YES 9.34 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 a, Ord b) => FiniteMap (Either b a) c  ->  Either b a  ->  [c]) :: (Ord b, Ord a) => FiniteMap (Either b a) c  ->  Either b a  ->  [c])

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

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

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

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

  foldFM_GE :: Ord 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


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

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

  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


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

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

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

  foldFM_GE :: Ord 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


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 c, Ord b) => FiniteMap (Either c b) a  ->  Either c b  ->  [a]) :: (Ord c, Ord b) => FiniteMap (Either c b) a  ->  Either c 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 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 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 _ 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 _ fm_l fm_r) 
 | key >= fr = 
foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
 | otherwise = 
foldFM_GE k z fr fm_r

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

mainModule FiniteMap
  ((eltsFM_GE :: (Ord c, Ord b) => FiniteMap (Either c b) a  ->  Either c b  ->  [a]) :: (Ord b, Ord c) => FiniteMap (Either c b) a  ->  Either c 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 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 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 c => (c  ->  a  ->  b  ->  b)  ->  b  ->  c  ->  FiniteMap c a  ->  b
foldFM_GE k z fr EmptyFM = z
foldFM_GE k z fr (Branch key elt 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

compare0 x y True = GT

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

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

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

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

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

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

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

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

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

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

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM = 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
reduce2Reduce0 vyw vyx x y True = x `quot` reduce2D vyw vyx :% (y `quot` reduce2D vyw vyx)

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

reduce2D vyw vyx = gcd vyw vyx

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

are unpacked to the following functions on top level
gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y)

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

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

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



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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Haskell To QDPs


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

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

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

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

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



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

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

new_primPlusNat(Succ(vyy13400), Succ(vyy401000)) → new_primPlusNat(vyy13400, vyy401000)

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

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



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

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

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

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

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



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

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

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

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

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



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

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

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

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

The TRS R consists of the following rules:

new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, dae)) → new_esEs7(vyy3000, vyy400, dae)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], daf)) → new_esEs15(vyy3000, vyy400, daf)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_@0, bh) → new_ltEs14(vyy9000, vyy9100)
new_esEs18(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_ltEs15(True, False) → False
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, app(ty_Maybe, bbd)) → new_ltEs9(vyy9000, vyy9100, bbd)
new_esEs10(vyy3002, vyy402, app(app(app(ty_@3, bfb), bfc), bfd)) → new_esEs4(vyy3002, vyy402, bfb, bfc, bfd)
new_ltEs4(EQ, GT) → True
new_esEs23(vyy3001, vyy401, ty_Float) → new_esEs20(vyy3001, vyy401)
new_ltEs14(vyy90, vyy91) → new_not(new_esEs8(new_compare27(vyy90, vyy91), GT))
new_esEs23(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_compare15(vyy900, vyy910, True, be, bf) → LT
new_compare24(vyy900, vyy910, False, bg, bh) → new_compare14(vyy900, vyy910, new_ltEs7(vyy900, vyy910, bg, bh), bg, bh)
new_ltEs9(Nothing, Just(vyy910), cac) → True
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_ltEs19(vyy901, vyy911, ty_Double) → new_ltEs11(vyy901, vyy911)
new_ltEs9(Just(vyy900), Just(vyy910), app(ty_Ratio, cad)) → new_ltEs13(vyy900, vyy910, cad)
new_esEs21(vyy901, vyy911, ty_Int) → new_esEs14(vyy901, vyy911)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, dah), dba)) → new_esEs6(vyy3000, vyy400, dah, dba)
new_ltEs7(Left(vyy9000), Right(vyy9100), bg, bh) → True
new_primMulNat0(Zero, Zero) → Zero
new_compare13(vyy900, vyy910, False, h, ba, bb) → GT
new_esEs25(vyy3000, vyy400, app(app(ty_Either, chc), chd)) → new_esEs6(vyy3000, vyy400, chc, chd)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(app(ty_@2, hg), hh), bh) → new_ltEs8(vyy9000, vyy9100, hg, hh)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, cah), cae) → new_esEs16(vyy3000, vyy400, cah)
new_esEs21(vyy901, vyy911, ty_Bool) → new_esEs17(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, cbc), cbd), cbe), cae) → new_esEs4(vyy3000, vyy400, cbc, cbd, cbe)
new_esEs21(vyy901, vyy911, app(ty_[], de)) → new_esEs15(vyy901, vyy911, de)
new_lt12(vyy901, vyy911, app(ty_Ratio, cde)) → new_lt5(vyy901, vyy911, cde)
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, app(app(ty_@2, bah), bba)) → new_ltEs8(vyy9000, vyy9100, bah, bba)
new_esEs25(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_lt12(vyy901, vyy911, ty_Integer) → new_lt13(vyy901, vyy911)
new_esEs23(vyy3001, vyy401, ty_@0) → new_esEs9(vyy3001, vyy401)
new_compare25(vyy900, vyy910, False, be, bf) → new_compare15(vyy900, vyy910, new_ltEs8(vyy900, vyy910, be, bf), be, bf)
new_esEs21(vyy901, vyy911, ty_Integer) → new_esEs19(vyy901, vyy911)
new_esEs12(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs17(True, True) → True
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs20(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs22(vyy900, vyy910, app(app(ty_@2, be), bf)) → new_esEs5(vyy900, vyy910, be, bf)
new_esEs24(vyy3000, vyy400, app(app(ty_@2, cgc), cgd)) → new_esEs5(vyy3000, vyy400, cgc, cgd)
new_compare28(vyy900, vyy910, ty_Ordering) → new_compare8(vyy900, vyy910)
new_esEs23(vyy3001, vyy401, ty_Double) → new_esEs13(vyy3001, vyy401)
new_compare28(vyy900, vyy910, app(ty_[], bdh)) → new_compare4(vyy900, vyy910, bdh)
new_esEs10(vyy3002, vyy402, app(ty_[], bef)) → new_esEs15(vyy3002, vyy402, bef)
new_ltEs9(Just(vyy900), Just(vyy910), ty_@0) → new_ltEs14(vyy900, vyy910)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, cae) → new_esEs14(vyy3000, vyy400)
new_esEs12(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs21(vyy901, vyy911, app(app(ty_Either, db), dc)) → new_esEs6(vyy901, vyy911, db, dc)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, cae) → new_esEs17(vyy3000, vyy400)
new_ltEs16(vyy90, vyy91) → new_not(new_esEs8(new_compare30(vyy90, vyy91), GT))
new_esEs22(vyy900, vyy910, ty_Float) → new_esEs20(vyy900, vyy910)
new_lt20(vyy900, vyy910, ty_Float) → new_lt17(vyy900, vyy910)
new_esEs12(vyy3000, vyy400, app(ty_[], bhb)) → new_esEs15(vyy3000, vyy400, bhb)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Double) → new_ltEs11(vyy900, vyy910)
new_ltEs19(vyy901, vyy911, app(app(ty_@2, gf), gg)) → new_ltEs8(vyy901, vyy911, gf, gg)
new_ltEs19(vyy901, vyy911, ty_Float) → new_ltEs16(vyy901, vyy911)
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, app(ty_[], bbe)) → new_ltEs17(vyy9000, vyy9100, bbe)
new_pePe(False, vyy150) → vyy150
new_ltEs15(True, True) → True
new_ltEs17(vyy90, vyy91, bcg) → new_not(new_esEs8(new_compare4(vyy90, vyy91, bcg), GT))
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, cae) → new_esEs18(vyy3000, vyy400)
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, app(ty_Ratio, cgf)) → new_ltEs13(vyy9000, vyy9100, cgf)
new_lt6(vyy900, vyy910) → new_esEs8(new_compare8(vyy900, vyy910), LT)
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, app(app(app(ty_@3, bae), baf), bag)) → new_ltEs6(vyy9000, vyy9100, bae, baf, bag)
new_ltEs15(False, True) → True
new_esEs24(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs10(vyy3002, vyy402, app(ty_Maybe, bee)) → new_esEs7(vyy3002, vyy402, bee)
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, ty_Bool) → new_ltEs15(vyy9000, vyy9100)
new_esEs24(vyy3000, vyy400, app(ty_Maybe, cfc)) → new_esEs7(vyy3000, vyy400, cfc)
new_lt9(vyy900, vyy910) → new_esEs8(new_compare18(vyy900, vyy910), LT)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(app(app(ty_@3, hd), he), hf), bh) → new_ltEs6(vyy9000, vyy9100, hd, he, hf)
new_esEs23(vyy3001, vyy401, app(ty_Maybe, cea)) → new_esEs7(vyy3001, vyy401, cea)
new_lt15(vyy900, vyy910, be, bf) → new_esEs8(new_compare16(vyy900, vyy910, be, bf), LT)
new_compare23(vyy900, vyy910, True, h, ba, bb) → EQ
new_ltEs9(Just(vyy900), Just(vyy910), ty_Float) → new_ltEs16(vyy900, vyy910)
new_lt8(vyy900, vyy910) → new_esEs8(new_compare12(vyy900, vyy910), LT)
new_esEs22(vyy900, vyy910, ty_Ordering) → new_esEs8(vyy900, vyy910)
new_esEs11(vyy3001, vyy401, app(ty_[], bfh)) → new_esEs15(vyy3001, vyy401, bfh)
new_compare6(Double(vyy900, vyy901), Double(vyy910, vyy911)) → new_compare12(new_sr(vyy900, vyy910), new_sr(vyy901, vyy911))
new_lt11(vyy900, vyy910, app(app(ty_Either, bg), bh)) → new_lt16(vyy900, vyy910, bg, bh)
new_esEs12(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_ltEs15(False, False) → True
new_ltEs12(vyy90, vyy91) → new_not(new_esEs8(new_compare29(vyy90, vyy91), GT))
new_compare28(vyy900, vyy910, ty_Double) → new_compare6(vyy900, vyy910)
new_lt12(vyy901, vyy911, app(ty_Maybe, dd)) → new_lt18(vyy901, vyy911, dd)
new_primCmpNat0(Zero, Succ(vyy9100)) → LT
new_esEs6(Right(vyy3000), Right(vyy400), cbh, ty_Int) → new_esEs14(vyy3000, vyy400)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(ty_Ratio, cge), bh) → new_ltEs13(vyy9000, vyy9100, cge)
new_esEs11(vyy3001, vyy401, ty_Char) → new_esEs18(vyy3001, vyy401)
new_lt20(vyy900, vyy910, ty_Ordering) → new_lt6(vyy900, vyy910)
new_lt20(vyy900, vyy910, app(app(app(ty_@3, eg), eh), fa)) → new_lt14(vyy900, vyy910, eg, eh, fa)
new_lt19(vyy900, vyy910, cb) → new_esEs8(new_compare4(vyy900, vyy910, cb), LT)
new_lt11(vyy900, vyy910, app(app(ty_@2, be), bf)) → new_lt15(vyy900, vyy910, be, bf)
new_esEs6(Left(vyy3000), Right(vyy400), cbh, cae) → False
new_esEs6(Right(vyy3000), Left(vyy400), cbh, cae) → False
new_esEs8(LT, LT) → True
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, cae) → new_esEs20(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Char) → new_esEs18(vyy3001, vyy401)
new_esEs23(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_pePe(True, vyy150) → True
new_compare14(vyy900, vyy910, False, bg, bh) → GT
new_primEqNat0(Zero, Zero) → True
new_compare26(vyy900, vyy910, True) → EQ
new_compare11(vyy900, vyy910, True, ca) → LT
new_esEs23(vyy3001, vyy401, app(app(ty_Either, ced), cee)) → new_esEs6(vyy3001, vyy401, ced, cee)
new_compare28(vyy900, vyy910, ty_Integer) → new_compare29(vyy900, vyy910)
new_esEs6(Right(vyy3000), Right(vyy400), cbh, app(app(app(ty_@3, ccf), ccg), cch)) → new_esEs4(vyy3000, vyy400, ccf, ccg, cch)
new_esEs6(Right(vyy3000), Right(vyy400), cbh, app(app(ty_Either, ccd), cce)) → new_esEs6(vyy3000, vyy400, ccd, cce)
new_lt20(vyy900, vyy910, ty_Bool) → new_lt7(vyy900, vyy910)
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_esEs6(Right(vyy3000), Right(vyy400), cbh, ty_Char) → new_esEs18(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), cbh, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), cbh, app(ty_[], ccb)) → new_esEs15(vyy3000, vyy400, ccb)
new_ltEs18(vyy902, vyy912, ty_Int) → new_ltEs5(vyy902, vyy912)
new_ltEs18(vyy902, vyy912, ty_Char) → new_ltEs10(vyy902, vyy912)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs24(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_compare211(vyy900, vyy910, False, ca) → new_compare11(vyy900, vyy910, new_ltEs9(vyy900, vyy910, ca), ca)
new_primCompAux0(vyy900, vyy910, vyy151, bcg) → new_primCompAux00(vyy151, new_compare28(vyy900, vyy910, bcg))
new_compare7(:%(vyy900, vyy901), :%(vyy910, vyy911), ty_Integer) → new_compare29(new_sr0(vyy900, vyy911), new_sr0(vyy910, vyy901))
new_esEs25(vyy3000, vyy400, app(ty_[], cha)) → new_esEs15(vyy3000, vyy400, cha)
new_esEs23(vyy3001, vyy401, app(ty_[], ceb)) → new_esEs15(vyy3001, vyy401, ceb)
new_esEs25(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, ty_Double) → new_esEs13(vyy3001, vyy401)
new_esEs10(vyy3002, vyy402, ty_Int) → new_esEs14(vyy3002, vyy402)
new_esEs26(vyy900, vyy910, ty_Ordering) → new_esEs8(vyy900, vyy910)
new_lt11(vyy900, vyy910, ty_@0) → new_lt10(vyy900, vyy910)
new_ltEs19(vyy901, vyy911, ty_Char) → new_ltEs10(vyy901, vyy911)
new_esEs12(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(vyy1340), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1340, vyy40100)))
new_compare4([], [], bcg) → EQ
new_esEs11(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs9(Just(vyy900), Just(vyy910), app(ty_[], bcf)) → new_ltEs17(vyy900, vyy910, bcf)
new_esEs10(vyy3002, vyy402, ty_Double) → new_esEs13(vyy3002, vyy402)
new_ltEs19(vyy901, vyy911, ty_Bool) → new_ltEs15(vyy901, vyy911)
new_esEs26(vyy900, vyy910, app(app(app(ty_@3, eg), eh), fa)) → new_esEs4(vyy900, vyy910, eg, eh, fa)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs19(vyy901, vyy911, app(ty_Maybe, hb)) → new_ltEs9(vyy901, vyy911, hb)
new_compare16(vyy900, vyy910, be, bf) → new_compare25(vyy900, vyy910, new_esEs5(vyy900, vyy910, be, bf), be, bf)
new_esEs11(vyy3001, vyy401, app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs4(vyy3001, vyy401, bgd, bge, bgf)
new_compare211(vyy900, vyy910, True, ca) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs24(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs18(vyy902, vyy912, app(app(ty_Either, ec), ed)) → new_ltEs7(vyy902, vyy912, ec, ed)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy13400), Zero) → Succ(vyy13400)
new_esEs10(vyy3002, vyy402, ty_@0) → new_esEs9(vyy3002, vyy402)
new_esEs25(vyy3000, vyy400, ty_Char) → new_esEs18(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs11(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_lt20(vyy900, vyy910, app(ty_Maybe, fh)) → new_lt18(vyy900, vyy910, fh)
new_ltEs7(Right(vyy9000), Left(vyy9100), bg, bh) → False
new_esEs26(vyy900, vyy910, ty_Integer) → new_esEs19(vyy900, vyy910)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Bool, bh) → new_ltEs15(vyy9000, vyy9100)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs9(Just(vyy900), Just(vyy910), app(app(ty_Either, bcc), bcd)) → new_ltEs7(vyy900, vyy910, bcc, bcd)
new_ltEs19(vyy901, vyy911, ty_Ordering) → new_ltEs4(vyy901, vyy911)
new_ltEs6(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), cc, bc, bd) → new_pePe(new_lt11(vyy900, vyy910, cc), new_asAs(new_esEs22(vyy900, vyy910, cc), new_pePe(new_lt12(vyy901, vyy911, bc), new_asAs(new_esEs21(vyy901, vyy911, bc), new_ltEs18(vyy902, vyy912, bd)))))
new_lt11(vyy900, vyy910, ty_Char) → new_lt9(vyy900, vyy910)
new_ltEs18(vyy902, vyy912, ty_@0) → new_ltEs14(vyy902, vyy912)
new_esEs6(Right(vyy3000), Right(vyy400), cbh, ty_Double) → new_esEs13(vyy3000, vyy400)
new_compare29(Integer(vyy900), Integer(vyy910)) → new_primCmpInt(vyy900, vyy910)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_esEs8(EQ, EQ) → True
new_esEs22(vyy900, vyy910, ty_Integer) → new_esEs19(vyy900, vyy910)
new_lt20(vyy900, vyy910, ty_@0) → new_lt10(vyy900, vyy910)
new_compare26(vyy900, vyy910, False) → new_compare10(vyy900, vyy910, new_ltEs4(vyy900, vyy910))
new_esEs23(vyy3001, vyy401, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs4(vyy3001, vyy401, cef, ceg, ceh)
new_compare24(vyy900, vyy910, True, bg, bh) → EQ
new_esEs11(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_lt11(vyy900, vyy910, app(ty_[], cb)) → new_lt19(vyy900, vyy910, cb)
new_compare28(vyy900, vyy910, app(ty_Maybe, bdg)) → new_compare31(vyy900, vyy910, bdg)
new_lt11(vyy900, vyy910, ty_Ordering) → new_lt6(vyy900, vyy910)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs18(vyy902, vyy912, ty_Ordering) → new_ltEs4(vyy902, vyy912)
new_ltEs4(EQ, LT) → False
new_esEs6(Right(vyy3000), Right(vyy400), cbh, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs12(vyy3000, vyy400, app(ty_Maybe, bha)) → new_esEs7(vyy3000, vyy400, bha)
new_ltEs8(@2(vyy900, vyy901), @2(vyy910, vyy911), gb, fb) → new_pePe(new_lt20(vyy900, vyy910, gb), new_asAs(new_esEs26(vyy900, vyy910, gb), new_ltEs19(vyy901, vyy911, fb)))
new_lt20(vyy900, vyy910, ty_Int) → new_lt8(vyy900, vyy910)
new_primCmpNat0(Succ(vyy9000), Succ(vyy9100)) → new_primCmpNat0(vyy9000, vyy9100)
new_lt20(vyy900, vyy910, ty_Integer) → new_lt13(vyy900, vyy910)
new_compare11(vyy900, vyy910, False, ca) → GT
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare30(Float(vyy900, vyy901), Float(vyy910, vyy911)) → new_compare12(new_sr(vyy900, vyy910), new_sr(vyy901, vyy911))
new_lt5(vyy900, vyy910, bea) → new_esEs8(new_compare7(vyy900, vyy910, bea), LT)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs18(vyy3000, vyy400)
new_esEs24(vyy3000, vyy400, app(ty_Ratio, cfe)) → new_esEs16(vyy3000, vyy400, cfe)
new_esEs21(vyy901, vyy911, ty_Float) → new_esEs20(vyy901, vyy911)
new_ltEs18(vyy902, vyy912, app(ty_Maybe, ee)) → new_ltEs9(vyy902, vyy912, ee)
new_lt11(vyy900, vyy910, ty_Integer) → new_lt13(vyy900, vyy910)
new_compare28(vyy900, vyy910, ty_Float) → new_compare30(vyy900, vyy910)
new_compare23(vyy900, vyy910, False, h, ba, bb) → new_compare13(vyy900, vyy910, new_ltEs6(vyy900, vyy910, h, ba, bb), h, ba, bb)
new_lt11(vyy900, vyy910, app(ty_Maybe, ca)) → new_lt18(vyy900, vyy910, ca)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_esEs5(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cdg, cdh) → new_asAs(new_esEs24(vyy3000, vyy400, cdg), new_esEs23(vyy3001, vyy401, cdh))
new_lt11(vyy900, vyy910, app(app(app(ty_@3, h), ba), bb)) → new_lt14(vyy900, vyy910, h, ba, bb)
new_esEs6(Right(vyy3000), Right(vyy400), cbh, app(app(ty_@2, cda), cdb)) → new_esEs5(vyy3000, vyy400, cda, cdb)
new_esEs10(vyy3002, vyy402, app(ty_Ratio, beg)) → new_esEs16(vyy3002, vyy402, beg)
new_esEs9(@0, @0) → True
new_lt12(vyy901, vyy911, ty_Ordering) → new_lt6(vyy901, vyy911)
new_primCompAux00(vyy160, LT) → LT
new_ltEs4(GT, EQ) → False
new_compare210(vyy900, vyy910, False) → new_compare110(vyy900, vyy910, new_ltEs15(vyy900, vyy910))
new_esEs11(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_primCmpInt(Neg(Succ(vyy9000)), Neg(vyy910)) → new_primCmpNat0(vyy910, Succ(vyy9000))
new_ltEs19(vyy901, vyy911, app(app(ty_Either, gh), ha)) → new_ltEs7(vyy901, vyy911, gh, ha)
new_ltEs19(vyy901, vyy911, app(ty_[], hc)) → new_ltEs17(vyy901, vyy911, hc)
new_esEs24(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt7(vyy900, vyy910) → new_esEs8(new_compare9(vyy900, vyy910), LT)
new_ltEs18(vyy902, vyy912, ty_Double) → new_ltEs11(vyy902, vyy912)
new_esEs7(Nothing, Nothing, dad) → True
new_esEs15([], [], cgg) → True
new_ltEs9(Just(vyy900), Just(vyy910), app(app(app(ty_@3, bbf), bbg), bbh)) → new_ltEs6(vyy900, vyy910, bbf, bbg, bbh)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_lt20(vyy900, vyy910, app(ty_Ratio, dab)) → new_lt5(vyy900, vyy910, dab)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Double, bh) → new_ltEs11(vyy9000, vyy9100)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Char) → new_ltEs10(vyy900, vyy910)
new_lt4(vyy900, vyy910) → new_esEs8(new_compare6(vyy900, vyy910), LT)
new_ltEs4(EQ, EQ) → True
new_compare28(vyy900, vyy910, ty_@0) → new_compare27(vyy900, vyy910)
new_compare28(vyy900, vyy910, app(app(ty_@2, bdc), bdd)) → new_compare16(vyy900, vyy910, bdc, bdd)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Bool) → new_ltEs15(vyy900, vyy910)
new_primCmpNat0(Zero, Zero) → EQ
new_compare17(vyy900, vyy910, bg, bh) → new_compare24(vyy900, vyy910, new_esEs6(vyy900, vyy910, bg, bh), bg, bh)
new_lt12(vyy901, vyy911, ty_@0) → new_lt10(vyy901, vyy911)
new_esEs6(Right(vyy3000), Right(vyy400), cbh, app(ty_Maybe, cca)) → new_esEs7(vyy3000, vyy400, cca)
new_primCmpNat0(Succ(vyy9000), Zero) → GT
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, ty_Ordering) → new_ltEs4(vyy9000, vyy9100)
new_esEs23(vyy3001, vyy401, app(app(ty_@2, cfa), cfb)) → new_esEs5(vyy3001, vyy401, cfa, cfb)
new_ltEs9(Just(vyy900), Just(vyy910), app(ty_Maybe, bce)) → new_ltEs9(vyy900, vyy910, bce)
new_ltEs19(vyy901, vyy911, app(ty_Ratio, dac)) → new_ltEs13(vyy901, vyy911, dac)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy9100))) → LT
new_esEs6(Right(vyy3000), Right(vyy400), cbh, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_ltEs4(GT, LT) → False
new_esEs21(vyy901, vyy911, ty_Double) → new_esEs13(vyy901, vyy911)
new_sr0(Integer(vyy9000), Integer(vyy9110)) → Integer(new_primMulInt(vyy9000, vyy9110))
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs4(vyy3000, vyy400, dbb, dbc, dbd)
new_primPlusNat1(Succ(vyy13400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy13400, vyy401000)))
new_ltEs13(vyy90, vyy91, cdc) → new_not(new_esEs8(new_compare7(vyy90, vyy91, cdc), GT))
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_esEs10(vyy3002, vyy402, ty_Char) → new_esEs18(vyy3002, vyy402)
new_lt20(vyy900, vyy910, app(ty_[], ga)) → new_lt19(vyy900, vyy910, ga)
new_esEs26(vyy900, vyy910, ty_Double) → new_esEs13(vyy900, vyy910)
new_esEs7(Nothing, Just(vyy400), dad) → False
new_esEs7(Just(vyy3000), Nothing, dad) → False
new_esEs24(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_lt11(vyy900, vyy910, ty_Double) → new_lt4(vyy900, vyy910)
new_esEs26(vyy900, vyy910, app(ty_Ratio, dab)) → new_esEs16(vyy900, vyy910, dab)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Ordering, bh) → new_ltEs4(vyy9000, vyy9100)
new_compare12(vyy90, vyy91) → new_primCmpInt(vyy90, vyy91)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Int, bh) → new_ltEs5(vyy9000, vyy9100)
new_ltEs9(Just(vyy900), Nothing, cac) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy9100))) → new_primCmpNat0(Zero, Succ(vyy9100))
new_primCompAux00(vyy160, EQ) → vyy160
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], cag), cae) → new_esEs15(vyy3000, vyy400, cag)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs21(vyy901, vyy911, ty_Char) → new_esEs18(vyy901, vyy911)
new_esEs26(vyy900, vyy910, app(app(ty_@2, fc), fd)) → new_esEs5(vyy900, vyy910, fc, fd)
new_lt12(vyy901, vyy911, app(app(ty_@2, cg), da)) → new_lt15(vyy901, vyy911, cg, da)
new_esEs21(vyy901, vyy911, app(app(ty_@2, cg), da)) → new_esEs5(vyy901, vyy911, cg, da)
new_not(False) → True
new_lt20(vyy900, vyy910, ty_Char) → new_lt9(vyy900, vyy910)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, cba), cbb), cae) → new_esEs6(vyy3000, vyy400, cba, cbb)
new_esEs25(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_primCmpInt(Pos(Succ(vyy9000)), Pos(vyy910)) → new_primCmpNat0(Succ(vyy9000), vyy910)
new_ltEs18(vyy902, vyy912, app(ty_Ratio, cdf)) → new_ltEs13(vyy902, vyy912, cdf)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs12(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Ordering) → new_ltEs4(vyy900, vyy910)
new_ltEs9(Nothing, Nothing, cac) → True
new_esEs24(vyy3000, vyy400, app(app(ty_Either, cff), cfg)) → new_esEs6(vyy3000, vyy400, cff, cfg)
new_esEs22(vyy900, vyy910, ty_Bool) → new_esEs17(vyy900, vyy910)
new_esEs19(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs18(vyy902, vyy912, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(vyy902, vyy912, df, dg, dh)
new_esEs11(vyy3001, vyy401, app(app(ty_Either, bgb), bgc)) → new_esEs6(vyy3001, vyy401, bgb, bgc)
new_esEs12(vyy3000, vyy400, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs4(vyy3000, vyy400, bhf, bhg, bhh)
new_esEs25(vyy3000, vyy400, app(ty_Ratio, chb)) → new_esEs16(vyy3000, vyy400, chb)
new_esEs11(vyy3001, vyy401, ty_@0) → new_esEs9(vyy3001, vyy401)
new_esEs25(vyy3000, vyy400, app(app(app(ty_@3, che), chf), chg)) → new_esEs4(vyy3000, vyy400, che, chf, chg)
new_lt20(vyy900, vyy910, app(app(ty_Either, ff), fg)) → new_lt16(vyy900, vyy910, ff, fg)
new_lt12(vyy901, vyy911, ty_Int) → new_lt8(vyy901, vyy911)
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, ty_Integer) → new_ltEs12(vyy9000, vyy9100)
new_ltEs19(vyy901, vyy911, app(app(app(ty_@3, gc), gd), ge)) → new_ltEs6(vyy901, vyy911, gc, gd, ge)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, cae) → new_esEs13(vyy3000, vyy400)
new_esEs22(vyy900, vyy910, app(app(app(ty_@3, h), ba), bb)) → new_esEs4(vyy900, vyy910, h, ba, bb)
new_lt11(vyy900, vyy910, app(ty_Ratio, bea)) → new_lt5(vyy900, vyy910, bea)
new_lt12(vyy901, vyy911, app(ty_[], de)) → new_lt19(vyy901, vyy911, de)
new_primCmpInt(Pos(Succ(vyy9000)), Neg(vyy910)) → GT
new_esEs22(vyy900, vyy910, ty_Char) → new_esEs18(vyy900, vyy910)
new_ltEs19(vyy901, vyy911, ty_Integer) → new_ltEs12(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, cae) → new_esEs19(vyy3000, vyy400)
new_lt12(vyy901, vyy911, ty_Char) → new_lt9(vyy901, vyy911)
new_lt16(vyy900, vyy910, bg, bh) → new_esEs8(new_compare17(vyy900, vyy910, bg, bh), LT)
new_esEs21(vyy901, vyy911, app(ty_Maybe, dd)) → new_esEs7(vyy901, vyy911, dd)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs22(vyy900, vyy910, ty_Double) → new_esEs13(vyy900, vyy910)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, cbf), cbg), cae) → new_esEs5(vyy3000, vyy400, cbf, cbg)
new_compare19(vyy900, vyy910, h, ba, bb) → new_compare23(vyy900, vyy910, new_esEs4(vyy900, vyy910, h, ba, bb), h, ba, bb)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare110(vyy900, vyy910, True) → LT
new_ltEs19(vyy901, vyy911, ty_Int) → new_ltEs5(vyy901, vyy911)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs9(vyy3000, vyy400)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(app(ty_Either, baa), bab), bh) → new_ltEs7(vyy9000, vyy9100, baa, bab)
new_compare25(vyy900, vyy910, True, be, bf) → EQ
new_compare110(vyy900, vyy910, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt12(vyy901, vyy911, app(app(ty_Either, db), dc)) → new_lt16(vyy901, vyy911, db, dc)
new_esEs24(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, ty_Float) → new_esEs20(vyy3001, vyy401)
new_compare4(:(vyy900, vyy901), [], bcg) → GT
new_ltEs18(vyy902, vyy912, app(ty_[], ef)) → new_ltEs17(vyy902, vyy912, ef)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Integer, bh) → new_ltEs12(vyy9000, vyy9100)
new_lt11(vyy900, vyy910, ty_Float) → new_lt17(vyy900, vyy910)
new_compare210(vyy900, vyy910, True) → EQ
new_esEs10(vyy3002, vyy402, app(app(ty_@2, bfe), bff)) → new_esEs5(vyy3002, vyy402, bfe, bff)
new_esEs12(vyy3000, vyy400, app(app(ty_@2, caa), cab)) → new_esEs5(vyy3000, vyy400, caa, cab)
new_compare28(vyy900, vyy910, app(app(ty_Either, bde), bdf)) → new_compare17(vyy900, vyy910, bde, bdf)
new_ltEs4(LT, GT) → True
new_lt12(vyy901, vyy911, ty_Double) → new_lt4(vyy901, vyy911)
new_esEs22(vyy900, vyy910, app(ty_[], cb)) → new_esEs15(vyy900, vyy910, cb)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy9100))) → new_primCmpNat0(Succ(vyy9100), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy9100))) → GT
new_esEs23(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_lt20(vyy900, vyy910, app(app(ty_@2, fc), fd)) → new_lt15(vyy900, vyy910, fc, fd)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, caf), cae) → new_esEs7(vyy3000, vyy400, caf)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, cae) → new_esEs8(vyy3000, vyy400)
new_compare4([], :(vyy910, vyy911), bcg) → LT
new_compare9(vyy900, vyy910) → new_compare210(vyy900, vyy910, new_esEs17(vyy900, vyy910))
new_esEs12(vyy3000, vyy400, ty_Char) → new_esEs18(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, app(ty_Maybe, bfg)) → new_esEs7(vyy3001, vyy401, bfg)
new_compare15(vyy900, vyy910, False, be, bf) → GT
new_esEs21(vyy901, vyy911, app(app(app(ty_@3, cd), ce), cf)) → new_esEs4(vyy901, vyy911, cd, ce, cf)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, cae) → new_esEs9(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, app(app(ty_@2, bgg), bgh)) → new_esEs5(vyy3001, vyy401, bgg, bgh)
new_esEs12(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs15([], :(vyy400, vyy401), cgg) → False
new_esEs15(:(vyy3000, vyy3001), [], cgg) → False
new_esEs26(vyy900, vyy910, ty_@0) → new_esEs9(vyy900, vyy910)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(ty_[], bad), bh) → new_ltEs17(vyy9000, vyy9100, bad)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, app(ty_Maybe, cgh)) → new_esEs7(vyy3000, vyy400, cgh)
new_esEs23(vyy3001, vyy401, app(ty_Ratio, cec)) → new_esEs16(vyy3001, vyy401, cec)
new_esEs22(vyy900, vyy910, app(ty_Ratio, bea)) → new_esEs16(vyy900, vyy910, bea)
new_lt10(vyy900, vyy910) → new_esEs8(new_compare27(vyy900, vyy910), LT)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs10(vyy3002, vyy402, ty_Integer) → new_esEs19(vyy3002, vyy402)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), cbh, ty_Float) → new_esEs20(vyy3000, vyy400)
new_ltEs4(LT, EQ) → True
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, ty_Char) → new_ltEs10(vyy9000, vyy9100)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Char, bh) → new_ltEs10(vyy9000, vyy9100)
new_ltEs9(Just(vyy900), Just(vyy910), app(app(ty_@2, bca), bcb)) → new_ltEs8(vyy900, vyy910, bca, bcb)
new_esEs12(vyy3000, vyy400, app(app(ty_Either, bhd), bhe)) → new_esEs6(vyy3000, vyy400, bhd, bhe)
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, app(app(ty_Either, bbb), bbc)) → new_ltEs7(vyy9000, vyy9100, bbb, bbc)
new_esEs26(vyy900, vyy910, ty_Int) → new_esEs14(vyy900, vyy910)
new_asAs(False, vyy123) → False
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_compare28(vyy900, vyy910, app(ty_Ratio, cdd)) → new_compare7(vyy900, vyy910, cdd)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_ltEs11(vyy90, vyy91) → new_not(new_esEs8(new_compare6(vyy90, vyy91), GT))
new_esEs24(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs15(:(vyy3000, vyy3001), :(vyy400, vyy401), cgg) → new_asAs(new_esEs25(vyy3000, vyy400, cgg), new_esEs15(vyy3001, vyy401, cgg))
new_esEs21(vyy901, vyy911, ty_Ordering) → new_esEs8(vyy901, vyy911)
new_compare4(:(vyy900, vyy901), :(vyy910, vyy911), bcg) → new_primCompAux0(vyy900, vyy910, new_compare4(vyy901, vyy911, bcg), bcg)
new_lt14(vyy900, vyy910, h, ba, bb) → new_esEs8(new_compare19(vyy900, vyy910, h, ba, bb), LT)
new_esEs6(Right(vyy3000), Right(vyy400), cbh, app(ty_Ratio, ccc)) → new_esEs16(vyy3000, vyy400, ccc)
new_esEs26(vyy900, vyy910, app(ty_Maybe, fh)) → new_esEs7(vyy900, vyy910, fh)
new_compare28(vyy900, vyy910, ty_Bool) → new_compare9(vyy900, vyy910)
new_compare31(vyy900, vyy910, ca) → new_compare211(vyy900, vyy910, new_esEs7(vyy900, vyy910, ca), ca)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Float, bh) → new_ltEs16(vyy9000, vyy9100)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Integer) → new_ltEs12(vyy900, vyy910)
new_compare8(vyy900, vyy910) → new_compare26(vyy900, vyy910, new_esEs8(vyy900, vyy910))
new_ltEs18(vyy902, vyy912, app(app(ty_@2, ea), eb)) → new_ltEs8(vyy902, vyy912, ea, eb)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_compare28(vyy900, vyy910, ty_Char) → new_compare18(vyy900, vyy910)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Int) → new_ltEs5(vyy900, vyy910)
new_ltEs5(vyy90, vyy91) → new_not(new_esEs8(new_compare12(vyy90, vyy91), GT))
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, ty_Double) → new_ltEs11(vyy9000, vyy9100)
new_ltEs19(vyy901, vyy911, ty_@0) → new_ltEs14(vyy901, vyy911)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs21(vyy901, vyy911, app(ty_Ratio, cde)) → new_esEs16(vyy901, vyy911, cde)
new_esEs26(vyy900, vyy910, app(ty_[], ga)) → new_esEs15(vyy900, vyy910, ga)
new_compare7(:%(vyy900, vyy901), :%(vyy910, vyy911), ty_Int) → new_compare12(new_sr(vyy900, vyy911), new_sr(vyy910, vyy901))
new_esEs14(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, dag)) → new_esEs16(vyy3000, vyy400, dag)
new_esEs13(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs7(Left(vyy9000), Left(vyy9100), app(ty_Maybe, bac), bh) → new_ltEs9(vyy9000, vyy9100, bac)
new_ltEs4(LT, LT) → True
new_esEs25(vyy3000, vyy400, app(app(ty_@2, chh), daa)) → new_esEs5(vyy3000, vyy400, chh, daa)
new_esEs26(vyy900, vyy910, ty_Bool) → new_esEs17(vyy900, vyy910)
new_ltEs18(vyy902, vyy912, ty_Float) → new_ltEs16(vyy902, vyy912)
new_esEs21(vyy901, vyy911, ty_@0) → new_esEs9(vyy901, vyy911)
new_compare18(Char(vyy900), Char(vyy910)) → new_primCmpNat0(vyy900, vyy910)
new_esEs22(vyy900, vyy910, app(app(ty_Either, bg), bh)) → new_esEs6(vyy900, vyy910, bg, bh)
new_compare14(vyy900, vyy910, True, bg, bh) → LT
new_lt11(vyy900, vyy910, ty_Bool) → new_lt7(vyy900, vyy910)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, dbe), dbf)) → new_esEs5(vyy3000, vyy400, dbe, dbf)
new_esEs26(vyy900, vyy910, ty_Float) → new_esEs20(vyy900, vyy910)
new_lt11(vyy900, vyy910, ty_Int) → new_lt8(vyy900, vyy910)
new_esEs10(vyy3002, vyy402, ty_Float) → new_esEs20(vyy3002, vyy402)
new_esEs26(vyy900, vyy910, ty_Char) → new_esEs18(vyy900, vyy910)
new_esEs22(vyy900, vyy910, ty_Int) → new_esEs14(vyy900, vyy910)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs14(vyy3000, vyy400)
new_lt12(vyy901, vyy911, ty_Float) → new_lt17(vyy901, vyy911)
new_esEs10(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_esEs26(vyy900, vyy910, app(app(ty_Either, ff), fg)) → new_esEs6(vyy900, vyy910, ff, fg)
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, ty_Int) → new_ltEs5(vyy9000, vyy9100)
new_ltEs18(vyy902, vyy912, ty_Bool) → new_ltEs15(vyy902, vyy912)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_asAs(True, vyy123) → vyy123
new_esEs22(vyy900, vyy910, ty_@0) → new_esEs9(vyy900, vyy910)
new_compare27(@0, @0) → EQ
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_compare28(vyy900, vyy910, ty_Int) → new_compare12(vyy900, vyy910)
new_esEs10(vyy3002, vyy402, app(app(ty_Either, beh), bfa)) → new_esEs6(vyy3002, vyy402, beh, bfa)
new_esEs16(:%(vyy3000, vyy3001), :%(vyy400, vyy401), dbg) → new_asAs(new_esEs28(vyy3000, vyy400, dbg), new_esEs27(vyy3001, vyy401, dbg))
new_esEs11(vyy3001, vyy401, app(ty_Ratio, bga)) → new_esEs16(vyy3001, vyy401, bga)
new_esEs12(vyy3000, vyy400, app(ty_Ratio, bhc)) → new_esEs16(vyy3000, vyy400, bhc)
new_lt12(vyy901, vyy911, app(app(app(ty_@3, cd), ce), cf)) → new_lt14(vyy901, vyy911, cd, ce, cf)
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, ty_Float) → new_ltEs16(vyy9000, vyy9100)
new_compare10(vyy900, vyy910, True) → LT
new_ltEs4(GT, GT) → True
new_esEs20(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt20(vyy900, vyy910, ty_Double) → new_lt4(vyy900, vyy910)
new_lt17(vyy900, vyy910) → new_esEs8(new_compare30(vyy900, vyy910), LT)
new_lt12(vyy901, vyy911, ty_Bool) → new_lt7(vyy901, vyy911)
new_compare13(vyy900, vyy910, True, h, ba, bb) → LT
new_esEs24(vyy3000, vyy400, app(app(app(ty_@3, cfh), cga), cgb)) → new_esEs4(vyy3000, vyy400, cfh, cga, cgb)
new_ltEs10(vyy90, vyy91) → new_not(new_esEs8(new_compare18(vyy90, vyy91), GT))
new_compare10(vyy900, vyy910, False) → GT
new_primCompAux00(vyy160, GT) → GT
new_ltEs18(vyy902, vyy912, ty_Integer) → new_ltEs12(vyy902, vyy912)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), cbh, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare28(vyy900, vyy910, app(app(app(ty_@3, bch), bda), bdb)) → new_compare19(vyy900, vyy910, bch, bda, bdb)
new_esEs24(vyy3000, vyy400, app(ty_[], cfd)) → new_esEs15(vyy3000, vyy400, cfd)
new_esEs24(vyy3000, vyy400, ty_Char) → new_esEs18(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs10(vyy3002, vyy402, ty_Bool) → new_esEs17(vyy3002, vyy402)
new_lt18(vyy900, vyy910, ca) → new_esEs8(new_compare31(vyy900, vyy910, ca), LT)
new_lt13(vyy900, vyy910) → new_esEs8(new_compare29(vyy900, vyy910), LT)
new_esEs22(vyy900, vyy910, app(ty_Maybe, ca)) → new_esEs7(vyy900, vyy910, ca)
new_esEs4(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), beb, bec, bed) → new_asAs(new_esEs12(vyy3000, vyy400, beb), new_asAs(new_esEs11(vyy3001, vyy401, bec), new_esEs10(vyy3002, vyy402, bed)))
new_ltEs7(Right(vyy9000), Right(vyy9100), bg, ty_@0) → new_ltEs14(vyy9000, vyy9100)
new_primCmpInt(Neg(Succ(vyy9000)), Pos(vyy910)) → LT
new_not(True) → False

The set Q consists of the following terms:

new_esEs11(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Float)
new_compare18(Char(x0), Char(x1))
new_compare13(x0, x1, False, x2, x3, x4)
new_esEs10(x0, x1, ty_Float)
new_compare29(Integer(x0), Integer(x1))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_asAs(True, x0)
new_compare4(:(x0, x1), :(x2, x3), x4)
new_compare211(x0, x1, False, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_lt12(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs10(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare4([], [], x0)
new_esEs28(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs15(True, True)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Integer)
new_compare28(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_pePe(True, x0)
new_esEs21(x0, x1, ty_Bool)
new_esEs8(GT, GT)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs15(False, False)
new_compare28(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs25(x0, x1, ty_Double)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_compare14(x0, x1, True, x2, x3)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_ltEs17(x0, x1, x2)
new_esEs26(x0, x1, ty_Ordering)
new_esEs8(LT, LT)
new_lt12(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs11(x0, x1)
new_esEs17(False, False)
new_esEs15(:(x0, x1), [], x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare4(:(x0, x1), [], x2)
new_sr(x0, x1)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare28(x0, x1, ty_Bool)
new_lt9(x0, x1)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare10(x0, x1, True)
new_esEs23(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs22(x0, x1, ty_Bool)
new_lt18(x0, x1, x2)
new_lt20(x0, x1, ty_Bool)
new_compare28(x0, x1, ty_Int)
new_primCompAux0(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_asAs(False, x0)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs9(Nothing, Just(x0), x1)
new_esEs23(x0, x1, ty_Char)
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_compare210(x0, x1, True)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Zero, Zero)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_compare28(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(x0, x1, ty_Char)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, True, x2, x3, x4)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare12(x0, x1)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare15(x0, x1, True, x2, x3)
new_ltEs4(GT, GT)
new_esEs25(x0, x1, ty_Bool)
new_esEs14(x0, x1)
new_compare28(x0, x1, ty_Float)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_lt13(x0, x1)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primCmpNat0(Succ(x0), Zero)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs19(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_Int)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Char)
new_compare10(x0, x1, False)
new_ltEs18(x0, x1, app(ty_[], x2))
new_compare25(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, ty_Char)
new_lt11(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs11(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Double)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs11(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs18(x0, x1, ty_Bool)
new_lt16(x0, x1, x2, x3)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, Zero)
new_lt12(x0, x1, ty_Double)
new_ltEs13(x0, x1, x2)
new_primMulNat0(Succ(x0), Zero)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpNat0(Zero, Succ(x0))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Float)
new_esEs15([], :(x0, x1), x2)
new_esEs10(x0, x1, ty_@0)
new_lt11(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs18(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare11(x0, x1, False, x2)
new_esEs21(x0, x1, ty_Integer)
new_ltEs4(EQ, EQ)
new_primCompAux00(x0, LT)
new_esEs24(x0, x1, ty_Integer)
new_esEs7(Just(x0), Nothing, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs11(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1, x2, x3, x4)
new_ltEs4(EQ, LT)
new_lt19(x0, x1, x2)
new_esEs27(x0, x1, ty_Int)
new_ltEs4(LT, EQ)
new_esEs11(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs15(True, False)
new_ltEs15(False, True)
new_esEs11(x0, x1, ty_Bool)
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, ty_@0)
new_esEs18(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Bool)
new_compare23(x0, x1, True, x2, x3, x4)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare24(x0, x1, False, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, ty_Float)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, True)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_esEs12(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Char)
new_lt5(x0, x1, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare8(x0, x1)
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Float)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs18(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Nothing, Nothing, x0)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs28(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs4(LT, LT)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_compare110(x0, x1, False)
new_esEs10(x0, x1, ty_Double)
new_ltEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs11(x0, x1, ty_Char)
new_compare19(x0, x1, x2, x3, x4)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_compare4([], :(x0, x1), x2)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_lt12(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, ty_@0)
new_esEs9(@0, @0)
new_esEs10(x0, x1, ty_Char)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqNat0(Zero, Succ(x0))
new_lt11(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(Float(x0, x1), Float(x2, x3))
new_lt12(x0, x1, ty_Int)
new_primPlusNat0(Zero, x0)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Zero, Zero)
new_esEs10(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_@0)
new_lt12(x0, x1, ty_Integer)
new_lt4(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare211(x0, x1, True, x2)
new_lt17(x0, x1)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_pePe(False, x0)
new_lt11(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt12(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare28(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_compare15(x0, x1, False, x2, x3)
new_esEs10(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs11(x0, x1, ty_Ordering)
new_esEs20(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_lt11(x0, x1, ty_Bool)
new_compare14(x0, x1, False, x2, x3)
new_esEs24(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Float)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare24(x0, x1, True, x2, x3)
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, ty_Int)
new_lt11(x0, x1, ty_Int)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_not(True)
new_lt11(x0, x1, ty_Char)
new_ltEs9(Nothing, Nothing, x0)
new_lt6(x0, x1)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs26(x0, x1, ty_Double)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt7(x0, x1)
new_not(False)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs12(x0, x1, ty_Int)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare26(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs19(x0, x1, ty_@0)
new_compare26(x0, x1, False)
new_esEs12(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_lt20(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_lt15(x0, x1, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_compare28(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Double)
new_ltEs12(x0, x1)
new_esEs24(x0, x1, ty_Double)
new_ltEs5(x0, x1)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs18(x0, x1, ty_Ordering)
new_compare23(x0, x1, False, x2, x3, x4)
new_esEs22(x0, x1, ty_Int)
new_compare16(x0, x1, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1)
new_esEs17(True, False)
new_esEs17(False, True)
new_lt11(x0, x1, ty_Integer)
new_compare27(@0, @0)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Int)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs24(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs16(x0, x1)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, ty_@0)
new_compare17(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs22(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs18(x0, x1, ty_Float)
new_ltEs14(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs19(Integer(x0), Integer(x1))
new_esEs15([], [], x0)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_primMulInt(Neg(x0), Neg(x1))
new_lt8(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare11(x0, x1, True, x2)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt10(x0, x1)
new_lt11(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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP

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

new_foldFM_GE(vyy78, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba, bb) → new_foldFM_GE1(vyy78, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, ba, bb), h, ba, bb)
new_foldFM_GE2(vyy330, vyy331, vyy103, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb) → new_foldFM_GE1(new_eltsFM_GE0(vyy330, vyy331, vyy103, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, ba, bb), h, ba, bb)
new_foldFM_GE1(vyy78, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba, bb) → new_foldFM_GE(vyy78, vyy40, vyy334, h, ba, bb)
new_foldFM_GE1(vyy78, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba, bb) → new_foldFM_GE(vyy78, vyy40, vyy334, h, ba, bb)
new_foldFM_GE1(vyy78, vyy40, vyy330, vyy331, vyy332, vyy333, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), False, h, ba, bb) → new_foldFM_GE1(vyy78, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, ba, bb), h, ba, bb)
new_foldFM_GE1(vyy78, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba, bb) → new_foldFM_GE2(vyy330, vyy331, new_foldFM_GE0(vyy78, vyy40, vyy334, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb)

The TRS R consists of the following rules:

new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, dah)) → new_esEs7(vyy3000, vyy400, dah)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], dba)) → new_esEs15(vyy3000, vyy400, dba)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_@0, gd) → new_ltEs14(vyy9000, vyy9100)
new_esEs18(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_ltEs15(True, False) → False
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, app(ty_Maybe, ced)) → new_ltEs9(vyy9000, vyy9100, ced)
new_esEs10(vyy3002, vyy402, app(app(app(ty_@3, ce), cf), cg)) → new_esEs4(vyy3002, vyy402, ce, cf, cg)
new_ltEs4(EQ, GT) → True
new_esEs23(vyy3001, vyy401, ty_Float) → new_esEs20(vyy3001, vyy401)
new_ltEs14(vyy90, vyy91) → new_not(new_esEs8(new_compare27(vyy90, vyy91), GT))
new_esEs23(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_compare15(vyy900, vyy910, True, ge, gf) → LT
new_compare24(vyy900, vyy910, False, gc, gd) → new_compare14(vyy900, vyy910, new_ltEs7(vyy900, vyy910, gc, gd), gc, gd)
new_ltEs9(Nothing, Just(vyy910), gg) → True
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_ltEs19(vyy901, vyy911, ty_Double) → new_ltEs11(vyy901, vyy911)
new_ltEs9(Just(vyy900), Just(vyy910), app(ty_Ratio, he)) → new_ltEs13(vyy900, vyy910, he)
new_esEs21(vyy901, vyy911, ty_Int) → new_esEs14(vyy901, vyy911)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, dbc), dbd)) → new_esEs6(vyy3000, vyy400, dbc, dbd)
new_ltEs7(Left(vyy9000), Right(vyy9100), gc, gd) → True
new_primMulNat0(Zero, Zero) → Zero
new_compare13(vyy900, vyy910, False, fh, ga, gb) → GT
new_esEs25(vyy3000, vyy400, app(app(ty_Either, cfb), cfc)) → new_esEs6(vyy3000, vyy400, cfb, cfc)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(app(ty_@2, cce), ccf), gd) → new_ltEs8(vyy9000, vyy9100, cce, ccf)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, bae), bab) → new_esEs16(vyy3000, vyy400, bae)
new_esEs21(vyy901, vyy911, ty_Bool) → new_esEs17(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bah), bba), bbb), bab) → new_esEs4(vyy3000, vyy400, bah, bba, bbb)
new_esEs21(vyy901, vyy911, app(ty_[], bga)) → new_esEs15(vyy901, vyy911, bga)
new_lt12(vyy901, vyy911, app(ty_Ratio, bfe)) → new_lt5(vyy901, vyy911, bfe)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, app(app(ty_@2, cdg), cdh)) → new_ltEs8(vyy9000, vyy9100, cdg, cdh)
new_esEs25(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_lt12(vyy901, vyy911, ty_Integer) → new_lt13(vyy901, vyy911)
new_esEs23(vyy3001, vyy401, ty_@0) → new_esEs9(vyy3001, vyy401)
new_compare25(vyy900, vyy910, False, ge, gf) → new_compare15(vyy900, vyy910, new_ltEs8(vyy900, vyy910, ge, gf), ge, gf)
new_esEs21(vyy901, vyy911, ty_Integer) → new_esEs19(vyy901, vyy911)
new_esEs12(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs17(True, True) → True
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs20(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs22(vyy900, vyy910, app(app(ty_@2, ge), gf)) → new_esEs5(vyy900, vyy910, ge, gf)
new_esEs24(vyy3000, vyy400, app(app(ty_@2, cbh), cca)) → new_esEs5(vyy3000, vyy400, cbh, cca)
new_compare28(vyy900, vyy910, ty_Ordering) → new_compare8(vyy900, vyy910)
new_esEs23(vyy3001, vyy401, ty_Double) → new_esEs13(vyy3001, vyy401)
new_compare28(vyy900, vyy910, app(ty_[], beb)) → new_compare4(vyy900, vyy910, beb)
new_esEs10(vyy3002, vyy402, app(ty_[], ca)) → new_esEs15(vyy3002, vyy402, ca)
new_ltEs9(Just(vyy900), Just(vyy910), ty_@0) → new_ltEs14(vyy900, vyy910)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, bab) → new_esEs14(vyy3000, vyy400)
new_esEs12(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs21(vyy901, vyy911, app(app(ty_Either, bff), bfg)) → new_esEs6(vyy901, vyy911, bff, bfg)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, bab) → new_esEs17(vyy3000, vyy400)
new_ltEs16(vyy90, vyy91) → new_not(new_esEs8(new_compare30(vyy90, vyy91), GT))
new_esEs22(vyy900, vyy910, ty_Float) → new_esEs20(vyy900, vyy910)
new_lt20(vyy900, vyy910, ty_Float) → new_lt17(vyy900, vyy910)
new_esEs12(vyy3000, vyy400, app(ty_[], ef)) → new_esEs15(vyy3000, vyy400, ef)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Double) → new_ltEs11(vyy900, vyy910)
new_ltEs19(vyy901, vyy911, app(app(ty_@2, chh), daa)) → new_ltEs8(vyy901, vyy911, chh, daa)
new_ltEs19(vyy901, vyy911, ty_Float) → new_ltEs16(vyy901, vyy911)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, app(ty_[], cee)) → new_ltEs17(vyy9000, vyy9100, cee)
new_pePe(False, vyy150) → vyy150
new_ltEs15(True, True) → True
new_ltEs17(vyy90, vyy91, bch) → new_not(new_esEs8(new_compare4(vyy90, vyy91, bch), GT))
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, bab) → new_esEs18(vyy3000, vyy400)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, app(ty_Ratio, cea)) → new_ltEs13(vyy9000, vyy9100, cea)
new_lt6(vyy900, vyy910) → new_esEs8(new_compare8(vyy900, vyy910), LT)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, app(app(app(ty_@3, cdd), cde), cdf)) → new_ltEs6(vyy9000, vyy9100, cdd, cde, cdf)
new_ltEs15(False, True) → True
new_esEs24(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs10(vyy3002, vyy402, app(ty_Maybe, bh)) → new_esEs7(vyy3002, vyy402, bh)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Bool) → new_ltEs15(vyy9000, vyy9100)
new_esEs24(vyy3000, vyy400, app(ty_Maybe, cah)) → new_esEs7(vyy3000, vyy400, cah)
new_lt9(vyy900, vyy910) → new_esEs8(new_compare18(vyy900, vyy910), LT)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(app(app(ty_@3, ccb), ccc), ccd), gd) → new_ltEs6(vyy9000, vyy9100, ccb, ccc, ccd)
new_esEs23(vyy3001, vyy401, app(ty_Maybe, bhf)) → new_esEs7(vyy3001, vyy401, bhf)
new_lt15(vyy900, vyy910, ge, gf) → new_esEs8(new_compare16(vyy900, vyy910, ge, gf), LT)
new_compare23(vyy900, vyy910, True, fh, ga, gb) → EQ
new_ltEs9(Just(vyy900), Just(vyy910), ty_Float) → new_ltEs16(vyy900, vyy910)
new_lt8(vyy900, vyy910) → new_esEs8(new_compare12(vyy900, vyy910), LT)
new_esEs22(vyy900, vyy910, ty_Ordering) → new_esEs8(vyy900, vyy910)
new_esEs11(vyy3001, vyy401, app(ty_[], dd)) → new_esEs15(vyy3001, vyy401, dd)
new_compare6(Double(vyy900, vyy901), Double(vyy910, vyy911)) → new_compare12(new_sr(vyy900, vyy910), new_sr(vyy901, vyy911))
new_lt11(vyy900, vyy910, app(app(ty_Either, gc), gd)) → new_lt16(vyy900, vyy910, gc, gd)
new_esEs12(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_ltEs15(False, False) → True
new_ltEs12(vyy90, vyy91) → new_not(new_esEs8(new_compare29(vyy90, vyy91), GT))
new_compare28(vyy900, vyy910, ty_Double) → new_compare6(vyy900, vyy910)
new_lt12(vyy901, vyy911, app(ty_Maybe, bfh)) → new_lt18(vyy901, vyy911, bfh)
new_primCmpNat0(Zero, Succ(vyy9100)) → LT
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Int) → new_esEs14(vyy3000, vyy400)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(ty_Ratio, ccg), gd) → new_ltEs13(vyy9000, vyy9100, ccg)
new_esEs11(vyy3001, vyy401, ty_Char) → new_esEs18(vyy3001, vyy401)
new_lt20(vyy900, vyy910, ty_Ordering) → new_lt6(vyy900, vyy910)
new_lt20(vyy900, vyy910, app(app(app(ty_@3, cgc), cgd), cge)) → new_lt14(vyy900, vyy910, cgc, cgd, cge)
new_lt19(vyy900, vyy910, beg) → new_esEs8(new_compare4(vyy900, vyy910, beg), LT)
new_lt11(vyy900, vyy910, app(app(ty_@2, ge), gf)) → new_lt15(vyy900, vyy910, ge, gf)
new_esEs6(Left(vyy3000), Right(vyy400), bbe, bab) → False
new_esEs6(Right(vyy3000), Left(vyy400), bbe, bab) → False
new_esEs8(LT, LT) → True
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, bab) → new_esEs20(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Char) → new_esEs18(vyy3001, vyy401)
new_esEs23(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_pePe(True, vyy150) → True
new_compare14(vyy900, vyy910, False, gc, gd) → GT
new_primEqNat0(Zero, Zero) → True
new_compare26(vyy900, vyy910, True) → EQ
new_compare11(vyy900, vyy910, True, bc) → LT
new_esEs23(vyy3001, vyy401, app(app(ty_Either, caa), cab)) → new_esEs6(vyy3001, vyy401, caa, cab)
new_compare28(vyy900, vyy910, ty_Integer) → new_compare29(vyy900, vyy910)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs4(vyy3000, vyy400, bcc, bcd, bce)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, app(app(ty_Either, bca), bcb)) → new_esEs6(vyy3000, vyy400, bca, bcb)
new_foldFM_GE10(vyy78, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba, bb) → new_foldFM_GE3(vyy330, vyy331, new_foldFM_GE0(vyy78, vyy40, vyy334, h, ba, bb), vyy40, h, ba, bb)
new_lt20(vyy900, vyy910, ty_Bool) → new_lt7(vyy900, vyy910)
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Char) → new_esEs18(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, app(ty_[], bbg)) → new_esEs15(vyy3000, vyy400, bbg)
new_ltEs18(vyy902, vyy912, ty_Int) → new_ltEs5(vyy902, vyy912)
new_ltEs18(vyy902, vyy912, ty_Char) → new_ltEs10(vyy902, vyy912)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs24(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_compare211(vyy900, vyy910, False, bc) → new_compare11(vyy900, vyy910, new_ltEs9(vyy900, vyy910, bc), bc)
new_primCompAux0(vyy900, vyy910, vyy151, bch) → new_primCompAux00(vyy151, new_compare28(vyy900, vyy910, bch))
new_esEs25(vyy3000, vyy400, app(ty_[], ceh)) → new_esEs15(vyy3000, vyy400, ceh)
new_esEs23(vyy3001, vyy401, app(ty_[], bhg)) → new_esEs15(vyy3001, vyy401, bhg)
new_compare7(:%(vyy900, vyy901), :%(vyy910, vyy911), ty_Integer) → new_compare29(new_sr0(vyy900, vyy911), new_sr0(vyy910, vyy901))
new_esEs25(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, ty_Double) → new_esEs13(vyy3001, vyy401)
new_esEs10(vyy3002, vyy402, ty_Int) → new_esEs14(vyy3002, vyy402)
new_esEs26(vyy900, vyy910, ty_Ordering) → new_esEs8(vyy900, vyy910)
new_lt11(vyy900, vyy910, ty_@0) → new_lt10(vyy900, vyy910)
new_ltEs19(vyy901, vyy911, ty_Char) → new_ltEs10(vyy901, vyy911)
new_esEs12(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(vyy1340), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1340, vyy40100)))
new_compare4([], [], bch) → EQ
new_esEs11(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs10(vyy3002, vyy402, ty_Double) → new_esEs13(vyy3002, vyy402)
new_ltEs9(Just(vyy900), Just(vyy910), app(ty_[], baa)) → new_ltEs17(vyy900, vyy910, baa)
new_ltEs19(vyy901, vyy911, ty_Bool) → new_ltEs15(vyy901, vyy911)
new_esEs26(vyy900, vyy910, app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs4(vyy900, vyy910, cgc, cgd, cge)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs19(vyy901, vyy911, app(ty_Maybe, dae)) → new_ltEs9(vyy901, vyy911, dae)
new_compare16(vyy900, vyy910, ge, gf) → new_compare25(vyy900, vyy910, new_esEs5(vyy900, vyy910, ge, gf), ge, gf)
new_esEs11(vyy3001, vyy401, app(app(app(ty_@3, dh), ea), eb)) → new_esEs4(vyy3001, vyy401, dh, ea, eb)
new_compare211(vyy900, vyy910, True, bc) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs24(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs18(vyy902, vyy912, app(app(ty_Either, bgh), bha)) → new_ltEs7(vyy902, vyy912, bgh, bha)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy13400), Zero) → Succ(vyy13400)
new_esEs10(vyy3002, vyy402, ty_@0) → new_esEs9(vyy3002, vyy402)
new_foldFM_GE10(vyy78, vyy40, vyy330, vyy331, vyy332, vyy333, vyy334, False, h, ba, bb) → new_foldFM_GE0(vyy78, vyy40, vyy334, h, ba, bb)
new_esEs25(vyy3000, vyy400, ty_Char) → new_esEs18(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs11(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_lt20(vyy900, vyy910, app(ty_Maybe, chc)) → new_lt18(vyy900, vyy910, chc)
new_ltEs7(Right(vyy9000), Left(vyy9100), gc, gd) → False
new_esEs26(vyy900, vyy910, ty_Integer) → new_esEs19(vyy900, vyy910)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Bool, gd) → new_ltEs15(vyy9000, vyy9100)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs9(Just(vyy900), Just(vyy910), app(app(ty_Either, hf), hg)) → new_ltEs7(vyy900, vyy910, hf, hg)
new_ltEs19(vyy901, vyy911, ty_Ordering) → new_ltEs4(vyy901, vyy911)
new_ltEs6(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), bed, bee, bef) → new_pePe(new_lt11(vyy900, vyy910, bed), new_asAs(new_esEs22(vyy900, vyy910, bed), new_pePe(new_lt12(vyy901, vyy911, bee), new_asAs(new_esEs21(vyy901, vyy911, bee), new_ltEs18(vyy902, vyy912, bef)))))
new_lt11(vyy900, vyy910, ty_Char) → new_lt9(vyy900, vyy910)
new_ltEs18(vyy902, vyy912, ty_@0) → new_ltEs14(vyy902, vyy912)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Double) → new_esEs13(vyy3000, vyy400)
new_compare29(Integer(vyy900), Integer(vyy910)) → new_primCmpInt(vyy900, vyy910)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_esEs8(EQ, EQ) → True
new_esEs22(vyy900, vyy910, ty_Integer) → new_esEs19(vyy900, vyy910)
new_lt20(vyy900, vyy910, ty_@0) → new_lt10(vyy900, vyy910)
new_compare26(vyy900, vyy910, False) → new_compare10(vyy900, vyy910, new_ltEs4(vyy900, vyy910))
new_esEs23(vyy3001, vyy401, app(app(app(ty_@3, cac), cad), cae)) → new_esEs4(vyy3001, vyy401, cac, cad, cae)
new_compare24(vyy900, vyy910, True, gc, gd) → EQ
new_esEs11(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_lt11(vyy900, vyy910, app(ty_[], beg)) → new_lt19(vyy900, vyy910, beg)
new_compare28(vyy900, vyy910, app(ty_Maybe, bea)) → new_compare31(vyy900, vyy910, bea)
new_lt11(vyy900, vyy910, ty_Ordering) → new_lt6(vyy900, vyy910)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs18(vyy902, vyy912, ty_Ordering) → new_ltEs4(vyy902, vyy912)
new_ltEs4(EQ, LT) → False
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs12(vyy3000, vyy400, app(ty_Maybe, ee)) → new_esEs7(vyy3000, vyy400, ee)
new_ltEs8(@2(vyy900, vyy901), @2(vyy910, vyy911), cga, cgb) → new_pePe(new_lt20(vyy900, vyy910, cga), new_asAs(new_esEs26(vyy900, vyy910, cga), new_ltEs19(vyy901, vyy911, cgb)))
new_lt20(vyy900, vyy910, ty_Int) → new_lt8(vyy900, vyy910)
new_primCmpNat0(Succ(vyy9000), Succ(vyy9100)) → new_primCmpNat0(vyy9000, vyy9100)
new_lt20(vyy900, vyy910, ty_Integer) → new_lt13(vyy900, vyy910)
new_compare11(vyy900, vyy910, False, bc) → GT
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare30(Float(vyy900, vyy901), Float(vyy910, vyy911)) → new_compare12(new_sr(vyy900, vyy910), new_sr(vyy901, vyy911))
new_lt5(vyy900, vyy910, bd) → new_esEs8(new_compare7(vyy900, vyy910, bd), LT)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs18(vyy3000, vyy400)
new_esEs24(vyy3000, vyy400, app(ty_Ratio, cbb)) → new_esEs16(vyy3000, vyy400, cbb)
new_esEs21(vyy901, vyy911, ty_Float) → new_esEs20(vyy901, vyy911)
new_ltEs18(vyy902, vyy912, app(ty_Maybe, bhb)) → new_ltEs9(vyy902, vyy912, bhb)
new_lt11(vyy900, vyy910, ty_Integer) → new_lt13(vyy900, vyy910)
new_compare28(vyy900, vyy910, ty_Float) → new_compare30(vyy900, vyy910)
new_compare23(vyy900, vyy910, False, fh, ga, gb) → new_compare13(vyy900, vyy910, new_ltEs6(vyy900, vyy910, fh, ga, gb), fh, ga, gb)
new_lt11(vyy900, vyy910, app(ty_Maybe, bc)) → new_lt18(vyy900, vyy910, bc)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_foldFM_GE3(vyy330, vyy331, vyy102, vyy40, h, ba, bb) → new_eltsFM_GE0(vyy330, vyy331, vyy102, h, ba, bb)
new_esEs5(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bhd, bhe) → new_asAs(new_esEs24(vyy3000, vyy400, bhd), new_esEs23(vyy3001, vyy401, bhe))
new_lt11(vyy900, vyy910, app(app(app(ty_@3, fh), ga), gb)) → new_lt14(vyy900, vyy910, fh, ga, gb)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, app(app(ty_@2, bcf), bcg)) → new_esEs5(vyy3000, vyy400, bcf, bcg)
new_esEs10(vyy3002, vyy402, app(ty_Ratio, cb)) → new_esEs16(vyy3002, vyy402, cb)
new_lt12(vyy901, vyy911, ty_Ordering) → new_lt6(vyy901, vyy911)
new_esEs9(@0, @0) → True
new_primCompAux00(vyy160, LT) → LT
new_ltEs4(GT, EQ) → False
new_compare210(vyy900, vyy910, False) → new_compare110(vyy900, vyy910, new_ltEs15(vyy900, vyy910))
new_esEs11(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_primCmpInt(Neg(Succ(vyy9000)), Neg(vyy910)) → new_primCmpNat0(vyy910, Succ(vyy9000))
new_ltEs19(vyy901, vyy911, app(app(ty_Either, dac), dad)) → new_ltEs7(vyy901, vyy911, dac, dad)
new_ltEs19(vyy901, vyy911, app(ty_[], daf)) → new_ltEs17(vyy901, vyy911, daf)
new_esEs24(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt7(vyy900, vyy910) → new_esEs8(new_compare9(vyy900, vyy910), LT)
new_ltEs18(vyy902, vyy912, ty_Double) → new_ltEs11(vyy902, vyy912)
new_esEs7(Nothing, Nothing, dag) → True
new_esEs15([], [], cef) → True
new_ltEs9(Just(vyy900), Just(vyy910), app(app(app(ty_@3, gh), ha), hb)) → new_ltEs6(vyy900, vyy910, gh, ha, hb)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_lt20(vyy900, vyy910, app(ty_Ratio, cgh)) → new_lt5(vyy900, vyy910, cgh)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Double, gd) → new_ltEs11(vyy9000, vyy9100)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Char) → new_ltEs10(vyy900, vyy910)
new_lt4(vyy900, vyy910) → new_esEs8(new_compare6(vyy900, vyy910), LT)
new_ltEs4(EQ, EQ) → True
new_compare28(vyy900, vyy910, ty_@0) → new_compare27(vyy900, vyy910)
new_foldFM_GE0(vyy78, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba, bb) → new_foldFM_GE10(vyy78, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, ba, bb), h, ba, bb)
new_compare28(vyy900, vyy910, app(app(ty_@2, bdd), bde)) → new_compare16(vyy900, vyy910, bdd, bde)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Bool) → new_ltEs15(vyy900, vyy910)
new_primCmpNat0(Zero, Zero) → EQ
new_compare17(vyy900, vyy910, gc, gd) → new_compare24(vyy900, vyy910, new_esEs6(vyy900, vyy910, gc, gd), gc, gd)
new_lt12(vyy901, vyy911, ty_@0) → new_lt10(vyy901, vyy911)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, app(ty_Maybe, bbf)) → new_esEs7(vyy3000, vyy400, bbf)
new_primCmpNat0(Succ(vyy9000), Zero) → GT
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Ordering) → new_ltEs4(vyy9000, vyy9100)
new_esEs23(vyy3001, vyy401, app(app(ty_@2, caf), cag)) → new_esEs5(vyy3001, vyy401, caf, cag)
new_ltEs9(Just(vyy900), Just(vyy910), app(ty_Maybe, hh)) → new_ltEs9(vyy900, vyy910, hh)
new_ltEs19(vyy901, vyy911, app(ty_Ratio, dab)) → new_ltEs13(vyy901, vyy911, dab)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy9100))) → LT
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_ltEs4(GT, LT) → False
new_esEs21(vyy901, vyy911, ty_Double) → new_esEs13(vyy901, vyy911)
new_sr0(Integer(vyy9000), Integer(vyy9110)) → Integer(new_primMulInt(vyy9000, vyy9110))
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs4(vyy3000, vyy400, dbe, dbf, dbg)
new_primPlusNat1(Succ(vyy13400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy13400, vyy401000)))
new_ltEs13(vyy90, vyy91, bec) → new_not(new_esEs8(new_compare7(vyy90, vyy91, bec), GT))
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_esEs10(vyy3002, vyy402, ty_Char) → new_esEs18(vyy3002, vyy402)
new_lt20(vyy900, vyy910, app(ty_[], chd)) → new_lt19(vyy900, vyy910, chd)
new_esEs26(vyy900, vyy910, ty_Double) → new_esEs13(vyy900, vyy910)
new_esEs7(Nothing, Just(vyy400), dag) → False
new_esEs7(Just(vyy3000), Nothing, dag) → False
new_esEs24(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_lt11(vyy900, vyy910, ty_Double) → new_lt4(vyy900, vyy910)
new_esEs26(vyy900, vyy910, app(ty_Ratio, cgh)) → new_esEs16(vyy900, vyy910, cgh)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Ordering, gd) → new_ltEs4(vyy9000, vyy9100)
new_compare12(vyy90, vyy91) → new_primCmpInt(vyy90, vyy91)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Int, gd) → new_ltEs5(vyy9000, vyy9100)
new_ltEs9(Just(vyy900), Nothing, gg) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy9100))) → new_primCmpNat0(Zero, Succ(vyy9100))
new_primCompAux00(vyy160, EQ) → vyy160
new_eltsFM_GE0(vyy170, vyy171, vyy100, dcb, dcc, dcd) → :(vyy171, vyy100)
new_foldFM_GE10(vyy78, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba, bb) → new_foldFM_GE20(vyy330, vyy331, new_foldFM_GE0(vyy78, vyy40, vyy334, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], bad), bab) → new_esEs15(vyy3000, vyy400, bad)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs21(vyy901, vyy911, ty_Char) → new_esEs18(vyy901, vyy911)
new_esEs26(vyy900, vyy910, app(app(ty_@2, cgf), cgg)) → new_esEs5(vyy900, vyy910, cgf, cgg)
new_lt12(vyy901, vyy911, app(app(ty_@2, bfc), bfd)) → new_lt15(vyy901, vyy911, bfc, bfd)
new_esEs21(vyy901, vyy911, app(app(ty_@2, bfc), bfd)) → new_esEs5(vyy901, vyy911, bfc, bfd)
new_not(False) → True
new_lt20(vyy900, vyy910, ty_Char) → new_lt9(vyy900, vyy910)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, baf), bag), bab) → new_esEs6(vyy3000, vyy400, baf, bag)
new_esEs25(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_gtEs(vyy3330, vyy40, ba, bb) → new_not(new_esEs8(new_compare24(vyy3330, Right(vyy40), new_esEs6(vyy3330, Right(vyy40), ba, bb), ba, bb), LT))
new_primCmpInt(Pos(Succ(vyy9000)), Pos(vyy910)) → new_primCmpNat0(Succ(vyy9000), vyy910)
new_ltEs18(vyy902, vyy912, app(ty_Ratio, bgg)) → new_ltEs13(vyy902, vyy912, bgg)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs12(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Ordering) → new_ltEs4(vyy900, vyy910)
new_ltEs9(Nothing, Nothing, gg) → True
new_esEs24(vyy3000, vyy400, app(app(ty_Either, cbc), cbd)) → new_esEs6(vyy3000, vyy400, cbc, cbd)
new_esEs22(vyy900, vyy910, ty_Bool) → new_esEs17(vyy900, vyy910)
new_esEs19(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs18(vyy902, vyy912, app(app(app(ty_@3, bgb), bgc), bgd)) → new_ltEs6(vyy902, vyy912, bgb, bgc, bgd)
new_esEs11(vyy3001, vyy401, app(app(ty_Either, df), dg)) → new_esEs6(vyy3001, vyy401, df, dg)
new_esEs12(vyy3000, vyy400, app(app(app(ty_@3, fb), fc), fd)) → new_esEs4(vyy3000, vyy400, fb, fc, fd)
new_esEs25(vyy3000, vyy400, app(ty_Ratio, cfa)) → new_esEs16(vyy3000, vyy400, cfa)
new_esEs11(vyy3001, vyy401, ty_@0) → new_esEs9(vyy3001, vyy401)
new_esEs25(vyy3000, vyy400, app(app(app(ty_@3, cfd), cfe), cff)) → new_esEs4(vyy3000, vyy400, cfd, cfe, cff)
new_lt20(vyy900, vyy910, app(app(ty_Either, cha), chb)) → new_lt16(vyy900, vyy910, cha, chb)
new_lt12(vyy901, vyy911, ty_Int) → new_lt8(vyy901, vyy911)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Integer) → new_ltEs12(vyy9000, vyy9100)
new_ltEs19(vyy901, vyy911, app(app(app(ty_@3, che), chf), chg)) → new_ltEs6(vyy901, vyy911, che, chf, chg)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, bab) → new_esEs13(vyy3000, vyy400)
new_esEs22(vyy900, vyy910, app(app(app(ty_@3, fh), ga), gb)) → new_esEs4(vyy900, vyy910, fh, ga, gb)
new_lt11(vyy900, vyy910, app(ty_Ratio, bd)) → new_lt5(vyy900, vyy910, bd)
new_lt12(vyy901, vyy911, app(ty_[], bga)) → new_lt19(vyy901, vyy911, bga)
new_foldFM_GE20(vyy330, vyy331, vyy103, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb) → new_foldFM_GE10(new_eltsFM_GE0(vyy330, vyy331, vyy103, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, ba, bb), h, ba, bb)
new_primCmpInt(Pos(Succ(vyy9000)), Neg(vyy910)) → GT
new_esEs22(vyy900, vyy910, ty_Char) → new_esEs18(vyy900, vyy910)
new_ltEs19(vyy901, vyy911, ty_Integer) → new_ltEs12(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, bab) → new_esEs19(vyy3000, vyy400)
new_lt12(vyy901, vyy911, ty_Char) → new_lt9(vyy901, vyy911)
new_lt16(vyy900, vyy910, gc, gd) → new_esEs8(new_compare17(vyy900, vyy910, gc, gd), LT)
new_esEs21(vyy901, vyy911, app(ty_Maybe, bfh)) → new_esEs7(vyy901, vyy911, bfh)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs22(vyy900, vyy910, ty_Double) → new_esEs13(vyy900, vyy910)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, bbc), bbd), bab) → new_esEs5(vyy3000, vyy400, bbc, bbd)
new_compare19(vyy900, vyy910, fh, ga, gb) → new_compare23(vyy900, vyy910, new_esEs4(vyy900, vyy910, fh, ga, gb), fh, ga, gb)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare110(vyy900, vyy910, True) → LT
new_ltEs19(vyy901, vyy911, ty_Int) → new_ltEs5(vyy901, vyy911)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs9(vyy3000, vyy400)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(app(ty_Either, cch), cda), gd) → new_ltEs7(vyy9000, vyy9100, cch, cda)
new_compare25(vyy900, vyy910, True, ge, gf) → EQ
new_compare110(vyy900, vyy910, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt12(vyy901, vyy911, app(app(ty_Either, bff), bfg)) → new_lt16(vyy901, vyy911, bff, bfg)
new_esEs24(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, ty_Float) → new_esEs20(vyy3001, vyy401)
new_compare4(:(vyy900, vyy901), [], bch) → GT
new_ltEs18(vyy902, vyy912, app(ty_[], bhc)) → new_ltEs17(vyy902, vyy912, bhc)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Integer, gd) → new_ltEs12(vyy9000, vyy9100)
new_lt11(vyy900, vyy910, ty_Float) → new_lt17(vyy900, vyy910)
new_compare210(vyy900, vyy910, True) → EQ
new_esEs10(vyy3002, vyy402, app(app(ty_@2, da), db)) → new_esEs5(vyy3002, vyy402, da, db)
new_esEs12(vyy3000, vyy400, app(app(ty_@2, ff), fg)) → new_esEs5(vyy3000, vyy400, ff, fg)
new_compare28(vyy900, vyy910, app(app(ty_Either, bdg), bdh)) → new_compare17(vyy900, vyy910, bdg, bdh)
new_ltEs4(LT, GT) → True
new_lt12(vyy901, vyy911, ty_Double) → new_lt4(vyy901, vyy911)
new_esEs22(vyy900, vyy910, app(ty_[], beg)) → new_esEs15(vyy900, vyy910, beg)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy9100))) → new_primCmpNat0(Succ(vyy9100), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy9100))) → GT
new_esEs23(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_lt20(vyy900, vyy910, app(app(ty_@2, cgf), cgg)) → new_lt15(vyy900, vyy910, cgf, cgg)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, bac), bab) → new_esEs7(vyy3000, vyy400, bac)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, bab) → new_esEs8(vyy3000, vyy400)
new_compare4([], :(vyy910, vyy911), bch) → LT
new_compare9(vyy900, vyy910) → new_compare210(vyy900, vyy910, new_esEs17(vyy900, vyy910))
new_esEs12(vyy3000, vyy400, ty_Char) → new_esEs18(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, app(ty_Maybe, dc)) → new_esEs7(vyy3001, vyy401, dc)
new_compare15(vyy900, vyy910, False, ge, gf) → GT
new_esEs21(vyy901, vyy911, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs4(vyy901, vyy911, beh, bfa, bfb)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, bab) → new_esEs9(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, app(app(ty_@2, ec), ed)) → new_esEs5(vyy3001, vyy401, ec, ed)
new_esEs12(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs15([], :(vyy400, vyy401), cef) → False
new_esEs15(:(vyy3000, vyy3001), [], cef) → False
new_esEs26(vyy900, vyy910, ty_@0) → new_esEs9(vyy900, vyy910)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(ty_[], cdc), gd) → new_ltEs17(vyy9000, vyy9100, cdc)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, app(ty_Maybe, ceg)) → new_esEs7(vyy3000, vyy400, ceg)
new_esEs23(vyy3001, vyy401, app(ty_Ratio, bhh)) → new_esEs16(vyy3001, vyy401, bhh)
new_esEs22(vyy900, vyy910, app(ty_Ratio, bd)) → new_esEs16(vyy900, vyy910, bd)
new_lt10(vyy900, vyy910) → new_esEs8(new_compare27(vyy900, vyy910), LT)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs10(vyy3002, vyy402, ty_Integer) → new_esEs19(vyy3002, vyy402)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Float) → new_esEs20(vyy3000, vyy400)
new_ltEs4(LT, EQ) → True
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Char) → new_ltEs10(vyy9000, vyy9100)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Char, gd) → new_ltEs10(vyy9000, vyy9100)
new_ltEs9(Just(vyy900), Just(vyy910), app(app(ty_@2, hc), hd)) → new_ltEs8(vyy900, vyy910, hc, hd)
new_esEs12(vyy3000, vyy400, app(app(ty_Either, eh), fa)) → new_esEs6(vyy3000, vyy400, eh, fa)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, app(app(ty_Either, ceb), cec)) → new_ltEs7(vyy9000, vyy9100, ceb, cec)
new_esEs26(vyy900, vyy910, ty_Int) → new_esEs14(vyy900, vyy910)
new_asAs(False, vyy123) → False
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_compare28(vyy900, vyy910, app(ty_Ratio, bdf)) → new_compare7(vyy900, vyy910, bdf)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_ltEs11(vyy90, vyy91) → new_not(new_esEs8(new_compare6(vyy90, vyy91), GT))
new_esEs24(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs15(:(vyy3000, vyy3001), :(vyy400, vyy401), cef) → new_asAs(new_esEs25(vyy3000, vyy400, cef), new_esEs15(vyy3001, vyy401, cef))
new_esEs21(vyy901, vyy911, ty_Ordering) → new_esEs8(vyy901, vyy911)
new_compare4(:(vyy900, vyy901), :(vyy910, vyy911), bch) → new_primCompAux0(vyy900, vyy910, new_compare4(vyy901, vyy911, bch), bch)
new_lt14(vyy900, vyy910, fh, ga, gb) → new_esEs8(new_compare19(vyy900, vyy910, fh, ga, gb), LT)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, app(ty_Ratio, bbh)) → new_esEs16(vyy3000, vyy400, bbh)
new_esEs26(vyy900, vyy910, app(ty_Maybe, chc)) → new_esEs7(vyy900, vyy910, chc)
new_compare28(vyy900, vyy910, ty_Bool) → new_compare9(vyy900, vyy910)
new_compare31(vyy900, vyy910, bc) → new_compare211(vyy900, vyy910, new_esEs7(vyy900, vyy910, bc), bc)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Float, gd) → new_ltEs16(vyy9000, vyy9100)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Integer) → new_ltEs12(vyy900, vyy910)
new_compare8(vyy900, vyy910) → new_compare26(vyy900, vyy910, new_esEs8(vyy900, vyy910))
new_ltEs18(vyy902, vyy912, app(app(ty_@2, bge), bgf)) → new_ltEs8(vyy902, vyy912, bge, bgf)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_compare28(vyy900, vyy910, ty_Char) → new_compare18(vyy900, vyy910)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Int) → new_ltEs5(vyy900, vyy910)
new_ltEs5(vyy90, vyy91) → new_not(new_esEs8(new_compare12(vyy90, vyy91), GT))
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Double) → new_ltEs11(vyy9000, vyy9100)
new_ltEs19(vyy901, vyy911, ty_@0) → new_ltEs14(vyy901, vyy911)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs21(vyy901, vyy911, app(ty_Ratio, bfe)) → new_esEs16(vyy901, vyy911, bfe)
new_esEs26(vyy900, vyy910, app(ty_[], chd)) → new_esEs15(vyy900, vyy910, chd)
new_compare7(:%(vyy900, vyy901), :%(vyy910, vyy911), ty_Int) → new_compare12(new_sr(vyy900, vyy911), new_sr(vyy910, vyy901))
new_esEs14(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, dbb)) → new_esEs16(vyy3000, vyy400, dbb)
new_esEs13(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs7(Left(vyy9000), Left(vyy9100), app(ty_Maybe, cdb), gd) → new_ltEs9(vyy9000, vyy9100, cdb)
new_ltEs4(LT, LT) → True
new_esEs25(vyy3000, vyy400, app(app(ty_@2, cfg), cfh)) → new_esEs5(vyy3000, vyy400, cfg, cfh)
new_esEs26(vyy900, vyy910, ty_Bool) → new_esEs17(vyy900, vyy910)
new_ltEs18(vyy902, vyy912, ty_Float) → new_ltEs16(vyy902, vyy912)
new_esEs21(vyy901, vyy911, ty_@0) → new_esEs9(vyy901, vyy911)
new_compare18(Char(vyy900), Char(vyy910)) → new_primCmpNat0(vyy900, vyy910)
new_esEs22(vyy900, vyy910, app(app(ty_Either, gc), gd)) → new_esEs6(vyy900, vyy910, gc, gd)
new_compare14(vyy900, vyy910, True, gc, gd) → LT
new_lt11(vyy900, vyy910, ty_Bool) → new_lt7(vyy900, vyy910)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, dbh), dca)) → new_esEs5(vyy3000, vyy400, dbh, dca)
new_esEs26(vyy900, vyy910, ty_Float) → new_esEs20(vyy900, vyy910)
new_lt11(vyy900, vyy910, ty_Int) → new_lt8(vyy900, vyy910)
new_esEs10(vyy3002, vyy402, ty_Float) → new_esEs20(vyy3002, vyy402)
new_esEs26(vyy900, vyy910, ty_Char) → new_esEs18(vyy900, vyy910)
new_esEs22(vyy900, vyy910, ty_Int) → new_esEs14(vyy900, vyy910)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs14(vyy3000, vyy400)
new_lt12(vyy901, vyy911, ty_Float) → new_lt17(vyy901, vyy911)
new_esEs10(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_esEs26(vyy900, vyy910, app(app(ty_Either, cha), chb)) → new_esEs6(vyy900, vyy910, cha, chb)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Int) → new_ltEs5(vyy9000, vyy9100)
new_ltEs18(vyy902, vyy912, ty_Bool) → new_ltEs15(vyy902, vyy912)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_asAs(True, vyy123) → vyy123
new_esEs22(vyy900, vyy910, ty_@0) → new_esEs9(vyy900, vyy910)
new_compare27(@0, @0) → EQ
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_compare28(vyy900, vyy910, ty_Int) → new_compare12(vyy900, vyy910)
new_esEs10(vyy3002, vyy402, app(app(ty_Either, cc), cd)) → new_esEs6(vyy3002, vyy402, cc, cd)
new_esEs16(:%(vyy3000, vyy3001), :%(vyy400, vyy401), dce) → new_asAs(new_esEs28(vyy3000, vyy400, dce), new_esEs27(vyy3001, vyy401, dce))
new_esEs11(vyy3001, vyy401, app(ty_Ratio, de)) → new_esEs16(vyy3001, vyy401, de)
new_esEs12(vyy3000, vyy400, app(ty_Ratio, eg)) → new_esEs16(vyy3000, vyy400, eg)
new_lt12(vyy901, vyy911, app(app(app(ty_@3, beh), bfa), bfb)) → new_lt14(vyy901, vyy911, beh, bfa, bfb)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Float) → new_ltEs16(vyy9000, vyy9100)
new_compare10(vyy900, vyy910, True) → LT
new_ltEs4(GT, GT) → True
new_esEs20(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt20(vyy900, vyy910, ty_Double) → new_lt4(vyy900, vyy910)
new_lt17(vyy900, vyy910) → new_esEs8(new_compare30(vyy900, vyy910), LT)
new_lt12(vyy901, vyy911, ty_Bool) → new_lt7(vyy901, vyy911)
new_compare13(vyy900, vyy910, True, fh, ga, gb) → LT
new_esEs24(vyy3000, vyy400, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs4(vyy3000, vyy400, cbe, cbf, cbg)
new_ltEs10(vyy90, vyy91) → new_not(new_esEs8(new_compare18(vyy90, vyy91), GT))
new_compare10(vyy900, vyy910, False) → GT
new_primCompAux00(vyy160, GT) → GT
new_ltEs18(vyy902, vyy912, ty_Integer) → new_ltEs12(vyy902, vyy912)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare28(vyy900, vyy910, app(app(app(ty_@3, bda), bdb), bdc)) → new_compare19(vyy900, vyy910, bda, bdb, bdc)
new_esEs24(vyy3000, vyy400, app(ty_[], cba)) → new_esEs15(vyy3000, vyy400, cba)
new_foldFM_GE0(vyy78, vyy40, EmptyFM, h, ba, bb) → vyy78
new_esEs24(vyy3000, vyy400, ty_Char) → new_esEs18(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs10(vyy3002, vyy402, ty_Bool) → new_esEs17(vyy3002, vyy402)
new_lt18(vyy900, vyy910, bc) → new_esEs8(new_compare31(vyy900, vyy910, bc), LT)
new_lt13(vyy900, vyy910) → new_esEs8(new_compare29(vyy900, vyy910), LT)
new_esEs22(vyy900, vyy910, app(ty_Maybe, bc)) → new_esEs7(vyy900, vyy910, bc)
new_esEs4(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), be, bf, bg) → new_asAs(new_esEs12(vyy3000, vyy400, be), new_asAs(new_esEs11(vyy3001, vyy401, bf), new_esEs10(vyy3002, vyy402, bg)))
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_@0) → new_ltEs14(vyy9000, vyy9100)
new_primCmpInt(Neg(Succ(vyy9000)), Pos(vyy910)) → LT
new_not(True) → False

The set Q consists of the following terms:

new_compare25(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Float)
new_compare18(Char(x0), Char(x1))
new_esEs10(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_compare29(Integer(x0), Integer(x1))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt18(x0, x1, x2)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_asAs(True, x0)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_lt12(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_compare4(:(x0, x1), [], x2)
new_ltEs15(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Integer)
new_compare28(x0, x1, ty_Char)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(True, x0)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt19(x0, x1, x2)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Bool)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs15(False, False)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Char)
new_foldFM_GE0(x0, x1, EmptyFM, x2, x3, x4)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Ordering)
new_esEs8(LT, LT)
new_lt12(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1)
new_esEs17(False, False)
new_sr(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1)
new_esEs12(x0, x1, ty_Double)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, True)
new_esEs23(x0, x1, ty_Integer)
new_compare24(x0, x1, False, x2, x3)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Bool)
new_compare28(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_asAs(False, x0)
new_compare6(Double(x0, x1), Double(x2, x3))
new_esEs23(x0, x1, ty_Char)
new_esEs15([], [], x0)
new_compare210(x0, x1, True)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Zero)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare4([], :(x0, x1), x2)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_lt11(x0, x1, app(ty_[], x2))
new_ltEs9(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_Int)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False)
new_compare28(x0, x1, ty_Double)
new_sr0(Integer(x0), Integer(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_compare211(x0, x1, False, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(ty_[], x2))
new_compare12(x0, x1)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(GT, GT)
new_esEs25(x0, x1, ty_Bool)
new_esEs14(x0, x1)
new_compare28(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primPlusNat1(Succ(x0), Succ(x1))
new_lt13(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primCmpNat0(Succ(x0), Zero)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs19(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(x0, x1, ty_Int)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Char)
new_compare10(x0, x1, False)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Char)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_lt11(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs11(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Double)
new_compare11(x0, x1, False, x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, ty_@0)
new_compare13(x0, x1, True, x2, x3, x4)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs18(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt11(x0, x1, ty_Double)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, False, x2, x3, x4)
new_primPlusNat1(Zero, Zero)
new_lt12(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpNat0(Zero, Succ(x0))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_@0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare14(x0, x1, False, x2, x3)
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs4(EQ, EQ)
new_primCompAux00(x0, LT)
new_esEs24(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Ordering)
new_esEs11(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare16(x0, x1, x2, x3)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(EQ, LT)
new_esEs27(x0, x1, ty_Int)
new_ltEs4(LT, EQ)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs15(True, False)
new_ltEs15(False, True)
new_esEs11(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs15(:(x0, x1), [], x2)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(x0, x1, app(ty_[], x2))
new_lt15(x0, x1, x2, x3)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_compare110(x0, x1, True)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs12(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_compare8(x0, x1)
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs12(x0, x1, ty_Float)
new_compare211(x0, x1, True, x2)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_lt14(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs18(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_compare15(x0, x1, False, x2, x3)
new_ltEs4(LT, LT)
new_compare110(x0, x1, False)
new_esEs10(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_GE10(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, True, x11, x12, x13)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs11(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Bool)
new_ltEs17(x0, x1, x2)
new_foldFM_GE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs22(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt12(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, ty_@0)
new_esEs9(@0, @0)
new_gtEs(x0, x1, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_Char)
new_compare14(x0, x1, True, x2, x3)
new_primEqNat0(Zero, Succ(x0))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_GE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_lt11(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Ordering)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare30(Float(x0, x1), Float(x2, x3))
new_lt12(x0, x1, ty_Int)
new_primPlusNat0(Zero, x0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Zero, Zero)
new_esEs10(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, ty_Int)
new_lt16(x0, x1, x2, x3)
new_esEs22(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_@0)
new_compare17(x0, x1, x2, x3)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Integer)
new_lt4(x0, x1)
new_esEs7(Nothing, Just(x0), x1)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_lt17(x0, x1)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0)
new_esEs12(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt12(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs11(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Double)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_primCompAux0(x0, x1, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare28(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_compare25(x0, x1, True, x2, x3)
new_esEs10(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2, x3, x4)
new_compare23(x0, x1, True, x2, x3, x4)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Ordering)
new_esEs20(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_lt11(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Float)
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, ty_Int)
new_lt11(x0, x1, ty_Int)
new_esEs7(Nothing, Nothing, x0)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_eltsFM_GE0(x0, x1, x2, x3, x4, x5)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_not(True)
new_lt11(x0, x1, ty_Char)
new_lt6(x0, x1)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt7(x0, x1)
new_not(False)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_foldFM_GE3(x0, x1, x2, x3, x4, x5, x6)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs12(x0, x1, ty_Int)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(x0, x1, False, x2, x3, x4)
new_compare26(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(x0, x1, ty_Integer)
new_lt11(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, ty_@0)
new_compare26(x0, x1, False)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs24(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_ltEs9(Nothing, Just(x0), x1)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_compare28(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Double)
new_ltEs12(x0, x1)
new_esEs24(x0, x1, ty_Double)
new_esEs7(Just(x0), Nothing, x1)
new_ltEs5(x0, x1)
new_foldFM_GE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs15([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_Int)
new_compare9(x0, x1)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17(True, False)
new_esEs17(False, True)
new_lt11(x0, x1, ty_Integer)
new_compare27(@0, @0)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_lt5(x0, x1, x2)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), :(x2, x3), x4)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Bool)
new_ltEs16(x0, x1)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Zero)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare4([], [], x0)
new_esEs17(True, True)
new_esEs22(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_ltEs14(x0, x1)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs19(Integer(x0), Integer(x1))
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_lt8(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True, x2)
new_esEs25(x0, x1, ty_Float)
new_compare31(x0, x1, x2)
new_foldFM_GE10(x0, x1, x2, x3, x4, EmptyFM, x5, True, x6, x7, x8)
new_ltEs13(x0, x1, x2)
new_lt10(x0, x1)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)

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

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



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

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

new_foldFM_GE21(vyy170, vyy171, vyy101, vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb) → new_foldFM_GE11(new_eltsFM_GE0(vyy170, vyy171, vyy101, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, new_gtEs0(vyy1730, vyy13, ba, bb), h, ba, bb)
new_foldFM_GE11(vyy77, vyy13, vyy170, vyy171, vyy172, Branch(vyy1730, vyy1731, vyy1732, vyy1733, vyy1734), vyy174, True, h, ba, bb) → new_foldFM_GE4(vyy77, vyy13, vyy174, h, ba, bb)
new_foldFM_GE11(vyy77, vyy13, vyy170, vyy171, vyy172, Branch(vyy1730, vyy1731, vyy1732, vyy1733, vyy1734), vyy174, True, h, ba, bb) → new_foldFM_GE21(vyy170, vyy171, new_foldFM_GE5(vyy77, vyy13, vyy174, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb)
new_foldFM_GE4(vyy77, vyy13, Branch(vyy1740, vyy1741, vyy1742, vyy1743, vyy1744), h, ba, bb) → new_foldFM_GE11(vyy77, vyy13, vyy1740, vyy1741, vyy1742, vyy1743, vyy1744, new_gtEs0(vyy1740, vyy13, ba, bb), h, ba, bb)
new_foldFM_GE11(vyy77, vyy13, vyy170, vyy171, vyy172, vyy173, Branch(vyy1740, vyy1741, vyy1742, vyy1743, vyy1744), False, h, ba, bb) → new_foldFM_GE11(vyy77, vyy13, vyy1740, vyy1741, vyy1742, vyy1743, vyy1744, new_gtEs0(vyy1740, vyy13, ba, bb), h, ba, bb)
new_foldFM_GE11(vyy77, vyy13, vyy170, vyy171, vyy172, EmptyFM, vyy174, True, h, ba, bb) → new_foldFM_GE4(vyy77, vyy13, vyy174, h, ba, bb)

The TRS R consists of the following rules:

new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, dah)) → new_esEs7(vyy3000, vyy400, dah)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], dba)) → new_esEs15(vyy3000, vyy400, dba)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_@0, gd) → new_ltEs14(vyy9000, vyy9100)
new_esEs18(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_ltEs15(True, False) → False
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, app(ty_Maybe, ced)) → new_ltEs9(vyy9000, vyy9100, ced)
new_esEs10(vyy3002, vyy402, app(app(app(ty_@3, ce), cf), cg)) → new_esEs4(vyy3002, vyy402, ce, cf, cg)
new_ltEs4(EQ, GT) → True
new_esEs23(vyy3001, vyy401, ty_Float) → new_esEs20(vyy3001, vyy401)
new_ltEs14(vyy90, vyy91) → new_not(new_esEs8(new_compare27(vyy90, vyy91), GT))
new_esEs23(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_compare15(vyy900, vyy910, True, ge, gf) → LT
new_compare24(vyy900, vyy910, False, gc, gd) → new_compare14(vyy900, vyy910, new_ltEs7(vyy900, vyy910, gc, gd), gc, gd)
new_ltEs9(Nothing, Just(vyy910), gg) → True
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_ltEs19(vyy901, vyy911, ty_Double) → new_ltEs11(vyy901, vyy911)
new_ltEs9(Just(vyy900), Just(vyy910), app(ty_Ratio, he)) → new_ltEs13(vyy900, vyy910, he)
new_esEs21(vyy901, vyy911, ty_Int) → new_esEs14(vyy901, vyy911)
new_foldFM_GE12(vyy77, vyy13, vyy170, vyy171, vyy172, Branch(vyy1730, vyy1731, vyy1732, vyy1733, vyy1734), vyy174, True, h, ba, bb) → new_foldFM_GE22(vyy170, vyy171, new_foldFM_GE5(vyy77, vyy13, vyy174, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, dbc), dbd)) → new_esEs6(vyy3000, vyy400, dbc, dbd)
new_ltEs7(Left(vyy9000), Right(vyy9100), gc, gd) → True
new_primMulNat0(Zero, Zero) → Zero
new_compare13(vyy900, vyy910, False, fh, ga, gb) → GT
new_foldFM_GE22(vyy170, vyy171, vyy101, vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb) → new_foldFM_GE12(new_eltsFM_GE0(vyy170, vyy171, vyy101, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, new_gtEs0(vyy1730, vyy13, ba, bb), h, ba, bb)
new_esEs25(vyy3000, vyy400, app(app(ty_Either, cfb), cfc)) → new_esEs6(vyy3000, vyy400, cfb, cfc)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(app(ty_@2, cce), ccf), gd) → new_ltEs8(vyy9000, vyy9100, cce, ccf)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, bae), bab) → new_esEs16(vyy3000, vyy400, bae)
new_esEs21(vyy901, vyy911, ty_Bool) → new_esEs17(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bah), bba), bbb), bab) → new_esEs4(vyy3000, vyy400, bah, bba, bbb)
new_esEs21(vyy901, vyy911, app(ty_[], bga)) → new_esEs15(vyy901, vyy911, bga)
new_lt12(vyy901, vyy911, app(ty_Ratio, bfe)) → new_lt5(vyy901, vyy911, bfe)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, app(app(ty_@2, cdg), cdh)) → new_ltEs8(vyy9000, vyy9100, cdg, cdh)
new_esEs25(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_lt12(vyy901, vyy911, ty_Integer) → new_lt13(vyy901, vyy911)
new_esEs23(vyy3001, vyy401, ty_@0) → new_esEs9(vyy3001, vyy401)
new_compare25(vyy900, vyy910, False, ge, gf) → new_compare15(vyy900, vyy910, new_ltEs8(vyy900, vyy910, ge, gf), ge, gf)
new_esEs21(vyy901, vyy911, ty_Integer) → new_esEs19(vyy901, vyy911)
new_esEs12(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs17(True, True) → True
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs20(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs22(vyy900, vyy910, app(app(ty_@2, ge), gf)) → new_esEs5(vyy900, vyy910, ge, gf)
new_esEs24(vyy3000, vyy400, app(app(ty_@2, cbh), cca)) → new_esEs5(vyy3000, vyy400, cbh, cca)
new_compare28(vyy900, vyy910, ty_Ordering) → new_compare8(vyy900, vyy910)
new_esEs23(vyy3001, vyy401, ty_Double) → new_esEs13(vyy3001, vyy401)
new_compare28(vyy900, vyy910, app(ty_[], beb)) → new_compare4(vyy900, vyy910, beb)
new_esEs10(vyy3002, vyy402, app(ty_[], ca)) → new_esEs15(vyy3002, vyy402, ca)
new_ltEs9(Just(vyy900), Just(vyy910), ty_@0) → new_ltEs14(vyy900, vyy910)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, bab) → new_esEs14(vyy3000, vyy400)
new_esEs12(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs21(vyy901, vyy911, app(app(ty_Either, bff), bfg)) → new_esEs6(vyy901, vyy911, bff, bfg)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, bab) → new_esEs17(vyy3000, vyy400)
new_ltEs16(vyy90, vyy91) → new_not(new_esEs8(new_compare30(vyy90, vyy91), GT))
new_esEs22(vyy900, vyy910, ty_Float) → new_esEs20(vyy900, vyy910)
new_lt20(vyy900, vyy910, ty_Float) → new_lt17(vyy900, vyy910)
new_esEs12(vyy3000, vyy400, app(ty_[], ef)) → new_esEs15(vyy3000, vyy400, ef)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Double) → new_ltEs11(vyy900, vyy910)
new_ltEs19(vyy901, vyy911, app(app(ty_@2, chh), daa)) → new_ltEs8(vyy901, vyy911, chh, daa)
new_ltEs19(vyy901, vyy911, ty_Float) → new_ltEs16(vyy901, vyy911)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, app(ty_[], cee)) → new_ltEs17(vyy9000, vyy9100, cee)
new_pePe(False, vyy150) → vyy150
new_ltEs15(True, True) → True
new_ltEs17(vyy90, vyy91, bch) → new_not(new_esEs8(new_compare4(vyy90, vyy91, bch), GT))
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, bab) → new_esEs18(vyy3000, vyy400)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, app(ty_Ratio, cea)) → new_ltEs13(vyy9000, vyy9100, cea)
new_lt6(vyy900, vyy910) → new_esEs8(new_compare8(vyy900, vyy910), LT)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, app(app(app(ty_@3, cdd), cde), cdf)) → new_ltEs6(vyy9000, vyy9100, cdd, cde, cdf)
new_ltEs15(False, True) → True
new_esEs24(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs10(vyy3002, vyy402, app(ty_Maybe, bh)) → new_esEs7(vyy3002, vyy402, bh)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Bool) → new_ltEs15(vyy9000, vyy9100)
new_esEs24(vyy3000, vyy400, app(ty_Maybe, cah)) → new_esEs7(vyy3000, vyy400, cah)
new_lt9(vyy900, vyy910) → new_esEs8(new_compare18(vyy900, vyy910), LT)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(app(app(ty_@3, ccb), ccc), ccd), gd) → new_ltEs6(vyy9000, vyy9100, ccb, ccc, ccd)
new_esEs23(vyy3001, vyy401, app(ty_Maybe, bhf)) → new_esEs7(vyy3001, vyy401, bhf)
new_lt15(vyy900, vyy910, ge, gf) → new_esEs8(new_compare16(vyy900, vyy910, ge, gf), LT)
new_compare23(vyy900, vyy910, True, fh, ga, gb) → EQ
new_ltEs9(Just(vyy900), Just(vyy910), ty_Float) → new_ltEs16(vyy900, vyy910)
new_lt8(vyy900, vyy910) → new_esEs8(new_compare12(vyy900, vyy910), LT)
new_esEs22(vyy900, vyy910, ty_Ordering) → new_esEs8(vyy900, vyy910)
new_esEs11(vyy3001, vyy401, app(ty_[], dd)) → new_esEs15(vyy3001, vyy401, dd)
new_compare6(Double(vyy900, vyy901), Double(vyy910, vyy911)) → new_compare12(new_sr(vyy900, vyy910), new_sr(vyy901, vyy911))
new_lt11(vyy900, vyy910, app(app(ty_Either, gc), gd)) → new_lt16(vyy900, vyy910, gc, gd)
new_esEs12(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_ltEs15(False, False) → True
new_ltEs12(vyy90, vyy91) → new_not(new_esEs8(new_compare29(vyy90, vyy91), GT))
new_compare28(vyy900, vyy910, ty_Double) → new_compare6(vyy900, vyy910)
new_lt12(vyy901, vyy911, app(ty_Maybe, bfh)) → new_lt18(vyy901, vyy911, bfh)
new_primCmpNat0(Zero, Succ(vyy9100)) → LT
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Int) → new_esEs14(vyy3000, vyy400)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(ty_Ratio, ccg), gd) → new_ltEs13(vyy9000, vyy9100, ccg)
new_esEs11(vyy3001, vyy401, ty_Char) → new_esEs18(vyy3001, vyy401)
new_lt20(vyy900, vyy910, ty_Ordering) → new_lt6(vyy900, vyy910)
new_lt20(vyy900, vyy910, app(app(app(ty_@3, cgc), cgd), cge)) → new_lt14(vyy900, vyy910, cgc, cgd, cge)
new_gtEs0(vyy1730, vyy13, ba, bb) → new_not(new_esEs8(new_compare24(vyy1730, Left(vyy13), new_esEs6(vyy1730, Left(vyy13), ba, bb), ba, bb), LT))
new_lt19(vyy900, vyy910, beg) → new_esEs8(new_compare4(vyy900, vyy910, beg), LT)
new_lt11(vyy900, vyy910, app(app(ty_@2, ge), gf)) → new_lt15(vyy900, vyy910, ge, gf)
new_esEs6(Left(vyy3000), Right(vyy400), bbe, bab) → False
new_esEs6(Right(vyy3000), Left(vyy400), bbe, bab) → False
new_esEs8(LT, LT) → True
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, bab) → new_esEs20(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Char) → new_esEs18(vyy3001, vyy401)
new_esEs23(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_pePe(True, vyy150) → True
new_compare14(vyy900, vyy910, False, gc, gd) → GT
new_primEqNat0(Zero, Zero) → True
new_compare26(vyy900, vyy910, True) → EQ
new_compare11(vyy900, vyy910, True, bc) → LT
new_esEs23(vyy3001, vyy401, app(app(ty_Either, caa), cab)) → new_esEs6(vyy3001, vyy401, caa, cab)
new_compare28(vyy900, vyy910, ty_Integer) → new_compare29(vyy900, vyy910)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs4(vyy3000, vyy400, bcc, bcd, bce)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, app(app(ty_Either, bca), bcb)) → new_esEs6(vyy3000, vyy400, bca, bcb)
new_lt20(vyy900, vyy910, ty_Bool) → new_lt7(vyy900, vyy910)
new_esEs17(False, False) → True
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Char) → new_esEs18(vyy3000, vyy400)
new_foldFM_GE12(vyy77, vyy13, vyy170, vyy171, vyy172, EmptyFM, vyy174, True, h, ba, bb) → new_foldFM_GE30(vyy170, vyy171, new_foldFM_GE5(vyy77, vyy13, vyy174, h, ba, bb), vyy13, h, ba, bb)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, app(ty_[], bbg)) → new_esEs15(vyy3000, vyy400, bbg)
new_ltEs18(vyy902, vyy912, ty_Int) → new_ltEs5(vyy902, vyy912)
new_ltEs18(vyy902, vyy912, ty_Char) → new_ltEs10(vyy902, vyy912)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs24(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_compare211(vyy900, vyy910, False, bc) → new_compare11(vyy900, vyy910, new_ltEs9(vyy900, vyy910, bc), bc)
new_primCompAux0(vyy900, vyy910, vyy151, bch) → new_primCompAux00(vyy151, new_compare28(vyy900, vyy910, bch))
new_esEs25(vyy3000, vyy400, app(ty_[], ceh)) → new_esEs15(vyy3000, vyy400, ceh)
new_esEs23(vyy3001, vyy401, app(ty_[], bhg)) → new_esEs15(vyy3001, vyy401, bhg)
new_compare7(:%(vyy900, vyy901), :%(vyy910, vyy911), ty_Integer) → new_compare29(new_sr0(vyy900, vyy911), new_sr0(vyy910, vyy901))
new_esEs25(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, ty_Double) → new_esEs13(vyy3001, vyy401)
new_esEs10(vyy3002, vyy402, ty_Int) → new_esEs14(vyy3002, vyy402)
new_esEs26(vyy900, vyy910, ty_Ordering) → new_esEs8(vyy900, vyy910)
new_lt11(vyy900, vyy910, ty_@0) → new_lt10(vyy900, vyy910)
new_ltEs19(vyy901, vyy911, ty_Char) → new_ltEs10(vyy901, vyy911)
new_esEs12(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(vyy1340), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1340, vyy40100)))
new_compare4([], [], bch) → EQ
new_esEs11(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs10(vyy3002, vyy402, ty_Double) → new_esEs13(vyy3002, vyy402)
new_ltEs9(Just(vyy900), Just(vyy910), app(ty_[], baa)) → new_ltEs17(vyy900, vyy910, baa)
new_ltEs19(vyy901, vyy911, ty_Bool) → new_ltEs15(vyy901, vyy911)
new_esEs26(vyy900, vyy910, app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs4(vyy900, vyy910, cgc, cgd, cge)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs19(vyy901, vyy911, app(ty_Maybe, dae)) → new_ltEs9(vyy901, vyy911, dae)
new_compare16(vyy900, vyy910, ge, gf) → new_compare25(vyy900, vyy910, new_esEs5(vyy900, vyy910, ge, gf), ge, gf)
new_esEs11(vyy3001, vyy401, app(app(app(ty_@3, dh), ea), eb)) → new_esEs4(vyy3001, vyy401, dh, ea, eb)
new_compare211(vyy900, vyy910, True, bc) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs24(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs18(vyy902, vyy912, app(app(ty_Either, bgh), bha)) → new_ltEs7(vyy902, vyy912, bgh, bha)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy13400), Zero) → Succ(vyy13400)
new_esEs10(vyy3002, vyy402, ty_@0) → new_esEs9(vyy3002, vyy402)
new_esEs25(vyy3000, vyy400, ty_Char) → new_esEs18(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs11(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_lt20(vyy900, vyy910, app(ty_Maybe, chc)) → new_lt18(vyy900, vyy910, chc)
new_ltEs7(Right(vyy9000), Left(vyy9100), gc, gd) → False
new_esEs26(vyy900, vyy910, ty_Integer) → new_esEs19(vyy900, vyy910)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Bool, gd) → new_ltEs15(vyy9000, vyy9100)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs9(Just(vyy900), Just(vyy910), app(app(ty_Either, hf), hg)) → new_ltEs7(vyy900, vyy910, hf, hg)
new_ltEs19(vyy901, vyy911, ty_Ordering) → new_ltEs4(vyy901, vyy911)
new_ltEs6(@3(vyy900, vyy901, vyy902), @3(vyy910, vyy911, vyy912), bed, bee, bef) → new_pePe(new_lt11(vyy900, vyy910, bed), new_asAs(new_esEs22(vyy900, vyy910, bed), new_pePe(new_lt12(vyy901, vyy911, bee), new_asAs(new_esEs21(vyy901, vyy911, bee), new_ltEs18(vyy902, vyy912, bef)))))
new_lt11(vyy900, vyy910, ty_Char) → new_lt9(vyy900, vyy910)
new_ltEs18(vyy902, vyy912, ty_@0) → new_ltEs14(vyy902, vyy912)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Double) → new_esEs13(vyy3000, vyy400)
new_compare29(Integer(vyy900), Integer(vyy910)) → new_primCmpInt(vyy900, vyy910)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_esEs8(EQ, EQ) → True
new_esEs22(vyy900, vyy910, ty_Integer) → new_esEs19(vyy900, vyy910)
new_lt20(vyy900, vyy910, ty_@0) → new_lt10(vyy900, vyy910)
new_compare26(vyy900, vyy910, False) → new_compare10(vyy900, vyy910, new_ltEs4(vyy900, vyy910))
new_esEs23(vyy3001, vyy401, app(app(app(ty_@3, cac), cad), cae)) → new_esEs4(vyy3001, vyy401, cac, cad, cae)
new_compare24(vyy900, vyy910, True, gc, gd) → EQ
new_esEs11(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_lt11(vyy900, vyy910, app(ty_[], beg)) → new_lt19(vyy900, vyy910, beg)
new_compare28(vyy900, vyy910, app(ty_Maybe, bea)) → new_compare31(vyy900, vyy910, bea)
new_lt11(vyy900, vyy910, ty_Ordering) → new_lt6(vyy900, vyy910)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs18(vyy902, vyy912, ty_Ordering) → new_ltEs4(vyy902, vyy912)
new_ltEs4(EQ, LT) → False
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs12(vyy3000, vyy400, app(ty_Maybe, ee)) → new_esEs7(vyy3000, vyy400, ee)
new_ltEs8(@2(vyy900, vyy901), @2(vyy910, vyy911), cga, cgb) → new_pePe(new_lt20(vyy900, vyy910, cga), new_asAs(new_esEs26(vyy900, vyy910, cga), new_ltEs19(vyy901, vyy911, cgb)))
new_lt20(vyy900, vyy910, ty_Int) → new_lt8(vyy900, vyy910)
new_primCmpNat0(Succ(vyy9000), Succ(vyy9100)) → new_primCmpNat0(vyy9000, vyy9100)
new_lt20(vyy900, vyy910, ty_Integer) → new_lt13(vyy900, vyy910)
new_compare11(vyy900, vyy910, False, bc) → GT
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare30(Float(vyy900, vyy901), Float(vyy910, vyy911)) → new_compare12(new_sr(vyy900, vyy910), new_sr(vyy901, vyy911))
new_lt5(vyy900, vyy910, bd) → new_esEs8(new_compare7(vyy900, vyy910, bd), LT)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs18(vyy3000, vyy400)
new_esEs24(vyy3000, vyy400, app(ty_Ratio, cbb)) → new_esEs16(vyy3000, vyy400, cbb)
new_esEs21(vyy901, vyy911, ty_Float) → new_esEs20(vyy901, vyy911)
new_ltEs18(vyy902, vyy912, app(ty_Maybe, bhb)) → new_ltEs9(vyy902, vyy912, bhb)
new_lt11(vyy900, vyy910, ty_Integer) → new_lt13(vyy900, vyy910)
new_compare28(vyy900, vyy910, ty_Float) → new_compare30(vyy900, vyy910)
new_compare23(vyy900, vyy910, False, fh, ga, gb) → new_compare13(vyy900, vyy910, new_ltEs6(vyy900, vyy910, fh, ga, gb), fh, ga, gb)
new_lt11(vyy900, vyy910, app(ty_Maybe, bc)) → new_lt18(vyy900, vyy910, bc)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_esEs5(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bhd, bhe) → new_asAs(new_esEs24(vyy3000, vyy400, bhd), new_esEs23(vyy3001, vyy401, bhe))
new_lt11(vyy900, vyy910, app(app(app(ty_@3, fh), ga), gb)) → new_lt14(vyy900, vyy910, fh, ga, gb)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, app(app(ty_@2, bcf), bcg)) → new_esEs5(vyy3000, vyy400, bcf, bcg)
new_esEs10(vyy3002, vyy402, app(ty_Ratio, cb)) → new_esEs16(vyy3002, vyy402, cb)
new_lt12(vyy901, vyy911, ty_Ordering) → new_lt6(vyy901, vyy911)
new_esEs9(@0, @0) → True
new_primCompAux00(vyy160, LT) → LT
new_ltEs4(GT, EQ) → False
new_compare210(vyy900, vyy910, False) → new_compare110(vyy900, vyy910, new_ltEs15(vyy900, vyy910))
new_esEs11(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_primCmpInt(Neg(Succ(vyy9000)), Neg(vyy910)) → new_primCmpNat0(vyy910, Succ(vyy9000))
new_ltEs19(vyy901, vyy911, app(app(ty_Either, dac), dad)) → new_ltEs7(vyy901, vyy911, dac, dad)
new_ltEs19(vyy901, vyy911, app(ty_[], daf)) → new_ltEs17(vyy901, vyy911, daf)
new_esEs24(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt7(vyy900, vyy910) → new_esEs8(new_compare9(vyy900, vyy910), LT)
new_ltEs18(vyy902, vyy912, ty_Double) → new_ltEs11(vyy902, vyy912)
new_esEs7(Nothing, Nothing, dag) → True
new_esEs15([], [], cef) → True
new_ltEs9(Just(vyy900), Just(vyy910), app(app(app(ty_@3, gh), ha), hb)) → new_ltEs6(vyy900, vyy910, gh, ha, hb)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_lt20(vyy900, vyy910, app(ty_Ratio, cgh)) → new_lt5(vyy900, vyy910, cgh)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Double, gd) → new_ltEs11(vyy9000, vyy9100)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Char) → new_ltEs10(vyy900, vyy910)
new_lt4(vyy900, vyy910) → new_esEs8(new_compare6(vyy900, vyy910), LT)
new_ltEs4(EQ, EQ) → True
new_compare28(vyy900, vyy910, ty_@0) → new_compare27(vyy900, vyy910)
new_compare28(vyy900, vyy910, app(app(ty_@2, bdd), bde)) → new_compare16(vyy900, vyy910, bdd, bde)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Bool) → new_ltEs15(vyy900, vyy910)
new_primCmpNat0(Zero, Zero) → EQ
new_compare17(vyy900, vyy910, gc, gd) → new_compare24(vyy900, vyy910, new_esEs6(vyy900, vyy910, gc, gd), gc, gd)
new_lt12(vyy901, vyy911, ty_@0) → new_lt10(vyy901, vyy911)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, app(ty_Maybe, bbf)) → new_esEs7(vyy3000, vyy400, bbf)
new_primCmpNat0(Succ(vyy9000), Zero) → GT
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Ordering) → new_ltEs4(vyy9000, vyy9100)
new_esEs23(vyy3001, vyy401, app(app(ty_@2, caf), cag)) → new_esEs5(vyy3001, vyy401, caf, cag)
new_ltEs9(Just(vyy900), Just(vyy910), app(ty_Maybe, hh)) → new_ltEs9(vyy900, vyy910, hh)
new_ltEs19(vyy901, vyy911, app(ty_Ratio, dab)) → new_ltEs13(vyy901, vyy911, dab)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy9100))) → LT
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_ltEs4(GT, LT) → False
new_esEs21(vyy901, vyy911, ty_Double) → new_esEs13(vyy901, vyy911)
new_sr0(Integer(vyy9000), Integer(vyy9110)) → Integer(new_primMulInt(vyy9000, vyy9110))
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs4(vyy3000, vyy400, dbe, dbf, dbg)
new_primPlusNat1(Succ(vyy13400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy13400, vyy401000)))
new_ltEs13(vyy90, vyy91, bec) → new_not(new_esEs8(new_compare7(vyy90, vyy91, bec), GT))
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_esEs10(vyy3002, vyy402, ty_Char) → new_esEs18(vyy3002, vyy402)
new_lt20(vyy900, vyy910, app(ty_[], chd)) → new_lt19(vyy900, vyy910, chd)
new_esEs26(vyy900, vyy910, ty_Double) → new_esEs13(vyy900, vyy910)
new_esEs7(Nothing, Just(vyy400), dag) → False
new_esEs7(Just(vyy3000), Nothing, dag) → False
new_esEs24(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_lt11(vyy900, vyy910, ty_Double) → new_lt4(vyy900, vyy910)
new_esEs26(vyy900, vyy910, app(ty_Ratio, cgh)) → new_esEs16(vyy900, vyy910, cgh)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Ordering, gd) → new_ltEs4(vyy9000, vyy9100)
new_compare12(vyy90, vyy91) → new_primCmpInt(vyy90, vyy91)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Int, gd) → new_ltEs5(vyy9000, vyy9100)
new_ltEs9(Just(vyy900), Nothing, gg) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy9100))) → new_primCmpNat0(Zero, Succ(vyy9100))
new_primCompAux00(vyy160, EQ) → vyy160
new_foldFM_GE12(vyy77, vyy13, vyy170, vyy171, vyy172, vyy173, vyy174, False, h, ba, bb) → new_foldFM_GE5(vyy77, vyy13, vyy174, h, ba, bb)
new_eltsFM_GE0(vyy170, vyy171, vyy100, h, ba, bb) → :(vyy171, vyy100)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], bad), bab) → new_esEs15(vyy3000, vyy400, bad)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs21(vyy901, vyy911, ty_Char) → new_esEs18(vyy901, vyy911)
new_esEs26(vyy900, vyy910, app(app(ty_@2, cgf), cgg)) → new_esEs5(vyy900, vyy910, cgf, cgg)
new_lt12(vyy901, vyy911, app(app(ty_@2, bfc), bfd)) → new_lt15(vyy901, vyy911, bfc, bfd)
new_esEs21(vyy901, vyy911, app(app(ty_@2, bfc), bfd)) → new_esEs5(vyy901, vyy911, bfc, bfd)
new_not(False) → True
new_lt20(vyy900, vyy910, ty_Char) → new_lt9(vyy900, vyy910)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, baf), bag), bab) → new_esEs6(vyy3000, vyy400, baf, bag)
new_esEs25(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_primCmpInt(Pos(Succ(vyy9000)), Pos(vyy910)) → new_primCmpNat0(Succ(vyy9000), vyy910)
new_ltEs18(vyy902, vyy912, app(ty_Ratio, bgg)) → new_ltEs13(vyy902, vyy912, bgg)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs12(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Ordering) → new_ltEs4(vyy900, vyy910)
new_ltEs9(Nothing, Nothing, gg) → True
new_esEs24(vyy3000, vyy400, app(app(ty_Either, cbc), cbd)) → new_esEs6(vyy3000, vyy400, cbc, cbd)
new_esEs22(vyy900, vyy910, ty_Bool) → new_esEs17(vyy900, vyy910)
new_esEs19(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs18(vyy902, vyy912, app(app(app(ty_@3, bgb), bgc), bgd)) → new_ltEs6(vyy902, vyy912, bgb, bgc, bgd)
new_esEs11(vyy3001, vyy401, app(app(ty_Either, df), dg)) → new_esEs6(vyy3001, vyy401, df, dg)
new_esEs12(vyy3000, vyy400, app(app(app(ty_@3, fb), fc), fd)) → new_esEs4(vyy3000, vyy400, fb, fc, fd)
new_esEs25(vyy3000, vyy400, app(ty_Ratio, cfa)) → new_esEs16(vyy3000, vyy400, cfa)
new_esEs11(vyy3001, vyy401, ty_@0) → new_esEs9(vyy3001, vyy401)
new_esEs25(vyy3000, vyy400, app(app(app(ty_@3, cfd), cfe), cff)) → new_esEs4(vyy3000, vyy400, cfd, cfe, cff)
new_lt20(vyy900, vyy910, app(app(ty_Either, cha), chb)) → new_lt16(vyy900, vyy910, cha, chb)
new_lt12(vyy901, vyy911, ty_Int) → new_lt8(vyy901, vyy911)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Integer) → new_ltEs12(vyy9000, vyy9100)
new_ltEs19(vyy901, vyy911, app(app(app(ty_@3, che), chf), chg)) → new_ltEs6(vyy901, vyy911, che, chf, chg)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, bab) → new_esEs13(vyy3000, vyy400)
new_esEs22(vyy900, vyy910, app(app(app(ty_@3, fh), ga), gb)) → new_esEs4(vyy900, vyy910, fh, ga, gb)
new_lt11(vyy900, vyy910, app(ty_Ratio, bd)) → new_lt5(vyy900, vyy910, bd)
new_lt12(vyy901, vyy911, app(ty_[], bga)) → new_lt19(vyy901, vyy911, bga)
new_primCmpInt(Pos(Succ(vyy9000)), Neg(vyy910)) → GT
new_esEs22(vyy900, vyy910, ty_Char) → new_esEs18(vyy900, vyy910)
new_ltEs19(vyy901, vyy911, ty_Integer) → new_ltEs12(vyy901, vyy911)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, bab) → new_esEs19(vyy3000, vyy400)
new_lt12(vyy901, vyy911, ty_Char) → new_lt9(vyy901, vyy911)
new_lt16(vyy900, vyy910, gc, gd) → new_esEs8(new_compare17(vyy900, vyy910, gc, gd), LT)
new_esEs21(vyy901, vyy911, app(ty_Maybe, bfh)) → new_esEs7(vyy901, vyy911, bfh)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs22(vyy900, vyy910, ty_Double) → new_esEs13(vyy900, vyy910)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, bbc), bbd), bab) → new_esEs5(vyy3000, vyy400, bbc, bbd)
new_compare19(vyy900, vyy910, fh, ga, gb) → new_compare23(vyy900, vyy910, new_esEs4(vyy900, vyy910, fh, ga, gb), fh, ga, gb)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare110(vyy900, vyy910, True) → LT
new_ltEs19(vyy901, vyy911, ty_Int) → new_ltEs5(vyy901, vyy911)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs9(vyy3000, vyy400)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(app(ty_Either, cch), cda), gd) → new_ltEs7(vyy9000, vyy9100, cch, cda)
new_compare25(vyy900, vyy910, True, ge, gf) → EQ
new_compare110(vyy900, vyy910, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt12(vyy901, vyy911, app(app(ty_Either, bff), bfg)) → new_lt16(vyy901, vyy911, bff, bfg)
new_esEs24(vyy3000, vyy400, ty_Float) → new_esEs20(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, ty_Float) → new_esEs20(vyy3001, vyy401)
new_compare4(:(vyy900, vyy901), [], bch) → GT
new_ltEs18(vyy902, vyy912, app(ty_[], bhc)) → new_ltEs17(vyy902, vyy912, bhc)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Integer, gd) → new_ltEs12(vyy9000, vyy9100)
new_lt11(vyy900, vyy910, ty_Float) → new_lt17(vyy900, vyy910)
new_compare210(vyy900, vyy910, True) → EQ
new_esEs10(vyy3002, vyy402, app(app(ty_@2, da), db)) → new_esEs5(vyy3002, vyy402, da, db)
new_esEs12(vyy3000, vyy400, app(app(ty_@2, ff), fg)) → new_esEs5(vyy3000, vyy400, ff, fg)
new_compare28(vyy900, vyy910, app(app(ty_Either, bdg), bdh)) → new_compare17(vyy900, vyy910, bdg, bdh)
new_ltEs4(LT, GT) → True
new_lt12(vyy901, vyy911, ty_Double) → new_lt4(vyy901, vyy911)
new_esEs22(vyy900, vyy910, app(ty_[], beg)) → new_esEs15(vyy900, vyy910, beg)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy9100))) → new_primCmpNat0(Succ(vyy9100), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy9100))) → GT
new_esEs23(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_lt20(vyy900, vyy910, app(app(ty_@2, cgf), cgg)) → new_lt15(vyy900, vyy910, cgf, cgg)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, bac), bab) → new_esEs7(vyy3000, vyy400, bac)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, bab) → new_esEs8(vyy3000, vyy400)
new_compare4([], :(vyy910, vyy911), bch) → LT
new_compare9(vyy900, vyy910) → new_compare210(vyy900, vyy910, new_esEs17(vyy900, vyy910))
new_esEs12(vyy3000, vyy400, ty_Char) → new_esEs18(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, app(ty_Maybe, dc)) → new_esEs7(vyy3001, vyy401, dc)
new_compare15(vyy900, vyy910, False, ge, gf) → GT
new_esEs21(vyy901, vyy911, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs4(vyy901, vyy911, beh, bfa, bfb)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, bab) → new_esEs9(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, app(app(ty_@2, ec), ed)) → new_esEs5(vyy3001, vyy401, ec, ed)
new_esEs12(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs15([], :(vyy400, vyy401), cef) → False
new_esEs15(:(vyy3000, vyy3001), [], cef) → False
new_esEs26(vyy900, vyy910, ty_@0) → new_esEs9(vyy900, vyy910)
new_ltEs7(Left(vyy9000), Left(vyy9100), app(ty_[], cdc), gd) → new_ltEs17(vyy9000, vyy9100, cdc)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs14(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, app(ty_Maybe, ceg)) → new_esEs7(vyy3000, vyy400, ceg)
new_esEs23(vyy3001, vyy401, app(ty_Ratio, bhh)) → new_esEs16(vyy3001, vyy401, bhh)
new_esEs22(vyy900, vyy910, app(ty_Ratio, bd)) → new_esEs16(vyy900, vyy910, bd)
new_lt10(vyy900, vyy910) → new_esEs8(new_compare27(vyy900, vyy910), LT)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs14(vyy3001, vyy401)
new_esEs10(vyy3002, vyy402, ty_Integer) → new_esEs19(vyy3002, vyy402)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Float) → new_esEs20(vyy3000, vyy400)
new_ltEs4(LT, EQ) → True
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Char) → new_ltEs10(vyy9000, vyy9100)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Char, gd) → new_ltEs10(vyy9000, vyy9100)
new_ltEs9(Just(vyy900), Just(vyy910), app(app(ty_@2, hc), hd)) → new_ltEs8(vyy900, vyy910, hc, hd)
new_esEs12(vyy3000, vyy400, app(app(ty_Either, eh), fa)) → new_esEs6(vyy3000, vyy400, eh, fa)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, app(app(ty_Either, ceb), cec)) → new_ltEs7(vyy9000, vyy9100, ceb, cec)
new_esEs26(vyy900, vyy910, ty_Int) → new_esEs14(vyy900, vyy910)
new_asAs(False, vyy123) → False
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_compare28(vyy900, vyy910, app(ty_Ratio, bdf)) → new_compare7(vyy900, vyy910, bdf)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_ltEs11(vyy90, vyy91) → new_not(new_esEs8(new_compare6(vyy90, vyy91), GT))
new_esEs24(vyy3000, vyy400, ty_Double) → new_esEs13(vyy3000, vyy400)
new_esEs15(:(vyy3000, vyy3001), :(vyy400, vyy401), cef) → new_asAs(new_esEs25(vyy3000, vyy400, cef), new_esEs15(vyy3001, vyy401, cef))
new_esEs21(vyy901, vyy911, ty_Ordering) → new_esEs8(vyy901, vyy911)
new_compare4(:(vyy900, vyy901), :(vyy910, vyy911), bch) → new_primCompAux0(vyy900, vyy910, new_compare4(vyy901, vyy911, bch), bch)
new_lt14(vyy900, vyy910, fh, ga, gb) → new_esEs8(new_compare19(vyy900, vyy910, fh, ga, gb), LT)
new_esEs6(Right(vyy3000), Right(vyy400), bbe, app(ty_Ratio, bbh)) → new_esEs16(vyy3000, vyy400, bbh)
new_esEs26(vyy900, vyy910, app(ty_Maybe, chc)) → new_esEs7(vyy900, vyy910, chc)
new_compare28(vyy900, vyy910, ty_Bool) → new_compare9(vyy900, vyy910)
new_compare31(vyy900, vyy910, bc) → new_compare211(vyy900, vyy910, new_esEs7(vyy900, vyy910, bc), bc)
new_ltEs7(Left(vyy9000), Left(vyy9100), ty_Float, gd) → new_ltEs16(vyy9000, vyy9100)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Integer) → new_ltEs12(vyy900, vyy910)
new_compare8(vyy900, vyy910) → new_compare26(vyy900, vyy910, new_esEs8(vyy900, vyy910))
new_foldFM_GE30(vyy170, vyy171, vyy100, vyy13, h, ba, bb) → new_eltsFM_GE0(vyy170, vyy171, vyy100, h, ba, bb)
new_ltEs18(vyy902, vyy912, app(app(ty_@2, bge), bgf)) → new_ltEs8(vyy902, vyy912, bge, bgf)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_compare28(vyy900, vyy910, ty_Char) → new_compare18(vyy900, vyy910)
new_ltEs9(Just(vyy900), Just(vyy910), ty_Int) → new_ltEs5(vyy900, vyy910)
new_ltEs5(vyy90, vyy91) → new_not(new_esEs8(new_compare12(vyy90, vyy91), GT))
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Double) → new_ltEs11(vyy9000, vyy9100)
new_ltEs19(vyy901, vyy911, ty_@0) → new_ltEs14(vyy901, vyy911)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs21(vyy901, vyy911, app(ty_Ratio, bfe)) → new_esEs16(vyy901, vyy911, bfe)
new_esEs26(vyy900, vyy910, app(ty_[], chd)) → new_esEs15(vyy900, vyy910, chd)
new_compare7(:%(vyy900, vyy901), :%(vyy910, vyy911), ty_Int) → new_compare12(new_sr(vyy900, vyy911), new_sr(vyy910, vyy901))
new_esEs14(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, dbb)) → new_esEs16(vyy3000, vyy400, dbb)
new_esEs13(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs7(Left(vyy9000), Left(vyy9100), app(ty_Maybe, cdb), gd) → new_ltEs9(vyy9000, vyy9100, cdb)
new_ltEs4(LT, LT) → True
new_esEs25(vyy3000, vyy400, app(app(ty_@2, cfg), cfh)) → new_esEs5(vyy3000, vyy400, cfg, cfh)
new_esEs26(vyy900, vyy910, ty_Bool) → new_esEs17(vyy900, vyy910)
new_ltEs18(vyy902, vyy912, ty_Float) → new_ltEs16(vyy902, vyy912)
new_esEs21(vyy901, vyy911, ty_@0) → new_esEs9(vyy901, vyy911)
new_compare18(Char(vyy900), Char(vyy910)) → new_primCmpNat0(vyy900, vyy910)
new_esEs22(vyy900, vyy910, app(app(ty_Either, gc), gd)) → new_esEs6(vyy900, vyy910, gc, gd)
new_compare14(vyy900, vyy910, True, gc, gd) → LT
new_lt11(vyy900, vyy910, ty_Bool) → new_lt7(vyy900, vyy910)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, dbh), dca)) → new_esEs5(vyy3000, vyy400, dbh, dca)
new_esEs26(vyy900, vyy910, ty_Float) → new_esEs20(vyy900, vyy910)
new_lt11(vyy900, vyy910, ty_Int) → new_lt8(vyy900, vyy910)
new_esEs10(vyy3002, vyy402, ty_Float) → new_esEs20(vyy3002, vyy402)
new_esEs26(vyy900, vyy910, ty_Char) → new_esEs18(vyy900, vyy910)
new_esEs22(vyy900, vyy910, ty_Int) → new_esEs14(vyy900, vyy910)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs14(vyy3000, vyy400)
new_lt12(vyy901, vyy911, ty_Float) → new_lt17(vyy901, vyy911)
new_esEs10(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_esEs26(vyy900, vyy910, app(app(ty_Either, cha), chb)) → new_esEs6(vyy900, vyy910, cha, chb)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Int) → new_ltEs5(vyy9000, vyy9100)
new_ltEs18(vyy902, vyy912, ty_Bool) → new_ltEs15(vyy902, vyy912)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_asAs(True, vyy123) → vyy123
new_esEs22(vyy900, vyy910, ty_@0) → new_esEs9(vyy900, vyy910)
new_compare27(@0, @0) → EQ
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_compare28(vyy900, vyy910, ty_Int) → new_compare12(vyy900, vyy910)
new_esEs10(vyy3002, vyy402, app(app(ty_Either, cc), cd)) → new_esEs6(vyy3002, vyy402, cc, cd)
new_esEs16(:%(vyy3000, vyy3001), :%(vyy400, vyy401), dcb) → new_asAs(new_esEs28(vyy3000, vyy400, dcb), new_esEs27(vyy3001, vyy401, dcb))
new_foldFM_GE5(vyy77, vyy13, Branch(vyy1740, vyy1741, vyy1742, vyy1743, vyy1744), h, ba, bb) → new_foldFM_GE12(vyy77, vyy13, vyy1740, vyy1741, vyy1742, vyy1743, vyy1744, new_gtEs0(vyy1740, vyy13, ba, bb), h, ba, bb)
new_esEs11(vyy3001, vyy401, app(ty_Ratio, de)) → new_esEs16(vyy3001, vyy401, de)
new_esEs12(vyy3000, vyy400, app(ty_Ratio, eg)) → new_esEs16(vyy3000, vyy400, eg)
new_lt12(vyy901, vyy911, app(app(app(ty_@3, beh), bfa), bfb)) → new_lt14(vyy901, vyy911, beh, bfa, bfb)
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_Float) → new_ltEs16(vyy9000, vyy9100)
new_compare10(vyy900, vyy910, True) → LT
new_ltEs4(GT, GT) → True
new_esEs20(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs14(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt20(vyy900, vyy910, ty_Double) → new_lt4(vyy900, vyy910)
new_lt17(vyy900, vyy910) → new_esEs8(new_compare30(vyy900, vyy910), LT)
new_lt12(vyy901, vyy911, ty_Bool) → new_lt7(vyy901, vyy911)
new_foldFM_GE5(vyy77, vyy13, EmptyFM, h, ba, bb) → vyy77
new_compare13(vyy900, vyy910, True, fh, ga, gb) → LT
new_esEs24(vyy3000, vyy400, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs4(vyy3000, vyy400, cbe, cbf, cbg)
new_ltEs10(vyy90, vyy91) → new_not(new_esEs8(new_compare18(vyy90, vyy91), GT))
new_compare10(vyy900, vyy910, False) → GT
new_primCompAux00(vyy160, GT) → GT
new_ltEs18(vyy902, vyy912, ty_Integer) → new_ltEs12(vyy902, vyy912)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), bbe, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare28(vyy900, vyy910, app(app(app(ty_@3, bda), bdb), bdc)) → new_compare19(vyy900, vyy910, bda, bdb, bdc)
new_esEs24(vyy3000, vyy400, app(ty_[], cba)) → new_esEs15(vyy3000, vyy400, cba)
new_esEs24(vyy3000, vyy400, ty_Char) → new_esEs18(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs10(vyy3002, vyy402, ty_Bool) → new_esEs17(vyy3002, vyy402)
new_lt18(vyy900, vyy910, bc) → new_esEs8(new_compare31(vyy900, vyy910, bc), LT)
new_lt13(vyy900, vyy910) → new_esEs8(new_compare29(vyy900, vyy910), LT)
new_esEs22(vyy900, vyy910, app(ty_Maybe, bc)) → new_esEs7(vyy900, vyy910, bc)
new_esEs4(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), be, bf, bg) → new_asAs(new_esEs12(vyy3000, vyy400, be), new_asAs(new_esEs11(vyy3001, vyy401, bf), new_esEs10(vyy3002, vyy402, bg)))
new_ltEs7(Right(vyy9000), Right(vyy9100), gc, ty_@0) → new_ltEs14(vyy9000, vyy9100)
new_primCmpInt(Neg(Succ(vyy9000)), Pos(vyy910)) → LT
new_not(True) → False

The set Q consists of the following terms:

new_compare25(x0, x1, False, x2, x3)
new_foldFM_GE12(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, True, x11, x12, x13)
new_esEs23(x0, x1, ty_Float)
new_compare18(Char(x0), Char(x1))
new_esEs10(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_compare29(Integer(x0), Integer(x1))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt18(x0, x1, x2)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_asAs(True, x0)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_lt12(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Integer)
new_gtEs0(x0, x1, x2, x3)
new_primMulNat0(Zero, Succ(x0))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_compare4(:(x0, x1), [], x2)
new_ltEs15(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_foldFM_GE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Integer)
new_compare28(x0, x1, ty_Char)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(True, x0)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt19(x0, x1, x2)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Bool)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs15(False, False)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Ordering)
new_esEs8(LT, LT)
new_lt12(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1)
new_esEs17(False, False)
new_sr(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1)
new_esEs12(x0, x1, ty_Double)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, True)
new_esEs23(x0, x1, ty_Integer)
new_compare24(x0, x1, False, x2, x3)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Bool)
new_compare28(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_asAs(False, x0)
new_compare6(Double(x0, x1), Double(x2, x3))
new_esEs23(x0, x1, ty_Char)
new_esEs15([], [], x0)
new_compare210(x0, x1, True)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Zero)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare4([], :(x0, x1), x2)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_lt11(x0, x1, app(ty_[], x2))
new_ltEs9(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_Int)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False)
new_compare28(x0, x1, ty_Double)
new_sr0(Integer(x0), Integer(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_foldFM_GE12(x0, x1, x2, x3, x4, EmptyFM, x5, True, x6, x7, x8)
new_compare211(x0, x1, False, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(ty_[], x2))
new_compare12(x0, x1)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(GT, GT)
new_esEs25(x0, x1, ty_Bool)
new_esEs14(x0, x1)
new_compare28(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primPlusNat1(Succ(x0), Succ(x1))
new_lt13(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primCmpNat0(Succ(x0), Zero)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs19(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(x0, x1, ty_Int)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Char)
new_compare10(x0, x1, False)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Char)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_lt11(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs11(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Double)
new_compare11(x0, x1, False, x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, ty_@0)
new_compare13(x0, x1, True, x2, x3, x4)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs18(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt11(x0, x1, ty_Double)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, False, x2, x3, x4)
new_primPlusNat1(Zero, Zero)
new_lt12(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpNat0(Zero, Succ(x0))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_@0)
new_foldFM_GE30(x0, x1, x2, x3, x4, x5, x6)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare14(x0, x1, False, x2, x3)
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs4(EQ, EQ)
new_primCompAux00(x0, LT)
new_esEs24(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Ordering)
new_esEs11(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare16(x0, x1, x2, x3)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(EQ, LT)
new_esEs27(x0, x1, ty_Int)
new_ltEs4(LT, EQ)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs15(True, False)
new_ltEs15(False, True)
new_esEs11(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs15(:(x0, x1), [], x2)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(x0, x1, app(ty_[], x2))
new_lt15(x0, x1, x2, x3)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_compare110(x0, x1, True)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs12(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_foldFM_GE12(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_compare8(x0, x1)
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs12(x0, x1, ty_Float)
new_compare211(x0, x1, True, x2)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_lt14(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs18(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_compare15(x0, x1, False, x2, x3)
new_ltEs4(LT, LT)
new_eltsFM_GE0(x0, x1, x2, x3, x4, x5)
new_compare110(x0, x1, False)
new_esEs10(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs11(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Bool)
new_ltEs17(x0, x1, x2)
new_esEs22(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt12(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, ty_@0)
new_esEs9(@0, @0)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_Char)
new_compare14(x0, x1, True, x2, x3)
new_primEqNat0(Zero, Succ(x0))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt11(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Ordering)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Char)
new_foldFM_GE5(x0, x1, EmptyFM, x2, x3, x4)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare30(Float(x0, x1), Float(x2, x3))
new_lt12(x0, x1, ty_Int)
new_primPlusNat0(Zero, x0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Zero, Zero)
new_esEs10(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, ty_Int)
new_lt16(x0, x1, x2, x3)
new_esEs22(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_@0)
new_compare17(x0, x1, x2, x3)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Integer)
new_lt4(x0, x1)
new_esEs7(Nothing, Just(x0), x1)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_lt17(x0, x1)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0)
new_esEs12(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt12(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs11(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Double)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_primCompAux0(x0, x1, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare28(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_foldFM_GE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_compare25(x0, x1, True, x2, x3)
new_esEs10(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2, x3, x4)
new_compare23(x0, x1, True, x2, x3, x4)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Ordering)
new_esEs20(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_lt11(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Float)
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, ty_Int)
new_lt11(x0, x1, ty_Int)
new_esEs7(Nothing, Nothing, x0)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_not(True)
new_lt11(x0, x1, ty_Char)
new_lt6(x0, x1)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt7(x0, x1)
new_not(False)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs12(x0, x1, ty_Int)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(x0, x1, False, x2, x3, x4)
new_compare26(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(x0, x1, ty_Integer)
new_lt11(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, ty_@0)
new_compare26(x0, x1, False)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs24(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs9(Nothing, Just(x0), x1)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_compare28(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Double)
new_ltEs12(x0, x1)
new_esEs24(x0, x1, ty_Double)
new_esEs7(Just(x0), Nothing, x1)
new_ltEs5(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs15([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_Int)
new_compare9(x0, x1)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17(False, True)
new_esEs17(True, False)
new_lt11(x0, x1, ty_Integer)
new_compare27(@0, @0)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_lt5(x0, x1, x2)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), :(x2, x3), x4)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Bool)
new_ltEs16(x0, x1)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Zero)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare4([], [], x0)
new_esEs17(True, True)
new_esEs22(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_ltEs14(x0, x1)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs19(Integer(x0), Integer(x1))
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_lt8(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True, x2)
new_esEs25(x0, x1, ty_Float)
new_compare31(x0, x1, x2)
new_ltEs13(x0, x1, x2)
new_lt10(x0, x1)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)

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

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