEs8(vyy582, vyy592)
new_esEs23(vyy580, vyy590, ty_Double) → new_esEs14(vyy580, vyy590)
new_primCmpNat0(Zero, Succ(vyy5900)) → LT
new_esEs21(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_ltEs13(Nothing, Nothing, bh) → True
new_esEs8(LT, LT) → True
new_lt20(vyy581, vyy591, ty_@0) → new_lt15(vyy581, vyy591)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Int, dg) → new_ltEs8(vyy580, vyy590)
new_lt13(vyy580, vyy590, bh) → new_esEs8(new_compare28(vyy580, vyy590, bh), LT)
new_lt19(vyy580, vyy590, ty_@0) → new_lt15(vyy580, vyy590)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs14(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), bga, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs9(Right(vyy580), Right(vyy590), eg, ty_@0) → new_ltEs16(vyy580, vyy590)
new_ltEs17(vyy58, vyy59, bda) → new_not(new_esEs8(new_compare5(vyy58, vyy59, bda), GT))
new_ltEs4(vyy58, vyy59, bec) → new_not(new_esEs8(new_compare7(vyy58, vyy59, bec), GT))
new_esEs19(vyy3002, vyy402, app(ty_Maybe, cab)) → new_esEs7(vyy3002, vyy402, cab)
new_esEs20(vyy3001, vyy401, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs6(vyy3001, vyy401, cbh, cca, ccb)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_pePe(True, vyy114) → True
new_primEqNat0(Zero, Zero) → True
new_esEs20(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_lt9(vyy580, vyy590, bc, bd) → new_esEs8(new_compare15(vyy580, vyy590, bc, bd), LT)
new_ltEs11(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), he, gd, ge) → new_pePe(new_lt19(vyy580, vyy590, he), new_asAs(new_esEs23(vyy580, vyy590, he), new_pePe(new_lt20(vyy581, vyy591, gd), new_asAs(new_esEs22(vyy581, vyy591, gd), new_ltEs19(vyy582, vyy592, ge)))))
new_compare11(vyy580, vyy590, True, bh) → LT
new_ltEs5(@2(vyy580, vyy581), @2(vyy590, vyy591), cb, bb) → new_pePe(new_lt5(vyy580, vyy590, cb), new_asAs(new_esEs9(vyy580, vyy590, cb), new_ltEs6(vyy581, vyy591, bb)))
new_compare18(vyy580, vyy590, ty_Float) → new_compare14(vyy580, vyy590)
new_compare24(vyy580, vyy590, False, bh) → new_compare11(vyy580, vyy590, new_ltEs13(vyy580, vyy590, bh), bh)
new_esEs4(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cfg, cfh) → new_asAs(new_esEs28(vyy3000, vyy400, cfg), new_esEs27(vyy3001, vyy401, cfh))
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_ltEs9(Right(vyy580), Right(vyy590), eg, ty_Double) → new_ltEs15(vyy580, vyy590)
new_lt5(vyy580, vyy590, ty_Double) → new_lt4(vyy580, vyy590)
new_esEs9(vyy580, vyy590, ty_Float) → new_esEs10(vyy580, vyy590)
new_compare110(vyy580, vyy590, False, bc, bd) → GT
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Char) → new_ltEs14(vyy5800, vyy5900)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], dba)) → new_esEs16(vyy3000, vyy400, dba)
new_lt19(vyy580, vyy590, ty_Int) → new_lt8(vyy580, vyy590)
new_esEs9(vyy580, vyy590, app(ty_[], ca)) → new_esEs16(vyy580, vyy590, ca)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs9(Right(vyy580), Right(vyy590), eg, app(ty_[], ga)) → new_ltEs17(vyy580, vyy590, ga)
new_esEs5(Right(vyy3000), Right(vyy400), bga, app(ty_Ratio, bhc)) → new_esEs18(vyy3000, vyy400, bhc)
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(vyy890), vyy40100) → Succ(Succ(new_primPlusNat1(vyy890, vyy40100)))
new_lt5(vyy580, vyy590, app(ty_Maybe, bh)) → new_lt13(vyy580, vyy590, bh)
new_ltEs9(Left(vyy580), Left(vyy590), ty_@0, dg) → new_ltEs16(vyy580, vyy590)
new_ltEs9(Right(vyy580), Left(vyy590), eg, dg) → False
new_lt19(vyy580, vyy590, app(app(app(ty_@3, gh), ha), hb)) → new_lt11(vyy580, vyy590, gh, ha, hb)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, cfa), cfb), cfc)) → new_esEs6(vyy3000, vyy400, cfa, cfb, cfc)
new_esEs20(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_compare18(vyy580, vyy590, ty_Int) → new_compare9(vyy580, vyy590)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs12(vyy3000, vyy400)
new_compare17(vyy580, vyy590, True, h, ba) → LT
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy582, vyy592, ty_Float) → new_ltEs7(vyy582, vyy592)
new_compare25(vyy580, vyy590, True) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare18(vyy580, vyy590, ty_@0) → new_compare30(vyy580, vyy590)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Float, bef) → new_esEs10(vyy3000, vyy400)
new_ltEs9(Left(vyy580), Left(vyy590), app(ty_Maybe, ee), dg) → new_ltEs13(vyy580, vyy590, ee)
new_esEs20(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs22(vyy581, vyy591, app(app(app(ty_@3, bab), bac), bad)) → new_esEs6(vyy581, vyy591, bab, bac, bad)
new_esEs23(vyy580, vyy590, ty_Ordering) → new_esEs8(vyy580, vyy590)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_[], bfb), bef) → new_esEs16(vyy3000, vyy400, bfb)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy8900), Zero) → Succ(vyy8900)
new_lt5(vyy580, vyy590, ty_Integer) → new_lt12(vyy580, vyy590)
new_lt19(vyy580, vyy590, ty_Char) → new_lt14(vyy580, vyy590)
new_esEs21(vyy3000, vyy400, ty_@0) → new_esEs15(vyy3000, vyy400)
new_ltEs18(True, True) → True
new_esEs21(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Maybe, beg), bef) → new_esEs7(vyy3000, vyy400, beg)
new_esEs27(vyy3001, vyy401, app(app(ty_Either, cgb), cgc)) → new_esEs5(vyy3001, vyy401, cgb, cgc)
new_lt19(vyy580, vyy590, ty_Integer) → new_lt12(vyy580, vyy590)
new_lt5(vyy580, vyy590, app(app(ty_@2, h), ba)) → new_lt7(vyy580, vyy590, h, ba)
new_esEs19(vyy3002, vyy402, ty_Integer) → new_esEs12(vyy3002, vyy402)
new_compare18(vyy580, vyy590, ty_Char) → new_compare29(vyy580, vyy590)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primCompAux0(vyy124, GT) → GT
new_ltEs18(False, False) → True
new_esEs8(EQ, EQ) → True
new_esEs5(Left(vyy3000), Left(vyy400), ty_Double, bef) → new_esEs14(vyy3000, vyy400)
new_compare26(vyy580, vyy590, True, h, ba) → EQ
new_ltEs9(Left(vyy580), Left(vyy590), ty_Char, dg) → new_ltEs14(vyy580, vyy590)
new_ltEs9(Left(vyy580), Left(vyy590), app(app(app(ty_@3, eb), ec), ed), dg) → new_ltEs11(vyy580, vyy590, eb, ec, ed)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_lt20(vyy581, vyy591, ty_Int) → new_lt8(vyy581, vyy591)
new_esEs21(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_primCmpNat0(Succ(vyy5800), Succ(vyy5900)) → new_primCmpNat0(vyy5800, vyy5900)
new_esEs23(vyy580, vyy590, ty_Float) → new_esEs10(vyy580, vyy590)
new_ltEs19(vyy582, vyy592, app(ty_Ratio, ceb)) → new_ltEs4(vyy582, vyy592, ceb)
new_compare5(:(vyy580, vyy581), [], bda) → GT
new_compare11(vyy580, vyy590, False, bh) → GT
new_compare18(vyy580, vyy590, app(ty_Maybe, bea)) → new_compare28(vyy580, vyy590, bea)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_lt19(vyy580, vyy590, ty_Double) → new_lt4(vyy580, vyy590)
new_compare19(vyy580, vyy590) → new_compare25(vyy580, vyy590, new_esEs8(vyy580, vyy590))
new_compare15(vyy580, vyy590, bc, bd) → new_compare210(vyy580, vyy590, new_esEs5(vyy580, vyy590, bc, bd), bc, bd)
new_ltEs10(GT, EQ) → False
new_esEs5(Right(vyy3000), Right(vyy400), bga, app(app(ty_Either, bgc), bgd)) → new_esEs5(vyy3000, vyy400, bgc, bgd)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs9(Left(vyy580), Left(vyy590), app(app(ty_@2, de), df), dg) → new_ltEs5(vyy580, vyy590, de, df)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Ordering, dg) → new_ltEs10(vyy580, vyy590)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs6(vyy581, vyy591, ty_Int) → new_ltEs8(vyy581, vyy591)
new_ltEs12(vyy58, vyy59) → new_not(new_esEs8(new_compare8(vyy58, vyy59), GT))
new_esEs19(vyy3002, vyy402, app(app(app(ty_@3, caf), cag), cah)) → new_esEs6(vyy3002, vyy402, caf, cag, cah)
new_ltEs9(Right(vyy580), Right(vyy590), eg, ty_Integer) → new_ltEs12(vyy580, vyy590)
new_compare14(Float(vyy580, vyy581), Float(vyy590, vyy591)) → new_compare9(new_sr(vyy580, vyy590), new_sr(vyy581, vyy591))
new_esEs20(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_compare111(vyy580, vyy590, True, be, bf, bg) → LT
new_esEs20(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Integer) → new_ltEs12(vyy5800, vyy5900)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy5800)), Neg(vyy590)) → new_primCmpNat0(vyy590, Succ(vyy5800))
new_ltEs19(vyy582, vyy592, app(ty_[], bbg)) → new_ltEs17(vyy582, vyy592, bbg)
new_ltEs6(vyy581, vyy591, app(ty_Ratio, bee)) → new_ltEs4(vyy581, vyy591, bee)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, cfd), cfe)) → new_esEs4(vyy3000, vyy400, cfd, cfe)
new_ltEs6(vyy581, vyy591, app(ty_[], dd)) → new_ltEs17(vyy581, vyy591, dd)
new_esEs10(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs21(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs7(Nothing, Nothing, dae) → True
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_lt4(vyy580, vyy590) → new_esEs8(new_compare6(vyy580, vyy590), LT)
new_esEs23(vyy580, vyy590, ty_Char) → new_esEs13(vyy580, vyy590)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs5(Right(vyy3000), Right(vyy400), bga, ty_Float) → new_esEs10(vyy3000, vyy400)
new_ltEs9(Right(vyy580), Right(vyy590), eg, ty_Float) → new_ltEs7(vyy580, vyy590)
new_primCmpNat0(Succ(vyy5800), Zero) → GT
new_ltEs6(vyy581, vyy591, ty_Double) → new_ltEs15(vyy581, vyy591)
new_ltEs9(Left(vyy580), Right(vyy590), eg, dg) → True
new_compare18(vyy580, vyy590, ty_Bool) → new_compare13(vyy580, vyy590)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(vyy5900))) → LT
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, dag), dah)) → new_esEs5(vyy3000, vyy400, dag, dah)
new_esEs20(vyy3001, vyy401, app(app(ty_Either, cbe), cbf)) → new_esEs5(vyy3001, vyy401, cbe, cbf)
new_sr0(Integer(vyy5900), Integer(vyy5810)) → Integer(new_primMulInt(vyy5900, vyy5810))
new_ltEs13(Just(vyy5800), Just(vyy5900), app(ty_[], bch)) → new_ltEs17(vyy5800, vyy5900, bch)
new_primPlusNat1(Succ(vyy8900), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy8900, vyy401000)))
new_ltEs9(Right(vyy580), Right(vyy590), eg, app(app(app(ty_@3, fd), ff), fg)) → new_ltEs11(vyy580, vyy590, fd, ff, fg)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Ratio, bfh), bef) → new_esEs18(vyy3000, vyy400, bfh)
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_esEs28(vyy3000, vyy400, app(app(ty_Either, chd), che)) → new_esEs5(vyy3000, vyy400, chd, che)
new_esEs7(Nothing, Just(vyy400), dae) → False
new_esEs7(Just(vyy3000), Nothing, dae) → False
new_esEs20(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_lt5(vyy580, vyy590, app(ty_Ratio, bed)) → new_lt18(vyy580, vyy590, bed)
new_ltEs10(GT, GT) → True
new_esEs9(vyy580, vyy590, app(app(ty_Either, bc), bd)) → new_esEs5(vyy580, vyy590, bc, bd)
new_compare26(vyy580, vyy590, False, h, ba) → new_compare17(vyy580, vyy590, new_ltEs5(vyy580, vyy590, h, ba), h, ba)
new_ltEs9(Right(vyy580), Right(vyy590), eg, ty_Bool) → new_ltEs18(vyy580, vyy590)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_@2, bff), bfg), bef) → new_esEs4(vyy3000, vyy400, bff, bfg)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy5900))) → new_primCmpNat0(Zero, Succ(vyy5900))
new_compare12(vyy580, vyy590, False) → GT
new_lt5(vyy580, vyy590, ty_Char) → new_lt14(vyy580, vyy590)
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_ltEs6(vyy581, vyy591, ty_Integer) → new_ltEs12(vyy581, vyy591)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_compare17(vyy580, vyy590, False, h, ba) → GT
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Float) → new_ltEs7(vyy5800, vyy5900)
new_ltEs6(vyy581, vyy591, app(app(app(ty_@3, cg), da), db)) → new_ltEs11(vyy581, vyy591, cg, da, db)
new_primCompAux0(vyy124, LT) → LT
new_esEs9(vyy580, vyy590, ty_Ordering) → new_esEs8(vyy580, vyy590)
new_esEs6(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bhg, bhh, caa) → new_asAs(new_esEs21(vyy3000, vyy400, bhg), new_asAs(new_esEs20(vyy3001, vyy401, bhh), new_esEs19(vyy3002, vyy402, caa)))
new_not(False) → True
new_esEs11(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_esEs28(vyy3000, vyy400, app(ty_[], chf)) → new_esEs16(vyy3000, vyy400, chf)
new_esEs14(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare24(vyy580, vyy590, True, bh) → EQ
new_esEs9(vyy580, vyy590, ty_Char) → new_esEs13(vyy580, vyy590)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_primCmpInt(Pos(Succ(vyy5800)), Pos(vyy590)) → new_primCmpNat0(Succ(vyy5800), vyy590)
new_compare210(vyy580, vyy590, True, bc, bd) → EQ
new_esEs23(vyy580, vyy590, ty_@0) → new_esEs15(vyy580, vyy590)
new_lt10(vyy580, vyy590) → new_esEs8(new_compare19(vyy580, vyy590), LT)
new_esEs19(vyy3002, vyy402, ty_Int) → new_esEs11(vyy3002, vyy402)
new_esEs22(vyy581, vyy591, ty_Bool) → new_esEs17(vyy581, vyy591)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, cff)) → new_esEs18(vyy3000, vyy400, cff)
new_lt14(vyy580, vyy590) → new_esEs8(new_compare29(vyy580, vyy590), LT)
new_esEs9(vyy580, vyy590, ty_Int) → new_esEs11(vyy580, vyy590)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, cef), ceg)) → new_esEs5(vyy3000, vyy400, cef, ceg)
new_ltEs8(vyy58, vyy59) → new_not(new_esEs8(new_compare9(vyy58, vyy59), GT))
new_lt19(vyy580, vyy590, app(ty_Ratio, cdh)) → new_lt18(vyy580, vyy590, cdh)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_primCmpInt(Pos(Succ(vyy5800)), Neg(vyy590)) → GT
new_ltEs19(vyy582, vyy592, ty_Integer) → new_ltEs12(vyy582, vyy592)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, chc)) → new_esEs7(vyy3000, vyy400, chc)
new_lt15(vyy580, vyy590) → new_esEs8(new_compare30(vyy580, vyy590), LT)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs15(vyy3001, vyy401)
new_esEs22(vyy581, vyy591, app(ty_[], baf)) → new_esEs16(vyy581, vyy591, baf)
new_lt19(vyy580, vyy590, ty_Ordering) → new_lt10(vyy580, vyy590)
new_esEs21(vyy3000, vyy400, app(ty_Maybe, ccf)) → new_esEs7(vyy3000, vyy400, ccf)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs21(vyy3000, vyy400, app(app(ty_@2, cde), cdf)) → new_esEs4(vyy3000, vyy400, cde, cdf)
new_lt5(vyy580, vyy590, ty_@0) → new_lt15(vyy580, vyy590)
new_ltEs6(vyy581, vyy591, ty_Char) → new_ltEs14(vyy581, vyy591)
new_ltEs15(vyy58, vyy59) → new_not(new_esEs8(new_compare6(vyy58, vyy59), GT))
new_esEs9(vyy580, vyy590, app(ty_Ratio, bed)) → new_esEs18(vyy580, vyy590, bed)
new_ltEs6(vyy581, vyy591, ty_Ordering) → new_ltEs10(vyy581, vyy591)
new_ltEs9(Right(vyy580), Right(vyy590), eg, app(app(ty_Either, fb), fc)) → new_ltEs9(vyy580, vyy590, fb, fc)
new_compare18(vyy580, vyy590, app(app(ty_@2, bdb), bdc)) → new_compare16(vyy580, vyy590, bdb, bdc)
new_esEs5(Right(vyy3000), Right(vyy400), bga, app(ty_[], bge)) → new_esEs16(vyy3000, vyy400, bge)
new_esEs5(Right(vyy3000), Left(vyy400), bga, bef) → False
new_esEs5(Left(vyy3000), Right(vyy400), bga, bef) → False
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs5(Right(vyy3000), Right(vyy400), bga, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt20(vyy581, vyy591, app(app(app(ty_@3, bab), bac), bad)) → new_lt11(vyy581, vyy591, bab, bac, bad)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_esEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs13(vyy3000, vyy400)
new_lt5(vyy580, vyy590, app(app(ty_Either, bc), bd)) → new_lt9(vyy580, vyy590, bc, bd)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs20(vyy3001, vyy401, ty_@0) → new_esEs15(vyy3001, vyy401)
new_esEs22(vyy581, vyy591, ty_Double) → new_esEs14(vyy581, vyy591)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(vyy580, vyy590, app(ty_Ratio, cdh)) → new_esEs18(vyy580, vyy590, cdh)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, chg), chh), daa)) → new_esEs6(vyy3000, vyy400, chg, chh, daa)
new_lt8(vyy580, vyy590) → new_esEs8(new_compare9(vyy580, vyy590), LT)
new_compare111(vyy580, vyy590, False, be, bf, bg) → GT
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, cge), cgf), cgg)) → new_esEs6(vyy3001, vyy401, cge, cgf, cgg)
new_esEs16([], :(vyy400, vyy401), ced) → False
new_esEs16(:(vyy3000, vyy3001), [], ced) → False
new_esEs23(vyy580, vyy590, ty_Int) → new_esEs11(vyy580, vyy590)
new_esEs9(vyy580, vyy590, ty_Integer) → new_esEs12(vyy580, vyy590)
new_lt20(vyy581, vyy591, ty_Char) → new_lt14(vyy581, vyy591)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Ordering) → new_ltEs10(vyy5800, vyy5900)
new_ltEs9(Right(vyy580), Right(vyy590), eg, app(app(ty_@2, eh), fa)) → new_ltEs5(vyy580, vyy590, eh, fa)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy5900))) → new_primCmpNat0(Succ(vyy5900), Zero)
new_ltEs13(Just(vyy5800), Just(vyy5900), app(ty_Ratio, dbh)) → new_ltEs4(vyy5800, vyy5900, dbh)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy5900))) → GT
new_esEs23(vyy580, vyy590, ty_Bool) → new_esEs17(vyy580, vyy590)
new_esEs5(Right(vyy3000), Right(vyy400), bga, ty_Int) → new_esEs11(vyy3000, vyy400)
new_lt5(vyy580, vyy590, ty_Float) → new_lt6(vyy580, vyy590)
new_ltEs6(vyy581, vyy591, ty_Float) → new_ltEs7(vyy581, vyy591)
new_compare30(@0, @0) → EQ
new_esEs5(Right(vyy3000), Right(vyy400), bga, ty_Double) → new_esEs14(vyy3000, vyy400)
new_ltEs9(Right(vyy580), Right(vyy590), eg, app(ty_Maybe, fh)) → new_ltEs13(vyy580, vyy590, fh)
new_esEs19(vyy3002, vyy402, ty_Double) → new_esEs14(vyy3002, vyy402)
new_esEs20(vyy3001, vyy401, app(ty_Ratio, cce)) → new_esEs18(vyy3001, vyy401, cce)
new_ltEs19(vyy582, vyy592, ty_Char) → new_ltEs14(vyy582, vyy592)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_esEs9(vyy580, vyy590, ty_Bool) → new_esEs17(vyy580, vyy590)
new_compare5([], :(vyy590, vyy591), bda) → LT
new_esEs9(vyy580, vyy590, ty_Double) → new_esEs14(vyy580, vyy590)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs6(vyy3000, vyy400, dbb, dbc, dbd)
new_ltEs6(vyy581, vyy591, app(app(ty_@2, cc), cd)) → new_ltEs5(vyy581, vyy591, cc, cd)
new_ltEs13(Just(vyy5800), Just(vyy5900), app(ty_Maybe, bcg)) → new_ltEs13(vyy5800, vyy5900, bcg)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Char, bef) → new_esEs13(vyy3000, vyy400)
new_esEs9(vyy580, vyy590, app(app(ty_@2, h), ba)) → new_esEs4(vyy580, vyy590, h, ba)
new_lt20(vyy581, vyy591, app(ty_[], baf)) → new_lt16(vyy581, vyy591, baf)
new_compare18(vyy580, vyy590, ty_Integer) → new_compare8(vyy580, vyy590)
new_ltEs9(Right(vyy580), Right(vyy590), eg, ty_Int) → new_ltEs8(vyy580, vyy590)
new_ltEs13(Just(vyy5800), Nothing, bh) → False
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare211(vyy580, vyy590, False, be, bf, bg) → new_compare111(vyy580, vyy590, new_ltEs11(vyy580, vyy590, be, bf, bg), be, bf, bg)
new_esEs15(@0, @0) → True
new_esEs20(vyy3001, vyy401, app(ty_[], cbg)) → new_esEs16(vyy3001, vyy401, cbg)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dab), dac)) → new_esEs4(vyy3000, vyy400, dab, dac)
new_compare27(vyy580, vyy590, be, bf, bg) → new_compare211(vyy580, vyy590, new_esEs6(vyy580, vyy590, be, bf, bg), be, bf, bg)
new_asAs(False, vyy77) → False
new_esEs19(vyy3002, vyy402, ty_Float) → new_esEs10(vyy3002, vyy402)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_ltEs10(LT, GT) → True
new_esEs5(Right(vyy3000), Right(vyy400), bga, ty_Char) → new_esEs13(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs21(vyy3000, vyy400, app(app(ty_Either, ccg), cch)) → new_esEs5(vyy3000, vyy400, ccg, cch)
new_esEs23(vyy580, vyy590, app(app(app(ty_@3, gh), ha), hb)) → new_esEs6(vyy580, vyy590, gh, ha, hb)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Double, dg) → new_ltEs15(vyy580, vyy590)
new_esEs21(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt5(vyy580, vyy590, ty_Int) → new_lt8(vyy580, vyy590)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bfc), bfd), bfe), bef) → new_esEs6(vyy3000, vyy400, bfc, bfd, bfe)
new_ltEs9(Left(vyy580), Left(vyy590), app(ty_[], ef), dg) → new_ltEs17(vyy580, vyy590, ef)
new_ltEs19(vyy582, vyy592, app(app(ty_Either, bba), bbb)) → new_ltEs9(vyy582, vyy592, bba, bbb)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, cee)) → new_esEs7(vyy3000, vyy400, cee)
new_compare12(vyy580, vyy590, True) → LT
new_ltEs6(vyy581, vyy591, app(ty_Maybe, dc)) → new_ltEs13(vyy581, vyy591, dc)
new_lt18(vyy580, vyy590, bed) → new_esEs8(new_compare7(vyy580, vyy590, bed), LT)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Bool, dg) → new_ltEs18(vyy580, vyy590)
new_lt5(vyy580, vyy590, app(app(app(ty_@3, be), bf), bg)) → new_lt11(vyy580, vyy590, be, bf, bg)
new_ltEs10(EQ, EQ) → True
new_lt20(vyy581, vyy591, app(ty_Ratio, cea)) → new_lt18(vyy581, vyy591, cea)
new_esEs20(vyy3001, vyy401, app(app(ty_@2, ccc), ccd)) → new_esEs4(vyy3001, vyy401, ccc, ccd)
new_ltEs10(LT, LT) → True
new_esEs20(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs5(Left(vyy3000), Left(vyy400), ty_@0, bef) → new_esEs15(vyy3000, vyy400)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Int) → new_ltEs8(vyy5800, vyy5900)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Bool, bef) → new_esEs17(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, app(app(ty_@2, cgh), cha)) → new_esEs4(vyy3001, vyy401, cgh, cha)
new_ltEs18(True, False) → False
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs19(vyy582, vyy592, app(ty_Maybe, bbf)) → new_ltEs13(vyy582, vyy592, bbf)
new_ltEs19(vyy582, vyy592, app(app(app(ty_@3, bbc), bbd), bbe)) → new_ltEs11(vyy582, vyy592, bbc, bbd, bbe)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs16([], [], ced) → True
new_esEs5(Right(vyy3000), Right(vyy400), bga, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_lt5(vyy580, vyy590, ty_Ordering) → new_lt10(vyy580, vyy590)
new_esEs22(vyy581, vyy591, ty_Char) → new_esEs13(vyy581, vyy591)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_compare28(vyy580, vyy590, bh) → new_compare24(vyy580, vyy590, new_esEs7(vyy580, vyy590, bh), bh)
new_lt20(vyy581, vyy591, ty_Integer) → new_lt12(vyy581, vyy591)
new_esEs9(vyy580, vyy590, app(ty_Maybe, bh)) → new_esEs7(vyy580, vyy590, bh)
new_ltEs9(Left(vyy580), Left(vyy590), app(app(ty_Either, dh), ea), dg) → new_ltEs9(vyy580, vyy590, dh, ea)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_Either, beh), bfa), bef) → new_esEs5(vyy3000, vyy400, beh, bfa)
new_esEs13(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs19(vyy3002, vyy402, ty_Bool) → new_esEs17(vyy3002, vyy402)
new_ltEs10(EQ, LT) → False
new_compare18(vyy580, vyy590, app(ty_[], beb)) → new_compare5(vyy580, vyy590, beb)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Bool) → new_ltEs18(vyy5800, vyy5900)
new_esEs18(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cec) → new_asAs(new_esEs25(vyy3000, vyy400, cec), new_esEs24(vyy3001, vyy401, cec))
new_esEs22(vyy581, vyy591, ty_Float) → new_esEs10(vyy581, vyy591)
new_ltEs19(vyy582, vyy592, ty_Double) → new_ltEs15(vyy582, vyy592)
new_lt19(vyy580, vyy590, app(app(ty_@2, gb), gc)) → new_lt7(vyy580, vyy590, gb, gc)
new_ltEs10(GT, LT) → False
new_ltEs18(False, True) → True
new_esEs23(vyy580, vyy590, app(ty_[], hd)) → new_esEs16(vyy580, vyy590, hd)
new_esEs9(vyy580, vyy590, app(app(app(ty_@3, be), bf), bg)) → new_esEs6(vyy580, vyy590, be, bf, bg)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Integer, bef) → new_esEs12(vyy3000, vyy400)
new_lt20(vyy581, vyy591, ty_Ordering) → new_lt10(vyy581, vyy591)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs21(vyy3000, vyy400, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs6(vyy3000, vyy400, cdb, cdc, cdd)
new_asAs(True, vyy77) → vyy77
new_lt19(vyy580, vyy590, app(ty_Maybe, hc)) → new_lt13(vyy580, vyy590, hc)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_compare7(:%(vyy580, vyy581), :%(vyy590, vyy591), ty_Int) → new_compare9(new_sr(vyy580, vyy591), new_sr(vyy590, vyy581))
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_lt20(vyy581, vyy591, ty_Bool) → new_lt17(vyy581, vyy591)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dad)) → new_esEs18(vyy3000, vyy400, dad)
new_ltEs13(Just(vyy5800), Just(vyy5900), app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs11(vyy5800, vyy5900, bcd, bce, bcf)
new_esEs19(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_compare5([], [], bda) → EQ
new_lt6(vyy580, vyy590) → new_esEs8(new_compare14(vyy580, vyy590), LT)
new_esEs21(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_compare10(vyy580, vyy590, True) → LT
new_esEs16(:(vyy3000, vyy3001), :(vyy400, vyy401), ced) → new_asAs(new_esEs26(vyy3000, vyy400, ced), new_esEs16(vyy3001, vyy401, ced))
new_lt20(vyy581, vyy591, ty_Double) → new_lt4(vyy581, vyy591)
new_compare18(vyy580, vyy590, ty_Double) → new_compare6(vyy580, vyy590)
new_compare10(vyy580, vyy590, False) → GT
new_esEs22(vyy581, vyy591, app(app(ty_Either, hh), baa)) → new_esEs5(vyy581, vyy591, hh, baa)
new_compare13(vyy580, vyy590) → new_compare23(vyy580, vyy590, new_esEs17(vyy580, vyy590))
new_compare211(vyy580, vyy590, True, be, bf, bg) → EQ
new_esEs21(vyy3000, vyy400, app(ty_[], cda)) → new_esEs16(vyy3000, vyy400, cda)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(vyy124, EQ) → vyy124
new_esEs19(vyy3002, vyy402, app(app(ty_@2, cba), cbb)) → new_esEs4(vyy3002, vyy402, cba, cbb)
new_ltEs9(Right(vyy580), Right(vyy590), eg, app(ty_Ratio, bhf)) → new_ltEs4(vyy580, vyy590, bhf)
new_ltEs19(vyy582, vyy592, ty_@0) → new_ltEs16(vyy582, vyy592)
new_compare210(vyy580, vyy590, False, bc, bd) → new_compare110(vyy580, vyy590, new_ltEs9(vyy580, vyy590, bc, bd), bc, bd)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(vyy581, vyy591, app(ty_Maybe, bae)) → new_esEs7(vyy581, vyy591, bae)
new_lt20(vyy581, vyy591, app(app(ty_Either, hh), baa)) → new_lt9(vyy581, vyy591, hh, baa)
new_esEs5(Right(vyy3000), Right(vyy400), bga, app(ty_Maybe, bgb)) → new_esEs7(vyy3000, vyy400, bgb)
new_ltEs6(vyy581, vyy591, ty_Bool) → new_ltEs18(vyy581, vyy591)
new_esEs21(vyy3000, vyy400, app(ty_Ratio, cdg)) → new_esEs18(vyy3000, vyy400, cdg)
new_primCmpInt(Neg(Succ(vyy5800)), Pos(vyy590)) → LT
new_ltEs9(Left(vyy580), Left(vyy590), app(ty_Ratio, bhe), dg) → new_ltEs4(vyy580, vyy590, bhe)
new_not(True) → False

The set Q consists of the following terms:

new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Int)
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_primCompAux0(x0, LT)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Ordering)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_@0)
new_ltEs13(Nothing, Nothing, x0)
new_compare30(@0, @0)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_compare18(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, ty_@0)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs7(Just(x0), Nothing, x1)
new_ltEs12(x0, x1)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16([], [], x0)
new_compare18(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Int)
new_lt13(x0, x1, x2)
new_esEs27(x0, x1, ty_Float)
new_ltEs10(LT, LT)
new_esEs25(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs22(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_primCompAux0(x0, EQ)
new_compare18(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(GT, GT)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare26(x0, x1, False, x2, x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(x0, x1, True)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs6(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Double)
new_esEs8(LT, LT)
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Bool)
new_ltEs9(Right(x0), Right(x1), x2, ty_Double)
new_esEs17(False, False)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, ty_Integer)
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare10(x0, x1, False)
new_esEs23(x0, x1, ty_Bool)
new_ltEs9(Left(x0), Left(x1), ty_@0, x2)
new_ltEs9(Left(x0), Left(x1), ty_Float, x2)
new_esEs20(x0, x1, ty_Integer)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, False, x2, x3)
new_compare12(x0, x1, False)
new_esEs13(Char(x0), Char(x1))
new_ltEs9(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_lt5(x0, x1, ty_Char)
new_ltEs4(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs19(x0, x1, ty_Double)
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqNat0(Zero, Zero)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Int)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare18(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Char)
new_lt12(x0, x1)
new_ltEs9(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Bool)
new_primPlusNat1(Zero, Succ(x0))
new_esEs20(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Zero)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs11(x0, x1)
new_lt16(x0, x1, x2)
new_lt18(x0, x1, x2)
new_esEs26(x0, x1, ty_Int)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_compare5([], [], x0)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_lt14(x0, x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_@0)
new_esEs16([], :(x0, x1), x2)
new_ltEs9(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare18(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Char)
new_lt5(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Char)
new_ltEs6(x0, x1, ty_Float)
new_lt15(x0, x1)
new_compare11(x0, x1, True, x2)
new_sr0(Integer(x0), Integer(x1))
new_compare11(x0, x1, False, x2)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(:(x0, x1), [], x2)
new_compare18(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_lt7(x0, x1, x2, x3)
new_compare25(x0, x1, True)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Double)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Succ(x0))
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_pePe(True, x0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_ltEs9(Left(x0), Left(x1), ty_Int, x2)
new_primPlusNat1(Zero, Zero)
new_ltEs18(True, True)
new_esEs21(x0, x1, ty_Char)
new_ltEs6(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_compare5(:(x0, x1), :(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare110(x0, x1, True, x2, x3)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Char)
new_compare111(x0, x1, True, x2, x3, x4)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(x0, x1, x2, x3)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_compare211(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Bool)
new_lt10(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(False, False)
new_ltEs9(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Right(x0), Left(x1), x2, x3)
new_ltEs9(Left(x0), Right(x1), x2, x3)
new_primPlusNat1(Succ(x0), Zero)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_@0)
new_ltEs15(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs9(Right(x0), Right(x1), x2, ty_Integer)
new_compare9(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Float)
new_ltEs13(Just(x0), Nothing, x1)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Integer)
new_compare12(x0, x1, True)
new_compare28(x0, x1, x2)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1)
new_ltEs9(Right(x0), Right(x1), x2, ty_Bool)
new_compare18(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs14(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_compare10(x0, x1, True)
new_esEs23(x0, x1, ty_@0)
new_compare211(x0, x1, False, x2, x3, x4)
new_esEs21(x0, x1, ty_Float)
new_ltEs8(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_compare24(x0, x1, False, x2)
new_lt11(x0, x1, x2, x3, x4)
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_pePe(False, x0)
new_lt5(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_ltEs9(Left(x0), Left(x1), ty_Char, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Left(x0), Left(x1), ty_Integer, x2)
new_compare27(x0, x1, x2, x3, x4)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primPlusNat0(Zero, x0)
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_compare18(x0, x1, app(ty_Maybe, x2))
new_compare6(Double(x0, x1), Double(x2, x3))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Zero, Zero)
new_lt17(x0, x1)
new_esEs23(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Double)
new_ltEs9(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_compare19(x0, x1)
new_lt20(x0, x1, ty_Int)
new_compare23(x0, x1, False)
new_lt19(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_lt5(x0, x1, ty_Ordering)
new_ltEs17(x0, x1, x2)
new_esEs20(x0, x1, ty_@0)
new_esEs15(@0, @0)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs21(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare17(x0, x1, True, x2, x3)
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_esEs9(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare210(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Nothing, Just(x0), x1)
new_compare8(Integer(x0), Integer(x1))
new_compare5(:(x0, x1), [], x2)
new_ltEs10(GT, GT)
new_esEs22(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_primCompAux0(x0, GT)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Right(x0), Right(x1), x2, ty_Int)
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Left(x0), Left(x1), ty_Double, x2)
new_esEs20(x0, x1, ty_Int)
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_not(True)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs9(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_compare25(x0, x1, False)
new_ltEs9(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Integer)
new_compare29(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt19(x0, x1, ty_@0)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(False, True)
new_ltEs18(True, False)
new_esEs19(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs9(Right(x0), Right(x1), x2, ty_Float)
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Char)
new_ltEs9(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_Float)
new_compare24(x0, x1, True, x2)
new_asAs(True, x0)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Ordering)
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1)
new_esEs22(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs9(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17(True, False)
new_esEs17(False, True)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Double)
new_ltEs9(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs13(Nothing, Just(x0), x1)
new_esEs9(x0, x1, ty_Integer)
new_compare5([], :(x0, x1), x2)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_compare26(x0, x1, True, x2, x3)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Succ(x0), Zero)
new_compare210(x0, x1, False, x2, x3)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs7(x0, x1)
new_ltEs9(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs19(x0, x1, ty_Integer)
new_compare110(x0, x1, False, x2, x3)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare16(x0, x1, x2, x3)
new_esEs7(Nothing, Nothing, x0)
new_esEs9(x0, x1, ty_@0)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_primMulInt(Neg(x0), Neg(x1))
new_lt8(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_compare18(x0, x1, ty_Bool)
new_ltEs9(Left(x0), Left(x1), ty_Bool, x2)
new_esEs23(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs16(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare18(x0, x1, app(ty_[], x2))
new_ltEs10(EQ, EQ)
new_lt9(x0, x1, x2, x3)
new_ltEs9(Right(x0), Right(x1), x2, ty_@0)
new_compare18(x0, x1, ty_Integer)

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

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



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

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

new_foldFM_GE(vyy43, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba) → new_foldFM_GE1(vyy43, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h), h, ba)
new_foldFM_GE1(vyy43, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE2(vyy330, vyy331, new_foldFM_GE0(vyy43, vyy40, vyy334, h, ba), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba)
new_foldFM_GE1(vyy43, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE(vyy43, vyy40, vyy334, h, ba)
new_foldFM_GE1(vyy43, vyy40, vyy330, vyy331, vyy332, vyy333, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), False, h, ba) → new_foldFM_GE1(vyy43, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h), h, ba)
new_foldFM_GE2(vyy330, vyy331, vyy64, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba) → new_foldFM_GE1(new_fmToList_GE0(vyy330, vyy331, vyy64, h, ba), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, h), h, ba)
new_foldFM_GE1(vyy43, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba) → new_foldFM_GE(vyy43, vyy40, vyy334, h, ba)

The TRS R consists of the following rules:

new_lt19(vyy580, vyy590, ty_Float) → new_lt6(vyy580, vyy590)
new_ltEs19(vyy582, vyy592, app(app(ty_@2, ccb), ccc)) → new_ltEs5(vyy582, vyy592, ccb, ccc)
new_compare25(vyy580, vyy590, False) → new_compare12(vyy580, vyy590, new_ltEs10(vyy580, vyy590))
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, chg)) → new_esEs7(vyy3000, vyy400, chg)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs15(vyy3000, vyy400)
new_esEs20(vyy3001, vyy401, app(ty_Maybe, beg)) → new_esEs7(vyy3001, vyy401, beg)
new_ltEs13(Just(vyy5800), Just(vyy5900), app(app(ty_Either, dbc), dbd)) → new_ltEs9(vyy5800, vyy5900, dbc, dbd)
new_ltEs7(vyy58, vyy59) → new_not(new_esEs8(new_compare14(vyy58, vyy59), GT))
new_esEs27(vyy3001, vyy401, app(ty_[], cfe)) → new_esEs16(vyy3001, vyy401, cfe)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_compare18(vyy580, vyy590, app(app(app(ty_@3, hf), hg), hh)) → new_compare27(vyy580, vyy590, hf, hg, hh)
new_compare8(Integer(vyy580), Integer(vyy590)) → new_primCmpInt(vyy580, vyy590)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_compare110(vyy580, vyy590, True, bg, bh) → LT
new_esEs23(vyy580, vyy590, app(app(ty_Either, bhh), caa)) → new_esEs5(vyy580, vyy590, bhh, caa)
new_esEs27(vyy3001, vyy401, app(ty_Ratio, cgc)) → new_esEs18(vyy3001, vyy401, cgc)
new_esEs23(vyy580, vyy590, app(app(ty_@2, bhf), bhg)) → new_esEs4(vyy580, vyy590, bhf, bhg)
new_esEs19(vyy3002, vyy402, app(ty_[], bdh)) → new_esEs16(vyy3002, vyy402, bdh)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_esEs19(vyy3002, vyy402, ty_Char) → new_esEs13(vyy3002, vyy402)
new_esEs27(vyy3001, vyy401, app(ty_Maybe, cfb)) → new_esEs7(vyy3001, vyy401, cfb)
new_foldFM_GE10(vyy43, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba) → new_foldFM_GE3(vyy330, vyy331, new_foldFM_GE0(vyy43, vyy40, vyy334, h, ba), vyy40, h, ba)
new_primCompAux1(vyy580, vyy590, vyy115, ha) → new_primCompAux0(vyy115, new_compare18(vyy580, vyy590, ha))
new_compare18(vyy580, vyy590, app(ty_Ratio, bac)) → new_compare7(vyy580, vyy590, bac)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Double) → new_ltEs15(vyy5800, vyy5900)
new_esEs19(vyy3002, vyy402, app(ty_Ratio, bef)) → new_esEs18(vyy3002, vyy402, bef)
new_primMulNat0(Zero, Zero) → Zero
new_compare5(:(vyy580, vyy581), :(vyy590, vyy591), ha) → new_primCompAux1(vyy580, vyy590, new_compare5(vyy581, vyy591, ha), ha)
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs15(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_[], cea)) → new_esEs16(vyy3000, vyy400, cea)
new_lt12(vyy580, vyy590) → new_esEs8(new_compare8(vyy580, vyy590), LT)
new_compare16(vyy580, vyy590, be, bf) → new_compare26(vyy580, vyy590, new_esEs4(vyy580, vyy590, be, bf), be, bf)
new_esEs9(vyy580, vyy590, ty_@0) → new_esEs15(vyy580, vyy590)
new_ltEs13(Nothing, Just(vyy5900), cd) → True
new_esEs21(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_lt20(vyy581, vyy591, ty_Float) → new_lt6(vyy581, vyy591)
new_lt5(vyy580, vyy590, ty_Bool) → new_lt17(vyy580, vyy590)
new_lt20(vyy581, vyy591, app(ty_Maybe, cbg)) → new_lt13(vyy581, vyy591, cbg)
new_lt11(vyy580, vyy590, ca, cb, cc) → new_esEs8(new_compare27(vyy580, vyy590, ca, cb, cc), LT)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_ltEs19(vyy582, vyy592, ty_Bool) → new_ltEs18(vyy582, vyy592)
new_esEs17(True, True) → True
new_ltEs13(Just(vyy5800), Just(vyy5900), app(app(ty_@2, dba), dbb)) → new_ltEs5(vyy5800, vyy5900, dba, dbb)
new_lt19(vyy580, vyy590, ty_Bool) → new_lt17(vyy580, vyy590)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Integer, bad) → new_ltEs12(vyy580, vyy590)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs17(vyy3000, vyy400)
new_compare23(vyy580, vyy590, False) → new_compare10(vyy580, vyy590, new_ltEs18(vyy580, vyy590))
new_ltEs14(vyy58, vyy59) → new_not(new_esEs8(new_compare29(vyy58, vyy59), GT))
new_ltEs19(vyy582, vyy592, ty_Ordering) → new_ltEs10(vyy582, vyy592)
new_lt17(vyy580, vyy590) → new_esEs8(new_compare13(vyy580, vyy590), LT)
new_compare29(Char(vyy580), Char(vyy590)) → new_primCmpNat0(vyy580, vyy590)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_@0) → new_ltEs16(vyy5800, vyy5900)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, daf), dag)) → new_esEs4(vyy3000, vyy400, daf, dag)
new_ltEs10(EQ, GT) → True
new_compare7(:%(vyy580, vyy581), :%(vyy590, vyy591), ty_Integer) → new_compare8(new_sr0(vyy580, vyy591), new_sr0(vyy590, vyy581))
new_esEs23(vyy580, vyy590, ty_Integer) → new_esEs12(vyy580, vyy590)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs12(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_compare18(vyy580, vyy590, ty_Ordering) → new_compare19(vyy580, vyy590)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_ltEs16(vyy58, vyy59) → new_not(new_esEs8(new_compare30(vyy58, vyy59), GT))
new_esEs22(vyy581, vyy591, app(ty_Ratio, cca)) → new_esEs18(vyy581, vyy591, cca)
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_esEs19(vyy3002, vyy402, app(app(ty_Either, bdf), bdg)) → new_esEs5(vyy3002, vyy402, bdf, bdg)
new_esEs5(Right(vyy3000), Right(vyy400), ff, app(app(app(ty_@3, gc), gd), ge)) → new_esEs6(vyy3000, vyy400, gc, gd, ge)
new_ltEs6(vyy581, vyy591, ty_@0) → new_ltEs16(vyy581, vyy591)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Float, bad) → new_ltEs7(vyy580, vyy590)
new_pePe(False, vyy114) → vyy114
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Ordering) → new_ltEs10(vyy580, vyy590)
new_ltEs6(vyy581, vyy591, app(app(ty_Either, db), dc)) → new_ltEs9(vyy581, vyy591, db, dc)
new_compare18(vyy580, vyy590, app(app(ty_Either, hd), he)) → new_compare15(vyy580, vyy590, hd, he)
new_esEs19(vyy3002, vyy402, ty_@0) → new_esEs15(vyy3002, vyy402)
new_compare23(vyy580, vyy590, True) → EQ
new_lt19(vyy580, vyy590, app(ty_[], caf)) → new_lt16(vyy580, vyy590, caf)
new_lt5(vyy580, vyy590, app(ty_[], ce)) → new_lt16(vyy580, vyy590, ce)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs22(vyy581, vyy591, ty_@0) → new_esEs15(vyy581, vyy591)
new_esEs22(vyy581, vyy591, app(app(ty_@2, cah), cba)) → new_esEs4(vyy581, vyy591, cah, cba)
new_esEs22(vyy581, vyy591, ty_Int) → new_esEs11(vyy581, vyy591)
new_esEs22(vyy581, vyy591, ty_Integer) → new_esEs12(vyy581, vyy591)
new_esEs23(vyy580, vyy590, app(ty_Maybe, cae)) → new_esEs7(vyy580, vyy590, cae)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs15(vyy3000, vyy400)
new_compare6(Double(vyy580, vyy581), Double(vyy590, vyy591)) → new_compare9(new_sr(vyy580, vyy590), new_sr(vyy581, vyy591))
new_compare9(vyy58, vyy59) → new_primCmpInt(vyy58, vyy59)
new_lt19(vyy580, vyy590, app(app(ty_Either, bhh), caa)) → new_lt9(vyy580, vyy590, bhh, caa)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Char) → new_ltEs14(vyy580, vyy590)
new_esEs22(vyy581, vyy591, ty_Ordering) → new_esEs8(vyy581, vyy591)
new_lt7(vyy580, vyy590, be, bf) → new_esEs8(new_compare16(vyy580, vyy590, be, bf), LT)
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_@0) → new_esEs15(vyy3000, vyy400)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Int, eb) → new_esEs11(vyy3000, vyy400)
new_lt20(vyy581, vyy591, app(app(ty_@2, cah), cba)) → new_lt7(vyy581, vyy591, cah, cba)
new_lt16(vyy580, vyy590, ce) → new_esEs8(new_compare5(vyy580, vyy590, ce), LT)
new_esEs5(Right(vyy3000), Right(vyy400), ff, app(app(ty_@2, gf), gg)) → new_esEs4(vyy3000, vyy400, gf, gg)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Ordering, eb) → new_esEs8(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, dah)) → new_esEs18(vyy3000, vyy400, dah)
new_ltEs19(vyy582, vyy592, ty_Int) → new_ltEs8(vyy582, vyy592)
new_esEs23(vyy580, vyy590, ty_Double) → new_esEs14(vyy580, vyy590)
new_primCmpNat0(Zero, Succ(vyy5900)) → LT
new_esEs21(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_ltEs13(Nothing, Nothing, cd) → True
new_esEs8(LT, LT) → True
new_lt20(vyy581, vyy591, ty_@0) → new_lt15(vyy581, vyy591)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Int, bad) → new_ltEs8(vyy580, vyy590)
new_lt19(vyy580, vyy590, ty_@0) → new_lt15(vyy580, vyy590)
new_lt13(vyy580, vyy590, cd) → new_esEs8(new_compare28(vyy580, vyy590, cd), LT)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs14(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_@0) → new_ltEs16(vyy580, vyy590)
new_ltEs17(vyy58, vyy59, ha) → new_not(new_esEs8(new_compare5(vyy58, vyy59, ha), GT))
new_ltEs4(vyy58, vyy59, bb) → new_not(new_esEs8(new_compare7(vyy58, vyy59, bb), GT))
new_esEs19(vyy3002, vyy402, app(ty_Maybe, bde)) → new_esEs7(vyy3002, vyy402, bde)
new_esEs20(vyy3001, vyy401, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs6(vyy3001, vyy401, bfc, bfd, bfe)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_pePe(True, vyy114) → True
new_primEqNat0(Zero, Zero) → True
new_esEs20(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_lt9(vyy580, vyy590, bg, bh) → new_esEs8(new_compare15(vyy580, vyy590, bg, bh), LT)
new_ltEs11(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), bhc, bhd, bhe) → new_pePe(new_lt19(vyy580, vyy590, bhc), new_asAs(new_esEs23(vyy580, vyy590, bhc), new_pePe(new_lt20(vyy581, vyy591, bhd), new_asAs(new_esEs22(vyy581, vyy591, bhd), new_ltEs19(vyy582, vyy592, bhe)))))
new_compare11(vyy580, vyy590, True, cd) → LT
new_ltEs5(@2(vyy580, vyy581), @2(vyy590, vyy591), bc, bd) → new_pePe(new_lt5(vyy580, vyy590, bc), new_asAs(new_esEs9(vyy580, vyy590, bc), new_ltEs6(vyy581, vyy591, bd)))
new_compare18(vyy580, vyy590, ty_Float) → new_compare14(vyy580, vyy590)
new_compare24(vyy580, vyy590, False, cd) → new_compare11(vyy580, vyy590, new_ltEs13(vyy580, vyy590, cd), cd)
new_foldFM_GE20(vyy330, vyy331, vyy64, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba) → new_foldFM_GE10(new_fmToList_GE0(vyy330, vyy331, vyy64, h, ba), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, h), h, ba)
new_esEs4(@2(vyy3000, vyy3001), @2(vyy400, vyy401), ceh, cfa) → new_asAs(new_esEs28(vyy3000, vyy400, ceh), new_esEs27(vyy3001, vyy401, cfa))
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Double) → new_ltEs15(vyy580, vyy590)
new_lt5(vyy580, vyy590, ty_Double) → new_lt4(vyy580, vyy590)
new_esEs9(vyy580, vyy590, ty_Float) → new_esEs10(vyy580, vyy590)
new_compare110(vyy580, vyy590, False, bg, bh) → GT
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Char) → new_ltEs14(vyy5800, vyy5900)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], dab)) → new_esEs16(vyy3000, vyy400, dab)
new_lt19(vyy580, vyy590, ty_Int) → new_lt8(vyy580, vyy590)
new_esEs9(vyy580, vyy590, app(ty_[], ce)) → new_esEs16(vyy580, vyy590, ce)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, app(ty_[], bch)) → new_ltEs17(vyy580, vyy590, bch)
new_esEs5(Right(vyy3000), Right(vyy400), ff, app(ty_Ratio, gh)) → new_esEs18(vyy3000, vyy400, gh)
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(vyy890), vyy40100) → Succ(Succ(new_primPlusNat1(vyy890, vyy40100)))
new_lt5(vyy580, vyy590, app(ty_Maybe, cd)) → new_lt13(vyy580, vyy590, cd)
new_ltEs9(Left(vyy580), Left(vyy590), ty_@0, bad) → new_ltEs16(vyy580, vyy590)
new_ltEs9(Right(vyy580), Left(vyy590), bbg, bad) → False
new_lt19(vyy580, vyy590, app(app(app(ty_@3, cab), cac), cad)) → new_lt11(vyy580, vyy590, cab, cac, cad)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, ceb), cec), ced)) → new_esEs6(vyy3000, vyy400, ceb, cec, ced)
new_esEs20(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_compare18(vyy580, vyy590, ty_Int) → new_compare9(vyy580, vyy590)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs12(vyy3000, vyy400)
new_compare17(vyy580, vyy590, True, be, bf) → LT
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy582, vyy592, ty_Float) → new_ltEs7(vyy582, vyy592)
new_compare25(vyy580, vyy590, True) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare18(vyy580, vyy590, ty_@0) → new_compare30(vyy580, vyy590)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Float, eb) → new_esEs10(vyy3000, vyy400)
new_ltEs9(Left(vyy580), Left(vyy590), app(ty_Maybe, bbd), bad) → new_ltEs13(vyy580, vyy590, bbd)
new_esEs20(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs22(vyy581, vyy591, app(app(app(ty_@3, cbd), cbe), cbf)) → new_esEs6(vyy581, vyy591, cbd, cbe, cbf)
new_esEs23(vyy580, vyy590, ty_Ordering) → new_esEs8(vyy580, vyy590)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_[], ef), eb) → new_esEs16(vyy3000, vyy400, ef)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy8900), Zero) → Succ(vyy8900)
new_lt5(vyy580, vyy590, ty_Integer) → new_lt12(vyy580, vyy590)
new_lt19(vyy580, vyy590, ty_Char) → new_lt14(vyy580, vyy590)
new_esEs21(vyy3000, vyy400, ty_@0) → new_esEs15(vyy3000, vyy400)
new_ltEs18(True, True) → True
new_esEs21(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Maybe, ec), eb) → new_esEs7(vyy3000, vyy400, ec)
new_esEs27(vyy3001, vyy401, app(app(ty_Either, cfc), cfd)) → new_esEs5(vyy3001, vyy401, cfc, cfd)
new_lt19(vyy580, vyy590, ty_Integer) → new_lt12(vyy580, vyy590)
new_lt5(vyy580, vyy590, app(app(ty_@2, be), bf)) → new_lt7(vyy580, vyy590, be, bf)
new_esEs19(vyy3002, vyy402, ty_Integer) → new_esEs12(vyy3002, vyy402)
new_compare18(vyy580, vyy590, ty_Char) → new_compare29(vyy580, vyy590)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primCompAux0(vyy124, GT) → GT
new_ltEs18(False, False) → True
new_esEs8(EQ, EQ) → True
new_esEs5(Left(vyy3000), Left(vyy400), ty_Double, eb) → new_esEs14(vyy3000, vyy400)
new_compare26(vyy580, vyy590, True, be, bf) → EQ
new_ltEs9(Left(vyy580), Left(vyy590), ty_Char, bad) → new_ltEs14(vyy580, vyy590)
new_ltEs9(Left(vyy580), Left(vyy590), app(app(app(ty_@3, bba), bbb), bbc), bad) → new_ltEs11(vyy580, vyy590, bba, bbb, bbc)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_lt20(vyy581, vyy591, ty_Int) → new_lt8(vyy581, vyy591)
new_esEs21(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_primCmpNat0(Succ(vyy5800), Succ(vyy5900)) → new_primCmpNat0(vyy5800, vyy5900)
new_esEs23(vyy580, vyy590, ty_Float) → new_esEs10(vyy580, vyy590)
new_ltEs19(vyy582, vyy592, app(ty_Ratio, cdc)) → new_ltEs4(vyy582, vyy592, cdc)
new_compare5(:(vyy580, vyy581), [], ha) → GT
new_compare11(vyy580, vyy590, False, cd) → GT
new_compare18(vyy580, vyy590, app(ty_Maybe, baa)) → new_compare28(vyy580, vyy590, baa)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_lt19(vyy580, vyy590, ty_Double) → new_lt4(vyy580, vyy590)
new_compare19(vyy580, vyy590) → new_compare25(vyy580, vyy590, new_esEs8(vyy580, vyy590))
new_compare15(vyy580, vyy590, bg, bh) → new_compare210(vyy580, vyy590, new_esEs5(vyy580, vyy590, bg, bh), bg, bh)
new_ltEs10(GT, EQ) → False
new_esEs5(Right(vyy3000), Right(vyy400), ff, app(app(ty_Either, fh), ga)) → new_esEs5(vyy3000, vyy400, fh, ga)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs9(Left(vyy580), Left(vyy590), app(app(ty_@2, bae), baf), bad) → new_ltEs5(vyy580, vyy590, bae, baf)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Ordering, bad) → new_ltEs10(vyy580, vyy590)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs6(vyy581, vyy591, ty_Int) → new_ltEs8(vyy581, vyy591)
new_ltEs12(vyy58, vyy59) → new_not(new_esEs8(new_compare8(vyy58, vyy59), GT))
new_esEs19(vyy3002, vyy402, app(app(app(ty_@3, bea), beb), bec)) → new_esEs6(vyy3002, vyy402, bea, beb, bec)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Integer) → new_ltEs12(vyy580, vyy590)
new_compare14(Float(vyy580, vyy581), Float(vyy590, vyy591)) → new_compare9(new_sr(vyy580, vyy590), new_sr(vyy581, vyy591))
new_esEs20(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_foldFM_GE10(vyy43, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE20(vyy330, vyy331, new_foldFM_GE0(vyy43, vyy40, vyy334, h, ba), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba)
new_gtEs(vyy3330, vyy40, h) → new_not(new_esEs8(new_compare24(vyy3330, Just(vyy40), new_esEs7(vyy3330, Just(vyy40), h), h), LT))
new_compare111(vyy580, vyy590, True, ca, cb, cc) → LT
new_esEs20(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Integer) → new_ltEs12(vyy5800, vyy5900)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy5800)), Neg(vyy590)) → new_primCmpNat0(vyy590, Succ(vyy5800))
new_ltEs19(vyy582, vyy592, app(ty_[], cdb)) → new_ltEs17(vyy582, vyy592, cdb)
new_ltEs6(vyy581, vyy591, app(ty_Ratio, ea)) → new_ltEs4(vyy581, vyy591, ea)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, cee), cef)) → new_esEs4(vyy3000, vyy400, cee, cef)
new_ltEs6(vyy581, vyy591, app(ty_[], dh)) → new_ltEs17(vyy581, vyy591, dh)
new_esEs10(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs21(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs7(Nothing, Nothing, chf) → True
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_foldFM_GE10(vyy43, vyy40, vyy330, vyy331, vyy332, vyy333, vyy334, False, h, ba) → new_foldFM_GE0(vyy43, vyy40, vyy334, h, ba)
new_lt4(vyy580, vyy590) → new_esEs8(new_compare6(vyy580, vyy590), LT)
new_esEs23(vyy580, vyy590, ty_Char) → new_esEs13(vyy580, vyy590)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Float) → new_esEs10(vyy3000, vyy400)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Float) → new_ltEs7(vyy580, vyy590)
new_primCmpNat0(Succ(vyy5800), Zero) → GT
new_ltEs6(vyy581, vyy591, ty_Double) → new_ltEs15(vyy581, vyy591)
new_ltEs9(Left(vyy580), Right(vyy590), bbg, bad) → True
new_compare18(vyy580, vyy590, ty_Bool) → new_compare13(vyy580, vyy590)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(vyy5900))) → LT
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, chh), daa)) → new_esEs5(vyy3000, vyy400, chh, daa)
new_esEs20(vyy3001, vyy401, app(app(ty_Either, beh), bfa)) → new_esEs5(vyy3001, vyy401, beh, bfa)
new_sr0(Integer(vyy5900), Integer(vyy5810)) → Integer(new_primMulInt(vyy5900, vyy5810))
new_ltEs13(Just(vyy5800), Just(vyy5900), app(ty_[], dca)) → new_ltEs17(vyy5800, vyy5900, dca)
new_primPlusNat1(Succ(vyy8900), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy8900, vyy401000)))
new_foldFM_GE0(vyy43, vyy40, EmptyFM, h, ba) → vyy43
new_ltEs9(Right(vyy580), Right(vyy590), bbg, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs11(vyy580, vyy590, bcd, bce, bcf)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Ratio, fd), eb) → new_esEs18(vyy3000, vyy400, fd)
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_esEs28(vyy3000, vyy400, app(app(ty_Either, cge), cgf)) → new_esEs5(vyy3000, vyy400, cge, cgf)
new_esEs7(Nothing, Just(vyy400), chf) → False
new_esEs7(Just(vyy3000), Nothing, chf) → False
new_esEs20(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_lt5(vyy580, vyy590, app(ty_Ratio, cf)) → new_lt18(vyy580, vyy590, cf)
new_ltEs10(GT, GT) → True
new_esEs9(vyy580, vyy590, app(app(ty_Either, bg), bh)) → new_esEs5(vyy580, vyy590, bg, bh)
new_compare26(vyy580, vyy590, False, be, bf) → new_compare17(vyy580, vyy590, new_ltEs5(vyy580, vyy590, be, bf), be, bf)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Bool) → new_ltEs18(vyy580, vyy590)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_@2, fb), fc), eb) → new_esEs4(vyy3000, vyy400, fb, fc)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy5900))) → new_primCmpNat0(Zero, Succ(vyy5900))
new_compare12(vyy580, vyy590, False) → GT
new_lt5(vyy580, vyy590, ty_Char) → new_lt14(vyy580, vyy590)
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_ltEs6(vyy581, vyy591, ty_Integer) → new_ltEs12(vyy581, vyy591)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_compare17(vyy580, vyy590, False, be, bf) → GT
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Float) → new_ltEs7(vyy5800, vyy5900)
new_ltEs6(vyy581, vyy591, app(app(app(ty_@3, dd), de), df)) → new_ltEs11(vyy581, vyy591, dd, de, df)
new_primCompAux0(vyy124, LT) → LT
new_esEs9(vyy580, vyy590, ty_Ordering) → new_esEs8(vyy580, vyy590)
new_esEs6(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bdb, bdc, bdd) → new_asAs(new_esEs21(vyy3000, vyy400, bdb), new_asAs(new_esEs20(vyy3001, vyy401, bdc), new_esEs19(vyy3002, vyy402, bdd)))
new_not(False) → True
new_esEs11(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_esEs28(vyy3000, vyy400, app(ty_[], cgg)) → new_esEs16(vyy3000, vyy400, cgg)
new_esEs14(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare24(vyy580, vyy590, True, cd) → EQ
new_esEs9(vyy580, vyy590, ty_Char) → new_esEs13(vyy580, vyy590)
new_primCmpInt(Pos(Succ(vyy5800)), Pos(vyy590)) → new_primCmpNat0(Succ(vyy5800), vyy590)
new_compare210(vyy580, vyy590, True, bg, bh) → EQ
new_esEs23(vyy580, vyy590, ty_@0) → new_esEs15(vyy580, vyy590)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs19(vyy3002, vyy402, ty_Int) → new_esEs11(vyy3002, vyy402)
new_lt10(vyy580, vyy590) → new_esEs8(new_compare19(vyy580, vyy590), LT)
new_esEs22(vyy581, vyy591, ty_Bool) → new_esEs17(vyy581, vyy591)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, ceg)) → new_esEs18(vyy3000, vyy400, ceg)
new_lt14(vyy580, vyy590) → new_esEs8(new_compare29(vyy580, vyy590), LT)
new_esEs9(vyy580, vyy590, ty_Int) → new_esEs11(vyy580, vyy590)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, cdg), cdh)) → new_esEs5(vyy3000, vyy400, cdg, cdh)
new_ltEs8(vyy58, vyy59) → new_not(new_esEs8(new_compare9(vyy58, vyy59), GT))
new_lt19(vyy580, vyy590, app(ty_Ratio, cag)) → new_lt18(vyy580, vyy590, cag)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_primCmpInt(Pos(Succ(vyy5800)), Neg(vyy590)) → GT
new_ltEs19(vyy582, vyy592, ty_Integer) → new_ltEs12(vyy582, vyy592)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, cgd)) → new_esEs7(vyy3000, vyy400, cgd)
new_lt15(vyy580, vyy590) → new_esEs8(new_compare30(vyy580, vyy590), LT)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs15(vyy3001, vyy401)
new_esEs22(vyy581, vyy591, app(ty_[], cbh)) → new_esEs16(vyy581, vyy591, cbh)
new_lt19(vyy580, vyy590, ty_Ordering) → new_lt10(vyy580, vyy590)
new_esEs21(vyy3000, vyy400, app(ty_Maybe, bga)) → new_esEs7(vyy3000, vyy400, bga)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs21(vyy3000, vyy400, app(app(ty_@2, bgh), bha)) → new_esEs4(vyy3000, vyy400, bgh, bha)
new_lt5(vyy580, vyy590, ty_@0) → new_lt15(vyy580, vyy590)
new_ltEs6(vyy581, vyy591, ty_Char) → new_ltEs14(vyy581, vyy591)
new_ltEs15(vyy58, vyy59) → new_not(new_esEs8(new_compare6(vyy58, vyy59), GT))
new_esEs9(vyy580, vyy590, app(ty_Ratio, cf)) → new_esEs18(vyy580, vyy590, cf)
new_ltEs6(vyy581, vyy591, ty_Ordering) → new_ltEs10(vyy581, vyy591)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, app(app(ty_Either, bcb), bcc)) → new_ltEs9(vyy580, vyy590, bcb, bcc)
new_compare18(vyy580, vyy590, app(app(ty_@2, hb), hc)) → new_compare16(vyy580, vyy590, hb, hc)
new_esEs5(Right(vyy3000), Right(vyy400), ff, app(ty_[], gb)) → new_esEs16(vyy3000, vyy400, gb)
new_esEs5(Right(vyy3000), Left(vyy400), ff, eb) → False
new_esEs5(Left(vyy3000), Right(vyy400), ff, eb) → False
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt20(vyy581, vyy591, app(app(app(ty_@3, cbd), cbe), cbf)) → new_lt11(vyy581, vyy591, cbd, cbe, cbf)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_esEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs13(vyy3000, vyy400)
new_lt5(vyy580, vyy590, app(app(ty_Either, bg), bh)) → new_lt9(vyy580, vyy590, bg, bh)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs20(vyy3001, vyy401, ty_@0) → new_esEs15(vyy3001, vyy401)
new_esEs22(vyy581, vyy591, ty_Double) → new_esEs14(vyy581, vyy591)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(vyy580, vyy590, app(ty_Ratio, cag)) → new_esEs18(vyy580, vyy590, cag)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, cgh), cha), chb)) → new_esEs6(vyy3000, vyy400, cgh, cha, chb)
new_lt8(vyy580, vyy590) → new_esEs8(new_compare9(vyy580, vyy590), LT)
new_compare111(vyy580, vyy590, False, ca, cb, cc) → GT
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs6(vyy3001, vyy401, cff, cfg, cfh)
new_esEs16([], :(vyy400, vyy401), cde) → False
new_esEs16(:(vyy3000, vyy3001), [], cde) → False
new_esEs23(vyy580, vyy590, ty_Int) → new_esEs11(vyy580, vyy590)
new_esEs9(vyy580, vyy590, ty_Integer) → new_esEs12(vyy580, vyy590)
new_lt20(vyy581, vyy591, ty_Char) → new_lt14(vyy581, vyy591)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Ordering) → new_ltEs10(vyy5800, vyy5900)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, app(app(ty_@2, bbh), bca)) → new_ltEs5(vyy580, vyy590, bbh, bca)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy5900))) → new_primCmpNat0(Succ(vyy5900), Zero)
new_ltEs13(Just(vyy5800), Just(vyy5900), app(ty_Ratio, dcb)) → new_ltEs4(vyy5800, vyy5900, dcb)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy5900))) → GT
new_esEs23(vyy580, vyy590, ty_Bool) → new_esEs17(vyy580, vyy590)
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Int) → new_esEs11(vyy3000, vyy400)
new_lt5(vyy580, vyy590, ty_Float) → new_lt6(vyy580, vyy590)
new_ltEs6(vyy581, vyy591, ty_Float) → new_ltEs7(vyy581, vyy591)
new_compare30(@0, @0) → EQ
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Double) → new_esEs14(vyy3000, vyy400)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, app(ty_Maybe, bcg)) → new_ltEs13(vyy580, vyy590, bcg)
new_esEs19(vyy3002, vyy402, ty_Double) → new_esEs14(vyy3002, vyy402)
new_esEs20(vyy3001, vyy401, app(ty_Ratio, bfh)) → new_esEs18(vyy3001, vyy401, bfh)
new_ltEs19(vyy582, vyy592, ty_Char) → new_ltEs14(vyy582, vyy592)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_esEs9(vyy580, vyy590, ty_Bool) → new_esEs17(vyy580, vyy590)
new_compare5([], :(vyy590, vyy591), ha) → LT
new_esEs9(vyy580, vyy590, ty_Double) → new_esEs14(vyy580, vyy590)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, dac), dad), dae)) → new_esEs6(vyy3000, vyy400, dac, dad, dae)
new_ltEs6(vyy581, vyy591, app(app(ty_@2, cg), da)) → new_ltEs5(vyy581, vyy591, cg, da)
new_ltEs13(Just(vyy5800), Just(vyy5900), app(ty_Maybe, dbh)) → new_ltEs13(vyy5800, vyy5900, dbh)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Char, eb) → new_esEs13(vyy3000, vyy400)
new_esEs9(vyy580, vyy590, app(app(ty_@2, be), bf)) → new_esEs4(vyy580, vyy590, be, bf)
new_lt20(vyy581, vyy591, app(ty_[], cbh)) → new_lt16(vyy581, vyy591, cbh)
new_compare18(vyy580, vyy590, ty_Integer) → new_compare8(vyy580, vyy590)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Int) → new_ltEs8(vyy580, vyy590)
new_ltEs13(Just(vyy5800), Nothing, cd) → False
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare211(vyy580, vyy590, False, ca, cb, cc) → new_compare111(vyy580, vyy590, new_ltEs11(vyy580, vyy590, ca, cb, cc), ca, cb, cc)
new_esEs15(@0, @0) → True
new_esEs20(vyy3001, vyy401, app(ty_[], bfb)) → new_esEs16(vyy3001, vyy401, bfb)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, chc), chd)) → new_esEs4(vyy3000, vyy400, chc, chd)
new_compare27(vyy580, vyy590, ca, cb, cc) → new_compare211(vyy580, vyy590, new_esEs6(vyy580, vyy590, ca, cb, cc), ca, cb, cc)
new_asAs(False, vyy77) → False
new_esEs19(vyy3002, vyy402, ty_Float) → new_esEs10(vyy3002, vyy402)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_ltEs10(LT, GT) → True
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Char) → new_esEs13(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs21(vyy3000, vyy400, app(app(ty_Either, bgb), bgc)) → new_esEs5(vyy3000, vyy400, bgb, bgc)
new_esEs23(vyy580, vyy590, app(app(app(ty_@3, cab), cac), cad)) → new_esEs6(vyy580, vyy590, cab, cac, cad)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Double, bad) → new_ltEs15(vyy580, vyy590)
new_esEs21(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt5(vyy580, vyy590, ty_Int) → new_lt8(vyy580, vyy590)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, eg), eh), fa), eb) → new_esEs6(vyy3000, vyy400, eg, eh, fa)
new_ltEs9(Left(vyy580), Left(vyy590), app(ty_[], bbe), bad) → new_ltEs17(vyy580, vyy590, bbe)
new_ltEs19(vyy582, vyy592, app(app(ty_Either, ccd), cce)) → new_ltEs9(vyy582, vyy592, ccd, cce)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, cdf)) → new_esEs7(vyy3000, vyy400, cdf)
new_compare12(vyy580, vyy590, True) → LT
new_ltEs6(vyy581, vyy591, app(ty_Maybe, dg)) → new_ltEs13(vyy581, vyy591, dg)
new_foldFM_GE0(vyy43, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba) → new_foldFM_GE10(vyy43, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h), h, ba)
new_lt18(vyy580, vyy590, cf) → new_esEs8(new_compare7(vyy580, vyy590, cf), LT)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Bool, bad) → new_ltEs18(vyy580, vyy590)
new_lt5(vyy580, vyy590, app(app(app(ty_@3, ca), cb), cc)) → new_lt11(vyy580, vyy590, ca, cb, cc)
new_ltEs10(EQ, EQ) → True
new_lt20(vyy581, vyy591, app(ty_Ratio, cca)) → new_lt18(vyy581, vyy591, cca)
new_esEs20(vyy3001, vyy401, app(app(ty_@2, bff), bfg)) → new_esEs4(vyy3001, vyy401, bff, bfg)
new_ltEs10(LT, LT) → True
new_esEs20(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs5(Left(vyy3000), Left(vyy400), ty_@0, eb) → new_esEs15(vyy3000, vyy400)
new_fmToList_GE0(vyy330, vyy331, vyy61, h, ba) → :(@2(vyy330, vyy331), vyy61)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Int) → new_ltEs8(vyy5800, vyy5900)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Bool, eb) → new_esEs17(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, app(app(ty_@2, cga), cgb)) → new_esEs4(vyy3001, vyy401, cga, cgb)
new_ltEs18(True, False) → False
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs19(vyy582, vyy592, app(ty_Maybe, cda)) → new_ltEs13(vyy582, vyy592, cda)
new_ltEs19(vyy582, vyy592, app(app(app(ty_@3, ccf), ccg), cch)) → new_ltEs11(vyy582, vyy592, ccf, ccg, cch)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs16([], [], cde) → True
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_lt5(vyy580, vyy590, ty_Ordering) → new_lt10(vyy580, vyy590)
new_esEs22(vyy581, vyy591, ty_Char) → new_esEs13(vyy581, vyy591)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_compare28(vyy580, vyy590, cd) → new_compare24(vyy580, vyy590, new_esEs7(vyy580, vyy590, cd), cd)
new_lt20(vyy581, vyy591, ty_Integer) → new_lt12(vyy581, vyy591)
new_esEs9(vyy580, vyy590, app(ty_Maybe, cd)) → new_esEs7(vyy580, vyy590, cd)
new_ltEs9(Left(vyy580), Left(vyy590), app(app(ty_Either, bag), bah), bad) → new_ltEs9(vyy580, vyy590, bag, bah)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_Either, ed), ee), eb) → new_esEs5(vyy3000, vyy400, ed, ee)
new_esEs13(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs19(vyy3002, vyy402, ty_Bool) → new_esEs17(vyy3002, vyy402)
new_ltEs10(EQ, LT) → False
new_compare18(vyy580, vyy590, app(ty_[], bab)) → new_compare5(vyy580, vyy590, bab)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Bool) → new_ltEs18(vyy5800, vyy5900)
new_esEs18(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cdd) → new_asAs(new_esEs25(vyy3000, vyy400, cdd), new_esEs24(vyy3001, vyy401, cdd))
new_esEs22(vyy581, vyy591, ty_Float) → new_esEs10(vyy581, vyy591)
new_ltEs19(vyy582, vyy592, ty_Double) → new_ltEs15(vyy582, vyy592)
new_lt19(vyy580, vyy590, app(app(ty_@2, bhf), bhg)) → new_lt7(vyy580, vyy590, bhf, bhg)
new_ltEs10(GT, LT) → False
new_ltEs18(False, True) → True
new_esEs23(vyy580, vyy590, app(ty_[], caf)) → new_esEs16(vyy580, vyy590, caf)
new_esEs9(vyy580, vyy590, app(app(app(ty_@3, ca), cb), cc)) → new_esEs6(vyy580, vyy590, ca, cb, cc)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Integer, eb) → new_esEs12(vyy3000, vyy400)
new_lt20(vyy581, vyy591, ty_Ordering) → new_lt10(vyy581, vyy591)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs21(vyy3000, vyy400, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs6(vyy3000, vyy400, bge, bgf, bgg)
new_asAs(True, vyy77) → vyy77
new_lt19(vyy580, vyy590, app(ty_Maybe, cae)) → new_lt13(vyy580, vyy590, cae)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_compare7(:%(vyy580, vyy581), :%(vyy590, vyy591), ty_Int) → new_compare9(new_sr(vyy580, vyy591), new_sr(vyy590, vyy581))
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_lt20(vyy581, vyy591, ty_Bool) → new_lt17(vyy581, vyy591)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, che)) → new_esEs18(vyy3000, vyy400, che)
new_ltEs13(Just(vyy5800), Just(vyy5900), app(app(app(ty_@3, dbe), dbf), dbg)) → new_ltEs11(vyy5800, vyy5900, dbe, dbf, dbg)
new_esEs19(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_compare5([], [], ha) → EQ
new_lt6(vyy580, vyy590) → new_esEs8(new_compare14(vyy580, vyy590), LT)
new_esEs21(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_compare10(vyy580, vyy590, True) → LT
new_esEs16(:(vyy3000, vyy3001), :(vyy400, vyy401), cde) → new_asAs(new_esEs26(vyy3000, vyy400, cde), new_esEs16(vyy3001, vyy401, cde))
new_lt20(vyy581, vyy591, ty_Double) → new_lt4(vyy581, vyy591)
new_compare18(vyy580, vyy590, ty_Double) → new_compare6(vyy580, vyy590)
new_compare10(vyy580, vyy590, False) → GT
new_esEs22(vyy581, vyy591, app(app(ty_Either, cbb), cbc)) → new_esEs5(vyy581, vyy591, cbb, cbc)
new_foldFM_GE3(vyy330, vyy331, vyy63, vyy40, h, ba) → new_fmToList_GE0(vyy330, vyy331, vyy63, h, ba)
new_compare13(vyy580, vyy590) → new_compare23(vyy580, vyy590, new_esEs17(vyy580, vyy590))
new_compare211(vyy580, vyy590, True, ca, cb, cc) → EQ
new_esEs21(vyy3000, vyy400, app(ty_[], bgd)) → new_esEs16(vyy3000, vyy400, bgd)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(vyy124, EQ) → vyy124
new_esEs19(vyy3002, vyy402, app(app(ty_@2, bed), bee)) → new_esEs4(vyy3002, vyy402, bed, bee)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, app(ty_Ratio, bda)) → new_ltEs4(vyy580, vyy590, bda)
new_ltEs19(vyy582, vyy592, ty_@0) → new_ltEs16(vyy582, vyy592)
new_compare210(vyy580, vyy590, False, bg, bh) → new_compare110(vyy580, vyy590, new_ltEs9(vyy580, vyy590, bg, bh), bg, bh)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(vyy581, vyy591, app(ty_Maybe, cbg)) → new_esEs7(vyy581, vyy591, cbg)
new_lt20(vyy581, vyy591, app(app(ty_Either, cbb), cbc)) → new_lt9(vyy581, vyy591, cbb, cbc)
new_esEs5(Right(vyy3000), Right(vyy400), ff, app(ty_Maybe, fg)) → new_esEs7(vyy3000, vyy400, fg)
new_ltEs6(vyy581, vyy591, ty_Bool) → new_ltEs18(vyy581, vyy591)
new_esEs21(vyy3000, vyy400, app(ty_Ratio, bhb)) → new_esEs18(vyy3000, vyy400, bhb)
new_primCmpInt(Neg(Succ(vyy5800)), Pos(vyy590)) → LT
new_ltEs9(Left(vyy580), Left(vyy590), app(ty_Ratio, bbf), bad) → new_ltEs4(vyy580, vyy590, bbf)
new_not(True) → False

The set Q consists of the following terms:

new_foldFM_GE10(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, True, x11, x12)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux0(x0, LT)
new_ltEs6(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_@0)
new_compare30(@0, @0)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_compare18(x0, x1, ty_@0)
new_lt16(x0, x1, x2)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs9(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs6(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_@0)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt11(x0, x1, x2, x3, x4)
new_esEs16(:(x0, x1), [], x2)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs12(x0, x1)
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2, x3)
new_compare18(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Float)
new_ltEs10(LT, LT)
new_esEs25(x0, x1, ty_Integer)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs22(x0, x1, ty_Double)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_ltEs9(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, ty_Ordering)
new_primCompAux0(x0, EQ)
new_compare18(x0, x1, ty_Float)
new_compare17(x0, x1, True, x2, x3)
new_lt5(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, ty_Integer)
new_compare5([], [], x0)
new_esEs8(GT, GT)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_compare23(x0, x1, True)
new_esEs24(x0, x1, ty_Integer)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs9(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs6(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Double)
new_esEs8(LT, LT)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Bool)
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_esEs17(False, False)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_sr(x0, x1)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs17(x0, x1, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_compare18(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, ty_Integer)
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare10(x0, x1, False)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Integer)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_compare12(x0, x1, False)
new_esEs13(Char(x0), Char(x1))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_lt5(x0, x1, ty_Char)
new_ltEs9(Left(x0), Left(x1), ty_Bool, x2)
new_esEs19(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Zero, Zero)
new_ltEs9(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, ty_Char)
new_compare28(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Int)
new_foldFM_GE10(x0, x1, x2, x3, x4, EmptyFM, x5, True, x6, x7)
new_compare18(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Char)
new_lt12(x0, x1)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Float)
new_compare5([], :(x0, x1), x2)
new_esEs20(x0, x1, ty_Bool)
new_ltEs9(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primPlusNat1(Zero, Succ(x0))
new_esEs20(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs11(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_ltEs9(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_lt19(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_lt14(x0, x1)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1, x2)
new_lt5(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare11(x0, x1, True, x2)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(x0, x1, x2)
new_lt20(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_compare18(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Char)
new_ltEs9(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs9(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_esEs9(x0, x1, ty_Char)
new_ltEs6(x0, x1, ty_Float)
new_lt15(x0, x1)
new_sr0(Integer(x0), Integer(x1))
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare25(x0, x1, True)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs9(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_esEs16([], [], x0)
new_esEs27(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Double)
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_lt5(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Succ(x0))
new_pePe(True, x0)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_primPlusNat1(Zero, Zero)
new_ltEs18(True, True)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Char)
new_ltEs6(x0, x1, ty_Integer)
new_primCompAux1(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_compare211(x0, x1, True, x2, x3, x4)
new_ltEs9(Left(x0), Left(x1), ty_Double, x2)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_compare13(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs14(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Int)
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs22(x0, x1, ty_Bool)
new_lt10(x0, x1)
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(False, False)
new_compare5(:(x0, x1), [], x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs9(Right(x0), Left(x1), x2, x3)
new_ltEs9(Left(x0), Right(x1), x2, x3)
new_foldFM_GE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_primPlusNat1(Succ(x0), Zero)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_foldFM_GE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs15(x0, x1)
new_foldFM_GE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Right(x0), Right(x1), x2, ty_Float)
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs9(Right(x0), Right(x1), x2, ty_Double)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_compare9(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Integer)
new_compare12(x0, x1, True)
new_ltEs13(Just(x0), Nothing, x1)
new_compare111(x0, x1, True, x2, x3, x4)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs16([], :(x0, x1), x2)
new_compare17(x0, x1, False, x2, x3)
new_compare110(x0, x1, True, x2, x3)
new_lt4(x0, x1)
new_ltEs9(Left(x0), Left(x1), ty_Char, x2)
new_compare18(x0, x1, ty_Int)
new_esEs7(Just(x0), Nothing, x1)
new_ltEs14(x0, x1)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs6(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_compare10(x0, x1, True)
new_ltEs9(Left(x0), Left(x1), ty_Integer, x2)
new_esEs23(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Float)
new_ltEs8(x0, x1)
new_ltEs9(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare26(x0, x1, False, x2, x3)
new_compare27(x0, x1, x2, x3, x4)
new_pePe(False, x0)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare211(x0, x1, False, x2, x3, x4)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_lt5(x0, x1, ty_Double)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Bool)
new_ltEs13(Nothing, Just(x0), x1)
new_compare6(Double(x0, x1), Double(x2, x3))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Zero, Zero)
new_lt17(x0, x1)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_esEs21(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Double)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_compare19(x0, x1)
new_lt20(x0, x1, ty_Int)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_compare23(x0, x1, False)
new_lt19(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_Float)
new_lt5(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs15(@0, @0)
new_esEs19(x0, x1, app(ty_[], x2))
new_compare210(x0, x1, True, x2, x3)
new_lt20(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Nothing, Just(x0), x1)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, ty_@0)
new_compare26(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs9(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs27(x0, x1, ty_Double)
new_compare24(x0, x1, False, x2)
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_esEs9(x0, x1, ty_Float)
new_ltEs9(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs6(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare8(Integer(x0), Integer(x1))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs10(GT, GT)
new_fmToList_GE0(x0, x1, x2, x3, x4)
new_esEs22(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Float)
new_lt20(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, GT)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs9(Left(x0), Left(x1), ty_@0, x2)
new_esEs20(x0, x1, ty_Int)
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_not(True)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpNat0(Succ(x0), Zero)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare25(x0, x1, False)
new_lt7(x0, x1, x2, x3)
new_lt19(x0, x1, ty_Integer)
new_compare29(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs28(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, ty_@0)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_ltEs9(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(False, True)
new_ltEs18(True, False)
new_esEs19(x0, x1, ty_@0)
new_esEs7(Nothing, Nothing, x0)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs28(x0, x1, ty_Ordering)
new_compare24(x0, x1, True, x2)
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_esEs9(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, ty_Float)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_Float)
new_ltEs13(Nothing, Nothing, x0)
new_compare18(x0, x1, app(ty_Maybe, x2))
new_asAs(True, x0)
new_esEs9(x0, x1, ty_Ordering)
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_lt6(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, ty_Char)
new_ltEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs9(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_foldFM_GE3(x0, x1, x2, x3, x4, x5)
new_esEs17(True, False)
new_esEs17(False, True)
new_esEs20(x0, x1, ty_Double)
new_ltEs9(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Integer)
new_compare11(x0, x1, False, x2)
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, x2, x3)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Left(x0), Left(x1), ty_Float, x2)
new_primEqNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs7(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt9(x0, x1, x2, x3)
new_esEs17(True, True)
new_esEs19(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare5(:(x0, x1), :(x2, x3), x4)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_lt8(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_foldFM_GE0(x0, x1, EmptyFM, x2, x3)
new_esEs21(x0, x1, ty_Integer)
new_compare16(x0, x1, x2, x3)
new_compare18(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Double)
new_ltEs9(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_gtEs(x0, x1, x2)
new_ltEs16(x0, x1)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(EQ, EQ)
new_compare18(x0, x1, ty_Integer)

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

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



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

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

new_foldFM_GE21(vyy330, vyy331, vyy62, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba) → new_foldFM_GE11(new_fmToList_GE0(vyy330, vyy331, vyy62, h, ba), vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs0(vyy3330, h), h, ba)
new_foldFM_GE11(vyy42, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE21(vyy330, vyy331, new_foldFM_GE5(vyy42, vyy334, h, ba), vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba)
new_foldFM_GE11(vyy42, vyy330, vyy331, vyy332, vyy333, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), False, h, ba) → new_foldFM_GE11(vyy42, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs0(vyy3340, h), h, ba)
new_foldFM_GE4(vyy42, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba) → new_foldFM_GE11(vyy42, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs0(vyy3340, h), h, ba)
new_foldFM_GE11(vyy42, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba) → new_foldFM_GE4(vyy42, vyy334, h, ba)
new_foldFM_GE11(vyy42, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE4(vyy42, vyy334, h, ba)

The TRS R consists of the following rules:

new_lt19(vyy580, vyy590, ty_Float) → new_lt6(vyy580, vyy590)
new_ltEs19(vyy582, vyy592, app(app(ty_@2, ccb), ccc)) → new_ltEs5(vyy582, vyy592, ccb, ccc)
new_compare25(vyy580, vyy590, False) → new_compare12(vyy580, vyy590, new_ltEs10(vyy580, vyy590))
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, chg)) → new_esEs7(vyy3000, vyy400, chg)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs15(vyy3000, vyy400)
new_esEs20(vyy3001, vyy401, app(ty_Maybe, beg)) → new_esEs7(vyy3001, vyy401, beg)
new_ltEs13(Just(vyy5800), Just(vyy5900), app(app(ty_Either, dbc), dbd)) → new_ltEs9(vyy5800, vyy5900, dbc, dbd)
new_ltEs7(vyy58, vyy59) → new_not(new_esEs8(new_compare14(vyy58, vyy59), GT))
new_esEs27(vyy3001, vyy401, app(ty_[], cfe)) → new_esEs16(vyy3001, vyy401, cfe)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_compare18(vyy580, vyy590, app(app(app(ty_@3, hf), hg), hh)) → new_compare27(vyy580, vyy590, hf, hg, hh)
new_compare8(Integer(vyy580), Integer(vyy590)) → new_primCmpInt(vyy580, vyy590)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_compare110(vyy580, vyy590, True, bg, bh) → LT
new_esEs23(vyy580, vyy590, app(app(ty_Either, bhh), caa)) → new_esEs5(vyy580, vyy590, bhh, caa)
new_esEs27(vyy3001, vyy401, app(ty_Ratio, cgc)) → new_esEs18(vyy3001, vyy401, cgc)
new_esEs23(vyy580, vyy590, app(app(ty_@2, bhf), bhg)) → new_esEs4(vyy580, vyy590, bhf, bhg)
new_esEs19(vyy3002, vyy402, app(ty_[], bdh)) → new_esEs16(vyy3002, vyy402, bdh)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_esEs19(vyy3002, vyy402, ty_Char) → new_esEs13(vyy3002, vyy402)
new_esEs27(vyy3001, vyy401, app(ty_Maybe, cfb)) → new_esEs7(vyy3001, vyy401, cfb)
new_primCompAux1(vyy580, vyy590, vyy115, ha) → new_primCompAux0(vyy115, new_compare18(vyy580, vyy590, ha))
new_compare18(vyy580, vyy590, app(ty_Ratio, bac)) → new_compare7(vyy580, vyy590, bac)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Double) → new_ltEs15(vyy5800, vyy5900)
new_esEs19(vyy3002, vyy402, app(ty_Ratio, bef)) → new_esEs18(vyy3002, vyy402, bef)
new_primMulNat0(Zero, Zero) → Zero
new_compare5(:(vyy580, vyy581), :(vyy590, vyy591), ha) → new_primCompAux1(vyy580, vyy590, new_compare5(vyy581, vyy591, ha), ha)
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs15(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_[], cea)) → new_esEs16(vyy3000, vyy400, cea)
new_lt12(vyy580, vyy590) → new_esEs8(new_compare8(vyy580, vyy590), LT)
new_compare16(vyy580, vyy590, be, bf) → new_compare26(vyy580, vyy590, new_esEs4(vyy580, vyy590, be, bf), be, bf)
new_esEs9(vyy580, vyy590, ty_@0) → new_esEs15(vyy580, vyy590)
new_ltEs13(Nothing, Just(vyy5900), cd) → True
new_esEs21(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_lt20(vyy581, vyy591, ty_Float) → new_lt6(vyy581, vyy591)
new_lt5(vyy580, vyy590, ty_Bool) → new_lt17(vyy580, vyy590)
new_lt20(vyy581, vyy591, app(ty_Maybe, cbg)) → new_lt13(vyy581, vyy591, cbg)
new_lt11(vyy580, vyy590, ca, cb, cc) → new_esEs8(new_compare27(vyy580, vyy590, ca, cb, cc), LT)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_foldFM_GE12(vyy42, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba) → new_foldFM_GE30(vyy330, vyy331, new_foldFM_GE5(vyy42, vyy334, h, ba), h, ba)
new_ltEs19(vyy582, vyy592, ty_Bool) → new_ltEs18(vyy582, vyy592)
new_esEs17(True, True) → True
new_ltEs13(Just(vyy5800), Just(vyy5900), app(app(ty_@2, dba), dbb)) → new_ltEs5(vyy5800, vyy5900, dba, dbb)
new_lt19(vyy580, vyy590, ty_Bool) → new_lt17(vyy580, vyy590)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Integer, bad) → new_ltEs12(vyy580, vyy590)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs17(vyy3000, vyy400)
new_compare23(vyy580, vyy590, False) → new_compare10(vyy580, vyy590, new_ltEs18(vyy580, vyy590))
new_ltEs14(vyy58, vyy59) → new_not(new_esEs8(new_compare29(vyy58, vyy59), GT))
new_ltEs19(vyy582, vyy592, ty_Ordering) → new_ltEs10(vyy582, vyy592)
new_lt17(vyy580, vyy590) → new_esEs8(new_compare13(vyy580, vyy590), LT)
new_compare29(Char(vyy580), Char(vyy590)) → new_primCmpNat0(vyy580, vyy590)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_@0) → new_ltEs16(vyy5800, vyy5900)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, daf), dag)) → new_esEs4(vyy3000, vyy400, daf, dag)
new_ltEs10(EQ, GT) → True
new_compare7(:%(vyy580, vyy581), :%(vyy590, vyy591), ty_Integer) → new_compare8(new_sr0(vyy580, vyy591), new_sr0(vyy590, vyy581))
new_foldFM_GE22(vyy330, vyy331, vyy62, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba) → new_foldFM_GE12(new_fmToList_GE0(vyy330, vyy331, vyy62, h, ba), vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs0(vyy3330, h), h, ba)
new_esEs23(vyy580, vyy590, ty_Integer) → new_esEs12(vyy580, vyy590)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs12(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_compare18(vyy580, vyy590, ty_Ordering) → new_compare19(vyy580, vyy590)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_ltEs16(vyy58, vyy59) → new_not(new_esEs8(new_compare30(vyy58, vyy59), GT))
new_esEs22(vyy581, vyy591, app(ty_Ratio, cca)) → new_esEs18(vyy581, vyy591, cca)
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_esEs19(vyy3002, vyy402, app(app(ty_Either, bdf), bdg)) → new_esEs5(vyy3002, vyy402, bdf, bdg)
new_esEs5(Right(vyy3000), Right(vyy400), ff, app(app(app(ty_@3, gc), gd), ge)) → new_esEs6(vyy3000, vyy400, gc, gd, ge)
new_ltEs6(vyy581, vyy591, ty_@0) → new_ltEs16(vyy581, vyy591)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Float, bad) → new_ltEs7(vyy580, vyy590)
new_pePe(False, vyy114) → vyy114
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Ordering) → new_ltEs10(vyy580, vyy590)
new_ltEs6(vyy581, vyy591, app(app(ty_Either, db), dc)) → new_ltEs9(vyy581, vyy591, db, dc)
new_compare18(vyy580, vyy590, app(app(ty_Either, hd), he)) → new_compare15(vyy580, vyy590, hd, he)
new_esEs19(vyy3002, vyy402, ty_@0) → new_esEs15(vyy3002, vyy402)
new_compare23(vyy580, vyy590, True) → EQ
new_lt19(vyy580, vyy590, app(ty_[], caf)) → new_lt16(vyy580, vyy590, caf)
new_lt5(vyy580, vyy590, app(ty_[], ce)) → new_lt16(vyy580, vyy590, ce)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs22(vyy581, vyy591, ty_@0) → new_esEs15(vyy581, vyy591)
new_esEs22(vyy581, vyy591, app(app(ty_@2, cah), cba)) → new_esEs4(vyy581, vyy591, cah, cba)
new_esEs22(vyy581, vyy591, ty_Int) → new_esEs11(vyy581, vyy591)
new_esEs22(vyy581, vyy591, ty_Integer) → new_esEs12(vyy581, vyy591)
new_esEs23(vyy580, vyy590, app(ty_Maybe, cae)) → new_esEs7(vyy580, vyy590, cae)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs15(vyy3000, vyy400)
new_compare9(vyy58, vyy59) → new_primCmpInt(vyy58, vyy59)
new_compare6(Double(vyy580, vyy581), Double(vyy590, vyy591)) → new_compare9(new_sr(vyy580, vyy590), new_sr(vyy581, vyy591))
new_lt19(vyy580, vyy590, app(app(ty_Either, bhh), caa)) → new_lt9(vyy580, vyy590, bhh, caa)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Char) → new_ltEs14(vyy580, vyy590)
new_esEs22(vyy581, vyy591, ty_Ordering) → new_esEs8(vyy581, vyy591)
new_lt7(vyy580, vyy590, be, bf) → new_esEs8(new_compare16(vyy580, vyy590, be, bf), LT)
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_@0) → new_esEs15(vyy3000, vyy400)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Int, eb) → new_esEs11(vyy3000, vyy400)
new_lt20(vyy581, vyy591, app(app(ty_@2, cah), cba)) → new_lt7(vyy581, vyy591, cah, cba)
new_lt16(vyy580, vyy590, ce) → new_esEs8(new_compare5(vyy580, vyy590, ce), LT)
new_esEs5(Right(vyy3000), Right(vyy400), ff, app(app(ty_@2, gf), gg)) → new_esEs4(vyy3000, vyy400, gf, gg)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Ordering, eb) → new_esEs8(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, dah)) → new_esEs18(vyy3000, vyy400, dah)
new_ltEs19(vyy582, vyy592, ty_Int) → new_ltEs8(vyy582, vyy592)
new_esEs23(vyy580, vyy590, ty_Double) → new_esEs14(vyy580, vyy590)
new_primCmpNat0(Zero, Succ(vyy5900)) → LT
new_esEs21(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_ltEs13(Nothing, Nothing, cd) → True
new_esEs8(LT, LT) → True
new_lt20(vyy581, vyy591, ty_@0) → new_lt15(vyy581, vyy591)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Int, bad) → new_ltEs8(vyy580, vyy590)
new_lt19(vyy580, vyy590, ty_@0) → new_lt15(vyy580, vyy590)
new_lt13(vyy580, vyy590, cd) → new_esEs8(new_compare28(vyy580, vyy590, cd), LT)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs14(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_@0) → new_ltEs16(vyy580, vyy590)
new_ltEs17(vyy58, vyy59, ha) → new_not(new_esEs8(new_compare5(vyy58, vyy59, ha), GT))
new_ltEs4(vyy58, vyy59, bb) → new_not(new_esEs8(new_compare7(vyy58, vyy59, bb), GT))
new_esEs19(vyy3002, vyy402, app(ty_Maybe, bde)) → new_esEs7(vyy3002, vyy402, bde)
new_esEs20(vyy3001, vyy401, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs6(vyy3001, vyy401, bfc, bfd, bfe)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_pePe(True, vyy114) → True
new_primEqNat0(Zero, Zero) → True
new_esEs20(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_lt9(vyy580, vyy590, bg, bh) → new_esEs8(new_compare15(vyy580, vyy590, bg, bh), LT)
new_ltEs11(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), bhc, bhd, bhe) → new_pePe(new_lt19(vyy580, vyy590, bhc), new_asAs(new_esEs23(vyy580, vyy590, bhc), new_pePe(new_lt20(vyy581, vyy591, bhd), new_asAs(new_esEs22(vyy581, vyy591, bhd), new_ltEs19(vyy582, vyy592, bhe)))))
new_compare11(vyy580, vyy590, True, cd) → LT
new_ltEs5(@2(vyy580, vyy581), @2(vyy590, vyy591), bc, bd) → new_pePe(new_lt5(vyy580, vyy590, bc), new_asAs(new_esEs9(vyy580, vyy590, bc), new_ltEs6(vyy581, vyy591, bd)))
new_compare18(vyy580, vyy590, ty_Float) → new_compare14(vyy580, vyy590)
new_compare24(vyy580, vyy590, False, cd) → new_compare11(vyy580, vyy590, new_ltEs13(vyy580, vyy590, cd), cd)
new_esEs4(@2(vyy3000, vyy3001), @2(vyy400, vyy401), ceh, cfa) → new_asAs(new_esEs28(vyy3000, vyy400, ceh), new_esEs27(vyy3001, vyy401, cfa))
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Double) → new_ltEs15(vyy580, vyy590)
new_lt5(vyy580, vyy590, ty_Double) → new_lt4(vyy580, vyy590)
new_esEs9(vyy580, vyy590, ty_Float) → new_esEs10(vyy580, vyy590)
new_compare110(vyy580, vyy590, False, bg, bh) → GT
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Char) → new_ltEs14(vyy5800, vyy5900)
new_foldFM_GE12(vyy42, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE22(vyy330, vyy331, new_foldFM_GE5(vyy42, vyy334, h, ba), vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], dab)) → new_esEs16(vyy3000, vyy400, dab)
new_lt19(vyy580, vyy590, ty_Int) → new_lt8(vyy580, vyy590)
new_esEs9(vyy580, vyy590, app(ty_[], ce)) → new_esEs16(vyy580, vyy590, ce)
new_foldFM_GE30(vyy330, vyy331, vyy61, h, ba) → new_fmToList_GE0(vyy330, vyy331, vyy61, h, ba)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, app(ty_[], bch)) → new_ltEs17(vyy580, vyy590, bch)
new_esEs5(Right(vyy3000), Right(vyy400), ff, app(ty_Ratio, gh)) → new_esEs18(vyy3000, vyy400, gh)
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(vyy890), vyy40100) → Succ(Succ(new_primPlusNat1(vyy890, vyy40100)))
new_lt5(vyy580, vyy590, app(ty_Maybe, cd)) → new_lt13(vyy580, vyy590, cd)
new_ltEs9(Left(vyy580), Left(vyy590), ty_@0, bad) → new_ltEs16(vyy580, vyy590)
new_ltEs9(Right(vyy580), Left(vyy590), bbg, bad) → False
new_lt19(vyy580, vyy590, app(app(app(ty_@3, cab), cac), cad)) → new_lt11(vyy580, vyy590, cab, cac, cad)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, ceb), cec), ced)) → new_esEs6(vyy3000, vyy400, ceb, cec, ced)
new_esEs20(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_compare18(vyy580, vyy590, ty_Int) → new_compare9(vyy580, vyy590)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs12(vyy3000, vyy400)
new_compare17(vyy580, vyy590, True, be, bf) → LT
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy582, vyy592, ty_Float) → new_ltEs7(vyy582, vyy592)
new_compare25(vyy580, vyy590, True) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare18(vyy580, vyy590, ty_@0) → new_compare30(vyy580, vyy590)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Float, eb) → new_esEs10(vyy3000, vyy400)
new_ltEs9(Left(vyy580), Left(vyy590), app(ty_Maybe, bbd), bad) → new_ltEs13(vyy580, vyy590, bbd)
new_esEs20(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs22(vyy581, vyy591, app(app(app(ty_@3, cbd), cbe), cbf)) → new_esEs6(vyy581, vyy591, cbd, cbe, cbf)
new_esEs23(vyy580, vyy590, ty_Ordering) → new_esEs8(vyy580, vyy590)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_[], ef), eb) → new_esEs16(vyy3000, vyy400, ef)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy8900), Zero) → Succ(vyy8900)
new_lt5(vyy580, vyy590, ty_Integer) → new_lt12(vyy580, vyy590)
new_lt19(vyy580, vyy590, ty_Char) → new_lt14(vyy580, vyy590)
new_esEs21(vyy3000, vyy400, ty_@0) → new_esEs15(vyy3000, vyy400)
new_ltEs18(True, True) → True
new_esEs21(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Maybe, ec), eb) → new_esEs7(vyy3000, vyy400, ec)
new_esEs27(vyy3001, vyy401, app(app(ty_Either, cfc), cfd)) → new_esEs5(vyy3001, vyy401, cfc, cfd)
new_lt19(vyy580, vyy590, ty_Integer) → new_lt12(vyy580, vyy590)
new_lt5(vyy580, vyy590, app(app(ty_@2, be), bf)) → new_lt7(vyy580, vyy590, be, bf)
new_esEs19(vyy3002, vyy402, ty_Integer) → new_esEs12(vyy3002, vyy402)
new_compare18(vyy580, vyy590, ty_Char) → new_compare29(vyy580, vyy590)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primCompAux0(vyy124, GT) → GT
new_ltEs18(False, False) → True
new_esEs8(EQ, EQ) → True
new_esEs5(Left(vyy3000), Left(vyy400), ty_Double, eb) → new_esEs14(vyy3000, vyy400)
new_compare26(vyy580, vyy590, True, be, bf) → EQ
new_ltEs9(Left(vyy580), Left(vyy590), ty_Char, bad) → new_ltEs14(vyy580, vyy590)
new_ltEs9(Left(vyy580), Left(vyy590), app(app(app(ty_@3, bba), bbb), bbc), bad) → new_ltEs11(vyy580, vyy590, bba, bbb, bbc)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_lt20(vyy581, vyy591, ty_Int) → new_lt8(vyy581, vyy591)
new_esEs21(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_primCmpNat0(Succ(vyy5800), Succ(vyy5900)) → new_primCmpNat0(vyy5800, vyy5900)
new_esEs23(vyy580, vyy590, ty_Float) → new_esEs10(vyy580, vyy590)
new_ltEs19(vyy582, vyy592, app(ty_Ratio, cdc)) → new_ltEs4(vyy582, vyy592, cdc)
new_compare5(:(vyy580, vyy581), [], ha) → GT
new_compare11(vyy580, vyy590, False, cd) → GT
new_compare18(vyy580, vyy590, app(ty_Maybe, baa)) → new_compare28(vyy580, vyy590, baa)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_lt19(vyy580, vyy590, ty_Double) → new_lt4(vyy580, vyy590)
new_compare19(vyy580, vyy590) → new_compare25(vyy580, vyy590, new_esEs8(vyy580, vyy590))
new_compare15(vyy580, vyy590, bg, bh) → new_compare210(vyy580, vyy590, new_esEs5(vyy580, vyy590, bg, bh), bg, bh)
new_ltEs10(GT, EQ) → False
new_esEs5(Right(vyy3000), Right(vyy400), ff, app(app(ty_Either, fh), ga)) → new_esEs5(vyy3000, vyy400, fh, ga)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs9(Left(vyy580), Left(vyy590), app(app(ty_@2, bae), baf), bad) → new_ltEs5(vyy580, vyy590, bae, baf)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Ordering, bad) → new_ltEs10(vyy580, vyy590)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs6(vyy581, vyy591, ty_Int) → new_ltEs8(vyy581, vyy591)
new_ltEs12(vyy58, vyy59) → new_not(new_esEs8(new_compare8(vyy58, vyy59), GT))
new_esEs19(vyy3002, vyy402, app(app(app(ty_@3, bea), beb), bec)) → new_esEs6(vyy3002, vyy402, bea, beb, bec)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Integer) → new_ltEs12(vyy580, vyy590)
new_compare14(Float(vyy580, vyy581), Float(vyy590, vyy591)) → new_compare9(new_sr(vyy580, vyy590), new_sr(vyy581, vyy591))
new_esEs20(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_compare111(vyy580, vyy590, True, ca, cb, cc) → LT
new_esEs20(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Integer) → new_ltEs12(vyy5800, vyy5900)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy5800)), Neg(vyy590)) → new_primCmpNat0(vyy590, Succ(vyy5800))
new_ltEs19(vyy582, vyy592, app(ty_[], cdb)) → new_ltEs17(vyy582, vyy592, cdb)
new_ltEs6(vyy581, vyy591, app(ty_Ratio, ea)) → new_ltEs4(vyy581, vyy591, ea)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, cee), cef)) → new_esEs4(vyy3000, vyy400, cee, cef)
new_ltEs6(vyy581, vyy591, app(ty_[], dh)) → new_ltEs17(vyy581, vyy591, dh)
new_esEs10(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs21(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs7(Nothing, Nothing, chf) → True
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_lt4(vyy580, vyy590) → new_esEs8(new_compare6(vyy580, vyy590), LT)
new_esEs23(vyy580, vyy590, ty_Char) → new_esEs13(vyy580, vyy590)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Float) → new_esEs10(vyy3000, vyy400)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Float) → new_ltEs7(vyy580, vyy590)
new_primCmpNat0(Succ(vyy5800), Zero) → GT
new_ltEs6(vyy581, vyy591, ty_Double) → new_ltEs15(vyy581, vyy591)
new_ltEs9(Left(vyy580), Right(vyy590), bbg, bad) → True
new_compare18(vyy580, vyy590, ty_Bool) → new_compare13(vyy580, vyy590)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(vyy5900))) → LT
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, chh), daa)) → new_esEs5(vyy3000, vyy400, chh, daa)
new_esEs20(vyy3001, vyy401, app(app(ty_Either, beh), bfa)) → new_esEs5(vyy3001, vyy401, beh, bfa)
new_sr0(Integer(vyy5900), Integer(vyy5810)) → Integer(new_primMulInt(vyy5900, vyy5810))
new_ltEs13(Just(vyy5800), Just(vyy5900), app(ty_[], dca)) → new_ltEs17(vyy5800, vyy5900, dca)
new_primPlusNat1(Succ(vyy8900), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy8900, vyy401000)))
new_ltEs9(Right(vyy580), Right(vyy590), bbg, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs11(vyy580, vyy590, bcd, bce, bcf)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Ratio, fd), eb) → new_esEs18(vyy3000, vyy400, fd)
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_esEs28(vyy3000, vyy400, app(app(ty_Either, cge), cgf)) → new_esEs5(vyy3000, vyy400, cge, cgf)
new_esEs7(Nothing, Just(vyy400), chf) → False
new_esEs7(Just(vyy3000), Nothing, chf) → False
new_esEs20(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_lt5(vyy580, vyy590, app(ty_Ratio, cf)) → new_lt18(vyy580, vyy590, cf)
new_ltEs10(GT, GT) → True
new_esEs9(vyy580, vyy590, app(app(ty_Either, bg), bh)) → new_esEs5(vyy580, vyy590, bg, bh)
new_compare26(vyy580, vyy590, False, be, bf) → new_compare17(vyy580, vyy590, new_ltEs5(vyy580, vyy590, be, bf), be, bf)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Bool) → new_ltEs18(vyy580, vyy590)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_@2, fb), fc), eb) → new_esEs4(vyy3000, vyy400, fb, fc)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy5900))) → new_primCmpNat0(Zero, Succ(vyy5900))
new_foldFM_GE5(vyy42, EmptyFM, h, ba) → vyy42
new_compare12(vyy580, vyy590, False) → GT
new_foldFM_GE5(vyy42, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba) → new_foldFM_GE12(vyy42, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs0(vyy3340, h), h, ba)
new_lt5(vyy580, vyy590, ty_Char) → new_lt14(vyy580, vyy590)
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_ltEs6(vyy581, vyy591, ty_Integer) → new_ltEs12(vyy581, vyy591)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_compare17(vyy580, vyy590, False, be, bf) → GT
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Float) → new_ltEs7(vyy5800, vyy5900)
new_ltEs6(vyy581, vyy591, app(app(app(ty_@3, dd), de), df)) → new_ltEs11(vyy581, vyy591, dd, de, df)
new_primCompAux0(vyy124, LT) → LT
new_esEs9(vyy580, vyy590, ty_Ordering) → new_esEs8(vyy580, vyy590)
new_esEs6(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bdb, bdc, bdd) → new_asAs(new_esEs21(vyy3000, vyy400, bdb), new_asAs(new_esEs20(vyy3001, vyy401, bdc), new_esEs19(vyy3002, vyy402, bdd)))
new_not(False) → True
new_esEs11(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_esEs28(vyy3000, vyy400, app(ty_[], cgg)) → new_esEs16(vyy3000, vyy400, cgg)
new_esEs14(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare24(vyy580, vyy590, True, cd) → EQ
new_esEs9(vyy580, vyy590, ty_Char) → new_esEs13(vyy580, vyy590)
new_primCmpInt(Pos(Succ(vyy5800)), Pos(vyy590)) → new_primCmpNat0(Succ(vyy5800), vyy590)
new_compare210(vyy580, vyy590, True, bg, bh) → EQ
new_esEs23(vyy580, vyy590, ty_@0) → new_esEs15(vyy580, vyy590)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_lt10(vyy580, vyy590) → new_esEs8(new_compare19(vyy580, vyy590), LT)
new_esEs19(vyy3002, vyy402, ty_Int) → new_esEs11(vyy3002, vyy402)
new_esEs22(vyy581, vyy591, ty_Bool) → new_esEs17(vyy581, vyy591)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, ceg)) → new_esEs18(vyy3000, vyy400, ceg)
new_lt14(vyy580, vyy590) → new_esEs8(new_compare29(vyy580, vyy590), LT)
new_esEs9(vyy580, vyy590, ty_Int) → new_esEs11(vyy580, vyy590)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, cdg), cdh)) → new_esEs5(vyy3000, vyy400, cdg, cdh)
new_ltEs8(vyy58, vyy59) → new_not(new_esEs8(new_compare9(vyy58, vyy59), GT))
new_lt19(vyy580, vyy590, app(ty_Ratio, cag)) → new_lt18(vyy580, vyy590, cag)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_gtEs0(vyy3330, h) → new_not(new_esEs8(new_compare24(vyy3330, Nothing, new_esEs7(vyy3330, Nothing, h), h), LT))
new_primCmpInt(Pos(Succ(vyy5800)), Neg(vyy590)) → GT
new_ltEs19(vyy582, vyy592, ty_Integer) → new_ltEs12(vyy582, vyy592)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, cgd)) → new_esEs7(vyy3000, vyy400, cgd)
new_lt15(vyy580, vyy590) → new_esEs8(new_compare30(vyy580, vyy590), LT)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs15(vyy3001, vyy401)
new_esEs22(vyy581, vyy591, app(ty_[], cbh)) → new_esEs16(vyy581, vyy591, cbh)
new_lt19(vyy580, vyy590, ty_Ordering) → new_lt10(vyy580, vyy590)
new_esEs21(vyy3000, vyy400, app(ty_Maybe, bga)) → new_esEs7(vyy3000, vyy400, bga)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs21(vyy3000, vyy400, app(app(ty_@2, bgh), bha)) → new_esEs4(vyy3000, vyy400, bgh, bha)
new_lt5(vyy580, vyy590, ty_@0) → new_lt15(vyy580, vyy590)
new_ltEs6(vyy581, vyy591, ty_Char) → new_ltEs14(vyy581, vyy591)
new_ltEs15(vyy58, vyy59) → new_not(new_esEs8(new_compare6(vyy58, vyy59), GT))
new_esEs9(vyy580, vyy590, app(ty_Ratio, cf)) → new_esEs18(vyy580, vyy590, cf)
new_ltEs6(vyy581, vyy591, ty_Ordering) → new_ltEs10(vyy581, vyy591)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, app(app(ty_Either, bcb), bcc)) → new_ltEs9(vyy580, vyy590, bcb, bcc)
new_compare18(vyy580, vyy590, app(app(ty_@2, hb), hc)) → new_compare16(vyy580, vyy590, hb, hc)
new_esEs5(Right(vyy3000), Right(vyy400), ff, app(ty_[], gb)) → new_esEs16(vyy3000, vyy400, gb)
new_esEs5(Right(vyy3000), Left(vyy400), ff, eb) → False
new_esEs5(Left(vyy3000), Right(vyy400), ff, eb) → False
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt20(vyy581, vyy591, app(app(app(ty_@3, cbd), cbe), cbf)) → new_lt11(vyy581, vyy591, cbd, cbe, cbf)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_esEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs13(vyy3000, vyy400)
new_lt5(vyy580, vyy590, app(app(ty_Either, bg), bh)) → new_lt9(vyy580, vyy590, bg, bh)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs20(vyy3001, vyy401, ty_@0) → new_esEs15(vyy3001, vyy401)
new_esEs22(vyy581, vyy591, ty_Double) → new_esEs14(vyy581, vyy591)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(vyy580, vyy590, app(ty_Ratio, cag)) → new_esEs18(vyy580, vyy590, cag)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, cgh), cha), chb)) → new_esEs6(vyy3000, vyy400, cgh, cha, chb)
new_lt8(vyy580, vyy590) → new_esEs8(new_compare9(vyy580, vyy590), LT)
new_compare111(vyy580, vyy590, False, ca, cb, cc) → GT
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs6(vyy3001, vyy401, cff, cfg, cfh)
new_esEs16([], :(vyy400, vyy401), cde) → False
new_esEs16(:(vyy3000, vyy3001), [], cde) → False
new_esEs23(vyy580, vyy590, ty_Int) → new_esEs11(vyy580, vyy590)
new_esEs9(vyy580, vyy590, ty_Integer) → new_esEs12(vyy580, vyy590)
new_lt20(vyy581, vyy591, ty_Char) → new_lt14(vyy581, vyy591)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Ordering) → new_ltEs10(vyy5800, vyy5900)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, app(app(ty_@2, bbh), bca)) → new_ltEs5(vyy580, vyy590, bbh, bca)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy5900))) → new_primCmpNat0(Succ(vyy5900), Zero)
new_ltEs13(Just(vyy5800), Just(vyy5900), app(ty_Ratio, dcb)) → new_ltEs4(vyy5800, vyy5900, dcb)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy5900))) → GT
new_esEs23(vyy580, vyy590, ty_Bool) → new_esEs17(vyy580, vyy590)
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Int) → new_esEs11(vyy3000, vyy400)
new_lt5(vyy580, vyy590, ty_Float) → new_lt6(vyy580, vyy590)
new_ltEs6(vyy581, vyy591, ty_Float) → new_ltEs7(vyy581, vyy591)
new_compare30(@0, @0) → EQ
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Double) → new_esEs14(vyy3000, vyy400)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, app(ty_Maybe, bcg)) → new_ltEs13(vyy580, vyy590, bcg)
new_esEs19(vyy3002, vyy402, ty_Double) → new_esEs14(vyy3002, vyy402)
new_esEs20(vyy3001, vyy401, app(ty_Ratio, bfh)) → new_esEs18(vyy3001, vyy401, bfh)
new_ltEs19(vyy582, vyy592, ty_Char) → new_ltEs14(vyy582, vyy592)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_esEs9(vyy580, vyy590, ty_Bool) → new_esEs17(vyy580, vyy590)
new_compare5([], :(vyy590, vyy591), ha) → LT
new_esEs9(vyy580, vyy590, ty_Double) → new_esEs14(vyy580, vyy590)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, dac), dad), dae)) → new_esEs6(vyy3000, vyy400, dac, dad, dae)
new_ltEs6(vyy581, vyy591, app(app(ty_@2, cg), da)) → new_ltEs5(vyy581, vyy591, cg, da)
new_ltEs13(Just(vyy5800), Just(vyy5900), app(ty_Maybe, dbh)) → new_ltEs13(vyy5800, vyy5900, dbh)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Char, eb) → new_esEs13(vyy3000, vyy400)
new_esEs9(vyy580, vyy590, app(app(ty_@2, be), bf)) → new_esEs4(vyy580, vyy590, be, bf)
new_lt20(vyy581, vyy591, app(ty_[], cbh)) → new_lt16(vyy581, vyy591, cbh)
new_compare18(vyy580, vyy590, ty_Integer) → new_compare8(vyy580, vyy590)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, ty_Int) → new_ltEs8(vyy580, vyy590)
new_ltEs13(Just(vyy5800), Nothing, cd) → False
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare211(vyy580, vyy590, False, ca, cb, cc) → new_compare111(vyy580, vyy590, new_ltEs11(vyy580, vyy590, ca, cb, cc), ca, cb, cc)
new_esEs15(@0, @0) → True
new_esEs20(vyy3001, vyy401, app(ty_[], bfb)) → new_esEs16(vyy3001, vyy401, bfb)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, chc), chd)) → new_esEs4(vyy3000, vyy400, chc, chd)
new_compare27(vyy580, vyy590, ca, cb, cc) → new_compare211(vyy580, vyy590, new_esEs6(vyy580, vyy590, ca, cb, cc), ca, cb, cc)
new_asAs(False, vyy77) → False
new_esEs19(vyy3002, vyy402, ty_Float) → new_esEs10(vyy3002, vyy402)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_ltEs10(LT, GT) → True
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Char) → new_esEs13(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs21(vyy3000, vyy400, app(app(ty_Either, bgb), bgc)) → new_esEs5(vyy3000, vyy400, bgb, bgc)
new_esEs23(vyy580, vyy590, app(app(app(ty_@3, cab), cac), cad)) → new_esEs6(vyy580, vyy590, cab, cac, cad)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Double, bad) → new_ltEs15(vyy580, vyy590)
new_esEs21(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt5(vyy580, vyy590, ty_Int) → new_lt8(vyy580, vyy590)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, eg), eh), fa), eb) → new_esEs6(vyy3000, vyy400, eg, eh, fa)
new_ltEs9(Left(vyy580), Left(vyy590), app(ty_[], bbe), bad) → new_ltEs17(vyy580, vyy590, bbe)
new_ltEs19(vyy582, vyy592, app(app(ty_Either, ccd), cce)) → new_ltEs9(vyy582, vyy592, ccd, cce)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, cdf)) → new_esEs7(vyy3000, vyy400, cdf)
new_compare12(vyy580, vyy590, True) → LT
new_ltEs6(vyy581, vyy591, app(ty_Maybe, dg)) → new_ltEs13(vyy581, vyy591, dg)
new_lt18(vyy580, vyy590, cf) → new_esEs8(new_compare7(vyy580, vyy590, cf), LT)
new_ltEs9(Left(vyy580), Left(vyy590), ty_Bool, bad) → new_ltEs18(vyy580, vyy590)
new_lt5(vyy580, vyy590, app(app(app(ty_@3, ca), cb), cc)) → new_lt11(vyy580, vyy590, ca, cb, cc)
new_ltEs10(EQ, EQ) → True
new_lt20(vyy581, vyy591, app(ty_Ratio, cca)) → new_lt18(vyy581, vyy591, cca)
new_esEs20(vyy3001, vyy401, app(app(ty_@2, bff), bfg)) → new_esEs4(vyy3001, vyy401, bff, bfg)
new_ltEs10(LT, LT) → True
new_esEs20(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs5(Left(vyy3000), Left(vyy400), ty_@0, eb) → new_esEs15(vyy3000, vyy400)
new_foldFM_GE12(vyy42, vyy330, vyy331, vyy332, vyy333, vyy334, False, h, ba) → new_foldFM_GE5(vyy42, vyy334, h, ba)
new_fmToList_GE0(vyy330, vyy331, vyy61, h, ba) → :(@2(vyy330, vyy331), vyy61)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Int) → new_ltEs8(vyy5800, vyy5900)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Bool, eb) → new_esEs17(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, app(app(ty_@2, cga), cgb)) → new_esEs4(vyy3001, vyy401, cga, cgb)
new_ltEs18(True, False) → False
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs19(vyy582, vyy592, app(ty_Maybe, cda)) → new_ltEs13(vyy582, vyy592, cda)
new_ltEs19(vyy582, vyy592, app(app(app(ty_@3, ccf), ccg), cch)) → new_ltEs11(vyy582, vyy592, ccf, ccg, cch)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs16([], [], cde) → True
new_esEs5(Right(vyy3000), Right(vyy400), ff, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_lt5(vyy580, vyy590, ty_Ordering) → new_lt10(vyy580, vyy590)
new_esEs22(vyy581, vyy591, ty_Char) → new_esEs13(vyy581, vyy591)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_compare28(vyy580, vyy590, cd) → new_compare24(vyy580, vyy590, new_esEs7(vyy580, vyy590, cd), cd)
new_lt20(vyy581, vyy591, ty_Integer) → new_lt12(vyy581, vyy591)
new_esEs9(vyy580, vyy590, app(ty_Maybe, cd)) → new_esEs7(vyy580, vyy590, cd)
new_ltEs9(Left(vyy580), Left(vyy590), app(app(ty_Either, bag), bah), bad) → new_ltEs9(vyy580, vyy590, bag, bah)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_Either, ed), ee), eb) → new_esEs5(vyy3000, vyy400, ed, ee)
new_esEs13(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs19(vyy3002, vyy402, ty_Bool) → new_esEs17(vyy3002, vyy402)
new_ltEs10(EQ, LT) → False
new_compare18(vyy580, vyy590, app(ty_[], bab)) → new_compare5(vyy580, vyy590, bab)
new_ltEs13(Just(vyy5800), Just(vyy5900), ty_Bool) → new_ltEs18(vyy5800, vyy5900)
new_esEs18(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cdd) → new_asAs(new_esEs25(vyy3000, vyy400, cdd), new_esEs24(vyy3001, vyy401, cdd))
new_esEs22(vyy581, vyy591, ty_Float) → new_esEs10(vyy581, vyy591)
new_ltEs19(vyy582, vyy592, ty_Double) → new_ltEs15(vyy582, vyy592)
new_lt19(vyy580, vyy590, app(app(ty_@2, bhf), bhg)) → new_lt7(vyy580, vyy590, bhf, bhg)
new_ltEs10(GT, LT) → False
new_ltEs18(False, True) → True
new_esEs23(vyy580, vyy590, app(ty_[], caf)) → new_esEs16(vyy580, vyy590, caf)
new_esEs9(vyy580, vyy590, app(app(app(ty_@3, ca), cb), cc)) → new_esEs6(vyy580, vyy590, ca, cb, cc)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Integer, eb) → new_esEs12(vyy3000, vyy400)
new_lt20(vyy581, vyy591, ty_Ordering) → new_lt10(vyy581, vyy591)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs21(vyy3000, vyy400, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs6(vyy3000, vyy400, bge, bgf, bgg)
new_asAs(True, vyy77) → vyy77
new_lt19(vyy580, vyy590, app(ty_Maybe, cae)) → new_lt13(vyy580, vyy590, cae)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_compare7(:%(vyy580, vyy581), :%(vyy590, vyy591), ty_Int) → new_compare9(new_sr(vyy580, vyy591), new_sr(vyy590, vyy581))
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_lt20(vyy581, vyy591, ty_Bool) → new_lt17(vyy581, vyy591)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, che)) → new_esEs18(vyy3000, vyy400, che)
new_ltEs13(Just(vyy5800), Just(vyy5900), app(app(app(ty_@3, dbe), dbf), dbg)) → new_ltEs11(vyy5800, vyy5900, dbe, dbf, dbg)
new_esEs19(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_compare5([], [], ha) → EQ
new_lt6(vyy580, vyy590) → new_esEs8(new_compare14(vyy580, vyy590), LT)
new_esEs21(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_compare10(vyy580, vyy590, True) → LT
new_esEs16(:(vyy3000, vyy3001), :(vyy400, vyy401), cde) → new_asAs(new_esEs26(vyy3000, vyy400, cde), new_esEs16(vyy3001, vyy401, cde))
new_lt20(vyy581, vyy591, ty_Double) → new_lt4(vyy581, vyy591)
new_compare18(vyy580, vyy590, ty_Double) → new_compare6(vyy580, vyy590)
new_compare10(vyy580, vyy590, False) → GT
new_esEs22(vyy581, vyy591, app(app(ty_Either, cbb), cbc)) → new_esEs5(vyy581, vyy591, cbb, cbc)
new_compare13(vyy580, vyy590) → new_compare23(vyy580, vyy590, new_esEs17(vyy580, vyy590))
new_compare211(vyy580, vyy590, True, ca, cb, cc) → EQ
new_esEs21(vyy3000, vyy400, app(ty_[], bgd)) → new_esEs16(vyy3000, vyy400, bgd)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(vyy124, EQ) → vyy124
new_esEs19(vyy3002, vyy402, app(app(ty_@2, bed), bee)) → new_esEs4(vyy3002, vyy402, bed, bee)
new_ltEs9(Right(vyy580), Right(vyy590), bbg, app(ty_Ratio, bda)) → new_ltEs4(vyy580, vyy590, bda)
new_ltEs19(vyy582, vyy592, ty_@0) → new_ltEs16(vyy582, vyy592)
new_compare210(vyy580, vyy590, False, bg, bh) → new_compare110(vyy580, vyy590, new_ltEs9(vyy580, vyy590, bg, bh), bg, bh)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(vyy581, vyy591, app(ty_Maybe, cbg)) → new_esEs7(vyy581, vyy591, cbg)
new_lt20(vyy581, vyy591, app(app(ty_Either, cbb), cbc)) → new_lt9(vyy581, vyy591, cbb, cbc)
new_esEs5(Right(vyy3000), Right(vyy400), ff, app(ty_Maybe, fg)) → new_esEs7(vyy3000, vyy400, fg)
new_ltEs6(vyy581, vyy591, ty_Bool) → new_ltEs18(vyy581, vyy591)
new_esEs21(vyy3000, vyy400, app(ty_Ratio, bhb)) → new_esEs18(vyy3000, vyy400, bhb)
new_primCmpInt(Neg(Succ(vyy5800)), Pos(vyy590)) → LT
new_ltEs9(Left(vyy580), Left(vyy590), app(ty_Ratio, bbf), bad) → new_ltEs4(vyy580, vyy590, bbf)
new_not(True) → False

The set Q consists of the following terms:

new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux0(x0, LT)
new_ltEs6(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_@0)
new_compare30(@0, @0)
new_gtEs0(x0, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_compare18(x0, x1, ty_@0)
new_lt16(x0, x1, x2)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs9(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs6(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_@0)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt11(x0, x1, x2, x3, x4)
new_esEs16(:(x0, x1), [], x2)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs12(x0, x1)
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2, x3)
new_compare18(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Float)
new_ltEs10(LT, LT)
new_esEs25(x0, x1, ty_Integer)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs22(x0, x1, ty_Double)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_ltEs9(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, ty_Ordering)
new_primCompAux0(x0, EQ)
new_compare18(x0, x1, ty_Float)
new_compare17(x0, x1, True, x2, x3)
new_lt5(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, ty_Integer)
new_compare5([], [], x0)
new_esEs8(GT, GT)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_compare23(x0, x1, True)
new_esEs24(x0, x1, ty_Integer)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs9(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs6(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Double)
new_esEs8(LT, LT)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Bool)
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_esEs17(False, False)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_sr(x0, x1)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs17(x0, x1, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_compare18(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, ty_Integer)
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare10(x0, x1, False)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Integer)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_compare12(x0, x1, False)
new_esEs13(Char(x0), Char(x1))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_lt5(x0, x1, ty_Char)
new_ltEs9(Left(x0), Left(x1), ty_Bool, x2)
new_esEs19(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Zero, Zero)
new_ltEs9(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, ty_Char)
new_compare28(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Int)
new_compare18(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Char)
new_lt12(x0, x1)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Float)
new_compare5([], :(x0, x1), x2)
new_esEs20(x0, x1, ty_Bool)
new_ltEs9(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primPlusNat1(Zero, Succ(x0))
new_esEs20(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs11(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_ltEs9(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_lt19(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_lt14(x0, x1)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1, x2)
new_lt5(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare11(x0, x1, True, x2)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(x0, x1, x2)
new_lt20(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_compare18(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Char)
new_ltEs9(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs9(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_esEs9(x0, x1, ty_Char)
new_ltEs6(x0, x1, ty_Float)
new_lt15(x0, x1)
new_sr0(Integer(x0), Integer(x1))
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_foldFM_GE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare25(x0, x1, True)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs9(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_esEs16([], [], x0)
new_esEs27(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Double)
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_lt5(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Succ(x0))
new_pePe(True, x0)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_primPlusNat1(Zero, Zero)
new_ltEs18(True, True)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Char)
new_ltEs6(x0, x1, ty_Integer)
new_primCompAux1(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_compare211(x0, x1, True, x2, x3, x4)
new_ltEs9(Left(x0), Left(x1), ty_Double, x2)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_foldFM_GE5(x0, EmptyFM, x1, x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_compare13(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs14(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Int)
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs22(x0, x1, ty_Bool)
new_lt10(x0, x1)
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(False, False)
new_compare5(:(x0, x1), [], x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs9(Right(x0), Left(x1), x2, x3)
new_ltEs9(Left(x0), Right(x1), x2, x3)
new_primPlusNat1(Succ(x0), Zero)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs15(x0, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Right(x0), Right(x1), x2, ty_Float)
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs9(Right(x0), Right(x1), x2, ty_Double)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_compare9(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Integer)
new_compare12(x0, x1, True)
new_ltEs13(Just(x0), Nothing, x1)
new_compare111(x0, x1, True, x2, x3, x4)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs16([], :(x0, x1), x2)
new_compare17(x0, x1, False, x2, x3)
new_compare110(x0, x1, True, x2, x3)
new_lt4(x0, x1)
new_ltEs9(Left(x0), Left(x1), ty_Char, x2)
new_compare18(x0, x1, ty_Int)
new_esEs7(Just(x0), Nothing, x1)
new_ltEs14(x0, x1)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs6(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_compare10(x0, x1, True)
new_ltEs9(Left(x0), Left(x1), ty_Integer, x2)
new_esEs23(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Float)
new_ltEs8(x0, x1)
new_foldFM_GE12(x0, x1, x2, x3, EmptyFM, x4, True, x5, x6)
new_ltEs9(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare26(x0, x1, False, x2, x3)
new_compare27(x0, x1, x2, x3, x4)
new_pePe(False, x0)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare211(x0, x1, False, x2, x3, x4)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_lt5(x0, x1, ty_Double)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Bool)
new_ltEs13(Nothing, Just(x0), x1)
new_compare6(Double(x0, x1), Double(x2, x3))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Zero, Zero)
new_lt17(x0, x1)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_esEs21(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Double)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_compare19(x0, x1)
new_lt20(x0, x1, ty_Int)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_compare23(x0, x1, False)
new_lt19(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_Float)
new_lt5(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs15(@0, @0)
new_esEs19(x0, x1, app(ty_[], x2))
new_compare210(x0, x1, True, x2, x3)
new_lt20(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Nothing, Just(x0), x1)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_foldFM_GE12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, ty_@0)
new_compare26(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs9(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs27(x0, x1, ty_Double)
new_compare24(x0, x1, False, x2)
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_esEs9(x0, x1, ty_Float)
new_ltEs9(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs6(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare8(Integer(x0), Integer(x1))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs10(GT, GT)
new_fmToList_GE0(x0, x1, x2, x3, x4)
new_esEs22(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Float)
new_lt20(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, GT)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs9(Left(x0), Left(x1), ty_@0, x2)
new_esEs20(x0, x1, ty_Int)
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_not(True)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpNat0(Succ(x0), Zero)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare25(x0, x1, False)
new_foldFM_GE12(x0, x1, x2, x3, Branch(x4, x5, x6, x7, x8), x9, True, x10, x11)
new_lt7(x0, x1, x2, x3)
new_lt19(x0, x1, ty_Integer)
new_compare29(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs28(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, ty_@0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs9(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(False, True)
new_ltEs18(True, False)
new_esEs19(x0, x1, ty_@0)
new_esEs7(Nothing, Nothing, x0)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs28(x0, x1, ty_Ordering)
new_compare24(x0, x1, True, x2)
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_esEs9(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, ty_Float)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_Float)
new_ltEs13(Nothing, Nothing, x0)
new_compare18(x0, x1, app(ty_Maybe, x2))
new_asAs(True, x0)
new_esEs9(x0, x1, ty_Ordering)
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_lt6(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, ty_Char)
new_ltEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs9(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs17(True, False)
new_esEs17(False, True)
new_esEs20(x0, x1, ty_Double)
new_ltEs9(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Integer)
new_compare11(x0, x1, False, x2)
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, x2, x3)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Left(x0), Left(x1), ty_Float, x2)
new_primEqNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs7(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt9(x0, x1, x2, x3)
new_esEs17(True, True)
new_esEs19(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare5(:(x0, x1), :(x2, x3), x4)
new_esEs26(x0, x1, app(ty_[], x2))
new_foldFM_GE30(x0, x1, x2, x3, x4)
new_esEs9(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_lt8(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Integer)
new_compare16(x0, x1, x2, x3)
new_compare18(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_foldFM_GE5(x0, Branch(x1, x2, x3, x4, x5), x6, x7)
new_esEs28(x0, x1, ty_Double)
new_ltEs9(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_ltEs16(x0, x1)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(EQ, EQ)
new_compare18(x0, x1, ty_Integer)

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: