YES 8.695 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
  ((eltsFM_GE :: Ord b => FiniteMap (Maybe b) a  ->  Maybe b  ->  [a]) :: Ord b => FiniteMap (Maybe b) a  ->  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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

is transformed to
eltsFM_GE0 key elt rest = 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
  ((eltsFM_GE :: Ord b => FiniteMap (Maybe b) a  ->  Maybe b  ->  [a]) :: Ord b => FiniteMap (Maybe b) a  ->  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 b a) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

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

  foldFM_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


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

  eltsFM_GE :: Ord b => FiniteMap b a  ->  b  ->  [a]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

  foldFM :: (b  ->  a  ->  c  ->  c)  ->  c  ->  FiniteMap b a  ->  c
foldFM k z EmptyFM = z
foldFM k z (Branch key elt _ 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 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
  ((eltsFM_GE :: Ord b => FiniteMap (Maybe b) a  ->  Maybe b  ->  [a]) :: Ord b => FiniteMap (Maybe b) a  ->  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

  eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

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

  foldFM_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


Replaced joker patterns by fresh variables and removed binding patterns.

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

mainModule FiniteMap
  ((eltsFM_GE :: Ord a => FiniteMap (Maybe a) b  ->  Maybe a  ->  [b]) :: Ord a => FiniteMap (Maybe a) b  ->  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 a b) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

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

  foldFM_GE :: Ord a => (a  ->  b  ->  c  ->  c)  ->  c  ->  a  ->  FiniteMap a b  ->  c
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 a b  ->  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

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

mainModule FiniteMap
  ((eltsFM_GE :: Ord a => FiniteMap (Maybe a) b  ->  Maybe a  ->  [b]) :: Ord a => FiniteMap (Maybe a) b  ->  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 a b) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

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

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

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

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

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

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

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

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

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



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

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

  eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

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

  foldFM_GE :: Ord b => (b  ->  a  ->  c  ->  c)  ->  c  ->  b  ->  FiniteMap b a  ->  c
foldFM_GE k z fr EmptyFM = 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
  (eltsFM_GE :: Ord b => FiniteMap (Maybe b) a  ->  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

  eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

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

  foldFM_GE :: Ord b => (b  ->  a  ->  c  ->  c)  ->  c  ->  b  ->  FiniteMap b a  ->  c
foldFM_GE k z fr EmptyFM = 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(vyy10400), Succ(vyy401000)) → new_primPlusNat(vyy10400, 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(vyy6500), Succ(vyy6600)) → new_primCmpNat(vyy6500, vyy6600)

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

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_compare20(Just(vyy6500), Just(vyy6600), False, app(ty_[], fc)) → new_ltEs1(vyy6500, vyy6600, fc)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), app(app(ty_@2, baa), bab), hf) → new_lt2(vyy650, vyy660, baa, bab)
new_compare0(vyy650, vyy660, h, ba, bb) → new_compare2(vyy650, vyy660, new_esEs4(vyy650, vyy660, h, ba, bb), h, ba, bb)
new_ltEs1(:(vyy650, vyy651), :(vyy660, vyy661), ga) → new_compare(vyy651, vyy661, ga)
new_ltEs3(Left(vyy650), Left(vyy660), app(app(ty_Either, bcg), bch), bcb) → new_ltEs3(vyy650, vyy660, bcg, bch)
new_compare22(vyy650, vyy660, False, ca, cb) → new_ltEs3(vyy650, vyy660, ca, cb)
new_compare(:(vyy650, vyy651), :(vyy660, vyy661), ga) → new_primCompAux(vyy650, vyy660, new_compare3(vyy651, vyy661, ga), ga)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cc, bc, app(app(ty_@2, ec), ed)) → new_ltEs2(vyy652, vyy662, ec, ed)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), bae, app(app(app(ty_@3, baf), bag), bah)) → new_ltEs(vyy651, vyy661, baf, bag, bah)
new_primCompAux(vyy650, vyy660, vyy127, app(app(app(ty_@3, gb), gc), gd)) → new_compare0(vyy650, vyy660, gb, gc, gd)
new_ltEs0(Just(vyy6500), Just(vyy6600), app(ty_Maybe, fb)) → new_ltEs0(vyy6500, vyy6600, fb)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), app(app(ty_Either, bac), bad), hf) → new_lt3(vyy650, vyy660, bac, bad)
new_ltEs1(:(vyy650, vyy651), :(vyy660, vyy661), ga) → new_primCompAux(vyy650, vyy660, new_compare3(vyy651, vyy661, ga), ga)
new_lt3(vyy650, vyy660, ca, cb) → new_compare22(vyy650, vyy660, new_esEs7(vyy650, vyy660, ca, cb), ca, cb)
new_primCompAux(vyy650, vyy660, vyy127, app(ty_[], gf)) → new_compare(vyy650, vyy660, gf)
new_ltEs3(Left(vyy650), Left(vyy660), app(ty_Maybe, bcc), bcb) → new_ltEs0(vyy650, vyy660, bcc)
new_ltEs0(Just(vyy6500), Just(vyy6600), app(app(ty_Either, fg), fh)) → new_ltEs3(vyy6500, vyy6600, fg, fh)
new_ltEs3(Right(vyy650), Right(vyy660), bda, app(app(ty_@2, bdg), bdh)) → new_ltEs2(vyy650, vyy660, bdg, bdh)
new_primCompAux(vyy650, vyy660, vyy127, app(app(ty_Either, ha), hb)) → new_compare5(vyy650, vyy660, ha, hb)
new_lt(vyy650, vyy660, h, ba, bb) → new_compare2(vyy650, vyy660, new_esEs4(vyy650, vyy660, h, ba, bb), h, ba, bb)
new_compare1(vyy650, vyy660, be) → new_compare20(vyy650, vyy660, new_esEs5(vyy650, vyy660, be), be)
new_ltEs3(Right(vyy650), Right(vyy660), bda, app(app(ty_Either, bea), beb)) → new_ltEs3(vyy650, vyy660, bea, beb)
new_ltEs3(Left(vyy650), Left(vyy660), app(app(app(ty_@3, bbg), bbh), bca), bcb) → new_ltEs(vyy650, vyy660, bbg, bbh, bca)
new_compare21(vyy650, vyy660, False, bg, bh) → new_ltEs2(vyy650, vyy660, bg, bh)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cc, bc, app(app(ty_Either, ee), ef)) → new_ltEs3(vyy652, vyy662, ee, ef)
new_compare20(Just(vyy6500), Just(vyy6600), False, app(app(ty_Either, fg), fh)) → new_ltEs3(vyy6500, vyy6600, fg, fh)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cc, app(app(ty_@2, db), dc), bd) → new_lt2(vyy651, vyy661, db, dc)
new_ltEs3(Right(vyy650), Right(vyy660), bda, app(ty_[], bdf)) → new_ltEs1(vyy650, vyy660, bdf)
new_ltEs3(Left(vyy650), Left(vyy660), app(app(ty_@2, bce), bcf), bcb) → new_ltEs2(vyy650, vyy660, bce, bcf)
new_lt1(vyy650, vyy660, bf) → new_compare(vyy650, vyy660, bf)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cc, app(app(ty_Either, dd), de), bd) → new_lt3(vyy651, vyy661, dd, de)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), app(app(app(ty_@3, hc), hd), he), hf) → new_lt(vyy650, vyy660, hc, hd, he)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cc, app(ty_Maybe, cg), bd) → new_lt0(vyy651, vyy661, cg)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cc, app(app(app(ty_@3, cd), ce), cf), bd) → new_lt(vyy651, vyy661, cd, ce, cf)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), bae, app(ty_Maybe, bba)) → new_ltEs0(vyy651, vyy661, bba)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cc, bc, app(ty_Maybe, ea)) → new_ltEs0(vyy652, vyy662, ea)
new_lt2(vyy650, vyy660, bg, bh) → new_compare21(vyy650, vyy660, new_esEs6(vyy650, vyy660, bg, bh), bg, bh)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), bae, app(app(ty_@2, bbc), bbd)) → new_ltEs2(vyy651, vyy661, bbc, bbd)
new_ltEs3(Right(vyy650), Right(vyy660), bda, app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs(vyy650, vyy660, bdb, bdc, bdd)
new_compare(:(vyy650, vyy651), :(vyy660, vyy661), ga) → new_compare(vyy651, vyy661, ga)
new_primCompAux(vyy650, vyy660, vyy127, app(ty_Maybe, ge)) → new_compare1(vyy650, vyy660, ge)
new_compare2(vyy650, vyy660, False, h, ba, bb) → new_ltEs(vyy650, vyy660, h, ba, bb)
new_compare5(vyy650, vyy660, ca, cb) → new_compare22(vyy650, vyy660, new_esEs7(vyy650, vyy660, ca, cb), ca, cb)
new_ltEs0(Just(vyy6500), Just(vyy6600), app(app(ty_@2, fd), ff)) → new_ltEs2(vyy6500, vyy6600, fd, ff)
new_primCompAux(vyy650, vyy660, vyy127, app(app(ty_@2, gg), gh)) → new_compare4(vyy650, vyy660, gg, gh)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), bae, app(ty_[], bbb)) → new_ltEs1(vyy651, vyy661, bbb)
new_ltEs3(Left(vyy650), Left(vyy660), app(ty_[], bcd), bcb) → new_ltEs1(vyy650, vyy660, bcd)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), app(ty_Maybe, be), bc, bd) → new_compare20(vyy650, vyy660, new_esEs5(vyy650, vyy660, be), be)
new_ltEs0(Just(vyy6500), Just(vyy6600), app(ty_[], fc)) → new_ltEs1(vyy6500, vyy6600, fc)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), app(ty_[], bf), bc, bd) → new_compare(vyy650, vyy660, bf)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), app(app(app(ty_@3, h), ba), bb), bc, bd) → new_compare2(vyy650, vyy660, new_esEs4(vyy650, vyy660, h, ba, bb), h, ba, bb)
new_compare20(Just(vyy6500), Just(vyy6600), False, app(app(app(ty_@3, eg), eh), fa)) → new_ltEs(vyy6500, vyy6600, eg, eh, fa)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cc, app(ty_[], da), bd) → new_lt1(vyy651, vyy661, da)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cc, bc, app(app(app(ty_@3, df), dg), dh)) → new_ltEs(vyy652, vyy662, df, dg, dh)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), app(ty_Maybe, hg), hf) → new_lt0(vyy650, vyy660, hg)
new_ltEs3(Right(vyy650), Right(vyy660), bda, app(ty_Maybe, bde)) → new_ltEs0(vyy650, vyy660, bde)
new_ltEs0(Just(vyy6500), Just(vyy6600), app(app(app(ty_@3, eg), eh), fa)) → new_ltEs(vyy6500, vyy6600, eg, eh, fa)
new_compare4(vyy650, vyy660, bg, bh) → new_compare21(vyy650, vyy660, new_esEs6(vyy650, vyy660, bg, bh), bg, bh)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), app(app(ty_Either, ca), cb), bc, bd) → new_compare22(vyy650, vyy660, new_esEs7(vyy650, vyy660, ca, cb), ca, cb)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), bae, app(app(ty_Either, bbe), bbf)) → new_ltEs3(vyy651, vyy661, bbe, bbf)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), app(app(ty_@2, bg), bh), bc, bd) → new_compare21(vyy650, vyy660, new_esEs6(vyy650, vyy660, bg, bh), bg, bh)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), app(ty_[], hh), hf) → new_lt1(vyy650, vyy660, hh)
new_lt0(vyy650, vyy660, be) → new_compare20(vyy650, vyy660, new_esEs5(vyy650, vyy660, be), be)
new_compare20(Just(vyy6500), Just(vyy6600), False, app(ty_Maybe, fb)) → new_ltEs0(vyy6500, vyy6600, fb)
new_ltEs(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cc, bc, app(ty_[], eb)) → new_ltEs1(vyy652, vyy662, eb)
new_compare20(Just(vyy6500), Just(vyy6600), False, app(app(ty_@2, fd), ff)) → new_ltEs2(vyy6500, vyy6600, fd, ff)

The TRS R consists of the following rules:

new_compare18(vyy650, vyy660, ty_Char) → new_compare16(vyy650, vyy660)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Int) → new_ltEs13(vyy6500, vyy6600)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_Either, bhe), bhf), bhd) → new_esEs7(vyy3000, vyy400, bhe, bhf)
new_compare3(:(vyy650, vyy651), :(vyy660, vyy661), ga) → new_primCompAux0(vyy650, vyy660, new_compare3(vyy651, vyy661, ga), ga)
new_esEs21(vyy3001, vyy401, app(app(ty_@2, ceh), cfa)) → new_esEs6(vyy3001, vyy401, ceh, cfa)
new_esEs10(vyy3000, vyy400, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs4(vyy3000, vyy400, bfc, bfd, bfe)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Char) → new_ltEs11(vyy6500, vyy6600)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs10(False, True) → True
new_compare15(vyy650, vyy660, True, bg, bh) → LT
new_lt20(vyy650, vyy660, ty_Int) → new_lt10(vyy650, vyy660)
new_compare110(vyy650, vyy660, True, ca, cb) → LT
new_esEs7(Right(vyy3000), Right(vyy400), cag, app(ty_[], cbf)) → new_esEs17(vyy3000, vyy400, cbf)
new_ltEs14(GT, GT) → True
new_ltEs8(Right(vyy650), Right(vyy660), bda, ty_Char) → new_ltEs11(vyy650, vyy660)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Int, bhd) → new_esEs9(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs16(vyy3000, vyy400)
new_lt16(vyy651, vyy661, app(app(app(ty_@3, cd), ce), cf)) → new_lt6(vyy651, vyy661, cd, ce, cf)
new_lt15(vyy650, vyy660, app(ty_[], bf)) → new_lt4(vyy650, vyy660, bf)
new_esEs20(vyy3000, vyy400, ty_Int) → new_esEs9(vyy3000, vyy400)
new_ltEs4(vyy65, vyy66) → new_not(new_esEs8(new_compare8(vyy65, vyy66), GT))
new_ltEs11(vyy65, vyy66) → new_not(new_esEs8(new_compare16(vyy65, vyy66), GT))
new_esEs20(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy651, vyy661, ty_Float) → new_ltEs4(vyy651, vyy661)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Float, bcb) → new_ltEs4(vyy650, vyy660)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Double, bhd) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy651, vyy661, app(ty_Ratio, dae)) → new_ltEs5(vyy651, vyy661, dae)
new_esEs7(Right(vyy3000), Right(vyy400), cag, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_primMulNat0(Zero, Zero) → Zero
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_esEs25(vyy650, vyy660, ty_Double) → new_esEs12(vyy650, vyy660)
new_lt16(vyy651, vyy661, app(ty_Ratio, cgg)) → new_lt19(vyy651, vyy661, cgg)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs9(vyy3000, vyy400)
new_esEs27(vyy650, vyy660, app(app(app(ty_@3, hc), hd), he)) → new_esEs4(vyy650, vyy660, hc, hd, he)
new_compare17(vyy650, vyy660, bg, bh) → new_compare23(vyy650, vyy660, new_esEs6(vyy650, vyy660, bg, bh), bg, bh)
new_ltEs19(vyy651, vyy661, ty_Double) → new_ltEs9(vyy651, vyy661)
new_ltEs15(Nothing, Just(vyy6600), be) → True
new_ltEs8(Left(vyy650), Left(vyy660), ty_Double, bcb) → new_ltEs9(vyy650, vyy660)
new_ltEs19(vyy651, vyy661, app(ty_Maybe, bba)) → new_ltEs15(vyy651, vyy661, bba)
new_lt20(vyy650, vyy660, app(ty_Maybe, hg)) → new_lt13(vyy650, vyy660, hg)
new_esEs7(Right(vyy3000), Right(vyy400), cag, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_ltEs9(vyy65, vyy66) → new_not(new_esEs8(new_compare6(vyy65, vyy66), GT))
new_lt15(vyy650, vyy660, ty_@0) → new_lt11(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, app(ty_[], bgh)) → new_esEs17(vyy3001, vyy401, bgh)
new_lt17(vyy650, vyy660) → new_esEs8(new_compare19(vyy650, vyy660), LT)
new_lt15(vyy650, vyy660, app(ty_Maybe, be)) → new_lt13(vyy650, vyy660, be)
new_lt9(vyy650, vyy660, ca, cb) → new_esEs8(new_compare26(vyy650, vyy660, ca, cb), LT)
new_esEs20(vyy3000, vyy400, app(ty_Ratio, cda)) → new_esEs13(vyy3000, vyy400, cda)
new_lt10(vyy650, vyy660) → new_esEs8(new_compare7(vyy650, vyy660), LT)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Ordering) → new_ltEs14(vyy6500, vyy6600)
new_esEs4(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ccd, cce, ccf) → new_asAs(new_esEs20(vyy3000, vyy400, ccd), new_asAs(new_esEs21(vyy3001, vyy401, cce), new_esEs22(vyy3002, vyy402, ccf)))
new_esEs10(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_Maybe, dac)) → new_esEs5(vyy3000, vyy400, dac)
new_ltEs8(Right(vyy650), Right(vyy660), bda, ty_Int) → new_ltEs13(vyy650, vyy660)
new_esEs26(vyy651, vyy661, ty_Float) → new_esEs18(vyy651, vyy661)
new_esEs15(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs17(@2(vyy650, vyy651), @2(vyy660, vyy661), bae, hf) → new_pePe(new_lt20(vyy650, vyy660, bae), new_asAs(new_esEs27(vyy650, vyy660, bae), new_ltEs19(vyy651, vyy661, hf)))
new_ltEs18(vyy652, vyy662, ty_Bool) → new_ltEs10(vyy652, vyy662)
new_ltEs8(Left(vyy650), Left(vyy660), app(ty_Maybe, bcc), bcb) → new_ltEs15(vyy650, vyy660, bcc)
new_lt15(vyy650, vyy660, ty_Integer) → new_lt14(vyy650, vyy660)
new_ltEs10(False, False) → True
new_esEs20(vyy3000, vyy400, app(app(ty_@2, cdf), cdg)) → new_esEs6(vyy3000, vyy400, cdf, cdg)
new_ltEs8(Left(vyy650), Left(vyy660), app(ty_Ratio, bed), bcb) → new_ltEs5(vyy650, vyy660, bed)
new_esEs20(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_esEs22(vyy3002, vyy402, app(app(ty_Either, cfc), cfd)) → new_esEs7(vyy3002, vyy402, cfc, cfd)
new_compare13(vyy650, vyy660, h, ba, bb) → new_compare210(vyy650, vyy660, new_esEs4(vyy650, vyy660, h, ba, bb), h, ba, bb)
new_ltEs18(vyy652, vyy662, ty_Float) → new_ltEs4(vyy652, vyy662)
new_ltEs8(Right(vyy650), Right(vyy660), bda, app(app(ty_@2, bdg), bdh)) → new_ltEs17(vyy650, vyy660, bdg, bdh)
new_pePe(False, vyy126) → vyy126
new_lt4(vyy650, vyy660, bf) → new_esEs8(new_compare3(vyy650, vyy660, bf), LT)
new_esEs7(Left(vyy3000), Right(vyy400), cag, bhd) → False
new_esEs7(Right(vyy3000), Left(vyy400), cag, bhd) → False
new_ltEs8(Left(vyy650), Left(vyy660), app(app(ty_@2, bce), bcf), bcb) → new_ltEs17(vyy650, vyy660, bce, bcf)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs18(vyy3000, vyy400)
new_esEs27(vyy650, vyy660, app(app(ty_Either, bac), bad)) → new_esEs7(vyy650, vyy660, bac, bad)
new_ltEs14(GT, EQ) → False
new_compare18(vyy650, vyy660, ty_Int) → new_compare7(vyy650, vyy660)
new_ltEs8(Right(vyy650), Right(vyy660), bda, ty_Bool) → new_ltEs10(vyy650, vyy660)
new_ltEs18(vyy652, vyy662, app(app(app(ty_@3, df), dg), dh)) → new_ltEs12(vyy652, vyy662, df, dg, dh)
new_esEs7(Right(vyy3000), Right(vyy400), cag, ty_Char) → new_esEs16(vyy3000, vyy400)
new_compare14(@0, @0) → EQ
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs4(vyy3000, vyy400, dbb, dbc, dbd)
new_lt16(vyy651, vyy661, ty_Float) → new_lt18(vyy651, vyy661)
new_esEs27(vyy650, vyy660, app(ty_[], hh)) → new_esEs17(vyy650, vyy660, hh)
new_esEs22(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Bool, bcb) → new_ltEs10(vyy650, vyy660)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs15(vyy3000, vyy400)
new_ltEs8(Right(vyy650), Right(vyy660), bda, ty_Ordering) → new_ltEs14(vyy650, vyy660)
new_lt20(vyy650, vyy660, app(app(ty_@2, baa), bab)) → new_lt7(vyy650, vyy660, baa, bab)
new_ltEs18(vyy652, vyy662, ty_Int) → new_ltEs13(vyy652, vyy662)
new_ltEs15(Just(vyy6500), Just(vyy6600), app(ty_Maybe, fb)) → new_ltEs15(vyy6500, vyy6600, fb)
new_esEs10(vyy3000, vyy400, app(app(ty_@2, bfg), bfh)) → new_esEs6(vyy3000, vyy400, bfg, bfh)
new_compare18(vyy650, vyy660, ty_Ordering) → new_compare24(vyy650, vyy660)
new_ltEs18(vyy652, vyy662, ty_Char) → new_ltEs11(vyy652, vyy662)
new_ltEs7(vyy65, vyy66) → new_not(new_esEs8(new_compare12(vyy65, vyy66), GT))
new_lt15(vyy650, vyy660, app(ty_Ratio, cgf)) → new_lt19(vyy650, vyy660, cgf)
new_primCmpNat0(Zero, Succ(vyy6600)) → LT
new_esEs26(vyy651, vyy661, ty_Double) → new_esEs12(vyy651, vyy661)
new_ltEs18(vyy652, vyy662, ty_@0) → new_ltEs6(vyy652, vyy662)
new_esEs25(vyy650, vyy660, app(app(ty_@2, bg), bh)) → new_esEs6(vyy650, vyy660, bg, bh)
new_lt16(vyy651, vyy661, app(app(ty_@2, db), dc)) → new_lt7(vyy651, vyy661, db, dc)
new_esEs8(LT, LT) → True
new_esEs21(vyy3001, vyy401, app(ty_Ratio, cec)) → new_esEs13(vyy3001, vyy401, cec)
new_lt18(vyy650, vyy660) → new_esEs8(new_compare8(vyy650, vyy660), LT)
new_lt11(vyy650, vyy660) → new_esEs8(new_compare14(vyy650, vyy660), LT)
new_compare19(vyy650, vyy660) → new_compare28(vyy650, vyy660, new_esEs19(vyy650, vyy660))
new_esEs25(vyy650, vyy660, ty_Ordering) → new_esEs8(vyy650, vyy660)
new_esEs25(vyy650, vyy660, app(ty_Ratio, cgf)) → new_esEs13(vyy650, vyy660, cgf)
new_ltEs8(Right(vyy650), Right(vyy660), bda, app(ty_Maybe, bde)) → new_ltEs15(vyy650, vyy660, bde)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Double) → new_ltEs9(vyy6500, vyy6600)
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_[], chh)) → new_esEs17(vyy3000, vyy400, chh)
new_pePe(True, vyy126) → True
new_primEqNat0(Zero, Zero) → True
new_ltEs19(vyy651, vyy661, ty_Int) → new_ltEs13(vyy651, vyy661)
new_compare18(vyy650, vyy660, app(app(app(ty_@3, gb), gc), gd)) → new_compare13(vyy650, vyy660, gb, gc, gd)
new_ltEs15(Just(vyy6500), Just(vyy6600), app(ty_Ratio, ccc)) → new_ltEs5(vyy6500, vyy6600, ccc)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat1(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_compare29(vyy650, vyy660, True, ca, cb) → EQ
new_esEs14(@0, @0) → True
new_esEs11(vyy3001, vyy401, ty_Double) → new_esEs12(vyy3001, vyy401)
new_ltEs19(vyy651, vyy661, app(app(ty_Either, bbe), bbf)) → new_ltEs8(vyy651, vyy661, bbe, bbf)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Integer) → new_ltEs7(vyy6500, vyy6600)
new_esEs26(vyy651, vyy661, app(ty_Ratio, cgg)) → new_esEs13(vyy651, vyy661, cgg)
new_esEs27(vyy650, vyy660, app(ty_Ratio, dad)) → new_esEs13(vyy650, vyy660, dad)
new_esEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bef, beg) → new_asAs(new_esEs10(vyy3000, vyy400, bef), new_esEs11(vyy3001, vyy401, beg))
new_esEs19(True, True) → True
new_esEs7(Left(vyy3000), Left(vyy400), ty_Ordering, bhd) → new_esEs8(vyy3000, vyy400)
new_compare110(vyy650, vyy660, False, ca, cb) → GT
new_ltEs8(Left(vyy650), Left(vyy660), app(app(app(ty_@3, bbg), bbh), bca), bcb) → new_ltEs12(vyy650, vyy660, bbg, bbh, bca)
new_esEs11(vyy3001, vyy401, ty_Char) → new_esEs16(vyy3001, vyy401)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Float) → new_ltEs4(vyy6500, vyy6600)
new_ltEs14(EQ, LT) → False
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_compare7(vyy65, vyy66) → new_primCmpInt(vyy65, vyy66)
new_ltEs19(vyy651, vyy661, app(app(app(ty_@3, baf), bag), bah)) → new_ltEs12(vyy651, vyy661, baf, bag, bah)
new_ltEs8(Right(vyy650), Right(vyy660), bda, ty_@0) → new_ltEs6(vyy650, vyy660)
new_esEs26(vyy651, vyy661, ty_Ordering) → new_esEs8(vyy651, vyy661)
new_esEs8(GT, GT) → True
new_esEs7(Right(vyy3000), Right(vyy400), cag, ty_Double) → new_esEs12(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs7(Right(vyy3000), Right(vyy400), cag, app(app(ty_Either, cah), cba)) → new_esEs7(vyy3000, vyy400, cah, cba)
new_esEs22(vyy3002, vyy402, ty_Char) → new_esEs16(vyy3002, vyy402)
new_esEs26(vyy651, vyy661, app(app(app(ty_@3, cd), ce), cf)) → new_esEs4(vyy651, vyy661, cd, ce, cf)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs16(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_@0) → new_ltEs6(vyy6500, vyy6600)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs12(vyy3000, vyy400)
new_ltEs15(Just(vyy6500), Just(vyy6600), app(app(ty_Either, fg), fh)) → new_ltEs8(vyy6500, vyy6600, fg, fh)
new_esEs11(vyy3001, vyy401, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs4(vyy3001, vyy401, bge, bgf, bgg)
new_compare211(vyy650, vyy660, True, be) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs19(vyy651, vyy661, app(app(ty_@2, bbc), bbd)) → new_ltEs17(vyy651, vyy661, bbc, bbd)
new_esEs20(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt15(vyy650, vyy660, ty_Double) → new_lt5(vyy650, vyy660)
new_esEs12(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs20(vyy3000, vyy400, ty_Float) → new_esEs18(vyy3000, vyy400)
new_compare210(vyy650, vyy660, False, h, ba, bb) → new_compare112(vyy650, vyy660, new_ltEs12(vyy650, vyy660, h, ba, bb), h, ba, bb)
new_compare24(vyy650, vyy660) → new_compare27(vyy650, vyy660, new_esEs8(vyy650, vyy660))
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_[], cac), bhd) → new_esEs17(vyy3000, vyy400, cac)
new_compare3([], :(vyy660, vyy661), ga) → LT
new_esEs7(Right(vyy3000), Right(vyy400), cag, app(ty_Ratio, cbb)) → new_esEs13(vyy3000, vyy400, cbb)
new_esEs11(vyy3001, vyy401, ty_Int) → new_esEs9(vyy3001, vyy401)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(vyy3000), Left(vyy400), ty_Integer, bhd) → new_esEs15(vyy3000, vyy400)
new_esEs19(False, False) → True
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Ratio, bhg), bhd) → new_esEs13(vyy3000, vyy400, bhg)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_@2, cad), cae), bhd) → new_esEs6(vyy3000, vyy400, cad, cae)
new_ltEs8(Right(vyy650), Right(vyy660), bda, app(ty_[], bdf)) → new_ltEs16(vyy650, vyy660, bdf)
new_compare3(:(vyy650, vyy651), [], ga) → GT
new_esEs7(Right(vyy3000), Right(vyy400), cag, app(ty_Maybe, cca)) → new_esEs5(vyy3000, vyy400, cca)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_esEs8(EQ, EQ) → True
new_primPlusNat1(Zero, vyy40100) → Succ(vyy40100)
new_compare111(vyy650, vyy660, True, be) → LT
new_lt20(vyy650, vyy660, ty_Ordering) → new_lt8(vyy650, vyy660)
new_esEs25(vyy650, vyy660, ty_Char) → new_esEs16(vyy650, vyy660)
new_esEs7(Right(vyy3000), Right(vyy400), cag, ty_Float) → new_esEs18(vyy3000, vyy400)
new_esEs26(vyy651, vyy661, app(app(ty_Either, dd), de)) → new_esEs7(vyy651, vyy661, dd, de)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs8(Right(vyy650), Right(vyy660), bda, app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs12(vyy650, vyy660, bdb, bdc, bdd)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_compare28(vyy650, vyy660, False) → new_compare11(vyy650, vyy660, new_ltEs10(vyy650, vyy660))
new_ltEs8(Left(vyy650), Left(vyy660), app(ty_[], bcd), bcb) → new_ltEs16(vyy650, vyy660, bcd)
new_esEs10(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_lt20(vyy650, vyy660, app(app(app(ty_@3, hc), hd), he)) → new_lt6(vyy650, vyy660, hc, hd, he)
new_primCmpNat0(Succ(vyy6500), Succ(vyy6600)) → new_primCmpNat0(vyy6500, vyy6600)
new_esEs7(Right(vyy3000), Right(vyy400), cag, ty_Int) → new_esEs9(vyy3000, vyy400)
new_ltEs18(vyy652, vyy662, app(ty_Ratio, cgh)) → new_ltEs5(vyy652, vyy662, cgh)
new_esEs7(Right(vyy3000), Right(vyy400), cag, app(app(ty_@2, cbg), cbh)) → new_esEs6(vyy3000, vyy400, cbg, cbh)
new_lt15(vyy650, vyy660, ty_Char) → new_lt12(vyy650, vyy660)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs16(vyy3000, vyy400)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, che), chf), chg)) → new_esEs4(vyy3000, vyy400, che, chf, chg)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Char, bcb) → new_ltEs11(vyy650, vyy660)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs8(Right(vyy650), Right(vyy660), bda, ty_Double) → new_ltEs9(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_Bool) → new_esEs19(vyy3001, vyy401)
new_esEs25(vyy650, vyy660, app(ty_Maybe, be)) → new_esEs5(vyy650, vyy660, be)
new_esEs26(vyy651, vyy661, ty_Bool) → new_esEs19(vyy651, vyy661)
new_esEs25(vyy650, vyy660, ty_Int) → new_esEs9(vyy650, vyy660)
new_compare18(vyy650, vyy660, app(ty_Ratio, ccb)) → new_compare9(vyy650, vyy660, ccb)
new_esEs26(vyy651, vyy661, ty_Integer) → new_esEs15(vyy651, vyy661)
new_esEs7(Right(vyy3000), Right(vyy400), cag, app(app(app(ty_@3, cbc), cbd), cbe)) → new_esEs4(vyy3000, vyy400, cbc, cbd, cbe)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_esEs27(vyy650, vyy660, ty_Ordering) → new_esEs8(vyy650, vyy660)
new_esEs10(vyy3000, vyy400, ty_Int) → new_esEs9(vyy3000, vyy400)
new_compare18(vyy650, vyy660, app(ty_Maybe, ge)) → new_compare25(vyy650, vyy660, ge)
new_compare18(vyy650, vyy660, ty_@0) → new_compare14(vyy650, vyy660)
new_lt8(vyy650, vyy660) → new_esEs8(new_compare24(vyy650, vyy660), LT)
new_esEs27(vyy650, vyy660, ty_Char) → new_esEs16(vyy650, vyy660)
new_esEs13(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cge) → new_asAs(new_esEs23(vyy3000, vyy400, cge), new_esEs24(vyy3001, vyy401, cge))
new_compare6(Double(vyy650, vyy651), Double(vyy660, vyy661)) → new_compare7(new_sr(vyy650, vyy660), new_sr(vyy651, vyy661))
new_primCompAux00(vyy136, LT) → LT
new_primCmpInt(Neg(Succ(vyy6500)), Neg(vyy660)) → new_primCmpNat0(vyy660, Succ(vyy6500))
new_lt16(vyy651, vyy661, ty_Bool) → new_lt17(vyy651, vyy661)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_esEs10(vyy3000, vyy400, app(app(ty_Either, beh), bfa)) → new_esEs7(vyy3000, vyy400, beh, bfa)
new_lt14(vyy650, vyy660) → new_esEs8(new_compare12(vyy650, vyy660), LT)
new_primPlusNat0(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat0(Succ(vyy10400), Zero) → Succ(vyy10400)
new_lt16(vyy651, vyy661, ty_Integer) → new_lt14(vyy651, vyy661)
new_esEs21(vyy3001, vyy401, ty_Bool) → new_esEs19(vyy3001, vyy401)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs8(Right(vyy650), Right(vyy660), bda, ty_Integer) → new_ltEs7(vyy650, vyy660)
new_compare8(Float(vyy650, vyy651), Float(vyy660, vyy661)) → new_compare7(new_sr(vyy650, vyy660), new_sr(vyy651, vyy661))
new_primCmpNat0(Succ(vyy6500), Zero) → GT
new_esEs20(vyy3000, vyy400, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs4(vyy3000, vyy400, cdb, cdc, cdd)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy6600))) → LT
new_esEs19(True, False) → False
new_esEs19(False, True) → False
new_esEs21(vyy3001, vyy401, ty_Char) → new_esEs16(vyy3001, vyy401)
new_compare210(vyy650, vyy660, True, h, ba, bb) → EQ
new_ltEs15(Just(vyy6500), Just(vyy6600), app(app(app(ty_@3, eg), eh), fa)) → new_ltEs12(vyy6500, vyy6600, eg, eh, fa)
new_esEs22(vyy3002, vyy402, app(ty_Ratio, cfe)) → new_esEs13(vyy3002, vyy402, cfe)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_sr0(Integer(vyy6600), Integer(vyy6510)) → Integer(new_primMulInt(vyy6600, vyy6510))
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_esEs25(vyy650, vyy660, ty_Bool) → new_esEs19(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_esEs27(vyy650, vyy660, app(ty_Maybe, hg)) → new_esEs5(vyy650, vyy660, hg)
new_esEs27(vyy650, vyy660, ty_Double) → new_esEs12(vyy650, vyy660)
new_esEs18(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare18(vyy650, vyy660, app(ty_[], gf)) → new_compare3(vyy650, vyy660, gf)
new_esEs22(vyy3002, vyy402, app(app(ty_@2, cgb), cgc)) → new_esEs6(vyy3002, vyy402, cgb, cgc)
new_esEs26(vyy651, vyy661, ty_Int) → new_esEs9(vyy651, vyy661)
new_lt7(vyy650, vyy660, bg, bh) → new_esEs8(new_compare17(vyy650, vyy660, bg, bh), LT)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_esEs26(vyy651, vyy661, app(ty_[], da)) → new_esEs17(vyy651, vyy661, da)
new_esEs21(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy6600))) → new_primCmpNat0(Zero, Succ(vyy6600))
new_primCompAux00(vyy136, EQ) → vyy136
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dag), dah)) → new_esEs7(vyy3000, vyy400, dag, dah)
new_esEs25(vyy650, vyy660, ty_@0) → new_esEs14(vyy650, vyy660)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Int, bcb) → new_ltEs13(vyy650, vyy660)
new_esEs22(vyy3002, vyy402, ty_Bool) → new_esEs19(vyy3002, vyy402)
new_ltEs8(Right(vyy650), Right(vyy660), bda, ty_Float) → new_ltEs4(vyy650, vyy660)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs21(vyy3001, vyy401, app(ty_[], ceg)) → new_esEs17(vyy3001, vyy401, ceg)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bhh), caa), cab), bhd) → new_esEs4(vyy3000, vyy400, bhh, caa, cab)
new_esEs22(vyy3002, vyy402, ty_Float) → new_esEs18(vyy3002, vyy402)
new_lt20(vyy650, vyy660, ty_Double) → new_lt5(vyy650, vyy660)
new_not(False) → True
new_ltEs8(Right(vyy650), Right(vyy660), bda, app(app(ty_Either, bea), beb)) → new_ltEs8(vyy650, vyy660, bea, beb)
new_lt15(vyy650, vyy660, ty_Bool) → new_lt17(vyy650, vyy660)
new_esEs10(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_ltEs18(vyy652, vyy662, app(app(ty_Either, ee), ef)) → new_ltEs8(vyy652, vyy662, ee, ef)
new_primCmpInt(Pos(Succ(vyy6500)), Pos(vyy660)) → new_primCmpNat0(Succ(vyy6500), vyy660)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs19(vyy3000, vyy400)
new_compare18(vyy650, vyy660, app(app(ty_Either, ha), hb)) → new_compare26(vyy650, vyy660, ha, hb)
new_esEs25(vyy650, vyy660, ty_Integer) → new_esEs15(vyy650, vyy660)
new_ltEs18(vyy652, vyy662, ty_Ordering) → new_ltEs14(vyy652, vyy662)
new_ltEs14(LT, LT) → True
new_esEs7(Right(vyy3000), Right(vyy400), cag, ty_@0) → new_esEs14(vyy3000, vyy400)
new_lt16(vyy651, vyy661, ty_Double) → new_lt5(vyy651, vyy661)
new_esEs25(vyy650, vyy660, ty_Float) → new_esEs18(vyy650, vyy660)
new_esEs25(vyy650, vyy660, app(app(app(ty_@3, h), ba), bb)) → new_esEs4(vyy650, vyy660, h, ba, bb)
new_compare29(vyy650, vyy660, False, ca, cb) → new_compare110(vyy650, vyy660, new_ltEs8(vyy650, vyy660, ca, cb), ca, cb)
new_esEs27(vyy650, vyy660, ty_@0) → new_esEs14(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_@0) → new_esEs14(vyy3001, vyy401)
new_esEs5(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs14(vyy3000, vyy400)
new_compare12(Integer(vyy650), Integer(vyy660)) → new_primCmpInt(vyy650, vyy660)
new_compare28(vyy650, vyy660, True) → EQ
new_esEs22(vyy3002, vyy402, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs4(vyy3002, vyy402, cff, cfg, cfh)
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_Ratio, chd)) → new_esEs13(vyy3000, vyy400, chd)
new_compare16(Char(vyy650), Char(vyy660)) → new_primCmpNat0(vyy650, vyy660)
new_lt19(vyy650, vyy660, cgf) → new_esEs8(new_compare9(vyy650, vyy660, cgf), LT)
new_primCmpInt(Pos(Succ(vyy6500)), Neg(vyy660)) → GT
new_ltEs16(vyy65, vyy66, ga) → new_not(new_esEs8(new_compare3(vyy65, vyy66, ga), GT))
new_esEs11(vyy3001, vyy401, app(ty_Maybe, bhc)) → new_esEs5(vyy3001, vyy401, bhc)
new_lt6(vyy650, vyy660, h, ba, bb) → new_esEs8(new_compare13(vyy650, vyy660, h, ba, bb), LT)
new_ltEs19(vyy651, vyy661, app(ty_[], bbb)) → new_ltEs16(vyy651, vyy661, bbb)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs20(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_esEs7(Left(vyy3000), Left(vyy400), ty_@0, bhd) → new_esEs14(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs27(vyy650, vyy660, app(app(ty_@2, baa), bab)) → new_esEs6(vyy650, vyy660, baa, bab)
new_esEs20(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs10(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_ltEs12(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cc, bc, bd) → new_pePe(new_lt15(vyy650, vyy660, cc), new_asAs(new_esEs25(vyy650, vyy660, cc), new_pePe(new_lt16(vyy651, vyy661, bc), new_asAs(new_esEs26(vyy651, vyy661, bc), new_ltEs18(vyy652, vyy662, bd)))))
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_ltEs8(Left(vyy650), Left(vyy660), app(app(ty_Either, bcg), bch), bcb) → new_ltEs8(vyy650, vyy660, bcg, bch)
new_esEs21(vyy3001, vyy401, ty_Int) → new_esEs9(vyy3001, vyy401)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs8(Right(vyy650), Right(vyy660), bda, app(ty_Ratio, bee)) → new_ltEs5(vyy650, vyy660, bee)
new_lt13(vyy650, vyy660, be) → new_esEs8(new_compare25(vyy650, vyy660, be), LT)
new_ltEs19(vyy651, vyy661, ty_@0) → new_ltEs6(vyy651, vyy661)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs18(vyy652, vyy662, ty_Integer) → new_ltEs7(vyy652, vyy662)
new_compare25(vyy650, vyy660, be) → new_compare211(vyy650, vyy660, new_esEs5(vyy650, vyy660, be), be)
new_esEs20(vyy3000, vyy400, app(ty_[], cde)) → new_esEs17(vyy3000, vyy400, cde)
new_esEs22(vyy3002, vyy402, ty_Int) → new_esEs9(vyy3002, vyy402)
new_ltEs15(Just(vyy6500), Nothing, be) → False
new_lt20(vyy650, vyy660, ty_Float) → new_lt18(vyy650, vyy660)
new_esEs22(vyy3002, vyy402, app(ty_[], cga)) → new_esEs17(vyy3002, vyy402, cga)
new_ltEs8(Left(vyy650), Left(vyy660), ty_@0, bcb) → new_ltEs6(vyy650, vyy660)
new_ltEs18(vyy652, vyy662, app(app(ty_@2, ec), ed)) → new_ltEs17(vyy652, vyy662, ec, ed)
new_lt16(vyy651, vyy661, app(ty_[], da)) → new_lt4(vyy651, vyy661, da)
new_ltEs19(vyy651, vyy661, ty_Bool) → new_ltEs10(vyy651, vyy661)
new_esEs21(vyy3001, vyy401, app(app(ty_Either, cea), ceb)) → new_esEs7(vyy3001, vyy401, cea, ceb)
new_esEs26(vyy651, vyy661, app(ty_Maybe, cg)) → new_esEs5(vyy651, vyy661, cg)
new_primPlusNat1(Succ(vyy1040), vyy40100) → Succ(Succ(new_primPlusNat0(vyy1040, vyy40100)))
new_lt15(vyy650, vyy660, app(app(ty_Either, ca), cb)) → new_lt9(vyy650, vyy660, ca, cb)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs9(vyy3001, vyy401)
new_esEs10(vyy3000, vyy400, app(ty_Maybe, bga)) → new_esEs5(vyy3000, vyy400, bga)
new_compare112(vyy650, vyy660, True, h, ba, bb) → LT
new_compare23(vyy650, vyy660, True, bg, bh) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(vyy6600))) → new_primCmpNat0(Succ(vyy6600), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy6600))) → GT
new_compare15(vyy650, vyy660, False, bg, bh) → GT
new_esEs27(vyy650, vyy660, ty_Int) → new_esEs9(vyy650, vyy660)
new_esEs21(vyy3001, vyy401, app(app(app(ty_@3, ced), cee), cef)) → new_esEs4(vyy3001, vyy401, ced, cee, cef)
new_esEs26(vyy651, vyy661, ty_@0) → new_esEs14(vyy651, vyy661)
new_primCompAux0(vyy650, vyy660, vyy127, ga) → new_primCompAux00(vyy127, new_compare18(vyy650, vyy660, ga))
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dbf), dbg)) → new_esEs6(vyy3000, vyy400, dbf, dbg)
new_esEs11(vyy3001, vyy401, app(app(ty_Either, bgb), bgc)) → new_esEs7(vyy3001, vyy401, bgb, bgc)
new_ltEs6(vyy65, vyy66) → new_not(new_esEs8(new_compare14(vyy65, vyy66), GT))
new_lt20(vyy650, vyy660, app(ty_Ratio, dad)) → new_lt19(vyy650, vyy660, dad)
new_lt15(vyy650, vyy660, ty_Float) → new_lt18(vyy650, vyy660)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Bool, bhd) → new_esEs19(vyy3000, vyy400)
new_ltEs19(vyy651, vyy661, ty_Ordering) → new_ltEs14(vyy651, vyy661)
new_lt15(vyy650, vyy660, ty_Int) → new_lt10(vyy650, vyy660)
new_esEs21(vyy3001, vyy401, ty_Float) → new_esEs18(vyy3001, vyy401)
new_esEs20(vyy3000, vyy400, app(app(ty_Either, ccg), cch)) → new_esEs7(vyy3000, vyy400, ccg, cch)
new_lt15(vyy650, vyy660, app(app(app(ty_@3, h), ba), bb)) → new_lt6(vyy650, vyy660, h, ba, bb)
new_compare18(vyy650, vyy660, ty_Bool) → new_compare19(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, app(app(ty_@2, bha), bhb)) → new_esEs6(vyy3001, vyy401, bha, bhb)
new_lt15(vyy650, vyy660, app(app(ty_@2, bg), bh)) → new_lt7(vyy650, vyy660, bg, bh)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Bool) → new_ltEs10(vyy6500, vyy6600)
new_lt12(vyy650, vyy660) → new_esEs8(new_compare16(vyy650, vyy660), LT)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs21(vyy3001, vyy401, ty_@0) → new_esEs14(vyy3001, vyy401)
new_lt16(vyy651, vyy661, ty_Ordering) → new_lt8(vyy651, vyy661)
new_esEs20(vyy3000, vyy400, app(ty_Maybe, cdh)) → new_esEs5(vyy3000, vyy400, cdh)
new_esEs27(vyy650, vyy660, ty_Float) → new_esEs18(vyy650, vyy660)
new_ltEs10(True, False) → False
new_asAs(False, vyy91) → False
new_esEs22(vyy3002, vyy402, ty_Double) → new_esEs12(vyy3002, vyy402)
new_lt16(vyy651, vyy661, ty_@0) → new_lt11(vyy651, vyy661)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(ty_Either, chb), chc)) → new_esEs7(vyy3000, vyy400, chb, chc)
new_compare3([], [], ga) → EQ
new_compare211(vyy650, vyy660, False, be) → new_compare111(vyy650, vyy660, new_ltEs15(vyy650, vyy660, be), be)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_ltEs19(vyy651, vyy661, ty_Char) → new_ltEs11(vyy651, vyy661)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs7(Right(vyy3000), Right(vyy400), cag, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_ltEs5(vyy65, vyy66, bec) → new_not(new_esEs8(new_compare9(vyy65, vyy66, bec), GT))
new_esEs21(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs10(vyy3000, vyy400, app(ty_[], bff)) → new_esEs17(vyy3000, vyy400, bff)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs9(vyy3000, vyy400)
new_esEs10(vyy3000, vyy400, app(ty_Ratio, bfb)) → new_esEs13(vyy3000, vyy400, bfb)
new_compare23(vyy650, vyy660, False, bg, bh) → new_compare15(vyy650, vyy660, new_ltEs17(vyy650, vyy660, bg, bh), bg, bh)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(ty_@2, daa), dab)) → new_esEs6(vyy3000, vyy400, daa, dab)
new_ltEs14(GT, LT) → False
new_lt20(vyy650, vyy660, app(ty_[], hh)) → new_lt4(vyy650, vyy660, hh)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Float, bhd) → new_esEs18(vyy3000, vyy400)
new_ltEs8(Right(vyy650), Left(vyy660), bda, bcb) → False
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs25(vyy650, vyy660, app(ty_[], bf)) → new_esEs17(vyy650, vyy660, bf)
new_compare18(vyy650, vyy660, ty_Integer) → new_compare12(vyy650, vyy660)
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_compare112(vyy650, vyy660, False, h, ba, bb) → GT
new_compare27(vyy650, vyy660, True) → EQ
new_esEs10(vyy3000, vyy400, ty_Float) → new_esEs18(vyy3000, vyy400)
new_compare111(vyy650, vyy660, False, be) → GT
new_compare27(vyy650, vyy660, False) → new_compare10(vyy650, vyy660, new_ltEs14(vyy650, vyy660))
new_ltEs15(Nothing, Nothing, be) → True
new_compare9(:%(vyy650, vyy651), :%(vyy660, vyy661), ty_Int) → new_compare7(new_sr(vyy650, vyy661), new_sr(vyy660, vyy651))
new_esEs5(Just(vyy3000), Nothing, cha) → False
new_esEs5(Nothing, Just(vyy400), cha) → False
new_esEs11(vyy3001, vyy401, app(ty_Ratio, bgd)) → new_esEs13(vyy3001, vyy401, bgd)
new_lt16(vyy651, vyy661, app(ty_Maybe, cg)) → new_lt13(vyy651, vyy661, cg)
new_lt5(vyy650, vyy660) → new_esEs8(new_compare6(vyy650, vyy660), LT)
new_esEs28(vyy3000, vyy400, app(ty_[], dbe)) → new_esEs17(vyy3000, vyy400, dbe)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dba)) → new_esEs13(vyy3000, vyy400, dba)
new_compare11(vyy650, vyy660, False) → GT
new_ltEs14(LT, GT) → True
new_ltEs14(LT, EQ) → True
new_compare11(vyy650, vyy660, True) → LT
new_esEs22(vyy3002, vyy402, ty_@0) → new_esEs14(vyy3002, vyy402)
new_esEs5(Nothing, Nothing, cha) → True
new_ltEs18(vyy652, vyy662, app(ty_Maybe, ea)) → new_ltEs15(vyy652, vyy662, ea)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dbh)) → new_esEs5(vyy3000, vyy400, dbh)
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Maybe, caf), bhd) → new_esEs5(vyy3000, vyy400, caf)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs18(vyy3000, vyy400)
new_esEs21(vyy3001, vyy401, ty_Double) → new_esEs12(vyy3001, vyy401)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs9(vyy3000, vyy400)
new_lt15(vyy650, vyy660, ty_Ordering) → new_lt8(vyy650, vyy660)
new_lt16(vyy651, vyy661, ty_Char) → new_lt12(vyy651, vyy661)
new_lt20(vyy650, vyy660, ty_Char) → new_lt12(vyy650, vyy660)
new_ltEs19(vyy651, vyy661, ty_Integer) → new_ltEs7(vyy651, vyy661)
new_esEs10(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs22(vyy3002, vyy402, app(ty_Maybe, cgd)) → new_esEs5(vyy3002, vyy402, cgd)
new_primPlusNat0(Succ(vyy10400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat0(vyy10400, vyy401000)))
new_lt20(vyy650, vyy660, ty_Integer) → new_lt14(vyy650, vyy660)
new_esEs21(vyy3001, vyy401, app(ty_Maybe, cfb)) → new_esEs5(vyy3001, vyy401, cfb)
new_esEs22(vyy3002, vyy402, ty_Integer) → new_esEs15(vyy3002, vyy402)
new_ltEs18(vyy652, vyy662, app(ty_[], eb)) → new_ltEs16(vyy652, vyy662, eb)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Ordering, bcb) → new_ltEs14(vyy650, vyy660)
new_compare18(vyy650, vyy660, app(app(ty_@2, gg), gh)) → new_compare17(vyy650, vyy660, gg, gh)
new_ltEs10(True, True) → True
new_ltEs15(Just(vyy6500), Just(vyy6600), app(app(ty_@2, fd), ff)) → new_ltEs17(vyy6500, vyy6600, fd, ff)
new_ltEs14(EQ, EQ) → True
new_asAs(True, vyy91) → vyy91
new_lt16(vyy651, vyy661, app(app(ty_Either, dd), de)) → new_lt9(vyy651, vyy661, dd, de)
new_esEs17(:(vyy3000, vyy3001), :(vyy400, vyy401), daf) → new_asAs(new_esEs28(vyy3000, vyy400, daf), new_esEs17(vyy3001, vyy401, daf))
new_lt20(vyy650, vyy660, ty_Bool) → new_lt17(vyy650, vyy660)
new_lt16(vyy651, vyy661, ty_Int) → new_lt10(vyy651, vyy661)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Char, bhd) → new_esEs16(vyy3000, vyy400)
new_compare18(vyy650, vyy660, ty_Float) → new_compare8(vyy650, vyy660)
new_esEs17([], [], daf) → True
new_esEs17(:(vyy3000, vyy3001), [], daf) → False
new_esEs17([], :(vyy400, vyy401), daf) → False
new_lt20(vyy650, vyy660, ty_@0) → new_lt11(vyy650, vyy660)
new_esEs26(vyy651, vyy661, app(app(ty_@2, db), dc)) → new_esEs6(vyy651, vyy661, db, dc)
new_esEs26(vyy651, vyy661, ty_Char) → new_esEs16(vyy651, vyy661)
new_ltEs8(Left(vyy650), Right(vyy660), bda, bcb) → True
new_compare10(vyy650, vyy660, True) → LT
new_esEs9(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_compare26(vyy650, vyy660, ca, cb) → new_compare29(vyy650, vyy660, new_esEs7(vyy650, vyy660, ca, cb), ca, cb)
new_esEs20(vyy3000, vyy400, ty_Char) → new_esEs16(vyy3000, vyy400)
new_esEs10(vyy3000, vyy400, ty_Char) → new_esEs16(vyy3000, vyy400)
new_compare18(vyy650, vyy660, ty_Double) → new_compare6(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_Float) → new_esEs18(vyy3001, vyy401)
new_compare10(vyy650, vyy660, False) → GT
new_ltEs13(vyy65, vyy66) → new_not(new_esEs8(new_compare7(vyy65, vyy66), GT))
new_primCompAux00(vyy136, GT) → GT
new_esEs25(vyy650, vyy660, app(app(ty_Either, ca), cb)) → new_esEs7(vyy650, vyy660, ca, cb)
new_ltEs18(vyy652, vyy662, ty_Double) → new_ltEs9(vyy652, vyy662)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_ltEs8(Left(vyy650), Left(vyy660), ty_Integer, bcb) → new_ltEs7(vyy650, vyy660)
new_esEs27(vyy650, vyy660, ty_Bool) → new_esEs19(vyy650, vyy660)
new_ltEs15(Just(vyy6500), Just(vyy6600), app(ty_[], fc)) → new_ltEs16(vyy6500, vyy6600, fc)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_lt20(vyy650, vyy660, app(app(ty_Either, bac), bad)) → new_lt9(vyy650, vyy660, bac, bad)
new_esEs27(vyy650, vyy660, ty_Integer) → new_esEs15(vyy650, vyy660)
new_compare9(:%(vyy650, vyy651), :%(vyy660, vyy661), ty_Integer) → new_compare12(new_sr0(vyy650, vyy661), new_sr0(vyy660, vyy651))
new_primCmpInt(Neg(Succ(vyy6500)), Pos(vyy660)) → LT
new_not(True) → False

The set Q consists of the following terms:

new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs21(x0, x1, ty_Integer)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True)
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_lt16(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt16(x0, x1, app(app(ty_Either, x2), x3))
new_compare112(x0, x1, True, x2, x3, x4)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs16(Char(x0), Char(x1))
new_ltEs18(x0, x1, ty_Double)
new_lt16(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_@0)
new_esEs10(x0, x1, ty_Bool)
new_lt16(x0, x1, app(ty_[], x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs28(x0, x1, ty_Int)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulNat0(Zero, Succ(x0))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare3(:(x0, x1), [], x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs15(Just(x0), Just(x1), ty_@0)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Nothing, Nothing, x0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Bool)
new_esEs8(GT, GT)
new_lt13(x0, x1, x2)
new_ltEs15(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Int)
new_ltEs15(Just(x0), Just(x1), ty_Bool)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_lt7(x0, x1, x2, x3)
new_esEs17([], :(x0, x1), x2)
new_esEs24(x0, x1, ty_Integer)
new_lt11(x0, x1)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_esEs20(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs5(Just(x0), Nothing, x1)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_Integer)
new_sr(x0, x1)
new_esEs10(x0, x1, ty_Int)
new_compare23(x0, x1, True, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_Ordering)
new_esEs19(True, True)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs27(x0, x1, ty_Bool)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, ty_Int)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_ltEs19(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Zero)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs14(EQ, EQ)
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqNat0(Zero, Zero)
new_sr0(Integer(x0), Integer(x1))
new_compare211(x0, x1, True, x2)
new_esEs25(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Integer)
new_ltEs15(Just(x0), Just(x1), app(ty_[], x2))
new_esEs10(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(True, x0)
new_lt19(x0, x1, x2)
new_lt20(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_compare11(x0, x1, True)
new_esEs22(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_primCompAux00(x0, GT)
new_primCmpNat0(Succ(x0), Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_lt16(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt16(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, x0)
new_lt15(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Char)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt15(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1)
new_lt16(x0, x1, ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, app(ty_[], x2))
new_lt5(x0, x1)
new_esEs27(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs15(Nothing, Just(x0), x1)
new_primCompAux00(x0, EQ)
new_ltEs15(Just(x0), Just(x1), ty_Double)
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_lt16(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs14(@0, @0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(x0, x1, x2, x3)
new_lt17(x0, x1)
new_esEs27(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt15(x0, x1, app(ty_Ratio, x2))
new_compare15(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_lt9(x0, x1, x2, x3)
new_esEs11(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_compare17(x0, x1, x2, x3)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(False, True)
new_esEs19(True, False)
new_esEs22(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_lt15(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs25(x0, x1, ty_Double)
new_primPlusNat0(Zero, Zero)
new_compare6(Double(x0, x1), Double(x2, x3))
new_lt6(x0, x1, x2, x3, x4)
new_ltEs15(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare210(x0, x1, True, x2, x3, x4)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs10(False, False)
new_ltEs14(LT, LT)
new_lt14(x0, x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt16(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_compare18(x0, x1, ty_@0)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare13(x0, x1, x2, x3, x4)
new_compare110(x0, x1, True, x2, x3)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_lt4(x0, x1, x2)
new_esEs11(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_compare15(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_@0)
new_compare28(x0, x1, True)
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_Char)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt8(x0, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt16(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_Double)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare29(x0, x1, True, x2, x3)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare27(x0, x1, True)
new_esEs11(x0, x1, ty_Bool)
new_lt15(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_compare23(x0, x1, False, x2, x3)
new_compare18(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt15(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Ordering)
new_compare16(Char(x0), Char(x1))
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_esEs25(x0, x1, ty_Int)
new_compare11(x0, x1, False)
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_lt15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_compare111(x0, x1, True, x2)
new_compare24(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs5(Nothing, Just(x0), x1)
new_esEs19(False, False)
new_esEs21(x0, x1, ty_Char)
new_ltEs15(Nothing, Nothing, x0)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), x1)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs19(x0, x1, ty_Double)
new_compare28(x0, x1, False)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_compare14(@0, @0)
new_esEs28(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare18(x0, x1, ty_Float)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs28(x0, x1, ty_Integer)
new_compare29(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Double)
new_compare8(Float(x0, x1), Float(x2, x3))
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Ordering)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare110(x0, x1, False, x2, x3)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare211(x0, x1, False, x2)
new_ltEs15(Just(x0), Just(x1), ty_Int)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare3([], [], x0)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs28(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_ltEs16(x0, x1, x2)
new_esEs20(x0, x1, ty_Char)
new_lt15(x0, x1, ty_Int)
new_lt16(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_esEs9(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_compare18(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Int)
new_lt12(x0, x1)
new_compare112(x0, x1, False, x2, x3, x4)
new_compare210(x0, x1, False, x2, x3, x4)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs28(x0, x1, ty_Bool)
new_pePe(False, x0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCmpNat0(Zero, Zero)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt16(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs22(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs18(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs10(True, True)
new_esEs22(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt15(x0, x1, ty_Double)
new_ltEs15(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs11(x0, x1, ty_Double)
new_lt20(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Float)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs22(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Float)
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_ltEs18(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_asAs(True, x0)
new_esEs11(x0, x1, ty_Ordering)
new_esEs17(:(x0, x1), [], x2)
new_compare25(x0, x1, x2)
new_esEs27(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Char)
new_ltEs15(Just(x0), Just(x1), ty_Float)
new_compare18(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare27(x0, x1, False)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Zero, Succ(x0))
new_esEs10(x0, x1, ty_@0)
new_compare19(x0, x1)
new_ltEs14(GT, GT)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs15(Integer(x0), Integer(x1))
new_ltEs15(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_esEs21(x0, x1, ty_Double)
new_lt10(x0, x1)
new_esEs20(x0, x1, ty_Integer)
new_compare7(x0, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare111(x0, x1, False, x2)
new_esEs25(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Bool)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_compare18(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs13(x0, x1)
new_esEs24(x0, x1, ty_Int)
new_compare18(x0, x1, app(ty_[], x2))
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt15(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs17([], [], x0)
new_ltEs18(x0, x1, ty_Char)
new_ltEs15(Just(x0), Just(x1), ty_Ordering)
new_ltEs15(Just(x0), Just(x1), ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs4(x0, x1)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Char)
new_compare18(x0, x1, ty_Bool)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs27(x0, x1, ty_@0)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_compare12(Integer(x0), Integer(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Float)
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs10(False, True)
new_ltEs10(True, False)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt16(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs12(Double(x0, x1), Double(x2, x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt15(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primEqNat0(Succ(x0), Zero)
new_compare18(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Float)
new_compare18(x0, x1, ty_Integer)
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare18(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs6(x0, x1)
new_ltEs5(x0, x1, x2)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_compare3([], :(x0, x1), x2)
new_lt20(x0, x1, ty_Float)
new_ltEs9(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt15(x0, x1, ty_@0)
new_compare10(x0, x1, False)
new_esEs20(x0, x1, ty_@0)

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

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



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

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

new_foldFM_GE1(vyy50, vyy40, vyy330, vyy331, vyy332, vyy333, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), False, h, ba) → new_foldFM_GE1(vyy50, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, ba), h, ba)
new_foldFM_GE(vyy50, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba) → new_foldFM_GE1(vyy50, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, ba), h, ba)
new_foldFM_GE1(vyy50, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE2(vyy330, vyy331, new_foldFM_GE0(vyy50, vyy40, vyy334, h, ba), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba)
new_foldFM_GE1(vyy50, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE(vyy50, vyy40, vyy334, h, ba)
new_foldFM_GE2(vyy330, vyy331, vyy71, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba) → new_foldFM_GE1(new_eltsFM_GE0(vyy330, vyy331, vyy71, h, ba), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, ba), h, ba)
new_foldFM_GE1(vyy50, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba) → new_foldFM_GE(vyy50, vyy40, vyy334, h, ba)

The TRS R consists of the following rules:

new_compare18(vyy650, vyy660, ty_Char) → new_compare16(vyy650, vyy660)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Int) → new_ltEs13(vyy6500, vyy6600)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_Either, hh), baa), hg) → new_esEs7(vyy3000, vyy400, hh, baa)
new_compare3(:(vyy650, vyy651), :(vyy660, vyy661), bce) → new_primCompAux0(vyy650, vyy660, new_compare3(vyy651, vyy661, bce), bce)
new_esEs21(vyy3001, vyy401, app(app(ty_@2, caa), cab)) → new_esEs6(vyy3001, vyy401, caa, cab)
new_esEs10(vyy3000, vyy400, app(app(app(ty_@3, ff), fg), fh)) → new_esEs4(vyy3000, vyy400, ff, fg, fh)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Char) → new_ltEs11(vyy6500, vyy6600)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs10(False, True) → True
new_compare15(vyy650, vyy660, True, ef, eg) → LT
new_lt20(vyy650, vyy660, ty_Int) → new_lt10(vyy650, vyy660)
new_compare110(vyy650, vyy660, True, bdh, bea) → LT
new_esEs7(Right(vyy3000), Right(vyy400), bbb, app(ty_[], bca)) → new_esEs17(vyy3000, vyy400, bca)
new_ltEs14(GT, GT) → True
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Char) → new_ltEs11(vyy650, vyy660)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Int, hg) → new_esEs9(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs16(vyy3000, vyy400)
new_lt16(vyy651, vyy661, app(app(app(ty_@3, ccc), ccd), cce)) → new_lt6(vyy651, vyy661, ccc, ccd, cce)
new_foldFM_GE10(vyy50, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba) → new_foldFM_GE3(vyy330, vyy331, new_foldFM_GE0(vyy50, vyy40, vyy334, h, ba), vyy40, h, ba)
new_lt15(vyy650, vyy660, app(ty_[], bb)) → new_lt4(vyy650, vyy660, bb)
new_esEs20(vyy3000, vyy400, ty_Int) → new_esEs9(vyy3000, vyy400)
new_ltEs4(vyy65, vyy66) → new_not(new_esEs8(new_compare8(vyy65, vyy66), GT))
new_ltEs11(vyy65, vyy66) → new_not(new_esEs8(new_compare16(vyy65, vyy66), GT))
new_esEs20(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy651, vyy661, ty_Float) → new_ltEs4(vyy651, vyy661)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Float, bg) → new_ltEs4(vyy650, vyy660)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Double, hg) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy651, vyy661, app(ty_Ratio, dae)) → new_ltEs5(vyy651, vyy661, dae)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_primMulNat0(Zero, Zero) → Zero
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_esEs25(vyy650, vyy660, ty_Double) → new_esEs12(vyy650, vyy660)
new_lt16(vyy651, vyy661, app(ty_Ratio, cdb)) → new_lt19(vyy651, vyy661, cdb)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs9(vyy3000, vyy400)
new_esEs27(vyy650, vyy660, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs4(vyy650, vyy660, cgd, cge, cgf)
new_compare17(vyy650, vyy660, ef, eg) → new_compare23(vyy650, vyy660, new_esEs6(vyy650, vyy660, ef, eg), ef, eg)
new_ltEs19(vyy651, vyy661, ty_Double) → new_ltEs9(vyy651, vyy661)
new_ltEs15(Nothing, Just(vyy6600), beb) → True
new_ltEs8(Left(vyy650), Left(vyy660), ty_Double, bg) → new_ltEs9(vyy650, vyy660)
new_ltEs19(vyy651, vyy661, app(ty_Maybe, daa)) → new_ltEs15(vyy651, vyy661, daa)
new_foldFM_GE0(vyy50, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba) → new_foldFM_GE10(vyy50, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, ba), h, ba)
new_lt20(vyy650, vyy660, app(ty_Maybe, cgg)) → new_lt13(vyy650, vyy660, cgg)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_ltEs9(vyy65, vyy66) → new_not(new_esEs8(new_compare6(vyy65, vyy66), GT))
new_lt15(vyy650, vyy660, ty_@0) → new_lt11(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, app(ty_[], hc)) → new_esEs17(vyy3001, vyy401, hc)
new_lt17(vyy650, vyy660) → new_esEs8(new_compare19(vyy650, vyy660), LT)
new_lt15(vyy650, vyy660, app(ty_Maybe, beb)) → new_lt13(vyy650, vyy660, beb)
new_lt9(vyy650, vyy660, bdh, bea) → new_esEs8(new_compare26(vyy650, vyy660, bdh, bea), LT)
new_esEs20(vyy3000, vyy400, app(ty_Ratio, bgb)) → new_esEs13(vyy3000, vyy400, bgb)
new_lt10(vyy650, vyy660) → new_esEs8(new_compare7(vyy650, vyy660), LT)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Ordering) → new_ltEs14(vyy6500, vyy6600)
new_esEs4(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bfe, bff, bfg) → new_asAs(new_esEs20(vyy3000, vyy400, bfe), new_asAs(new_esEs21(vyy3001, vyy401, bff), new_esEs22(vyy3002, vyy402, bfg)))
new_esEs10(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_Maybe, cga)) → new_esEs5(vyy3000, vyy400, cga)
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Int) → new_ltEs13(vyy650, vyy660)
new_esEs26(vyy651, vyy661, ty_Float) → new_esEs18(vyy651, vyy661)
new_esEs15(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_eltsFM_GE0(vyy330, vyy331, vyy68, h, ba) → :(vyy331, vyy68)
new_ltEs17(@2(vyy650, vyy651), @2(vyy660, vyy661), cgb, cgc) → new_pePe(new_lt20(vyy650, vyy660, cgb), new_asAs(new_esEs27(vyy650, vyy660, cgb), new_ltEs19(vyy651, vyy661, cgc)))
new_ltEs18(vyy652, vyy662, ty_Bool) → new_ltEs10(vyy652, vyy662)
new_ltEs8(Left(vyy650), Left(vyy660), app(ty_Maybe, cc), bg) → new_ltEs15(vyy650, vyy660, cc)
new_lt15(vyy650, vyy660, ty_Integer) → new_lt14(vyy650, vyy660)
new_ltEs10(False, False) → True
new_esEs20(vyy3000, vyy400, app(app(ty_@2, bgg), bgh)) → new_esEs6(vyy3000, vyy400, bgg, bgh)
new_ltEs8(Left(vyy650), Left(vyy660), app(ty_Ratio, cg), bg) → new_ltEs5(vyy650, vyy660, cg)
new_esEs20(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_esEs22(vyy3002, vyy402, app(app(ty_Either, cad), cae)) → new_esEs7(vyy3002, vyy402, cad, cae)
new_compare13(vyy650, vyy660, bd, be, bf) → new_compare210(vyy650, vyy660, new_esEs4(vyy650, vyy660, bd, be, bf), bd, be, bf)
new_ltEs18(vyy652, vyy662, ty_Float) → new_ltEs4(vyy652, vyy662)
new_ltEs8(Right(vyy650), Right(vyy660), dc, app(app(ty_@2, ea), eb)) → new_ltEs17(vyy650, vyy660, ea, eb)
new_pePe(False, vyy126) → vyy126
new_lt4(vyy650, vyy660, bb) → new_esEs8(new_compare3(vyy650, vyy660, bb), LT)
new_esEs7(Left(vyy3000), Right(vyy400), bbb, hg) → False
new_esEs7(Right(vyy3000), Left(vyy400), bbb, hg) → False
new_ltEs8(Left(vyy650), Left(vyy660), app(app(ty_@2, ce), cf), bg) → new_ltEs17(vyy650, vyy660, ce, cf)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs18(vyy3000, vyy400)
new_esEs27(vyy650, vyy660, app(app(ty_Either, chd), che)) → new_esEs7(vyy650, vyy660, chd, che)
new_ltEs14(GT, EQ) → False
new_compare18(vyy650, vyy660, ty_Int) → new_compare7(vyy650, vyy660)
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Bool) → new_ltEs10(vyy650, vyy660)
new_ltEs18(vyy652, vyy662, app(app(app(ty_@3, cde), cdf), cdg)) → new_ltEs12(vyy652, vyy662, cde, cdf, cdg)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Char) → new_esEs16(vyy3000, vyy400)
new_compare14(@0, @0) → EQ
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs4(vyy3000, vyy400, dbd, dbe, dbf)
new_lt16(vyy651, vyy661, ty_Float) → new_lt18(vyy651, vyy661)
new_esEs27(vyy650, vyy660, app(ty_[], cgh)) → new_esEs17(vyy650, vyy660, cgh)
new_esEs22(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Bool, bg) → new_ltEs10(vyy650, vyy660)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs15(vyy3000, vyy400)
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Ordering) → new_ltEs14(vyy650, vyy660)
new_lt20(vyy650, vyy660, app(app(ty_@2, cha), chb)) → new_lt7(vyy650, vyy660, cha, chb)
new_ltEs18(vyy652, vyy662, ty_Int) → new_ltEs13(vyy652, vyy662)
new_ltEs15(Just(vyy6500), Just(vyy6600), app(ty_Maybe, bef)) → new_ltEs15(vyy6500, vyy6600, bef)
new_esEs10(vyy3000, vyy400, app(app(ty_@2, gb), gc)) → new_esEs6(vyy3000, vyy400, gb, gc)
new_compare18(vyy650, vyy660, ty_Ordering) → new_compare24(vyy650, vyy660)
new_ltEs18(vyy652, vyy662, ty_Char) → new_ltEs11(vyy652, vyy662)
new_ltEs7(vyy65, vyy66) → new_not(new_esEs8(new_compare12(vyy65, vyy66), GT))
new_lt15(vyy650, vyy660, app(ty_Ratio, ccb)) → new_lt19(vyy650, vyy660, ccb)
new_primCmpNat0(Zero, Succ(vyy6600)) → LT
new_esEs26(vyy651, vyy661, ty_Double) → new_esEs12(vyy651, vyy661)
new_ltEs18(vyy652, vyy662, ty_@0) → new_ltEs6(vyy652, vyy662)
new_esEs25(vyy650, vyy660, app(app(ty_@2, ef), eg)) → new_esEs6(vyy650, vyy660, ef, eg)
new_lt16(vyy651, vyy661, app(app(ty_@2, cch), cda)) → new_lt7(vyy651, vyy661, cch, cda)
new_esEs8(LT, LT) → True
new_esEs21(vyy3001, vyy401, app(ty_Ratio, bhd)) → new_esEs13(vyy3001, vyy401, bhd)
new_lt18(vyy650, vyy660) → new_esEs8(new_compare8(vyy650, vyy660), LT)
new_lt11(vyy650, vyy660) → new_esEs8(new_compare14(vyy650, vyy660), LT)
new_compare19(vyy650, vyy660) → new_compare28(vyy650, vyy660, new_esEs19(vyy650, vyy660))
new_esEs25(vyy650, vyy660, ty_Ordering) → new_esEs8(vyy650, vyy660)
new_esEs25(vyy650, vyy660, app(ty_Ratio, ccb)) → new_esEs13(vyy650, vyy660, ccb)
new_ltEs8(Right(vyy650), Right(vyy660), dc, app(ty_Maybe, dg)) → new_ltEs15(vyy650, vyy660, dg)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Double) → new_ltEs9(vyy6500, vyy6600)
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_[], cff)) → new_esEs17(vyy3000, vyy400, cff)
new_pePe(True, vyy126) → True
new_primEqNat0(Zero, Zero) → True
new_ltEs19(vyy651, vyy661, ty_Int) → new_ltEs13(vyy651, vyy661)
new_compare18(vyy650, vyy660, app(app(app(ty_@3, bcf), bcg), bch)) → new_compare13(vyy650, vyy660, bcf, bcg, bch)
new_ltEs15(Just(vyy6500), Just(vyy6600), app(ty_Ratio, bfb)) → new_ltEs5(vyy6500, vyy6600, bfb)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat1(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_compare29(vyy650, vyy660, True, bdh, bea) → EQ
new_esEs14(@0, @0) → True
new_esEs11(vyy3001, vyy401, ty_Double) → new_esEs12(vyy3001, vyy401)
new_ltEs19(vyy651, vyy661, app(app(ty_Either, daf), dag)) → new_ltEs8(vyy651, vyy661, daf, dag)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Integer) → new_ltEs7(vyy6500, vyy6600)
new_esEs26(vyy651, vyy661, app(ty_Ratio, cdb)) → new_esEs13(vyy651, vyy661, cdb)
new_esEs27(vyy650, vyy660, app(ty_Ratio, chc)) → new_esEs13(vyy650, vyy660, chc)
new_esEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), eh, fa) → new_asAs(new_esEs10(vyy3000, vyy400, eh), new_esEs11(vyy3001, vyy401, fa))
new_esEs19(True, True) → True
new_esEs7(Left(vyy3000), Left(vyy400), ty_Ordering, hg) → new_esEs8(vyy3000, vyy400)
new_compare110(vyy650, vyy660, False, bdh, bea) → GT
new_ltEs8(Left(vyy650), Left(vyy660), app(app(app(ty_@3, bh), ca), cb), bg) → new_ltEs12(vyy650, vyy660, bh, ca, cb)
new_esEs11(vyy3001, vyy401, ty_Char) → new_esEs16(vyy3001, vyy401)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Float) → new_ltEs4(vyy6500, vyy6600)
new_ltEs14(EQ, LT) → False
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_compare7(vyy65, vyy66) → new_primCmpInt(vyy65, vyy66)
new_gtEs(vyy3330, vyy40, ba) → new_not(new_esEs8(new_compare211(vyy3330, Just(vyy40), new_esEs5(vyy3330, Just(vyy40), ba), ba), LT))
new_ltEs19(vyy651, vyy661, app(app(app(ty_@3, chf), chg), chh)) → new_ltEs12(vyy651, vyy661, chf, chg, chh)
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_@0) → new_ltEs6(vyy650, vyy660)
new_esEs26(vyy651, vyy661, ty_Ordering) → new_esEs8(vyy651, vyy661)
new_esEs8(GT, GT) → True
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Double) → new_esEs12(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, app(app(ty_Either, bbc), bbd)) → new_esEs7(vyy3000, vyy400, bbc, bbd)
new_esEs22(vyy3002, vyy402, ty_Char) → new_esEs16(vyy3002, vyy402)
new_esEs26(vyy651, vyy661, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs4(vyy651, vyy661, ccc, ccd, cce)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs16(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_@0) → new_ltEs6(vyy6500, vyy6600)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs12(vyy3000, vyy400)
new_ltEs15(Just(vyy6500), Just(vyy6600), app(app(ty_Either, bfc), bfd)) → new_ltEs8(vyy6500, vyy6600, bfc, bfd)
new_esEs11(vyy3001, vyy401, app(app(app(ty_@3, gh), ha), hb)) → new_esEs4(vyy3001, vyy401, gh, ha, hb)
new_compare211(vyy650, vyy660, True, beb) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs19(vyy651, vyy661, app(app(ty_@2, dac), dad)) → new_ltEs17(vyy651, vyy661, dac, dad)
new_esEs20(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt15(vyy650, vyy660, ty_Double) → new_lt5(vyy650, vyy660)
new_esEs12(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs20(vyy3000, vyy400, ty_Float) → new_esEs18(vyy3000, vyy400)
new_compare210(vyy650, vyy660, False, bd, be, bf) → new_compare112(vyy650, vyy660, new_ltEs12(vyy650, vyy660, bd, be, bf), bd, be, bf)
new_compare24(vyy650, vyy660) → new_compare27(vyy650, vyy660, new_esEs8(vyy650, vyy660))
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_[], baf), hg) → new_esEs17(vyy3000, vyy400, baf)
new_compare3([], :(vyy660, vyy661), bce) → LT
new_esEs7(Right(vyy3000), Right(vyy400), bbb, app(ty_Ratio, bbe)) → new_esEs13(vyy3000, vyy400, bbe)
new_esEs11(vyy3001, vyy401, ty_Int) → new_esEs9(vyy3001, vyy401)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(vyy3000), Left(vyy400), ty_Integer, hg) → new_esEs15(vyy3000, vyy400)
new_esEs19(False, False) → True
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Ratio, bab), hg) → new_esEs13(vyy3000, vyy400, bab)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_@2, bag), bah), hg) → new_esEs6(vyy3000, vyy400, bag, bah)
new_ltEs8(Right(vyy650), Right(vyy660), dc, app(ty_[], dh)) → new_ltEs16(vyy650, vyy660, dh)
new_compare3(:(vyy650, vyy651), [], bce) → GT
new_esEs7(Right(vyy3000), Right(vyy400), bbb, app(ty_Maybe, bcd)) → new_esEs5(vyy3000, vyy400, bcd)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_esEs8(EQ, EQ) → True
new_primPlusNat1(Zero, vyy40100) → Succ(vyy40100)
new_compare111(vyy650, vyy660, True, beb) → LT
new_lt20(vyy650, vyy660, ty_Ordering) → new_lt8(vyy650, vyy660)
new_esEs25(vyy650, vyy660, ty_Char) → new_esEs16(vyy650, vyy660)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Float) → new_esEs18(vyy3000, vyy400)
new_esEs26(vyy651, vyy661, app(app(ty_Either, cdc), cdd)) → new_esEs7(vyy651, vyy661, cdc, cdd)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs8(Right(vyy650), Right(vyy660), dc, app(app(app(ty_@3, dd), de), df)) → new_ltEs12(vyy650, vyy660, dd, de, df)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_compare28(vyy650, vyy660, False) → new_compare11(vyy650, vyy660, new_ltEs10(vyy650, vyy660))
new_ltEs8(Left(vyy650), Left(vyy660), app(ty_[], cd), bg) → new_ltEs16(vyy650, vyy660, cd)
new_esEs10(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_lt20(vyy650, vyy660, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt6(vyy650, vyy660, cgd, cge, cgf)
new_primCmpNat0(Succ(vyy6500), Succ(vyy6600)) → new_primCmpNat0(vyy6500, vyy6600)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Int) → new_esEs9(vyy3000, vyy400)
new_ltEs18(vyy652, vyy662, app(ty_Ratio, ced)) → new_ltEs5(vyy652, vyy662, ced)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, app(app(ty_@2, bcb), bcc)) → new_esEs6(vyy3000, vyy400, bcb, bcc)
new_lt15(vyy650, vyy660, ty_Char) → new_lt12(vyy650, vyy660)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs16(vyy3000, vyy400)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs4(vyy3000, vyy400, cfc, cfd, cfe)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Char, bg) → new_ltEs11(vyy650, vyy660)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Double) → new_ltEs9(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_Bool) → new_esEs19(vyy3001, vyy401)
new_esEs25(vyy650, vyy660, app(ty_Maybe, beb)) → new_esEs5(vyy650, vyy660, beb)
new_esEs26(vyy651, vyy661, ty_Bool) → new_esEs19(vyy651, vyy661)
new_esEs25(vyy650, vyy660, ty_Int) → new_esEs9(vyy650, vyy660)
new_compare18(vyy650, vyy660, app(ty_Ratio, bde)) → new_compare9(vyy650, vyy660, bde)
new_esEs26(vyy651, vyy661, ty_Integer) → new_esEs15(vyy651, vyy661)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs4(vyy3000, vyy400, bbf, bbg, bbh)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_esEs27(vyy650, vyy660, ty_Ordering) → new_esEs8(vyy650, vyy660)
new_esEs10(vyy3000, vyy400, ty_Int) → new_esEs9(vyy3000, vyy400)
new_compare18(vyy650, vyy660, app(ty_Maybe, bda)) → new_compare25(vyy650, vyy660, bda)
new_compare18(vyy650, vyy660, ty_@0) → new_compare14(vyy650, vyy660)
new_lt8(vyy650, vyy660) → new_esEs8(new_compare24(vyy650, vyy660), LT)
new_esEs27(vyy650, vyy660, ty_Char) → new_esEs16(vyy650, vyy660)
new_foldFM_GE10(vyy50, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE20(vyy330, vyy331, new_foldFM_GE0(vyy50, vyy40, vyy334, h, ba), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba)
new_esEs13(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cbf) → new_asAs(new_esEs23(vyy3000, vyy400, cbf), new_esEs24(vyy3001, vyy401, cbf))
new_compare6(Double(vyy650, vyy651), Double(vyy660, vyy661)) → new_compare7(new_sr(vyy650, vyy660), new_sr(vyy651, vyy661))
new_primCompAux00(vyy136, LT) → LT
new_primCmpInt(Neg(Succ(vyy6500)), Neg(vyy660)) → new_primCmpNat0(vyy660, Succ(vyy6500))
new_lt16(vyy651, vyy661, ty_Bool) → new_lt17(vyy651, vyy661)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_esEs10(vyy3000, vyy400, app(app(ty_Either, fb), fc)) → new_esEs7(vyy3000, vyy400, fb, fc)
new_foldFM_GE10(vyy50, vyy40, vyy330, vyy331, vyy332, vyy333, vyy334, False, h, ba) → new_foldFM_GE0(vyy50, vyy40, vyy334, h, ba)
new_lt14(vyy650, vyy660) → new_esEs8(new_compare12(vyy650, vyy660), LT)
new_primPlusNat0(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat0(Succ(vyy10400), Zero) → Succ(vyy10400)
new_lt16(vyy651, vyy661, ty_Integer) → new_lt14(vyy651, vyy661)
new_esEs21(vyy3001, vyy401, ty_Bool) → new_esEs19(vyy3001, vyy401)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Integer) → new_ltEs7(vyy650, vyy660)
new_compare8(Float(vyy650, vyy651), Float(vyy660, vyy661)) → new_compare7(new_sr(vyy650, vyy660), new_sr(vyy651, vyy661))
new_primCmpNat0(Succ(vyy6500), Zero) → GT
new_esEs20(vyy3000, vyy400, app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs4(vyy3000, vyy400, bgc, bgd, bge)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy6600))) → LT
new_esEs19(True, False) → False
new_esEs19(False, True) → False
new_esEs21(vyy3001, vyy401, ty_Char) → new_esEs16(vyy3001, vyy401)
new_compare210(vyy650, vyy660, True, bd, be, bf) → EQ
new_ltEs15(Just(vyy6500), Just(vyy6600), app(app(app(ty_@3, bec), bed), bee)) → new_ltEs12(vyy6500, vyy6600, bec, bed, bee)
new_esEs22(vyy3002, vyy402, app(ty_Ratio, caf)) → new_esEs13(vyy3002, vyy402, caf)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_sr0(Integer(vyy6600), Integer(vyy6510)) → Integer(new_primMulInt(vyy6600, vyy6510))
new_foldFM_GE0(vyy50, vyy40, EmptyFM, h, ba) → vyy50
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_foldFM_GE20(vyy330, vyy331, vyy71, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba) → new_foldFM_GE10(new_eltsFM_GE0(vyy330, vyy331, vyy71, h, ba), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, ba), h, ba)
new_esEs25(vyy650, vyy660, ty_Bool) → new_esEs19(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_esEs27(vyy650, vyy660, app(ty_Maybe, cgg)) → new_esEs5(vyy650, vyy660, cgg)
new_esEs27(vyy650, vyy660, ty_Double) → new_esEs12(vyy650, vyy660)
new_esEs18(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare18(vyy650, vyy660, app(ty_[], bdb)) → new_compare3(vyy650, vyy660, bdb)
new_esEs22(vyy3002, vyy402, app(app(ty_@2, cbc), cbd)) → new_esEs6(vyy3002, vyy402, cbc, cbd)
new_esEs26(vyy651, vyy661, ty_Int) → new_esEs9(vyy651, vyy661)
new_lt7(vyy650, vyy660, ef, eg) → new_esEs8(new_compare17(vyy650, vyy660, ef, eg), LT)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_esEs26(vyy651, vyy661, app(ty_[], ccg)) → new_esEs17(vyy651, vyy661, ccg)
new_esEs21(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy6600))) → new_primCmpNat0(Zero, Succ(vyy6600))
new_primCompAux00(vyy136, EQ) → vyy136
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dba), dbb)) → new_esEs7(vyy3000, vyy400, dba, dbb)
new_esEs25(vyy650, vyy660, ty_@0) → new_esEs14(vyy650, vyy660)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Int, bg) → new_ltEs13(vyy650, vyy660)
new_esEs22(vyy3002, vyy402, ty_Bool) → new_esEs19(vyy3002, vyy402)
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Float) → new_ltEs4(vyy650, vyy660)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs21(vyy3001, vyy401, app(ty_[], bhh)) → new_esEs17(vyy3001, vyy401, bhh)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bac), bad), bae), hg) → new_esEs4(vyy3000, vyy400, bac, bad, bae)
new_esEs22(vyy3002, vyy402, ty_Float) → new_esEs18(vyy3002, vyy402)
new_lt20(vyy650, vyy660, ty_Double) → new_lt5(vyy650, vyy660)
new_not(False) → True
new_ltEs8(Right(vyy650), Right(vyy660), dc, app(app(ty_Either, ed), ee)) → new_ltEs8(vyy650, vyy660, ed, ee)
new_lt15(vyy650, vyy660, ty_Bool) → new_lt17(vyy650, vyy660)
new_esEs10(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_ltEs18(vyy652, vyy662, app(app(ty_Either, cee), cef)) → new_ltEs8(vyy652, vyy662, cee, cef)
new_primCmpInt(Pos(Succ(vyy6500)), Pos(vyy660)) → new_primCmpNat0(Succ(vyy6500), vyy660)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs19(vyy3000, vyy400)
new_compare18(vyy650, vyy660, app(app(ty_Either, bdf), bdg)) → new_compare26(vyy650, vyy660, bdf, bdg)
new_esEs25(vyy650, vyy660, ty_Integer) → new_esEs15(vyy650, vyy660)
new_ltEs18(vyy652, vyy662, ty_Ordering) → new_ltEs14(vyy652, vyy662)
new_ltEs14(LT, LT) → True
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_@0) → new_esEs14(vyy3000, vyy400)
new_lt16(vyy651, vyy661, ty_Double) → new_lt5(vyy651, vyy661)
new_esEs25(vyy650, vyy660, ty_Float) → new_esEs18(vyy650, vyy660)
new_esEs25(vyy650, vyy660, app(app(app(ty_@3, bd), be), bf)) → new_esEs4(vyy650, vyy660, bd, be, bf)
new_compare29(vyy650, vyy660, False, bdh, bea) → new_compare110(vyy650, vyy660, new_ltEs8(vyy650, vyy660, bdh, bea), bdh, bea)
new_esEs27(vyy650, vyy660, ty_@0) → new_esEs14(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_@0) → new_esEs14(vyy3001, vyy401)
new_esEs5(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs14(vyy3000, vyy400)
new_compare12(Integer(vyy650), Integer(vyy660)) → new_primCmpInt(vyy650, vyy660)
new_compare28(vyy650, vyy660, True) → EQ
new_esEs22(vyy3002, vyy402, app(app(app(ty_@3, cag), cah), cba)) → new_esEs4(vyy3002, vyy402, cag, cah, cba)
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_Ratio, cfb)) → new_esEs13(vyy3000, vyy400, cfb)
new_compare16(Char(vyy650), Char(vyy660)) → new_primCmpNat0(vyy650, vyy660)
new_lt19(vyy650, vyy660, ccb) → new_esEs8(new_compare9(vyy650, vyy660, ccb), LT)
new_primCmpInt(Pos(Succ(vyy6500)), Neg(vyy660)) → GT
new_ltEs16(vyy65, vyy66, bce) → new_not(new_esEs8(new_compare3(vyy65, vyy66, bce), GT))
new_esEs11(vyy3001, vyy401, app(ty_Maybe, hf)) → new_esEs5(vyy3001, vyy401, hf)
new_lt6(vyy650, vyy660, bd, be, bf) → new_esEs8(new_compare13(vyy650, vyy660, bd, be, bf), LT)
new_ltEs19(vyy651, vyy661, app(ty_[], dab)) → new_ltEs16(vyy651, vyy661, dab)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs20(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_esEs7(Left(vyy3000), Left(vyy400), ty_@0, hg) → new_esEs14(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs27(vyy650, vyy660, app(app(ty_@2, cha), chb)) → new_esEs6(vyy650, vyy660, cha, chb)
new_esEs20(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs10(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_ltEs12(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cbg, cbh, cca) → new_pePe(new_lt15(vyy650, vyy660, cbg), new_asAs(new_esEs25(vyy650, vyy660, cbg), new_pePe(new_lt16(vyy651, vyy661, cbh), new_asAs(new_esEs26(vyy651, vyy661, cbh), new_ltEs18(vyy652, vyy662, cca)))))
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_ltEs8(Left(vyy650), Left(vyy660), app(app(ty_Either, da), db), bg) → new_ltEs8(vyy650, vyy660, da, db)
new_esEs21(vyy3001, vyy401, ty_Int) → new_esEs9(vyy3001, vyy401)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs8(Right(vyy650), Right(vyy660), dc, app(ty_Ratio, ec)) → new_ltEs5(vyy650, vyy660, ec)
new_lt13(vyy650, vyy660, beb) → new_esEs8(new_compare25(vyy650, vyy660, beb), LT)
new_ltEs19(vyy651, vyy661, ty_@0) → new_ltEs6(vyy651, vyy661)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs18(vyy652, vyy662, ty_Integer) → new_ltEs7(vyy652, vyy662)
new_compare25(vyy650, vyy660, beb) → new_compare211(vyy650, vyy660, new_esEs5(vyy650, vyy660, beb), beb)
new_esEs20(vyy3000, vyy400, app(ty_[], bgf)) → new_esEs17(vyy3000, vyy400, bgf)
new_esEs22(vyy3002, vyy402, ty_Int) → new_esEs9(vyy3002, vyy402)
new_ltEs15(Just(vyy6500), Nothing, beb) → False
new_esEs22(vyy3002, vyy402, app(ty_[], cbb)) → new_esEs17(vyy3002, vyy402, cbb)
new_ltEs8(Left(vyy650), Left(vyy660), ty_@0, bg) → new_ltEs6(vyy650, vyy660)
new_lt20(vyy650, vyy660, ty_Float) → new_lt18(vyy650, vyy660)
new_ltEs18(vyy652, vyy662, app(app(ty_@2, ceb), cec)) → new_ltEs17(vyy652, vyy662, ceb, cec)
new_lt16(vyy651, vyy661, app(ty_[], ccg)) → new_lt4(vyy651, vyy661, ccg)
new_ltEs19(vyy651, vyy661, ty_Bool) → new_ltEs10(vyy651, vyy661)
new_esEs21(vyy3001, vyy401, app(app(ty_Either, bhb), bhc)) → new_esEs7(vyy3001, vyy401, bhb, bhc)
new_esEs26(vyy651, vyy661, app(ty_Maybe, ccf)) → new_esEs5(vyy651, vyy661, ccf)
new_primPlusNat1(Succ(vyy1040), vyy40100) → Succ(Succ(new_primPlusNat0(vyy1040, vyy40100)))
new_lt15(vyy650, vyy660, app(app(ty_Either, bdh), bea)) → new_lt9(vyy650, vyy660, bdh, bea)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs9(vyy3001, vyy401)
new_esEs10(vyy3000, vyy400, app(ty_Maybe, gd)) → new_esEs5(vyy3000, vyy400, gd)
new_compare112(vyy650, vyy660, True, bd, be, bf) → LT
new_compare23(vyy650, vyy660, True, ef, eg) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(vyy6600))) → new_primCmpNat0(Succ(vyy6600), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy6600))) → GT
new_compare15(vyy650, vyy660, False, ef, eg) → GT
new_esEs27(vyy650, vyy660, ty_Int) → new_esEs9(vyy650, vyy660)
new_esEs21(vyy3001, vyy401, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs4(vyy3001, vyy401, bhe, bhf, bhg)
new_esEs26(vyy651, vyy661, ty_@0) → new_esEs14(vyy651, vyy661)
new_primCompAux0(vyy650, vyy660, vyy127, bce) → new_primCompAux00(vyy127, new_compare18(vyy650, vyy660, bce))
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dbh), dca)) → new_esEs6(vyy3000, vyy400, dbh, dca)
new_esEs11(vyy3001, vyy401, app(app(ty_Either, ge), gf)) → new_esEs7(vyy3001, vyy401, ge, gf)
new_ltEs6(vyy65, vyy66) → new_not(new_esEs8(new_compare14(vyy65, vyy66), GT))
new_lt20(vyy650, vyy660, app(ty_Ratio, chc)) → new_lt19(vyy650, vyy660, chc)
new_lt15(vyy650, vyy660, ty_Float) → new_lt18(vyy650, vyy660)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Bool, hg) → new_esEs19(vyy3000, vyy400)
new_ltEs19(vyy651, vyy661, ty_Ordering) → new_ltEs14(vyy651, vyy661)
new_lt15(vyy650, vyy660, ty_Int) → new_lt10(vyy650, vyy660)
new_esEs21(vyy3001, vyy401, ty_Float) → new_esEs18(vyy3001, vyy401)
new_esEs20(vyy3000, vyy400, app(app(ty_Either, bfh), bga)) → new_esEs7(vyy3000, vyy400, bfh, bga)
new_lt15(vyy650, vyy660, app(app(app(ty_@3, bd), be), bf)) → new_lt6(vyy650, vyy660, bd, be, bf)
new_compare18(vyy650, vyy660, ty_Bool) → new_compare19(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, app(app(ty_@2, hd), he)) → new_esEs6(vyy3001, vyy401, hd, he)
new_lt15(vyy650, vyy660, app(app(ty_@2, ef), eg)) → new_lt7(vyy650, vyy660, ef, eg)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Bool) → new_ltEs10(vyy6500, vyy6600)
new_lt12(vyy650, vyy660) → new_esEs8(new_compare16(vyy650, vyy660), LT)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs21(vyy3001, vyy401, ty_@0) → new_esEs14(vyy3001, vyy401)
new_lt16(vyy651, vyy661, ty_Ordering) → new_lt8(vyy651, vyy661)
new_esEs20(vyy3000, vyy400, app(ty_Maybe, bha)) → new_esEs5(vyy3000, vyy400, bha)
new_esEs27(vyy650, vyy660, ty_Float) → new_esEs18(vyy650, vyy660)
new_ltEs10(True, False) → False
new_asAs(False, vyy91) → False
new_esEs22(vyy3002, vyy402, ty_Double) → new_esEs12(vyy3002, vyy402)
new_lt16(vyy651, vyy661, ty_@0) → new_lt11(vyy651, vyy661)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(ty_Either, ceh), cfa)) → new_esEs7(vyy3000, vyy400, ceh, cfa)
new_compare3([], [], bce) → EQ
new_compare211(vyy650, vyy660, False, beb) → new_compare111(vyy650, vyy660, new_ltEs15(vyy650, vyy660, beb), beb)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_ltEs19(vyy651, vyy661, ty_Char) → new_ltEs11(vyy651, vyy661)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_ltEs5(vyy65, vyy66, bc) → new_not(new_esEs8(new_compare9(vyy65, vyy66, bc), GT))
new_esEs21(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs10(vyy3000, vyy400, app(ty_[], ga)) → new_esEs17(vyy3000, vyy400, ga)
new_foldFM_GE3(vyy330, vyy331, vyy70, vyy40, h, ba) → new_eltsFM_GE0(vyy330, vyy331, vyy70, h, ba)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs9(vyy3000, vyy400)
new_esEs10(vyy3000, vyy400, app(ty_Ratio, fd)) → new_esEs13(vyy3000, vyy400, fd)
new_compare23(vyy650, vyy660, False, ef, eg) → new_compare15(vyy650, vyy660, new_ltEs17(vyy650, vyy660, ef, eg), ef, eg)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(ty_@2, cfg), cfh)) → new_esEs6(vyy3000, vyy400, cfg, cfh)
new_ltEs14(GT, LT) → False
new_lt20(vyy650, vyy660, app(ty_[], cgh)) → new_lt4(vyy650, vyy660, cgh)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Float, hg) → new_esEs18(vyy3000, vyy400)
new_ltEs8(Right(vyy650), Left(vyy660), dc, bg) → False
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs25(vyy650, vyy660, app(ty_[], bb)) → new_esEs17(vyy650, vyy660, bb)
new_compare18(vyy650, vyy660, ty_Integer) → new_compare12(vyy650, vyy660)
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_compare112(vyy650, vyy660, False, bd, be, bf) → GT
new_compare27(vyy650, vyy660, True) → EQ
new_esEs10(vyy3000, vyy400, ty_Float) → new_esEs18(vyy3000, vyy400)
new_compare111(vyy650, vyy660, False, beb) → GT
new_compare27(vyy650, vyy660, False) → new_compare10(vyy650, vyy660, new_ltEs14(vyy650, vyy660))
new_ltEs15(Nothing, Nothing, beb) → True
new_compare9(:%(vyy650, vyy651), :%(vyy660, vyy661), ty_Int) → new_compare7(new_sr(vyy650, vyy661), new_sr(vyy660, vyy651))
new_esEs5(Just(vyy3000), Nothing, ceg) → False
new_esEs5(Nothing, Just(vyy400), ceg) → False
new_esEs11(vyy3001, vyy401, app(ty_Ratio, gg)) → new_esEs13(vyy3001, vyy401, gg)
new_lt16(vyy651, vyy661, app(ty_Maybe, ccf)) → new_lt13(vyy651, vyy661, ccf)
new_lt5(vyy650, vyy660) → new_esEs8(new_compare6(vyy650, vyy660), LT)
new_esEs28(vyy3000, vyy400, app(ty_[], dbg)) → new_esEs17(vyy3000, vyy400, dbg)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dbc)) → new_esEs13(vyy3000, vyy400, dbc)
new_compare11(vyy650, vyy660, False) → GT
new_ltEs14(LT, GT) → True
new_ltEs14(LT, EQ) → True
new_compare11(vyy650, vyy660, True) → LT
new_esEs22(vyy3002, vyy402, ty_@0) → new_esEs14(vyy3002, vyy402)
new_esEs5(Nothing, Nothing, ceg) → True
new_ltEs18(vyy652, vyy662, app(ty_Maybe, cdh)) → new_ltEs15(vyy652, vyy662, cdh)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dcb)) → new_esEs5(vyy3000, vyy400, dcb)
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Maybe, bba), hg) → new_esEs5(vyy3000, vyy400, bba)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs18(vyy3000, vyy400)
new_esEs21(vyy3001, vyy401, ty_Double) → new_esEs12(vyy3001, vyy401)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs9(vyy3000, vyy400)
new_lt15(vyy650, vyy660, ty_Ordering) → new_lt8(vyy650, vyy660)
new_lt16(vyy651, vyy661, ty_Char) → new_lt12(vyy651, vyy661)
new_lt20(vyy650, vyy660, ty_Char) → new_lt12(vyy650, vyy660)
new_ltEs19(vyy651, vyy661, ty_Integer) → new_ltEs7(vyy651, vyy661)
new_esEs10(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs22(vyy3002, vyy402, app(ty_Maybe, cbe)) → new_esEs5(vyy3002, vyy402, cbe)
new_primPlusNat0(Succ(vyy10400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat0(vyy10400, vyy401000)))
new_lt20(vyy650, vyy660, ty_Integer) → new_lt14(vyy650, vyy660)
new_esEs21(vyy3001, vyy401, app(ty_Maybe, cac)) → new_esEs5(vyy3001, vyy401, cac)
new_esEs22(vyy3002, vyy402, ty_Integer) → new_esEs15(vyy3002, vyy402)
new_ltEs18(vyy652, vyy662, app(ty_[], cea)) → new_ltEs16(vyy652, vyy662, cea)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Ordering, bg) → new_ltEs14(vyy650, vyy660)
new_compare18(vyy650, vyy660, app(app(ty_@2, bdc), bdd)) → new_compare17(vyy650, vyy660, bdc, bdd)
new_ltEs10(True, True) → True
new_ltEs15(Just(vyy6500), Just(vyy6600), app(app(ty_@2, beh), bfa)) → new_ltEs17(vyy6500, vyy6600, beh, bfa)
new_ltEs14(EQ, EQ) → True
new_asAs(True, vyy91) → vyy91
new_lt16(vyy651, vyy661, app(app(ty_Either, cdc), cdd)) → new_lt9(vyy651, vyy661, cdc, cdd)
new_esEs17(:(vyy3000, vyy3001), :(vyy400, vyy401), dah) → new_asAs(new_esEs28(vyy3000, vyy400, dah), new_esEs17(vyy3001, vyy401, dah))
new_lt20(vyy650, vyy660, ty_Bool) → new_lt17(vyy650, vyy660)
new_lt16(vyy651, vyy661, ty_Int) → new_lt10(vyy651, vyy661)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Char, hg) → new_esEs16(vyy3000, vyy400)
new_compare18(vyy650, vyy660, ty_Float) → new_compare8(vyy650, vyy660)
new_esEs17([], [], dah) → True
new_esEs17(:(vyy3000, vyy3001), [], dah) → False
new_esEs17([], :(vyy400, vyy401), dah) → False
new_lt20(vyy650, vyy660, ty_@0) → new_lt11(vyy650, vyy660)
new_esEs26(vyy651, vyy661, app(app(ty_@2, cch), cda)) → new_esEs6(vyy651, vyy661, cch, cda)
new_esEs26(vyy651, vyy661, ty_Char) → new_esEs16(vyy651, vyy661)
new_ltEs8(Left(vyy650), Right(vyy660), dc, bg) → True
new_compare10(vyy650, vyy660, True) → LT
new_esEs9(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_compare26(vyy650, vyy660, bdh, bea) → new_compare29(vyy650, vyy660, new_esEs7(vyy650, vyy660, bdh, bea), bdh, bea)
new_esEs20(vyy3000, vyy400, ty_Char) → new_esEs16(vyy3000, vyy400)
new_esEs10(vyy3000, vyy400, ty_Char) → new_esEs16(vyy3000, vyy400)
new_compare18(vyy650, vyy660, ty_Double) → new_compare6(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_Float) → new_esEs18(vyy3001, vyy401)
new_compare10(vyy650, vyy660, False) → GT
new_ltEs13(vyy65, vyy66) → new_not(new_esEs8(new_compare7(vyy65, vyy66), GT))
new_primCompAux00(vyy136, GT) → GT
new_esEs25(vyy650, vyy660, app(app(ty_Either, bdh), bea)) → new_esEs7(vyy650, vyy660, bdh, bea)
new_ltEs18(vyy652, vyy662, ty_Double) → new_ltEs9(vyy652, vyy662)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_ltEs8(Left(vyy650), Left(vyy660), ty_Integer, bg) → new_ltEs7(vyy650, vyy660)
new_esEs27(vyy650, vyy660, ty_Bool) → new_esEs19(vyy650, vyy660)
new_ltEs15(Just(vyy6500), Just(vyy6600), app(ty_[], beg)) → new_ltEs16(vyy6500, vyy6600, beg)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_lt20(vyy650, vyy660, app(app(ty_Either, chd), che)) → new_lt9(vyy650, vyy660, chd, che)
new_esEs27(vyy650, vyy660, ty_Integer) → new_esEs15(vyy650, vyy660)
new_compare9(:%(vyy650, vyy651), :%(vyy660, vyy661), ty_Integer) → new_compare12(new_sr0(vyy650, vyy661), new_sr0(vyy660, vyy651))
new_primCmpInt(Neg(Succ(vyy6500)), Pos(vyy660)) → LT
new_not(True) → False

The set Q consists of the following terms:

new_esEs21(x0, x1, ty_Integer)
new_ltEs15(Just(x0), Just(x1), app(ty_[], x2))
new_compare10(x0, x1, True)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs16(Char(x0), Char(x1))
new_lt16(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Double)
new_lt16(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primCompAux0(x0, x1, x2, x3)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_@0)
new_esEs10(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Succ(x0))
new_esEs28(x0, x1, ty_Int)
new_primPlusNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, False, x2, x3, x4)
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primMulNat0(Zero, Succ(x0))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, True, x2, x3, x4)
new_ltEs15(Just(x0), Just(x1), ty_@0)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Bool)
new_lt15(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs8(GT, GT)
new_foldFM_GE0(x0, x1, EmptyFM, x2, x3)
new_lt16(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Int)
new_ltEs15(Just(x0), Just(x1), ty_Bool)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs24(x0, x1, ty_Integer)
new_lt11(x0, x1)
new_ltEs19(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_esEs20(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_Integer)
new_sr(x0, x1)
new_esEs10(x0, x1, ty_Int)
new_compare3([], [], x0)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_Ordering)
new_esEs19(True, True)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_compare13(x0, x1, x2, x3, x4)
new_esEs5(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare112(x0, x1, True, x2, x3, x4)
new_esEs23(x0, x1, ty_Int)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Zero)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt4(x0, x1, x2)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_sr0(Integer(x0), Integer(x1))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Integer)
new_compare26(x0, x1, x2, x3)
new_esEs10(x0, x1, ty_Float)
new_ltEs15(Just(x0), Just(x1), app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs15(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_Ordering)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_compare11(x0, x1, True)
new_esEs22(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_foldFM_GE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_primMulNat0(Zero, Zero)
new_primCompAux00(x0, GT)
new_primCmpNat0(Succ(x0), Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_lt16(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, x0)
new_lt15(x0, x1, ty_Char)
new_asAs(False, x0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1)
new_lt16(x0, x1, ty_Integer)
new_lt16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1)
new_esEs27(x0, x1, ty_Float)
new_primCompAux00(x0, EQ)
new_ltEs15(Just(x0), Just(x1), ty_Double)
new_lt16(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs14(@0, @0)
new_esEs20(x0, x1, ty_Double)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_foldFM_GE10(x0, x1, x2, x3, x4, EmptyFM, x5, True, x6, x7)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt17(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt15(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs27(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Ordering)
new_esEs11(x0, x1, ty_Int)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs5(Nothing, Nothing, x0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_compare18(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_foldFM_GE3(x0, x1, x2, x3, x4, x5)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(False, True)
new_esEs19(True, False)
new_esEs22(x0, x1, ty_Bool)
new_ltEs15(Just(x0), Nothing, x1)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt20(x0, x1, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_lt15(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs25(x0, x1, ty_Double)
new_primPlusNat0(Zero, Zero)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs10(False, False)
new_ltEs14(LT, LT)
new_lt14(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt16(x0, x1, ty_Ordering)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_lt7(x0, x1, x2, x3)
new_compare18(x0, x1, ty_@0)
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_lt15(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs11(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True)
new_esEs27(x0, x1, ty_Char)
new_esEs5(Nothing, Just(x0), x1)
new_lt20(x0, x1, app(ty_[], x2))
new_lt8(x0, x1)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_Double)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare15(x0, x1, True, x2, x3)
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_compare27(x0, x1, True)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs11(x0, x1, ty_Bool)
new_lt15(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, x2)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_compare18(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs21(x0, x1, ty_Ordering)
new_lt15(x0, x1, ty_Bool)
new_compare16(Char(x0), Char(x1))
new_lt6(x0, x1, x2, x3, x4)
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Int)
new_compare11(x0, x1, False)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs17([], [], x0)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare24(x0, x1)
new_ltEs16(x0, x1, x2)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs19(False, False)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Succ(x0), x1)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs19(x0, x1, ty_Double)
new_compare28(x0, x1, False)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, x2)
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_compare111(x0, x1, False, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare14(@0, @0)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare18(x0, x1, ty_Float)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare211(x0, x1, False, x2)
new_esEs28(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare8(Float(x0, x1), Float(x2, x3))
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare211(x0, x1, True, x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs15(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Char)
new_ltEs15(Just(x0), Just(x1), ty_Int)
new_compare25(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, ty_Ordering)
new_lt16(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_@0)
new_ltEs7(x0, x1)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Char)
new_lt15(x0, x1, ty_Int)
new_lt16(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Succ(x0))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_esEs9(x0, x1)
new_compare110(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs27(x0, x1, ty_Int)
new_lt15(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1)
new_compare3([], :(x0, x1), x2)
new_eltsFM_GE0(x0, x1, x2, x3, x4)
new_ltEs15(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs28(x0, x1, ty_Bool)
new_pePe(False, x0)
new_primCmpNat0(Zero, Zero)
new_lt15(x0, x1, ty_Float)
new_compare3(:(x0, x1), [], x2)
new_lt16(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1, x2, x3)
new_esEs22(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_lt15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_ltEs15(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt16(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_foldFM_GE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8)
new_ltEs10(True, True)
new_esEs22(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt15(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs11(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs22(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, ty_Float)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_ltEs18(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Char)
new_asAs(True, x0)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs25(x0, x1, ty_Char)
new_ltEs15(Just(x0), Just(x1), ty_Float)
new_compare18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs17(:(x0, x1), [], x2)
new_compare27(x0, x1, False)
new_primPlusNat0(Zero, Succ(x0))
new_esEs10(x0, x1, ty_@0)
new_compare19(x0, x1)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs14(GT, GT)
new_lt18(x0, x1)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare23(x0, x1, True, x2, x3)
new_esEs15(Integer(x0), Integer(x1))
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_not(True)
new_esEs21(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt10(x0, x1)
new_esEs20(x0, x1, ty_Integer)
new_compare111(x0, x1, True, x2)
new_compare7(x0, x1)
new_lt9(x0, x1, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, x2)
new_lt20(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs13(x0, x1)
new_esEs24(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs15(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs15(Just(x0), Just(x1), ty_Ordering)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs15(Just(x0), Just(x1), ty_Char)
new_compare112(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs4(x0, x1)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs15(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_compare18(x0, x1, ty_Bool)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs12(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs27(x0, x1, ty_@0)
new_compare29(x0, x1, True, x2, x3)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_compare12(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, ty_Float)
new_ltEs10(False, True)
new_ltEs10(True, False)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_lt16(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_lt16(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(Double(x0, x1), Double(x2, x3))
new_foldFM_GE10(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, True, x11, x12)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_compare18(x0, x1, ty_Char)
new_compare15(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_@0)
new_compare110(x0, x1, False, x2, x3)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_@0)
new_ltEs15(Nothing, Just(x0), x1)
new_esEs20(x0, x1, ty_Float)
new_compare18(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_compare18(x0, x1, ty_Integer)
new_gtEs(x0, x1, x2)
new_compare18(x0, x1, app(ty_Ratio, x2))
new_foldFM_GE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs17([], :(x0, x1), x2)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare18(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_compare29(x0, x1, False, x2, x3)
new_ltEs6(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_ltEs9(x0, x1)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1, ty_@0)
new_compare10(x0, x1, False)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))

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

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



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

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

new_foldFM_GE11(vyy49, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE21(vyy330, vyy331, new_foldFM_GE5(vyy49, vyy334, h, ba), vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba)
new_foldFM_GE21(vyy330, vyy331, vyy69, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba) → new_foldFM_GE11(new_eltsFM_GE0(vyy330, vyy331, vyy69, h, ba), vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs0(vyy3330, ba), h, ba)
new_foldFM_GE11(vyy49, vyy330, vyy331, vyy332, vyy333, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), False, h, ba) → new_foldFM_GE11(vyy49, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs0(vyy3340, ba), h, ba)
new_foldFM_GE11(vyy49, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba) → new_foldFM_GE4(vyy49, vyy334, h, ba)
new_foldFM_GE11(vyy49, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE4(vyy49, vyy334, h, ba)
new_foldFM_GE4(vyy49, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba) → new_foldFM_GE11(vyy49, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs0(vyy3340, ba), h, ba)

The TRS R consists of the following rules:

new_compare18(vyy650, vyy660, ty_Char) → new_compare16(vyy650, vyy660)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Int) → new_ltEs13(vyy6500, vyy6600)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_Either, hh), baa), hg) → new_esEs7(vyy3000, vyy400, hh, baa)
new_compare3(:(vyy650, vyy651), :(vyy660, vyy661), bce) → new_primCompAux0(vyy650, vyy660, new_compare3(vyy651, vyy661, bce), bce)
new_esEs21(vyy3001, vyy401, app(app(ty_@2, caa), cab)) → new_esEs6(vyy3001, vyy401, caa, cab)
new_esEs10(vyy3000, vyy400, app(app(app(ty_@3, ff), fg), fh)) → new_esEs4(vyy3000, vyy400, ff, fg, fh)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Char) → new_ltEs11(vyy6500, vyy6600)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs10(False, True) → True
new_compare15(vyy650, vyy660, True, ef, eg) → LT
new_lt20(vyy650, vyy660, ty_Int) → new_lt10(vyy650, vyy660)
new_compare110(vyy650, vyy660, True, bdh, bea) → LT
new_esEs7(Right(vyy3000), Right(vyy400), bbb, app(ty_[], bca)) → new_esEs17(vyy3000, vyy400, bca)
new_ltEs14(GT, GT) → True
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Char) → new_ltEs11(vyy650, vyy660)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Int, hg) → new_esEs9(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs16(vyy3000, vyy400)
new_lt16(vyy651, vyy661, app(app(app(ty_@3, ccc), ccd), cce)) → new_lt6(vyy651, vyy661, ccc, ccd, cce)
new_lt15(vyy650, vyy660, app(ty_[], bb)) → new_lt4(vyy650, vyy660, bb)
new_esEs20(vyy3000, vyy400, ty_Int) → new_esEs9(vyy3000, vyy400)
new_ltEs4(vyy65, vyy66) → new_not(new_esEs8(new_compare8(vyy65, vyy66), GT))
new_ltEs11(vyy65, vyy66) → new_not(new_esEs8(new_compare16(vyy65, vyy66), GT))
new_esEs20(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy651, vyy661, ty_Float) → new_ltEs4(vyy651, vyy661)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Float, bg) → new_ltEs4(vyy650, vyy660)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Double, hg) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy651, vyy661, app(ty_Ratio, dae)) → new_ltEs5(vyy651, vyy661, dae)
new_foldFM_GE5(vyy49, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba) → new_foldFM_GE12(vyy49, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs0(vyy3340, ba), h, ba)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_primMulNat0(Zero, Zero) → Zero
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_esEs25(vyy650, vyy660, ty_Double) → new_esEs12(vyy650, vyy660)
new_lt16(vyy651, vyy661, app(ty_Ratio, cdb)) → new_lt19(vyy651, vyy661, cdb)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs9(vyy3000, vyy400)
new_esEs27(vyy650, vyy660, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs4(vyy650, vyy660, cgd, cge, cgf)
new_compare17(vyy650, vyy660, ef, eg) → new_compare23(vyy650, vyy660, new_esEs6(vyy650, vyy660, ef, eg), ef, eg)
new_ltEs19(vyy651, vyy661, ty_Double) → new_ltEs9(vyy651, vyy661)
new_ltEs15(Nothing, Just(vyy6600), beb) → True
new_ltEs8(Left(vyy650), Left(vyy660), ty_Double, bg) → new_ltEs9(vyy650, vyy660)
new_ltEs19(vyy651, vyy661, app(ty_Maybe, daa)) → new_ltEs15(vyy651, vyy661, daa)
new_lt20(vyy650, vyy660, app(ty_Maybe, cgg)) → new_lt13(vyy650, vyy660, cgg)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_ltEs9(vyy65, vyy66) → new_not(new_esEs8(new_compare6(vyy65, vyy66), GT))
new_foldFM_GE12(vyy49, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba) → new_foldFM_GE30(vyy330, vyy331, new_foldFM_GE5(vyy49, vyy334, h, ba), h, ba)
new_lt15(vyy650, vyy660, ty_@0) → new_lt11(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, app(ty_[], hc)) → new_esEs17(vyy3001, vyy401, hc)
new_lt17(vyy650, vyy660) → new_esEs8(new_compare19(vyy650, vyy660), LT)
new_lt15(vyy650, vyy660, app(ty_Maybe, beb)) → new_lt13(vyy650, vyy660, beb)
new_lt9(vyy650, vyy660, bdh, bea) → new_esEs8(new_compare26(vyy650, vyy660, bdh, bea), LT)
new_esEs20(vyy3000, vyy400, app(ty_Ratio, bgb)) → new_esEs13(vyy3000, vyy400, bgb)
new_lt10(vyy650, vyy660) → new_esEs8(new_compare7(vyy650, vyy660), LT)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Ordering) → new_ltEs14(vyy6500, vyy6600)
new_esEs4(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bfe, bff, bfg) → new_asAs(new_esEs20(vyy3000, vyy400, bfe), new_asAs(new_esEs21(vyy3001, vyy401, bff), new_esEs22(vyy3002, vyy402, bfg)))
new_esEs10(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_Maybe, cga)) → new_esEs5(vyy3000, vyy400, cga)
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Int) → new_ltEs13(vyy650, vyy660)
new_esEs26(vyy651, vyy661, ty_Float) → new_esEs18(vyy651, vyy661)
new_esEs15(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_eltsFM_GE0(vyy330, vyy331, vyy68, h, ba) → :(vyy331, vyy68)
new_ltEs17(@2(vyy650, vyy651), @2(vyy660, vyy661), cgb, cgc) → new_pePe(new_lt20(vyy650, vyy660, cgb), new_asAs(new_esEs27(vyy650, vyy660, cgb), new_ltEs19(vyy651, vyy661, cgc)))
new_ltEs18(vyy652, vyy662, ty_Bool) → new_ltEs10(vyy652, vyy662)
new_ltEs8(Left(vyy650), Left(vyy660), app(ty_Maybe, cc), bg) → new_ltEs15(vyy650, vyy660, cc)
new_lt15(vyy650, vyy660, ty_Integer) → new_lt14(vyy650, vyy660)
new_ltEs10(False, False) → True
new_esEs20(vyy3000, vyy400, app(app(ty_@2, bgg), bgh)) → new_esEs6(vyy3000, vyy400, bgg, bgh)
new_ltEs8(Left(vyy650), Left(vyy660), app(ty_Ratio, cg), bg) → new_ltEs5(vyy650, vyy660, cg)
new_esEs20(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_esEs22(vyy3002, vyy402, app(app(ty_Either, cad), cae)) → new_esEs7(vyy3002, vyy402, cad, cae)
new_compare13(vyy650, vyy660, bd, be, bf) → new_compare210(vyy650, vyy660, new_esEs4(vyy650, vyy660, bd, be, bf), bd, be, bf)
new_ltEs18(vyy652, vyy662, ty_Float) → new_ltEs4(vyy652, vyy662)
new_ltEs8(Right(vyy650), Right(vyy660), dc, app(app(ty_@2, ea), eb)) → new_ltEs17(vyy650, vyy660, ea, eb)
new_gtEs0(vyy3330, ba) → new_not(new_esEs8(new_compare211(vyy3330, Nothing, new_esEs5(vyy3330, Nothing, ba), ba), LT))
new_pePe(False, vyy126) → vyy126
new_lt4(vyy650, vyy660, bb) → new_esEs8(new_compare3(vyy650, vyy660, bb), LT)
new_esEs7(Left(vyy3000), Right(vyy400), bbb, hg) → False
new_esEs7(Right(vyy3000), Left(vyy400), bbb, hg) → False
new_ltEs8(Left(vyy650), Left(vyy660), app(app(ty_@2, ce), cf), bg) → new_ltEs17(vyy650, vyy660, ce, cf)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs18(vyy3000, vyy400)
new_esEs27(vyy650, vyy660, app(app(ty_Either, chd), che)) → new_esEs7(vyy650, vyy660, chd, che)
new_ltEs14(GT, EQ) → False
new_compare18(vyy650, vyy660, ty_Int) → new_compare7(vyy650, vyy660)
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Bool) → new_ltEs10(vyy650, vyy660)
new_ltEs18(vyy652, vyy662, app(app(app(ty_@3, cde), cdf), cdg)) → new_ltEs12(vyy652, vyy662, cde, cdf, cdg)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Char) → new_esEs16(vyy3000, vyy400)
new_compare14(@0, @0) → EQ
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs4(vyy3000, vyy400, dbd, dbe, dbf)
new_lt16(vyy651, vyy661, ty_Float) → new_lt18(vyy651, vyy661)
new_esEs27(vyy650, vyy660, app(ty_[], cgh)) → new_esEs17(vyy650, vyy660, cgh)
new_esEs22(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Bool, bg) → new_ltEs10(vyy650, vyy660)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs15(vyy3000, vyy400)
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Ordering) → new_ltEs14(vyy650, vyy660)
new_lt20(vyy650, vyy660, app(app(ty_@2, cha), chb)) → new_lt7(vyy650, vyy660, cha, chb)
new_ltEs18(vyy652, vyy662, ty_Int) → new_ltEs13(vyy652, vyy662)
new_ltEs15(Just(vyy6500), Just(vyy6600), app(ty_Maybe, bef)) → new_ltEs15(vyy6500, vyy6600, bef)
new_esEs10(vyy3000, vyy400, app(app(ty_@2, gb), gc)) → new_esEs6(vyy3000, vyy400, gb, gc)
new_compare18(vyy650, vyy660, ty_Ordering) → new_compare24(vyy650, vyy660)
new_ltEs18(vyy652, vyy662, ty_Char) → new_ltEs11(vyy652, vyy662)
new_ltEs7(vyy65, vyy66) → new_not(new_esEs8(new_compare12(vyy65, vyy66), GT))
new_lt15(vyy650, vyy660, app(ty_Ratio, ccb)) → new_lt19(vyy650, vyy660, ccb)
new_primCmpNat0(Zero, Succ(vyy6600)) → LT
new_esEs26(vyy651, vyy661, ty_Double) → new_esEs12(vyy651, vyy661)
new_ltEs18(vyy652, vyy662, ty_@0) → new_ltEs6(vyy652, vyy662)
new_esEs25(vyy650, vyy660, app(app(ty_@2, ef), eg)) → new_esEs6(vyy650, vyy660, ef, eg)
new_lt16(vyy651, vyy661, app(app(ty_@2, cch), cda)) → new_lt7(vyy651, vyy661, cch, cda)
new_esEs8(LT, LT) → True
new_esEs21(vyy3001, vyy401, app(ty_Ratio, bhd)) → new_esEs13(vyy3001, vyy401, bhd)
new_lt18(vyy650, vyy660) → new_esEs8(new_compare8(vyy650, vyy660), LT)
new_lt11(vyy650, vyy660) → new_esEs8(new_compare14(vyy650, vyy660), LT)
new_compare19(vyy650, vyy660) → new_compare28(vyy650, vyy660, new_esEs19(vyy650, vyy660))
new_esEs25(vyy650, vyy660, ty_Ordering) → new_esEs8(vyy650, vyy660)
new_esEs25(vyy650, vyy660, app(ty_Ratio, ccb)) → new_esEs13(vyy650, vyy660, ccb)
new_ltEs8(Right(vyy650), Right(vyy660), dc, app(ty_Maybe, dg)) → new_ltEs15(vyy650, vyy660, dg)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Double) → new_ltEs9(vyy6500, vyy6600)
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_[], cff)) → new_esEs17(vyy3000, vyy400, cff)
new_pePe(True, vyy126) → True
new_primEqNat0(Zero, Zero) → True
new_ltEs19(vyy651, vyy661, ty_Int) → new_ltEs13(vyy651, vyy661)
new_compare18(vyy650, vyy660, app(app(app(ty_@3, bcf), bcg), bch)) → new_compare13(vyy650, vyy660, bcf, bcg, bch)
new_ltEs15(Just(vyy6500), Just(vyy6600), app(ty_Ratio, bfb)) → new_ltEs5(vyy6500, vyy6600, bfb)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat1(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_compare29(vyy650, vyy660, True, bdh, bea) → EQ
new_esEs14(@0, @0) → True
new_esEs11(vyy3001, vyy401, ty_Double) → new_esEs12(vyy3001, vyy401)
new_ltEs19(vyy651, vyy661, app(app(ty_Either, daf), dag)) → new_ltEs8(vyy651, vyy661, daf, dag)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Integer) → new_ltEs7(vyy6500, vyy6600)
new_esEs26(vyy651, vyy661, app(ty_Ratio, cdb)) → new_esEs13(vyy651, vyy661, cdb)
new_esEs27(vyy650, vyy660, app(ty_Ratio, chc)) → new_esEs13(vyy650, vyy660, chc)
new_esEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), eh, fa) → new_asAs(new_esEs10(vyy3000, vyy400, eh), new_esEs11(vyy3001, vyy401, fa))
new_esEs19(True, True) → True
new_esEs7(Left(vyy3000), Left(vyy400), ty_Ordering, hg) → new_esEs8(vyy3000, vyy400)
new_compare110(vyy650, vyy660, False, bdh, bea) → GT
new_ltEs8(Left(vyy650), Left(vyy660), app(app(app(ty_@3, bh), ca), cb), bg) → new_ltEs12(vyy650, vyy660, bh, ca, cb)
new_esEs11(vyy3001, vyy401, ty_Char) → new_esEs16(vyy3001, vyy401)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Float) → new_ltEs4(vyy6500, vyy6600)
new_foldFM_GE12(vyy49, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE22(vyy330, vyy331, new_foldFM_GE5(vyy49, vyy334, h, ba), vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba)
new_ltEs14(EQ, LT) → False
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_compare7(vyy65, vyy66) → new_primCmpInt(vyy65, vyy66)
new_ltEs19(vyy651, vyy661, app(app(app(ty_@3, chf), chg), chh)) → new_ltEs12(vyy651, vyy661, chf, chg, chh)
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_@0) → new_ltEs6(vyy650, vyy660)
new_esEs26(vyy651, vyy661, ty_Ordering) → new_esEs8(vyy651, vyy661)
new_esEs8(GT, GT) → True
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Double) → new_esEs12(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, app(app(ty_Either, bbc), bbd)) → new_esEs7(vyy3000, vyy400, bbc, bbd)
new_esEs22(vyy3002, vyy402, ty_Char) → new_esEs16(vyy3002, vyy402)
new_esEs26(vyy651, vyy661, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs4(vyy651, vyy661, ccc, ccd, cce)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs16(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_@0) → new_ltEs6(vyy6500, vyy6600)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs12(vyy3000, vyy400)
new_ltEs15(Just(vyy6500), Just(vyy6600), app(app(ty_Either, bfc), bfd)) → new_ltEs8(vyy6500, vyy6600, bfc, bfd)
new_esEs11(vyy3001, vyy401, app(app(app(ty_@3, gh), ha), hb)) → new_esEs4(vyy3001, vyy401, gh, ha, hb)
new_compare211(vyy650, vyy660, True, beb) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs19(vyy651, vyy661, app(app(ty_@2, dac), dad)) → new_ltEs17(vyy651, vyy661, dac, dad)
new_esEs20(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt15(vyy650, vyy660, ty_Double) → new_lt5(vyy650, vyy660)
new_esEs12(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs20(vyy3000, vyy400, ty_Float) → new_esEs18(vyy3000, vyy400)
new_compare210(vyy650, vyy660, False, bd, be, bf) → new_compare112(vyy650, vyy660, new_ltEs12(vyy650, vyy660, bd, be, bf), bd, be, bf)
new_compare24(vyy650, vyy660) → new_compare27(vyy650, vyy660, new_esEs8(vyy650, vyy660))
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_[], baf), hg) → new_esEs17(vyy3000, vyy400, baf)
new_compare3([], :(vyy660, vyy661), bce) → LT
new_esEs7(Right(vyy3000), Right(vyy400), bbb, app(ty_Ratio, bbe)) → new_esEs13(vyy3000, vyy400, bbe)
new_esEs11(vyy3001, vyy401, ty_Int) → new_esEs9(vyy3001, vyy401)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(vyy3000), Left(vyy400), ty_Integer, hg) → new_esEs15(vyy3000, vyy400)
new_esEs19(False, False) → True
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Ratio, bab), hg) → new_esEs13(vyy3000, vyy400, bab)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_@2, bag), bah), hg) → new_esEs6(vyy3000, vyy400, bag, bah)
new_ltEs8(Right(vyy650), Right(vyy660), dc, app(ty_[], dh)) → new_ltEs16(vyy650, vyy660, dh)
new_compare3(:(vyy650, vyy651), [], bce) → GT
new_esEs7(Right(vyy3000), Right(vyy400), bbb, app(ty_Maybe, bcd)) → new_esEs5(vyy3000, vyy400, bcd)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_esEs8(EQ, EQ) → True
new_primPlusNat1(Zero, vyy40100) → Succ(vyy40100)
new_compare111(vyy650, vyy660, True, beb) → LT
new_lt20(vyy650, vyy660, ty_Ordering) → new_lt8(vyy650, vyy660)
new_esEs25(vyy650, vyy660, ty_Char) → new_esEs16(vyy650, vyy660)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Float) → new_esEs18(vyy3000, vyy400)
new_esEs26(vyy651, vyy661, app(app(ty_Either, cdc), cdd)) → new_esEs7(vyy651, vyy661, cdc, cdd)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs8(Right(vyy650), Right(vyy660), dc, app(app(app(ty_@3, dd), de), df)) → new_ltEs12(vyy650, vyy660, dd, de, df)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_compare28(vyy650, vyy660, False) → new_compare11(vyy650, vyy660, new_ltEs10(vyy650, vyy660))
new_ltEs8(Left(vyy650), Left(vyy660), app(ty_[], cd), bg) → new_ltEs16(vyy650, vyy660, cd)
new_esEs10(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_lt20(vyy650, vyy660, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt6(vyy650, vyy660, cgd, cge, cgf)
new_primCmpNat0(Succ(vyy6500), Succ(vyy6600)) → new_primCmpNat0(vyy6500, vyy6600)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Int) → new_esEs9(vyy3000, vyy400)
new_ltEs18(vyy652, vyy662, app(ty_Ratio, ced)) → new_ltEs5(vyy652, vyy662, ced)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, app(app(ty_@2, bcb), bcc)) → new_esEs6(vyy3000, vyy400, bcb, bcc)
new_lt15(vyy650, vyy660, ty_Char) → new_lt12(vyy650, vyy660)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs16(vyy3000, vyy400)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs4(vyy3000, vyy400, cfc, cfd, cfe)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Char, bg) → new_ltEs11(vyy650, vyy660)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Double) → new_ltEs9(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_Bool) → new_esEs19(vyy3001, vyy401)
new_esEs25(vyy650, vyy660, app(ty_Maybe, beb)) → new_esEs5(vyy650, vyy660, beb)
new_esEs26(vyy651, vyy661, ty_Bool) → new_esEs19(vyy651, vyy661)
new_esEs25(vyy650, vyy660, ty_Int) → new_esEs9(vyy650, vyy660)
new_compare18(vyy650, vyy660, app(ty_Ratio, bde)) → new_compare9(vyy650, vyy660, bde)
new_esEs26(vyy651, vyy661, ty_Integer) → new_esEs15(vyy651, vyy661)
new_esEs7(Right(vyy3000), Right(vyy400), bbb, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs4(vyy3000, vyy400, bbf, bbg, bbh)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_esEs27(vyy650, vyy660, ty_Ordering) → new_esEs8(vyy650, vyy660)
new_esEs10(vyy3000, vyy400, ty_Int) → new_esEs9(vyy3000, vyy400)
new_compare18(vyy650, vyy660, app(ty_Maybe, bda)) → new_compare25(vyy650, vyy660, bda)
new_compare18(vyy650, vyy660, ty_@0) → new_compare14(vyy650, vyy660)
new_lt8(vyy650, vyy660) → new_esEs8(new_compare24(vyy650, vyy660), LT)
new_esEs27(vyy650, vyy660, ty_Char) → new_esEs16(vyy650, vyy660)
new_esEs13(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cbf) → new_asAs(new_esEs23(vyy3000, vyy400, cbf), new_esEs24(vyy3001, vyy401, cbf))
new_compare6(Double(vyy650, vyy651), Double(vyy660, vyy661)) → new_compare7(new_sr(vyy650, vyy660), new_sr(vyy651, vyy661))
new_primCompAux00(vyy136, LT) → LT
new_primCmpInt(Neg(Succ(vyy6500)), Neg(vyy660)) → new_primCmpNat0(vyy660, Succ(vyy6500))
new_lt16(vyy651, vyy661, ty_Bool) → new_lt17(vyy651, vyy661)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_esEs10(vyy3000, vyy400, app(app(ty_Either, fb), fc)) → new_esEs7(vyy3000, vyy400, fb, fc)
new_lt14(vyy650, vyy660) → new_esEs8(new_compare12(vyy650, vyy660), LT)
new_primPlusNat0(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat0(Succ(vyy10400), Zero) → Succ(vyy10400)
new_lt16(vyy651, vyy661, ty_Integer) → new_lt14(vyy651, vyy661)
new_esEs21(vyy3001, vyy401, ty_Bool) → new_esEs19(vyy3001, vyy401)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Integer) → new_ltEs7(vyy650, vyy660)
new_compare8(Float(vyy650, vyy651), Float(vyy660, vyy661)) → new_compare7(new_sr(vyy650, vyy660), new_sr(vyy651, vyy661))
new_primCmpNat0(Succ(vyy6500), Zero) → GT
new_esEs20(vyy3000, vyy400, app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs4(vyy3000, vyy400, bgc, bgd, bge)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy6600))) → LT
new_esEs19(True, False) → False
new_esEs19(False, True) → False
new_esEs21(vyy3001, vyy401, ty_Char) → new_esEs16(vyy3001, vyy401)
new_compare210(vyy650, vyy660, True, bd, be, bf) → EQ
new_ltEs15(Just(vyy6500), Just(vyy6600), app(app(app(ty_@3, bec), bed), bee)) → new_ltEs12(vyy6500, vyy6600, bec, bed, bee)
new_esEs22(vyy3002, vyy402, app(ty_Ratio, caf)) → new_esEs13(vyy3002, vyy402, caf)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_sr0(Integer(vyy6600), Integer(vyy6510)) → Integer(new_primMulInt(vyy6600, vyy6510))
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_esEs25(vyy650, vyy660, ty_Bool) → new_esEs19(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_esEs27(vyy650, vyy660, app(ty_Maybe, cgg)) → new_esEs5(vyy650, vyy660, cgg)
new_esEs27(vyy650, vyy660, ty_Double) → new_esEs12(vyy650, vyy660)
new_esEs18(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare18(vyy650, vyy660, app(ty_[], bdb)) → new_compare3(vyy650, vyy660, bdb)
new_esEs22(vyy3002, vyy402, app(app(ty_@2, cbc), cbd)) → new_esEs6(vyy3002, vyy402, cbc, cbd)
new_esEs26(vyy651, vyy661, ty_Int) → new_esEs9(vyy651, vyy661)
new_lt7(vyy650, vyy660, ef, eg) → new_esEs8(new_compare17(vyy650, vyy660, ef, eg), LT)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_esEs26(vyy651, vyy661, app(ty_[], ccg)) → new_esEs17(vyy651, vyy661, ccg)
new_esEs21(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy6600))) → new_primCmpNat0(Zero, Succ(vyy6600))
new_primCompAux00(vyy136, EQ) → vyy136
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dba), dbb)) → new_esEs7(vyy3000, vyy400, dba, dbb)
new_esEs25(vyy650, vyy660, ty_@0) → new_esEs14(vyy650, vyy660)
new_foldFM_GE5(vyy49, EmptyFM, h, ba) → vyy49
new_ltEs8(Left(vyy650), Left(vyy660), ty_Int, bg) → new_ltEs13(vyy650, vyy660)
new_esEs22(vyy3002, vyy402, ty_Bool) → new_esEs19(vyy3002, vyy402)
new_ltEs8(Right(vyy650), Right(vyy660), dc, ty_Float) → new_ltEs4(vyy650, vyy660)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs21(vyy3001, vyy401, app(ty_[], bhh)) → new_esEs17(vyy3001, vyy401, bhh)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bac), bad), bae), hg) → new_esEs4(vyy3000, vyy400, bac, bad, bae)
new_esEs22(vyy3002, vyy402, ty_Float) → new_esEs18(vyy3002, vyy402)
new_lt20(vyy650, vyy660, ty_Double) → new_lt5(vyy650, vyy660)
new_not(False) → True
new_ltEs8(Right(vyy650), Right(vyy660), dc, app(app(ty_Either, ed), ee)) → new_ltEs8(vyy650, vyy660, ed, ee)
new_lt15(vyy650, vyy660, ty_Bool) → new_lt17(vyy650, vyy660)
new_esEs10(vyy3000, vyy400, ty_@0) → new_esEs14(vyy3000, vyy400)
new_ltEs18(vyy652, vyy662, app(app(ty_Either, cee), cef)) → new_ltEs8(vyy652, vyy662, cee, cef)
new_primCmpInt(Pos(Succ(vyy6500)), Pos(vyy660)) → new_primCmpNat0(Succ(vyy6500), vyy660)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs19(vyy3000, vyy400)
new_compare18(vyy650, vyy660, app(app(ty_Either, bdf), bdg)) → new_compare26(vyy650, vyy660, bdf, bdg)
new_esEs25(vyy650, vyy660, ty_Integer) → new_esEs15(vyy650, vyy660)
new_ltEs18(vyy652, vyy662, ty_Ordering) → new_ltEs14(vyy652, vyy662)
new_ltEs14(LT, LT) → True
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_@0) → new_esEs14(vyy3000, vyy400)
new_lt16(vyy651, vyy661, ty_Double) → new_lt5(vyy651, vyy661)
new_esEs25(vyy650, vyy660, ty_Float) → new_esEs18(vyy650, vyy660)
new_esEs25(vyy650, vyy660, app(app(app(ty_@3, bd), be), bf)) → new_esEs4(vyy650, vyy660, bd, be, bf)
new_compare29(vyy650, vyy660, False, bdh, bea) → new_compare110(vyy650, vyy660, new_ltEs8(vyy650, vyy660, bdh, bea), bdh, bea)
new_esEs27(vyy650, vyy660, ty_@0) → new_esEs14(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_@0) → new_esEs14(vyy3001, vyy401)
new_esEs5(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs14(vyy3000, vyy400)
new_compare12(Integer(vyy650), Integer(vyy660)) → new_primCmpInt(vyy650, vyy660)
new_compare28(vyy650, vyy660, True) → EQ
new_esEs22(vyy3002, vyy402, app(app(app(ty_@3, cag), cah), cba)) → new_esEs4(vyy3002, vyy402, cag, cah, cba)
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_Ratio, cfb)) → new_esEs13(vyy3000, vyy400, cfb)
new_compare16(Char(vyy650), Char(vyy660)) → new_primCmpNat0(vyy650, vyy660)
new_lt19(vyy650, vyy660, ccb) → new_esEs8(new_compare9(vyy650, vyy660, ccb), LT)
new_primCmpInt(Pos(Succ(vyy6500)), Neg(vyy660)) → GT
new_ltEs16(vyy65, vyy66, bce) → new_not(new_esEs8(new_compare3(vyy65, vyy66, bce), GT))
new_esEs11(vyy3001, vyy401, app(ty_Maybe, hf)) → new_esEs5(vyy3001, vyy401, hf)
new_lt6(vyy650, vyy660, bd, be, bf) → new_esEs8(new_compare13(vyy650, vyy660, bd, be, bf), LT)
new_ltEs19(vyy651, vyy661, app(ty_[], dab)) → new_ltEs16(vyy651, vyy661, dab)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs20(vyy3000, vyy400, ty_Bool) → new_esEs19(vyy3000, vyy400)
new_esEs7(Left(vyy3000), Left(vyy400), ty_@0, hg) → new_esEs14(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs27(vyy650, vyy660, app(app(ty_@2, cha), chb)) → new_esEs6(vyy650, vyy660, cha, chb)
new_esEs20(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_foldFM_GE22(vyy330, vyy331, vyy69, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba) → new_foldFM_GE12(new_eltsFM_GE0(vyy330, vyy331, vyy69, h, ba), vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs0(vyy3330, ba), h, ba)
new_esEs10(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_ltEs12(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cbg, cbh, cca) → new_pePe(new_lt15(vyy650, vyy660, cbg), new_asAs(new_esEs25(vyy650, vyy660, cbg), new_pePe(new_lt16(vyy651, vyy661, cbh), new_asAs(new_esEs26(vyy651, vyy661, cbh), new_ltEs18(vyy652, vyy662, cca)))))
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_ltEs8(Left(vyy650), Left(vyy660), app(app(ty_Either, da), db), bg) → new_ltEs8(vyy650, vyy660, da, db)
new_esEs21(vyy3001, vyy401, ty_Int) → new_esEs9(vyy3001, vyy401)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs8(Right(vyy650), Right(vyy660), dc, app(ty_Ratio, ec)) → new_ltEs5(vyy650, vyy660, ec)
new_lt13(vyy650, vyy660, beb) → new_esEs8(new_compare25(vyy650, vyy660, beb), LT)
new_ltEs19(vyy651, vyy661, ty_@0) → new_ltEs6(vyy651, vyy661)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs18(vyy652, vyy662, ty_Integer) → new_ltEs7(vyy652, vyy662)
new_compare25(vyy650, vyy660, beb) → new_compare211(vyy650, vyy660, new_esEs5(vyy650, vyy660, beb), beb)
new_esEs20(vyy3000, vyy400, app(ty_[], bgf)) → new_esEs17(vyy3000, vyy400, bgf)
new_esEs22(vyy3002, vyy402, ty_Int) → new_esEs9(vyy3002, vyy402)
new_ltEs15(Just(vyy6500), Nothing, beb) → False
new_esEs22(vyy3002, vyy402, app(ty_[], cbb)) → new_esEs17(vyy3002, vyy402, cbb)
new_ltEs8(Left(vyy650), Left(vyy660), ty_@0, bg) → new_ltEs6(vyy650, vyy660)
new_lt20(vyy650, vyy660, ty_Float) → new_lt18(vyy650, vyy660)
new_ltEs18(vyy652, vyy662, app(app(ty_@2, ceb), cec)) → new_ltEs17(vyy652, vyy662, ceb, cec)
new_lt16(vyy651, vyy661, app(ty_[], ccg)) → new_lt4(vyy651, vyy661, ccg)
new_ltEs19(vyy651, vyy661, ty_Bool) → new_ltEs10(vyy651, vyy661)
new_esEs21(vyy3001, vyy401, app(app(ty_Either, bhb), bhc)) → new_esEs7(vyy3001, vyy401, bhb, bhc)
new_esEs26(vyy651, vyy661, app(ty_Maybe, ccf)) → new_esEs5(vyy651, vyy661, ccf)
new_primPlusNat1(Succ(vyy1040), vyy40100) → Succ(Succ(new_primPlusNat0(vyy1040, vyy40100)))
new_lt15(vyy650, vyy660, app(app(ty_Either, bdh), bea)) → new_lt9(vyy650, vyy660, bdh, bea)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs9(vyy3001, vyy401)
new_esEs10(vyy3000, vyy400, app(ty_Maybe, gd)) → new_esEs5(vyy3000, vyy400, gd)
new_compare112(vyy650, vyy660, True, bd, be, bf) → LT
new_compare23(vyy650, vyy660, True, ef, eg) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(vyy6600))) → new_primCmpNat0(Succ(vyy6600), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy6600))) → GT
new_compare15(vyy650, vyy660, False, ef, eg) → GT
new_esEs27(vyy650, vyy660, ty_Int) → new_esEs9(vyy650, vyy660)
new_esEs21(vyy3001, vyy401, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs4(vyy3001, vyy401, bhe, bhf, bhg)
new_esEs26(vyy651, vyy661, ty_@0) → new_esEs14(vyy651, vyy661)
new_primCompAux0(vyy650, vyy660, vyy127, bce) → new_primCompAux00(vyy127, new_compare18(vyy650, vyy660, bce))
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dbh), dca)) → new_esEs6(vyy3000, vyy400, dbh, dca)
new_esEs11(vyy3001, vyy401, app(app(ty_Either, ge), gf)) → new_esEs7(vyy3001, vyy401, ge, gf)
new_ltEs6(vyy65, vyy66) → new_not(new_esEs8(new_compare14(vyy65, vyy66), GT))
new_lt20(vyy650, vyy660, app(ty_Ratio, chc)) → new_lt19(vyy650, vyy660, chc)
new_lt15(vyy650, vyy660, ty_Float) → new_lt18(vyy650, vyy660)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Bool, hg) → new_esEs19(vyy3000, vyy400)
new_ltEs19(vyy651, vyy661, ty_Ordering) → new_ltEs14(vyy651, vyy661)
new_lt15(vyy650, vyy660, ty_Int) → new_lt10(vyy650, vyy660)
new_esEs21(vyy3001, vyy401, ty_Float) → new_esEs18(vyy3001, vyy401)
new_esEs20(vyy3000, vyy400, app(app(ty_Either, bfh), bga)) → new_esEs7(vyy3000, vyy400, bfh, bga)
new_lt15(vyy650, vyy660, app(app(app(ty_@3, bd), be), bf)) → new_lt6(vyy650, vyy660, bd, be, bf)
new_compare18(vyy650, vyy660, ty_Bool) → new_compare19(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, app(app(ty_@2, hd), he)) → new_esEs6(vyy3001, vyy401, hd, he)
new_lt15(vyy650, vyy660, app(app(ty_@2, ef), eg)) → new_lt7(vyy650, vyy660, ef, eg)
new_ltEs15(Just(vyy6500), Just(vyy6600), ty_Bool) → new_ltEs10(vyy6500, vyy6600)
new_lt12(vyy650, vyy660) → new_esEs8(new_compare16(vyy650, vyy660), LT)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs21(vyy3001, vyy401, ty_@0) → new_esEs14(vyy3001, vyy401)
new_lt16(vyy651, vyy661, ty_Ordering) → new_lt8(vyy651, vyy661)
new_esEs20(vyy3000, vyy400, app(ty_Maybe, bha)) → new_esEs5(vyy3000, vyy400, bha)
new_esEs27(vyy650, vyy660, ty_Float) → new_esEs18(vyy650, vyy660)
new_ltEs10(True, False) → False
new_asAs(False, vyy91) → False
new_esEs22(vyy3002, vyy402, ty_Double) → new_esEs12(vyy3002, vyy402)
new_lt16(vyy651, vyy661, ty_@0) → new_lt11(vyy651, vyy661)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(ty_Either, ceh), cfa)) → new_esEs7(vyy3000, vyy400, ceh, cfa)
new_compare3([], [], bce) → EQ
new_compare211(vyy650, vyy660, False, beb) → new_compare111(vyy650, vyy660, new_ltEs15(vyy650, vyy660, beb), beb)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_ltEs19(vyy651, vyy661, ty_Char) → new_ltEs11(vyy651, vyy661)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs7(Right(vyy3000), Right(vyy400), bbb, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_ltEs5(vyy65, vyy66, bc) → new_not(new_esEs8(new_compare9(vyy65, vyy66, bc), GT))
new_esEs21(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs10(vyy3000, vyy400, app(ty_[], ga)) → new_esEs17(vyy3000, vyy400, ga)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs9(vyy3000, vyy400)
new_esEs10(vyy3000, vyy400, app(ty_Ratio, fd)) → new_esEs13(vyy3000, vyy400, fd)
new_compare23(vyy650, vyy660, False, ef, eg) → new_compare15(vyy650, vyy660, new_ltEs17(vyy650, vyy660, ef, eg), ef, eg)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(ty_@2, cfg), cfh)) → new_esEs6(vyy3000, vyy400, cfg, cfh)
new_ltEs14(GT, LT) → False
new_lt20(vyy650, vyy660, app(ty_[], cgh)) → new_lt4(vyy650, vyy660, cgh)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Float, hg) → new_esEs18(vyy3000, vyy400)
new_ltEs8(Right(vyy650), Left(vyy660), dc, bg) → False
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs25(vyy650, vyy660, app(ty_[], bb)) → new_esEs17(vyy650, vyy660, bb)
new_compare18(vyy650, vyy660, ty_Integer) → new_compare12(vyy650, vyy660)
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_compare112(vyy650, vyy660, False, bd, be, bf) → GT
new_compare27(vyy650, vyy660, True) → EQ
new_esEs10(vyy3000, vyy400, ty_Float) → new_esEs18(vyy3000, vyy400)
new_compare111(vyy650, vyy660, False, beb) → GT
new_compare27(vyy650, vyy660, False) → new_compare10(vyy650, vyy660, new_ltEs14(vyy650, vyy660))
new_ltEs15(Nothing, Nothing, beb) → True
new_compare9(:%(vyy650, vyy651), :%(vyy660, vyy661), ty_Int) → new_compare7(new_sr(vyy650, vyy661), new_sr(vyy660, vyy651))
new_foldFM_GE12(vyy49, vyy330, vyy331, vyy332, vyy333, vyy334, False, h, ba) → new_foldFM_GE5(vyy49, vyy334, h, ba)
new_esEs5(Just(vyy3000), Nothing, ceg) → False
new_esEs5(Nothing, Just(vyy400), ceg) → False
new_esEs11(vyy3001, vyy401, app(ty_Ratio, gg)) → new_esEs13(vyy3001, vyy401, gg)
new_lt16(vyy651, vyy661, app(ty_Maybe, ccf)) → new_lt13(vyy651, vyy661, ccf)
new_foldFM_GE30(vyy330, vyy331, vyy68, h, ba) → new_eltsFM_GE0(vyy330, vyy331, vyy68, h, ba)
new_lt5(vyy650, vyy660) → new_esEs8(new_compare6(vyy650, vyy660), LT)
new_esEs28(vyy3000, vyy400, app(ty_[], dbg)) → new_esEs17(vyy3000, vyy400, dbg)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dbc)) → new_esEs13(vyy3000, vyy400, dbc)
new_compare11(vyy650, vyy660, False) → GT
new_ltEs14(LT, GT) → True
new_ltEs14(LT, EQ) → True
new_compare11(vyy650, vyy660, True) → LT
new_esEs22(vyy3002, vyy402, ty_@0) → new_esEs14(vyy3002, vyy402)
new_esEs5(Nothing, Nothing, ceg) → True
new_ltEs18(vyy652, vyy662, app(ty_Maybe, cdh)) → new_ltEs15(vyy652, vyy662, cdh)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dcb)) → new_esEs5(vyy3000, vyy400, dcb)
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Maybe, bba), hg) → new_esEs5(vyy3000, vyy400, bba)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs18(vyy3000, vyy400)
new_esEs21(vyy3001, vyy401, ty_Double) → new_esEs12(vyy3001, vyy401)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs9(vyy3000, vyy400)
new_lt15(vyy650, vyy660, ty_Ordering) → new_lt8(vyy650, vyy660)
new_lt16(vyy651, vyy661, ty_Char) → new_lt12(vyy651, vyy661)
new_lt20(vyy650, vyy660, ty_Char) → new_lt12(vyy650, vyy660)
new_ltEs19(vyy651, vyy661, ty_Integer) → new_ltEs7(vyy651, vyy661)
new_esEs10(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs22(vyy3002, vyy402, app(ty_Maybe, cbe)) → new_esEs5(vyy3002, vyy402, cbe)
new_primPlusNat0(Succ(vyy10400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat0(vyy10400, vyy401000)))
new_lt20(vyy650, vyy660, ty_Integer) → new_lt14(vyy650, vyy660)
new_esEs21(vyy3001, vyy401, app(ty_Maybe, cac)) → new_esEs5(vyy3001, vyy401, cac)
new_esEs22(vyy3002, vyy402, ty_Integer) → new_esEs15(vyy3002, vyy402)
new_ltEs18(vyy652, vyy662, app(ty_[], cea)) → new_ltEs16(vyy652, vyy662, cea)
new_ltEs8(Left(vyy650), Left(vyy660), ty_Ordering, bg) → new_ltEs14(vyy650, vyy660)
new_compare18(vyy650, vyy660, app(app(ty_@2, bdc), bdd)) → new_compare17(vyy650, vyy660, bdc, bdd)
new_ltEs10(True, True) → True
new_ltEs15(Just(vyy6500), Just(vyy6600), app(app(ty_@2, beh), bfa)) → new_ltEs17(vyy6500, vyy6600, beh, bfa)
new_ltEs14(EQ, EQ) → True
new_asAs(True, vyy91) → vyy91
new_lt16(vyy651, vyy661, app(app(ty_Either, cdc), cdd)) → new_lt9(vyy651, vyy661, cdc, cdd)
new_esEs17(:(vyy3000, vyy3001), :(vyy400, vyy401), dah) → new_asAs(new_esEs28(vyy3000, vyy400, dah), new_esEs17(vyy3001, vyy401, dah))
new_lt20(vyy650, vyy660, ty_Bool) → new_lt17(vyy650, vyy660)
new_lt16(vyy651, vyy661, ty_Int) → new_lt10(vyy651, vyy661)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Char, hg) → new_esEs16(vyy3000, vyy400)
new_compare18(vyy650, vyy660, ty_Float) → new_compare8(vyy650, vyy660)
new_esEs17([], [], dah) → True
new_esEs17(:(vyy3000, vyy3001), [], dah) → False
new_esEs17([], :(vyy400, vyy401), dah) → False
new_lt20(vyy650, vyy660, ty_@0) → new_lt11(vyy650, vyy660)
new_esEs26(vyy651, vyy661, app(app(ty_@2, cch), cda)) → new_esEs6(vyy651, vyy661, cch, cda)
new_esEs26(vyy651, vyy661, ty_Char) → new_esEs16(vyy651, vyy661)
new_ltEs8(Left(vyy650), Right(vyy660), dc, bg) → True
new_compare10(vyy650, vyy660, True) → LT
new_esEs9(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_compare26(vyy650, vyy660, bdh, bea) → new_compare29(vyy650, vyy660, new_esEs7(vyy650, vyy660, bdh, bea), bdh, bea)
new_esEs20(vyy3000, vyy400, ty_Char) → new_esEs16(vyy3000, vyy400)
new_esEs10(vyy3000, vyy400, ty_Char) → new_esEs16(vyy3000, vyy400)
new_compare18(vyy650, vyy660, ty_Double) → new_compare6(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_Float) → new_esEs18(vyy3001, vyy401)
new_compare10(vyy650, vyy660, False) → GT
new_ltEs13(vyy65, vyy66) → new_not(new_esEs8(new_compare7(vyy65, vyy66), GT))
new_primCompAux00(vyy136, GT) → GT
new_esEs25(vyy650, vyy660, app(app(ty_Either, bdh), bea)) → new_esEs7(vyy650, vyy660, bdh, bea)
new_ltEs18(vyy652, vyy662, ty_Double) → new_ltEs9(vyy652, vyy662)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_ltEs8(Left(vyy650), Left(vyy660), ty_Integer, bg) → new_ltEs7(vyy650, vyy660)
new_esEs27(vyy650, vyy660, ty_Bool) → new_esEs19(vyy650, vyy660)
new_ltEs15(Just(vyy6500), Just(vyy6600), app(ty_[], beg)) → new_ltEs16(vyy6500, vyy6600, beg)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_lt20(vyy650, vyy660, app(app(ty_Either, chd), che)) → new_lt9(vyy650, vyy660, chd, che)
new_esEs27(vyy650, vyy660, ty_Integer) → new_esEs15(vyy650, vyy660)
new_compare9(:%(vyy650, vyy651), :%(vyy660, vyy661), ty_Integer) → new_compare12(new_sr0(vyy650, vyy661), new_sr0(vyy660, vyy651))
new_primCmpInt(Neg(Succ(vyy6500)), Pos(vyy660)) → LT
new_not(True) → False

The set Q consists of the following terms:

new_esEs21(x0, x1, ty_Integer)
new_ltEs15(Just(x0), Just(x1), app(ty_[], x2))
new_compare10(x0, x1, True)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs16(Char(x0), Char(x1))
new_lt16(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Double)
new_lt16(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primCompAux0(x0, x1, x2, x3)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_@0)
new_esEs10(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Succ(x0))
new_esEs28(x0, x1, ty_Int)
new_primPlusNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, False, x2, x3, x4)
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primMulNat0(Zero, Succ(x0))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, True, x2, x3, x4)
new_foldFM_GE12(x0, x1, x2, x3, EmptyFM, x4, True, x5, x6)
new_ltEs15(Just(x0), Just(x1), ty_@0)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Bool)
new_lt15(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs8(GT, GT)
new_lt16(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Int)
new_ltEs15(Just(x0), Just(x1), ty_Bool)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs24(x0, x1, ty_Integer)
new_lt11(x0, x1)
new_ltEs19(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_esEs20(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_Integer)
new_sr(x0, x1)
new_esEs10(x0, x1, ty_Int)
new_compare3([], [], x0)
new_foldFM_GE30(x0, x1, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_Ordering)
new_esEs19(True, True)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_compare13(x0, x1, x2, x3, x4)
new_esEs5(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare112(x0, x1, True, x2, x3, x4)
new_esEs23(x0, x1, ty_Int)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Zero)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt4(x0, x1, x2)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_sr0(Integer(x0), Integer(x1))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Integer)
new_compare26(x0, x1, x2, x3)
new_esEs10(x0, x1, ty_Float)
new_ltEs15(Just(x0), Just(x1), app(ty_Maybe, x2))
new_foldFM_GE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_pePe(True, x0)
new_ltEs19(x0, x1, app(ty_[], x2))
new_foldFM_GE5(x0, EmptyFM, x1, x2)
new_ltEs15(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_Ordering)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_compare11(x0, x1, True)
new_esEs22(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primCompAux00(x0, GT)
new_primCmpNat0(Succ(x0), Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_lt16(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, x0)
new_lt15(x0, x1, ty_Char)
new_asAs(False, x0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1)
new_lt16(x0, x1, ty_Integer)
new_gtEs0(x0, x1)
new_lt16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1)
new_esEs27(x0, x1, ty_Float)
new_primCompAux00(x0, EQ)
new_ltEs15(Just(x0), Just(x1), ty_Double)
new_lt16(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs14(@0, @0)
new_esEs20(x0, x1, ty_Double)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt17(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt15(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs27(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Ordering)
new_esEs11(x0, x1, ty_Int)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs5(Nothing, Nothing, x0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_foldFM_GE12(x0, x1, x2, x3, Branch(x4, x5, x6, x7, x8), x9, True, x10, x11)
new_compare18(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(False, True)
new_esEs19(True, False)
new_esEs22(x0, x1, ty_Bool)
new_ltEs15(Just(x0), Nothing, x1)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt20(x0, x1, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_lt15(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs25(x0, x1, ty_Double)
new_primPlusNat0(Zero, Zero)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs10(False, False)
new_ltEs14(LT, LT)
new_lt14(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt16(x0, x1, ty_Ordering)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_lt7(x0, x1, x2, x3)
new_compare18(x0, x1, ty_@0)
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_lt15(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs11(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True)
new_esEs27(x0, x1, ty_Char)
new_esEs5(Nothing, Just(x0), x1)
new_lt20(x0, x1, app(ty_[], x2))
new_lt8(x0, x1)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_Double)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare15(x0, x1, True, x2, x3)
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_compare27(x0, x1, True)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs11(x0, x1, ty_Bool)
new_lt15(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, x2)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_compare18(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs21(x0, x1, ty_Ordering)
new_lt15(x0, x1, ty_Bool)
new_compare16(Char(x0), Char(x1))
new_lt6(x0, x1, x2, x3, x4)
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Int)
new_compare11(x0, x1, False)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs17([], [], x0)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare24(x0, x1)
new_ltEs16(x0, x1, x2)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs19(False, False)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Succ(x0), x1)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs19(x0, x1, ty_Double)
new_compare28(x0, x1, False)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, x2)
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_compare111(x0, x1, False, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare14(@0, @0)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare18(x0, x1, ty_Float)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare211(x0, x1, False, x2)
new_esEs28(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare8(Float(x0, x1), Float(x2, x3))
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare211(x0, x1, True, x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs15(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Char)
new_ltEs15(Just(x0), Just(x1), ty_Int)
new_compare25(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, ty_Ordering)
new_lt16(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_@0)
new_ltEs7(x0, x1)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Char)
new_lt15(x0, x1, ty_Int)
new_lt16(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Succ(x0))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_esEs9(x0, x1)
new_compare110(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs27(x0, x1, ty_Int)
new_lt15(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1)
new_compare3([], :(x0, x1), x2)
new_eltsFM_GE0(x0, x1, x2, x3, x4)
new_foldFM_GE5(x0, Branch(x1, x2, x3, x4, x5), x6, x7)
new_ltEs15(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs28(x0, x1, ty_Bool)
new_pePe(False, x0)
new_primCmpNat0(Zero, Zero)
new_lt15(x0, x1, ty_Float)
new_compare3(:(x0, x1), [], x2)
new_lt16(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1, x2, x3)
new_esEs22(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_lt15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_ltEs15(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt16(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_ltEs10(True, True)
new_esEs22(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt15(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs11(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs22(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, ty_Float)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_ltEs18(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Char)
new_asAs(True, x0)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs25(x0, x1, ty_Char)
new_ltEs15(Just(x0), Just(x1), ty_Float)
new_compare18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs17(:(x0, x1), [], x2)
new_compare27(x0, x1, False)
new_primPlusNat0(Zero, Succ(x0))
new_esEs10(x0, x1, ty_@0)
new_compare19(x0, x1)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs14(GT, GT)
new_lt18(x0, x1)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare23(x0, x1, True, x2, x3)
new_esEs15(Integer(x0), Integer(x1))
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_not(True)
new_esEs21(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt10(x0, x1)
new_esEs20(x0, x1, ty_Integer)
new_compare111(x0, x1, True, x2)
new_compare7(x0, x1)
new_lt9(x0, x1, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, x2)
new_lt20(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs13(x0, x1)
new_esEs24(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs15(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs15(Just(x0), Just(x1), ty_Ordering)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs15(Just(x0), Just(x1), ty_Char)
new_compare112(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs4(x0, x1)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs15(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_compare18(x0, x1, ty_Bool)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs12(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_foldFM_GE12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs27(x0, x1, ty_@0)
new_compare29(x0, x1, True, x2, x3)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_compare12(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, ty_Float)
new_ltEs10(False, True)
new_ltEs10(True, False)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_lt16(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_lt16(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(Double(x0, x1), Double(x2, x3))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_compare18(x0, x1, ty_Char)
new_compare15(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_@0)
new_compare110(x0, x1, False, x2, x3)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_@0)
new_ltEs15(Nothing, Just(x0), x1)
new_esEs20(x0, x1, ty_Float)
new_compare18(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_compare18(x0, x1, ty_Integer)
new_compare18(x0, x1, app(ty_Ratio, x2))
new_esEs17([], :(x0, x1), x2)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare18(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_compare29(x0, x1, False, x2, x3)
new_ltEs6(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_ltEs9(x0, x1)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1, ty_@0)
new_compare10(x0, x1, False)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))

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

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